Improved simple optimization (SOPT algorithm for unconstrained non-linear optimization problems
Directory of Open Access Journals (Sweden)
J. Thomas
2016-09-01
Full Text Available In the recent years, population based meta-heuristic are developed to solve non-linear optimization problems. These problems are difficult to solve using traditional methods. Simple optimization (SOPT algorithm is one of the simple and efficient meta-heuristic techniques to solve the non-linear optimization problems. In this paper, SOPT is compared with some of the well-known meta-heuristic techniques viz. Artificial Bee Colony algorithm (ABC, Particle Swarm Optimization (PSO, Genetic Algorithm (GA and Differential Evolutions (DE. For comparison, SOPT algorithm is coded in MATLAB and 25 standard test functions for unconstrained optimization having different characteristics are run for 30 times each. The results of experiments are compared with previously reported results of other algorithms. Promising and comparable results are obtained for most of the test problems. To improve the performance of SOPT, an improvement in the algorithm is proposed which helps it to come out of local optima when algorithm gets trapped in it. In almost all the test problems, improved SOPT is able to get the actual solution at least once in 30 runs.
DEFF Research Database (Denmark)
Ghoreishi, Newsha; Sørensen, Jan Corfixen; Jørgensen, Bo Nørregaard
2015-01-01
compare the performance of state-of-the-art multi-objective evolutionary algorithms to solve a non-linear multi-objective multi-issue optimisation problem found in Greenhouse climate control. The chosen algorithms in the study includes NSGAII, eNSGAII, eMOEA, PAES, PESAII and SPEAII. The performance...
Optimal non-linear health insurance.
Blomqvist, A
1997-06-01
Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.
DEFF Research Database (Denmark)
Stolpe, Mathias; Bendsøe, Martin P.
2007-01-01
This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities...
Energy Technology Data Exchange (ETDEWEB)
Delbos, F.
2004-11-01
Reflexion tomography allows the determination of a subsurface velocity model from the travel times of seismic waves. The introduction of a priori information in this inverse problem can lead to the resolution of a constrained non-linear least-squares problem. The goal of the thesis is to improve the resolution techniques of this optimization problem, whose main difficulties are its ill-conditioning, its large scale and an expensive cost function in terms of CPU time. Thanks to a detailed study of the problem and to numerous numerical experiments, we justify the use of a sequential quadratic programming method, in which the tangential quadratic programs are solved by an original augmented Lagrangian method. We show the global linear convergence of the latter. The efficiency and robustness of the approach are demonstrated on several synthetic examples and on two real data cases. (author)
Robust C subroutines for non-linear optimization
DEFF Research Database (Denmark)
Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun
2004-01-01
This report presents a package of robust and easy-to-use C subroutines for solving unconstrained and constrained non-linear optimization problems. The intention is that the routines should use the currently best algorithms available. All routines have standardized calls, and the user does not have...... by changing 1 to 0. The present report is a new and updated version of a previous report NI-91-03 with the same title, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated from Fortran to C. The reason for writing the present report is that some...... of the C subroutines have been replaced by more effective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modi ed to some extent. For a description of the original Fortran subroutines see the report [17]. The software...
Non-linear and signal energy optimal asymptotic filter design
Directory of Open Access Journals (Sweden)
Josef Hrusak
2003-10-01
Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.
Non-linear DSGE Models and The Optimized Particle Filter
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper improves the accuracy and speed of particle filtering for non-linear DSGE models with potentially non-normal shocks. This is done by introducing a new proposal distribution which i) incorporates information from new observables and ii) has a small optimization step that minimizes...... the distance to the optimal proposal distribution. A particle filter with this proposal distribution is shown to deliver a high level of accuracy even with relatively few particles, and this filter is therefore much more efficient than the standard particle filter....
Scenarios for solving a non-linear transportation problem in multi-agent systems
DEFF Research Database (Denmark)
Brehm, Robert; Top, Søren; Mátéfi-Tempfli, Stefan
2017-01-01
We introduce and provide an evaluation on two scenarios and related algorithms for implementation of a multi-agent system to solve a type of non-linear transportation problem using distributed optimization algorithms based on dual decomposition and consensus. The underlying fundamental optimization...
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
Solutions of Multi Objective Fuzzy Transportation Problems with Non-Linear Membership Functions
Directory of Open Access Journals (Sweden)
Dr. M. S. Annie Christi
2016-11-01
Full Text Available Multi-objective transportation problem with fuzzy interval numbers are considered. The solution of linear MOTP is obtained by using non-linear membership functions. The optimal compromise solution obtained is compared with the solution got by using a linear membership function. Some numerical examples are presented to illustrate this.
Optimal experimental design for non-linear models theory and applications
Kitsos, Christos P
2013-01-01
This book tackles the Optimal Non-Linear Experimental Design problem from an applications perspective. At the same time it offers extensive mathematical background material that avoids technicalities, making it accessible to non-mathematicians: Biologists, Medical Statisticians, Sociologists, Engineers, Chemists and Physicists will find new approaches to conducting their experiments. The book is recommended for Graduate Students and Researchers.
A general non-linear optimization algorithm for lower bound limit analysis
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular...... finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound...... load optimization problem. and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non-linear yield criteria. Copyright (C) 2002 John Wiley Sons. Ltd....
Robust non-gradient C subroutines for non-linear optimization
DEFF Research Database (Denmark)
Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun
2004-01-01
This report presents a package of robust and easy-to-use C subroutines for solving unconstrained and constrained non-linear optimization problems, where gradient information is not required. The intention is that the routines should use the currently best algorithms available. All routines have...... subroutines are obtained by changing 0 to 1. The present report is a new and updated version of a previous report NI-91-04 with the title Non-gradient c Subroutines for Non- Linear Optimization, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated...... from Fortran to C. The reason for writing the present report is that some of the C subroutines have been replaced by more e ective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modified to some extent...
Analytical Solutions to Non-linear Mechanical Oscillation Problems
DEFF Research Database (Denmark)
Kaliji, H. D.; Ghadimi, M.; Barari, Amin
2011-01-01
In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...
Royston, T. J.; Singh, R.
1996-07-01
While significant non-linear behavior has been observed in many vibration mounting applications, most design studies are typically based on the concept of linear system theory in terms of force or motion transmissibility. In this paper, an improved analytical strategy is presented for the design optimization of complex, active of passive, non-linear mounting systems. This strategy is built upon the computational Galerkin method of weighted residuals, and incorporates order reduction and numerical continuation in an iterative optimization scheme. The overall dynamic characteristics of the mounting system are considered and vibratory power transmission is minimized via adjustment of mount parameters by using both passive and active means. The method is first applied through a computational example case to the optimization of basic passive and active, non-linear isolation configurations. It is found that either active control or intentionally introduced non-linearity can improve the mount's performance; but a combination of both produces the greatest benefit. Next, a novel experimental, active, non-linear isolation system is studied. The effect of non-linearity on vibratory power transmission and active control are assessed via experimental measurements and the enhanced Galerkin method. Results show how harmonic excitation can result in multiharmonic vibratory power transmission. The proposed optimization strategy offers designers some flexibility in utilizing both passive and active means in combination with linear and non-linear components for improved vibration mounts.
The Expansion of Dynamic Solving Process About a Class of Non-linear Programming Problems
Institute of Scientific and Technical Information of China (English)
ZANG Zhen-chun
2001-01-01
In this paper, we research non-linear programming problems which have a given specialstructure, some simple forms of this kind structure have been solved in some papers, here we focus on othercomplex ones.
Robust C subroutines for non-linear optimization
DEFF Research Database (Denmark)
Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun
2004-01-01
to worry about special parameters controlling the iterations. For convenience we include an option for numerical checking of the user s implementation of the gradient. Note that another report [3] presents a collection of robust subroutines for both unconstrained and constrained optimization...... by changing 1 to 0. The present report is a new and updated version of a previous report NI-91-03 with the same title, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated from Fortran to C. The reason for writing the present report is that some...... of the C subroutines have been replaced by more effective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modi ed to some extent. For a description of the original Fortran subroutines see the report [17]. The software...
Identification of a Non-Linear Landing Gear Model Using Nature-Inspired Optimization
Directory of Open Access Journals (Sweden)
Felipe A.C. Viana
2008-01-01
Full Text Available This work deals with the application of a nature-inspired optimization technique to solve an inverse problem represented by the identification of an aircraft landing gear model. The model is described in terms of the landing gear geometry, internal volumes and areas, shock absorber travel, tire type, and gas and oil characteristics of the shock absorber. The solution to this inverse problem can be obtained by using classical gradient-based optimization methods. However, this is a difficult task due to the existence of local minima in the design space and the requirement of an initial guess. These aspects have motivated the authors to explore a nature-inspired approach using a method known as LifeCycle Model. In the present formulation two nature-based methods, namely the Genetic Algorithms and the Particle Swarm Optimization were used. An optimization problem is formulated in which the objective function represents the difference between the measured characteristics of the system and its model counterpart. The polytropic coefficient of the gas and the damping parameter of the shock absorber are assumed as being unknown: they are considered as design variables. As an illustration, experimental drop test data, obtained under zero horizontal speed, were used in the non-linear landing gear model updating of a small aircraft.
Alart, P.; Barboteu, M.; Gril, J.
2004-09-01
In this paper a numerical modelling of non linear problems involving large deformations and frictional contact conditions is proposed. The motivation of this work comes from the study of the cellular materials (such as wood or foams) undergoing strong deformations. We restrict our study to a regular cellular network of hexagonal cells with thin walls. Strong loadings can generate at first buckling phenomena, then self-contact in the cell. Renouncing homogenization procedures, not always pertinent in this case, we have developed direct simulations. After giving the mechanical and mathematical formulations of the problem, we present two advanced numerical tools to solve large non linear frictional multicontact problems. This numerical modelling is based on an arc-length continuation method which permits to snap through singular points due to buckling phenomena and on an optimal domain decomposition method adapted to frictional contact problems. Finally, mechanical investigations of the contactless buckling and the post-buckling provide some pertinent parameters controlling the deformation process.
Optimal Reservoir Operation for Hydropower Generation using Non-linear Programming Model
Arunkumar, R.; Jothiprakash, V.
2012-05-01
Hydropower generation is one of the vital components of reservoir operation, especially for a large multi-purpose reservoir. Deriving optimal operational rules for such a large multi-purpose reservoir serving various purposes like irrigation, hydropower and flood control are complex, because of the large dimension of the problem and the complexity is more if the hydropower production is not an incidental. Thus optimizing the operations of a reservoir serving various purposes requires a systematic study. In the present study such a large multi-purpose reservoir, namely, Koyna reservoir operations are optimized for maximizing the hydropower production subject to the condition of satisfying the irrigation demands using a non-linear programming model. The hydropower production from the reservoir is analysed for three different dependable inflow conditions, representing wet, normal and dry years. For each dependable inflow conditions, various scenarios have been analyzed based on the constraints on the releases and the results are compared. The annual power production, combined monthly power production from all the powerhouses, end of month storage levels, evaporation losses and surplus are discussed. From different scenarios, it is observed that more hydropower can be generated for various dependable inflow conditions, if the restrictions on releases are slightly relaxed. The study shows that Koyna dam is having potential to generate more hydropower.
On the algebraic representation of certain optimal non-linear binary codes
Greferath, Marcus
2011-01-01
This paper investigates some optimal non-linear codes, in particular cyclic codes, by considering them as (non-linear) codes over Z_4. We use the Fourier transform as well as subgroups of the unit group of a group ring to analyse these codes. In particular we find a presentation of Best's (10, 40, 4) code as a coset of a subgroup in the unit group of a ring, and derive a simple decoding algorithm from this presentation. We also apply this technique to analyse Julin's (12, 144, 4) code and the (12, 24, 12) Hadamard code, as well as to construct a (14, 56, 6) binary code.
Zhang, Chao; Ren, Pinyi; Peng, Jingbo; Wei, Guo; Du, Qinghe; Wang, Yichen
2011-01-01
In this paper, we propose an optimal relay power allocation of an Amplify-and-Forward relay networks with non-linear power amplifiers. Based on Bussgang Linearization Theory, we depict the non-linear amplifying process into a linear system, which lets analyzing system performance easier. To obtain spatial diversity, we design a complete practical framework of a non-linear distortion aware receiver. Consider a total relay power constraint, we propose an optimal power allocation scheme to maxim...
Field computation in non-linear magnetic media using particle swarm optimization
Energy Technology Data Exchange (ETDEWEB)
Adly, A.A. E-mail: amradlya@intouch.com; Abd-El-Hafiz, S.K
2004-05-01
This paper presents an automated particle swarm optimization approach using which field computations may be carried out in devices involving non-linear magnetic media. Among the advantages of the proposed approach are its ability to handle complex geometries and its computational efficiency. The proposed approach has been implemented and computations were carried out for an electromagnet subject to different DC excitation conditions. These computations showed good agreement with the results obtained by the finite-element approach.
Directory of Open Access Journals (Sweden)
M. Pattnaik
2013-08-01
Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.
Directory of Open Access Journals (Sweden)
Pattnaik Monalisha
2015-01-01
Full Text Available In this paper, the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model for restricted budget and space. Since various types of uncertainties and imprecision are inherent in real inventory problems, they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by the usual probabilistic models. The questions are how to define inventory optimization tasks in such environment and how to interpret the optimal solutions. This paper allow the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price, and the setup cost varies with the quantity produced/Purchased. The modification of objective function, budget, and storage area in the presence of imprecisely estimated parameters are considered. The model is developed by employing different approaches over an infinite planning horizon. It incorporates all the concepts of a fuzzy arithmetic approach and comparative analysis with other non linear models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated by an example problem, and two and three dimensional diagrams are represented to this application through MATL(R2009a software. Sensitivity analysis of the optimal solution is studied with respect to the changes of different parameter values for obtaining managerial insights of the decision problem.
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
-numerical techniques suitable for Markov response problems such as moments equation, Petrov-Galerkin and cell-to-cell mapping techniques are briefly discussed. Usefulness of these techniques is limited by the fact that effectiveness of each of them depends on the mean rate of impulses. Another limitation is the size...... of the problem, i.e. the number of state variables of the dynamical systems. In contrast, the application of the simulation techniques is not limited to Markov problems, nor is it dependent on the mean rate of impulses. Moreover their use is straightforward for a large class of point processes, at least......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...
Solving Directly Two Point Non Linear Boundary Value Problems Using Direct Adams Moulton Method
Directory of Open Access Journals (Sweden)
Zanariah A. Majid
2011-01-01
Full Text Available Problem statement: In this study, a direct method of Adams Moulton type was developed for solving non linear two point Boundary Value Problems (BVPs directly. Most of the existence researches involving BVPs will reduced the problem to a system of first order Ordinary Differential Equations (ODEs. This approach is very well established but it obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the second order BVPs directly without reducing it to first order ODEs. Approach: Lagrange interpolation polynomial was applied in the derivation of the proposed method. The method was implemented using constant step size via shooting technique in order to determine the approximated solutions. The shooting technique will employ the Newtons method for checking the convergent of the guessing values for the next iteration. Results: Numerical results confirmed that the direct method gave better accuracy and converged faster compared to the existing method. Conclusion: The proposed direct method is suitable for solving two point non linear boundary value problems.
A Reduced Basis Framework: Application to large scale non-linear multi-physics problems
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Daversin C.
2013-12-01
Full Text Available In this paper we present applications of the reduced basis method (RBM to large-scale non-linear multi-physics problems. We first describe the mathematical framework in place and in particular the Empirical Interpolation Method (EIM to recover an affine decomposition and then we propose an implementation using the open-source library Feel++ which provides both the reduced basis and finite element layers. Large scale numerical examples are shown and are connected to real industrial applications arising from the High Field Resistive Magnets development at the Laboratoire National des Champs Magnétiques Intenses.
Directory of Open Access Journals (Sweden)
M. Kandasamy
2014-12-01
Full Text Available A comparison study of Firefly Algorithm (FA and Bacterial Foraging Algorithm (BFO optimization is carried out by applying them to a Non Linear pH neutralization process. In process control engineering, the Proportional, Derivative, Integral controller tuning parameters are deciding the performance of the controller to ensure the good performance of the plant. The FA and BFO algorithms are applied to obtain the optimum values of controller parameters. The performance indicators such as servo response and regulatory response tests are carried out to evaluate the efficiency of the heuristic algorithm based controllers. The error minimization criterion such as Integral Absolute Error (IAE, Integral Square Error (ISE, Integral Time Square Error (ITSE, Integral Time Absolute Error (ITAE and Time domain specifications – rise time, Peak Overshoot and settling time are considered for the study of the performance of the controllers. The study indicates that, FA tuned PID controller provides marginally better set point tracking, load disturbance rejection, time domain specifications and error minimization for the Non Linear pH neutralization process compared to BFO tuned PID controller.
An integer optimization algorithm for robust identification of non-linear gene regulatory networks
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Chemmangattuvalappil Nishanth
2012-09-01
Full Text Available Abstract Background Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. Results We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters
Energy Technology Data Exchange (ETDEWEB)
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
SOME PROBLEMS CONCERNING FREE NON-LINEAR VIBRATIONS OF BEAM STRUCTURES
Directory of Open Access Journals (Sweden)
S. V. Bosakov
2008-01-01
Full Text Available The paper analyzes an influence of physical non-linearity material account on vibrations of single beams with various support fixing. The authors also analyze power criteria for existing stable periodic vibrations and dependence of vibration period on initial power is determined in the paper. Accurate values of an amplitude and non-linear bending vibration period of beams have been also determined as a conservative system with due account of initial conditions. A number of examples are given that clearly illustrate the obtained solutions and show an influence rate of the mentioned effects on amplitude-frequency characteristics of non-linear systems.
Non-linear stochastic optimal control of acceleration parametrically excited systems
Wang, Yong; Jin, Xiaoling; Huang, Zhilong
2016-02-01
Acceleration parametrical excitations have not been taken into account due to the lack of physical significance in macroscopic structures. The explosive development of microtechnology and nanotechnology, however, motivates the investigation of the acceleration parametrically excited systems. The adsorption and desorption effects dramatically change the mass of nano-sized structures, which significantly reduces the precision of nanoscale sensors or can be reasonably utilised to detect molecular mass. This manuscript proposes a non-linear stochastic optimal control strategy for stochastic systems with acceleration parametric excitation based on stochastic averaging of energy envelope and stochastic dynamic programming principle. System acceleration is approximately expressed as a function of system displacement in a short time range under the conditions of light damping and weak excitations, and the acceleration parametrically excited system is shown to be equivalent to a constructed system with an additional displacement parametric excitation term. Then, the controlled system is converted into a partially averaged Itô equation with respect to the total system energy through stochastic averaging of energy envelope, and the optimal control strategy for the averaged system is derived from solving the associated dynamic programming equation. Numerical results for a controlled Duffing oscillator indicate the efficacy of the proposed control strategy.
Optimization of elstomeric micro-fluidic valve dimensions using non-linear finite element methods
Directory of Open Access Journals (Sweden)
H Khawaja
2016-04-01
Full Text Available We use a nonlinear finite element (FE method model to compare,optimize and determine the limits for useful geometries of microfluidicvalves in elastomer polydimethylsiloxane (PDMS. Simulations havebeen performed with the aim of finding the optimal shape, size andlocation of pressurization that minimizes the pressure required to operatethe valve. One important constraint governing the design parameters isthat the stresses should be within elastic limits, so that the componentremains safe from any type of structural failure. To obtain reliable results,non-linear stress analysis was performed using the Mooney-Rivlin 9parameter approximation which is based on the Hyper Elastic MaterialModel. A 20 noded brick element was used for the development of FEmodel. Mesh sensitivity analysis was also performed to assess the qualityof the results. The simulations were performed with commerciallyavailable FE modeling software, developed by ANSYS Inc. to determinethe effect of varying different geometric parameters on the performanceof micro-fluidic valves.The aim of this work is to determine the geometry of the channel crosssectionthat would result in the largest deflection for the least appliedpressure, i.e. to minimize the pressure needed to operate the valve.
A new non-linear vortex lattice method:Applications to wing aerodynamic optimizations
Institute of Scientific and Technical Information of China (English)
Oliviu S? ugar Gabor; Andreea Koreanschi; Ruxandra Mihaela Botez
2016-01-01
This paper presents a new non-linear formulation of the classical Vortex Lattice Method (VLM) approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.
A new non-linear vortex lattice method: Applications to wing aerodynamic optimizations
Directory of Open Access Journals (Sweden)
Oliviu Şugar Gabor
2016-10-01
Full Text Available This paper presents a new non-linear formulation of the classical Vortex Lattice Method (VLM approach for calculating the aerodynamic properties of lifting surfaces. The method accounts for the effects of viscosity, and due to its low computational cost, it represents a very good tool to perform rapid and accurate wing design and optimization procedures. The mathematical model is constructed by using two-dimensional viscous analyses of the wing span-wise sections, according to strip theory, and then coupling the strip viscous forces with the forces generated by the vortex rings distributed on the wing camber surface, calculated with a fully three-dimensional vortex lifting law. The numerical results obtained with the proposed method are validated with experimental data and show good agreement in predicting both the lift and pitching moment, as well as in predicting the wing drag. The method is applied to modifying the wing of an Unmanned Aerial System to increase its aerodynamic efficiency and to calculate the drag reductions obtained by an upper surface morphing technique for an adaptable regional aircraft wing.
Non-Linearity Analysis of Depth and Angular Indexes for Optimal Stereo SLAM
Directory of Open Access Journals (Sweden)
David Schleicher
2010-04-01
Full Text Available In this article, we present a real-time 6DoF egomotion estimation system for indoor environments using a wide-angle stereo camera as the only sensor. The stereo camera is carried in hand by a person walking at normal walking speeds 3–5 km/h. We present the basis for a vision-based system that would assist the navigation of the visually impaired by either providing information about their current position and orientation or guiding them to their destination through different sensing modalities. Our sensor combines two different types of feature parametrization: inverse depth and 3D in order to provide orientation and depth information at the same time. Natural landmarks are extracted from the image and are stored as 3D or inverse depth points, depending on a depth threshold. This depth threshold is used for switching between both parametrizations and it is computed by means of a non-linearity analysis of the stereo sensor. Main steps of our system approach are presented as well as an analysis about the optimal way to calculate the depth threshold. At the moment each landmark is initialized, the normal of the patch surface is computed using the information of the stereo pair. In order to improve long-term tracking, a patch warping is done considering the normal vector information. Some experimental results under indoor environments and conclusions are presented.
Non-linear optimization of track layouts in loop-sorting-systems
DEFF Research Database (Denmark)
Sørensen, Søren Emil; Hansen, Michael R.; Ebbesen, Morten K.
2013-01-01
Optimization used for enhancing geometric structures iswell known. Applying obstacles to the shape optimization problemis on the other hand not very common. It requires a fast contact search algorithmand an exact continuous formulation to solve the problem robustly. This paper focuses on combinin...
Umbarkar, A. J.; Balande, U. T.; Seth, P. D.
2017-06-01
The field of nature inspired computing and optimization techniques have evolved to solve difficult optimization problems in diverse fields of engineering, science and technology. The firefly attraction process is mimicked in the algorithm for solving optimization problems. In Firefly Algorithm (FA) sorting of fireflies is done by using sorting algorithm. The original FA is proposed with bubble sort for ranking the fireflies. In this paper, the quick sort replaces bubble sort to decrease the time complexity of FA. The dataset used is unconstrained benchmark functions from CEC 2005 [22]. The comparison of FA using bubble sort and FA using quick sort is performed with respect to best, worst, mean, standard deviation, number of comparisons and execution time. The experimental result shows that FA using quick sort requires less number of comparisons but requires more execution time. The increased number of fireflies helps to converge into optimal solution whereas by varying dimension for algorithm performed better at a lower dimension than higher dimension.
The late Universe with non-linear interaction in the dark sector: The coincidence problem
Bouhmadi-López, Mariam; Morais, João; Zhuk, Alexander
2016-12-01
We study the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such a scale the Universe is highly inhomogeneous and filled with discretely distributed inhomogeneities in the form of galaxies and groups of galaxies. As a matter source, we consider dark matter (DM) and dark energy (DE) with a non-linear interaction Q = 3 HγεbarDEεbarDM /(εbarDE +εbarDM) , where γ is a constant. We assume that DM is pressureless and DE has a constant equation of state parameter w. In the considered model, the energy densities of the dark sector components present a scaling behaviour with εbarDM /εbarDE ∼(a0 / a) - 3(w + γ). We investigate the possibility that the perturbations of DM and DE, which are interacting among themselves, could be coupled to the galaxies with the former being concentrated around them. To carry our analysis, we consider the theory of scalar perturbations (within the mechanical approach), and obtain the sets of parameters (w , γ) which do not contradict it. We conclude that two sets: (w = - 2 / 3 , γ = 1 / 3) and (w = - 1 , γ = 1 / 3) are of special interest. First, the energy densities of DM and DE on these cases are concentrated around galaxies confirming that they are coupled fluids. Second, we show that for both of them, the coincidence problem is less severe than in the standard ΛCDM. Third, the set (w = - 1 , γ = 1 / 3) is within the observational constraints. Finally, we also obtain an expression for the gravitational potential in the considered model.
Directory of Open Access Journals (Sweden)
Samir Dey
2015-07-01
Full Text Available This paper proposes a new multi-objective intuitionistic fuzzy goal programming approach to solve a multi-objective nonlinear programming problem in context of a structural design. Here we describe some basic properties of intuitionistic fuzzy optimization. We have considered a multi-objective structural optimization problem with several mutually conflicting objectives. The design objective is to minimize weight of the structure and minimize the vertical deflection at loading point of a statistically loaded three-bar planar truss subjected to stress constraints on each of the truss members. This approach is used to solve the above structural optimization model based on arithmetic mean and compare with the solution by intuitionistic fuzzy goal programming approach. A numerical solution is given to illustrate our approach.
Institute of Scientific and Technical Information of China (English)
WANG Rouhuai
2006-01-01
The main aim of this paper is to discuss the problem concerning the analyticity of the solutions of analytic non-linear elliptic boundary value problems.It is proved that if the corresponding first variation is regular in Lopatinski(i) sense,then the solution is analytic up to the boundary.The method of proof really covers the case that the corresponding first variation is regularly elliptic in the sense of Douglis-Nirenberg-Volevich,and hence completely generalize the previous result of C.B.Morrey.The author also discusses linear elliptic boundary value problems for systems of ellip tic partial differential equations where the boundary operators are allowed to have singular integral operators as their coefficients.Combining the standard Fourier transform technique with analytic continuation argument,the author constructs the Poisson and Green's kernel matrices related to the problems discussed and hence obtain some representation formulae to the solutions.Some a priori estimates of Schauder type and Lp type are obtained.
Ernest II, Charles Steven
2013-01-01
Despite the growing promise of pharmaceutical research, inferior experimentation or interpretation of data can inhibit breakthrough molecules from finding their way out of research institutions and reaching patients. This thesis provides evidence that better characterization of pre-clinical and clinical data can be accomplished using non-linear mixed effect modeling (NLMEM) and more effective experiments can be conducted using optimal design (OD). To demonstrate applicability of NLMEM and OD...
Energy Technology Data Exchange (ETDEWEB)
Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn [Department of Mechanics, Tianjin University, 300072, Tianjin (China); Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin (China); Zhang, W. D., E-mail: zhangwenditju@126.com; Xu, J., E-mail: xujia-ld@163.com [Department of Mechanics, Tianjin University, 300072, Tianjin (China)
2014-03-15
The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.
Computational Modelling and Optimal Control of Ebola Virus Disease with non-Linear Incidence Rate
Takaidza, I.; Makinde, O. D.; Okosun, O. K.
2017-03-01
The 2014 Ebola outbreak in West Africa has exposed the need to connect modellers and those with relevant data as pivotal to better understanding of how the disease spreads and quantifying the effects of possible interventions. In this paper, we model and analyse the Ebola virus disease with non-linear incidence rate. The epidemic model created is used to describe how the Ebola virus could potentially evolve in a population. We perform an uncertainty analysis of the basic reproductive number R 0 to quantify its sensitivity to other disease-related parameters. We also analyse the sensitivity of the final epidemic size to the time control interventions (education, vaccination, quarantine and safe handling) and provide the cost effective combination of the interventions.
The late Universe with non-linear interaction in the dark sector: the coincidence problem
Bouhmadi-López, Mariam; Zhuk, Alexander
2016-01-01
We study the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such a scale the Universe is highly inhomogeneous and filled with discretely distributed inhomogeneities in the form of galaxies and groups of galaxies. As a matter source, we consider dark matter (DM) and dark energy (DE) with a non-linear interaction $Q = 3\\mathcal{H}\\gamma \\overline\\varepsilon_{\\mathrm{DE}} \\overline\\varepsilon_{\\mathrm{DM}} / (\\overline\\varepsilon_{\\mathrm{DE}} + \\overline\\varepsilon_{\\mathrm{DM}})$, where $\\gamma$ is a constant. We assume that DM is pressureless and DE has a constant equation of state parameter $w$. In the considered model, the energy densities of the dark sector components present a scaling behaviour with $\\overline\\varepsilon_{\\mathrm{DM}} / \\overline\\varepsilon_{\\mathrm{DE}} \\sim \\left({a_0} / {a} \\right)^{-3(w+\\gamma)}$. We investigate the possibility that the perturbations of DM and DE, which are interacting among themselves, could be coupled to the galaxies with the ...
Elizondo, D.; Cappelaere, B.; Faure, Ch.
2002-04-01
Emerging tools for automatic differentiation (AD) of computer programs should be of great benefit for the implementation of many derivative-based numerical methods such as those used for inverse modeling. The Odyssée software, one such tool for Fortran 77 codes, has been tested on a sample model that solves a 2D non-linear diffusion-type equation. Odyssée offers both the forward and the reverse differentiation modes, that produce the tangent and the cotangent models, respectively. The two modes have been implemented on the sample application. A comparison is made with a manually-produced differentiated code for this model (MD), obtained by solving the adjoint equations associated with the model's discrete state equations. Following a presentation of the methods and tools and of their relative advantages and drawbacks, the performances of the codes produced by the manual and automatic methods are compared, in terms of accuracy and of computing efficiency (CPU and memory needs). The perturbation method (finite-difference approximation of derivatives) is also used as a reference. Based on the test of Taylor, the accuracy of the two AD modes proves to be excellent and as high as machine precision permits, a good indication of Odyssée's capability to produce error-free codes. In comparison, the manually-produced derivatives (MD) sometimes appear to be slightly biased, which is likely due to the fact that a theoretical model (state equations) and a practical model (computer program) do not exactly coincide, while the accuracy of the perturbation method is very uncertain. The MD code largely outperforms all other methods in computing efficiency, a subject of current research for the improvement of AD tools. Yet these tools can already be of considerable help for the computer implementation of many numerical methods, avoiding the tedious task of hand-coding the differentiation of complex algorithms.
Optimizing BAO measurements with non-linear transformations of Lyman-alpha forest
Wang, Xinkang; Seljak, Uros
2014-01-01
We explore the effect of applying a non-linear transformation to the Lyman-$\\alpha$ forest transmitted flux $F=e^{-\\tau}$ and the ability of analytic models to predict the resulting clustering amplitude. Both the large-scale bias of the transformed field (signal) and the amplitude of small scale fluctuations (noise) can be arbitrarily modified, but we were unable to find a transformation that increases significantly the signal-to-noise ratio on large scales using Taylor expansion up to third order. We achieve a 33% improvement in signal to noise for Gaussianized field in transverse direction. On the other hand, we explore analytic model for the large-scale biasing of the Ly$\\alpha$ forest, and present an extension of this model to describe the biasing of the transformed fields. Using hydrodynamic simulations we show that the model works best to describe the biasing with respect to velocity gradients, but is less successful in predicting the biasing with respect to large-scale density fluctuations, especially ...
a fuzzy logic approach to non-linearity problem of load frequency ...
African Journals Online (AJOL)
user
2016-07-03
Jul 3, 2016 ... mechanical energy by prime movers. The mechanical energy is in ... control theory and technology, optimization .... Controller design is a three-stage process which ... Controller using Multiple Tabuu Search Algorithm for Load ...
Non-linear Global Optimization using Interval Arithmetic and Constraint Propagation
DEFF Research Database (Denmark)
Kjøller, Steffen; Kozine, Pavel; Madsen, Kaj;
2006-01-01
In this Chapter a new branch-and-bound method for global optimization is presented. The method combines the classical interval global optimization method with constraint propagation techniques. The latter is used for including solutions of the necessary condition f'(x)=0. The constraint propagation...
Yang, Qin; Zou, Hong-Yan; Zhang, Yan; Tang, Li-Juan; Shen, Guo-Li; Jiang, Jian-Hui; Yu, Ru-Qin
2016-01-15
Most of the proteins locate more than one organelle in a cell. Unmixing the localization patterns of proteins is critical for understanding the protein functions and other vital cellular processes. Herein, non-linear machine learning technique is proposed for the first time upon protein pattern unmixing. Variable-weighted support vector machine (VW-SVM) is a demonstrated robust modeling technique with flexible and rational variable selection. As optimized by a global stochastic optimization technique, particle swarm optimization (PSO) algorithm, it makes VW-SVM to be an adaptive parameter-free method for automated unmixing of protein subcellular patterns. Results obtained by pattern unmixing of a set of fluorescence microscope images of cells indicate VW-SVM as optimized by PSO is able to extract useful pattern features by optimally rescaling each variable for non-linear SVM modeling, consequently leading to improved performances in multiplex protein pattern unmixing compared with conventional SVM and other exiting pattern unmixing methods.
Directory of Open Access Journals (Sweden)
Samira Salahi
2016-08-01
Full Text Available Reduction of fossil resources, increasing the production of greenhouse gas emissions and demand growth lead to greater use of distributed energy resources in power system especially in distribution networks. Integrating these resources in order to supply local loads creates a new concept called micro-grid. Optimal operation of micro-grid in the specific time period is one of the most important problems of them. In this paper, the operation problem of micro-grids is modeled considering the economical, technical and environmental issues, as well as uncertainties related to loads, wind speed and solar radiation. The resulting model is a Mixed-Integer Non-Linear Programming (MINLP. To demonstrate the effectiveness of the proposed model, Bisheh village in Iran is considered as a case study. The results showed that considering load curtailment costs, the power losses of the main grid, the penalties of pollutant gasses emissions and the elimination of energy subsides will tremendous impacts on the operation of microgrids. Article History: Received March 12, 2016; Received in revised form June 20, 2016; Accepted July 2nd 2016; Available online How to Cite This Article: Salahi, S., and Bahramara, S. (2016 Modeling Operation Problem of Micro-grids Considering Economical, Technical and Environmental issues as Mixed-Integer Non-Linear Programming. Int. Journal of Renewable Energy Development, 5(2, 139-149. http://dx.doi.org/10.14710/ijred.5.2.139-149
Sensitivity problems related to certain bifurcations in non-linear recurrence relations
Gumowski, I.
1969-01-01
This paper is concerned with certain qualitative aspects of the sensitivity problem in relation to small variations of a parameter of a system, the behaviour of which can be described by an autonomous recurrence relation: V$_{n+1}$ = F(V$_{n}, \\lambda$) (1) V being a vector, $\\lambda$ the parameter. The problem consists in the determination of the bifurcation values $\\lambda_{0}$ of $\\lambda$, i.e. values such that the qualitative behaviour of a solution of (1) should be different for $\\lambda = \\lambda \\pm \\epsilon$ where $\\epsilon$ is a small quantity. Bifurcations that correspond to a critical case in the Liapunov sense, and the crossing through this critical case, are considered. Examples of bifurcations, not connected with the presence of a critical case, and which correspond to a large deformation of the stability domain boundary of an equilibrium point, a fixed point of (1), under the effect of a parameter variation, are given where V is a two dimensional vector.
Energy Technology Data Exchange (ETDEWEB)
Samet Y. Kadioglu; Robert R. Nourgaliev; Vincent A. Mousseau
2008-03-01
We perform a comparative study for the harmonic versus arithmetic averaging of the heat conduction coefficient when solving non-linear heat transfer problems. In literature, the harmonic average is the method of choice, because it is widely believed that the harmonic average is more accurate model. However, our analysis reveals that this is not necessarily true. For instance, we show a case in which the harmonic average is less accurate when a coarser mesh is used. More importantly, we demonstrated that if the boundary layers are finely resolved, then the harmonic and arithmetic averaging techniques are identical in the truncation error sense. Our analysis further reveals that the accuracy of these two techniques depends on how the physical problem is modeled.
Directory of Open Access Journals (Sweden)
Yaping Hu
2015-01-01
the nonsmooth convex optimization problem. First, by using Moreau-Yosida regularization, we convert the original objective function to a continuously differentiable function; then we use approximate function and gradient values of the Moreau-Yosida regularization to substitute the corresponding exact values in the algorithm. The global convergence is proved under suitable assumptions. Numerical experiments are presented to show the effectiveness of this algorithm.
A non-linear constrained optimization technique for the mimetic finite difference method
Energy Technology Data Exchange (ETDEWEB)
Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Svyatskiy, Daniil [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Bertolazzi, Enrico [Univ. of Trento (Italy); Frego, Marco [Univ. of Trento (Italy)
2014-09-30
This is a strategy for the construction of monotone schemes in the framework of the mimetic finite difference method for the approximation of diffusion problems on unstructured polygonal and polyhedral meshes.
The electric vehicle routing problem with non-linear charging functions
2015-01-01
International audience; The use of electric vehicles (EVs) in freight and passenger transportation gives birth to a new family of vehicle routing problems (VRPs), the so-called electric VRPs (e-VRPs). As their name suggests, e-VRPs extend classical VRPs to account (mainly) for two constraining EV features: the short driving range and the long battery charging time. As a matter of fact, routes performed by EVs usually need to include time-consuming detours to charging stations. Most of the exi...
Efficient Non-Linear Finite Element Implementation of Elasto-Plasticity for Geotechnical Problems
DEFF Research Database (Denmark)
Clausen, Johan
of foundations, mainly due to its simplicity which allows simple solutions with simple geometries. But for complex geometries a numerical solution is needed. It turns out that the apparently simple Mohr-Coulomb model is non-trivial to implement in the finite-element method. This is due to the fact that the Mohr...... with the safety factors obtained with a linear Mohr envelope, with which they are directly comparable, when the presented method is used. The classical problem of yield surfaces with corners and apexes is elaborated upon. A small modification to the formulation of the constitutive matrices on corners and apexes...
Modeling Granular Materials as Compressible Non-Linear Fluids: Heat Transfer Boundary Value Problems
Energy Technology Data Exchange (ETDEWEB)
Massoudi, M.C.; Tran, P.X.
2006-01-01
We discuss three boundary value problems in the flow and heat transfer analysis in flowing granular materials: (i) the flow down an inclined plane with radiation effects at the free surface; (ii) the natural convection flow between two heated vertical walls; (iii) the shearing motion between two horizontal flat plates with heat conduction. It is assumed that the material behaves like a continuum, similar to a compressible nonlinear fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations are simplified to a system of three nonlinear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, radiation, and so forth are presented.
DEFF Research Database (Denmark)
Sorokin, Vladislav; Thomsen, Jon Juel
2015-01-01
Parametrically excited systems appear in many fields of science and technology, intrinsically or imposed purposefully; e.g. spatially periodic structures represent an important class of such systems [4]. When the parametric excitation can be considered weak, classical asymptotic methods like...... the method of averaging [2] or multiple scales [6] can be applied. However, with many practically important applications this simplification is inadequate, e.g. with spatially periodic structures it restricts the possibility to affect their effective dynamic properties by a structural parameter modulation...... of considerable magnitude. Approximate methods based on Floquet theory [4] for analyzing problems involving parametric excitation, e.g. the classical Hill’s method of infinite determinants [3,4], can be employed also in cases of strong excitation; however, with Floquet theory being applicable only for linear...
Data-driven non-linear elasticity: constitutive manifold construction and problem discretization
Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco
2017-07-01
The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.
Constrained Optimal Stochastic Control of Non-Linear Wave Energy Point Absorbers
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Chen, Jian-Bing; Kramer, Morten
2014-01-01
The paper deals with the stochastic optimal control of a wave energy point absorber with strong nonlinear buoyancy forces using the reactive force from the electric generator on the absorber as control force. The considered point absorber has only one degree of freedom, heave motion, which is used...... presented in the paper. The effect of nonlinear buoyancy force – in comparison to linear buoyancy force – and constraints of the controller on the power outtake of the device have been studied in details and supported by numerical simulations....
Sharqawy, Mostafa H.
2016-12-01
Pore network models (PNM) of Berea and Fontainebleau sandstones were constructed using nonlinear programming (NLP) and optimization methods. The constructed PNMs are considered as a digital representation of the rock samples which were based on matching the macroscopic properties of the porous media and used to conduct fluid transport simulations including single and two-phase flow. The PNMs consisted of cubic networks of randomly distributed pores and throats sizes and with various connectivity levels. The networks were optimized such that the upper and lower bounds of the pore sizes are determined using the capillary tube bundle model and the Nelder-Mead method instead of guessing them, which reduces the optimization computational time significantly. An open-source PNM framework was employed to conduct transport and percolation simulations such as invasion percolation and Darcian flow. The PNM model was subsequently used to compute the macroscopic properties; porosity, absolute permeability, specific surface area, breakthrough capillary pressure, and primary drainage curve. The pore networks were optimized to allow for the simulation results of the macroscopic properties to be in excellent agreement with the experimental measurements. This study demonstrates that non-linear programming and optimization methods provide a promising method for pore network modeling when computed tomography imaging may not be readily available.
Institute of Scientific and Technical Information of China (English)
Xiang Li; Serge Cescotto; Barbara Rossi
2009-01-01
The natural neighbour method can be considered as one of many variants of the meshless methods. In the present paper, a new approach based on the Fraeijs de Veubeke (FdV) functional, which is initially developed for linear elasticity, is extended to the case of geometrically linear but materially non-linear solids. The new approach provides an original treatment to two classical problems: the numerical evaluation of the integrals over the domain A and the enforcement of boundary conditions of the type ui = uion Su. In the absence of body forces (Fi = 0), it will be shown that the calculation of integrals of the type fA .dA can be avoided and that boundary conditions of the type ui = ui on Su can be imposed in the average sense in general and exactly if ui is linear between two contour nodes, which is obviously the case for ui = 0.
Vergnole, Sébastien; Lévesque, Daniel; Lamouche, Guy
2010-05-10
We evaluate various signal processing methods to handle the non-linearity in wavenumber space exhibited by most laser sources for swept-source optical coherence tomography. The following methods are compared for the same set of experimental data: non-uniform discrete Fourier transforms with Vandermonde matrix or with Lomb periodogram, resampling with linear interpolation or spline interpolation prior to fast-Fourier transform (FFT), and resampling with convolution prior to FFT. By selecting an optimized Kaiser-Bessel window to perform the convolution, we show that convolution followed by FFT is the most efficient method. It allows small fractional oversampling factor between 1 and 2, thus a minimal computational time, while retaining an excellent image quality. (c) 2010 Optical Society of America.
Generalized Benders’ Decomposition for topology optimization problems
DEFF Research Database (Denmark)
Munoz Queupumil, Eduardo Javier; Stolpe, Mathias
2011-01-01
This article considers the non-linear mixed 0–1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders’ Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness......–1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality....
Directory of Open Access Journals (Sweden)
Mkrtychev Oleg Vartanovich
Full Text Available In the article the problem of calculation of a construction basis system in case of earthquake is considered taking into account casual properties of basis soil in various points of the soil body. As a stochastic function in the calculation of linearly deformable basis, the deformation module, which accepts different values in the direction x, y, z, was chosen. In the calculation of the system on non-linearly deformable basis as incidentally distributed sizes the following parameters were accepted: deformation module, shear modulus, specific adhesion, angle of internal friction. The authors of the article offer to consider initial seismic influence in the form of casual stationary process. In order to solve such problems modern software systems are proposed that solve differential equations of motion via direct integration with explicit schemes. The calculation in this case will be held on the synthesized accelerograms. A short review of the task solution of the beam lying on elastic basis, which was received by D.N. Sobolev at casual distribution of pastel coefficient in the direction x, is provided in article. In order to define the objective, D.N. Sobolev gives expressions for a population mean and correlation function of stochastic function. As a result of the task solution population means and dispersions of function of movements and its derivatives were received. The problem formulation considered in the article is more complicated, but at the same time important from a practical standpoint.
Geiges, A.; Nowak, W.; Rubin, Y.
2013-12-01
Stochastic models of sub-surface systems generally suffer from parametric and conceptual uncertainty. To reduce the model uncertainty, model parameters are calibrated using additional collected data. These data often come from costly data acquisition campaigns that need to be optimized to collect the data with the highest data utility (DU) or value of information. In model-based approaches, the DU is evaluated based on the uncertain model itself and is therefore uncertain as well. Additionally, for non-linear models, data utility depends on the yet unobserved measurement values and can only be estimated as an expected value over an assumed distribution of possible measurement values. Both factors introduce uncertainty into the optimization of field campaigns. We propose and investigate a sequential interaction scheme between campaign optimization, data collection and model calibration. The field campaign is split in individual segments. Each segment consists of optimization, segment-wise data collection, and successive model calibration or data assimilation. By doing so, (1) the expected data utility for the newly collected data is replaced by their actual one, (2) the calibration restricts both conceptual and parametric model uncertainty, and thus (3) the distribution of possible future data values for the subsequent campaign segments also changes. Hence, the model to describe the real system improves successively with each collected data segment, and so does the estimate of the yet remaining data requirements to achieve the overall investigation goals. We will show that using the sequentially improved model for the optimal design (OD) of the remaining field campaign leads to superior and more targeted designs.However, this traditional sequential OD optimizes small data segments one-by-one. In such a strategy, possible mutual dependencies with the possible data values and the optimization of data values collection in later segments are neglected. This allows a
Energy Technology Data Exchange (ETDEWEB)
Jan Hesthaven
2012-02-06
Final report for DOE Contract DE-FG02-98ER25346 entitled Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences. Principal Investigator Jan S. Hesthaven Division of Applied Mathematics Brown University, Box F Providence, RI 02912 Jan.Hesthaven@Brown.edu February 6, 2012 Note: This grant was originally awarded to Professor David Gottlieb and the majority of the work envisioned reflects his original ideas. However, when Prof Gottlieb passed away in December 2008, Professor Hesthaven took over as PI to ensure proper mentoring of students and postdoctoral researchers already involved in the project. This unusual circumstance has naturally impacted the project and its timeline. However, as the report reflects, the planned work has been accomplished and some activities beyond the original scope have been pursued with success. Project overview and main results The effort in this project focuses on the development of high order accurate computational methods for the solution of hyperbolic equations with application to problems with strong shocks. While the methods are general, emphasis is on applications to gas dynamics with strong shocks.
Levy, Daniel; Roos, Jason; Robinson, Jace; Carpenter, William; Martin, Richard; Taylor, Clark; Sugrue, Joseph; Terzuoli, Andrew
2016-06-01
Multiple sensors are used in a variety of geolocation systems. Many use Time Difference of Arrival (TDOA) or Received Signal Strength (RSS) measurements to estimate the most likely location of a signal. When an object does not emit an RF signal, Angle of Arrival (AOA) measurements using optical or infrared frequencies become more feasible than TDOA or RSS measurements. AOA measurements can be created from any sensor platform with any sort of optical sensor, location and attitude knowledge to track passive objects. Previous work has created a non-linear optimization (NLO) method for calculating the most likely estimate from AOA measurements. Two new modifications to the NLO algorithm are created and shown to correct AOA measurement errors by estimating the inherent bias and time-drift in the Inertial Measurement Unit (IMU) of the AOA sensing platform. One method corrects the sensor bias in post processing while treating the NLO method as a module. The other method directly corrects the sensor bias within the NLO algorithm by incorporating the bias parameters as a state vector in the estimation process. These two methods are analyzed using various Monte-Carlo simulations to check the general performance of the two modifications in comparison to the original NLO algorithm.
Directory of Open Access Journals (Sweden)
Xudong Yin
2014-02-01
Full Text Available The authors propose to implement conditional non-linear optimal perturbation related to model parameters (CNOP-P through an ensemble-based approach. The approach was first used in our earlier study and is improved to be suitable for calculating CNOP-P. Idealised experiments using the Lorenz-63 model are conducted to evaluate the performance of the improved ensemble-based approach. The results show that the maximum prediction error after optimisation has been multiplied manifold compared with the initial-guess prediction error, and is extremely close to, or greater than, the maximum value of the exhaustive attack method (a million random samples. The calculation of CNOP-P by the ensemble-based approach is capable of maintaining a high accuracy over a long prediction time under different constraints and initial conditions. Further, the CNOP-P obtained by the approach is applied to sensitivity analysis of the Lorenz-63 model. The sensitivity analysis indicates that when the prediction time is set to 0.2 time units, the Lorenz-63 model becomes extremely insensitive to one parameter, which leaves the other two parameters to affect the uncertainty of the model. Finally, a serial of parameter estimation experiments are performed to verify sensitivity analysis. It is found that when the three parameters are estimated simultaneously, the insensitive parameter is estimated much worse, but the Lorenz-63 model can still generate a very good simulation thanks to the relatively accurate values of the other two parameters. When only two sensitive parameters are estimated simultaneously and the insensitive parameter is left to be non-optimised, the outcome is better than the case when the three parameters are estimated simultaneously. With the increase of prediction time and observation, however, the model sensitivity to the insensitive parameter increases accordingly and the insensitive parameter can also be estimated successfully.
Energy Technology Data Exchange (ETDEWEB)
Welsch, Dominic Markus
2010-03-10
The High-Energy Storage Ring (HESR) is part of the upcoming Facility for Antiproton and Ion Research (FAIR) which is planned as a major extension to the present facility of the Helmholtzzentrum fuer Schwerionenforschung (GSI) in Darmstadt. The HESR will provide antiprotons in the momentum range from 1.5 to 15 GeV/c for the internal target experiment PANDA. The demanding requirements of PANDA in terms of beam quality and luminosity together with a limited production rate of antiprotons call for a long beam life time and a minimum of beam loss. Therefore, an effective closed orbit correction and a sufficiently large dynamic aperture of the HESR are crucial. With this thesis I present my work on both of these topics. The expected misalignments of beam guiding magnets have been estimated and used to simulate the closed orbit in the HESR. A closed orbit correction scheme has been developed for different ion optical settings of the HESR and numerical simulations have been performed to validate the scheme. The proposed closed orbit correction method which uses the orbit response matrix has been benchmarked at the Cooler Synchrotron COSY of the Forschungszentrum Juelich. A chromaticity correction scheme for the HESR consisting of sextupole magnets has been developed to reduce tune spread and thus to minimize the emittance growth caused by betatron resonances. The chromaticity correction scheme has been optimized through dynamic aperture calculations. The estimated field errors of the HESR dipole and quadrupole magnets have been included in the non-linear beam dynamics studies. Investigations concerning their optimization have been carried out. The ion optical settings of the HESR have been improved using dynamic aperture calculations and the technique of frequency map analysis. The related diffusion coefficient was also used to predict long-term stability based on short-term particle tracking. With a reasonable reduction of the quadrupole magnets field errors and a
Directory of Open Access Journals (Sweden)
Chi-Chang Wang
2013-09-01
Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.
Directory of Open Access Journals (Sweden)
Jia Hui Ong
2016-07-01
Full Text Available Parameter searching is one of the most important aspects in getting favorable results in optimization problems. It is even more important if the optimization problems are limited by time constraints. In a limited time constraint problems, it is crucial for any algorithms to get the best results or near-optimum results. In a previous study, Differential Evolution (DE has been found as one of the best performing algorithms under time constraints. As this has help in answering which algorithm that yields results that are near-optimum under a limited time constraint. Hence to further enhance the performance of DE under time constraint evaluation, a throughout parameter searching for population size, mutation constant and f constant have been carried out. CEC 2015 Global Optimization Competition’s 15 scalable test problems are used as test suite for this study. In the previous study the same test suits has been used and the results from DE will be use as the benchmark for this study since it shows the best results among the previous tested algorithms. Eight different populations size are used and they are 10, 30, 50, 100, 150, 200, 300, and 500. Each of these populations size will run with mutation constant of 0.1 until 0.9 and from 0.1 until 0.9. It was found that population size 100, Cr = 0.9, F=0.5 outperform the benchmark results. It is also observed from the results that good higher Cr around 0.8 and 0.9 with low F around 0.3 to 0.4 yields good results for DE under time constraints evaluation
Algorithms for non-linear M-estimation
DEFF Research Database (Denmark)
Madsen, Kaj; Edlund, O; Ekblom, H
1997-01-01
a sequence of estimation problems for linearized models is solved. In the testing we apply four estimators to ten non-linear data fitting problems. The test problems are also solved by the Generalized Levenberg-Marquardt method and standard optimization BFGS method. It turns out that the new method...
Directory of Open Access Journals (Sweden)
K. Lenin
2013-03-01
Full Text Available Reactive Power Optimization is a complex combinatorial optimization problem involving non-linear function having multiple local minima, non-linear and discontinuous constrains. This paper presents Attractive and repulsive Particle Swarm Optimization (ARPSO and Random Virus Algorithm (RVA in trying to overcome the Problem of premature convergence. RVA and ARPSO is applied to Reactive Power Optimization problem and is evaluated on standard IEEE 30Bus System. The results show that RVA prevents premature convergence to high degree but still keeps a rapid convergence. It gives best solution when compared to Attractive and repulsive Particle Swarm Optimization (ARPSO and Particle Swarm Optimization (PSO.
Fonville, Judith M; Bylesjö, Max; Coen, Muireann; Nicholson, Jeremy K; Holmes, Elaine; Lindon, John C; Rantalainen, Mattias
2011-10-31
Linear multivariate projection methods are frequently applied for predictive modeling of spectroscopic data in metabonomic studies. The OPLS method is a commonly used computational procedure for characterizing spectral metabonomic data, largely due to its favorable model interpretation properties providing separate descriptions of predictive variation and response-orthogonal structured noise. However, when the relationship between descriptor variables and the response is non-linear, conventional linear models will perform sub-optimally. In this study we have evaluated to what extent a non-linear model, kernel-based orthogonal projections to latent structures (K-OPLS), can provide enhanced predictive performance compared to the linear OPLS model. Just like its linear counterpart, K-OPLS provides separate model components for predictive variation and response-orthogonal structured noise. The improved model interpretation by this separate modeling is a property unique to K-OPLS in comparison to other kernel-based models. Simulated annealing (SA) was used for effective and automated optimization of the kernel-function parameter in K-OPLS (SA-K-OPLS). Our results reveal that the non-linear K-OPLS model provides improved prediction performance in three separate metabonomic data sets compared to the linear OPLS model. We also demonstrate how response-orthogonal K-OPLS components provide valuable biological interpretation of model and data. The metabonomic data sets were acquired using proton Nuclear Magnetic Resonance (NMR) spectroscopy, and include a study of the liver toxin galactosamine, a study of the nephrotoxin mercuric chloride and a study of Trypanosoma brucei brucei infection. Automated and user-friendly procedures for the kernel-optimization have been incorporated into version 1.1.1 of the freely available K-OPLS software package for both R and Matlab to enable easy application of K-OPLS for non-linear prediction modeling.
Energy Technology Data Exchange (ETDEWEB)
NONE
1981-07-01
The main results contained in this report are the following: i ) Lagrangian universality holds in a precisely defined weak sense. II ) Isolation of 5th order polynomial evolution equations having high order conservation laws. III ) Hamiltonian formulation of a wide class of non-linear evolution equations. IV) Some properties of the symmetries of Gardner-like systems. v) Characterization of the range and Kernel of {zeta}/{zeta} u{sub {alpha}}, |{alpha} | - 1. vi) A generalized variational approach and application to the anharmonic oscillator. v II ) Relativistic correction and quasi-classical approximation to the anechoic oscillator. VII ) Properties of a special class of 6th-order anharmonic oscillators. ix) A new method for constructing conserved densities In PDE. (Author) 97 refs.
Non-linear canonical correlation
van der Burg, Eeke; de Leeuw, Jan
1983-01-01
Non-linear canonical correlation analysis is a method for canonical correlation analysis with optimal scaling features. The method fits many kinds of discrete data. The different parameters are solved for in an alternating least squares way and the corresponding program is called CANALS. An
Energy Technology Data Exchange (ETDEWEB)
Fonville, Judith M., E-mail: j.fonville07@imperial.ac.uk [Biomolecular Medicine, Department of Surgery and Cancer, Faculty of Medicine, Imperial College London, Sir Alexander Fleming Building, South Kensington, London SW7 2AZ (United Kingdom); Bylesjoe, Max, E-mail: max.bylesjo@almacgroup.com [Almac Diagnostics, 19 Seagoe Industrial Estate, Craigavon BT63 5QD (United Kingdom); Coen, Muireann, E-mail: m.coen@imperial.ac.uk [Biomolecular Medicine, Department of Surgery and Cancer, Faculty of Medicine, Imperial College London, Sir Alexander Fleming Building, South Kensington, London SW7 2AZ (United Kingdom); Nicholson, Jeremy K., E-mail: j.nicholson@imperial.ac.uk [Biomolecular Medicine, Department of Surgery and Cancer, Faculty of Medicine, Imperial College London, Sir Alexander Fleming Building, South Kensington, London SW7 2AZ (United Kingdom); Holmes, Elaine, E-mail: elaine.holmes@imperial.ac.uk [Biomolecular Medicine, Department of Surgery and Cancer, Faculty of Medicine, Imperial College London, Sir Alexander Fleming Building, South Kensington, London SW7 2AZ (United Kingdom); Lindon, John C., E-mail: j.lindon@imperial.ac.uk [Biomolecular Medicine, Department of Surgery and Cancer, Faculty of Medicine, Imperial College London, Sir Alexander Fleming Building, South Kensington, London SW7 2AZ (United Kingdom); Rantalainen, Mattias, E-mail: rantalai@stats.ox.ac.uk [Department of Statistics, Oxford University, 1 South Parks Road, Oxford OX1 3TG (United Kingdom)
2011-10-31
Highlights: {yields} Non-linear modeling of metabonomic data using K-OPLS. {yields} automated optimization of the kernel parameter by simulated annealing. {yields} K-OPLS provides improved prediction performance for exemplar spectral data sets. {yields} software implementation available for R and Matlab under GPL v2 license. - Abstract: Linear multivariate projection methods are frequently applied for predictive modeling of spectroscopic data in metabonomic studies. The OPLS method is a commonly used computational procedure for characterizing spectral metabonomic data, largely due to its favorable model interpretation properties providing separate descriptions of predictive variation and response-orthogonal structured noise. However, when the relationship between descriptor variables and the response is non-linear, conventional linear models will perform sub-optimally. In this study we have evaluated to what extent a non-linear model, kernel-based orthogonal projections to latent structures (K-OPLS), can provide enhanced predictive performance compared to the linear OPLS model. Just like its linear counterpart, K-OPLS provides separate model components for predictive variation and response-orthogonal structured noise. The improved model interpretation by this separate modeling is a property unique to K-OPLS in comparison to other kernel-based models. Simulated annealing (SA) was used for effective and automated optimization of the kernel-function parameter in K-OPLS (SA-K-OPLS). Our results reveal that the non-linear K-OPLS model provides improved prediction performance in three separate metabonomic data sets compared to the linear OPLS model. We also demonstrate how response-orthogonal K-OPLS components provide valuable biological interpretation of model and data. The metabonomic data sets were acquired using proton Nuclear Magnetic Resonance (NMR) spectroscopy, and include a study of the liver toxin galactosamine, a study of the nephrotoxin mercuric chloride and
Voorhies, Coerte V.
1993-01-01
The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.
Efficient Non Linear Loudspeakers
DEFF Research Database (Denmark)
Petersen, Bo R.; Agerkvist, Finn T.
2006-01-01
Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...... by changing the voice coil layout. This deliberate non-linear design has the benefit that a smaller amplifier can be used, which has the benefit of reducing system cost as well as reducing power consumption....
Pando, V.; García-Laguna, J.; San-José, L. A.
2012-11-01
In this article, we integrate a non-linear holding cost with a stock-dependent demand rate in a maximising profit per unit time model, extending several inventory models studied by other authors. After giving the mathematical formulation of the inventory system, we prove the existence and uniqueness of the optimal policy. Relying on this result, we can obtain the optimal solution using different numerical algorithms. Moreover, we provide a necessary and sufficient condition to determine whether a system is profitable, and we establish a rule to check when a given order quantity is the optimal lot size of the inventory model. The results are illustrated through numerical examples and the sensitivity of the optimal solution with respect to changes in some values of the parameters is assessed.
Bobály, Balázs; Randazzo, Giuseppe Marco; Rudaz, Serge; Guillarme, Davy; Fekete, Szabolcs
2017-01-20
The goal of this work was to evaluate the potential of non-linear gradients in hydrophobic interaction chromatography (HIC), to improve the separation between the different homologous species (drug-to-antibody, DAR) of commercial antibody-drug conjugates (ADC). The selectivities between Brentuximab Vedotin species were measured using three different gradient profiles, namely linear, power function based and logarithmic ones. The logarithmic gradient provides the most equidistant retention distribution for the DAR species and offers the best overall separation of cysteine linked ADC in HIC. Another important advantage of the logarithmic gradient, is its peak focusing effect for the DAR0 species, which is particularly useful to improve the quantitation limit of DAR0. Finally, the logarithmic behavior of DAR species of ADC in HIC was modelled using two different approaches, based on i) the linear solvent strength theory (LSS) and two scouting linear gradients and ii) a new derived equation and two logarithmic scouting gradients. In both cases, the retention predictions were excellent and systematically below 3% compared to the experimental values. Copyright © 2016 Elsevier B.V. All rights reserved.
Optimal obstacle control problem
Institute of Scientific and Technical Information of China (English)
ZHU Li; LI Xiu-hua; GUO Xing-ming
2008-01-01
In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality. Existence, uniqueness and regularity of the optimal control problem are established. In addition, the approximation of the optimal obstacle problem is also studied.
Practical use of SPRINT and a moving grid interface for a class of 1D non-linear transport problems
van Eijkeren JCH; Zegeling PA; Hassanizadeh SM
1991-01-01
Environmental problems tend to become of still greater complexity. The mathematical formulation of these problems often results in a set of differential equations, which urges the need for robust differential equation solvers. Moreover, these solvers should be implemented within a user-friendly an
Efficient Non Linear Loudspeakers
DEFF Research Database (Denmark)
Petersen, Bo R.; Agerkvist, Finn T.
2006-01-01
Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...... by changing the voice coil layout. This deliberate non-linear design has the benefit that a smaller amplifier can be used, which has the benefit of reducing system cost as well as reducing power consumption.......Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...
Jonker, J.B.; Meijaard, J.P.
2013-01-01
A beam finite element formulation for large deflection problems in the analysis of flexible multibody systems has been proposed. In this formulation, a set of independent discrete deformation modes are defined for each element which are related to conventional small deflection beam theory in a co-ro
The study of cuckoo optimization algorithm for production planning problem
Akbarzadeh, Afsane; Shadkam, Elham
2015-01-01
Constrained Nonlinear programming problems are hard problems, and one of the most widely used and common problems for production planning problem to optimize. In this study, one of the mathematical models of production planning is survey and the problem solved by cuckoo algorithm. Cuckoo Algorithm is efficient method to solve continues non linear problem. Moreover, mentioned models of production planning solved with Genetic algorithm and Lingo software and the results will compared. The Cucko...
Variational iteration method for solving non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Hemeda, A.A. [Department of Mathematics, Faculty of Science, University of Tanta, Tanta (Egypt)], E-mail: aahemeda@yahoo.com
2009-02-15
In this paper, we shall use the variational iteration method to solve some problems of non-linear partial differential equations (PDEs) such as the combined KdV-MKdV equation and Camassa-Holm equation. The variational iteration method is superior than the other non-linear methods, such as the perturbation methods where this method does not depend on small parameters, such that it can fined wide application in non-linear problems without linearization or small perturbation. In this method, the problems are initially approximated with possible unknowns, then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
A Numerical Embedding Method for Solving the Nonlinear Optimization Problem
Institute of Scientific and Technical Information of China (English)
田保锋; 戴云仙; 孟泽红; 张建军
2003-01-01
A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.
Non-Linear Logging Parameters Inversion
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The non-linear logging parameters inversion is based on the field theory, information optimization and predication theory. It uses seismic charaoters,geological model and logging data as a restriction to inverse 2D, 3D logging parameters data volume. Using this method,
An interpretation of the Gini coefficient in a Stiglitz two-type optimal tax problem
DEFF Research Database (Denmark)
Rasmussen, Bo Sandemann
2015-01-01
In a two-type Stiglitz (1982) model of optimal non-linear taxation it is shown that when the utility function relating to consumption is logaritmic the shadow price of the incentive constraint relating to the optimal tax problem exactly equals the Gini coefficient of the second-best optimal income...
An Interpretation of the Gini Coefficient in a Stiglitz Two-Type Optimal Tax Problem
DEFF Research Database (Denmark)
Rasmussen, Bo Sandemann
2014-01-01
In a two-type Stiglitz (1982) model of optimal non-linear taxation it is shown that when the utility function relating to consumption is logaritmic the shadow price of the incentive constraint relating to the optimal tax problem exactly equals the Gini coefficient of the second-best optimal income...
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Directory of Open Access Journals (Sweden)
Paras Bhatnagar
2012-10-01
Full Text Available Kaul and Kaur [7] obtained necessary optimality conditions for a non-linear programming problem by taking the objective and constraint functions to be semilocally convex and their right differentials at a point to be lower semi-continuous. Suneja and Gupta [12] established the necessary optimality conditions without assuming the semilocal convexity of the objective and constraint functions but their right differentials at the optimal point to be convex. Suneja and Gupta [13] established necessary optimality conditions for an efficient solution of a multiobjective non-linear programming problem by taking the right differentials of the objective functions and constraintfunctions at the efficient point to be convex. In this paper we obtain some results for a properly efficient solution of a multiobjective non-linear fractional programming problem involving semilocally convex and related functions by assuming generalized Slater type constraint qualification.
Institute of Scientific and Technical Information of China (English)
刘灿昌; 李红艳
2011-01-01
提出非线性的分阶最优控制策略,并将其应用于悬臂梁非线性振动的压电减振控制.建立悬臂梁非线性压电减振系统动力学模型,导出减振系统的非线性动力学运动微分方程.将梁振动挠度和压电驱动器的控制电压同时展开为小参数形式,利用摄动法实现非线性压电控制微分方程的线性化.通过空间解耦,得到状态空间方程.设计非线性分阶控制器,对该减振系统进行分阶最优控制.%A non-linear grade optimal control scheme is proposed and used in the piezoelectric vibration reduction control of non-linear cantilever beam. The dynamic model of non-linear vibration reduction beam with piezoelectric damper is built. The non-linear dynamic differential equations of the vibration reduction system are derived. The vibrational deflection and the piezoelectricity driver control voltage of beam are expanded as the small parametric form. The differential equation is linearized into a set of linear equations by means of perturbation. The state space equations are obtained by decoupling in the space coordinates. The vibration reduction system is controlled by the non-linear grade controllers.
Non-linear finite element analysis in structural mechanics
Rust, Wilhelm
2015-01-01
This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.
Directory of Open Access Journals (Sweden)
Diana M. Ortiz
2011-01-01
Full Text Available Estrategias de evolución es una técnica bio-inspirada, eficiente y robusta para resolver problemas de optimización donde el espacio de soluciones es no restringido. Sin embargo, esta suposición es irreal en muchos casos porque el espacio de soluciones es limitado por fronteras complejas en la forma de restricciones tanto lineales como no lineales. En este artículo de investigación, se propone una modificación al algoritmo original de estrategias de evolución para optimizar problemas donde el espacio de soluciones es limitado usando restricciones complejas. El método propuesto es basado en el uso de una función de penalización la cual es cero dentro de la región factible, e igual al máximo valor dentro de la región factible cuando se considera un punto que es no factible. La aproximación propuesta es probada usando seis problemas de prueba bien conocidos. En todos los casos, esta aproximación encontró un punto óptimo igual o menor que los valores reportados en la literatura.Evolution Strategies is a bio-inspired, robust, and efficient technique for solving optimization problems where the solution space is unrestricted. However, this assumption is unreal in many cases because the solution space is limited by complex boundaries in the form of linear and non-linear restrictions. In this paper, a modification of the original algorithm of Evolution Strategies for optimizing problems where the solution space is bounded using complex restrictions is proposed. The proposed method is based on the use of a penalization function which is zero inside of the feasible region and equal to the maximum value inside of the feasible region when an unfeasible point is considered. The proposed approach is proved using six benchmark problems. In all cases, our approach found an optimal point equal or lower than the values reported in the literature.
A numerical method for solving optimal control problems using state parametrization
Mehne, H.; Borzabadi, A.
2006-06-01
A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.
Class and Home Problems: Optimization Problems
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
Class and Home Problems: Optimization Problems
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations betwee...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models.......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under...
UDU factored Lyapunov recursions solve optimal reduced-order LQG problems
Willigenburg, van L.G.; Koning, de W.L.
2004-01-01
A new algorithm is presented to solve both the finite-horizon time-varying and infinite-horizon time-invariant discrete-time optimal reduced-order LQG problem. In both cases the first order necessary optimality conditions can be represented by two non-linearly coupled discrete-time Lyapunov equation
DEFF Research Database (Denmark)
Andersen, Steffen; Harrison, Glenn W.; Hole, Arne Risa
2012-01-01
We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discountin...
Non-Linear Dynamics and Fundamental Interactions
Khanna, Faqir
2006-01-01
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
Non-linear dendrites can tune neurons
Directory of Open Access Journals (Sweden)
Romain Daniel Cazé
2014-03-01
Full Text Available A signature of visual, auditory, and motor cortices is the presence of neurons tuned to distinct features of the environment. While neuronal tuning can be observed in most brain areas, its origin remains enigmatic, and new calcium imaging data complicate this problem. Dendritic calcium signals, in a L2/3 neuron from the mouse visual cortex, display a wide range of tunings that could be different from the neuronal tuning (Jia et al 2010. To elucidate this observation we use multi-compartmental models of increasing complexity, from a binary to a realistic biophysical model of L2/3 neuron. These models possess non-linear dendritic subunits inside which the result of multiple excitatory inputs is smaller than their arithmetic sum. While dendritic non-linear subunits are ad-hoc in the binary model, non-linearities in the realistic model come from the passive saturation of synaptic currents. Because of these non-linearities our neuron models are scatter sensitive: the somatic membrane voltage is higher when presynaptic inputs target different dendrites than when they target a single dendrite. This spatial bias in synaptic integration is, in our models, the origin of neuronal tuning. Indeed, assemblies of presynaptic inputs encode the stimulus property through an increase in correlation or activity, and only the assembly that encodes the preferred stimulus targets different dendrites. Assemblies coding for the non-preferred stimuli target single dendrites, explaining the wide range of observed tunings and the possible difference between dendritic and somatic tuning. We thus propose, in accordance with the latest experimental observations, that non-linear integration in dendrites can generate neuronal tuning independently of the coding regime.
Non-linear scalable TFETI domain decomposition based contact algorithm
Dobiáš, J.; Pták, S.; Dostál, Z.; Vondrák, V.; Kozubek, T.
2010-06-01
The paper is concerned with the application of our original variant of the Finite Element Tearing and Interconnecting (FETI) domain decomposition method, called the Total FETI (TFETI), to solve solid mechanics problems exhibiting geometric, material, and contact non-linearities. The TFETI enforces the prescribed displacements by the Lagrange multipliers, so that all the subdomains are 'floating', the kernels of their stiffness matrices are known a priori, and the projector to the natural coarse grid is more effective. The basic theory and relationships of both FETI and TFETI are briefly reviewed and a new version of solution algorithm is presented. It is shown that application of TFETI methodology to the contact problems converts the original problem to the strictly convex quadratic programming problem with bound and equality constraints, so that the effective, in a sense optimal algorithms is to be applied. Numerical experiments show that the method exhibits both numerical and parallel scalabilities.
DEFF Research Database (Denmark)
Du, Yigang
without iteration steps. The ASA is implemented in combination with Field II and extended to simulate the pulsed ultrasound fields. The simulated results from a linear array transducer are made by the ASA based on Field II, and by a released non-linear simulation program- Abersim, respectively....... The calculation speed of the ASA is increased approximately by a factor of 140. For the second harmonic point spread function the error of the full width is 1.5% at -6 dB and 6.4% at -12 dB compared to Abersim. To further investigate the linear and non-linear ultrasound fields, hydrophone measurements.......3% relative to the measurement from a 1 inch diameter transducer. A preliminary study for harmonic imaging using synthetic aperture sequential beamforming (SASB) has been demonstrated. A wire phantom underwater measurement is made by an experimental synthetic aperture real-time ultrasound scanner (SARUS...
Optimization techniques for Transportation Problems
Directory of Open Access Journals (Sweden)
Gauthaman.P
2017-06-01
Full Text Available This paper infers about optimization technique for various problems in transportation engineering. While for pavement engineering, maintenance is priority issue, for traffic it is signalling which is priority issue. Many optimization methods are discussed though given importance of genetic algorithm approach. While optimization techniques nearly approach practicality, research works are on for modern optimization techniques which not only adds ease of structure but also provide compatibility to modern day problems encountered in transportation engineering. Some of the modern tools are discussed to employ optimization techniques which are quite simple to use and implement once it is calibrated to the desired objective.
Lmfit: Non-Linear Least-Square Minimization and Curve-Fitting for Python
Newville, Matthew; Stensitzki, Till; Allen, Daniel B.; Rawlik, Michal; Ingargiola, Antonino; Nelson, Andrew
2016-06-01
Lmfit provides a high-level interface to non-linear optimization and curve fitting problems for Python. Lmfit builds on and extends many of the optimization algorithm of scipy.optimize, especially the Levenberg-Marquardt method from optimize.leastsq. Its enhancements to optimization and data fitting problems include using Parameter objects instead of plain floats as variables, the ability to easily change fitting algorithms, and improved estimation of confidence intervals and curve-fitting with the Model class. Lmfit includes many pre-built models for common lineshapes.
Solving Optimal Timing Problems Elegantly
Todorova, Tamara
2013-01-01
Few textbooks in mathematical economics cover optimal timing problems. Those which cover them do it scantly or in a rather clumsy way, making it hard for students to understand and apply the concept of optimal time in new contexts. Discussing the plentiful illustrations of optimal timing problems, we present an elegant and simple method of solving them. Whether the present value function is exponential or logarithmic, a convenient way to solve it is to convert the base to the exponential numb...
Reliability optimization problems with multiple constraints under fuzziness
Gupta, Neha; Haseen, Sanam; Bari, Abdul
2016-06-01
In reliability optimization problems diverse situation occurs due to which it is not always possible to get relevant precision in system reliability. The imprecision in data can often be represented by triangular fuzzy numbers. In this manuscript, we have considered different fuzzy environment for reliability optimization problem of redundancy. We formulate a redundancy allocation problem for a hypothetical series-parallel system in which the parameters of the system are fuzzy. Two different cases are then formulated as non-linear programming problem and the fuzzy nature is defuzzified into crisp problems using three different defuzzification methods viz. ranking function, graded mean integration value and α-cut. The result of the methods is compared at the end of the manuscript using a numerical example.
Modelling Loudspeaker Non-Linearities
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
Employment of CB models for non-linear dynamic analysis
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
A Projected Non-linear Conjugate Gradient Method for Interactive Inverse Kinematics
DEFF Research Database (Denmark)
Engell-Nørregård, Morten; Erleben, Kenny
2009-01-01
Inverse kinematics is the problem of posing an articulated figure to obtain a wanted goal, without regarding inertia and forces. Joint limits are modeled as bounds on individual degrees of freedom, leading to a box-constrained optimization problem. We present A projected Non-linear Conjugate...... Gradient optimization method suitable for box-constrained optimization problems for inverse kinematics. We show application on inverse kinematics positioning of a human figure. Performance is measured and compared to a traditional Jacobian Transpose method. Visual quality of the developed method...
Energy Technology Data Exchange (ETDEWEB)
Chavarette, Fabio Roberto [Department of Mechanical Design, State University of Campinas, 13083-970 Campinas, SP (Brazil); State University of Sao Paulo at Rio Claro, C.P. 178, 13500-230 Rio Claro, SP (Brazil); Balthazar, Jose Manoel [Department of Mechanical Design, State University of Campinas, 13083-970 Campinas, SP (Brazil); State University of Sao Paulo at Rio Claro, C.P. 178, 13500-230 Rio Claro, SP (Brazil)], E-mail: jmbaltha@rc.unesp.br; Rafikov, Marat [Universidade Regional do Noroeste do Estado do Rio Grande do Sul 98700-000, C.P. 560, Ijui, RS (Brazil); Hermini, Helder Anibal [Department of Mechanical Design, State University of Campinas, 13083-970 Campinas, SP (Brazil)
2009-02-28
In this paper, we have studied the plasmatic membrane behavior using an electric circuit developed by Hodgkin and Huxley in 1952 and have dealt with the variation of the amount of time related to the potassium and sodium conductances in the squid axon. They developed differential equations for the propagation of electric signals; the dynamics of the Hodgkin-Huxley model have been extensively studied both from the view point of its their biological implications and as a test bed for numerical methods, which can be applied to more complex models. Recently, an irregular chaotic movement of the action potential of the membrane was observed for a number of techniques of control with the objective to stabilize the variation of this potential. This paper analyzes the non-linear dynamics of the Hodgkin-Huxley mathematical model, and we present some modifications in the governing equations of the system in order to make it a non-ideal one (taking into account that the energy source has a limited power supply). We also developed an optimal linear control design for the action potential of membranes. Here, we discuss the conditions that allow the use of control linear feedback for this kind of non-linear system.
Evolution Strategies in Optimization Problems
Cruz, Pedro A F
2007-01-01
Evolution Strategies are inspired in biology and part of a larger research field known as Evolutionary Algorithms. Those strategies perform a random search in the space of admissible functions, aiming to optimize some given objective function. We show that simple evolution strategies are a useful tool in optimal control, permitting to obtain, in an efficient way, good approximations to the solutions of some recent and challenging optimal control problems.
Applications of Kalman filters based on non-linear functions to numerical weather predictions
Directory of Open Access Journals (Sweden)
G. Galanis
2006-10-01
Full Text Available This paper investigates the use of non-linear functions in classical Kalman filter algorithms on the improvement of regional weather forecasts. The main aim is the implementation of non linear polynomial mappings in a usual linear Kalman filter in order to simulate better non linear problems in numerical weather prediction. In addition, the optimal order of the polynomials applied for such a filter is identified. This work is based on observations and corresponding numerical weather predictions of two meteorological parameters characterized by essential differences in their evolution in time, namely, air temperature and wind speed. It is shown that in both cases, a polynomial of low order is adequate for eliminating any systematic error, while higher order functions lead to instabilities in the filtered results having, at the same time, trivial contribution to the sensitivity of the filter. It is further demonstrated that the filter is independent of the time period and the geographic location of application.
Topology Optimization for Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
2011-01-01
This report deals with the topology optimization of convection problems.That is, the aim of the project is to develop, implement and examine topology optimization of purely thermal and coupled thermomechanical problems,when the design-dependent eects of convection are taken into consideration.......This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...
de Jong, Roelof
2005-07-01
This program incorporates a number of tests to analyse the count rate dependent non-linearity seen in NICMOS spectro-photometric observations. In visit 1 we will observe a few fields with stars of a range in luminosity in NGC1850 with NICMOS in NIC1 in F090M, F110W and F160W and NIC2 F110W, F160W, and F180W. We will repeat the observations with flatfield lamp on, creating artificially high count-rates, allowing tests of NICMOS linearity as function of count rate. To access the effect of charge trapping and persistence, we first take darks {so there is not too much charge already trapped}, than take exposures with the lamp off, exposures with the lamp on, and repeat at the end with lamp off. Finally, we continue with taking darks during occultation. In visit 2 we will observe spectro-photometric standard P041C using the G096 and G141 grisms in NIC3, and repeat the lamp off/on/off test to artificially create a high background. In visits 3&4 we repeat photometry measurements of faint standard stars SNAP-2 and WD1657+343, on which the NICMOS non-linearity was originally discovered using grism observations. These measurements are repeated, because previous photometry was obtained with too short exposure times, hence substantially affected by charge trapping non-linearity. Measurements will be made with NIC1: Visit 5 forms the persistence test of the program. The bright star GL-390 {used in a previous persistence test} will iluminate the 3 NICMOS detectors in turn for a fixed time, saturating the center many times, after which a series of darks will be taken to measure the persistence {i.e. trapped electrons and the decay time of the traps}. To determine the wavelength dependence of the trap chance, exposures of the bright star in different filters will be taken, as well as one in the G096 grism with NIC3. Most exposures will be 128s long, but two exposures in the 3rd orbit will be 3x longer, to seperate the effects of count rate versus total counts of the trap
Topology optimization of flow problems
DEFF Research Database (Denmark)
Gersborg, Allan Roulund
2007-01-01
of the velocity field or mixing properties. To reduce the computational complexity of the topology optimization problems the primary focus is put on the Stokes equation in 2D and in 3D. However, the thesis also contains examples with the 2D Navier-Stokes equation as well as an example with convection dominated....... Although the study of the FVM is carried out using a simple heat conduction problem, the work illuminates and discusses the technicalities of employing the FVM in connection with topology optimization. Finally, parallelized solution methods are investigated using the high performance computing facility...
Optimization and geophysical inverse problems
Energy Technology Data Exchange (ETDEWEB)
Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F.; Gill, P.; Heinkenschloss, M.; Johnson, L.; McEvilly, T.; More, J.; Newman, G.; Oldenburg, D.; Parker, P.; Porto, B.; Sen, M.; Torczon, V.; Vasco, D.; Woodward, N.B.
2000-10-01
A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1994-01-01
The paper studies the problem of determining the number and dimensions of sizes of apparel so as to maximize profits. It develops a simple one-variable bisection search algorithm that gives the optimal solution. An example is solved interactively using a Macintosh LC and Math CAD, a mathematical ...
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
Non-linear elastic deformations
Ogden, R W
1997-01-01
Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
Modeling of non-linear CHP efficiency curves in distributed energy systems
DEFF Research Database (Denmark)
Milan, Christian; Stadler, Michael; Cardoso, Gonçalo
2015-01-01
Distributed energy resources gain an increased importance in commercial and industrial building design. Combined heat and power (CHP) units are considered as one of the key technologies for cost and emission reduction in buildings. In order to make optimal decisions on investment and operation...... for these technologies, detailed system models are needed. These models are often formulated as linear programming problems to keep computational costs and complexity in a reasonable range. However, CHP systems involve variations of the efficiency for large nameplate capacity ranges and in case of part load operation......, which can be even of non-linear nature. Since considering these characteristics would turn the models into non-linear problems, in most cases only constant efficiencies are assumed. This paper proposes possible solutions to address this issue. For a mixed integer linear programming problem two...
Iterative optimization in inverse problems
Byrne, Charles L
2014-01-01
Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author's considerable research in the field, including his recently developed class of SUMMA algorithms. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing. Organizing the topics from general to more
The Duality on Vector Optimization Problems
Institute of Scientific and Technical Information of China (English)
HUANG Long-guang
2012-01-01
Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.
Simulation of non-linear ultrasound fields
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Fox, Paul D.; Wilhjelm, Jens E.
2002-01-01
An approach for simulating non-linear ultrasound imaging using Field II has been implemented using the operator splitting approach, where diffraction, attenuation, and non-linear propagation can be handled individually. The method uses the Earnshaw/Poisson solution to Burgcrs' equation for the non......-linear ultrasound imaging in 3D using filters or pulse inversion for any kind of transducer, focusing, apodization, pulse emission and scattering phantom. This is done by first simulating the non-linear emitted field and assuming that the scattered field is weak and linear. The received signal is then the spatial...
Optimization in HIV screening problems
Directory of Open Access Journals (Sweden)
Lev Abolnikov
2003-01-01
Full Text Available In this article, the authors use both deterministic and stochastic approaches to the analysis of some optimization problems that arise in the group (pool HIV screening practice. Two kinds of testing policies are considered. For the first kind, group-individual testing, the optimal size of the group that should be selected for testing is found. For more general group-subgroup testing procedure the authors develop a numerical algorithm for finding the sequence of successively selected subgroups that minimizes the total cost of testing. Assuming that both arriving and testing processes have a random nature, the authors suggest a stochastic model in which the optimal size of the group in the group-individual testing procedure is found by using methods of queueing theory.
Performance investigation of multigrid optimization for DNS-based optimal control problems
Nita, Cornelia; Vandewalle, Stefan; Meyers, Johan
2016-11-01
Optimal control theory in Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES) of turbulent flow involves large computational cost and memory overhead for the optimization of the controls. In this context, the minimization of the cost functional is typically achieved by employing gradient-based iterative methods such as quasi-Newton, truncated Newton or non-linear conjugate gradient. In the current work, we investigate the multigrid optimization strategy (MGOpt) in order to speed up the convergence of the damped L-BFGS algorithm for DNS-based optimal control problems. The method consists in a hierarchy of optimization problems defined on different representation levels aiming to reduce the computational resources associated with the cost functional improvement on the finest level. We examine the MGOpt efficiency for the optimization of an internal volume force distribution with the goal of reducing the turbulent kinetic energy or increasing the energy extraction in a turbulent wall-bounded flow; problems that are respectively related to drag reduction in boundary layers, or energy extraction in large wind farms. Results indicate that in some cases the multigrid optimization method requires up to a factor two less DNS and adjoint DNS than single-grid damped L-BFGS. The authors acknowledge support from OPTEC (OPTimization in Engineering Center of Excellence, KU Leuven, Grant No PFV/10/002).
An algorithm for earthwork allocation considering non-linear factors
Institute of Scientific and Technical Information of China (English)
WANG Ren-chao; LIU Jin-fei
2008-01-01
For solving the optimization model of earthwork allocation considering non-linear factors, a hybrid al-gorithm combined with the ant algorithm (AA) and particle swarm optimization (PSO) is proposed in this pa-per. Then the proposed method and the LP method are used respectively in solving a linear allocation model of a high rockfill dam project. Results obtained by these two methods are compared each other. It can be conclu-ded that the solution got by the proposed method is extremely approximate to the analytic solution of LP method. The superiority of the proposed method over the LP method in solving a non-linear allocation model is illustrated by a non-linear case. Moreover, further researches on improvement of the algorithm and the allocation model are addressed.
Numerical simulation of non-linear phenomena in geotechnical engineering
DEFF Research Database (Denmark)
Sørensen, Emil Smed
Geotechnical problems are often characterized by the non-linear behavior of soils and rock which are strongly linked to the inherent properties of the porous structure of the material as well as the presence and possible flow of any surrounding fluids. Dynamic problems involving such soil-fluid i...
Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models
Institute of Scientific and Technical Information of China (English)
LI Chaokui; ZHU Qing; SONG Chengfang
2003-01-01
This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a nonlinear model. On the basis of the error definition, this paper puts forward a new adjustment criterion, SGPE.Last, this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.
Risks of non-linear climate change
Energy Technology Data Exchange (ETDEWEB)
Van Ham, J.; Van Beers, R.J.; Builtjes, P.J.H.; Koennen, G.P.; Oerlemans, J.; Roemer, M.G.M. [TNO-SCMO, Delft (Netherlands)
1995-12-31
Climate forcing as a result of increased concentrations of greenhouse gases has been primarily addressed as a problem of a possibly warmer climate. So far, such change has been obscured in observations, possibly as a result of natural climate variability and masking by aerosols. Consequently, projections of the effect of climate forcing have to be based on modelling, more specifically by applying Global Circulation Models GCMs. These GCMs do not cover all possible feedbacks; neither do they address all specific possible effects of climate forcing. The investigation reviews possible non-linear climate change which does not fall within the coverage of present GCMs. The review includes the potential relevance of changes in biogeochemical cycles, aerosol and cloud feedback, albedo instability, ice-flow instability, changes in the thermohaline circulation and changes resulting from stratospheric cooling. It is noted that these changes may have different time horizons. Three from the investigated issues provide indications for a possible non-linear change. On the decadal scale stratospheric cooling, which is the result of the enhanced greenhouse effect, in combination with a depleted ozone layer, could provide a positive feedback to further ozone depletion, in particular in the Arctic. Decreasing albedo on the Greenland ice sheet may enhance the runoff from this ice sheet significantly in case of warming on a timescale of a few centuries. Changes in ocean circulation in the North Atlantic could seasonally more than compensate a global warming of 3C in North-West Europe on a timescale of centuries to a millennium. 263 refs.
Optimization of constrained multiple-objective reliability problems using evolutionary algorithms
Energy Technology Data Exchange (ETDEWEB)
Salazar, Daniel [Instituto de Sistemas Inteligentes y Aplicaciones Numericas en Ingenieria (IUSIANI), Division de Computacion Evolutiva y Aplicaciones (CEANI), Universidad de Las Palmas de Gran Canaria, Islas Canarias (Spain) and Facultad de Ingenieria, Universidad Central Venezuela, Caracas (Venezuela)]. E-mail: danielsalazaraponte@gmail.com; Rocco, Claudio M. [Facultad de Ingenieria, Universidad Central Venezuela, Caracas (Venezuela)]. E-mail: crocco@reacciun.ve; Galvan, Blas J. [Instituto de Sistemas Inteligentes y Aplicaciones Numericas en Ingenieria (IUSIANI), Division de Computacion Evolutiva y Aplicaciones (CEANI), Universidad de Las Palmas de Gran Canaria, Islas Canarias (Spain)]. E-mail: bgalvan@step.es
2006-09-15
This paper illustrates the use of multi-objective optimization to solve three types of reliability optimization problems: to find the optimal number of redundant components, find the reliability of components, and determine both their redundancy and reliability. In general, these problems have been formulated as single objective mixed-integer non-linear programming problems with one or several constraints and solved by using mathematical programming techniques or special heuristics. In this work, these problems are reformulated as multiple-objective problems (MOP) and then solved by using a second-generation Multiple-Objective Evolutionary Algorithm (MOEA) that allows handling constraints. The MOEA used in this paper (NSGA-II) demonstrates the ability to identify a set of optimal solutions (Pareto front), which provides the Decision Maker with a complete picture of the optimal solution space. Finally, the advantages of both MOP and MOEA approaches are illustrated by solving four redundancy problems taken from the literature.
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Analyses of non-linear systems and their application to biology: a review.
Sato, S
1994-01-01
In this review article, Wiener's analyses of non-linear systems and other topics on non-linear noise and non-stationary signals are introduced. Firstly, application and limitation of linear aspects on a biological system and a background of introduction of the Wiener's theory to non-linear analysis are briefly mentioned. The practical applications, however, were not so successful for several reasons. We shall see how these problems are solved under collaboration between biologists and engineers who have a knowledge of the subject and utilizing computational facility. Several aspects of the methodology involving non-linear systems, non-linear noise and non-stationary signals are also reviewed.
On Alternative Optimal Solutions to Linear Fractional Optimization Problems
Institute of Scientific and Technical Information of China (English)
ShengjiaXue
2004-01-01
The structure of the optimal solution set is derived for linear fractional optimization problems with the representation theorem of polyhedral sets．And the computational procedure in determining all optimal solutions is also given．
Stability Analysis for Stochastic Optimization Problems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
Non-linear system identification in flow-induced vibration
Energy Technology Data Exchange (ETDEWEB)
Spanos, P.D.; Zeldin, B.A. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corp., Houston, TX (United States)
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
Iterated non-linear model predictive control based on tubes and contractive constraints.
Murillo, M; Sánchez, G; Giovanini, L
2016-05-01
This paper presents a predictive control algorithm for non-linear systems based on successive linearizations of the non-linear dynamic around a given trajectory. A linear time varying model is obtained and the non-convex constrained optimization problem is transformed into a sequence of locally convex ones. The robustness of the proposed algorithm is addressed adding a convex contractive constraint. To account for linearization errors and to obtain more accurate results an inner iteration loop is added to the algorithm. A simple methodology to obtain an outer bounding-tube for state trajectories is also presented. The convergence of the iterative process and the stability of the closed-loop system are analyzed. The simulation results show the effectiveness of the proposed algorithm in controlling a quadcopter type unmanned aerial vehicle.
Some Undecidable Problems on Approximability of NP Optimization Problems
Institute of Scientific and Technical Information of China (English)
黄雄
1996-01-01
In this paper some undecidable problems on approximability of NP optimization problems are investigated.In particular,the following problems are all undecidable:(1) Given an NP optimization problem,is it approximable in polynomial time?(2)For any polynomial-time computable function r(n),given a polynomial time approximable NP optimization problem,has it a polynomial-time approximation algorithm with approximation performance ratio r(n) (r(n)-approximable)?(3)For any polynomial-time computable functions r(n),r'(n),where r'(n)
Yamasaki, Tadashi; Houseman, Gregory; Hamling, Ian; Postek, Elek
2010-05-01
We have developed a new parallelized 3-D numerical code, OREGANO_VE, for the solution of the general visco-elastic problem in a rectangular block domain. The mechanical equilibrium equation is solved using the finite element method for a (non-)linear Maxwell visco-elastic rheology. Time-dependent displacement and/or traction boundary conditions can be applied. Matrix assembly is based on a tetrahedral element defined by 4 vertex nodes and 6 nodes located at the midpoints of the edges, and within which displacement is described by a quadratic interpolation function. For evaluating viscoelastic relaxation, an explicit time-stepping algorithm (Zienkiewicz and Cormeau, Int. J. Num. Meth. Eng., 8, 821-845, 1974) is employed. We test the accurate implementation of the OREGANO_VE by comparing numerical and analytic (or semi-analytic half-space) solutions to different problems in a range of applications: (1) equilibration of stress in a constant density layer after gravity is switched on at t = 0 tests the implementation of spatially variable viscosity and non-Newtonian viscosity; (2) displacement of the welded interface between two blocks of differing viscosity tests the implementation of viscosity discontinuities, (3) displacement of the upper surface of a layer under applied normal load tests the implementation of time-dependent surface tractions (4) visco-elastic response to dyke intrusion (compared with the solution in a half-space) tests the implementation of all aspects. In each case, the accuracy of the code is validated subject to use of a sufficiently small time step, providing assurance that the OREGANO_VE code can be applied to a range of visco-elastic relaxation processes in three dimensions, including post-seismic deformation and post-glacial uplift. The OREGANO_VE code includes a capability for representation of prescribed fault slip on an internal fault. The surface displacement associated with large earthquakes can be detected by some geodetic observations
2013-01-01
This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.
Ant colony optimization in continuous problem
Institute of Scientific and Technical Information of China (English)
YU Ling; LIU Kang; LI Kaishi
2007-01-01
Based on the analysis of the basic ant colony optimization and optimum problem in a continuous space,an ant colony optimization (ACO) for continuous problem is constructed and discussed. The algorithm is efficient and beneficial to the study of the ant colony optimization in a continuous space.
Non-Linear Relativity in Position Space
Kimberly, D; Medeiros-Neto, J F; Kimberly, Dagny; Magueijo, João; Medeiros, João
2003-01-01
We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently of the chosen representation in momentum space. This requires a non-linear definition for the invariant contraction between momentum and position spaces. The second approach, instead, respects the linearity of the invariant contraction. This fully fixes the dual of momentum space and dictates a set of energy-dependent space-time Lorentz transformations. We discuss a variety of physical implications that would distinguish these two strategies. We also show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.
Non-linear (loop) quantum cosmology
Bojowald, Martin; Dantas, Christine C; Jaffe, Matthew; Simpson, David
2012-01-01
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a low-curvature universe can arise from tiny local contributions adding up coherently in large regions.
Multiple optimal solutions to a sort of nonlinear optimization problem
Institute of Scientific and Technical Information of China (English)
Xue Shengjia
2007-01-01
The optimization problem is considered in which the objective function is pseudolinear(both pseudoconvex and pseudoconcave) and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions ( ifthe uniqueness condition is not satisfied ) are provided. Finally, an illustrative example is also given.
Adaptive spectral identification techniques in presence of undetected non linearities
Cella, G; Guidi, G M
2002-01-01
The standard procedure for detection of gravitational wave coalescing binaries signals is based on Wiener filtering with an appropriate bank of template filters. This is the optimal procedure in the hypothesis of addictive Gaussian and stationary noise. We study the possibility of improving the detection efficiency with a class of adaptive spectral identification techniques, analyzing their effect in presence of non stationarities and undetected non linearities in the noise
On Optimizing the Satisfiability (SAT) Problem
Institute of Scientific and Technical Information of China (English)
GU Jun; GU Qianping; DU Dingzhu
1999-01-01
The satisfiability(SAT) problem is abasic problem in computing theory. Presently, an active area of researchon SAT problem is to design efficient optimization algorithms forfinding a solution for a satisfiable CNF formula. A newformulation, the Universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real spacehas been developed. Many optimization techniques,such as the steepest descent method, Newton's method, and thecoordinate descent method, can be used to solve the Universal SAT problem. In this paper, we prove that, when the initial solution issufficiently close to the optimal solution, the steepest descent methodhas a linear convergence ratio β<1, Newton's method has aconvergence ratio of order two, and the convergence ratio of thecoordinate descent method is approximately (1-β/m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the Universal SAT problem is alsopresented in this paper.
Problem statement for optimal design of steel structures
Directory of Open Access Journals (Sweden)
Ginzburg Aleksandr Vital'evich
2014-07-01
Full Text Available The presented article considers the following complex of tasks. The main stages of the life cycle of a building construction with the indication of process entrance and process exit are described. Requirements imposed on steel constructions are considered. The optimum range of application for steel designs is specified, as well as merits and demerits of a design material. The nomenclature of metal designs is listed - the block diagram is constructed. Possible optimality criteria of steel designs, offered by various authors for various types of constructions are considered. It is established that most often the criterion of a minimum of design mass is accepted as criterion of optimality; more rarely - a minimum of the given expenses, a minimum of a design cost in business. In the present article special attention is paid to a type of objective function of optimization problem. It is also established that depending on the accepted optimality criterion, the use of different types of functions is possible. This complexity of objective function depends on completeness of optimality criterion application. In the work the authors consider the following objective functions: the mass of the main element of a design; objective function by criterion of factory cost; objective function by criterion of cost in business. According to these examples it can be seen that objective functions by the criteria of labor expenses for production of designs are generally non-linear, which complicates solving the optimization problem. Another important factor influencing the problem of optimal design solution for steel designs, which is analyzed, is account for operating restrictions. In the article 8 groups of restrictions are analyzed. Attempts to completely account for the parameters of objective function optimized by particular optimality criteria, taking into account all the operating restrictions, considerably complicates the problem of designing. For solving this
Evolutionary computation for dynamic optimization problems
Yao, Xin
2013-01-01
This book provides a compilation on the state-of-the-art and recent advances of evolutionary computation for dynamic optimization problems. The motivation for this book arises from the fact that many real-world optimization problems and engineering systems are subject to dynamic environments, where changes occur over time. Key issues for addressing dynamic optimization problems in evolutionary computation, including fundamentals, algorithm design, theoretical analysis, and real-world applications, are presented. "Evolutionary Computation for Dynamic Optimization Problems" is a valuable reference to scientists, researchers, professionals and students in the field of engineering and science, particularly in the areas of computational intelligence, nature- and bio-inspired computing, and evolutionary computation.
Directory of Open Access Journals (Sweden)
Ndiaye Abdourahmane
2015-08-01
Full Text Available This paper deals with the problem of resources allo-cation in the downlink of the radio mobile systems. The allocation of resources is established in the context of multi-path effect and Doppler effect. These phenomena cause randomly variations of the channel and make difficult the allocation of the resources. Therefore, the problem of resources allocation is a high non linear optimization problem. Thus, we propose an implementation of genetic algorithms approach to increase the total throughput of users while minimizing the consumption of the total power of the base station. Like the evolutionary algorithms approach, this method is characterized by its robustness, permitting to efficiently solve a non linear optimization problem.
Automated, non-linear registration between 3-dimensional brain map and medical head image
Energy Technology Data Exchange (ETDEWEB)
Mizuta, Shinobu; Urayama, Shin-ichi; Zoroofi, R.A.; Uyama, Chikao [National Cardiovascular Center, Suita, Osaka (Japan)
1998-05-01
In this paper, we propose an automated, non-linear registration method between 3-dimensional medical head image and brain map in order to efficiently extract the regions of interest. In our method, input 3-dimensional image is registered into a reference image extracted from a brain map. The problems to be solved are automated, non-linear image matching procedure, and cost function which represents the similarity between two images. Non-linear matching is carried out by dividing the input image into connected partial regions, transforming the partial regions preserving connectivity among the adjacent images, evaluating the image similarity between the transformed regions of the input image and the correspondent regions of the reference image, and iteratively searching the optimal transformation of the partial regions. In order to measure the voxelwise similarity of multi-modal images, a cost function is introduced, which is based on the mutual information. Some experiments using MR images presented the effectiveness of the proposed method. (author)
Optimal impulse control problems and linear programming.
Bauso, D.
2009-01-01
Optimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation in real-time problems. We do this by using a paradigm borrowed from the Operations Research field. As main result, ...
Non linear system become linear system
Directory of Open Access Journals (Sweden)
Petre Bucur
2007-01-01
Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.
Oscillatons formed by non linear gravity
Obregón, O; Schunck, F E; Obregon, Octavio; Schunck, Franz E.
2004-01-01
Oscillatons are solutions of the coupled Einstein-Klein-Gordon (EKG) equations that are globally regular and asymptotically flat. By means of a Legendre transformation we are able to visualize the behaviour of the corresponding objects in non-linear gravity where the scalar field has been absorbed by means of the conformal mapping.
Controller reconfiguration for non-linear systems
Kanev, S.; Verhaegen, M.
2000-01-01
This paper outlines an algorithm for controller reconfiguration for non-linear systems, based on a combination of a multiple model estimator and a generalized predictive controller. A set of models is constructed, each corresponding to a different operating condition of the system. The interacting m
Ant Colony Optimization and Hypergraph Covering Problems
Pat, Ankit
2011-01-01
Ant Colony Optimization (ACO) is a very popular metaheuristic for solving computationally hard combinatorial optimization problems. Runtime analysis of ACO with respect to various pseudo-boolean functions and different graph based combinatorial optimization problems has been taken up in recent years. In this paper, we investigate the runtime behavior of an MMAS*(Max-Min Ant System) ACO algorithm on some well known hypergraph covering problems that are NP-Hard. In particular, we have addressed the Minimum Edge Cover problem, the Minimum Vertex Cover problem and the Maximum Weak- Independent Set problem. The influence of pheromone values and heuristic information on the running time is analysed. The results indicate that the heuristic information has greater impact towards improving the expected optimization time as compared to pheromone values. For certain instances of hypergraphs, we show that the MMAS* algorithm gives a constant order expected optimization time when the dominance of heuristic information is ...
Defects in the discrete non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Doikou, Anastasia, E-mail: adoikou@upatras.gr [University of Patras, Department of Engineering Sciences, Physics Division, GR-26500 Patras (Greece)
2012-01-01
The discrete non-linear Schroedinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.
Linear Algebraic Method for Non-Linear Map Analysis
Energy Technology Data Exchange (ETDEWEB)
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for no...... for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions....
Control of Non-linear Marine Cooling System
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....
Constrained Graph Optimization: Interdiction and Preservation Problems
Energy Technology Data Exchange (ETDEWEB)
Schild, Aaron V [Los Alamos National Laboratory
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
Non-linear pattern formation in bone growth and architecture.
Salmon, Phil
2014-01-01
The three-dimensional morphology of bone arises through adaptation to its required engineering performance. Genetically and adaptively bone travels along a complex spatiotemporal trajectory to acquire optimal architecture. On a cellular, micro-anatomical scale, what mechanisms coordinate the activity of osteoblasts and osteoclasts to produce complex and efficient bone architectures? One mechanism is examined here - chaotic non-linear pattern formation (NPF) - which underlies in a unifying way natural structures as disparate as trabecular bone, swarms of birds flying, island formation, fluid turbulence, and others. At the heart of NPF is the fact that simple rules operating between interacting elements, and Turing-like interaction between global and local signals, lead to complex and structured patterns. The study of "group intelligence" exhibited by swarming birds or shoaling fish has led to an embodiment of NPF called "particle swarm optimization" (PSO). This theoretical model could be applicable to the behavior of osteoblasts, osteoclasts, and osteocytes, seeing them operating "socially" in response simultaneously to both global and local signals (endocrine, cytokine, mechanical), resulting in their clustered activity at formation and resorption sites. This represents problem-solving by social intelligence, and could potentially add further realism to in silico computer simulation of bone modeling. What insights has NPF provided to bone biology? One example concerns the genetic disorder juvenile Pagets disease or idiopathic hyperphosphatasia, where the anomalous parallel trabecular architecture characteristic of this pathology is consistent with an NPF paradigm by analogy with known experimental NPF systems. Here, coupling or "feedback" between osteoblasts and osteoclasts is the critical element. This NPF paradigm implies a profound link between bone regulation and its architecture: in bone the architecture is the regulation. The former is the emergent
A Mathematical Optimization Problem in Bioinformatics
Heyer, Laurie J.
2008-01-01
This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…
A Mathematical Optimization Problem in Bioinformatics
Heyer, Laurie J.
2008-01-01
This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…
Metaheuristic optimization of acoustic inverse problems.
van Leijen, A.V.; Rothkrantz, L.; Groen, F.
2011-01-01
Swift solving of geoacoustic inverse problems strongly depends on the application of a global optimization scheme. Given a particular inverse problem, this work aims to answer the questions how to select an appropriate metaheuristic search strategy, and how to configure it for optimal performance.
Metaheuristic optimization of acoustic inverse problems.
van Leijen, A.V.; Rothkrantz, L.; Groen, F.
2011-01-01
Swift solving of geoacoustic inverse problems strongly depends on the application of a global optimization scheme. Given a particular inverse problem, this work aims to answer the questions how to select an appropriate metaheuristic search strategy, and how to configure it for optimal performance. F
Topology optimization of wave-propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures.......Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures....
PARETO OPTIMAL SOLUTIONS FOR MULTI-OBJECTIVE GENERALIZED ASSIGNMENT PROBLEM
Directory of Open Access Journals (Sweden)
S. Prakash
2012-01-01
Full Text Available
ENGLISH ABSTRACT: The Multi-Objective Generalized Assignment Problem (MGAP with two objectives, where one objective is linear and the other one is non-linear, has been considered, with the constraints that a job is assigned to only one worker – though he may be assigned more than one job, depending upon the time available to him. An algorithm is proposed to find the set of Pareto optimal solutions of the problem, determining assignments of jobs to workers with two objectives without setting priorities for them. The two objectives are to minimise the total cost of the assignment and to reduce the time taken to complete all the jobs.
AFRIKAANSE OPSOMMING: ‘n Multi-doelwit veralgemeende toekenningsprobleem (“multi-objective generalised assignment problem – MGAP” met twee doelwitte, waar die een lineêr en die ander nielineêr is nie, word bestudeer, met die randvoorwaarde dat ‘n taak slegs toegedeel word aan een werker – alhoewel meer as een taak aan hom toegedeel kan word sou die tyd beskikbaar wees. ‘n Algoritme word voorgestel om die stel Pareto-optimale oplossings te vind wat die taaktoedelings aan werkers onderhewig aan die twee doelwitte doen sonder dat prioriteite toegeken word. Die twee doelwitte is om die totale koste van die opdrag te minimiseer en om die tyd te verminder om al die take te voltooi.
Problem Solving through an Optimization Problem in Geometry
Poon, Kin Keung; Wong, Hang-Chi
2011-01-01
This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…
Fast Solvers of Fredholm Optimal Control Problems
Institute of Scientific and Technical Information of China (English)
Mario; Borzì
2010-01-01
The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.
A non-linear UAV altitude PSO-PD control
Orlando, Calogero
2015-12-01
In this work, a nonlinear model based approach is presented for the altitude stabilization of a hexarotor unmanned aerial vehicle (UAV). The mathematical model and control of the hexacopter airframe is presented. To stabilize the system along the vertical direction, a Proportional Derivative (PD) control is taken into account. A particle swarm optimization (PSO) approach is used in this paper to select the optimal parameters of the control algorithm taking into account different objective functions. Simulation sets are performed to carry out the results for the non-linear system to show how the PSO tuned PD controller leads to zero the error of the position along Z earth direction.
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
Topology optimization for acoustic problems
DEFF Research Database (Denmark)
Dühring, Maria Bayard
2006-01-01
In this paper a method to control acoustic properties in a room with topology optimization is presented. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized by distribution of material in a design domain along the ceiling in 2D and 3D. Nice 0-1 designs...
Non-linear Young's double-slit experiment.
San Roman, Julio; Ruiz, Camilo; Perez, Jose Antonio; Delgado, Diego; Mendez, Cruz; Plaja, Luis; Roso, Luis
2006-04-01
The Young's double slit experiment is recreated using intense and short laser pulses. Our experiment evidences the role of the non-linear Kerr effect in the formation of interference patterns. In particular, our results evidence a mixed mechanism in which the zeroth diffraction order of each slit are mainly affected by self-focusing and self-phase modulation, while the higher orders propagate linearly. Despite of the complexity of the general problem of non-linear propagation, we demonstrate that this experiment retains its simplicity and allows for a geometrical interpretation in terms of simple optical paths. In consequence, our results may provide key ideas on experiments on the formation of interference patterns with intense laser fields in Kerr media.
Binary Cockroach Swarm Optimization for Combinatorial Optimization Problem
Directory of Open Access Journals (Sweden)
Ibidun Christiana Obagbuwa
2016-09-01
Full Text Available The Cockroach Swarm Optimization (CSO algorithm is inspired by cockroach social behavior. It is a simple and efficient meta-heuristic algorithm and has been applied to solve global optimization problems successfully. The original CSO algorithm and its variants operate mainly in continuous search space and cannot solve binary-coded optimization problems directly. Many optimization problems have their decision variables in binary. Binary Cockroach Swarm Optimization (BCSO is proposed in this paper to tackle such problems and was evaluated on the popular Traveling Salesman Problem (TSP, which is considered to be an NP-hard Combinatorial Optimization Problem (COP. A transfer function was employed to map a continuous search space CSO to binary search space. The performance of the proposed algorithm was tested firstly on benchmark functions through simulation studies and compared with the performance of existing binary particle swarm optimization and continuous space versions of CSO. The proposed BCSO was adapted to TSP and applied to a set of benchmark instances of symmetric TSP from the TSP library. The results of the proposed Binary Cockroach Swarm Optimization (BCSO algorithm on TSP were compared to other meta-heuristic algorithms.
Fliess, Michel; Join, Cédric; Sira-Ramirez, Hebertt
2008-01-01
International audience; Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line ...
Non-linear Loudspeaker Unit Modelling
DEFF Research Database (Denmark)
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of three...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
Fliess, Michel; Sira-Ramirez, Hebertt
2007-01-01
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.
Institute of Scientific and Technical Information of China (English)
李岳林; 王立标; 曾志伟; 汤彬; 杜宝杰
2009-01-01
针对发动机非稳态工况,建立了非线性模型.设计了滑模控制器和PID控制器分别对节气门开度和点火时刻进行自适应调节.对发动机怠速工况进行仿真的结果表明,发动机转速波动幅值低于6 r/min,表明所建的非线性模型适合于发动机非稳态工况控制.%A non-linear model is set up for engine transient operating conditions. Both sliding mode control-ler and PID controller are designed to realize adaptive regulation of throttle opening and ignition timing respectively.The results of simulation on engine idling show that the amplitude of engine speed fluctuation is less than 6 r/min,indicating that the non-linear model built is appropriate for the control over the transient operating conditions of en-gine.
Optimization and inverse problems in electromagnetism
Wiak, Sławomir
2003-01-01
From 12 to 14 September 2002, the Academy of Humanities and Economics (AHE) hosted the workshop "Optimization and Inverse Problems in Electromagnetism". After this bi-annual event, a large number of papers were assembled and combined in this book. During the workshop recent developments and applications in optimization and inverse methodologies for electromagnetic fields were discussed. The contributions selected for the present volume cover a wide spectrum of inverse and optimal electromagnetic methodologies, ranging from theoretical to practical applications. A number of new optimal and inverse methodologies were proposed. There are contributions related to dedicated software. Optimization and Inverse Problems in Electromagnetism consists of three thematic chapters, covering: -General papers (survey of specific aspects of optimization and inverse problems in electromagnetism), -Methodologies, -Industrial Applications. The book can be useful to students of electrical and electronics engineering, computer sci...
On the Ramified Optimal Allocation Problem
Xia, Qinglan
2011-01-01
This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and efficiently designed transport systems of branching structures. The ramified allocation problem aims at finding an optimal allocation plan as well as an associated optimal allocation path to minimize overall cost of transporting commodity from factories to households. This problem differentiates itself from existing ramified transportation literature in that the distribution of production among factories is not fixed but endogenously determined as observed in many allocation practices. It's shown that due to the transport economy of scale in ramified transportation, each optimal allocation plan corresponds equivalently to an optimal assignment map from households to factories. This optimal assignment map provides a natural partition of both households and allocation paths. We...
Dynamic consistency for Stochastic Optimal Control problems
Carpentier, Pierre; Cohen, Guy; De Lara, Michel; Girardeau, Pierre
2010-01-01
For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step $t_0$, the decision maker formulates an optimization problem that yields optimal decision rules for all the forthcoming time step $t_0, t_1, ..., T$; at the next time step $t_1$, he is able to formulate a new optimization problem starting at time $t_1$ that yields a new sequence of optimal decision rules. This process can be continued until final time $T$ is reached. A family of optimization problems formulated in this way is said to be time consistent if the optimal strategies obtained when solving the original problem remain optimal for all subsequent problems. The notion of time consistency, well-known in the field of Economics, has been recently introduced in the context of risk measures, notably by Artzner et al. (2007) and studied in the Stochastic Programming framework by Shapiro (2009) and for Markov Decision Processes...
Non-linear aeroelastic prediction for aircraft applications
de C. Henshaw, M. J.; Badcock, K. J.; Vio, G. A.; Allen, C. B.; Chamberlain, J.; Kaynes, I.; Dimitriadis, G.; Cooper, J. E.; Woodgate, M. A.; Rampurawala, A. M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.
2007-05-01
Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the methods have served the industry well, it is clear that for a number of reasons the inclusion of non-linearity in the mathematical and computational aeroelastic prediction tools is highly desirable. The increase in available and affordable computational resources, together with major advances in algorithms, mean that non-linear aeroelastic tools are now viable within the aircraft design and qualification environment. The Partnership for Unsteady Methods in Aerodynamics (PUMA) Defence and Aerospace Research Partnership (DARP) was sponsored in 2002 to conduct research into non-linear aeroelastic prediction methods and an academic, industry, and government consortium collaborated to address the following objectives: To develop useable methodologies to model and predict non-linear aeroelastic behaviour of complete aircraft. To evaluate the methodologies on real aircraft problems. To investigate the effect of non-linearities on aeroelastic behaviour and to determine which have the greatest effect on the flutter qualification process. These aims have been very effectively met during the course of the programme and the research outputs include: New methods available to industry for use in the flutter prediction process, together with the appropriate coaching of industry engineers. Interesting results in both linear and non-linear aeroelastics, with comprehensive comparison of methods and approaches for challenging problems. Additional embryonic techniques that, with further research, will further improve aeroelastics capability. This paper describes the methods that have been developed and how they are deployable within the industrial environment. We present a thorough review of the PUMA aeroelastics programme together with a comprehensive review of the relevant research
Optimal control problems with switching points
Seywald, Hans
1991-09-01
An overview is presented of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.
Non-linear Bayesian update of PCE coefficients
Litvinenko, Alexander
2014-01-06
Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).
Vector Broadcast Channels: Optimal Threshold Selection Problem
Samarasinghe, Tharaka; Evans, Jamie
2011-01-01
Threshold feedback policies are well known and provably rate-wise optimal selective feedback techniques for communication systems requiring partial channel state information (CSI). However, optimal selection of thresholds at mobile users to maximize information theoretic data rates subject to feedback constraints is an open problem. In this paper, we focus on the optimal threshold selection problem, and provide a solution for this problem for finite feedback systems. Rather surprisingly, we show that using the same threshold values at all mobile users is not always a rate-wise optimal feedback strategy, even for a system with identical users experiencing statistically the same channel conditions. By utilizing the theory of majorization, we identify an underlying Schur-concave structure in the rate function and obtain sufficient conditions for a homogenous threshold feedback policy to be optimal. Our results hold for most fading channel models, and we illustrate an application of our results to familiar Raylei...
Geoengineering as an optimization problem
Energy Technology Data Exchange (ETDEWEB)
Ban-Weiss, George A; Caldeira, Ken, E-mail: georgebw@stanford.edu [Department of Global Ecology, Carnegie Institution for Science, 260 Panama Street, Stanford, CA 94305 (United States)
2010-07-15
There is increasing evidence that Earth's climate is currently warming, primarily due to emissions of greenhouse gases from human activities, and Earth has been projected to continue warming throughout this century. Scientists have begun to investigate the potential for geoengineering options for reducing surface temperatures and whether such options could possibly contribute to environmental risk reduction. One proposed method involves deliberately increasing aerosol loading in the stratosphere to scatter additional sunlight to space. Previous modeling studies have attempted to predict the climate consequences of hypothetical aerosol additions to the stratosphere. These studies have shown that this method could potentially reduce surface temperatures, but could not recreate a low-CO{sub 2} climate in a high-CO{sub 2} world. In this study, we attempt to determine the latitudinal distribution of stratospheric aerosols that would most closely achieve a low-CO{sub 2} climate despite high CO{sub 2} levels. Using the NCAR CAM3.1 general circulation model, we find that having a stratospheric aerosol loading in polar regions higher than that in tropical regions leads to a temperature distribution that is more similar to the low-CO{sub 2} climate than that yielded by a globally uniform loading. However, such polar weighting of stratospheric sulfate tends to degrade the degree to which the hydrological cycle is restored, and thus does not markedly contribute to improved recovery of a low-CO{sub 2} climate. In the model, the optimal latitudinally varying aerosol distributions diminished the rms zonal mean land temperature change from a doubling of CO{sub 2} by 94% and the rms zonal mean land precipitation minus evaporation change by 74%. It is important to note that this idealized study represents a first attempt at optimizing the engineering of climate using a general circulation model; uncertainties are high and not all processes that are important in reality are
An optimal hostage rescue problem
Shi, Fengbo
2000-01-01
We propose the following mathematical model of optinal reacue problems concerning hostage.Suppose i persons are taken as hostages at any given point in time t,and we have to make a decision on attempting either rescue or no resuce. Let p be the probability of a hostage being killed in a rescue attempt,and let s be the probability of criminal(s) surrendering up to the following point in time if no rescue attempt is made.Futher,let g and r be the probabilities of a hostage being,respectively,ki...
OPTIMAL CONTROL PROBLEM FOR PARABOLIC VARIATIONAL INEQUALITIES
Institute of Scientific and Technical Information of China (English)
汪更生
2001-01-01
This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations.The maximum principle and some kind of approximate controllability are studied.
Institute of Scientific and Technical Information of China (English)
张毕西; 程硕
2014-01-01
This paper research the optimization of worker-assignment problem with different skills in non lin-ear pipeline for the made to order production of multi-product and small-batch , through using the combina-tion of improved genetic algorithm and linear programming phase, to optimise the workers' assignment and scheduling, achieving the cost optimal target in optimise system ,and demonstrate the results' effectiveness by the method.%文章就如何对多产品、小批量订单式生产模式下有着工人技能差异性的非线性流水线工人指派问题进行研究，通过利用改进的遗传算法和线性规划相结合的方法，对拥有不同技能、不同工序完成时间的工人进行指派和调度，实现非线性流水线生产系统下的成本较优的目标，并通过算例证明该方法的有效性。
A Problem-Oriented Mathematical Optimization Course
Wenger, Robert B.; Rhyner, Charles R.
1977-01-01
This article describes a one-semester junior and senior level course in applied mathematical optimization for undergraduates which provides the opportunity to test models by doing numerical experiments and to learn to use computer subroutines for solving optimization problems. (MN)
Non Linear Behaviour in Learning Processes
Manfredi, Paolo; Manfredi, Vicenzo Rosario
2003-01-01
This article is mainly based on R. E. Kahn's contribution to the book Non Linear Dynamics in Human Behavior. As stressed by Bronowski, both in art and in science, a person becomes creative by finding "a new unity" that is a link between things which were not thought alike before. Indeed the creative mind is a mind that looks for unexpected likeness finding a more profound unity, a pattern behind chaotic phenomena. In the context of scientific discovery, it can also be argued that creativi...
BRST structure of non-linear superalgebras
Asorey, M; Radchenko, O V; Sugamoto, A
2008-01-01
In this paper we analyse the structure of the BRST structure of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.
Limits on Non-Linear Electrodynamics
Fouché, M; Rizzo, C
2016-01-01
In this paper we set a framework in which experiments whose goal is to test QED predictions can be used in a more general way to test non-linear electrodynamics (NLED) which contains low-energy QED as a special case. We review some of these experiments and we establish limits on the different free parameters by generalizing QED predictions in the framework of NLED. We finally discuss the implications of these limits on bound systems and isolated charged particles for which QED has been widely and successfully tested.
An improved group search optimizer for mechanical design optimization problems
Institute of Scientific and Technical Information of China (English)
Hai Shen; Yunlong Zhu; Ben Niu; Q.H. Wu
2009-01-01
This paper presents an improved group search optimizer (iGSO) for solving mechanical design optimization problems.In the pro-posed algorithm,subpopulations and a co-operation evolutionary strategy were adopted to improve the global search capability and convergence performance.The iGSO is evaluated on two optimization problems of classical mechanical design:spring and pressure vessel.The experimental results are analyzed in comparison with those reported in the literatures.The results show that iGSO has much better convergence performance and is easier to implement in comparison with other existing evolutionary algorithms.
H∞ Synthesis Method for Control of Non-linear Flexible Joint Models
Axelsson, Patrik; Pipeleers, Goele; Helmersson, Anders; Norrlöf, Mikael
2014-01-01
An H∞ synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shaping paradigm and a change of variables, the non-linear optimisation problem can be rewritten as a con...
An optimal design problem in wave propagation
DEFF Research Database (Denmark)
Bellido, J.C.; Donoso, Alberto
2007-01-01
We consider an optimal design problem in wave propagation proposed in Sigmund and Jensen (Roy. Soc. Lond. Philos. Trans. Ser. A 361:1001-1019, 2003) in the one-dimensional situation: Given two materials at our disposal with different elastic Young modulus and different density, the problem consists...... of finding the best distributions of the two initial materials in a rod in order to minimize the vibration energy in the structure under periodic loading of driving frequency Omega. We comment on relaxation and optimality conditions, and perform numerical simulations of the optimal configurations. We prove...
Topology optimization for transient heat transfer problems
DEFF Research Database (Denmark)
Zeidan, Said; Sigmund, Ole; Lazarov, Boyan Stefanov
The focus of this work is on passive control of transient heat transfer problems using the topology optimization (TopOpt) method [1]. The goal is to find distributions of a limited amount of phase change material (PCM), within a given design domain, which optimizes the heat energy storage [2]. Our......, TopOpt has later been extended to transient problems in mechanics and photonics (e.g. [5], [6] and [7]). In the presented approach, the optimization is gradient-based, where in each iteration the non-steady heat conduction equation is solved,using the finite element method and an appropriate time...
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Shape flows for spectral optimization problems
Bucur, Dorin; Stefanelli, Ulisse
2011-01-01
We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the evolution of {\\it capacitary measures} with respect to the $\\gamma$-convergence dissipation distance and with the evolution of domains in spectral optimization problems.
Variable Expansion Techniques for Decomposable Optimization Problems
2011-03-05
meration or dynamic programming. Recall the edge partition problem studied by Taskin et al. above in reference 7. (Z. Caner Taskin was supported by the...Stochastic Integer Program- ming, August 2009 August 2009. 12 2. Z. Caner Taskin, Algorithms for Solving Multi-Level Optimization Problems with Dis
Topology optimization of fluid mechanics problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan
While topology optimization for solid continuum structures have been studied for about 20 years and for the special case of trusses for many more years, topology optimization of fluid mechanics problems is more recent. Borrvall and Petersson [1] is the seminal reference for topology optimization...... with respect to minimizing the energy loss, characteristic properties of the velocity field or mixing properties. To reduce the computational complexity of the topology optimization problems the primary focus is put on the Stokes equation in 2D and in 3D. However, the the talk also contains examples with the 2......D Navier-Stokes equation as well as an example with convection dominated transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the present work gives a proof-of-concept for the application of the method within fluid mechanics problems and it remains...
Belief Propagation Algorithm for Portfolio Optimization Problems.
Shinzato, Takashi; Yasuda, Muneki
2015-01-01
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.
Belief Propagation Algorithm for Portfolio Optimization Problems.
Directory of Open Access Journals (Sweden)
Takashi Shinzato
Full Text Available The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.
Topology optimization of Channel flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.
2005-01-01
]. Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity--driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost...... sensitivities. Our target application is optimal layout design of channels in fluid network systems. Using concepts borrowed from topology optimization of compliant mechanisms in solid mechanics, we introduce a method for the synthesis of fluidic components, such as switches, diodes, etc....
Abate, Alexandra; Bridle, Sarah; Teodoro, Luis F. A.; Warren, Michael S.; Hendry, Martin
2008-10-01
We investigate methods to best estimate the normalization of the mass density fluctuation power spectrum (σ8) using peculiar velocity data from a survey like the six-degree Field Galaxy Velocity Survey (6dFGSv). We focus on two potential problems: (i) biases from non-linear growth of structure and (ii) the large number of velocities in the survey. Simulations of ΛCDM-like models are used to test the methods. We calculate the likelihood from a full covariance matrix of velocities averaged in grid cells. This simultaneously reduces the number of data points and smoothes out non-linearities which tend to dominate on small scales. We show how the averaging can be taken into account in the predictions in a practical way, and show the effect of the choice of cell size. We find that a cell size can be chosen that significantly reduces the non-linearities without significantly increasing the error bars on cosmological parameters. We compare our results with those from a principal components analysis following Watkins et al. and Feldman et al. to select a set of optimal moments constructed from linear combinations of the peculiar velocities that are least sensitive to the non-linear scales. We conclude that averaging in grid cells performs equally well. We find that for a survey such as 6dFGSv we can estimate σ8 with less than 3 per cent bias from non-linearities. The expected error on σ8 after marginalizing over Ωm is approximately 16 per cent.
Non-linear feedback neural networks VLSI implementations and applications
Ansari, Mohd Samar
2014-01-01
This book aims to present a viable alternative to the Hopfield Neural Network (HNN) model for analog computation. It is well known that the standard HNN suffers from problems of convergence to local minima, and requirement of a large number of neurons and synaptic weights. Therefore, improved solutions are needed. The non-linear synapse neural network (NoSyNN) is one such possibility and is discussed in detail in this book. This book also discusses the applications in computationally intensive tasks like graph coloring, ranking, and linear as well as quadratic programming. The material in the book is useful to students, researchers and academician working in the area of analog computation.
Efficiency Improvements in Meta-Heuristic Algorithms to Solve the Optimal Power Flow Problem
Reddy, S. Surender; Bijwe, P. R.
2016-12-01
This paper proposes the efficient approaches for solving the Optimal Power Flow (OPF) problem using the meta-heuristic algorithms. Mathematically, OPF is formulated as non-linear equality and inequality constrained optimization problem. The main drawback of meta-heuristic algorithm based OPF is the excessive execution time required due to the large number of power flows needed in the solution process. The proposed efficient approaches uses the lower and upper bounds of objective function values. By using this approach, the number of power flows to be performed are reduced substantially, resulting in the solution speed up. The efficiently generated objective function bounds can result in the faster solutions of meta-heuristic algorithms. The original advantages of meta-heuristic algorithms, such as ability to handle complex non-linearities, discontinuities in the objective function, discrete variables handling, and multi-objective optimization, etc., are still available in the proposed efficient approaches. The proposed OPF formulation includes the active and reactive power generation limits, Valve Point Loading (VPL) and Prohibited Operating Zones (POZs) effects of generating units. The effectiveness of proposed approach is examined on IEEE 30, 118 and 300 bus test systems, and the simulation results confirm the efficiency and superiority of the proposed approaches over the other meta-heuristic algorithms. The proposed efficient approach is generic enough to use with any type of meta-heuristic algorithm based OPF.
Mitsos, Alexander; Melas, Ioannis N; Morris, Melody K; Saez-Rodriguez, Julio; Lauffenburger, Douglas A; Alexopoulos, Leonidas G
2012-01-01
Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms.
Non-Linear Dynamics of Saturn's Rings
Esposito, L. W.
2015-12-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw', as observed ny Cassini cameras. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn's rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. This confirms the triple architecture of ring particles: a broad size distribution of particles; these aggregate into temporary rubble piles; coated by a regolith of dust. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from
Parameter Scaling in Non-Linear Microwave Tomography
DEFF Research Database (Denmark)
Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar;
2012-01-01
Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag......Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when...... the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....
Parameter Scaling in Non-Linear Microwave Tomography
DEFF Research Database (Denmark)
Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar
2012-01-01
Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag......Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when...... the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....
Better relaxations of classical discrete optimization problems.
Energy Technology Data Exchange (ETDEWEB)
Lancia, Giuseppe; Konjevod, Goran; Carr, Robert D.; Parehk, Ojas
2008-08-01
A mathematical program is an optimization problem expressed as an objective function of multiple variables subject to set of constraints. When the optimization problem has specific structure, the problem class usually has a special name. A linear program is the optimization of a linear objective function subject to linear constraints. An integer program is a linear program where some of the variables must take only integer values. A semidefinite program is a linear program where the variables are arranged in a matrix and for all feasible solutions, this matrix must be positive semidefinite. There are general-purpose solvers for each of these classes of mathematical program. There are usually many ways to express a problem as a correct, say, linear program. However, equivalent formulations can have significantly different practical tractability. In this poster, we present new formulations for two classic discrete optimization problems, maximum cut (max cut) and the graphical traveling salesman problem (GTSP), that are significantly stronger, and hence more computationally tractable, than any previous formulations of their class. Both partially answer longstanding open theoretical questions in polyhedral combinatorics.
Chaotic Discrimination and Non-Linear Dynamics
Directory of Open Access Journals (Sweden)
Partha Gangopadhyay
2005-01-01
Full Text Available This study examines a particular form of price discrimination, known as chaotic discrimination, which has the following features: sellers quote a common price but, in reality, they engage in secret and apparently unsystematic price discounts. It is widely held that such forms of price discrimination are seriously inconsistent with profit maximization by sellers.. However, there is no theoretical salience to support this kind of price discrimination. By straining the logic of non-linear dynamics this study explains why such secret discounts are chaotic in the sense that sellers fail to adopt profit-maximising price discounts. A model is developed to argue that such forms of discrimination may derive from the regions of instability of a dynamic model of price discounts.
Symmetries in Non-Linear Mechanics
Aldaya, Victor; López-Ruiz, Francisco F; Cossío, Francisco
2014-01-01
In this paper we exploit the use of symmetries of a physical system so as to characterize the corresponding solution manifold by means of Noether invariants. This constitutes a necessary preliminary step towards the correct quantisation in non-linear cases, where the success of Canonical Quantisation is not guaranteed in general. To achieve this task "point symmetries" of the Lagrangian are generally not enough, and the notion of contact transformations is in order. The use of the Poincar\\'e-Cartan form permits finding both the symplectic structure on the solution manifold, through the Hamilton-Jacobi transformation, and the required symmetries, realized as Hamiltonian vector fields, associated with functions on the solution manifold (thus constituting an inverse of the Noether Theorem), lifted back to the evolution space through the inverse of this Hamilton-Jacobi mapping. In this framework, solutions and symmetries are somehow identified and this correspondence is also kept at a perturbative level. We prese...
Long-term cavity closure in non-linear rocks
Cornet, Jan; Dabrowski, Marcin; Schmid, Daniel Walter
2017-08-01
The time dependent closure of pressurized cavities in viscous rocks due to far-field loads is a problem encountered in many applications like drilling, cavity abandonment and porosity closure. The non-linear nature of the flow of rocks prevents the use of simple solutions for hole closure and calls for the development of appropriate expressions reproducing all the dependencies observed in nature. An approximate solution is presented for the closure velocity of a pressurized cylindrical cavity in a non-linear viscous medium subjected to a combined pressure and shear stress load in the far field. The embedding medium is treated as homogeneous, isotropic, and incompressible and follows a Carreau viscosity model. We derive analytical solutions for the end-member cases of the pressure and shear loads. The exact analytical solution for pressure loads shows that the closure velocity vR is given by the implicit expression {Δ p}/{2{μ _0D_{II}^*}} = - 1/2B( {{v_R^2}/{RD_{II^* + v_R^2}};1/2, - 1/{2n}} ), where Δp is the pressure load, R is the hole radius, B is the incomplete beta function, and μ0, D_{II}^*, n are, respectively, the threshold viscosity, transition rate and stress exponent of the Carreau model. The closure velocity is dominated by the linear mechanism under pressure loads smaller than 1.8{μ _0}D_{II}^* and by the non-linear one under large pressure loads. In the non-linear regime, pressure variations support an increasing part of the load with increasing degree of non-linearity. The decay of the stress perturbation in the non-linear zone varies as r- 2/n where r is the radial distance to the hole. A solution for the maximum closure velocity at the cavity rim vRmax under far-field shear is given: v_{R\\max} = ( 1 + {\\overline {M_s}} ^{-1/2})R\\overline D_{II}, where \\overline {M_s} = (1 + {\\overline {D_{II}} }^2 \\big/ {nD{_{II}^*}^2}) \\big/ ( 1 + {\\overline {D_{II}}^2} \\big/ D{_{II}^*}^2) and \\overline {D_{II}} is the second invariant of the far
A simple convex optimization problem with many applications
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1994-01-01
This paper presents an algorithm for the solution of a simple convex optimization problem. This problem is a generalization of several other optimization problems which have applications to resource allocation, optimal capacity expansion, and vehicle scheduling. The algorithm is based...
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Estrada, R.F.
1979-08-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly.
Topology Optimization for Transient Wave Propagation Problems
DEFF Research Database (Denmark)
Matzen, René
as for vectorial elastic wave propagation problems using finite element analysis [P2], [P4]. The concept is implemented in a parallel computing code that includes efficient techniques for performing gradient based topology optimization. Using the developed computational framework the thesis considers four...... new technology, by designing new materials and their layout. The thesis presents a general framework for applying topology optimization in the design of material layouts for transient wave propagation problems. In contrast to the high level of modeling in the frequency domain, time domain topology...
Trajectory metaheuristic algorithms to optimize problems combinatorics
Directory of Open Access Journals (Sweden)
Natalia Alancay
2016-12-01
Full Text Available The application of metaheuristic algorithms to optimization problems has been very important during the last decades. The main advantage of these techniques is their flexibility and robustness, which allows them to be applied to a wide range of problems. In this work we concentrate on metaheuristics based on Simulated Annealing, Tabu Search and Variable Neighborhood Search trajectory whose main characteristic is that they start from a point and through the exploration of the neighborhood vary the current solution, forming a trajectory. By means of the instances of the selected combinatorial problems, a computational experimentation is carried out that illustrates the behavior of the algorithmic methods to solve them. The main objective of this work is to perform the study and comparison of the results obtained for the selected trajectories metaheuristics in its application for the resolution of a set of academic problems of combinatorial optimization.
Solving global optimization problems on GPU cluster
Barkalov, Konstantin; Gergel, Victor; Lebedev, Ilya
2016-06-01
The paper contains the results of investigation of a parallel global optimization algorithm combined with a dimension reduction scheme. This allows solving multidimensional problems by means of reducing to data-independent subproblems with smaller dimension solved in parallel. The new element implemented in the research consists in using several graphic accelerators at different computing nodes. The paper also includes results of solving problems of well-known multiextremal test class GKLS on Lobachevsky supercomputer using tens of thousands of GPU cores.
Directory of Open Access Journals (Sweden)
Abbas v Y.A. Bayati
2010-01-01
Full Text Available Problem statement: The scaled hybrid Conjugate Gradient (CG algorithm which usually used for solving non-linear functions was presented and was compared with two standard well-Known NAG routines, yielding a new fast comparable algorithm. Approach: We proposed, a new hybrid technique based on the combination of two well-known scaled (CG formulas for the quadratic model in unconstrained optimization using exact line searches. A global convergence result for the new technique was proved, when the Wolfe line search conditions were used. Results: Computational results, for a set consisting of 1915 combinations of (unconstrained optimization test problems/dimensions were implemented in this research making a comparison between the new proposed algorithm and the other two similar algorithms in this field. Conclusion: Our numerical results showed that this new scaled hybrid CG-algorithm substantially outperforms Andrei-sufficient descent condition (CGSD algorithm and the well-known Andrei standard sufficient descent condition from (ACGA algorithm.
Particle swarm optimization with random keys applied to the nuclear reactor reload problem
Energy Technology Data Exchange (ETDEWEB)
Meneses, Anderson Alvarenga de Moura [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE). Programa de Engenharia Nuclear; Fundacao Educacional de Macae (FUNEMAC), RJ (Brazil). Faculdade Professor Miguel Angelo da Silva Santos; Machado, Marcelo Dornellas; Medeiros, Jose Antonio Carlos Canedo; Schirru, Roberto [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE). Programa de Engenharia Nuclear]. E-mails: ameneses@con.ufrj.br; marcelo@lmp.ufrj.br; canedo@lmp.ufrj.br; schirru@lmp.ufrj.br
2007-07-01
In 1995, Kennedy and Eberhart presented the Particle Swarm Optimization (PSO), an Artificial Intelligence metaheuristic technique to optimize non-linear continuous functions. The concept of Swarm Intelligence is based on the socials aspects of intelligence, it means, the ability of individuals to learn with their own experience in a group as well as to take advantage of the performance of other individuals. Some PSO models for discrete search spaces have been developed for combinatorial optimization, although none of them presented satisfactory results to optimize a combinatorial problem as the nuclear reactor fuel reloading problem (NRFRP). In this sense, we developed the Particle Swarm Optimization with Random Keys (PSORK) in previous research to solve Combinatorial Problems. Experiences demonstrated that PSORK performed comparable to or better than other techniques. Thus, PSORK metaheuristic is being applied in optimization studies of the NRFRP for Angra 1 Nuclear Power Plant. Results will be compared with Genetic Algorithms and the manual method provided by a specialist. In this experience, the problem is being modeled for an eight-core symmetry and three-dimensional geometry, aiming at the minimization of the Nuclear Enthalpy Power Peaking Factor as well as the maximization of the cycle length. (author)
Non-linear optical titanyl arsenates: Crystal growth and properties
Nordborg, Jenni Eva Louise
Crystals are appreciated not only for their appearance, but also for their unique physical properties which are utilized by the photonic industry in appliances that we come across every day. An important part of enabling the technical use of optical devices is the manufacture of crystals. This dissertation deals with a specific group of materials called the potassium titanyl phosphate (KIP) family, known for their non-linear optical and ferroelectric properties. The isomorphs vary in their linear optical and dielectric properties, which can be tuned to optimize device performance by forming solid solutions of the different materials. Titanyl arsenates have a wide range of near-infrared transmission which makes them useful for tunable infrared lasers. The isomorphs examined in the present work were primarily RbTiOASO4 (RTA) and CsTiOAsO4 (CTA) together with the mixtures RbxCs 1-xTiOAsO4 (RCTA). Large-scale crystals were grown by top seeding solution growth utilizing a three-zone furnace with excellent temperature control. Sufficiently slow cooling and constant upward lifting produced crystals with large volumes useable for technical applications. Optical quality RTA crystals up to 10 x 12 x 20 mm were grown. The greater difficulty in obtaining good crystals of CTA led to the use of mixed RCTA materials. The mixing of rubidium and cesium in RCTA is more favorable to crystal growth than the single components in pure RTA and CTA. Mixed crystals are rubidium-enriched and contain only 20-30% of the cesium concentration in the flux. The cesium atoms show a preference for the larger cation site. The network structure is very little affected by the cation substitution; consequently, the non-linear optical properties of the Rb-rich isomorphic mixtures of RTA and CTA can be expected to remain intact. Crystallographic methods utilizing conventional X-ray tubes, synchrotron radiation and neutron diffraction have been employed to investigate the properties of the atomic
The Non-Linear Effect of Corporate Taxes on Economic Growth
Directory of Open Access Journals (Sweden)
Huňady Ján
2015-03-01
Full Text Available The paper deals with the problem of taxation and its potential impact on economic growth and presents some new empirical insights into this topic. The main aim of the paper is to verify an assumed nonlinear impact of corporate tax rates on economic growth. Based on the theory of public finance and taxation, we hypothesize that at relatively low tax rates it is possible that the impact of taxation on economic growth become slightly positive. On the other hand when the tax rates are higher a negative impact of taxation on economic growth could be expected. Despite the fact that the most of the existing studies find a negative linear relationship between these variables, we can also find strong support for a non-linear relationship from several theoretical models as well as some empirical studies. Based on panel data fixed-effects econometric models, we, as well, find empirical evidence for a non-linear relationship between nominal and effective corporate tax rates and economic growth. Our data consists of annual observations for the period 1999 to 2011 for EU Member States. Based on the results, we also estimated the optimal level of the corporate tax rate in terms of maximizing economic growth in the average of the EU countries.
Shape Optimization Problems with Internal Constraint
Bucur, Dorin; Velichkov, Bozhidar
2011-01-01
We consider shape optimization problems with internal inclusion constraints, of the form $$\\min\\big\\{J(\\Omega)\\ :\\ \\Dr\\subset\\Omega\\subset\\R^d,\\ |\\Omega|=m\\big\\},$$ where the set $\\Dr$ is fixed, possibly unbounded, and $J$ depends on $\\Omega$ via the spectrum of the Dirichlet Laplacian. We analyze the existence of a solution and its qualitative properties, and rise some open questions.
Modelling Robust Design Problems via Conic Optimization
Chaerani, D.
2006-01-01
This thesis deals with optimization problems with uncertain data. Uncertainty here means that the data is not known exactly at the time when its solution has to be determined. In many models the uncertainty is ignored and a representative nominal value of the data is used. The uncertainty may be due
MCMC for non-linear state space models using ensembles of latent sequences
2013-01-01
Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no straightforward solution. We take a Bayesian approach to the inference of unknown parameters of a non-linear state model; this, in turn, requires the availability of efficient Markov Chain Monte Carlo (MCMC) sampling methods for the latent (hidden) variables and model parameters. Using the ensemble ...
Freely generated vertex algebras and non-linear Lie conformal algebras
De Sole, Alberto; Kac, Victor
2003-01-01
We introduce the notion of a non--linear Lie conformal superalgebra and prove a PBW theorem for its universal enveloping vertex algebra. We also show that conversely any graded freely generated vertex algebra is the universal enveloping algebra of a non--linear Lie conformal superalgebra. This correspondence will be applied in the subsequent work to the problem of classification of finitely generated simple graded vertex algebras.
Automatic design of synthetic gene circuits through mixed integer non-linear programming.
Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias
2012-01-01
Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits.
Maximum process problems in optimal control theory
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Goran Peskir
2005-01-01
Full Text Available Given a standard Brownian motion (Btt≥0 and the equation of motion dXt=vtdt+2dBt, we set St=max0≤s≤tXs and consider the optimal control problem supvE(Sτ−Cτ, where c>0 and the supremum is taken over all admissible controls v satisfying vt∈[μ0,μ1] for all t up to τ=inf{t>0|Xt∉(ℓ0,ℓ1} with μ0g∗(St, where s↦g∗(s is a switching curve that is determined explicitly (as the unique solution to a nonlinear differential equation. The solution found demonstrates that the problem formulations based on a maximum functional can be successfully included in optimal control theory (calculus of variations in addition to the classic problem formulations due to Lagrange, Mayer, and Bolza.
Non-Linear Sigma Model on Conifolds
Parthasarathy, R
2002-01-01
Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\\"{a}hler metrics on these manifolds. The K\\"{a}hler 2-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of 2-dimensional non-linear sigma model with the conifolds as target spaces. The action for the sigma model is shown to be bounded from below. By a suitable choice of the 'integration constants', arising in the solution of Ricci flatness requirement, the metric and the equations of motion are found to be {\\it{non-singular}}. As the target space is Ricci flat, the perturbative 1-loop counter terms being absent, the model becomes topological. The inherent U(1) fibre over the base of the conifolds is shown to correspond to a gauge connection in the sigma model. The same procedure is employed to construct the metric for the resolved conifold, in terms of complex coordinates and the action ...
Non-Linear Electrohydrodynamics in Microfluidic Devices
Directory of Open Access Journals (Sweden)
Jun Zeng
2011-03-01
Full Text Available Since the inception of microfluidics, the electric force has been exploited as one of the leading mechanisms for driving and controlling the movement of the operating fluid and the charged suspensions. Electric force has an intrinsic advantage in miniaturized devices. Because the electrodes are placed over a small distance, from sub-millimeter to a few microns, a very high electric field is easy to obtain. The electric force can be highly localized as its strength rapidly decays away from the peak. This makes the electric force an ideal candidate for precise spatial control. The geometry and placement of the electrodes can be used to design electric fields of varying distributions, which can be readily realized by Micro-Electro-Mechanical Systems (MEMS fabrication methods. In this paper, we examine several electrically driven liquid handling operations. The emphasis is given to non-linear electrohydrodynamic effects. We discuss the theoretical treatment and related numerical methods. Modeling and simulations are used to unveil the associated electrohydrodynamic phenomena. The modeling based investigation is interwoven with examples of microfluidic devices to illustrate the applications.
Non Linear Analysis of MPPT for Power Quality Improvement
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S. Sankar
2015-08-01
Full Text Available In this study the conventional inverter interfacing renewable energy sources with the grid, without any additional hardware cost. Here, the main idea is the maximum utilization of inverter rating which is most of the time underutilized due to intermittent nature of RES. Based on the non-linear characteristics of PV, these thesis designs a VSS controller to realize the maximum power output of PV arrays. The output power from renewable energy sources fluctuates because of weather variations. This study proposes an effective power quality control strategy of renewable energy sources connected to power system using Photovoltaic (PV array. If the main controller used is a PR controller, any dc offset in a control loop will propagate through the system and the inverter terminal voltage will have a nonzero average value. In this strategy both load and inverter current sensing is required to compensate the load current harmonics. The non-linear load current harmonics may result in voltage harmonics and can create a serious PQ problem in the power system network.
On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems
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Punčochár Ivo
2014-12-01
Full Text Available The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dynamic optimization problem. As the optimal solution obtained by dynamic programming requires solving the Bellman functional equation, approximate techniques are employed to obtain a suboptimal active fault detector.
Young, Katherine C.; Sobieszczanski-Sobieski, Jaroslaw
1988-01-01
This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.
Hitting probabilities for non-linear systems of stochastic waves
Dalang, Robert C
2012-01-01
We consider a $d$-dimensional random field $u = \\{u(t,x)\\}$ that solves a non-linear system of stochastic wave equations in spatial dimensions $k \\in \\{1,2,3\\}$, driven by a spatially homogeneous Gaussian noise that is white in time. We mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent $\\beta$. Using Malliavin calculus, we establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of $\\IR^d$, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when $d(2-\\beta) > 2(k+1)$, points are polar for $u$. Conversely, in low dimensions $d$, points are not polar. There is however an interval in which the question of polarity of points remains open.
On Optimal Harvesting Problems in Random Environments
Song, Qingshuo; Zhu, Chao
2010-01-01
This paper investigates the optimal harvesting strategy for a single species living in random environments, whose growth is given by a regime-switching diffusion. Harvesting is introduced as a stochastic control. The objective is to find a harvesting strategy which maximizes the expected total discounted income from harvesting up to extinction. This is a singular stochastic control problem, with both the extinction time and harvesting policy depending on the initial condition. Consequently one no longer obtains continuity of the value function for free using the standard arguments as those in regular or singular stochastic control problems. This paper provides a sufficient condition under which the continuity of the value function is obtained. Further, we show that the value function is a viscosity solution of a coupled system of quasi-variational inequalities. A verification theorem is also established. Based upon the verification theorem, we explicitly construct an $\\varepsilon$-optimal harvesting strategy ...
Interaction Prediction Optimization in Multidisciplinary Design Optimization Problems
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Debiao Meng
2014-01-01
Full Text Available The distributed strategy of Collaborative Optimization (CO is suitable for large-scale engineering systems. However, it is hard for CO to converge when there is a high level coupled dimension. Furthermore, the discipline objectives cannot be considered in each discipline optimization problem. In this paper, one large-scale systems control strategy, the interaction prediction method (IPM, is introduced to enhance CO. IPM is utilized for controlling subsystems and coordinating the produce process in large-scale systems originally. We combine the strategy of IPM with CO and propose the Interaction Prediction Optimization (IPO method to solve MDO problems. As a hierarchical strategy, there are a system level and a subsystem level in IPO. The interaction design variables (including shared design variables and linking design variables are operated at the system level and assigned to the subsystem level as design parameters. Each discipline objective is considered and optimized at the subsystem level simultaneously. The values of design variables are transported between system level and subsystem level. The compatibility constraints are replaced with the enhanced compatibility constraints to reduce the dimension of design variables in compatibility constraints. Two examples are presented to show the potential application of IPO for MDO.
Non-linear dynamics of a spur gear pair
Kahraman, A.; Singh, R.
1990-10-01
Non-linear frequency response characteristics of a spur gear pair with backlash are examined in this paper for both external and internal excitations. The internal excitation is of importance from the high frequency noise and vibration control viewpoint and it represents the overall kinematic or static transmission error. Such problems may be significantly different from the rattle problems associated with external, low frequency torque excitation. Two solution methods, namely the digital simulation technique and the method of harmonic balance, have been used to develop the steady state solutions for the internal sinusoidal excitation. Difficulties associated with the determination of the multiple solutions at a given frequency in the digital simulation technique have been resolved, as one must search the entire initial conditions map. Such solutions and the transition frequencies for various impact situations are easily found by the method of harmonic balance. Further, the principle of superposition can be employed to analyze the periodic transmission error excitation and/or combined excitation problems provided that the excitation frequencies are sufficiently apart from each other. Our analytical predictions match satisfactorily with the limited experimental data available in the literature. Using the digital simulation, we have also observed that the chaotic and subharmonic resonances may exist in a gear pair depending upon the mean or design load, mean to alternating force ratio, damping and backlash. Specifically, the mean load determines the conditions for no impacts, single-sided impacts and double-sided impacts. Our results are different from the frequency response characteristics of the conventional, single-degree-of-freedom, clearance type non-linear system. Our formulation should form the basis of further analytical and experimental work in the geared rotor dynamics area.
Mesh refinement strategy for optimal control problems
Paiva, Luis Tiago; Fontes, Fernando,
2013-01-01
International audience; Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform node...
Optimization problems for switched systems with impulsive control
Institute of Scientific and Technical Information of China (English)
Junhao HU; Huayou WANG; Xinzhi LIU; Bin LIU
2005-01-01
By using Impulsive Maximum Principal and three stage optimization method,this paper discusses optimization problems for linear impulsive switched systems with hybrid controls,which includes continuous control and impulsive control.The linear quadratic optimization problems without constraints such as optimal hybrid control,optimal stability and optimal switching instants are addressed in detail.These results are applicable to optimal control problems in economics,mechanics,and management.
Tractable problems in optimal decentralized control
Rotkowitz, Michael Charles
2005-07-01
This thesis considers the problem of constructing optimal decentralized controllers. The problem is formulated as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. The notion of quadratic invariance of a constraint set with respect to a system is defined. It is shown that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback. It is further shown that if the constraint set has this property, this allows the constrained minimum-norm problem to be solved via convex programming. These results are developed in a very general framework, and are shown to hold for continuous-time systems, discrete-time systems, or operators on Banach spaces, for stable or unstable plants, and for the minimization of any norm. The utility of these results is then demonstrated on some specific constraint classes. An explicit test is derived for sparsity constraints on a controller to be quadratically invariant, and thus amenable to convex synthesis. Symmetric synthesis is also shown to be quadratically invariant. The problem of control over networks with delays is then addressed as another constraint class. Multiple subsystems are considered, each with its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. It is shown that if the communication delays are less than the propagation delays, then the associated constraints are quadratically invariant, and thus optimal controllers can be synthesized. We further show that this result still holds in the presence of computational delays. This thesis unifies the few previous results on specific tractable decentralized control problems, identifies broad and useful classes of new solvable problems, and delineates the largest known class of convex problems in decentralized control.
Optimal control problem for the extended Fisher–Kolmogorov equation
Indian Academy of Sciences (India)
Ning Duan
2016-02-01
In this paper, the optimal control problem for the extended Fisher–Kolmogorov equation is studied. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved and the optimality system is established.
Distributed Algorithms for Optimal Power Flow Problem
Lam, Albert Y S; Tse, David
2011-01-01
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real time. With some special network structure, e.g. trees, the problem has been shown to have a zero duality gap and the convex dual problem yields the optimal solution. In this paper, we propose a primal and a dual algorithm to coordinate the smaller subproblems decomposed from the convexified OPF. We can arrange the subproblems to be solved sequentially and cumulatively in a central node or solved in parallel in distributed nodes. We test the algorithms on IEEE radial distribution test feeders, some random tree-structured networks, and the IEEE transmission system benchmarks. Simulation results show that the computation time can be improved dramatically with our algorithms over the centralized approach of solving the problem without decomposition, especially in tree-structured...
New holographic dark energy model with non-linear interaction
Oliveros, A
2014-01-01
In this paper the cosmological evolution of a holographic dark energy model with a non-linear interaction between the dark energy and dark matter components in a FRW type flat universe is analysed. In this context, the deceleration parameter $q$ and the equation state $w_{\\Lambda}$ are obtained. We found that, as the square of the speed of sound remains positive, the model is stable under perturbations since early times; it also shows that the evolution of the matter and dark energy densities are of the same order for a long period of time, avoiding the so--called coincidence problem. We have also made the correspondence of the model with the dark energy densities and pressures for the quintessence and tachyon fields. From this correspondence we have reconstructed the potential of scalar fields and their dynamics.
Computational models of signalling networks for non-linear control.
Fuente, Luis A; Lones, Michael A; Turner, Alexander P; Stepney, Susan; Caves, Leo S; Tyrrell, Andy M
2013-05-01
Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.
Non-linear Oscillations of Compact Stars and Gravitational Waves
Passamonti, A
2006-01-01
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem has been treated by developing a gauge invariant formalism based on the 2-parameter perturbation theory (Sopuerta, Bruni and Gualtieri, 2004) where the radial and non-radial perturbations have been separately parameterized. The non-linear perturbations obey inhomogeneous partial differential equations, where the structure of the differential operator is given by the previous perturbative orders and the source terms are quadratic in the first order perturbations. In the exterior spacetime the sources vanish, thus the gravitational wave properties are completely described by the second order Zerilli and Regge-Wheeler functions. As main initial configuration we have considered a first order differentially rotating and radially pulsating star. Although at first perturbative or...
Considering Complexity: Toward A Strategy for Non-linear Analysis
Directory of Open Access Journals (Sweden)
Ken Hatt
2009-01-01
Full Text Available This paper explores complexity and a strategy for non-linear analysis with a consistent ontological, epistemological and methodological orientation. Complexity is defined and approaches in the natural sciences, ecosystems research, discursive studies and the social sciences are reviewed. In social science, theoretical efforts associated with problems of social order (Luhmann, critical sociology (Byrne and post-structuralism (Cilliers as well as representative studies are examined. The review concludes that there is need for an approach that will address morphogenesis and facilitate analysis of multilateral mutual causal relations. The remainder of the paper approaches these matters by outlining Archer’s approach to morphogenesis, Maruyama’s morphogenetic casual-loop model of epistemology and illustrating Maruyama’s method for analysis which employs both positive and negative feedback loops. The result is a strategy based on morphogenetic causal loop models that can be used to analyze structuring and the connections through which structures may be reproduced or transformed.
Application of Bacterial Foraging Optimization in Non-linear Model Identification%细菌生存优化在非线性模型辨识中的应用
Institute of Scientific and Technical Information of China (English)
林卫星; Peter X.Liu; 李文磊; 陈炎海; 欧超
2009-01-01
提出了一种新的基于细菌生存优化(Bacterial Foraging Optimization BFO)的非线性模型辨识方法.它是利用群集智能仿生BFO算法对一类Hammerstein系统进行辨识,从而估计出它的参数模型.通过对这类输入非线性模型进行辨识,并用仿真实验说明BFO算法的参数设置与选择方法.比较基于粒子群优化(Particle Swarm Optimization PSO)的非线性模型辨识算法,特别是对有色噪声的鲁棒性、模型的辨识精度、辨识收敛速度进行对比分析,以得出BFO辨识算法的优缺点及其有效性.
Directory of Open Access Journals (Sweden)
Ahmet Demir
2017-01-01
Full Text Available In the fields which require finding the most appropriate value, optimization became a vital approach to employ effective solutions. With the use of optimization techniques, many different fields in the modern life have found solutions to their real-world based problems. In this context, classical optimization techniques have had an important popularity. But after a while, more advanced optimization problems required the use of more effective techniques. At this point, Computer Science took an important role on providing software related techniques to improve the associated literature. Today, intelligent optimization techniques based on Artificial Intelligence are widely used for optimization problems. The objective of this paper is to provide a comparative study on the employment of classical optimization solutions and Artificial Intelligence solutions for enabling readers to have idea about the potential of intelligent optimization techniques. At this point, two recently developed intelligent optimization algorithms, Vortex Optimization Algorithm (VOA and Cognitive Development Optimization Algorithm (CoDOA, have been used to solve some multidisciplinary optimization problems provided in the source book Thomas' Calculus 11th Edition and the obtained results have compared with classical optimization solutions.
Non-Linear Unit Root Properties of Crude Oil Production
Svetlana Maslyuk; Russell Smyth
2007-01-01
While there is good reason to expect crude oil production to be non-linear, previous studies that have examined the stochastic properties of crude oil production have assumed that crude oil production follows a linear process. If crude oil production is a non-linear process, conventional unit root tests, which assume linear and systematic adjustment, could interpret departure from linearity as permanent stochastic disturbances. The objective of this paper is to test for non-linearities and un...
Properties of solutions of optimization problems for set functions
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Slawomir Dorosiewicz
2001-01-01
Full Text Available A definition of a special class of optimization problems with set functions is given. The existence of optimal solutions and first-order optimality conditions are proved. This case of optimal problems can be transformed to standard mixed problems of mathematical programming in Euclidean space. It makes possible the applications of various algorithms for these optimization problems for finding conditional extrema of set functions.
Optimal Planning and Problem-Solving
Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg
2008-01-01
CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.
An Assessment of Linear Versus Non-linear Multigrid Methods for Unstructured Mesh Solvers
2001-05-01
problems is investigated. The first case consists of a transient radiation-diffusion problem for which an exact linearization is available, while the...to the Jacobian of a second-order accurate discretization. When an exact linearization is employed, the linear and non-linear multigrid methods
Linux software for large topology optimization problems
DEFF Research Database (Denmark)
evolving product, which allows a parallel solution of the PDE, it lacks the important feature that the matrix-generation part of the computations is localized to each processor. This is well-known to be critical for obtaining a useful speedup on a Linux cluster and it motivates the search for a COMSOL......-like package for large topology optimization problems. One candidate for such software is developed for Linux by Sandia Nat’l Lab in the USA being the Sundance system. Sundance also uses a symbolic representation of the PDE and a scalable numerical solution is achieved by employing the underlying Trilinos...
Hybrid intelligent optimization methods for engineering problems
Pehlivanoglu, Yasin Volkan
The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and
Graphical and Analytical Analysis of the Non-Linear PLL
de Boer, Bjorn; Radovanovic, S.; Annema, Anne J.; Nauta, Bram
The fixed width control pulses from the Bang-Bang Phase Detector in non-linear PLLs allow for operation at higher data rates than the linear PLL. The high non-linearity of the Bang- Bang Phase Detector gives rise to unwanted effects, such as limit-cycles, not yet fully described. This paper
Non-linear stochastic response of a shallow cable
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2004-01-01
The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two-degrees-of-freedom...
Non-linear Frequency Scaling Algorithm for FMCW SAR Data
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
This paper presents a novel approach for processing data acquired with Frequency Modulated Continuous Wave (FMCW) dechirp-on-receive systems by using a non-linear frequency scaling algorithm. The range frequency non-linearity correction, the Doppler shift induced by the continuous motion and the ran
Non Linear Gauge Fixing for FeynArts
Gajdosik, Thomas
2007-01-01
We review the non-linear gauge-fixing for the Standard Model, proposed by F. Boudjema and E. Chopin, and present our implementation of this non-linear gauge-fixing to the Standard Model and to the minimal supersymmetric Standard Model in FeynArts.
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
Non-linear dynamics of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
by the rotation of the aerodynamic load and the curvature, as well as inertial induced non-linearities caused by the support point motion. The non-linear partial differential equations of motion in the moving frame of reference have been discretized, using the fixed base eigenmodes as a functional basis......The paper deals with the formulation of non-linear vibrations of a wind turbine wing described in a wing fixed moving coordinate system. The considered structural model is a Bernoulli-Euler beam with due consideration to axial twist. The theory includes geometrical non-linearities induced....... Important non-linear couplings between the fundamental blade mode and edgewise modes have been identified based on a resonance excitation of the wing, caused by a harmonically varying support point motion with the circular frequency omega. Assuming that the fundamental blade and edgewise eigenfrequencies...
Non-linear dielectric monitoring of biological suspensions
Energy Technology Data Exchange (ETDEWEB)
Treo, E F; Felice, C J [Departamento de BioingenierIa, Universidad Nacional de Tucuman and Consejo Nacional de Investigaciones Cientificas y Tecnicas. CC327, CP4000, San Miguel de Tucuman (Argentina)
2007-11-15
Non-linear dielectric spectroscopy as a tool for in situ monitoring of enzyme assumes a non-linear behavior of the sample when a sinusoidal voltage is applied to it. Even many attempts have been made to improve the original experiments, all of them had limited success. In this paper we present upgrades made to a non-linear dielectric spectrometer developed and the results obtained when using different cells. We emphasized on the electrode surface, characterizing the grinding and polishing procedure. We found that the biological medium does not behave as expected, and the non-linear response is generated in the electrode-electrolyte interface. The electrochemistry of this interface can bias unpredictably the measured non-linear response.
Predictability of extremes in non-linear hierarchically organized systems
Kossobokov, V. G.; Soloviev, A.
2011-12-01
phenomena of highly complex origin, by their nature, implies using problem oriented methods, which design breaks the limits of classical statistical or econometric applications. The unambiguously designed forecast/prediction algorithms of the "yes or no" variety, analyze the observable quantitative integrals and indicators available to a given date, then provides unambiguous answer to the question whether a critical transition should be expected or not in the next time interval. Since the predictability of an originating non-linear dynamical system is limited in principle, the probabilistic component of forecast/prediction algorithms is represented by the empirical probabilities of alarms, on one side, and failures-to-predict, on the other, estimated on control sets achieved in the retro- and prospective experiments. Predicting in advance is the only decisive test of forecast/predictions and the relevant on-going experiments are conducted in the case seismic extremes, recessions, and increases of unemployment rate. The results achieved in real-time testing keep being encouraging and confirm predictability of the extremes.
Non-linear Langevin model for the early-stage dynamics of electrospinning jets
Lauricella, Marco; Pisignano, Dario; Succi, Sauro
2015-01-01
We present a non-linear Langevin model to investigate the early-stage dynamics of electrified polymer jets in electrospinning experiments. In particular, we study the effects of air drag force on the uniaxial elongation of the charged jet, right after ejection from the nozzle. Numerical simulations show that the elongation of the jet filament close to the injection point is significantly affected by the non-linear drag exerted by the surrounding air. These result provide useful insights for the optimal design of current and future electrospinning experiments.
Particle Swarm Optimization for Structural Design Problems
Directory of Open Access Journals (Sweden)
Hamit SARUHAN
2010-02-01
Full Text Available The aim of this paper is to employ the Particle Swarm Optimization (PSO technique to a mechanical engineering design problem which is minimizing the volume of a cantilevered beam subject to bending strength constraints. Mechanical engineering design problems are complex activities which are computing capability are more and more required. The most of these problems are solved by conventional mathematical programming techniques that require gradient information. These techniques have several drawbacks from which the main one is becoming trapped in local optima. As an alternative to gradient-based techniques, the PSO does not require the evaluation of gradients of the objective function. The PSO algorithm employs the generation of guided random positions when they search for the global optimum point. The PSO which is a nature inspired heuristics search technique imitates the social behavior of bird flocking. The results obtained by the PSO are compared with Mathematical Programming (MP. It is demonstrated that the PSO performed and obtained better convergence reliability on the global optimum point than the MP. Using the MP, the volume of 2961000 mm3 was obtained while the beam volume of 2945345 mm3 was obtained by the PSO.
Ideology and problems of systems and economic optimization of NPPs
Directory of Open Access Journals (Sweden)
A.V. Klimenko
2016-06-01
Problems of systems optimization of components of the NFEC system as the functional of NPP optimization are identified. The task of optimization of complex systems refers to the most complex class of degenerate optimization problems [1]. No theory of degenerate optimization problems exists as of the present moment, although specifically these problems are real. Degenerate optimization problems should not be associated with degenerate matrices. Degenerate optimization problems deal with non-singular matrices having inverse matrices and, consequently, having solutions. However, the nature of these problems is such, that these solutions are degenerate (one or more components of the basis vector of the solution are equal to zero. The problem of convergence in the optimization of arbitrary component of the NFEC system to locally optimal plan coordinated with locally optimal plans for other components of the NFEC system is one of the main problems of degenerate optimization problems. Appearance of iterating loops during internal iterations in the process of optimization of plans for separate component of the NFEC system is not less important for problems of this class. This feature requires including incorporation of additional algorithms for exiting from the loops in the optimization algorithms.
Filtering Non-Linear Transfer Functions on Surfaces.
Heitz, Eric; Nowrouzezahrai, Derek; Poulin, Pierre; Neyret, Fabrice
2014-07-01
Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view- and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few
Directory of Open Access Journals (Sweden)
Luiz Augusto da Cruz Meleiro
2005-06-01
Full Text Available In this work a MIMO non-linear predictive controller was developed for an extractive alcoholic fermentation process. The internal model of the controller was represented by two MISO Functional Link Networks (FLNs, identified using simulated data generated from a deterministic mathematical model whose kinetic parameters were determined experimentally. The FLN structure presents as advantages fast training and guaranteed convergence, since the estimation of the weights is a linear optimization problem. Besides, the elimination of non-significant weights generates parsimonious models, which allows for fast execution in an MPC-based algorithm. The proposed algorithm showed good potential in identification and control of non-linear processes.Neste trabalho um controlador preditivo não linear multivariável foi desenvolvido para um processo de fermentação alcoólica extrativa. O modelo interno do controlador foi representado por duas redes do tipo Functional Link (FLN, identificadas usando dados de simulação gerados a partir de um modelo validado experimentalmente. A estrutura FLN apresenta como vantagem o treinamento rápido e convergência garantida, já que a estimação dos seus pesos é um problema de otimização linear. Além disso, a eliminação de pesos não significativos gera modelos parsimoniosos, o que permite a rápida execução em algoritmos de controle preditivo baseado em modelo. Os resultados mostram que o algoritmo proposto tem grande potencial para identificação e controle de processos não lineares.
Non-linear effects in transition edge sensors for X-ray detection
Energy Technology Data Exchange (ETDEWEB)
Bandler, S.R. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States)]. E-mail: sbandler@milkyway.gsfc.nasa.gov; Figueroa-Feliciano, E. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Iyomoto, N. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Kelley, R.L. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Kilbourne, C.A. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Murphy, K.D. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Porter, F.S. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Saab, T. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Sadleir, J. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States)
2006-04-15
In a microcalorimeter that uses a transition-edge sensor to detect energy depositions, the small signal energy resolution improves with decreasing heat capacity. This improvement remains true up to the point where non-linear and saturation effects become significant. This happens when the energy deposition causes a significant change in the sensor resistance. Not only does the signal size become a non-linear function of the energy deposited, but also the noise becomes non-stationary over the duration of the pulse. Algorithms have been developed that can calculate the optimal performance given this non-linear behavior that typically requires significant processing and calibration work-both of which are impractical for space missions. We have investigated the relative importance of the various non-linear effects, with the hope that a computationally simple transformation can overcome the largest of the non-linear and non-stationary effects, producing a highly linear 'gain' for pulse-height versus energy, and close to the best energy resolution at all energies when using a Wiener filter.
Limitations in direct and indirect methods for solving optimal control problems in growth theory
Directory of Open Access Journals (Sweden)
Ratković Kruna
2016-01-01
Full Text Available The focus of this paper is on a comprehensive analysis of different methods and mathematical techniques used for solving optimal control problems (OCP in growth theory. Most important methods for solving dynamic non-linear infinite-horizon growth models using optimal control theory are presented and a critical view of the limitations of different methods is given. The main problem is to determine the optimal rate of growth over time in a way that maximizes the welfare function over an infinite horizon. The welfare function depends on capital-labor ratio, the state variable, and the per-capita consumption, the control variable. Numerical methods for solving OCP are divided into two classes: direct and indirect approach. How the indirect approach can be used is given in the example of the neo-classical growth model. In order to present the indirect and the direct approach simultaneously, two endogenous growth models, one written by Romer and another by Lucas and Uzawa, are studied. Advantages and efficiency of these different approaches will be discussed. Although the indirect methods for solving OCP are still the most expanded in growth theory, it will be seen that using direct methods can also be very efficient and help to overcome problems that can occur by using the indirect approach.
Chemical Reaction Optimization for Max Flow Problem
Directory of Open Access Journals (Sweden)
Reham Barham
2016-08-01
Full Text Available This study presents an algorithm for MaxFlow problem using "Chemical Reaction Optimization algorithm (CRO". CRO is a recently established meta-heuristics algorithm for optimization, inspired by the nature of chemical reactions. The main concern is to find the best maximum flow value at which the flow can be shipped from the source node to the sink node in a flow network without violating any capacity constraints in which the flow of each edge remains within the upper bound value of the capacity. The proposed MaxFlow-CRO algorithm is presented, analyzed asymptotically and experimental test is conducted. Asymptotic runtime is derived theoretically. The algorithm is implemented using JAVA programming language. Results show a good performance with a complexity of O(I E2, for I iterations and E edges. The number of iterations I in the algorithm, is an important factor that will affect the results obtained. As number of iterations is increased, best possible max-Flow value is obtained.
Optimization methods for activities selection problems
Mahad, Nor Faradilah; Alias, Suriana; Yaakop, Siti Zulaika; Arshad, Norul Amanina Mohd; Mazni, Elis Sofia
2017-08-01
Co-curriculum activities must be joined by every student in Malaysia and these activities bring a lot of benefits to the students. By joining these activities, the students can learn about the time management and they can developing many useful skills. This project focuses on the selection of co-curriculum activities in secondary school using the optimization methods which are the Analytic Hierarchy Process (AHP) and Zero-One Goal Programming (ZOGP). A secondary school in Negeri Sembilan, Malaysia was chosen as a case study. A set of questionnaires were distributed randomly to calculate the weighted for each activity based on the 3 chosen criteria which are soft skills, interesting activities and performances. The weighted was calculated by using AHP and the results showed that the most important criteria is soft skills. Then, the ZOGP model will be analyzed by using LINGO Software version 15.0. There are two priorities to be considered. The first priority which is to minimize the budget for the activities is achieved since the total budget can be reduced by RM233.00. Therefore, the total budget to implement the selected activities is RM11,195.00. The second priority which is to select the co-curriculum activities is also achieved. The results showed that 9 out of 15 activities were selected. Thus, it can concluded that AHP and ZOGP approach can be used as the optimization methods for activities selection problem.
Reproducing Kernel Particle Method for Non-Linear Fracture Analysis
Institute of Scientific and Technical Information of China (English)
Cao Zhongqing; Zhou Benkuan; Chen Dapeng
2006-01-01
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method (RKPM). Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
Wang, Gang; Wang, Chaoli; Du, Qinghui; Cai, Xuan
2016-10-01
In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.
Madsen, Niels K; Godtliebsen, Ian H; Christiansen, Ove
2017-04-07
Vibrational coupled-cluster (VCC) theory provides an accurate method for calculating vibrational spectra and properties of small to medium-sized molecules. Obtaining these properties requires the solution of the non-linear VCC equations which can in some cases be hard to converge depending on the molecule, the basis set, and the vibrational state in question. We present and compare a range of different algorithms for solving the VCC equations ranging from a full Newton-Raphson method to approximate quasi-Newton models using an array of different convergence-acceleration schemes. The convergence properties and computational cost of the algorithms are compared for the optimization of VCC states. This includes both simple ground-state problems and difficult excited states with strong non-linearities. Furthermore, the effects of using tensor-decomposed solution vectors and residuals are investigated and discussed. The results show that for standard ground-state calculations, the conjugate residual with optimal trial vectors algorithm has the shortest time-to-solution although the full Newton-Raphson method converges in fewer macro-iterations. Using decomposed tensors does not affect the observed convergence rates in our test calculations as long as the tensors are decomposed to sufficient accuracy.
Mesh refinement strategy for optimal control problems
Paiva, L. T.; Fontes, F. A. C. C.
2013-10-01
Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.
Non-Linearly Interacting Ghost Dark Energy in Brans-Dicke Cosmology
Ebrahimi, E
2016-01-01
In this paper we extend the form of interaction term into the non-linear regime in the ghost dark energy model. A general form of non-linear interaction term is presented and cosmic dynamic equations are obtained. Next, the model is detailed for two special choice of the non-linear interaction term. According to this the universe transits at suitable time ($z\\sim 0.8$) from deceleration to acceleration phase which alleviate the coincidence problem. Squared sound speed analysis revealed that for one class of non-linear interaction term $v_s^2$ can gets positive. This point is an impact of the non-linear interaction term and we never find such behavior in non interacting and linearly interacting ghost dark energy models. Also statefinder parameters are introduced for this model and we found that for one class the model meets the $\\Lambda CDM$ while in the second choice although the model approaches the $\\Lambda CDM$ but never touch that.
Free Convective Nonaligned Non-Newtonian Flow with Non-linear Thermal Radiation
Rana, S.; Mehmood, R.; Narayana, PV S.; Akbar, N. S.
2016-12-01
The present study explores the free convective oblique Casson fluid over a stretching surface with non-linear thermal radiation effects. The governing physical problem is modelled and transformed into a set of coupled non-linear ordinary differential equations by suitable similarity transformation, which are solved numerically with the help of shooting method keeping the convergence control of 10-5 in computations. Influence of pertinent physical parameters on normal, tangential velocity profiles and temperature are expressed through graphs. Physical quantities of interest such as skin friction coefficients and local heat flux are investigated numerically.
Energy Technology Data Exchange (ETDEWEB)
Ravi Kanth, A.S.V. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)], E-mail: asvravikanth@yahoo.com; Aruna, K. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)
2008-11-17
In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Scene matching based on non-linear pre-processing on reference image and sensed image
Institute of Scientific and Technical Information of China (English)
Zhong Sheng; Zhang Tianxu; Sang Nong
2005-01-01
To solve the heterogeneous image scene matching problem, a non-linear pre-processing method for the original images before intensity-based correlation is proposed. The result shows that the proper matching probability is raised greatly. Especially for the low S/N image pairs, the effect is more remarkable.
THE APPLICATION OF GENETIC ALGORITHM IN NON-LINEAR INVERSION OF ROCK MECHANICS PARAMETERS
Institute of Scientific and Technical Information of China (English)
赵晓东
1998-01-01
The non-linear inversion of rock mechanics parameters based on genetic algorithm ispresented. The principle and step of genetic algorithm is also given. A brief discussion of thismethod and an application example is presented at the end of this paper. From the satisfied re-sult, quick, convenient and practical new approach is developed to solve this kind of problems.
Non-linear Least Squares Fitting in IDL with MPFIT
Markwardt, Craig B
2009-01-01
MPFIT is a port to IDL of the non-linear least squares fitting program MINPACK-1. MPFIT inherits the robustness of the original FORTRAN version of MINPACK-1, but is optimized for performance and convenience in IDL. In addition to the main fitting engine, MPFIT, several specialized functions are provided to fit 1-D curves and 2-D images; 1-D and 2-D peaks; and interactive fitting from the IDL command line. Several constraints can be applied to model parameters, including fixed constraints, simple bounding constraints, and "tying" the value to another parameter. Several data weighting methods are allowed, and the parameter covariance matrix is computed. Extensive diagnostic capabilities are available during the fit, via a call-back subroutine, and after the fit is complete. Several different forms of documentation are provided, including a tutorial, reference pages, and frequently asked questions. The package has been translated to C and Python as well. The full IDL and C packages can be found at http://purl.co...
Mathematical programming methods for large-scale topology optimization problems
DEFF Research Database (Denmark)
Rojas Labanda, Susana
, and at the same time, reduce the number of function evaluations. Nonlinear optimization methods, such as sequential quadratic programming and interior point solvers, have almost not been embraced by the topology optimization community. Thus, this work is focused on the introduction of this kind of second......This thesis investigates new optimization methods for structural topology optimization problems. The aim of topology optimization is finding the optimal design of a structure. The physical problem is modelled as a nonlinear optimization problem. This powerful tool was initially developed...... for the classical minimum compliance problem. Two of the state-of-the-art optimization algorithms are investigated and implemented for this structural topology optimization problem. A Sequential Quadratic Programming (TopSQP) and an interior point method (TopIP) are developed exploiting the specific mathematical...
Series solutions of non-linear Riccati differential equations with fractional order
Energy Technology Data Exchange (ETDEWEB)
Cang Jie; Tan Yue; Xu Hang [School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030 (China); Liao Shijun [School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030 (China)], E-mail: sjliao@sjtu.edu.cn
2009-04-15
In this paper, based on the homotopy analysis method (HAM), a new analytic technique is proposed to solve non-linear Riccati differential equation with fractional order. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter h. Besides, it is proved that well-known Adomian's decomposition method is a special case of the homotopy analysis method when h = -1. This work illustrates the validity and great potential of the homotopy analysis method for the non-linear differential equations with fractional order. The basic ideas of this approach can be widely employed to solve other strongly non-linear problems in fractional calculus.
Enhanced Bee Colony Algorithm for Complex Optimization Problems
Directory of Open Access Journals (Sweden)
S.Suriya
2012-01-01
Full Text Available Optimization problems are considered to be one kind of NP hard problems. Usually heuristic approaches are found to provide solutions for NP hard problems. There are a plenty of heuristic algorithmsavailable to solve optimization problems namely: Ant Colony Optimization, Particle Swarm Optimization, Bee Colony Optimization, etc. The basic Bee Colony algorithm, a population based search algorithm, is analyzed to be a novel tool for complex optimization problems. The algorithm mimics the food foraging behavior of swarmsof honey bees. This paper deals with a modified fitness function of Bee Colony algorithm. The effect of problem dimensionality on the performance of the algorithms will be investigated. This enhanced Bee Colony Optimization will be evaluated based on the well-known benchmark problems. The testing functions like Rastrigin, Rosenbrock, Ackley, Griewank and Sphere are used to evaluavate the performance of the enhanced Bee Colony algorithm. The simulation will be developed on MATLAB.
SolveDB: Integrating Optimization Problem Solvers Into SQL Databases
DEFF Research Database (Denmark)
Siksnys, Laurynas; Pedersen, Torben Bach
2016-01-01
Many real-world decision problems involve solving optimization problems based on data in an SQL database. Traditionally, solving such problems requires combining a DBMS with optimization software packages for each required class of problems (e.g. linear and constraint programming) -- leading...... to workflows that are cumbersome, complex, inefficient, and error-prone. In this paper, we present SolveDB - a DBMS for optimization applications. SolveDB supports solvers for different problem classes and offers seamless data management and optimization problem solving in a pure SQL-based setting. This allows...... for much simpler and more effective solutions of database-based optimization problems. SolveDB is based on the 3-level ANSI/SPARC architecture and allows formulating, solving, and analysing solutions of optimization problems using a single so-called solve query. SolveDB provides (1) an SQL-based syntax...
Non-linear dynamics of a geared rotor-bearing system with multiple clearances
Kahraman, A.; Singh, R.
1991-02-01
Non-linear frequency response characteristics of a geared rotor-bearing system are examined in this paper. A three-degree-of-freedom dynamic model is developed which includes non-linearities associated with radial clearances in the radial rolling element bearings and backlash between a spur gear pair; linear time-invariant gear meshing stiffness is assumed. The corresponding linear system problem is also solved, and predicted natural frequencies and modes match with finite element method results. The bearing non-linear stiffness function is approximated for the sake of convenience by a simple model which is identical to that used for the gear mesh. This approximate bearing model has been verified by comparing steady state frequency spectra. Applicability of both analytical and numerical solution techniques to the multi-degree-of-freedom non-linear problem is investigated. Satisfactory agreement has been found between our theory and available experimental data. Several key issues such as non-linear modal interactions and differences between internal static transmission error excitation and external torque excitation are discussed. Additionally, parametric studies are performed to understand the effect of system parameters such as bearing stiffness to gear mesh stiffness ratio, alternating to mean force ratio and radial bearing preload to mean force ratio on the non-linear dynamic behavior. A criterion used to classify the steady state solutions is presented, and the conditions for chaotic, quasi-periodic and subharmonic steady state solutions are determined. Two typical routes to chaos observed in this geared system are also identified.
NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS
Institute of Scientific and Technical Information of China (English)
Yang Xiaodong; Chen Li-Qun
2006-01-01
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
NLHB : A Non-Linear Hopper Blum Protocol
Madhavan, Mukundan; Sankarasubramaniam, Yogesh; Viswanathan, Kapali
2010-01-01
In this paper, we propose a light-weight provably-secure authentication protocol called the NLHB protocol, which is a variant of the HB protocol. The HB protocol uses the complexity of decoding linear codes for security against passive attacks. In contrast, security for the NLHB protocol is proved by reducing passive attacks to the problem of decoding a class of non-linear codes\\footnote that are provably hard. We demonstrate that the existing passive attacks on the HB protocol family, which have contributed to considerable reduction in its effective key-size, are ineffective against the NLHB protocol. From the evidence, we conclude that smaller-key sizes are sufficient for the NLHB protocol to achieve the same level of passive attack security as the HB Protocol. Further, for this choice of parameters, we provide an implementation instance for the NLHB protocol for which the Prover/Verifier complexity is lower than the HB protocol, enabling authentication on very low-cost devices like RFID tags. Finally, in t...
Non-linear calibration models for near infrared spectroscopy.
Ni, Wangdong; Nørgaard, Lars; Mørup, Morten
2014-02-27
Different calibration techniques are available for spectroscopic applications that show nonlinear behavior. This comprehensive comparative study presents a comparison of different nonlinear calibration techniques: kernel PLS (KPLS), support vector machines (SVM), least-squares SVM (LS-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS-SVM is also attractive due to its good predictive performance for both linear and nonlinear calibrations.
A STABILITY THEOREM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS
Institute of Scientific and Technical Information of China (English)
M.H. Farag
2004-01-01
This paper presents the stability of difference approximations of an optimal control problem for a quasilinear parabolic equation with controls in the coefficients, boundary conditions and additional restrictions. The optimal control problem has been convered to one of the optimization problem using a penalty function technique. The difference approximations problem for the considered problem is obtained. The estimations of stability of the solution of difference approximations problem are proved. The stability estimation of the solution of difference approximations problem by the controls is obtained.
Group Search Optimizer for the Mobile Location Management Problem
Directory of Open Access Journals (Sweden)
Dan Wang
2014-01-01
Full Text Available We propose a diversity-guided group search optimizer-based approach for solving the location management problem in mobile computing. The location management problem, which is to find the optimal network configurations of management under the mobile computing environment, is considered here as an optimization problem. The proposed diversity-guided group search optimizer algorithm is realized with the aid of diversity operator, which helps alleviate the premature convergence problem of group search optimizer algorithm, a successful optimization algorithm inspired by the animal behavior. To address the location management problem, diversity-guided group search optimizer algorithm is exploited to optimize network configurations of management by minimizing the sum of location update cost and location paging cost. Experimental results illustrate the effectiveness of the proposed approach.
Group Search Optimizer for the Mobile Location Management Problem
Wang, Dan; Xiong, Congcong; Huang, Wei
2014-01-01
We propose a diversity-guided group search optimizer-based approach for solving the location management problem in mobile computing. The location management problem, which is to find the optimal network configurations of management under the mobile computing environment, is considered here as an optimization problem. The proposed diversity-guided group search optimizer algorithm is realized with the aid of diversity operator, which helps alleviate the premature convergence problem of group search optimizer algorithm, a successful optimization algorithm inspired by the animal behavior. To address the location management problem, diversity-guided group search optimizer algorithm is exploited to optimize network configurations of management by minimizing the sum of location update cost and location paging cost. Experimental results illustrate the effectiveness of the proposed approach. PMID:25180199
Hierarchical control based on Hopfield network for nonseparable optimization problems
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The nonseparable optimization control problem is considered, where the overall objective function is not of an additive form with respect to subsystems. Since there exists the problem that computation is very slow when using iterative algorithms in multiobjective optimization, Hopfield optimization hierarchical network based on IPM is presented to overcome such slow computation difficulty. Asymptotic stability of this Hopfield network is proved and its equilibrium point is the optimal point of the original problem. The simulation shows that the net is effective to deal with the optimization control problem for large-scale nonseparable steady state systems.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Energy Technology Data Exchange (ETDEWEB)
Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
About one problem of optimal stabilization of linear compound systems
Directory of Open Access Journals (Sweden)
Barseghyan V.R.
2014-12-01
Full Text Available The problem of optimal stabilization of linear compound system is investigated. Based on Lyapunov function method the method of building optimal stabilizing control action is suggested. The solution of the problem of optimal stabilization of a concrete compound system is given.
Non linear predictive control of a LEGO mobile robot
Merabti, H.; Bouchemal, B.; Belarbi, K.; Boucherma, D.; Amouri, A.
2014-10-01
Metaheuristics are general purpose heuristics which have shown a great potential for the solution of difficult optimization problems. In this work, we apply the meta heuristic, namely particle swarm optimization, PSO, for the solution of the optimization problem arising in NLMPC. This algorithm is easy to code and may be considered as alternatives for the more classical solution procedures. The PSO- NLMPC is applied to control a mobile robot for the tracking trajectory and obstacles avoidance. Experimental results show the strength of this approach.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper presents a method on non-linear correction of broadband LFMCW signal utilizing its relativenonlinear error. The deriving procedure and the results simulated by a computer and tested by a practical system arealso introduced. The method has two obvious advantages compared with the previous methods: (1) Correction has norelation with delay time td and sweep bandwidth B; (2) The inherent non-linear error of VCO has no influence on thecorrection and its last results.
Optimization, Randomized Approximability, and Boolean Constraint Satisfaction Problems
Yamakami, Tomoyuki
2011-01-01
We give a unified treatment to optimization problems that can be expressed in the form of nonnegative-real-weighted Boolean constraint satisfaction problems. Creignou, Khanna, Sudan, Trevisan, and Williamson studied the complexity of approximating their optimal solutions whose optimality is measured by the sums of outcomes of constraints. To explore a wider range of optimization constraint satisfaction problems, following an early work of Marchetti-Spaccamela and Romano, we study the case where the optimality is measured by products of constraints' outcomes. We completely classify those problems into three categories: PO problems, NPO-hard problems, and intermediate problems that lie between the former two categories. To prove this trichotomy theorem, we analyze characteristics of nonnegative-real-weighted constraints using a variant of the notion of T-constructibility developed earlier for complex-weighted counting constraint satisfaction problems.
Huang, Chung-Yuan
A new formulation of the stream function based on a stream function coordinate (SFC) concept for inviscid flow field calculations is presented. In addition, a new method is developed not only to accelerate, but also to stabilize the iterative schemes for steady and unsteady, linear and non-linear, scalar and system of coupled, partial differential equations. With this theory, the limitation on the time step size of an explicit scheme for solving unsteady problems and the limitation on the relaxation factors of an iterative scheme for solving steady state problems could be analytically determined. Moreover, this theory allows the determination of the optimal time steps for explicit time-stepping schemes and the optimal values of the acceleration factors for iterative schemes, if the transient behavior is immaterial.
Algorithmic Aspects of Several Data Transfer Service Optimization Problems
Andreica, Mugurel Ionut; Ionescu, Florin; Andreica, Cristina Teodora
2009-01-01
Optimized data transfer services are highly demanded nowadays, due to the large amounts of data which are frequently being produced and accessed. In this paper we consider several data transfer service optimization problems (optimal server location in path networks, optimal packet sequencing and minimum makespan packet scheduling), for which we provide novel algorithmic solutions.
Usage of the particle swarm optimization in problems of mechanics
Directory of Open Access Journals (Sweden)
Hajžman M.
2016-06-01
Full Text Available This paper deals with the optimization method called particle swarm optimization and its usage in mechanics. Basic versions of the method is introduced and several improvements and modifications are applied for better convergence of the algorithms. The performance of the optimization algorithm implemented in an original in-house software is investigated by means of three basic and one complex problems of mechanics. The goal of the first problem is to find optimal parameters of a dynamic absorber of vibrations. The second problem is about the tunning of eigenfrequencies of beam bending vibrations. The third problem is to optimize parameters of a clamped beam with various segments. The last complex problem is the optimization of a tilting mechanism with multilevel control. The presented results show that the particle swarm optimization can be efficiently used in mechanical tasks.
Particle Swarm Optimization with Genetic Operators for Vehicle Routing Problem
Directory of Open Access Journals (Sweden)
P. V. PURANIK
2012-07-01
Full Text Available Vehicle Routing Problem (VRP is to find shortest route thereby minimizing total cost. VRP is a NP-hard and Combinatorial optimization problem. Such problems increase exponentially with the problem size. Various derivative based optimization techniques are employed for optimization. Derivative based optimization techniques are difficult to evaluate. Therefore parallel search algorithm emerged to solve VRP. In this work, a particle swarm optimization (PSO algorithm and Genetic algorithm (GA with crossover and mutation operator are applied to two typical functions to deal with the problem of VRP efficiently using MATLAB software. Before solving VRP, optimization of functions using PSO and GA are checked. In this paper capacitate VRP with time window (CVRPTW is proposed. The computational result shows generation of input for VRP, optimization of Rastrigin function, Rosenbrock function using PSO and GA.
Topology optimization problems with design-dependent sets of constraints
DEFF Research Database (Denmark)
Schou, Marie-Louise Højlund
Topology optimization is a design tool which is used in numerous fields. It can be used whenever the design is driven by weight and strength considerations. The basic concept of topology optimization is the interpretation of partial differential equation coefficients as effective material...... structural topology optimization problems. For such problems a stress constraint for an element should only be present in the optimization problem when the structural design variable corresponding to this element has a value greater than zero. We model the stress constrained topology optimization problem...... using both discrete and continuous design variables. Using discrete design variables is the natural modeling frame. However, we cannot solve real-size problems with the technological limits of today. Using continuous design variables makes it possible to also study topology optimization problems...
Replica analysis for the duality of the portfolio optimization problem
Shinzato, Takashi
2016-11-01
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.
Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions
Feng, Lili; Yu, Fajun; Li, Li
2017-01-01
Starting from a 3×3 spectral problem, a Darboux transformation (DT) method for coupled Schrödinger (CNLS) equation is constructed, which is more complex than 2×2 spectral problems. A scheme of soliton solutions of an integrable CNLS system is realised by using DT. Then, we obtain the breather solutions for the integrable CNLS system. The method is also appropriate for more non-linear soliton equations in physics and mathematics.
some notes on discount factor restrictions for dynamic optimization problems
Gerhard Sorger
2008-01-01
We consider dynamic optimization problems on one-dimensional state spaces. Un- der standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation between the size of the discount factor of the dynamic optimization problem on the one hand and the properties of the dynamical system xt+1 = h(xt) on the other hand. The purpose of this paper is to survey...
LDRD Final Report: Global Optimization for Engineering Science Problems
Energy Technology Data Exchange (ETDEWEB)
HART,WILLIAM E.
1999-12-01
For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD ''Global Optimization for Engineering Science Problems'' was the development of new robust and efficient optimization algorithms that can be used to find globally optimal solutions to complex optimization problems. This SAND report summarizes the technical accomplishments of this LDRD, discusses lessons learned and describes open research issues.
Massive Neutrinos and the Non-linear Matter Power Spectrum
Bird, Simeon; Haehnelt, Martin G
2011-01-01
We perform an extensive suite of N-body simulations of the matter power spectrum, incorporating massive neutrinos in the range M = 0.15-0.6 eV, probing the non-linear regime at scales k < 10 hMpc-1 at z < 3. We extend the widely used HALOFIT approximation (Smith et al. 2003) to account for the effect of massive neutrinos on the power spectrum. In the strongly non-linear regime HALOFIT systematically over-predicts the suppression due to the free-streaming of the neutrinos. The maximal discrepancy occurs at k \\sim 1hMpc-1, and is at the level of 10% of the total suppression. Most published constraints on neutrino masses based on HALOFIT are not affected, as they rely on data probing the matter power spectrum in the linear or mildly non-linear regime. However, predictions for future galaxy, Lyman-alpha forest and weak lensing surveys extending to more non-linear scales will benefit from the improved approximation to the non-linear matter power spectrum we provide. Our approximation reproduces the induced n...
Analytical exact solution of the non-linear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica
2011-07-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
The Importance of Non-Linearity on Turbulent Fluxes
DEFF Research Database (Denmark)
Rokni, Masoud
2007-01-01
Two new non-linear models for the turbulent heat fluxes are derived and developed from the transport equation of the scalar passive flux. These models are called as non-linear eddy diffusivity and non-linear scalar flux. The structure of these models is compared with the exact solution which...... is derived from the Cayley-Hamilton theorem and contains a three term-basis plus a non-linear term due to scalar fluxes. In order to study the performance of the model itself, all other turbulent quantities are taken from a DNS channel flow data-base and thus the error source has been minimized. The results...... are compared with the DNS channel flow and good agreement is achieved. It has been shown that the non-linearity parts of the models are important to capture the true path of the streamwise scalar fluxes. It has also been shown that one of model constant should have negative sign rather than positive, which had...
An Effective Hybrid Optimization Algorithm for Capacitated Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.
Directory of Open Access Journals (Sweden)
Hokeš Filip
2015-12-01
Full Text Available The subject of this paper is to describe some of the aspects manifesting in the use of the elastoplastic material model library multiPlas, which was developed to support non-linear computations in the ANSYS system. The text focuses on the analysis of numerical simulations of a virtual tension test in several case studies, thereby the text endeavours to describe the problems connected with modelling non-linear behaviour of concrete in a tensile area.
Particle swarm optimization - Genetic algorithm (PSOGA) on linear transportation problem
Rahmalia, Dinita
2017-08-01
Linear Transportation Problem (LTP) is the case of constrained optimization where we want to minimize cost subject to the balance of the number of supply and the number of demand. The exact method such as northwest corner, vogel, russel, minimal cost have been applied at approaching optimal solution. In this paper, we use heurisitic like Particle Swarm Optimization (PSO) for solving linear transportation problem at any size of decision variable. In addition, we combine mutation operator of Genetic Algorithm (GA) at PSO to improve optimal solution. This method is called Particle Swarm Optimization - Genetic Algorithm (PSOGA). The simulations show that PSOGA can improve optimal solution resulted by PSO.
Institute of Scientific and Technical Information of China (English)
Xu Zhang; En-min Feng
2004-01-01
This paper studies the two-dimensional layout optimization problem.An optimization model with performance constraints is presented.The layout problem is partitioned intofinite subproblems in terms of graph theory,in such a way of that each subproblem overcomes its on-o inature optimal variable.A minimax problem is constructed that is locally equivalent to each subproblem.By using this minimax problem,we present the optimality function for every subproblem and prove that the first order necessary optimality condition is satisfied at a point if and only if this point is a zero of optimality function.
Hemanth, M; Deoli, Shilpi; Raghuveer, H P; Rani, M S; Hegde, Chatura; Vedavathi, B
2015-09-01
Simulation of periodontal ligament (PDL) using non-linear finite element method (FEM) analysis gives better insight into understanding of the biology of tooth movement. The stresses in the PDL were evaluated for intrusion and lingual root torque using non-linear properties. A three-dimensional (3D) FEM model of the maxillary incisors was generated using Solidworks modeling software. Stresses in the PDL were evaluated for intrusive and lingual root torque movements by 3D FEM using ANSYS software. These stresses were compared with linear and non-linear analyses. For intrusive and lingual root torque movements, distribution of stress over the PDL was within the range of optimal stress value as proposed by Lee, but was exceeding the force system given by Proffit as optimum forces for orthodontic tooth movement with linear properties. When same force load was applied in non-linear analysis, stresses were more compared to linear analysis and were beyond the optimal stress range as proposed by Lee for both intrusive and lingual root torque. To get the same stress as linear analysis, iterations were done using non-linear properties and the force level was reduced. This shows that the force level required for non-linear analysis is lesser than that of linear analysis.
A non-linear model predictive controller with obstacle avoidance for a space robot
Wang, Mingming; Luo, Jianjun; Walter, Ulrich
2016-04-01
This study investigates the use of the non-linear model predictive control (NMPC) strategy for a kinematically redundant space robot to approach an un-cooperative target in complex space environment. Collision avoidance, traditionally treated as a high level planning problem, can be effectively translated into control constraints as part of the NMPC. The objective of this paper is to evaluate the performance of the predictive controller in a constrained workspace and to investigate the feasibility of imposing additional constraints into the NMPC. In this paper, we reformulated the issue of the space robot motion control by using NMPC with predefined objectives under input, output and obstacle constraints over a receding horizon. An on-line quadratic programming (QP) procedure is employed to obtain the constrained optimal control decisions in real-time. This study has been implemented for a 7 degree-of-freedom (DOF) kinematically redundant manipulator mounted on a 6 DOF free-floating spacecraft via simulation studies. Real-time trajectory tracking and collision avoidance particularly demonstrate the effectiveness and potential of the proposed NMPC strategy for the space robot.
ISOGEOMETRIC SHAPE OPTIMIZATION FOR ELECTROMAGNETIC SCATTERING PROBLEMS
DEFF Research Database (Denmark)
Nguyen, D. M.; Evgrafov, Anton; Gravesen, Jens
2012-01-01
We consider the benchmark problem of magnetic energy density enhancement in a small spatial region by varying the shape of two symmetric conducting scatterers. We view this problem as a prototype for a wide variety of geometric design problems in electromagnetic applications. Our approach...
Non-Linear Second-Order Periodic Systems with Non-Smooth Potential
Indian Academy of Sciences (India)
Evgenia H Papageorgiou; Nikolaos S, Papageorgiou
2004-08-01
In this paper we study second order non-linear periodic systems driven by the ordinary vector -Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on the potential function. Then we establish the existence of non-trivial homoclinic (to zero) solutions. Our theorem appears to be the first such result (even for smooth problems) for systems monitored by the -Laplacian. In the last section of the paper we examine the scalar non-linear and semilinear problem. Our approach uses a generalized Landesman–Lazer type condition which generalizes previous ones used in the literature. Also for the semilinear case the problem is at resonance at any eigenvalue.
Energy Technology Data Exchange (ETDEWEB)
Combescure, D.; Sollogoub, P.; Jeanvoine, E.; Politopoulos, I
2000-07-01
Models for the sizing of new structures are more and more reliable. Meanwhile the seismic prediction of an old building is a more complex problem. The non-linear displacements have to be take into account in the sizing codes. The CEA developed assessment methods of these non-linear deformations. This paper presents the different non-linear models, their particularities and two examples of structure analysis. (A.L.B.)
Generalized non-linear strength theory and transformed stress space
Institute of Scientific and Technical Information of China (English)
YAO Yangping; LU Dechun; ZHOU Annan; ZOU Bo
2004-01-01
Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state.
Controlling ultrafast currents by the non-linear photogalvanic effect
Wachter, Georg; Lemell, Christoph; Tong, Xiao-Min; Yabana, Kazuhiro; Burgdörfer, Joachim
2015-01-01
We theoretically investigate the effect of broken inversion symmetry on the generation and control of ultrafast currents in a transparent dielectric (SiO2) by strong femto-second optical laser pulses. Ab-initio simulations based on time-dependent density functional theory predict ultrafast DC currents that can be viewed as a non-linear photogalvanic effect. Most surprisingly, the direction of the current undergoes a sudden reversal above a critical threshold value of laser intensity I_c ~ 3.8*10^13 W/cm2. We trace this switching to the transition from non-linear polarization currents to the tunneling excitation regime. We demonstrate control of the ultrafast currents by the time delay between two laser pulses. We find the ultrafast current control by the non-linear photogalvanic effect to be remarkably robust and insensitive to laser-pulse shape and carrier-envelope phase.
Non-linear behaviour of large-area avalanche photodiodes
Fernandes, L M P; Monteiro, C M B; Santos, J M; Morgado, R E
2002-01-01
The characterisation of photodiodes used as photosensors requires a determination of the number of electron-hole pairs produced by scintillation light. One method involves comparing signals produced by X-ray absorptions occurring directly in the avalanche photodiode with the light signals. When the light is derived from light-emitting diodes in the 400-600 nm range, significant non-linear behaviour is reported. In the present work, we extend the study of the linear behaviour to large-area avalanche photodiodes, of Advanced Photonix, used as photosensors of the vacuum ultraviolet (VUV) scintillation light produced by argon (128 nm) and xenon (173 nm). We observed greater non-linearities in the avalanche photodiodes for the VUV scintillation light than reported previously for visible light, but considerably less than the non-linearities observed in other commercially available avalanche photodiodes.
Pattern formation due to non-linear vortex diffusion
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.
Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.
Non-linear Growth Models in Mplus and SAS.
Grimm, Kevin J; Ram, Nilam
2009-10-01
Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included.
Change-Of-Bases Abstractions for Non-Linear Systems
Sankaranarayanan, Sriram
2012-01-01
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change-of-basis transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction. Furthermore, the techniques developed here apply to continuous systems defined by Ordinary Differential Equations (ODEs), discrete systems defined by transition systems and hybrid systems that combine continuous as well as discrete subsystems. The techniques presented here allow us to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding an alge...
Advances in bio-inspired computing for combinatorial optimization problems
Pintea, Camelia-Mihaela
2013-01-01
Advances in Bio-inspired Combinatorial Optimization Problems' illustrates several recent bio-inspired efficient algorithms for solving NP-hard problems.Theoretical bio-inspired concepts and models, in particular for agents, ants and virtual robots are described. Large-scale optimization problems, for example: the Generalized Traveling Salesman Problem and the Railway Traveling Salesman Problem, are solved and their results are discussed.Some of the main concepts and models described in this book are: inner rule to guide ant search - a recent model in ant optimization, heterogeneous sensitive a
A weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Weak Hamiltonian finite element method for optimal control problems
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Implementation of Travelling Salesman Problem Using ant Colony Optimization
Directory of Open Access Journals (Sweden)
Gaurav Singh,
2014-04-01
Full Text Available Within the Artificial Intelligence community, there is great need for fast and accurate traversal algorithms, specifically those that find a path from a start to goal with minimum cost. Cost can be distance, time, money, energy, etc. Travelling salesman problem (TSP is a combinatorial optimization problem. TSP is the most intensively studied problem in the area of optimization. Ant colony optimization (ACO is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. There have been many efforts in the past to provide time efficient solutions for the problem, both exact and approximate. This paper demonstrates the implementation of TSP using ant colony optimization(ACO.The solution to this problem enjoys wide applicability in a variety of practical fields.TSP in its purest form has several applications such as planning, logistics, and manufacture of microchips, military and traffic.
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
Effects of non-linear rheology on the electrospinning process: a model study
Pontrelli, Giuseppe; Coluzza, Ivan; Pisignano, Dario; Succi, Sauro
2014-01-01
We develop an analytical bead-spring model to investigate the role of non-linear rheology on the dynamics of electrified jets in the early stage of the electrospinning process. Qualitative arguments, parameter studies as well as numerical simulations, show that the elongation of the charged jet filament is significantly reduced in the presence of a non-zero yield stress. This may have beneficial implications for the optimal design of future electrospinning experiments.
Solving semi-infinite optimization problems with interior point techniques
Stein, Oliver; Still, Georg
2003-01-01
We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads
Solving semi-infinite optimization problems with interior point techniques
Stein, Oliver; Still, Georg J.
2003-01-01
We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads
Non-linear growth and condensation in multiplex networks
Nicosia, Vincenzo; Latora, Vito; Barthelemy, Marc
2013-01-01
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of non-linear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of non-linearity these models allow to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed state in which a single node connects to nearly all other nodes of a layer.
Realization of non-linear coherent states by photonic lattices
Directory of Open Access Journals (Sweden)
Shahram Dehdashti
2015-06-01
Full Text Available In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2 and su(1, 1 coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Comparison of Simulated and Measured Non-linear Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the emitting source. The measured pulses are rst compared with the linear...... simulation program Field II, which will be used to generate the source for the AS simulation. The generated non-linear ultrasound eld is measured by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with the AS simulation, which is used to calculate both...
Non-linear effects in bunch compressor of TARLA
Yildiz, Hüseyin; Aksoy, Avni; Arikan, Pervin
2016-03-01
Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects on bunch compressor of TARLA.
Foundations of the non-linear mechanics of continua
Sedov, L I
1966-01-01
International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable
Realization of non-linear coherent states by photonic lattices
Energy Technology Data Exchange (ETDEWEB)
Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn [State Key Laboratory of Modern Optical Instrumentations, Zhejiang University, Hangzhou 310027 (China); The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027 (China); Liu, Jiarui, E-mail: jrliu@zju.edu.cn; Yu, Faxin [School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027 (China)
2015-06-15
In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Non-Linear Stability of an Electrified Plane Interface in Porous Media
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
Degenerate optimization problems and competitiveness of NPPs
Directory of Open Access Journals (Sweden)
A.V. Klimenko
2016-12-01
Since, as it was demonstrated by the performed systems optimization calculations of power generation in Russia, the examined options of NPPs with fast reactors (SVBR-100, BN-1200 (three-circuit, BREST-1200 appeared to be included not into all optimal plans, there is a place for certain doubts that the chosen parameters of the NPPs and the associated nuclear fuel cycles (NFCs are not competitive although strenuous multi-parameter research in this direction is ongoing during already several decades.
Metaheuristic Optimization: Algorithm Analysis and Open Problems
2012-01-01
Metaheuristic algorithms are becoming an important part of modern optimization. A wide range of metaheuristic algorithms have emerged over the last two decades, and many metaheuristics such as particle swarm optimization are becoming increasingly popular. Despite their popularity, mathematical analysis of these algorithms lacks behind. Convergence analysis still remains unsolved for the majority of metaheuristic algorithms, while efficiency analysis is equally challenging. In this paper, we i...
An optimization approach for the satisfiability problem
Directory of Open Access Journals (Sweden)
S. Noureddine
2015-01-01
Full Text Available We describe a new approach for solving the satisfiability problem by geometric programming. We focus on the theoretical background and give details of the algorithmic procedure. The algorithm is provably efficient as geometric programming is in essence a polynomial problem. The correctness of the algorithm is discussed. The version of the satisfiability problem we study is exact satisfiability with only positive variables, which is known to be NP-complete.
一种求解最优控制问题的混合WNN-PSO算法%Hybrid WNN-PSO Algorithm for Optimal Control Problems
Institute of Scientific and Technical Information of China (English)
李树荣; 雷阳; 张强; 张晓东
2013-01-01
To solve optimal control problems with numerical methods, a hybrid wavelet neural network -particle swarm optimization (WNN-PSO) algorithm was developed. The first step of WNN-PSO was to parameterize the optimal control trajectory based on the non-linear approximation capability of the wavelet neural network. Then the optimal control problem was transformed into a non-linear programming problem where the decision variables are the parameters of the wavelet neural network. Lastly, the parameters of the network were optimized by the particle swarm optimization (PSO) algorithm and the global optimal solution of the NLP was obtained. Simulation study on a Bang-Bang optimal control problem and a benchmark chemical process optimal control problem shows the feasibility and effectiveness of the proposed method.%针对最优控制问题的数值求解,提出了一种混合小波神经网络粒子群(WNN-PSO)算法,算法首先利用小波神经网络的非线性逼近能力参数化最优控制轨迹,将最优控制问题转化为非线性规划(NLP)问题,其决策变量为小波神经网络的参数,然后采用粒子群(PSO)算法优化小波神经网络参数,获得NLP问题的全局最优解.针对Bang-Bang最优控制问题和一个经典的化工过程最优控制问题进行仿真研究,验证了所提出算法的可行性和有效性.
Frequency response as a surrogate eigenvalue problem in topology optimization
DEFF Research Database (Denmark)
Andreassen, Erik; Ferrari, Federico; Sigmund, Ole
2017-01-01
This article discusses the use of frequency response surrogates for eigenvalue optimization problems in topology optimization that may be used to avoid solving the eigenvalue problem. The motivation is to avoid complications that arise from multiple eigenvalues and the computational complexity as...
Ant Colony Optimization and the Minimum Cut Problem
DEFF Research Database (Denmark)
Kötzing, Timo; Lehre, Per Kristian; Neumann, Frank
2010-01-01
Ant Colony Optimization (ACO) is a powerful metaheuristic for solving combinatorial optimization problems. With this paper we contribute to the theoretical understanding of this kind of algorithm by investigating the classical minimum cut problem. An ACO algorithm similar to the one that was prov...
Optimization problems for fast AAM fitting in-the-wild
Tzimiropoulos, Georgios; Pantic, Maja
2013-01-01
We describe a very simple framework for deriving the most-well known optimization problems in Active Appearance Models (AAMs), and most importantly for providing efficient solutions. Our formulation results in two optimization problems for fast and exact AAM fitting, and one new algorithm which has
Applications of Fitzpatrick functions for solving optimization problems
Nashed, Z.; Raykov, I.
2012-10-01
This paper presents applications of Fitzparick functions to optimization problems. The main purpose of the present work is to introduce applications of the Fitzpatrick functions, involving their specific properties as the maximal monotonicity, or the proper, convex and lower semi-continuity, for solving optimization problems.
Applications of Fitzpatrick functions for solving optimization problems II
Nashed, Z.; Raykov, I.
2015-10-01
This paper is a continuation of the paper [8] and presents more applications of Fitzpatrick functions for solving optimization problems. The main purpose of the present work is to introduce some new properties of Fitzpatrick functions useful for solving optimization problems, using also their already presented specific properties, as the maximal monotonicity, proper, convex and lower semi-continuity.
Non-Linear Back-propagation: Doing Back-Propagation withoutDerivatives of the Activation Function
DEFF Research Database (Denmark)
Hertz, John; Krogh, Anders Stærmose; Lautrup, Benny
1997-01-01
The conventional linear back-propagation algorithm is replaced by a non-linear version, which avoids the necessity for calculating the derivative of the activation function. This may be exploited in hardware realizations of neural processors. In this paper we derive the non-linear back-propagatio......-propagation algorithms in the framework of recurrent back-propagation and present some numerical simulations of feed-forward networks on the NetTalk problem. A discussion of implementation in analog VLSI electronics concludes the paper.......The conventional linear back-propagation algorithm is replaced by a non-linear version, which avoids the necessity for calculating the derivative of the activation function. This may be exploited in hardware realizations of neural processors. In this paper we derive the non-linear back...
A Non-linear Scaling Algorithm Based on chirp-z Transform for Squint Mode FMCW-SAR
Directory of Open Access Journals (Sweden)
Yu Bin-bin
2012-03-01
Full Text Available A non-linear scaling chirp-z imaging algorithm for squint mode Frequency Modulated Continuous Wave Synthetic Aperture Radar (FMCW-SAR is presented to solve the problem of the focus accuracy decline. Based on the non-linear characteristics in range direction for the echo signal in Doppler domain, a non-linear modulated signal is introduced to perform a non-linear scaling based on chirp-z transform. Then the error due to range compression and range migration correction can be reduced, therefore the range resolution of radar image is improved. By using the imaging algorithm proposed, the imaging performances for point targets, compared with that from the original chirp-z algorithm, are demonstrated to be improved in range resolution and image contrast, and to be maintained the same in azimuth resolution.
Onset and non-linear regimes of Soret-induced convection in binary mixtures heated from above.
Lyubimova, T; Zubova, N; Shevtsova, V
2017-03-01
The paper deals with the investigation of the onset and non-linear regimes of convection of liquid binary mixtures with negative Soret effect heated from above. The linear stability of a convectionless state in a horizontal layer is studied by the numerical solution of the linearized problem on the temporal evolution of small perturbations of the unsteady base state. Non-linear regimes of convection are investigated by the numerical solution of the non-linear unsteady equations for a horizontally elongated rectangular cavity. The calculations are performed for water-ethanol and water-isopropanol liquid mixtures and for colloidal suspensions. The dependences of the instability onset time and wave number of the most dangerous perturbations on the solutal Rayleigh number (gravity level) obtained by a linear stability analysis and non-linear calculations are found to be in a very good agreement. A favorable comparison with the existing experimental and numerical data is presented.
Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem
Chen, Wei
2015-07-01
In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.
Optimal Control Problems for Nonlinear Variational Evolution Inequalities
Directory of Open Access Journals (Sweden)
Eun-Young Ju
2013-01-01
Full Text Available We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.
Optimal Component Lumping: problem formulation and solution techniques
DEFF Research Database (Denmark)
Lin, Bao; Leibovici, Claude F.; Jørgensen, Sten Bay
2008-01-01
to determine the lumping scheme. Given an objective function defined with a linear weighting rule, an optimal lumping problem is formulated as a mixed integer nonlinear programming (MINLP) problem both in discrete and in continuous settings. A reformulation of the original problem is also presented, which...... significantly reduces the number of independent variables. The application to a system with 144 components demonstrates that the optimal lumping problem can be efficiently solved with a stochastic optimization method, Tabu Search (TS) algorithm. The case study also reveals that the discrete formulation...
Implementation of neural network based non-linear predictive control
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1999-01-01
of non-linear systems. GPC is model based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model, a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis...
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found...
Range non-linearities correction in FMCW SAR
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
The limiting factor to the use of Frequency Modulated Continuous Wave (FMCW) technology with Synthetic Aperture Radar (SAR) techniques to produce lightweight, cost effective, low power consuming imaging sensors with high resolution, is the well known presence of non-linearities in the transmitted si
Non-Linear Langmuir Wave Modulation in Collisionless Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1977-01-01
A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially...
Non-Linear Interactive Stories in Computer Games
DEFF Research Database (Denmark)
Bangsø, Olav; Jensen, Ole Guttorm; Kocka, Tomas
2003-01-01
The paper introduces non-linear interactive stories (NOLIST) as a means to generate varied and interesting stories for computer games automatically. We give a compact representation of a NOLIST based on the specification of atomic stories, and show how to build an object-oriented Bayesian network...
Quantum-dot-based integrated non-linear sources
DEFF Research Database (Denmark)
Bernard, Alice; Mariani, Silvia; Andronico, Alessio
2015-01-01
The authors report on the design and the preliminary characterisation of two active non-linear sources in the terahertz and near-infrared range. The former is associated to difference-frequency generation between whispering gallery modes of an AlGaAs microring resonator, whereas the latter is gra...
Note About Hamiltonian Structure of Non-Linear Massive Gravity
Kluson, J
2011-01-01
We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of the second class constraints and hence all non physical degrees of freedom cannot be eliminated.
Locally supersymmetric D=3 non-linear sigma models
Wit, B. de; Tollsten, A. K.; Nicolai, H.
1992-01-01
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it general
Non-linear magnetorheological behaviour of an inverse ferrofluid
de Gans, B.J.; Hoekstra, Hans; Mellema, J.
1999-01-01
The non-linear magnetorheological behaviour is studied of a model system consisting of monodisperse silica particles suspended in a ferrofluid. The stress/strain curve as well as the flow curve was measured as a function of volume fraction silica particles and field strength, using a home-made
On the non-linearity of the subsidiary systems
Friedrich, H
2005-01-01
In hyperbolic reductions of the Einstein equations the evolution of gauge conditions or constraint quantities is controlled by subsidiary systems. We point out a class of non-linearities in these systems which may have the potential of generating catastrophic growth of gauge resp. constraint violations in numerical calculations.
Development and Control of a Non Linear Magnetic Levitation System
Directory of Open Access Journals (Sweden)
A Sanjeevi Gandhi
2013-06-01
Full Text Available Nowadays, studies to develop and control non linear systems is of great significance. Magnetic Levitation System has gained considerable interests due to its great practical importance in different engineering fields In this paper an electromagnetic levitation system was developed and mathematical model for the system was derived. The developed system was controlled manually.
An inhomogeneous wave equation and non-linear Diophantine approximation
DEFF Research Database (Denmark)
Beresnevich, V.; Dodson, M. M.; Kristensen, S.;
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...... is studied. Both the Lebesgue and Hausdorff measures of this set are obtained....
S-AMP for non-linear observation models
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...
Applications of non-linear methods in astronomy
Martens, P.C.H.
1984-01-01
In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such d
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...
OPTIMIZATION OF CAPACITATED VEHICLE ROUTING PROBLEM USING PSO
Directory of Open Access Journals (Sweden)
S.R.VENKATESAN
2011-10-01
Full Text Available This paper presents solution techniques for Capacitated Vehicle Routing Problem (CVRP using metaheuristics. Capacitated Vehicle Routing Problem is divided into set of customers called cluster, and find optimum travel distance of vehicle route. The CVRP is a combinatorial optimization problem; particle swarm optimization(PSO technique is adapted in this paper to solve this problem. The main problem is divided into subprograms/clusters and each subprogram is treated as travelling salesman problem and solved by usingparticle swarm optimization techniques (PSO. This paper presents a sweep, Clark and wright algorithm to form the clusters. This model is then solved by using a particle swarm optimization (PSO method to find optimum travel distance of vehicle route. Our analysis suggests that the proposed model enables users to establish route to serve all given customers with minimum distance of vehicles and maximum capacity.
Unconstrained Optimization Reformulations of Equilibrium Problems
Institute of Scientific and Technical Information of China (English)
Li Ping ZHANG; Ji Ye HAN
2009-01-01
We generalize the D-gap function developed in the literature for variational inequalities to a general equilibrium problem (EP). Through the D-gap function,the equilibrium problem is cast as an unconstrained minimization problem. We give conditions under which any stationary point of the D-gap function is a solution of EP and conditions under which it provides a global error bound for EP. Finally,these results are applied to box-constrained EP and then weaker conditions are established to obtain the desired results for box-constrained EP.
Improved Ant Colony Optimization for Seafood Product Delivery Routing Problem
Directory of Open Access Journals (Sweden)
Baozhen Yao
2014-02-01
Full Text Available This paper deals with a real-life vehicle delivery routing problem, which is a seafood product delivery routing problem. Considering the features of the seafood product delivery routing problem, this paper formulated this problem as a multi-depot open vehicle routing problem. Since the multi-depot open vehicle routing problem is a very complex problem, a method is used to reduce the complexity of the problem by changing the multi-depot open vehicle routing problem into an open vehicle routing problem with a dummy central depot in this paper. Then, ant colony optimization is used to solve the problem. To improve the performance of the algorithm, crossover operation and some adaptive strategies are used. Finally, the computational results for the benchmark problems of the multi-depot vehicle routing problem indicate that the proposed ant colony optimization is an effective method to solve the multi-depot vehicle routing problem. Furthermore, the computation results of the seafood product delivery problem from Dalian, China also suggest that the proposed ant colony optimization is feasible to solve the seafood product delivery routing problem.
Non-linear modal analysis of structural components subjected to unilateral constraints
Attar, M.; Karrech, A.; Regenauer-Lieb, K.
2017-02-01
In this paper, we present a detailed numerical study of the non-linear dynamics in structural components under unilateral contact constraints. Here, the unilateral term characterises the constitutive law of the restoring force in the constraints as they only sustain elastic reactions in one direction, either compressive or tensile. Thus, the non-differentiability of the contact law at the discontinuity point is the only source of non-linearity. In our approach, the discrete lattice method (DLM) is used to treat the continuous system as a piecewise linear model. Thus, the trajectory of each node in the discrete model would be a sequence of smooth solutions with the switching times between them. The application of the one-step integration scheme allows us to detect the occurrence of contact (i.e. the instants that the lattice nodes cross the discontinuity boundary) and consequently update the active constraints. We also consider embedding the bisection algorithm into the time integration procedure to localise the instants at which the nodes cross the boundary and minimise the accumulative error. Subsequently, the resulting unconditionally stable integration scheme is utilised as the modelling tool in combination with the shooting technique to perform a novel non-smooth modal analysis. In analogy with the smooth non-linear systems, the evolution of non-smooth periodic motions is presented in the frequency-stiffness plots. We apply our method to obtain non-linear normal modes (NNMs) for a number of representative problems, including a bar-obstacle system, a beam-substrate system and a granular chain with tensionless interactions. These numerical examples demonstrate the efficiency of the solution procedure to trace the family of energy-independent non-linear modes across the range of contact stiffnesses. Moreover, the stability analysis of the modes on the plot backbone reveal that they may become unstable due to the interaction with the higher modes or bifurcation of
Non-linear Elasticity and Monitoring of Stress in the Focus of an Earthquake
Bakulin, V.; Bakulin, A.
2001-05-01
Non-linear elasticity proved to give comprehensive framework for relating seismic velocities in rocks to stress. This powerful theory allows attacking the problem of estimating stress state at the focus of earthquakes. Such idea has been proposed long time ago [Kostrov and Nikitin, 1968] however its implementation requires a-priori knowledge of non-linear rock properties. Three non-linear constants needed to describe variation of any velocity with stress are typically estimated from core measurements [Bakulin et al., 2000]. More reliable estimates can be obtained from multi-mode inversions of borehole acoustic data [Sinha, 1996]. Nevertheless database of non-linear formation constants is still very limited. More measurements are required to estimate non-linear rock properties on larger scale and with independent stress constraints. Such measurements can be done in mines [Bakulin and Bakulin, 1999] or in hydrocarbon reservoirs where time-dependent pressure measurements are available. Without knowledge of non-linear rock properties seismic waves can still bring information about directions of tectonic stresses. In particular, shear wave polarizations can deliver directions of principal stresses in the focus of an earthquake, provided the overburden effects were removed. If rock non-linear properties are independently derived then estimation of stress magnitudes becomes feasible. Such techniques were applied in mining environment [Bakulin and Bakulin, 1999]. They may become routine for monitoring stress state in the focus of earthquakes and therefore can be used for forecasting the seismic activity. Bakulin, A. V., Troyan, V. N., and Bakulin, V. N., 2000, Acoustoelasticity of rocks, St. Petersburg (in Russian). Bakulin, V. and Bakulin, A., 1999, Acoustopolarizational method of measuring stress in rock mass and determination of Murnaghan constants: 69th Annual Internat. Mtg., Soc. Expl. Geophys., 1971-1974. Kostrov, B.V., and Nikitin, L.V., 1968, Influence of initial
Moments of random sums and Robbins' problem of optimal stopping
Gnedin, Alexander
2011-01-01
Robbins' problem of optimal stopping asks one to minimise the expected {\\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\\it value} of the stopped variable under the rule optimal in the sense of the rank, by embedding the problem in a much more general context of selection problems with the nonanticipation constraint lifted, and with the payoff growing like a power function of the rank.
Remarks on a benchmark nonlinear constrained optimization problem
Institute of Scientific and Technical Information of China (English)
Luo Yazhong; Lei Yongjun; Tang Guojin
2006-01-01
Remarks on a benchmark nonlinear constrained optimization problem are made. Due to a citation error, two absolutely different results for the benchmark problem are obtained by independent researchers. Parallel simulated annealing using simplex method is employed in our study to solve the benchmark nonlinear constrained problem with mistaken formula and the best-known solution is obtained, whose optimality is testified by the Kuhn-Tucker conditions.
Superdiffusions and positive solutions of non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Dynkin, E B [Cornell University, New York (United States)
2004-02-28
By using super-Brownian motion, all positive solutions of the non-linear differential equation {delta}u=u{sup {alpha}} with 1<{alpha}{<=}2 in a bounded smooth domain E are characterized by their (fine) traces on the boundary. This solves a problem posed by the author a few years ago. The special case {alpha}=2 was treated by B. Mselati in 2002.
Optimization Problems in Supply Chain Management
D. Romero Morales (Dolores)
2000-01-01
textabstractMaria Dolores Romero Morales was born on Augustus 5th, 1971, in Sevilla (Spain). She studied Mathematics at University of Sevilla from 1989 to 1994 and specialized in Statistics and Operations Research. She wrote her Master's thesis on Global Optimization in Location Theory under the sup
Problem optimalnih kartografskih projekcija : Problem of the optimal cartographic projections
Directory of Open Access Journals (Sweden)
Krešimir Frankić
2014-12-01
Full Text Available Kartografske projekcije primjenjuju se za grafičko prikazivanje teritorija u sitnom mjerilu. Pravilnim izborom projekcije smanjuju se deformacije prikazanog teritorija, koji je omeđen graničnom linijom. U većini slučajeva ta granična linija nije neka matematički definirana krivulja, koja se najlakše prikazuje u obliku zatvorenog poligona. Optimalne kartografske projekcije, slijedeći neki definirani kriterij, trebale bi utvrditi konstante projekcije s najmanjim mogućim deformacijama. Airy-Kavrajski kriterij vodi direktno do optimizacije Euklidske norme, a to znači do metode najmanjih kvadrata. Brzi moderni kompjutori omogućuju jednostavnu optimizaciju bilo koje analitički definirane projekcije za teritorije čija granica se aproksimira konačnim nizom individualnih točaka. : Cartographic projections are basis for the graphical representation of various territories in small scale mapping. Proper selection of projection reduces the deformation of the presented territory, which is bounded by a boundary line. In most cases, this border line is not a mathematically defined curve, which is most easily displayed in the form of a closed polygon. The optimal cartographic projections based on a selected criterion of quality are those whose constants lead to the smallest value of the criterion. In the presented work it is recommended to use Airy-Kavrajski criterion whose minimization is actually minimization of the second Euclidean norm. The solution of optimal projections of various classes is reduced to the method of least squares. Fast modern computers enable the optimization of an arbitrary territory by evaluating the selected criterion in a finite number of points.
Fuzzy optimization of primal-dual pair using piecewise linear membership functions
Directory of Open Access Journals (Sweden)
Pandey D.
2012-01-01
Full Text Available Present paper improves the model of Bector and Chandra [Fuzzy Sets and Systems, 125 (2002 317-325] on duality in fuzzy linear programming by using non-linear membership functions. Numerical problem discussed by these authors has also been worked out through our non-linear model to demonstrate improved optimality of the results.
Improved extremal optimization for the asymmetric traveling salesman problem
Chen, Yu-Wang; Zhu, Yao-Jia; Yang, Gen-Ke; Lu, Yong-Zai
2011-11-01
This paper presents an improved extremal optimization (IEO) algorithm for solving the asymmetric traveling salesman problem (ATSP). At each update step, the IEO algorithm proceeds through two main steps: extremal dynamics and cooperative optimization. As an improvement of extremal optimization (EO), the IEO provides a general combinatorial optimization framework by emphasizing the step of cooperative optimization. In the paper, an effective cooperative optimization strategy with combination of greedy search and random walk is designed in terms of the microscopic characteristics of the ATSP solutions. Simulation results on a set of benchmark ATSP instances show that the proposed IEO algorithm provides satisfactory performance on computational effectiveness and efficiency.
Stochastic non-linear oscillator models of EEG: the Alzheimer's disease case
Ghorbanian, Parham; Ramakrishnan, Subramanian; Ashrafiuon, Hashem
2015-01-01
In this article, the Electroencephalography (EEG) signal of the human brain is modeled as the output of stochastic non-linear coupled oscillator networks. It is shown that EEG signals recorded under different brain states in healthy as well as Alzheimer's disease (AD) patients may be understood as distinct, statistically significant realizations of the model. EEG signals recorded during resting eyes-open (EO) and eyes-closed (EC) resting conditions in a pilot study with AD patients and age-matched healthy control subjects (CTL) are employed. An optimization scheme is then utilized to match the output of the stochastic Duffing—van der Pol double oscillator network with EEG signals recorded during each condition for AD and CTL subjects by selecting the model physical parameters and noise intensity. The selected signal characteristics are power spectral densities in major brain frequency bands Shannon and sample entropies. These measures allow matching of linear time varying frequency content as well as non-linear signal information content and complexity. The main finding of the work is that statistically significant unique models represent the EC and EO conditions for both CTL and AD subjects. However, it is also shown that the inclusion of sample entropy in the optimization process, to match the complexity of the EEG signal, enhances the stochastic non-linear oscillator model performance. PMID:25964756
Optimal control problems related to the navigation channel engineering
Institute of Scientific and Technical Information of China (English)
朱江; 曾庆存; 郭冬建; 刘卓
1997-01-01
The navigation channel engineering poses optimal control problems of how to find the optimal way of engineering such that the water depth of the channel is maximum under certain budget constraint, or the cost of me en-gineering is minimum while certain goals are achieved. These are typical control problems of distributed system gov erned by hydraulic/sedimentation models. The problems and methods of solutions are discussed Since the models, usually complicated, are nonlinear, they can be solved by solving a series of linear problems For linear problems the solutions are given. Thus the algorithms are simplified.
[Radiation dose reduction using a non-linear image filter in MDCT].
Nakashima, Junya; Takahashi, Toshiyuki; Takahashi, Yoshimasa; Imai, Yasuhiro; Ishihara, Yotaro; Kato, Kyoichi; Nakazawa, Yasuo
2010-05-20
The development of MDCT enabled various high-quality 3D imaging and optimized scan timing with contrast injection in a multi-phase dynamic study. Since radiation dose tends to increase to yield such high-quality images, we have to make an effort to reduce radiation dose. A non-linear image filter (Neuro 3D filter: N3D filter) has been developed in order to improve image noise. The purpose of this study was to evaluate the physical performance and effectiveness of this non-linear image filter using phantoms, and show how we can reduce radiation dose in clinical use of this filter. This N3D filter reduced radiation dose by about 50%, with minimum deterioration of spatial reduction in phantom and clinical studies. This filter shows great potential for clinical application.
Topology optimization problems with design-dependent sets of constraints
DEFF Research Database (Denmark)
Schou, Marie-Louise Højlund
Topology optimization is a design tool which is used in numerous fields. It can be used whenever the design is driven by weight and strength considerations. The basic concept of topology optimization is the interpretation of partial differential equation coefficients as effective material...... properties and designing through changing these coefficients. For example, consider a continuous structure. Then the basic concept is to represent this structure by small pieces of material that are coinciding with the elements of a finite element model of the structure. This thesis treats stress constrained...... structural topology optimization problems. For such problems a stress constraint for an element should only be present in the optimization problem when the structural design variable corresponding to this element has a value greater than zero. We model the stress constrained topology optimization problem...
The Uniqueness of Optimal Solution for Linear Programming Problem
Institute of Scientific and Technical Information of China (English)
QuanlingWei; HongYan; JunWang
2004-01-01
This paper investigates an old problem in operations research, the uniqueness of the optimal solution to a linear programming problem. We discuss the problem on a general polyhedron, give some equivalent conditions for uniqueness testing. In addition, we discuss the implementation issues for linear programming based decision making procedures,which motivated this research.
Portfolio optimization and the random magnet problem
Rosenow, B.; Plerou, V.; Gopikrishnan, P.; Stanley, H. E.
2002-08-01
Diversification of an investment into independently fluctuating assets reduces its risk. In reality, movements of assets are mutually correlated and therefore knowledge of cross-correlations among asset price movements are of great importance. Our results support the possibility that the problem of finding an investment in stocks which exposes invested funds to a minimum level of risk is analogous to the problem of finding the magnetization of a random magnet. The interactions for this "random magnet problem" are given by the cross-correlation matrix C of stock returns. We find that random matrix theory allows us to make an estimate for C which outperforms the standard estimate in terms of constructing an investment which carries a minimum level of risk.
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems
Vázquez, Luis
2013-01-01
Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems explores how Newton's equation for the motion of one particle in classical mechanics combined with finite difference methods allows creation of a mechanical scenario to solve basic problems in linear algebra and programming. The authors present a novel, unified numerical and mechanical approach and an important analysis method of optimization. This book also: Presents mechanical method for determining matrix singularity or non-independence of dimension and complexity Illustrates novel mathematical applications of classical Newton’s law Offers a new approach and insight to basic, standard problems Includes numerous examples and applications Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems is an ideal book for undergraduate and graduate students as well as researchers interested in linear problems and optimization, and nonlinear dynamics.
Optimality conditions for the numerical solution of optimization problems with PDE constraints :
Energy Technology Data Exchange (ETDEWEB)
Aguilo Valentin, Miguel Alejandro; Ridzal, Denis
2014-03-01
A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.
Constraint Optimization for Highly Constrained Logistic Problems
DEFF Research Database (Denmark)
Mochnacs, Maria Kinga; Tanaka, Meang Akira; Nyborg, Anders
This report investigates whether propagators combined with branch and bound algorithm are suitable for solving the storage area stowage problem within reasonable time. The approach has not been attempted before and experiments show that the implementation was not capable of solving the storage ar...
Kumar, P; Kumar, Dinesh; Rai, K N
2016-08-01
In this article, a non-linear dual-phase-lag (DPL) bio-heat transfer model based on temperature dependent metabolic heat generation rate is derived to analyze the heat transfer phenomena in living tissues during thermal ablation treatment. The numerical solution of the present non-linear problem has been done by finite element Runge-Kutta (4,5) method which combines the essence of Runge-Kutta (4,5) method together with finite difference scheme. Our study demonstrates that at the thermal ablation position temperature predicted by non-linear and linear DPL models show significant differences. A comparison has been made among non-linear DPL, thermal wave and Pennes model and it has been found that non-linear DPL and thermal wave bio-heat model show almost same nature whereas non-linear Pennes model shows significantly different temperature profile at the initial stage of thermal ablation treatment. The effect of Fourier number and Vernotte number (relaxation Fourier number) on temperature profile in presence and absence of externally applied heat source has been studied in detail and it has been observed that the presence of externally applied heat source term highly affects the efficiency of thermal treatment method.
Present-day Problems and Methods of Optimization in Mechatronics
Directory of Open Access Journals (Sweden)
Tarnowski Wojciech
2017-06-01
Full Text Available It is justified that design is an inverse problem, and the optimization is a paradigm. Classes of design problems are proposed and typical obstacles are recognized. Peculiarities of the mechatronic designing are specified as a proof of a particle importance of optimization in the mechatronic design. Two main obstacles of optimization are discussed: a complexity of mathematical models and an uncertainty of the value system, in concrete case. Then a set of non-standard approaches and methods are presented and discussed, illustrated by examples: a fuzzy description, a constraint-based iterative optimization, AHP ranking method and a few MADM functions in Matlab.
Optimization and optimality test for the Max-Cut Problem
Hohmann, Chr.; Kern, Walter
1990-01-01
We show that the following two problems are polynomially equivalent: 1. Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not. 2. Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not, and in case it is not, find a better solutionC′. As a consequence, an
Finite Volumes Discretization of Topology Optimization Problems
DEFF Research Database (Denmark)
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
such a mature and versatile technique for discretiz- ing partial dierential equations in the form of conservation laws of varying types. Advantages of FVMs include the simplicity of implementation, their local conservation properties, and the ease of coupling various PDEs in a multi-physics setting. In fact...... attractive, as all involved PDEs on a given domain are discretized using the same and the low- est possible number of degrees of freedom. In spite of their numerous favourable advantages, FVMs have seen very little adoption within the topology optimization community, where the absolute majority of numerical...
Checking for Optimal Solutions in Some NP-Complete Problems
Bauer, Michel; Orland, Henri
2005-09-01
For some weighted NP-complete problems, checking whether a proposed solution is optimal is a nontrivial task. Such is the case for the traveling salesman problem, or the spin-glass problem in three dimensions. In this Letter, we consider the weighted tripartite matching problem, a well known NP-complete problem. We write mean-field finite temperature equations for this model and derive their zero temperature limit. We show that any solution of the zero temperature equations provides an exact absolute ground state of the system. As a consequence, we propose a criterion which can be checked in polynomial time, and such that given a putative optimal solution, if the criterion is satisfied, then the solution is indeed optimal. This criterion is generalized to a class of variants of the multiple traveling salesmen problems.
OPTIMIZATION PROBLEMS ON SUBURBAN TRANSPORT SYSTEMS
T. M. Grigorovа
2015-01-01
The paper considers problems that permit to solve such issue as organization of transport service for suburban population with due account of passenger transport fatigue which is considered as one of subconscious criteria for selection of a travel mode. Improvement of transportation process entails an increase in demand for such service. Demands predetermine transport supply and situation on the market depends on supply-and-demand balance. The paper presents an analysis of approaches to the...
Optimal Opinion Control: The Campaign Problem
2015-01-01
Opinion dynamics is nowadays a very common field of research. In this article we formulate and then study a novel, namely strategic perspective on such dynamics: There are the usual normal agents that update their opinions, for instance according the well-known bounded confidence mechanism. But, additionally, there is at least one strategic agent. That agent uses opinions as freely selectable strategies to get control on the dynamics: The strategic agent of our benchmark problem tries, during...
Optimization problems related to zigzag pocket machining
Energy Technology Data Exchange (ETDEWEB)
Arkin, E.M.; Held, M.; Smith, C.L. [State Univ. of New York, Stony Brook, NY (United States)
1996-12-31
A fundamental problem of manufacturing is to produce mechanical parts from billets by clearing areas within specified boundaries from the material. Based on a graph-theoretical formulation, the algorithmic handling of one particular machining problem {open_quote}zigzag pocket machining{close_quote} is investigated. We present a linear-time algorithm that ensures that no region of the pocket is machined repeatedly, thereby attempting to minimize the number of tool retractions required. This problem is shown to be NP-hard for pockets with holes. Our algorithm is a provable good in the sense that the machining path generated for a pocket with h holes requires at most 5. OPT+ 6 - h retractions, where OPT is the (unknown) minimum number of retractions required by any algorithm. The algorithm has been implemented, and practical tests for pockets without holes clearly showed that one can expect an approximation factor of about 1.5 for practical examples, rather than the factor 5 as proved by our analysis.
Non-linear effects for cylindrical gravitational two-soliton
Tomizawa, Shinya
2015-01-01
Using a cylindrical soliton solution to the four-dimensional vacuum Einstein equation, we study non-linear effects of gravitational waves such as Faraday rotation and time shift phenomenon. In the previous work, we analyzed the single-soliton solution constructed by the Pomeransky's improved inverse scattering method. In this work, we construct a new two-soliton solution with complex conjugate poles, by which we can avoid light-cone singularities unavoidable in a single soliton case. In particular, we compute amplitudes of such non-linear gravitational waves and time-dependence of the polarizations. Furthermore, we consider the time shift phenomenon for soliton waves, which means that a wave packet can propagate at slower velocity than light.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Directory of Open Access Journals (Sweden)
Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Non-linear irreversible thermodynamics of single-molecule experiments
Santamaria-Holek, I; Hidalgo-Soria, M; Perez-Madrid, A
2015-01-01
Irreversible thermodynamics of single-molecule experiments subject to external constraining forces of a mechanical nature is presented. Extending Onsager's formalism to the non-linear case of systems under non-equilibrium external constraints, we are able to calculate the entropy production and the general non-linear kinetic equations for the variables involved. In particular, we analyze the case of RNA stretching protocols obtaining critical oscillations between di?erent con?gurational states when forced by external means to remain in the unstable region of its free-energy landscape, as observed in experiments. We also calculate the entropy produced during these hopping events, and show how resonant phenomena in stretching experiments of single RNA macromolecules may arise. We also calculate the hopping rates using Kramer's approach obtaining a good comparison with experiments.
The linear-non-linear frontier for the Goldstone Higgs
Gavela, M B; Machado, P A N; Saa, S
2016-01-01
The minimal $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $\\sigma$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic compl...
SSNN toolbox for non-linear system identification
Luzar, Marcel; Czajkowski, Andrzej
2015-11-01
The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.
A non-linear model of economic production processes
Ponzi, A.; Yasutomi, A.; Kaneko, K.
2003-06-01
We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.
Integration of non-linear cellular mechanisms regulating microvascular perfusion.
Griffith, T M; Edwards, D H
1999-01-01
It is becoming increasingly evident that interactions between the different cell types present in the vessel wall and the physical forces that result from blood flow are highly complex. This short article will review evidence that irregular fluctuations in vascular resistance are generated by non-linearity in the control mechanisms intrinsic to the smooth muscle cell and can be classified as chaotic. Non-linear systems theory has provided insights into the mechanisms involved at the cellular level by allowing the identification of dominant control variables and the construction of one-dimensional iterative maps to model vascular dynamics. Experiments with novel peptide inhibitors of gap junctions have shown that the coordination of aggregate responses depends on direct intercellular communication. The sensitivity of chaotic trajectories to perturbation may nevertheless generate a high degree of variability in the response to pharmacological interventions and altered perfusion conditions.
Parametric Analysis of Fiber Non-Linearity in Optical systems
Directory of Open Access Journals (Sweden)
Abhishek Anand
2013-06-01
Full Text Available With the advent of technology Wavelength Division Multiplexing (WDM is always an area of interest in the field of optical communication. When combined with Erbium Doped Fiber Amplifier (EDFA, it provides high data transmission rate and low attenuation. But due to fiber non-linearity such as Self Phase Modulation (SPM and Cross Phase Modulation (XPM the system performance has degraded. This non-linearity depends on different parameters of an optical system such as channel spacing, power of the channel and length of the fiber section. The degradation can be seen in terms of phase deviation and Bit Error Rate (BER performance. Even after dispersion compensation at the fiber end, residual pulse broadening still exists due to cross talk penalty.
Non-linear Behavior of Curved Sandwich Panels
DEFF Research Database (Denmark)
Berggreen, Carl Christian; Jolma, P.; Karjalainen, J. P.;
2003-01-01
In this paper the non-linear behavior of curved sandwich panels is investigated both numerically and experimentally. Focus is on various aspects of finite element modeling and calculation procedures. A simply supported, singly curved, CFRP/PVC sandwich panel is analyzed under uniform pressure load...... and results are compared to test data. A novel test arrangement utilizing a water filled cushion to create the uniform pressure load on curved panel specimen is used to obtain the experimental data. The panel is modeled with three different commercial finite element codes. Two implicit and one explicit code...... are used with various element types, modeling approaches and material models. The results show that the theoretical and experimental methods generally show fair agreement in panel non-linear behavior before collapse. It is also shown that special attention to detail has to be taken, because the predicted...
Non-Linear Aeroelastic Stability of Wind Turbines
DEFF Research Database (Denmark)
Zhang, Zili; Sichani, Mahdi Teimouri; Li, Jie;
2013-01-01
As wind turbines increase in magnitude without a proportional increase in stiffness, the risk of dynamic instability is believed to increase. Wind turbines are time dependent systems due to the coupling between degrees of freedom defined in the fixed and moving frames of reference, which may...... trigger off internal resonances. Further, the rotational speed of the rotor is not constant due to the stochastic turbulence, which may also influence the stability. In this paper, a robust measure of the dynamic stability of wind turbines is suggested, which takes the collective blade pitch control...... and non-linear aero-elasticity into consideration. The stability of the wind turbine is determined by the maximum Lyapunov exponent of the system, which is operated directly on the non-linear state vector differential equations. Numerical examples show that this approach is promising for stability...
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)
2013-09-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Gradient Gene Algorithm: a Fast Optimization Method to MST Problem
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The extension of Minimum Spanning Tree(MST) problem is an NP hardproblem which does not exit a polynomial time algorithm. In this paper, a fast optimizat ion method on MST problem--the Gradient Gene Algorithm is introduced. Compar ed with other evolutionary algorithms on MST problem, it is more advanced: firstly, very simple and easy to realize; then, efficient and accurate; finally general on other combination optimization problems.
Comparison of optimal design methods in inverse problems
Banks, H. T.; Holm, K.; Kappel, F.
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem....
Measuring the Non-Linear Effects of Monetary Policy
Christian Matthes; Regis Barnichon
2015-01-01
This paper proposes a method to identify the non-linear effects of structural shocks by using Gaussian basis functions to parametrize impulse response functions. We apply our approach to monetary policy and find that the effect of a monetary intervention depends strongly on (i) the sign of the intervention, (ii) the size of the intervention, and (iii) the state of the business cycle at the time of the intervention. A contractionary policy has a strong adverse effect on output, much stronger t...
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France); University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Markou, Chrysoula [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France)
2015-12-15
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R - λ){sup 2} = 0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories. (orig.)
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios, E-mail: antoniad@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France); Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlestrasse 5, 3012, Bern (Switzerland); Markou, Chrysoula, E-mail: chrysoula@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France)
2015-12-09
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R-λ){sup 2}=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.
Non-linear high-frequency waves in the magnetosphere
Indian Academy of Sciences (India)
S Moolla; R Bharuthram; S V Singh; G S Lakhina
2003-12-01
Using ﬂuid theory, a set of equations is derived for non-linear high-frequency waves propagating oblique to an external magnetic ﬁeld in a three-component plasma consisting of hot electrons, cold electrons and cold ions. For parameters typical of the Earth’s magnetosphere, numerical solutions of the governing equations yield sinusoidal, sawtooth or bipolar wave-forms for the electric ﬁeld.
Likelihood inference for discretely observed non-linear diffusions
1998-01-01
This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis-Hastings algorithm, in conjunction with the Euler-Maruyama discretization scheme, are used to sample the posterior distribution of the lat...
Non-linear dark matter collapse under diffusion
Velten, Hermano E S
2014-01-01
Diffusion is one of the physical processes allowed for describing the large scale dark matter dynamics. At the same time, it can be seen as a possible mechanism behind the interacting cosmologies. We study the non-linear spherical "top-hat" collapse of dark matter which undergoes velocity diffusion into a solvent dark energy field. We show constraints on the maximum magnitude allowed for the dark matter diffusion. Our results reinforce previous analysis concerning the linear perturbation theory.
On the non-linear stability of scalar field cosmologies
Energy Technology Data Exchange (ETDEWEB)
Alho, Artur; Mena, Filipe C [Centro de Matematica, Universidade do Minho, 4710-057 Braga (Portugal); Kroon, Juan A Valiente, E-mail: aalho@math.uminho.pt, E-mail: fmena@math.uminho.pt, E-mail: jav@maths.qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
2011-09-22
We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.
Non-linear Higgs portal to Dark Matter
Bajo, Rocío del Rey
2016-01-01
The Higgs portal to scalar Dark Matter is considered in the context of non-linearly realised electroweak symmetry breaking. We determine the interactions of gauge bosons and the physical Higgs particle $h$ to a scalar singlet Dark Matter candidate $S$ in an effective description. The main phenomenological differences with respect to the standard scenario can be seen in the Dark Matter relic abundance, in direct/indirect searches and in signals at colliders.
Topology Optimization of Large Scale Stokes Flow Problems
DEFF Research Database (Denmark)
Aage, Niels; Poulsen, Thomas Harpsøe; Gersborg-Hansen, Allan
2008-01-01
This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs.......This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs....
Non-linear HRV indices under autonomic nervous system blockade.
Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel
2014-01-01
Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.
Non-linear polaronic conduction in magnetite nanowires
Energy Technology Data Exchange (ETDEWEB)
Singh, Pooja, E-mail: pooja7503@gmail.com [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Rout, P.K., E-mail: pkrout.phy@gmail.com [National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Husale, Sudhir; Gupta, Anurag [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Singh, Manju [National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Rakshit, R.K. [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Dogra, Anjana, E-mail: anjanad@nplindia.org [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India)
2016-12-01
We report the temperature dependent current (I) – voltage (V) characteristics of Fe{sub 3}O{sub 4} nanowires with varying width (w) of 132, 358, and 709 nm. While the widest nanowire (w=709 nm) shows ohmic I (V) curves for all temperatures, those for w=132 and 358 nm show nonlinearity, which can be expressed by a combination of linear (V) and cubic (V{sup 3}) terms. The behaviour of conductance (linear bias component of current) and non-linearity in these nanowires is related to small polaron hopping related conduction. Moreover, we observed an anomalously large hopping lengths, which may be related to the size of percolation cluster and/or antiphase domain. Our study presents first experimental evidence for such non-linear polaronic conduction in magnetite nanowires. - Highlights: • Temperature dependent I–V measurements of FIB fabricated magnetite nanowires. • Small polaron based conduction in non-linear I–V curves. • Anomalously large hopping lengths due to percolation effect and/or antiphase domains.
Non-linear Q-clouds around Kerr black holes
Directory of Open Access Journals (Sweden)
Carlos Herdeiro
2014-12-01
Full Text Available Q-balls are regular extended ‘objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.
Fitting and forecasting non-linear coupled dark energy
Casas, Santiago; Baldi, Marco; Pettorino, Valeria; Vollmer, Adrian
2015-01-01
We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range $z=0-1.6$ and wave modes below $k=10 \\text{h/Mpc}$. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and w...
Generalized Ghost Dark Energy with Non-Linear Interaction
Ebrahimi, E; Mehrabi, A; Movahed, S M S
2016-01-01
In this paper we investigate ghost dark energy model in the presence of non-linear interaction between dark energy and dark matter. The functional form of dark energy density in the generalized ghost dark energy (GGDE) model is $\\rho_D\\equiv f(H, H^2)$ with coefficient of $H^2$ represented by $\\zeta$ and the model contains three free parameters as $\\Omega_D, \\zeta$ and $b^2$ (the coupling coefficient of interactions). We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state, deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model. To compare the interacting GGDE model with observational data sets, we use more recent observational outcomes, namely SNIa, gamma-ray bursts, baryonic acoustic oscillation and the most relevant CMB parameters including, the position of acoustic peaks, shift parameters and redshift to recombination. For GGDE with the first non-linear interaction, the j...
Testing non-linear vacuum electrodynamics with Michelson interferometry
Schellstede, Gerold O; Lämmerzahl, Claus
2015-01-01
We discuss the theoretical foundations for testing non-linear vacuum electrodynamics with Michelson interferometry. Apart from some non-degeneracy conditions to be imposed, our discussion applies to all non-linear electrodynamical theories of the Pleba\\'nski class, i.e., to all Lagrangians that depend only on the two Lorentz-invariant scalars quadratic in the field strength. The main idea of the experiment proposed here is to use the fact that, according to non-linear electrodynamics, the phase velocity of light should depend on the strength and on the direction of an electromagnetic background field. There are two possible experimental set-ups for testing this prediction with Michelson interferometry. The first possibility is to apply a strong electromagnetic field to the beam in one arm of the interferometer and to compare the situation where the field is switched on with the situation where it is switched off. The second possibility is to place the whole interferometer in a strong electromagnetic field and...
Fabrication and characterization of non-linear parabolic microporous membranes.
Rajasekaran, Pradeep Ramiah; Sharifi, Payam; Wolff, Justin; Kohli, Punit
2015-01-01
Large scale fabrication of non-linear microporous membranes is of technological importance in many applications ranging from separation to microfluidics. However, their fabrication using traditional techniques is limited in scope. We report on fabrication and characterization of non-linear parabolic micropores (PMS) in polymer membranes by utilizing flow properties of fluids. The shape of the fabricated PMS corroborated well with simplified Navier-Stokes equation describing parabolic relationship of the form L - t(1/2). Here, L is a measure of the diameter of the fabricated micropores during flow time (t). The surface of PMS is smooth due to fluid surface tension at fluid-air interface. We demonstrate fabrication of PMS using curable polydimethylsiloxane (PDMS). The parabolic shape of micropores was a result of interplay between horizontal and vertical fluid movements due to capillary, viscoelastic, and gravitational forces. We also demonstrate fabrication of asymmetric "off-centered PMS" and an array of PMS membranes using this simple fabrication technique. PMS containing membranes with nanoscale dimensions are also possible by controlling the experimental conditions. The present method provides a simple, easy to adopt, and energy efficient way for fabricating non-linear parabolic shape pores at microscale. The prepared parabolic membranes may find applications in many areas including separation, parabolic optics, micro-nozzles / -valves / -pumps, and microfluidic and microelectronic delivery systems.
Topology optimization of 3D Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan
to different flow problems. However, this research has focused on 2D fluid modelling, which limits the practical impact of the computed designs. The explanation of the limitation is that the finite size domain used in topology optimization problems ensures that the velocity components couples, even for Stokes......Topology optimization has been applied to a multitude of physical systems and is now a mature technology used in industrial practice, see [1] for an overview. Borrvall and Petersson [2] introduced topology optimization of Stokes flow problems which initiated works on extending topology optimization...... flow [3]. Furthermore, it is questionable if such a coupling can be captured by a 2D model especially in non-trivial geometries as typically seen in topology design. This statement is widely accepted in the fluid mechanics community, i.e. that planar fluid models are useful for academic test problems...
Topology optimization of vibration and wave propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2007-01-01
The method of topology optimization is a versatile method to determine optimal material layouts in mechanical structures. The method relies on, in principle, unlimited design freedom that can be used to design materials, structures and devices with significantly improved performance and sometimes...... novel functionality. This paper addresses basic issues in simulation and topology design of vibration and wave propagation problems. Steady-state and transient wave propagation problems are addressed and application examples for both cases are presented....
Modified constrained differential evolution for solving nonlinear global optimization problems
2013-01-01
Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolut...
Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems
Zuliang Lu
2011-01-01
We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element ...
Existence and approximation results for shape optimization problems in rotordynamics
Strauß, Frank; Heuveline, Vincent; Schweizer, Ben
2006-01-01
We consider a shape optimization problem in rotordynamics where the mass of a rotor is minimized subject to constraints on the natural frequencies. Our analysis is based on a class of rotors described by a Rayleigh beam model including effects of rotary inertia and gyroscopic moments. The solution of the equation of motion leads to a generalized eigenvalue problem. The governing operators are non-symmetric due to the gyroscopic terms. We prove the existence of solutions for the optimization p...
Fuzzy Inspired Hybrid Genetic Approach to Optimize Travelling Salesman Problem
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Bindu
2012-06-01
Full Text Available One of the category of algorithm Problems are basically exponential problems. These problems are basically exponential problems and take time to find the solution. In the present work we are optimising one of the common NP complete problem called Travelling Salesman Problem. In our work we have defined a genetic approach by combining fuzzy approach along with genetics. In this work we have implemented the modified DPX crossover to improve genetic approach. The work is implemented in MATLAB environment and obtained results shows the define approach has optimized the existing genetic algorithm results
CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
WU Zhiyou; ZHANG Liansheng; BAI Fusheng; YANG Xinmin
2004-01-01
In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function,then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. Programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C. Programming problem using the existing algorithms about them.
Issues related to topology optimization of snap-through problems
DEFF Research Database (Denmark)
Lindgaard, Esben; Dahl, Jonas
2012-01-01
This work focuses on issues related to topology optimization of static geometrically nonlinear structures experiencing snap-through behaviour. Different compliance and buckling criterion functions are studied and applied to topology optimization of a point loaded curved beam problem with the aim ...
A Decision Support System for Solving Multiple Criteria Optimization Problems
Filatovas, Ernestas; Kurasova, Olga
2011-01-01
In this paper, multiple criteria optimization has been investigated. A new decision support system (DSS) has been developed for interactive solving of multiple criteria optimization problems (MOPs). The weighted-sum (WS) approach is implemented to solve the MOPs. The MOPs are solved by selecting different weight coefficient values for the criteria…
Comments on `A discrete optimal control problem for descriptor systems'
DEFF Research Database (Denmark)
Ravn, Hans
1990-01-01
In the above-mentioned work (see ibid., vol.34, p.177-81 (1989)), necessary and sufficient optimality conditions are derived for a discrete-time optimal problem, as well as other specific cases of implicit and explicit dynamic systems. The commenter corrects a mistake and demonstrates that there ...
Topology optimization problems for reflection and dissipation of elastic waves
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2007-01-01
This paper is devoted to topology optimization problems for elastic wave propagation. The objective of the study is to maximize the reflection or the dissipation in a finite slab of material for pressure and shear waves in a range of frequencies. The optimized designs consist of two or three mate...
Test problem construction for single-objective bilevel optimization.
Sinha, Ankur; Malo, Pekka; Deb, Kalyanmoy
2014-01-01
In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization. The construction procedure is flexible and allows its user to control the different complexities that are to be included in the test problems independently of each other. In addition to properties that control the difficulty in convergence, the procedure also allows the user to introduce difficulties caused by interaction of the two levels. As a companion to the test problem construction framework, the paper presents a standard test suite of 12 problems, which includes eight unconstrained and four constrained problems. Most of the problems are scalable in terms of variables and constraints. To provide baseline results, we have solved the proposed test problems using a nested bilevel evolutionary algorithm. The results can be used for comparison, while evaluating the performance of any other bilevel optimization algorithm. The code related to the paper may be accessed from the website http://bilevel.org .
borealis - A generalized global update algorithm for Boolean optimization problems
Zhu, Zheng; Katzgraber, Helmut G
2016-01-01
Optimization problems with Boolean variables that fall into the nondeterministic polynomial (NP) class are of fundamental importance in computer science, mathematics, physics and industrial applications. Most notably, solving constraint-satisfaction problems, which are related to spin-glass-like Hamiltonians in physics, remains a difficult numerical task. As such, there has been great interest in designing efficient heuristics to solve these computationally difficult problems. Inspired by parallel tempering Monte Carlo in conjunction with the rejection-free isoenergetic cluster algorithm developed for Ising spin glasses, we present a generalized global update optimization heuristic that can be applied to different NP-complete problems with Boolean variables. The global cluster updates allow for a wide-spread sampling of phase space, thus considerably speeding up optimization. By carefully tuning the pseudo-temperature (needed to randomize the configurations) of the problem, we show that the method can efficie...
Optimal Solutions for the Temporal Precedence Problem
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Makris, Christos; Sioutas, Spyros;
2002-01-01
a in the structure, while the operation precedes (a,b) returns true iff element a was inserted before element b temporally. In [11] a solution was provided to the problem with worst-case time complexity O (log log n ) per operation and O(n log log n) space, where n is the number of elements inserted. It was also...... demonstrated that the precedes operation has a lower bound of Ω (log log n ) for the Pure Pointer Machine model of computation. In this paper we present two simple solutions with linear space and worst-case constant insertion time. In addition, we describe two algorithms that can handle the precedes (a...
Non-linear absorption for concentrated solar energy transport
Energy Technology Data Exchange (ETDEWEB)
Jaramillo, O. A; Del Rio, J.A; Huelsz, G [Centro de Investigacion de Energia, UNAM, Temixco, Morelos (Mexico)
2000-07-01
In order to determine the maximum solar energy that can be transported using SiO{sub 2} optical fibers, analysis of non-linear absorption is required. In this work, we model the interaction between solar radiation and the SiO{sub 2} optical fiber core to determine the dependence of the absorption of the radioactive intensity. Using Maxwell's equations we obtain the relation between the refractive index and the electric susceptibility up to second order in terms of the electric field intensity. This is not enough to obtain an explicit expression for the non-linear absorption. Thus, to obtain the non-linear optical response, we develop a microscopic model of an harmonic driven oscillators with damp ing, based on the Drude-Lorentz theory. We solve this model using experimental information for the SiO{sub 2} optical fiber, and we determine the frequency-dependence of the non-linear absorption and the non-linear extinction of SiO{sub 2} optical fibers. Our results estimate that the average value over the solar spectrum for the non-linear extinction coefficient for SiO{sub 2} is k{sub 2}=10{sup -}29m{sup 2}V{sup -}2. With this result we conclude that the non-linear part of the absorption coefficient of SiO{sub 2} optical fibers during the transport of concentrated solar energy achieved by a circular concentrator is negligible, and therefore the use of optical fibers for solar applications is an actual option. [Spanish] Con el objeto de determinar la maxima energia solar que puede transportarse usando fibras opticas de SiO{sub 2} se requiere el analisis de absorcion no linear. En este trabajo modelamos la interaccion entre la radiacion solar y el nucleo de la fibra optica de SiO{sub 2} para determinar la dependencia de la absorcion de la intensidad radioactiva. Mediante el uso de las ecuaciones de Maxwell obtenemos la relacion entre el indice de refraccion y la susceptibilidad electrica hasta el segundo orden en terminos de intensidad del campo electrico. Esto no es
The non-linear evolution of edge localized modes
Energy Technology Data Exchange (ETDEWEB)
Wenninger, Ronald
2013-01-09
Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal
Global Optimization Problems in Optimal Design of Experiments in Regression Models
Boer, E.P.J.; Hendrix, E.M.T.
2000-01-01
In this paper we show that optimal design of experiments, a specific topic in statistics, constitutes a challenging application field for global optimization. This paper shows how various structures in optimal design of experiments problems determine the structure of corresponding challenging global
Phase optimization problems applications in wave field theory
Bulatsyk, Olena O; Topolyuk, Yury P; Bulatsyk, Olena; Voitovich, Nikolai N
2010-01-01
This is the only book available in English language to consider inverse and optimization problems in which phase field distributions are used as optimizing functions. The mathematical technique used relates to nonlinear integral equations, with numerical methods developed and applied to concrete problems. Written by a team of outstanding and renowned experts in the field, this monograph will appeal to all those dealing with the investigation, design, and optimization of electromagnetic and acoustic radiating and transmitting devices and systems, while also being of interest to mathematicians w
Upper Hölder continuity of parametric vector optimization problems
Directory of Open Access Journals (Sweden)
Xian-Fu Hu
2016-11-01
Full Text Available Abstract This paper is concerned with upper Hölder continuity and Hölder calmness of a perturbed vector optimization problem. We establish some new sufficient conditions for upper Hölder continuity and Hölder calmness of the perturbed solution mappings and the perturbed optimal value mappings of a vector optimization problem under the case that the objective function and the feasible set are, respectively, perturbed by parameters. Our results generalize and extend the corresponding ones of Li and Li (Appl. Math. Comput. 232:908-918, 2014.
OPTIMAL THICKNESS OF A CYLINDRICAL SHELL - AN OPTIMAL CONTROL PROBLEM IN LINEAR ELASTICITY THEORY
Directory of Open Access Journals (Sweden)
Peter Nestler
2013-01-01
Full Text Available In this paper we discuss optimization problems for cylindrical tubeswhich are loaded by an applied force. This is a problem of optimal control in linear elasticity theory (shape optimization. We are looking for an optimal thickness minimizing the deflection (deformation of the tube under the influence of an external force. From basic equations of mechanics, we derive the equation of deformation. We apply the displacement approach from shell theory and make use of the hypotheses of Mindlin and Reissner. A corresponding optimal control problem is formulated and first order necessary conditions for the optimal solution (optimal thickness are derived. We present numerical examples which were solved by the finite element method.
Directory of Open Access Journals (Sweden)
Harish Garg
2013-01-01
systems by utilizing uncertain, limited, and imprecise data. In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting objectives. Moreover, data collected or available for the systems are vague, ambiguous, qualitative, and imprecise in nature due to various practical constraints and hence create some difficulties in optimizing the design problems. To handle these problems, this work presents an interactive method for solving the fuzzy multiobjective optimization decision-making problem, which can be used for the optimization decision making of the reliability with two or more objectives. Based on the preference of the decision makers toward the objectives, fuzzy multi-objective optimization problem is converted into crisp optimization problem and then solved with evolutionary algorithm. The proposed approach has been applied to the decomposition unit of a urea fertilizer plant situated in the northern part of India producing 1500–2000 metric tons per day.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
We determine the asymptotic order of entropy number and optimal non - linear approximations of anisotropic periodic Besov class of Brpθ(Td) (1≤p≤∞, 1≤θ≤∞ ) by manifolds of finite pseudo-dimension in the metric Lq (Td), 1≤ q≤∞, where Td is the d-dimensional torus.
Strong Duality and Optimality Conditions for Generalized Equilibrium Problems
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D. H. Fang
2013-01-01
Full Text Available We consider a generalized equilibrium problem involving DC functions. By using the properties of the epigraph of the conjugate functions, some sufficient and/or necessary conditions for the weak and strong duality results and optimality conditions for generalized equilibrium problems are provided.
Multiplier methods for optimization problems with Lipschitzian derivatives
Izmailov, A. F.; Kurennoy, A. S.
2012-12-01
Optimization problems for which the objective function and the constraints have locally Lipschitzian derivatives but are not assumed to be twice differentiable are examined. For such problems, analyses of the local convergence and the convergence rate of the multiplier (or the augmented Lagrangian) method and the linearly constraint Lagrangian method are given.
Reverse convex problems: an approach based on optimality conditions
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Ider Tseveendorj
2006-01-01
Full Text Available We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.
Moments of random sums and Robbins' problem of optimal stopping
Gnedin, A.V.; Iksanov, A.
2011-01-01
Robbins' problem of optimal stopping is that of minimising the expected rank of an observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the value of the stopped variable under the rule that yields the minimal expected rank, by embedding the problem in a much
Continuity for vector optimization problems with equilibrium constraints
Institute of Scientific and Technical Information of China (English)
WU Yunan
2004-01-01
The concept of vector optimization problems with equilibrium constraints (VOPEC) is introduced. By using the continuity results of the approximate solution set to the equilibrium problem, we obtain the same results of the marginal map and the approximate value in VOPEC (ε) for vector-valued mapping.
Study of optimal control problems for hybrid dynamical systems
Institute of Scientific and Technical Information of China (English)
Gao Rui; Wang Lei; Wang Yuzhen
2006-01-01
From the viewpoint of continuous systems, optimal control problem is proposed for a class of controlled Hybrid dynamical systems. Then a mathematical method- HDS minimum principle is put forward, which can solve the above problem. The HDS minimum principle is proved by means of Ekeland's variational principle.
Moments of random sums and Robbins' problem of optimal stopping
Gnedin, A.V.; Iksanov, A.
2011-01-01
Robbins' problem of optimal stopping is that of minimising the expected rank of an observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the value of the stopped variable under the rule that yields the minimal expected rank, by embedding the problem in a much mor
Reverse convex problems: an approach based on optimality conditions
Ider Tseveendorj
2006-01-01
We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.
AN ALGORITHM FOR CONTINUOUS TYPE OPTIMAL SPHERICALFACILITY LOCATION PROBLEM
Institute of Scientific and Technical Information of China (English)
ZHANG Liping; WANG Changyu
1999-01-01
In this paper, we study the continuously spherical facilitylocation problem.(P)(minx∈S∫∫(x)=Ωφ(υ)cos-1(υTx)dΩ) We prove a hull property and optimality condition of the problem (P), andpropose an algorithm to solve (P). Global convergence is proved.
Examining the Bernstein global optimization approach to optimal power flow problem
Patil, Bhagyesh V.; Sampath, L. P. M. I.; Krishnan, Ashok; Ling, K. V.; Gooi, H. B.
2016-10-01
This work addresses a nonconvex optimal power flow problem (OPF). We introduce a `new approach' in the context of OPF problem based on the Bernstein polynomials. The applicability of the approach is studied on a real-world 3-bus power system. The numerical results obtained with this new approach for a 3-bus system reveal a satisfactory improvement in terms of optimality. The results are found to be competent with generic global optimization solvers BARON and COUENNE.
Josiński, Henryk; Kostrzewa, Daniel; Michalczuk, Agnieszka; Switoński, Adam
2014-01-01
This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature.
Directory of Open Access Journals (Sweden)
Henryk Josiński
2014-01-01
Full Text Available This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature.
Non-linear analysis and calculation of the performance of a shelving protection system by FEM
García Nieto, P. J.; del Coz Díaz, J. J.; Vilán Vilán, J. A.; Suárez Sierra, J. L.
2012-12-01
The aim of this paper consists on the study, analysis and calculation of the efficiency of a shelving protection system by means of the finite element method (FEM). These shelving protection systems are intended to prevent the eventual damage due to the impacts of transport elements in motion, such as: forklifts, dumpers, hand pallet trucks, and so on. The impact loads may threaten the structural integrity of the shelving system. The present structural problem is highly non-linear, due to the simultaneous presence of the following nonlinearities: material non-linearity (plasticity in this case), geometrical non-linearity (large displacements) and contact-type boundary conditions (between the rigid body and the protection system). A total of forty eight different FEM models are built varying the thickness of the steel plate (4, 5 and 6 mm), the impact height (0.1, 0.2, 0.3 and 0.4 meters) and the impact direction (head-on collision and side impact). Once the models are solved, the stress distribution, the overall displacements and the absorbed impact energy were calculated. In order to determine the best shelving protection's candidate, some constraints must be taken into account: the maximum allowable stress (235 MPa), the maximum displacement (0.05 m) and the absorbed impact energy (400 J according to the European Standard Rule PREN-15512). Finally, the most important results are shown and conclusions of this study are exposed.
Reservoir computing and extreme learning machines for non-linear time-series data analysis.
Butcher, J B; Verstraeten, D; Schrauwen, B; Day, C R; Haycock, P W
2013-02-01
Random projection architectures such as Echo state networks (ESNs) and Extreme Learning Machines (ELMs) use a network containing a randomly connected hidden layer and train only the output weights, overcoming the problems associated with the complex and computationally demanding training algorithms traditionally used to train neural networks, particularly recurrent neural networks. In this study an ESN is shown to contain an antagonistic trade-off between the amount of non-linear mapping and short-term memory it can exhibit when applied to time-series data which are highly non-linear. To overcome this trade-off a new architecture, Reservoir with Random Static Projections (R(2)SP) is investigated, that is shown to offer a significant improvement in performance. A similar approach using an ELM whose input is presented through a time delay (TD-ELM) is shown to further enhance performance where it significantly outperformed the ESN and R(2)SP as well other architectures when applied to a novel task which allows the short-term memory and non-linearity to be varied. The hard-limiting memory of the TD-ELM appears to be best suited for the data investigated in this study, although ESN-based approaches may offer improved performance when processing data which require a longer fading memory.
Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads
Directory of Open Access Journals (Sweden)
Donald Mark Santee
2006-01-01
Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.
Solving the Travelling Salesman Problem Using the Ant Colony Optimization
Directory of Open Access Journals (Sweden)
Zuzana Čičková
2011-12-01
Full Text Available In this article, we study a possibility of solving the well-known Travelling Salesman Problem (TSP, which ranges among NP-hard problems, and offer a theoretical overview of some methods used for solving this problem. We discuss the Ant Colony Optimization (ACO, which belongs to the group of evolutionary techniques and presents the approach used in the application of ACO to the TSP. We study the impact of some control parameters by implementing this algorithm. The quality of the solution is compared with the optimal solution.
Optimizing dictionary learning parameters for solving Audio Inpainting problem
Directory of Open Access Journals (Sweden)
Václav Mach
2013-01-01
Full Text Available Recovering missing or distorted audio signal sam-ples has been recently improved by solving an Audio Inpaintingproblem. This paper aims to connect this problem with K-SVD dictionary learning to improve reconstruction error formissing signal insertion problem. Our aim is to adapt an initialdictionary to the reliable signal to be more accurate in missingsamples estimation. This approach is based on sparse signalsreconstruction and optimization problem. In the paper two staplealgorithms, connection between them and emerging problemsare described. We tried to find optimal parameters for efficientdictionary learning.
3D Topology optimization of Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Dammann, Bernd
of energy efficient devices for 2D Stokes flow. Creeping flow problems are described by the Stokes equations which model very viscous fluids at macro scales or ordinary fluids at very small scales. The latter gives the motivation for topology optimization problems based on the Stokes equations being a model...... the designs are 3D. Moreover, preliminary results show that a formulation of an optimization problem that maximizes mixing with a constraint on the pressure drop across the device gives promising results. To measure the mixing a step temperature profile is convected through the design and the resulting...
Numerical methods for solving terminal optimal control problems
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
On the optimal control problem for two regions’ macroeconomic model
Directory of Open Access Journals (Sweden)
Surkov Platon G.
2015-12-01
Full Text Available In this paper we consider a model of joint economic growth of two regions. This model bases on the classical Kobb-Douglas function and is described by a nonlinear system of differential equations. The interaction between regions is carried out by changing the balance of trade. The optimal control problem for this system is posed and the Pontryagin maximum principle is used for analysis the problem. The maximized functional represents the global welfare of regions. The numeric solution of the optimal control problem for particular regions is found. The used parameters was obtained from the basic scenario of the MERGE
OPTIMIZATION PROBLEMS ON SUBURBAN TRANSPORT SYSTEMS
Directory of Open Access Journals (Sweden)
T. M. Grigorovа
2015-01-01
Full Text Available The paper considers problems that permit to solve such issue as organization of transport service for suburban population with due account of passenger transport fatigue which is considered as one of subconscious criteria for selection of a travel mode. Improvement of transportation process entails an increase in demand for such service. Demands predetermine transport supply and situation on the market depends on supply-and-demand balance. The paper presents an analysis of approaches to the estimation of parameters for a suburban transport system with due regard for influence of transport process parameters on the rate of passenger transport fatigue. This rate is estimated through value of an index which demonstrates an activity of passenger’s regulatory systems while performing every element of motion process. Nonlinear regression equation has been used to describe changes in the activity index of the passenger’s regulatory systems when a passenger is taking a standing position in a passenger compartment of a suburban transport facility. In this case value of activity index of regulatory systems before transportation, passenger age, transportation duration, operation factor of transport capacity and ratio of new bus cost to nominal capacity have been taken as variables for calculations.The paper proposes an index change model for assessment of passenger’s transport fatigue when a passenger has a standing position in a transport facility. The model has shown that an impact of the activity index of passenger’s regulatory systems before making any elemental motion is rather pertinent because this index provides information on an initial condition of a person before executing any other elemental motion. The influence of the activity index of passenger’s regulatory systems before making any elemental motion is considered as an important characteristic because it has an impact on passenger’s condition after executing
Chemical reaction optimization for solving shortest common supersequence problem.
Khaled Saifullah, C M; Rafiqul Islam, Md
2016-10-01
Shortest common supersequence (SCS) is a classical NP-hard problem, where a string to be constructed that is the supersequence of a given string set. The SCS problem has an enormous application of data compression, query optimization in the database and different bioinformatics activities. Due to NP-hardness, the exact algorithms fail to compute SCS for larger instances. Many heuristics and meta-heuristics approaches were proposed to solve this problem. In this paper, we propose a meta-heuristics approach based on chemical reaction optimization, CRO_SCS that is designed inspired by the nature of the chemical reactions. For different optimization problems like 0-1 knapsack, quadratic assignment, global numeric optimization problems CRO algorithm shows very good performance. We have redesigned the reaction operators and a new reform function to solve the SCS problem. The outcomes of the proposed CRO_SCS algorithm are compared with those of the enhanced beam search (IBS_SCS), deposition and reduction (DR), ant colony optimization (ACO) and artificial bee colony (ABC) algorithms. The length of supersequence, execution time and standard deviation of all related algorithms show that CRO_SCS gives better results on the average than all other algorithms.
A Global Optimization Algorithm for Sum of Linear Ratios Problem
Directory of Open Access Journals (Sweden)
Yuelin Gao
2013-01-01
Full Text Available We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.
A New Fenchel Dual Problem in Vector Optimization
Indian Academy of Sciences (India)
Radu Ioan Boţ; Anca Dumitru; Gert Wanka
2009-04-01
We introduce a new Fenchel dual for vector optimization problems inspired by the form of the Fenchel dual attached to the scalarized primal multiobjective problem. For the vector primal-dual pair we prove weak and strong duality. Furthermore, we recall two other Fenchel-type dual problems introduced in the past in the literature, in the vector case, and make a comparison among all three duals. Moreover, we show that their sets of maximal elements are equal.
Optimal vehicle planning and the search tour problem
Wettergren, Thomas A.; Bays, Matthew J.
2016-05-01
We describe a problem of optimal planning for unmanned vehicles and illustrate two distinct procedures for its solution. The problem under consideration, which we refer to as the search tour problem, involves the determination of multi-stage plans for unmanned vehicles conducting search operations. These types of problems are important in situations where the searcher has varying performance in different regions throughout the domain due to environmental complexity. The ability to provide robust planning for unmanned systems under diﬃcult environmental conditions is critical for their use in search operations. The problem we consider consists of searches with variable times for each of the stages, as well as an additional degree of freedom for each stage to select from one of a finite set of operational configurations. As each combination of configuration and stage time leads to a different performance level, there is a need to determine the optimal configuration of these stages. When the complexity of constraints on total time, as well as resources expended at each stage for a given configuration, are added, the problem becomes one of non-trivial search effort allocation and numerical methods of optimization are required. We show two solution approaches for this numerical optimization problem. The first solution technique is to use a mixed-integer linear programming formulation, for which commercially available solvers can find optimal solutions in a reasonable amount of time. We use this solution as a baseline and compare against a new inner/outer optimization formulation. This inner/outer optimization compares favorably to the baseline solution, but is also amenable to adaptation as the search operation progresses. Numerical examples illustrate the utility of the approach for unmanned vehicle search planning.
TSP based Evolutionary optimization approach for the Vehicle Routing Problem
Kouki, Zoulel; Chaar, Besma Fayech; Ksouri, Mekki
2009-03-01
Vehicle Routing and Flexible Job Shop Scheduling Problems (VRP and FJSSP) are two common hard combinatorial optimization problems that show many similarities in their conceptual level [2, 4]. It was proved for both problems that solving techniques like exact methods fail to provide good quality solutions in a reasonable amount of time when dealing with large scale instances [1, 5, 14]. In order to overcome this weakness, we decide in the favour of meta heuristics and we focalize on evolutionary algorithms that have been successfully used in scheduling problems [1, 5, 9]. In this paper we investigate the common properties of the VRP and the FJSSP in order to provide a new controlled evolutionary approach for the CVRP optimization inspired by the FJSSP evolutionary optimization algorithms introduced in [10].
Open Vehicle Routing Problem by Ant Colony Optimization
Directory of Open Access Journals (Sweden)
Er. Gurpreet Singh
2014-01-01
Full Text Available Vehicle routing problem (VRP is real-world combinatorial optimization problem which determine the optimal route of a vehicle. Generally, toprovide the efficientvehicle serving to the customer through different services by visiting the number of cities or stops. The VRP follows the Travelling Salesman Problem (TSP, in which each of vehicle visiting a set of cities such that every city is visited by exactly one vehicle only once. This work proposes the Ant Colony Optimization (ACO-TSP algorithm to eliminate the tour loop for Open Vehicle routing Problem (OVRP. A key aspect of this algorithm is to plan the routes of buses that must pick up and deliver the school students from various bus stops on time, especially in the case of far distance covered by the vehicle in a rural area and find out the efficient and safe vehicle route.
Global non-linear effect of temperature on economic production.
Burke, Marshall; Hsiang, Solomon M; Miguel, Edward
2015-11-12
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.
Global non-linear effect of temperature on economic production
Burke, Marshall; Hsiang, Solomon M.; Miguel, Edward
2015-11-01
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.
Institute of Scientific and Technical Information of China (English)
Hasan ABBASI NOZARI; Hamed DEHGHAN BANADAKI; Mohammad MOKHTARE; Somaveh HEKMATI VAHED
2012-01-01
This study deals with the neuro-fuzzy (NF) modelling of a real industrial winding process in which the acquired NF model can be exploited to improve control performance and achieve a robust fault-tolerant system.A new simulator model is proposed for a winding process using non-linear identification based on a recurrent local linear neuro-fuzzy (RLLNF) network trained by local linear model tree (LOLIMOT),which is an incremental tree-based learning algorithm.The proposed NF models are compared with other known intelligent identifiers,namely multilayer perceptron (MLP) and radial basis function (RBF).Comparison of our proposed non-linear models and associated models obtained through the least square error (LSE) technique (the optimal modelling method for linear systems) confirms that the winding process is a non-linear system.Experimental results show the effectiveness of our proposed NF modelling approach.
Linear and non-linear perturbations in dark energy models
Escamilla-Rivera, Celia; Fabris, Julio C; Alcaniz, Jailson S
2016-01-01
In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state $w(z)$. In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected $w(z)$ parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard $\\Lambda$CDM model.
Hans Hinterreiter’s non-linear transformations
DEFF Research Database (Denmark)
Makovicky, Emil
poster illustrates four different cases of this process, starting always with a plane-group pattern and showing both the application of non-linear transformations and coloured symmetry. In his more complex patterns, two of which are shown on the poster, Hinterreiter created domains of affinely...... of plane-group patterns onto curvilinear nets of different kinds, mostly combined with a skilful application of principles of dichroic or polychromatic symmetry. Unlike Escher, Hinterreiter strove to achieve the aesthetic ideal of a pure abstract form [2] with its inherent symmetries. His unique, two...
Studies for an alternative LHC non-linear collimation system
Lari, L; Boccone, V; Cerutti, F; Versaci, R; Vlachoudis, V; Mereghetti, A; Faus-Golfe, A; Resta-Lopez, J
2012-01-01
A LHC non-linear betatron cleaning collimation system would allow larger gap for the mechanical jaws, reducing as a consequence the collimator-induced impedance, which may limit the LHC beam intensity. In this paper, the performance of the proposed system is analyzed in terms of beam losses distribution around the LHC ring and cleaning efficiency in stable physics condition at 7TeV for Beam1. Moreover, the energy deposition distribution on the machine elements is compared to the present LHC Betatron cleaning collimation system in the Point 7 Insertion Region (IR).