Quadratic third-order tensor optimization problem with quadratic constraints
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Lixing Yang
2014-05-01
Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.
Hidden conic quadratic representation of some nonconvex quadratic optimization problems
Ben-Tal, A.; den Hertog, D.
The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated
Stochastic Linear Quadratic Optimal Control Problems
International Nuclear Information System (INIS)
Chen, S.; Yong, J.
2001-01-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well
A Linear Programming Reformulation of the Standard Quadratic Optimization Problem
de Klerk, E.; Pasechnik, D.V.
2005-01-01
The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially
Optimal Quadratic Programming Algorithms
Dostal, Zdenek
2009-01-01
Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This title presents various algorithms for solving large QP problems. It is suitable as an introductory text on quadratic programming for graduate students and researchers
Separability of diagonal symmetric states: a quadratic conic optimization problem
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Jordi Tura
2018-01-01
Full Text Available We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS states. First, we show that separability in the case of DS in $C^d\\otimes C^d$ (symmetric qudits can be reformulated as a quadratic conic optimization problem. This connection allows us to exchange concepts and ideas between quantum information and this field of mathematics. For instance, copositive matrices can be understood as indecomposable entanglement witnesses for DS states. As a consequence, we show that positivity of the partial transposition (PPT is sufficient and necessary for separability of DS states for $d \\leq 4$. Furthermore, for $d \\geq 5$, we provide analytic examples of PPT-entangled states. Second, we develop new sufficient separability conditions beyond the PPT criterion for bipartite DS states. Finally, we focus on $N$-partite DS qubits, where PPT is known to be necessary and sufficient for separability. In this case, we present a family of almost DS states that are PPT with respect to each partition but nevertheless entangled.
On the Equivalence of Quadratic Optimization Problems Commonly Used in Portfolio Theory
Taras Bodnar; Nestor Parolya; Wolfgang Schmid
2012-01-01
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean-variance optimal portfolios. It is shown that the solutions of the Markowitz optimization prob...
An L∞/L1-Constrained Quadratic Optimization Problem with Applications to Neural Networks
International Nuclear Information System (INIS)
Leizarowitz, Arie; Rubinstein, Jacob
2003-01-01
Pattern formation in associative neural networks is related to a quadratic optimization problem. Biological considerations imply that the functional is constrained in the L ∞ norm and in the L 1 norm. We consider such optimization problems. We derive the Euler-Lagrange equations, and construct basic properties of the maximizers. We study in some detail the case where the kernel of the quadratic functional is finite-dimensional. In this case the optimization problem can be fully characterized by the geometry of a certain convex and compact finite-dimensional set
Ito, Kazufumi; Teglas, Russell
1987-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Ito, K.; Teglas, R.
1984-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Lesmana, E.; Chaerani, D.; Khansa, H. N.
2018-03-01
Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method
Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah
2016-01-01
The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them.
Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah
2016-01-01
The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them. PMID:26819585
Permutation flow-shop scheduling problem to optimize a quadratic objective function
Ren, Tao; Zhao, Peng; Zhang, Da; Liu, Bingqian; Yuan, Huawei; Bai, Danyu
2017-09-01
A flow-shop scheduling model enables appropriate sequencing for each job and for processing on a set of machines in compliance with identical processing orders. The objective is to achieve a feasible schedule for optimizing a given criterion. Permutation is a special setting of the model in which the processing order of the jobs on the machines is identical for each subsequent step of processing. This article addresses the permutation flow-shop scheduling problem to minimize the criterion of total weighted quadratic completion time. With a probability hypothesis, the asymptotic optimality of the weighted shortest processing time schedule under a consistency condition (WSPT-CC) is proven for sufficiently large-scale problems. However, the worst case performance ratio of the WSPT-CC schedule is the square of the number of machines in certain situations. A discrete differential evolution algorithm, where a new crossover method with multiple-point insertion is used to improve the final outcome, is presented to obtain high-quality solutions for moderate-scale problems. A sequence-independent lower bound is designed for pruning in a branch-and-bound algorithm for small-scale problems. A set of random experiments demonstrates the performance of the lower bound and the effectiveness of the proposed algorithms.
Heinkenschloss, Matthias
2005-01-01
We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.
Multiobjective Optimization Involving Quadratic Functions
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Oscar Brito Augusto
2014-01-01
Full Text Available Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined in n-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
Linear quadratic optimization for positive LTI system
Muhafzan, Yenti, Syafrida Wirma; Zulakmal
2017-05-01
Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.
Directory of Open Access Journals (Sweden)
Weihua Jin
2013-01-01
Full Text Available This paper proposes a genetic-algorithms-based approach as an all-purpose problem-solving method for operation programming problems under uncertainty. The proposed method was applied for management of a municipal solid waste treatment system. Compared to the traditional interactive binary analysis, this approach has fewer limitations and is able to reduce the complexity in solving the inexact linear programming problems and inexact quadratic programming problems. The implementation of this approach was performed using the Genetic Algorithm Solver of MATLAB (trademark of MathWorks. The paper explains the genetic-algorithms-based method and presents details on the computation procedures for each type of inexact operation programming problems. A comparison of the results generated by the proposed method based on genetic algorithms with those produced by the traditional interactive binary analysis method is also presented.
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme
Banks, H. T.; Ito, K.
1991-01-01
A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.
Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients
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Xue-Gang Zhou
2014-01-01
Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2006-01-01
This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...
DEFF Research Database (Denmark)
Stolpe, Mathias
2004-01-01
of structures subjected to either static or periodic loads, design of composite materials with prescribed homogenized properties using the inverse homogenization approach, optimization of fluids in Stokes flow, design of band gap structures, and multi-physics problems involving coupled steady-state heat...
DEFF Research Database (Denmark)
Stolpe, Mathias
2007-01-01
of structures subjected to static or periodic loads, design of composite materials with prescribed homogenized properties using the inverse homogenization approach, optimization of fluids in Stokes flow, design of band gap structures, and multi-physics problems involving coupled steady-state heat conduction...
Least Squares Problems with Absolute Quadratic Constraints
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R. Schöne
2012-01-01
Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.
The Quadratic Selective Travelling Salesman Problem
DEFF Research Database (Denmark)
Thomadsen, Tommy; Stidsen, Thomas K.
2003-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...
On a linear-quadratic problem with Caputo derivative
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Dariusz Idczak
2016-01-01
Full Text Available In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.
Sequential Quadratic Programming Algorithms for Optimization
1989-08-01
quadratic program- ma ng (SQ(2l ) aIiatain.seenis to be relgarded aIs tie( buest choice for the solution of smiall. dlense problema (see S tour L)toS...For the step along d, note that a < nOing + 3 szH + i3.ninA A a K f~Iz,;nd and from Id1 _< ,,, we must have that for some /3 , np , 11P11 < dn"p. 5.2...Nevertheless, many of these problems are considered hard to solve. Moreover, for some of these problems the assumptions made in Chapter 2 to establish the
Quadratic stochastic operators: Results and open problems
International Nuclear Information System (INIS)
Ganikhodzhaev, R.N.; Rozikov, U.A.
2009-03-01
The history of the quadratic stochastic operators can be traced back to the work of S. Bernshtein (1924). For more than 80 years this theory has been developed and many papers were published. In recent years it has again become of interest in connection with numerous applications in many branches of mathematics, biology and physics. But most results of the theory were published in non English journals, full text of which are not accessible. In this paper we give a brief description of the results and discuss several open problems. (author)
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2004-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...
On a quadratic inverse eigenvalue problem
International Nuclear Information System (INIS)
Cai, Yunfeng; Xu, Shufang
2009-01-01
This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable
STRUCTURE OPTIMIZATION OF RESERVATION BY PRECISE QUADRATIC REGULARIZATION
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KOSOLAP A. I.
2015-11-01
Full Text Available The problem of optimization of the structure of systems redundancy elements. Such problems arise in the design of complex systems. To improve the reliability of operation of such systems of its elements are duplicated. This increases system cost and improves its reliability. When optimizing these systems is maximized probability of failure of the entire system while limiting its cost or the cost is minimized for a given probability of failure-free operation. A mathematical model of the problem is a discrete backup multiextremal. To search for the global extremum of currently used methods of Lagrange multipliers, coordinate descent, dynamic programming, random search. These methods guarantee a just and local solutions are used in the backup tasks of small dimension. In the work for solving redundancy uses a new method for accurate quadratic regularization. This method allows you to convert the original discrete problem to the maximization of multi vector norm on a convex set. This means that the diversity of the tasks given to the problem of redundancy maximize vector norm on a convex set. To solve the problem, a reformed straightdual interior point methods. Currently, it is the best method for local optimization of nonlinear problems. Transformed the task includes a new auxiliary variable, which is determined by dichotomy. There have been numerous comparative numerical experiments in problems with the number of redundant subsystems to one hundred. These experiments confirm the effectiveness of the method of precise quadratic regularization for solving problems of redundancy.
Extending the Scope of Robust Quadratic Optimization
Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand
In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in
Neural network for solving convex quadratic bilevel programming problems.
He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie
2014-03-01
In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.
Methods of using the quadratic assignment problem solution
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Izabela Kudelska
2012-09-01
Full Text Available Background: Quadratic assignment problem (QAP is one of the most interesting of combinatorial optimization. Was presented by Koopman and Beckamanna in 1957, as a mathematical model of the location of indivisible tasks. This problem belongs to the class NP-hard issues. This forces the application to the solution already approximate methods for tasks with a small size (over 30. Even though it is much harder than other combinatorial optimization problems, it enjoys wide interest because it models the important class of decision problems. Material and methods: The discussion was an artificial intelligence tool that allowed to solve the problem QAP, among others are: genetic algorithms, Tabu Search, Branch and Bound. Results and conclusions: QAP did not arise directly as a model for certain actions, but he found its application in many areas. Examples of applications of the problem is: arrangement of buildings on the campus of the university, layout design of electronic components in systems with large scale integration (VLSI, design a hospital, arrangement of keys on the keyboard.
Pareto optimality in infinite horizon linear quadratic differential games
Reddy, P.V.; Engwerda, J.C.
2013-01-01
In this article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal
Smoothing optimization of supporting quadratic surfaces with Zernike polynomials
Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu
2018-03-01
A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.
Special cases of the quadratic shortest path problem
Sotirov, Renata; Hu, Hao
2017-01-01
The quadratic shortest path problem (QSPP) is the problem of finding a path with prespecified start vertex s and end vertex t in a digraph such that the sum of weights of arcs and the sum of interaction costs over all pairs of arcs on the path is minimized. We first consider a variant of the QSPP
Numerical Methods for Solution of the Extended Linear Quadratic Control Problem
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog
2012-01-01
In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....
Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube
International Nuclear Information System (INIS)
Mittelmann, Hans; Peng Jiming; Wu Xiaolin
2009-01-01
In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs.Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n 3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.
Fast, multiple optimizations of quadratic dose objective functions in IMRT
International Nuclear Information System (INIS)
Breedveld, Sebastiaan; Storchi, Pascal R M; Keijzer, Marleen; Heijmen, Ben J M
2006-01-01
Inverse treatment planning for intensity-modulated radiotherapy may include time consuming, multiple minimizations of an objective function. In this paper, methods are presented to speed up the process of (repeated) minimization of the well-known quadratic dose objective function, extended with a smoothing term that ensures generation of clinically acceptable beam profiles. In between two subsequent optimizations, the voxel-dependent importance factors of the quadratic terms will generally be adjusted, based on an intermediate plan evaluation. The objective function has been written in matrix-vector format, facilitating the use of a recently published, fast quadratic minimization algorithm, instead of commonly applied gradient-based methods. This format also reduces the calculation time in between subsequent minimizations, related to adjustment of the voxel-dependent importance factors. Sparse matrices are used to limit the required amount of computer memory. For three patients, comparisons have been made with a gradient method. Mean speed improvements of up to a factor of 37 have been achieved
Musthofa, M.W.; Salmah, S.; Engwerda, Jacob; Suparwanto, A.
This paper studies the robust optimal control problem for descriptor systems. We applied differential game theory to solve the disturbance attenuation problem. The robust control problem was converted into a reduced ordinary zero-sum game. Within a linear quadratic setting, we solved the problem for
Trajectory generation for manipulators using linear quadratic optimal tracking
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Olav Egeland
1989-04-01
Full Text Available The reference trajectory is normally known in advance in manipulator control which makes it possible to apply linear quadratic optimal tracking. This gives a control system which rounds corners and generates optimal feedforward. The method may be used for references consisting of straight-line segments as an alternative to the two-step method of using splines to smooth the reference and then applying feedforward. In addition, the method can be used for more complex trajectories. The actual dynamics of the manipulator are taken into account, and this results in smooth and accurate tracking. The method has been applied in combination with the computed torque technique and excellent performance was demonstrated in a simulation study. The method has also been applied experimentally to an industrial spray-painting robot where a saw-tooth reference was tracked. The corner was rounded extremely well, and the steady-state tracking error was eliminated by the optimal feedforward.
Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics
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J. Petrzela
2012-04-01
Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided
The Optimization on Ranks and Inertias of a Quadratic Hermitian Matrix Function and Its Applications
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Yirong Yao
2013-01-01
Full Text Available We solve optimization problems on the ranks and inertias of the quadratic Hermitian matrix function subject to a consistent system of matrix equations and . As applications, we derive necessary and sufficient conditions for the solvability to the systems of matrix equations and matrix inequalities , and in the Löwner partial ordering to be feasible, respectively. The findings of this paper widely extend the known results in the literature.
Binary classification posed as a quadratically constrained quadratic ...
Indian Academy of Sciences (India)
Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...
Delayed Stochastic Linear-Quadratic Control Problem and Related Applications
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Li Chen
2012-01-01
stochastic differential equations (FBSDEs with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.
de Klerk, E.; Sotirov, R.
2007-01-01
We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard,
Linear versus quadratic portfolio optimization model with transaction cost
Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah
2014-06-01
Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.
ANALYSIS AND PERFORMANCE MEASUREMENT OF EXISTING SOLUTION METHODS OF QUADRATIC ASSIGNMENT PROBLEM
Directory of Open Access Journals (Sweden)
Morteza KARAMI
2014-01-01
Full Text Available Quadratic Assignment Problem (QAP is known as one of the most difficult combinatorial optimization problems that is classified in the category of NP-hard problems. Quadratic Assignment Problem Library (QAPLIB is a full database of QAPs which contains several problems from different authors and different sizes. Many exact and meta-heuristic solution methods have been introduced to solve QAP. In this study we focus on previously introduced solution methods of QAP e.g. Branch and Bound (B&B, Simulated Annealing (SA Algorithm, Greedy Randomized Adaptive Search Procedure (GRASP for dense and sparse QAPs. The codes of FORTRAN for these methods were downloaded from QAPLIB. All problems of QAPLIB were solved by the abovementioned methods. Several results were obtained from the computational experiments part. The Results show that the Branch and Bound method is able to introduce a feasible solution for all problems while Simulated Annealing Algorithm and GRASP methods are not able to find any solution for some problems. On the other hand, Simulated Annealing and GRASP methods have shorter run time comparing to the Branch and Bound method. In addition, the performance of the methods on the objective function value is discussed.
An Augmented Lagrangian Method for a Class of Inverse Quadratic Programming Problems
International Nuclear Information System (INIS)
Zhang Jianzhong; Zhang Liwei
2010-01-01
We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semidefinite cone constraint and its dual is a linearly constrained semismoothly differentiable (SC 1 ) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/r, and the rate of multiplier iterates is proportional to 1/√r, where r is the penalty parameter in the augmented Lagrangian. As the objective function of the dual problem is a SC 1 function involving the projection operator onto the cone of symmetrically semi-definite matrices, the analysis requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and properties of the projection operator in the symmetric-matrix space. Furthermore, the semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Finally numerical results, implemented by the augmented Lagrangian method, are reported.
New generalized conjugate gradient methods for the non-quadratic model in unconstrained optimization
International Nuclear Information System (INIS)
Al-Bayati, A.
2001-01-01
This paper present two new conjugate gradient algorithms which use the non-quadratic model in unconstrained optimization. The first is a new generalized self-scaling variable metric algorithm based on the sloboda generalized conjugate gradient method which is invariant to a nonlinear scaling of a stricity convex quadratic function; the second is an interleaving between the generalized sloboda method and the first algorithm; all these algorithm use exact line searches. Numerical comparisons over twenty test functions show that the interleaving algorithm is best overall and requires only about half the function evaluations of the Sloboda method: interleaving algorithms are likely to be preferred when the dimensionality of the problem is increased. (author). 29 refs., 1 tab
Burgers' turbulence problem with linear or quadratic external potential
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.
2005-01-01
We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....
Groenwold, A.A.; Wood, D.W.; Etman, L.F.P.; Tosserams, S.
2009-01-01
We implement and test a globally convergent sequential approximate optimization algorithm based on (convexified) diagonal quadratic approximations. The algorithm resides in the class of globally convergent optimization methods based on conservative convex separable approximations developed by
The regular indefinite linear-quadratic problem with linear endpoint constraints
Soethoudt, J.M.; Trentelman, H.L.
1989-01-01
This paper deals with the infinite horizon linear-quadratic problem with indefinite cost. Given a linear system, a quadratic cost functional and a subspace of the state space, we consider the problem of minimizing the cost functional over all inputs for which the state trajectory converges to that
Directory of Open Access Journals (Sweden)
Liyang Wang
2017-01-01
Full Text Available The application of biped robots is always trapped by their high energy consumption. This paper makes a contribution by optimizing the joint torques to decrease the energy consumption without changing the biped gaits. In this work, a constrained quadratic programming (QP problem for energy optimization is formulated. A neurodynamics-based solver is presented to solve the QP problem. Differing from the existing literatures, the proposed neurodynamics-based energy optimization (NEO strategy minimizes the energy consumption and guarantees the following three important constraints simultaneously: (i the force-moment equilibrium equation of biped robots, (ii frictions applied by each leg on the ground to hold the biped robot without slippage and tipping over, and (iii physical limits of the motors. Simulations demonstrate that the proposed strategy is effective for energy-efficient biped walking.
The Model and Quadratic Stability Problem of Buck Converter in DCM
Directory of Open Access Journals (Sweden)
Li Xiaojing
2016-01-01
Full Text Available Quadratic stability is an important performance for control systems. At first, the model of Buck Converter in DCM is built based on the theories of hybrid systems and switched linear systems primarily. Then quadratic stability of SLS and hybrid feedback switching rule are introduced. The problem of Buck Converter’s quadratic stability is researched afterwards. In the end, the simulation analysis and verification are provided. Both experimental verification and theoretical analysis results indicate that the output of Buck Converter in DCM has an excellent performance via quadratic stability control and switching rules.
Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs
Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.
2017-10-01
This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.
Kassa, Semu Mitiku; Tsegay, Teklay Hailay
2017-08-01
Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.
Directory of Open Access Journals (Sweden)
Anja Fischer
2015-06-01
Full Text Available One fundamental problem of bioinformatics is the computational recognition of DNA and RNA binding sites. Given a set of short DNA or RNA sequences of equal length such as transcription factor binding sites or RNA splice sites, the task is to learn a pattern from this set that allows the recognition of similar sites in another set of DNA or RNA sequences. Permuted Markov (PM models and permuted variable length Markov (PVLM models are two powerful models for this task, but the problem of finding an optimal PM model or PVLM model is NP-hard. While the problem of finding an optimal PM model or PVLM model of order one is equivalent to the traveling salesman problem (TSP, the problem of finding an optimal PM model or PVLM model of order two is equivalent to the quadratic TSP (QTSP. Several exact algorithms exist for solving the QTSP, but it is unclear if these algorithms are capable of solving QTSP instances resulting from RNA splice sites of at least 150 base pairs in a reasonable time frame. Here, we investigate the performance of three exact algorithms for solving the QTSP for ten datasets of splice acceptor sites and splice donor sites of five different species and find that one of these algorithms is capable of solving QTSP instances of up to 200 base pairs with a running time of less than two days.
On the Computation of Optimal Monotone Mean-Variance Portfolios via Truncated Quadratic Utility
Ales Cerný; Fabio Maccheroni; Massimo Marinacci; Aldo Rustichini
2008-01-01
We report a surprising link between optimal portfolios generated by a special type of variational preferences called divergence preferences (cf. [8]) and optimal portfolios generated by classical expected utility. As a special case we connect optimization of truncated quadratic utility (cf. [2]) to the optimal monotone mean-variance portfolios (cf. [9]), thus simplifying the computation of the latter.
Pinto Mariano, Adriano; Bastos Borba Costa, Caliane; de Franceschi de Angelis, Dejanira; Maugeri Filho, Francisco; Pires Atala, Daniel Ibraim; Wolf Maciel, Maria Regina; Maciel Filho, Rubens
2009-11-01
In this work, the mathematical optimization of a continuous flash fermentation process for the production of biobutanol was studied. The process consists of three interconnected units, as follows: fermentor, cell-retention system (tangential microfiltration), and vacuum flash vessel (responsible for the continuous recovery of butanol from the broth). The objective of the optimization was to maximize butanol productivity for a desired substrate conversion. Two strategies were compared for the optimization of the process. In one of them, the process was represented by a deterministic model with kinetic parameters determined experimentally and, in the other, by a statistical model obtained using the factorial design technique combined with simulation. For both strategies, the problem was written as a nonlinear programming problem and was solved with the sequential quadratic programming technique. The results showed that despite the very similar solutions obtained with both strategies, the problems found with the strategy using the deterministic model, such as lack of convergence and high computational time, make the use of the optimization strategy with the statistical model, which showed to be robust and fast, more suitable for the flash fermentation process, being recommended for real-time applications coupling optimization and control.
An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.
Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P
2012-01-01
The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example
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.
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1984-10-01
Full Text Available The problem of systematic derivation of a quasi-dynamic optimal control strategy for a non-linear dynamic process based upon a non-quadratic objective function is investigated. The wellknown LQG-control algorithm does not lead to an optimal solution when the process disturbances have non-zero mean. The relationships between the proposed control algorithm and LQG-control are presented. The problem of how to constrain process variables by means of 'penalty' - terms in the objective function is dealt with separately.
Mixed-Integer Nonconvex Quadratic Optimization Relaxations and Performance Analysis
2016-10-11
stationary point. These results are the state of art in complexity analysis of non-convex optimization. “Complexity of Unconstrained L2-Lp Minimization...Parameter Optimized Radiation Therapy ( SPORT )” (M Zarepisheh, Y Ye, S Boyd, R Li, L Xing), Medical Physics 41(6) (2014) 292-292. Station parameter...optimized radiation therapy ( SPORT ) was recently proposed to fully utilize the technical capability of emerging digital linear accelerators, in
Quadratic Assignment of Hubs in p-Hub Median Problem
DEFF Research Database (Denmark)
Gelareh, Shahin
We introduce Generalized p-Hub Median Problem (GpHMP) that seeks to locate p hub nodes and install p distinct hub facilities/operators on the hubs while discount factor resulted by consolidation of flow on the hub links depends on the facilities/operators that are installed/operating on both hub...
Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques
International Nuclear Information System (INIS)
Glowinski, R.; Le Tallec, P.
1984-01-01
The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity
Optimization for decision making linear and quadratic models
Murty, Katta G
2010-01-01
While maintaining the rigorous linear programming instruction required, Murty's new book is unique in its focus on developing modeling skills to support valid decision-making for complex real world problems, and includes solutions to brand new algorithms.
Probabilistic Quadratic Programming Problems with Some Fuzzy Parameters
Directory of Open Access Journals (Sweden)
S. K. Barik
2012-01-01
making problem by using some specified random variables and fuzzy numbers. In the present paper, randomness is characterized by Weibull random variables and fuzziness is characterized by triangular and trapezoidal fuzzy number. A defuzzification method has been introduced for finding the crisp values of the fuzzy numbers using the proportional probability density function associated with the membership functions of these fuzzy numbers. An equivalent deterministic crisp model has been established in order to solve the proposed model. Finally, a numerical example is presented to illustrate the solution procedure.
Quadratic head loss approximations for optimisation problems in water supply networks
Pecci, Filippo; Abraham, E.; I, Stoianov
2017-01-01
This paper presents a novel analysis of the accuracy of quadratic approximations for the Hazen–Williams (HW) head loss formula, which enables the control of constraint violations in optimisation problems for water supply networks. The two smooth polynomial approximations considered here minimise the
OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE.
Xie, Xianchao; Kou, S C; Brown, Lawrence
2016-03-01
This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results.
Li, Yanning
2014-03-01
This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.
Li, Yanning; Canepa, Edward S.; Claudel, Christian
2014-01-01
This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.
A Fast Condensing Method for Solution of Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
consider a condensing (or state elimination) method to solve an extended version of the LQ control problem, and we show how to exploit the structure of this problem to both factorize the dense Hessian matrix and solve the system. Furthermore, we present two efficient implementations. The first......In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper we...... implementation is formally identical to the Riccati recursion based solver and has a computational complexity that is linear in the control horizon length and cubic in the number of states. The second implementation has a computational complexity that is quadratic in the control horizon length as well...
Directory of Open Access Journals (Sweden)
Julio Michael Stern
2014-03-01
Full Text Available This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.
Parallel Implementation of Riccati Recursion for Solving Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper...... an alternative version of the Riccati recursion solver for LQ control problems is presented. The performance of both the classical and the alternative version is analyzed from a theoretical as well as a numerical point of view, and the alternative version is found to be approximately 50% faster than...
Robustness analysis of the Zhang neural network for online time-varying quadratic optimization
International Nuclear Information System (INIS)
Zhang Yunong; Ruan Gongqin; Li Kene; Yang Yiwen
2010-01-01
A general type of recurrent neural network (termed as Zhang neural network, ZNN) has recently been proposed by Zhang et al for the online solution of time-varying quadratic-minimization (QM) and quadratic-programming (QP) problems. Global exponential convergence of the ZNN could be achieved theoretically in an ideal error-free situation. In this paper, with the normal differentiation and dynamics-implementation errors considered, the robustness properties of the ZNN model are investigated for solving these time-varying problems. In addition, linear activation functions and power-sigmoid activation functions could be applied to such a perturbed ZNN model. Both theoretical-analysis and computer-simulation results demonstrate the good ZNN robustness and superior performance for online time-varying QM and QP problem solving, especially when using power-sigmoid activation functions.
Mathematical programming methods for large-scale topology optimization problems
DEFF Research Database (Denmark)
Rojas Labanda, Susana
for mechanical problems, but has rapidly extended to many other disciplines, such as fluid dynamics and biomechanical problems. However, the novelty and improvements of optimization methods has been very limited. It is, indeed, necessary to develop of new optimization methods to improve the final designs......, 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...... 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...
On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity
International Nuclear Information System (INIS)
Aristov, Anatoly I
2011-01-01
We investigate the asymptotic behaviour as t→∞ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.
Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration....... In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky...... factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver....
Lima, Ricardo
2016-06-16
This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York
Lima, Ricardo; Grossmann, Ignacio E.
2016-01-01
This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York
DEFF Research Database (Denmark)
Gutin, Gregory; Van Iersel, Leo; Mnich, Matthias
2010-01-01
A ternary Permutation-CSP is specified by a subset Π of the symmetric group S3. An instance of such a problem consists of a set of variables V and a multiset of constraints, which are ordered triples of distinct variables of V. The objective is to find a linear ordering α of V that maximizes...... the number of triples whose rearrangement (under α) follows a permutation in Π. We prove that all ternary Permutation-CSPs parameterized above average have kernels with quadratic numbers of variables....
Directory of Open Access Journals (Sweden)
Koh Kim Jie
2017-01-01
Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.
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…
Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection
Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.
2016-03-01
To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.
Polishchuk, Alexander
2005-01-01
Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.
Energy Technology Data Exchange (ETDEWEB)
Korotkov, S F; Khalitov, N T
1965-01-01
he quadratic method of programming is used to solve the following type of problem. A circular reservoir is subjected to a peripheral waterflood. The reservoir is drained by wells arranged in 3 concentric circles. The objective is to control the operation of producing wells, that a maximum quantity of water-free oil will be produced. The wells are flowed so that bottomhole pressure is above the bubble point. A quadratic equation is used to express the essential features of the problem; a system of linear equations is used to express the boundary conditions. The problem is solved by means of the Wolf algorithm method. The method is demonstrated by an illustrative example.
Global Sufficient Optimality Conditions for a Special Cubic Minimization Problem
Directory of Open Access Journals (Sweden)
Xiaomei Zhang
2012-01-01
Full Text Available We present some sufficient global optimality conditions for a special cubic minimization problem with box constraints or binary constraints by extending the global subdifferential approach proposed by V. Jeyakumar et al. (2006. The present conditions generalize the results developed in the work of V. Jeyakumar et al. where a quadratic minimization problem with box constraints or binary constraints was considered. In addition, a special diagonal matrix is constructed, which is used to provide a convenient method for justifying the proposed sufficient conditions. Then, the reformulation of the sufficient conditions follows. It is worth noting that this reformulation is also applicable to the quadratic minimization problem with box or binary constraints considered in the works of V. Jeyakumar et al. (2006 and Y. Wang et al. (2010. Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.
A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions
International Nuclear Information System (INIS)
Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan
2007-01-01
In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported
Bourne, D.P.; Elman, H.; Osborn, J.E.
2009-01-01
This paper is the second part of a two-part paper treating a non-self-adjoint quadratic eigenvalue problem for the linear stability of solutions to the Taylor-Couette problem for flow of a viscous liquid in a deformable cylinder, with the cylinder modelled as a membrane. The first part formulated
Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.
2018-04-01
We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.
Compiling Planning into Quantum Optimization Problems: A Comparative Study
2015-06-07
to SAT, and then reduces higher order terms to quadratic terms through a series of gadgets . Our mappings allow both positive and negative preconditions...to its being specific to this type of problem) and likely benefits from an homogeneous parameter setting (Venturelli et al. 2014), as it generates a...Guzik, A. 2013. Resource efficient gadgets for compiling adiabatic quan- tum optimization problems. Annalen der Physik 525(10- 11):877–888. Blum, A
Optimal Results and Numerical Simulations for Flow Shop Scheduling Problems
Directory of Open Access Journals (Sweden)
Tao Ren
2012-01-01
Full Text Available This paper considers the m-machine flow shop problem with two objectives: makespan with release dates and total quadratic completion time, respectively. For Fm|rj|Cmax, we prove the asymptotic optimality for any dense scheduling when the problem scale is large enough. For Fm‖ΣCj2, improvement strategy with local search is presented to promote the performance of the classical SPT heuristic. At the end of the paper, simulations show the effectiveness of the improvement strategy.
Directory of Open Access Journals (Sweden)
Mohammed Essaid Riffi
2017-11-01
Full Text Available The bat algorithm is one of the recent nature-inspired algorithms, which has been emerged as a powerful search method for solving continuous as well as discrete problems. The quadratic assignment problem is a well-known NP-hard problem in combinatorial optimization. The goal of this problem is to assign n facilities to n locations in such a way as to minimize the assignment cost. For that purpose, this paper introduces a novel discrete variant of bat algorithm to deal with this combinatorial optimization problem. The proposed algorithm was evaluated on a set of benchmark instances from the QAPLIB library and the performance was compared to other algorithms. The empirical results of exhaustive experiments were promising and illustrated the efficacy of the suggested approach.
Directory of Open Access Journals (Sweden)
m. s. osman
2017-09-01
Full Text Available In this paper, we consider fuzzy goal programming (FGP approach for solving multi-level multi-objective quadratic fractional programming (ML-MOQFP problem with fuzzy parameters in the constraints. Firstly, the concept of the ?-cut approach is applied to transform the set of fuzzy constraints into a common deterministic one. Then, the quadratic fractional objective functions in each level are transformed into quadratic objective functions based on a proposed transformation. Secondly, the FGP approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach.
A Problem on Optimal Transportation
Cechlarova, Katarina
2005-01-01
Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…
Applications of functional analysis to optimal control problems
International Nuclear Information System (INIS)
Mizukami, K.
1976-01-01
Some basic concepts in functional analysis, a general norm, the Hoelder inequality, functionals and the Hahn-Banach theorem are described; a mathematical formulation of two optimal control problems is introduced by the method of functional analysis. The problem of time-optimal control systems with both norm constraints on control inputs and on state variables at discrete intermediate times is formulated as an L-problem in the theory of moments. The simplex method is used for solving a non-linear minimizing problem inherent in the functional analysis solution to this problem. Numerical results are presented for a train operation. The second problem is that of optimal control of discrete linear systems with quadratic cost functionals. The problem is concerned with the case of unconstrained control and fixed endpoints. This problem is formulated in terms of norms of functionals on suitable Banach spaces. (author)
Expert Strategies in Solving Algebraic Structure Sense Problems: The Case of Quadratic Equations
Jupri, Al; Sispiyati, R.
2017-02-01
Structure sense, an intuitive ability towards symbolic expressions, including skills to interpret, to manipulate, and to perceive symbols in different roles, is considered as a key success in learning algebra. In this article, we report results of three phases of a case study on solving algebraic structure sense problems aiming at testing the appropriateness of algebraic structure sense tasks and at investigating expert strategies dealing with the tasks. First, we developed three tasks on quadratic equations based on the characteristics of structure sense for high school algebra. Next, we validated the tasks to seven experts. In the validation process, we requested these experts to solve each task using two different strategies. Finally, we analyzing expert solution strategies in the light of structure sense characteristics. We found that even if eventual expert strategies are in line with the characteristics of structure sense; some of their initial solution strategies used standard procedures which might pay less attention to algebraic structures. This finding suggests that experts have reconsidered their procedural work and have provided more efficient solution strategies. For further investigation, we consider to test the tasks to high school algebra students and to see whether they produce similar results as experts.
Directory of Open Access Journals (Sweden)
Jingtao Shi
2013-01-01
Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
Cost Cumulant-Based Control for a Class of Linear Quadratic Tracking Problems
National Research Council Canada - National Science Library
Pham, Khanh D
2007-01-01
.... For instance, the present paper extends the application of cost-cumulant controller design to control of a wide class of linear-quadratic tracking systems where output measurements of a tracker...
Newton-type method for the variational discretization of topology optimization problems
DEFF Research Database (Denmark)
Evgrafov, Anton
2013-01-01
We present a locally quadratically convergent optimization algorithm for solving topology optimization problems. The distinguishing feature of the algorithm is to treat the design as a smooth function of the state and not vice versa as in the traditional nested approach to topology optimization, ...
DEFF Research Database (Denmark)
Skajaa, Anders; Andersen, Erling D.; Ye, Yinyu
2013-01-01
and their negligible computational cost. This is a major advantage when compared to previously suggested strategies that require a pool of iterates from the solution process of the initial problem. Consequently our strategies are better suited for users who use optimization algorithms as black-box routines which...... worst-case complexity. We present extensive computational results showing work reductions when warmstarting compared to coldstarting in the range 30–75% depending on the problem class and magnitude of the problem perturbation. The computational experiments thus substantiate that the warmstarting...
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...
The optimal graph partitioning problem
DEFF Research Database (Denmark)
Sørensen, Michael Malmros; Holm, Søren
1993-01-01
. This problem can be formulated as a MILP, which turns out to be completely symmetrical with respect to the p classes, and the gap between the relaxed LP solution and the optimal solution is the largest one possible. These two properties make it very difficult to solve even smaller problems. In this paper...
Solving symmetric-definite quadratic lambda-matrix problems without factorization
International Nuclear Information System (INIS)
Scott, D.S.; Ward, R.C.
1982-01-01
Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda 2 C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented
Topology optimization of flow problems
DEFF Research Database (Denmark)
Gersborg, Allan Roulund
2007-01-01
This thesis investigates how to apply topology optimization using the material distribution technique to steady-state viscous incompressible flow problems. The target design applications are fluid devices that are optimized with respect to minimizing the energy loss, characteristic properties...... transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the thesis gives a proof-of-concept for the application of the method within fluid dynamic problems and it remains of interest for the design of microfluidic devices. Furthermore, the thesis contributes...... at the Technical University of Denmark. Large topology optimization problems with 2D and 3D Stokes flow modeling are solved with direct and iterative strategies employing the parallelized Sun Performance Library and the OpenMP parallelization technique, respectively....
About an Optimal Visiting Problem
Energy Technology Data Exchange (ETDEWEB)
Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it; Benetton, Michela [Unversita di Trento, Dipartimento di Matematica (Italy)
2012-02-15
In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous 'Traveling Salesman Problem' and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equation. We introduce some 'external' variables, one per target, which keep in memory whether the corresponding target is already visited or not, and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton-Jacobi equation turns out to be discontinuous.
Optimized Large-scale CMB Likelihood and Quadratic Maximum Likelihood Power Spectrum Estimation
Gjerløw, E.; Colombo, L. P. L.; Eriksen, H. K.; Górski, K. M.; Gruppuso, A.; Jewell, J. B.; Plaszczynski, S.; Wehus, I. K.
2015-11-01
We revisit the problem of exact cosmic microwave background (CMB) likelihood and power spectrum estimation with the goal of minimizing computational costs through linear compression. This idea was originally proposed for CMB purposes by Tegmark et al., and here we develop it into a fully functioning computational framework for large-scale polarization analysis, adopting WMAP as a working example. We compare five different linear bases (pixel space, harmonic space, noise covariance eigenvectors, signal-to-noise covariance eigenvectors, and signal-plus-noise covariance eigenvectors) in terms of compression efficiency, and find that the computationally most efficient basis is the signal-to-noise eigenvector basis, which is closely related to the Karhunen-Loeve and Principal Component transforms, in agreement with previous suggestions. For this basis, the information in 6836 unmasked WMAP sky map pixels can be compressed into a smaller set of 3102 modes, with a maximum error increase of any single multipole of 3.8% at ℓ ≤ 32 and a maximum shift in the mean values of a joint distribution of an amplitude-tilt model of 0.006σ. This compression reduces the computational cost of a single likelihood evaluation by a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust likelihood by implicitly regularizing nearly degenerate modes. Finally, we use the same compression framework to formulate a numerically stable and computationally efficient variation of the Quadratic Maximum Likelihood implementation, which requires less than 3 GB of memory and 2 CPU minutes per iteration for ℓ ≤ 32, rendering low-ℓ QML CMB power spectrum analysis fully tractable on a standard laptop.
Well-posed optimization problems
Dontchev, Asen L
1993-01-01
This book presents in a unified way the mathematical theory of well-posedness in optimization. The basic concepts of well-posedness and the links among them are studied, in particular Hadamard and Tykhonov well-posedness. Abstract optimization problems as well as applications to optimal control, calculus of variations and mathematical programming are considered. Both the pure and applied side of these topics are presented. The main subject is often introduced by heuristics, particular cases and examples. Complete proofs are provided. The expected knowledge of the reader does not extend beyond textbook (real and functional) analysis, some topology and differential equations and basic optimization. References are provided for more advanced topics. The book is addressed to mathematicians interested in optimization and related topics, and also to engineers, control theorists, economists and applied scientists who can find here a mathematical justification of practical procedures they encounter.
Energy Technology Data Exchange (ETDEWEB)
Tuereci, R.G. [Kirikkale Univ., Kirikkale (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School
2017-05-15
One speed, time independent and homogeneous medium neutron transport equation can be solved with the anisotropic scattering which includes both the linear anisotropic and the quadratic anisotropic scattering properties. Having solved Case's eigenfunctions and the orthogonality relations among these eigenfunctions, some neutron transport problems such as albedo problem can be calculated as numerically by using numerical or semi-analytic methods. In this study the half-space albedo problem is investigated by using the modified F{sub N} method.
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...
Problems of radiation protection optimization
International Nuclear Information System (INIS)
Morkunas, G.
2003-01-01
One of the basic principles - optimization of radiation protection - is rather well understood by everybody engaged in protection of humans from ionizing radiation. However, the practical application of this principle is very problematic. This fact can be explained by vagueness of concept of dose constraints, possible legal consequences of any decision based on this principle, traditions of prescriptive system of radiation protection requirements in some countries, insufficiency of qualified expertise. The examples of optimization problems are the different attention given to different kinds of practices, not optimized application of remedial measures, strict requirements for radioactive contamination of imported products, uncertainties in optimization in medical applications of ionizing radiation. Such tools as international co-operation including regional networks of information exchange, training of qualified experts, identification of measurable indicators used for judging about the level of optimization may be the helpful practical means in solving of these problems. It is evident that the principle of optimization can not be replaced by any other alternative despite its complexity. The means for its practical implementation shall be searched for. (author)
Newton-type methods for optimization and variational problems
Izmailov, Alexey F
2014-01-01
This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will b...
Domínguez, Luis F.
2012-06-25
An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).
Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution
Energy Technology Data Exchange (ETDEWEB)
Dall-Anese, Emiliano [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Zhao, Changhong [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Zamzam, Admed S. [University of Minnesota; Sidiropoulos, Nicholas D. [University of Minnesota; Taylor, Josh A. [University of Toronto
2018-01-12
This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successive convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.
International Nuclear Information System (INIS)
Kusakabe, Koichi
2009-01-01
To construct an optimization scheme for an extension of the Kohn-Sham approach, I introduce an operator form of the Coulomb interaction. This form is the sum of quadratic form pairs, which can be redefined in a self-consistent calculation of a multi-reference density functional theory. A detailed derivation of the form is given. A fluctuation term introduced in the extended Kohn-Sham scheme is expressed in this form for regularization. The present procedure also provides an exact derivation of effective negative interactions in charge fluctuation channels. Relevance to high-temperature superconductors is discussed.
Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.
1985-01-01
A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.
Management of linear quadratic regulator optimal control with full-vehicle control case study
Directory of Open Access Journals (Sweden)
Rodrigue Tchamna
2016-09-01
Full Text Available Linear quadratic regulator is a powerful technique for dealing with the control design of any linear and nonlinear system after linearization of the system around an operating point. For small systems, which have fewer state variables, the transformation of the performance index from scalar to matrix form can be straightforward. On the other hand, as the system becomes large with many state variables and controllers, appropriate design and notations should be defined to make it easy to automatically implement the technique for any large system without the need to redesign from scratch every time one requires a new system. The main aim of this article was to deal with this issue. This article shows how to automatically obtain the matrix form of the performance index matrices from the scalar version of the performance index. Control of a full-vehicle in cornering was taken as a case study in this article.
International Nuclear Information System (INIS)
Maksudov, F.G.; Gusejnov, G.Sh.
1986-01-01
Inverse scattering problem for the quadratic bundle of the Schroedinger one-dimensional operators in the whole axis is solved. The problem solution is given on the assumption of the discrete spectrum absence. In the discrete spectrum presence the inverse scattering problem solution is known for the Shroedinger differential equation considered
Fay, Temple H.
2012-01-01
Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…
Directory of Open Access Journals (Sweden)
Mohammad Hosein Rezaei
2011-10-01
Full Text Available Transformers perform many functions such as voltage transformation, isolation and noise decoupling. They are indispensable components in electric power distribution system. However, at low frequencies (50 Hz, they are one of the heaviest and the most expensive equipment in an electrical distribution system. Nowadays, electronic power transformers are used instead of conventional power transformers that do voltage transformation and power delivery in power system by power electronic converter. In this paper, the structure of distribution electronic power transformer (DEPT are analized and then paid attention on the design of a linear-quadratic-regulator (LQR with integral action to improve dynamic performance of DEPT with voltage unbalance, voltage sags, voltage harmonics and voltage ﬂicker. The presentation control strategy is simulated by MATLAB/SIMULINK. In addition, the results that are in terms of dc-link reference voltage, input and output voltages clearly show that a better dynamic performance can be achieved by using the LQR method when compared to other techniques.
STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING: A SURVEY
Directory of Open Access Journals (Sweden)
Damián Fernández
2014-12-01
Full Text Available We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.
SOCIAL NETWORK OPTIMIZATION A NEW METHAHEURISTIC FOR GENERAL OPTIMIZATION PROBLEMS
Directory of Open Access Journals (Sweden)
Hassan Sherafat
2017-12-01
Full Text Available In the recent years metaheuristics were studied and developed as powerful technics for hard optimization problems. Some of well-known technics in this field are: Genetic Algorithms, Tabu Search, Simulated Annealing, Ant Colony Optimization, and Swarm Intelligence, which are applied successfully to many complex optimization problems. In this paper, we introduce a new metaheuristic for solving such problems based on social networks concept, named as Social Network Optimization – SNO. We show that a wide range of np-hard optimization problems may be solved by SNO.
Asymptotic Method of Solution for a Problem of Construction of Optimal Gas-Lift Process Modes
Directory of Open Access Journals (Sweden)
Fikrat A. Aliev
2010-01-01
Full Text Available Mathematical model in oil extraction by gas-lift method for the case when the reciprocal value of well's depth represents a small parameter is considered. Problem of optimal mode construction (i.e., construction of optimal program trajectories and controls is reduced to the linear-quadratic optimal control problem with a small parameter. Analytic formulae for determining the solutions at the first-order approximation with respect to the small parameter are obtained. Comparison of the obtained results with known ones on a specific example is provided, which makes it, in particular, possible to use obtained results in realizations of oil extraction problems by gas-lift method.
Huo, Xiaoming; Elad, Michael; Flesia, Ana G.; Muise, Robert R.; Stanfill, S. Robert; Friedman, Jerome; Popescu, Bogdan; Chen, Jihong; Mahalanobis, Abhijit; Donoho, David L.
2003-09-01
In target recognition applications of discriminant of classification analysis, each 'feature' is a result of a convolution of an imagery with a filter, which may be derived from a feature vector. It is important to use relatively few features. We analyze an optimal reduced-rank classifier under the two-class situation. Assuming each population is Gaussian and has zero mean, and the classes differ through the covariance matrices: ∑1 and ∑2. The following matrix is considered: Λ=(∑1+∑2)-1/2∑1(∑1+∑2)-1/2. We show that the k eigenvectors of this matrix whose eigenvalues are most different from 1/2 offer the best rank k approximation to the maximum likelihood classifier. The matrix Λ and its eigenvectors have been introduced by Fukunaga and Koontz; hence this analysis gives a new interpretation of the well known Fukunaga-Koontz transform. The optimality that is promised in this method hold if the two populations are exactly Guassian with the same means. To check the applicability of this approach to real data, an experiment is performed, in which several 'modern' classifiers were used on an Infrared ATR data. In these experiments, a reduced-rank classifier-Tuned Basis Functions-outperforms others. The competitive performance of the optimal reduced-rank quadratic classifier suggests that, at least for classification purposes, the imagery data behaves in a nearly-Gaussian fashion.
International Nuclear Information System (INIS)
Ayvaz, Muzaffer; Demiralp, Metin
2011-01-01
In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.
International Nuclear Information System (INIS)
Parker, G.G.; Eisler, G.R.; Feddema, J.T.
1994-01-01
Procedures for trajectory planning and control of flexible link robots are becoming increasingly important to satisfy performance requirements of hazardous waste removal efforts. It has been shown that utilizing link flexibility in designing open loop joint commands can result in improved performance as opposed to damping vibration throughout a trajectory. The efficient use of link compliance is exploited in this work. Specifically, experimental verification of minimum time, straight line tracking using a two-link planar flexible robot is presented. A numerical optimization process, using an experimentally verified modal model, is used for obtaining minimum time joint torque and angle histories. The optimal joint states are used as commands to the proportional-derivative servo actuated joints. These commands are precompensated for the nonnegligible joint servo actuator dynamics. Using the precompensated joint commands, the optimal joint angles are tracked with such fidelity that the tip tracking error is less than 2.5 cm
Overlapping quadratic optimal control of linear time-varying commutative systems
Czech Academy of Sciences Publication Activity Database
Bakule, Lubomír; Rodellar, J.; Rossell, J. M.
2002-01-01
Roč. 40, č. 5 (2002), s. 1611-1627 ISSN 0363-0129 R&D Projects: GA AV ČR IAA2075802 Institutional research plan: CEZ:AV0Z1075907 Keywords : overlapping * optimal control * linear time-varying systems Subject RIV: BC - Control Systems Theory Impact factor: 1.441, year: 2002
Goldengorin, B.; Ghosh, D.
Maximization of submodular functions on a ground set is a NP-hard combinatorial optimization problem. Data correcting algorithms are among the several algorithms suggested for solving this problem exactly and approximately. From the point of view of Hasse diagrams data correcting algorithms use
Optimization problem in quantum cryptography
International Nuclear Information System (INIS)
Brandt, Howard E
2003-01-01
A complete optimization was recently performed, yielding the maximum information gain by a general unitary entangling probe in the four-state protocol of quantum cryptography. A larger set of optimum probe parameters was found than was known previously from an incomplete optimization. In the present work, a detailed comparison is made between the complete and incomplete optimizations. Also, a new set of optimum probe parameters is identified for the four-state protocol
International Nuclear Information System (INIS)
Shafie-khah, M.; Parsa Moghaddam, M.; Sheikh-El-Eslami, M.K.
2011-01-01
Highlights: → A hybrid SCUC solution is developed to deal with large-scale, real-time and long-term problems. → New formulations are proposed for considering valve point effect and warmth-dependent start-up cost. → A new algorithm is developed for modeling the AC power flow in SCUC problems. → Using the power flow algorithm both steps in traditional SCUC is done simultaneously. → The proposed method provides better solutions than previous ones with a fast speed. - Abstract: In this paper, a new practical method is presented for solving the non-convex security constraint unit commitment (SCUC) problem in power systems. The accuracy of the proposed method is desirable while the shorter computation time makes it useful for SCUC solution of large-scale power systems, real-time market operation and long-term SCUC problems. The proposed framework allows inclusion of the valve point effects, warmth-dependent start-up costs, ramp rates, minimum up/down time constraints, multiple fuels costs, emission costs, prohibited operating zones and AC power flow limits in normal and contingency conditions. To solve the non-convex problem, combination of a modified Branch-and-Bound method with the Quadratic Programming is used as an optimization tool and a developed AC power flow algorithm is applied for considering the security and contingency concerns using the nonlinear/linear AC model. These modifications improve the convergence speed and solution precision of SCUC problem. In the proposed method, in contrast with traditional SCUC algorithms, unit commitment solution, checking and satisfying the security constraints are managed simultaneously. The obtained results are compared with other reported methods for investigating the effectiveness of the proposed method. Also, the proposed method is applied to an Iranian power system including 493 thermal units.
SOCP relaxation bounds for the optimal subset selection problem applied to robust linear regression
Flores, Salvador
2015-01-01
This paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion, with an special emphasis on applications to computing the Least Trimmed Squares Estimator (LTSE) for robust regression. The computation of the LTSE is a challenging subset selection problem involving a nonlinear program with continuous and binary variables, linked in a highly nonlinear fashion. The selection of a ...
Janssen, D.M.; Paas, L.J.
2014-01-01
The authors hypothesize and find that an advertising model's body size has an inverted U-shaped relationship with ad attitude in the apparel product category, in which moderately thin advertising models are optimal. They assess the moderating effect of consumers' fashion leadership on this quadratic
Zhao, Wenzhu; Yu, Zhipeng; Liu, Jingbo; Yu, Yiding; Yin, Yongguang; Lin, Songyi; Chen, Feng
2011-09-01
Corn silk is a traditional Chinese herbal medicine, which has been widely used for treatment of some diseases. In this study the effects of pulsed electric field on the extraction of polysaccharides from corn silk were investigated. Polysaccharides in corn silk were extracted by pulsed electric field and optimized by response surface methodology (RSM), based on a Box-Behnken design (BBD). Three independent variables, including electric field intensity (kV cm(-1) ), ratio of liquid to raw material and pulse duration (µs), were investigated. The experimental data were fitted to a second-order polynomial equation and also profiled into the corresponding 3-D contour plots. Optimal extraction conditions were as follows: electric field intensity 30 kV cm(-1) , ratio of liquid to raw material 50, and pulse duration 6 µs. Under these condition, the experimental yield of extracted polysaccharides was 7.31% ± 0.15%, matching well with the predicted value. The results showed that a pulsed electric field could be applied to extract value-added products from foods and/or agricultural matrix. Copyright © 2011 Society of Chemical Industry.
Huang, Tsung-Ming; Lin, Wen-Wei; Tian, Heng; Chen, Guan-Hua
2018-03-01
Full spectrum of a large sparse ⊤-palindromic quadratic eigenvalue problem (⊤-PQEP) is considered arguably for the first time in this article. Such a problem is posed by calculation of surface Green's functions (SGFs) of mesoscopic transistors with a tremendous non-periodic cross-section. For this problem, general purpose eigensolvers are not efficient, nor is advisable to resort to the decimation method etc. to obtain the Wiener-Hopf factorization. After reviewing some rigorous understanding of SGF calculation from the perspective of ⊤-PQEP and nonlinear matrix equation, we present our new approach to this problem. In a nutshell, the unit disk where the spectrum of interest lies is broken down adaptively into pieces small enough that they each can be locally tackled by the generalized ⊤-skew-Hamiltonian implicitly restarted shift-and-invert Arnoldi (G⊤SHIRA) algorithm with suitable shifts and other parameters, and the eigenvalues missed by this divide-and-conquer strategy can be recovered thanks to the accurate estimation provided by our newly developed scheme. Notably the novel non-equivalence deflation is proposed to avoid as much as possible duplication of nearby known eigenvalues when a new shift of G⊤SHIRA is determined. We demonstrate our new approach by calculating the SGF of a realistic nanowire whose unit cell is described by a matrix of size 4000 × 4000 at the density functional tight binding level, corresponding to a 8 × 8nm2 cross-section. We believe that quantum transport simulation of realistic nano-devices in the mesoscopic regime will greatly benefit from this work.
Separable quadratic stochastic operators
International Nuclear Information System (INIS)
Rozikov, U.A.; Nazir, S.
2009-04-01
We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)
A program package for solving linear optimization problems
International Nuclear Information System (INIS)
Horikami, Kunihiko; Fujimura, Toichiro; Nakahara, Yasuaki
1980-09-01
Seven computer programs for the solution of linear, integer and quadratic programming (four programs for linear programming, one for integer programming and two for quadratic programming) have been prepared and tested on FACOM M200 computer, and auxiliary programs have been written to make it easy to use the optimization program package. The characteristics of each program are explained and the detailed input/output descriptions are given in order to let users know how to use them. (author)
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....
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…
PSQP: Puzzle Solving by Quadratic Programming.
Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome
2017-02-01
In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
Generalized Benders’ Decomposition for topology optimization problems
DEFF Research Database (Denmark)
Munoz Queupumil, Eduardo Javier; Stolpe, Mathias
2011-01-01
) problems with discrete design variables to global optimality. We present the theoretical aspects of the method, including a proof of finite convergence and conditions for obtaining global optimal solutions. The method is also linked to, and compared with, an Outer-Approximation approach and a mixed 0......–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.......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...
Optimal control of LQG problem with an explicit trade-off between mean and variance
Qian, Fucai; Xie, Guo; Liu, Ding; Xie, Wenfang
2011-12-01
For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean-variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.
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...
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.
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...
International Nuclear Information System (INIS)
Jian Jinbao; Li Jianling; Mo Xingde
2006-01-01
This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998),5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported
Directory of Open Access Journals (Sweden)
Wanfang Shen
2012-01-01
Full Text Available The mathematical formulation for a quadratic optimal control problem governed by a linear quasiparabolic integrodifferential equation is studied. The control constrains are given in an integral sense: Uad={u∈X;∫ΩUu⩾0, t∈[0,T]}. Then the a posteriori error estimates in L∞(0,T;H1(Ω-norm and L2(0,T;L2(Ω-norm for both the state and the control approximation are given.
Global optimization of truss topology with discrete bar areas—Part I: Theory of relaxed problems
DEFF Research Database (Denmark)
Achtziger, Wolfgang; Stolpe, Mathias
2008-01-01
the case of discrete areas. This problem is of major practical relevance if the truss must be built from pre-produced bars with given areas. As a special case, we consider the design problem for a single bar area, i.e., a 0/1-problem. In contrast to heuristic methods considered in other approaches, Part I....... The main issue of the paper and of the approach lies in the fact that the relaxed nonlinear optimization problem can be formulated as a quadratic program (QP). Here the paper generalizes and extends the available theory from the literature. Although the Hessian of this QP is indefinite, it is possible...
FIREWORKS ALGORITHM FOR UNCONSTRAINED FUNCTION OPTIMIZATION PROBLEMS
Directory of Open Access Journals (Sweden)
Evans BAIDOO
2017-03-01
Full Text Available Modern real world science and engineering problems can be classified as multi-objective optimisation problems which demand for expedient and efficient stochastic algorithms to respond to the optimization needs. This paper presents an object-oriented software application that implements a firework optimization algorithm for function optimization problems. The algorithm, a kind of parallel diffuse optimization algorithm is based on the explosive phenomenon of fireworks. The algorithm presented promising results when compared to other population or iterative based meta-heuristic algorithm after it was experimented on five standard benchmark problems. The software application was implemented in Java with interactive interface which allow for easy modification and extended experimentation. Additionally, this paper validates the effect of runtime on the algorithm performance.
Bozkaya, Uǧur; Turney, Justin M.; Yamaguchi, Yukio; Schaefer, Henry F.; Sherrill, C. David
2011-09-01
Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order Møller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H2O, three diatomics, and the O_4^+ molecule. Results demonstrate that the CCSD and OD methods give nearly identical results for H2O and diatomics; however, in symmetry-breaking problems as exemplified by O_4^+, the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle density matrices, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that
Approximative solutions of stochastic optimization problem
Czech Academy of Sciences Publication Activity Database
Lachout, Petr
2010-01-01
Roč. 46, č. 3 (2010), s. 513-523 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic optimization problem * sensitivity * approximative solution Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/lachout-approximative solutions of stochastic optimization problem.pdf
Problem of detecting inclusions by topological optimization
Directory of Open Access Journals (Sweden)
I. Faye
2014-01-01
Full Text Available In this paper we propose a new method to detect inclusions. The proposed method is based on shape and topological optimization tools. In fact after presenting the problem, we use topologication optimization tools to detect inclusions in the domain. Numerical results are presented.
Stochastic global optimization as a filtering problem
International Nuclear Information System (INIS)
Stinis, Panos
2012-01-01
We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be optimized. Similarly, we may not be able to evaluate exactly the functions involved in iterative optimization algorithms. For example, we may only have access to noisy measurements of the functions or statistical estimates provided through Monte Carlo sampling. This makes iterative optimization algorithms behave like stochastic maps. Naive global optimization amounts to evolving a collection of realizations of this stochastic map and picking the realization with the best properties. This motivates the use of filtering techniques to allow focusing on realizations that are more promising than others. In particular, we present a filtering reformulation of global optimization in terms of a special case of sequential importance sampling methods called particle filters. The increasing popularity of particle filters is based on the simplicity of their implementation and their flexibility. We utilize the flexibility of particle filters to construct a stochastic global optimization algorithm which can converge to the optimal solution appreciably faster than naive global optimization. Several examples of parametric exponential density estimation are provided to demonstrate the efficiency of the approach.
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......-stepping scheme. A PCM can efficiently absorb heat while keeping its temperature nearly unchanged [8]. The use of PCM ine.g. electronics [9] and mechanics [10], yields improved performance and lower costs depending on a.o., the spatial distribution of PCM.The considered problem consists in optimizing...
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.
Directory of Open Access Journals (Sweden)
Xiangrong Li
Full Text Available It is generally acknowledged that the conjugate gradient (CG method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.
Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang
2015-01-01
It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.
Adjoint optimization of natural convection problems: differentially heated cavity
Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.
2017-12-01
Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here for
Sensitivity analysis in optimization and reliability problems
International Nuclear Information System (INIS)
Castillo, Enrique; Minguez, Roberto; Castillo, Carmen
2008-01-01
The paper starts giving the main results that allow a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. In particular, general results are given for non-linear programming, and closed formulas for linear programming problems are supplied. Next, the methods are applied to a collection of civil engineering reliability problems, which includes a bridge crane, a retaining wall and a composite breakwater. Finally, the sensitivity analysis formulas are extended to calculus of variations problems and a slope stability problem is used to illustrate the methods
Sensitivity analysis in optimization and reliability problems
Energy Technology Data Exchange (ETDEWEB)
Castillo, Enrique [Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. Castros s/n., 39005 Santander (Spain)], E-mail: castie@unican.es; Minguez, Roberto [Department of Applied Mathematics, University of Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: roberto.minguez@uclm.es; Castillo, Carmen [Department of Civil Engineering, University of Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: mariacarmen.castillo@uclm.es
2008-12-15
The paper starts giving the main results that allow a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. In particular, general results are given for non-linear programming, and closed formulas for linear programming problems are supplied. Next, the methods are applied to a collection of civil engineering reliability problems, which includes a bridge crane, a retaining wall and a composite breakwater. Finally, the sensitivity analysis formulas are extended to calculus of variations problems and a slope stability problem is used to illustrate the methods.
Utilizing Problem Structure in Optimization of Radiation Therapy
International Nuclear Information System (INIS)
Carlsson, Fredrik
2008-04-01
In this thesis, optimization approaches for intensity-modulated radiation therapy are developed and evaluated with focus on numerical efficiency and treatment delivery aspects. The first two papers deal with strategies for solving fluence map optimization problems efficiently while avoiding solutions with jagged fluence profiles. The last two papers concern optimization of step-and-shoot parameters with emphasis on generating treatment plans that can be delivered efficiently and accurately. In the first paper, the problem dimension of a fluence map optimization problem is reduced through a spectral decomposition of the Hessian of the objective function. The weights of the eigenvectors corresponding to the p largest eigenvalues are introduced as optimization variables, and the impact on the solution of varying p is studied. Including only a few eigenvector weights results in faster initial decrease of the objective value, but with an inferior solution, compared to optimization of the bixel weights. An approach combining eigenvector weights and bixel weights produces improved solutions, but at the expense of the pre-computational time for the spectral decomposition. So-called iterative regularization is performed on fluence map optimization problems in the second paper. The idea is to find regular solutions by utilizing an optimization method that is able to find near-optimal solutions with non-jagged fluence profiles in few iterations. The suitability of a quasi-Newton sequential quadratic programming method is demonstrated by comparing the treatment quality of deliverable step-and-shoot plans, generated through leaf sequencing with a fixed number of segments, for different number of bixel-weight iterations. A conclusion is that over-optimization of the fluence map optimization problem prior to leaf sequencing should be avoided. An approach for dynamically generating multileaf collimator segments using a column generation approach combined with optimization of
Topology optimization of Channel flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.
2005-01-01
function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical......This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low to moderate Reynolds numbers. This makes the flow problem non-linear and hence a non-trivial extension of the work of [Borrvall&Petersson 2002......]. 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...
Path optimization method for the sign problem
Directory of Open Access Journals (Sweden)
Ohnishi Akira
2018-01-01
Full Text Available We propose a path optimization method (POM to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are promising and extensively discussed. In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled. When we have singular points of the action or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem. One of the ways to avoid the singular points is to optimize the integration path which is designed not to hit the singular points of the Boltzmann weight. By specifying the one-dimensional integration-path as z = t +if(t(f ϵ R and by optimizing f(t to enhance the average phase factor, we demonstrate that we can avoid the sign problem in a one-variable toy model for which the complex Langevin method is found to fail. In this proceedings, we propose POM and discuss how we can avoid the sign problem in a toy model. We also discuss the possibility to utilize the neural network to optimize the path.
Directory of Open Access Journals (Sweden)
Zulqurnain Sabir
2014-06-01
Full Text Available In this paper, computational intelligence technique are presented for solving multi-point nonlinear boundary value problems based on artificial neural networks, evolutionary computing approach, and active-set technique. The neural network is to provide convenient methods for obtaining useful model based on unsupervised error for the differential equations. The motivation for presenting this work comes actually from the aim of introducing a reliable framework that combines the powerful features of ANN optimized with soft computing frameworks to cope with such challenging system. The applicability and reliability of such methods have been monitored thoroughly for various boundary value problems arises in science, engineering and biotechnology as well. Comprehensive numerical experimentations have been performed to validate the accuracy, convergence, and robustness of the designed scheme. Comparative studies have also been made with available standard solution to analyze the correctness of the proposed scheme.
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......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...... processing tool. Prior to design manufacturing this allows the engineer to quantify the performance of the computed topology design using standard, credible analysis tools with a body-fitted mesh. [1] Borrvall and Petersson (2003) "Topology optimization of fluids in Stokes flow", Int. J. Num. Meth. Fluids...
Topology Optimization for Transient Wave Propagation Problems
DEFF Research Database (Denmark)
Matzen, René
The study of elastic and optical waves together with intensive material research has revolutionized everyday as well as cutting edge technology in very tangible ways within the last century. Therefore it is important to continue the investigative work towards improving existing as well as innovate...... 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...... optimization is still in its infancy. A generic optimization problem is formulated with an objective function that can be field, velocity, and acceleration dependent, as well as it can accommodate the dependency of filtered signals essential in signal shape optimization [P3]. The analytical design gradients...
Directory of Open Access Journals (Sweden)
Charles Nkeki
2013-11-01
Full Text Available This paper examines a mean-variance portfolio selection problem with stochastic salary and inflation protection strategy in the accumulation phase of a defined contribution (DC pension plan. The utility function is assumed to be quadratic. It was assumed that the flow of contributions made by the PPM are invested into a market that is characterized by a cash account, an inflation-linked bond and a stock. In this paper, inflationlinked bond is traded and used to hedge inflation risks associated with the investment. The aim of this paper is to maximize the expected final wealth and minimize its variance. Efficient frontier for the three classes of assets (under quadratic utility function that will enable pension plan members (PPMs to decide their own wealth and risk in their investment profile at retirement was obtained.
A joint routing and speed optimization problem
Fukasawa, Ricardo; He, Qie; Santos, Fernando; Song, Yongjia
2016-01-01
Fuel cost contributes to a significant portion of operating cost in cargo transportation. Though classic routing models usually treat fuel cost as input data, fuel consumption heavily depends on the travel speed, which has led to the study of optimizing speeds over a given fixed route. In this paper, we propose a joint routing and speed optimization problem to minimize the total cost, which includes the fuel consumption cost. The only assumption made on the dependence between the fuel cost an...
Optimal consumption problem in the Vasicek model
Directory of Open Access Journals (Sweden)
Jakub Trybuła
2015-01-01
Full Text Available We consider the problem of an optimal consumption strategy on the infinite time horizon based on the hyperbolic absolute risk aversion utility when the interest rate is an Ornstein-Uhlenbeck process. Using the method of subsolution and supersolution we obtain the existence of solutions of the dynamic programming equation. We illustrate the paper with a numerical example of the optimal consumption strategy and the value function.
Multiparameter Optimization for Electromagnetic Inversion Problem
Directory of Open Access Journals (Sweden)
M. Elkattan
2017-10-01
Full Text Available Electromagnetic (EM methods have been extensively used in geophysical investigations such as mineral and hydrocarbon exploration as well as in geological mapping and structural studies. In this paper, we developed an inversion methodology for Electromagnetic data to determine physical parameters of a set of horizontal layers. We conducted Forward model using transmission line method. In the inversion part, we solved multi parameter optimization problem where, the parameters are conductivity, dielectric constant, and permeability of each layer. The optimization problem was solved by simulated annealing approach. The inversion methodology was tested using a set of models representing common geological formations.
Modeling of Mean-VaR portfolio optimization by risk tolerance when the utility function is quadratic
Sukono, Sidi, Pramono; Bon, Abdul Talib bin; Supian, Sudradjat
2017-03-01
The problems of investing in financial assets are to choose a combination of weighting a portfolio can be maximized return expectations and minimizing the risk. This paper discusses the modeling of Mean-VaR portfolio optimization by risk tolerance, when square-shaped utility functions. It is assumed that the asset return has a certain distribution, and the risk of the portfolio is measured using the Value-at-Risk (VaR). So, the process of optimization of the portfolio is done based on the model of Mean-VaR portfolio optimization model for the Mean-VaR done using matrix algebra approach, and the Lagrange multiplier method, as well as Khun-Tucker. The results of the modeling portfolio optimization is in the form of a weighting vector equations depends on the vector mean return vector assets, identities, and matrix covariance between return of assets, as well as a factor in risk tolerance. As an illustration of numeric, analyzed five shares traded on the stock market in Indonesia. Based on analysis of five stocks return data gained the vector of weight composition and graphics of efficient surface of portfolio. Vector composition weighting weights and efficient surface charts can be used as a guide for investors in decisions to invest.
Solving global optimization problems on GPU cluster
Energy Technology Data Exchange (ETDEWEB)
Barkalov, Konstantin; Gergel, Victor; Lebedev, Ilya [Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod (Russian Federation)
2016-06-08
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.
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....
Problems of the power plant shield optimization
International Nuclear Information System (INIS)
Abagyan, A.A.; Dubinin, A.A.; Zhuravlev, V.I.; Kurachenko, Yu.A.; Petrov, Eh.E.
1981-01-01
General approaches to the solution of problems on the nuclear power plant radiation shield optimization are considered. The requirements to the shield parameters are formulated in a form of restrictions on a number of functionals, determined by the solution of γ quantum and neutron transport equations or dimensional and weight characteristics of shield components. Functional determined by weight-dimensional parameters (shield cost, mass and thickness) and functionals, determined by radiation fields (equivalent dose rate, produced by neutrons and γ quanta, activation functional, radiation functional, heat flux, integral heat flux in a particular part of the shield volume, total energy flux through a particular shield surface are considered. The following methods of numerical solution of simplified optimization problems are discussed: semiempirical methods using radiation transport physical leaks, numerical solution of approximate transport equations, numerical solution of transport equations for the simplest configurations making possible to decrease essentially a number of variables in the problem. The conclusion is drawn that the attained level of investigations on the problem of nuclear power plant shield optimization gives the possibility to pass on at present to the solution of problems with a more detailed account of the real shield operating conditions (shield temperature field account, its strength and other characteristics) [ru
Statistical physics of hard optimization problems
International Nuclear Information System (INIS)
Zdeborova, L.
2009-01-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfy ability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named ”locked” constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfy ability.
Statistical physics of hard optimization problems
International Nuclear Information System (INIS)
Zdeborova, L.
2009-01-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an non-deterministic polynomial-complete problem the practically arising instances might, in fact, be easy to solve. The principal the question we address in the article is: How to recognize if an non-deterministic polynomial-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named 'locked' constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability (Authors)
Statistical physics of hard optimization problems
Zdeborová, Lenka
2009-06-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.
Indian Academy of Sciences (India)
V. Suresh University Of Hyderabad Hyderabad
2008-10-31
Oct 31, 2008 ... We say that (a1,··· ,an) is a zero of the polynomial f if f (a1,··· ,an) = 0. One of the main problems in Mathematics is to determine whether the given polynomial has a (non-trivial) zero or not. For example, let us recall the Fermat's last theorem: V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic ...
Ahmet Demir; Utku Kose
2016-01-01
ABSTRACT 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 Sc...
Ahmet Demir; Utku kose
2017-01-01
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...
Motiwalla, S. K.
1973-01-01
Using the first and the second derivative of flutter velocity with respect to the parameters, the velocity hypersurface is made quadratic. This greatly simplifies the numerical procedure developed for determining the values of the design parameters such that a specified flutter velocity constraint is satisfied and the total structural mass is near a relative minimum. A search procedure is presented utilizing two gradient search methods and a gradient projection method. The procedure is applied to the design of a box beam, using finite-element representation. The results indicate that the procedure developed yields substantial design improvement satisfying the specified constraint and does converge to near a local optimum.
Automation of reverse engineering process in aircraft modeling and related optimization problems
Li, W.; Swetits, J.
1994-01-01
During the year of 1994, the engineering problems in aircraft modeling were studied. The initial concern was to obtain a surface model with desirable geometric characteristics. Much of the effort during the first half of the year was to find an efficient way of solving a computationally difficult optimization model. Since the smoothing technique in the proposal 'Surface Modeling and Optimization Studies of Aerodynamic Configurations' requires solutions of a sequence of large-scale quadratic programming problems, it is important to design algorithms that can solve each quadratic program in a few interactions. This research led to three papers by Dr. W. Li, which were submitted to SIAM Journal on Optimization and Mathematical Programming. Two of these papers have been accepted for publication. Even though significant progress has been made during this phase of research and computation times was reduced from 30 min. to 2 min. for a sample problem, it was not good enough for on-line processing of digitized data points. After discussion with Dr. Robert E. Smith Jr., it was decided not to enforce shape constraints in order in order to simplify the model. As a consequence, P. Dierckx's nonparametric spline fitting approach was adopted, where one has only one control parameter for the fitting process - the error tolerance. At the same time the surface modeling software developed by Imageware was tested. Research indicated a substantially improved fitting of digitalized data points can be achieved if a proper parameterization of the spline surface is chosen. A winning strategy is to incorporate Dierckx's surface fitting with a natural parameterization for aircraft parts. The report consists of 4 chapters. Chapter 1 provides an overview of reverse engineering related to aircraft modeling and some preliminary findings of the effort in the second half of the year. Chapters 2-4 are the research results by Dr. W. Li on penalty functions and conjugate gradient methods for
Finite Optimal Stopping Problems: The Seller's Perspective
Hemmati, Mehdi; Smith, J. Cole
2011-01-01
We consider a version of an optimal stopping problem, in which a customer is presented with a finite set of items, one by one. The customer is aware of the number of items in the finite set and the minimum and maximum possible value of each item, and must purchase exactly one item. When an item is presented to the customer, she or he observes its…
Optimal control problem for the extended Fisher–Kolmogorov equation
Indian Academy of Sciences (India)
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.
Dynamical invariants for variable quadratic Hamiltonians
International Nuclear Information System (INIS)
Suslov, Sergei K
2010-01-01
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.
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.
Climate Intervention as an Optimization Problem
Caldeira, Ken; Ban-Weiss, George A.
2010-05-01
Typically, climate models simulations of intentional intervention in the climate system have taken the approach of imposing a change (eg, in solar flux, aerosol concentrations, aerosol emissions) and then predicting how that imposed change might affect Earth's climate or chemistry. Computations proceed from cause to effect. However, humans often proceed from "What do I want?" to "How do I get it?" One approach to thinking about intentional intervention in the climate system ("geoengineering") is to ask "What kind of climate do we want?" and then ask "What pattern of radiative forcing would come closest to achieving that desired climate state?" This involves defining climate goals and a cost function that measures how closely those goals are attained. (An important next step is to ask "How would we go about producing these desired patterns of radiative forcing?" However, this question is beyond the scope of our present study.) We performed a variety of climate simulations in NCAR's CAM3.1 atmospheric general circulation model with a slab ocean model and thermodynamic sea ice model. We then evaluated, for a specific set of climate forcing basis functions (ie, aerosol concentration distributions), the extent to which the climate response to a linear combination of those basis functions was similar to a linear combination of the climate response to each basis function taken individually. We then developed several cost functions (eg, relative to the 1xCO2 climate, minimize rms difference in zonal and annual mean land temperature, minimize rms difference in zonal and annual mean runoff, minimize rms difference in a combination of these temperature and runoff indices) and then predicted optimal combinations of our basis functions that would minimize these cost functions. Lastly, we produced forward simulations of the predicted optimal radiative forcing patterns and compared these with our expected results. Obviously, our climate model is much simpler than reality and
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...
Low-rank quadratic semidefinite programming
Yuan, Ganzhao
2013-04-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Low-rank quadratic semidefinite programming
Yuan, Ganzhao; Zhang, Zhenjie; Ghanem, Bernard; Hao, Zhifeng
2013-01-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Domí nguez, Luis F.; Pistikopoulos, Efstratios N.
2012-01-01
An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear
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
Relaxations to Sparse Optimization Problems and Applications
Skau, Erik West
Parsimony is a fundamental property that is applied to many characteristics in a variety of fields. Of particular interest are optimization problems that apply rank, dimensionality, or support in a parsimonious manner. In this thesis we study some optimization problems and their relaxations, and focus on properties and qualities of the solutions of these problems. The Gramian tensor decomposition problem attempts to decompose a symmetric tensor as a sum of rank one tensors.We approach the Gramian tensor decomposition problem with a relaxation to a semidefinite program. We study conditions which ensure that the solution of the relaxed semidefinite problem gives the minimal Gramian rank decomposition. Sparse representations with learned dictionaries are one of the leading image modeling techniques for image restoration. When learning these dictionaries from a set of training images, the sparsity parameter of the dictionary learning algorithm strongly influences the content of the dictionary atoms.We describe geometrically the content of trained dictionaries and how it changes with the sparsity parameter.We use statistical analysis to characterize how the different content is used in sparse representations. Finally, a method to control the structure of the dictionaries is demonstrated, allowing us to learn a dictionary which can later be tailored for specific applications. Variations of dictionary learning can be broadly applied to a variety of applications.We explore a pansharpening problem with a triple factorization variant of coupled dictionary learning. Another application of dictionary learning is computer vision. Computer vision relies heavily on object detection, which we explore with a hierarchical convolutional dictionary learning model. Data fusion of disparate modalities is a growing topic of interest.We do a case study to demonstrate the benefit of using social media data with satellite imagery to estimate hazard extents. In this case study analysis we
The bounds of feasible space on constrained nonconvex quadratic programming
Zhu, Jinghao
2008-03-01
This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.
A penalty method for PDE-constrained optimization in inverse problems
International Nuclear Information System (INIS)
Leeuwen, T van; Herrmann, F J
2016-01-01
Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the parameters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the nonlinearity of the problem and is less sensitive to the initial iterate. (paper)
A hybrid iterative scheme for optimal control problems governed by ...
African Journals Online (AJOL)
MRT
KEY WORDS: Optimal control problem; Fredholm integral equation; ... control problems governed by Fredholm integral and integro-differential equations is given in (Brunner and Yan, ..... The exact optimal trajectory and control functions are. 2.
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.
Directory of Open Access Journals (Sweden)
Wei Gao
2016-01-01
Full Text Available According to the regularization method in the inverse problem of load identification, a new method for determining the optimal regularization parameter is proposed. Firstly, quotient function (QF is defined by utilizing the regularization parameter as a variable based on the least squares solution of the minimization problem. Secondly, the quotient function method (QFM is proposed to select the optimal regularization parameter based on the quadratic programming theory. For employing the QFM, the characteristics of the values of QF with respect to the different regularization parameters are taken into consideration. Finally, numerical and experimental examples are utilized to validate the performance of the QFM. Furthermore, the Generalized Cross-Validation (GCV method and the L-curve method are taken as the comparison methods. The results indicate that the proposed QFM is adaptive to different measuring points, noise levels, and types of dynamic load.
System and economic optimization problems of NPPs and its ideology
International Nuclear Information System (INIS)
Klimenko, A.V.; Mironovich, V.L.
2016-01-01
The iterative circuit design of optimization of system of links of nuclear fuel and energy complex (NFEC) is presented in the paper. Problems of system optimization of links NFEC as functional of NPP optimization are indicated and investigated [ru
Finite Volumes Discretization of Topology Optimization Problems
DEFF Research Database (Denmark)
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly...... computations is done using nite element methods (FEMs). Despite some limited recent eorts [1, 2], we have only started to develop our understanding of the interplay between the control in the coecients and FVMs. Recent advances in discrete functional analysis allow us to analyze convergence of FVM...... of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout...
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.
On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations
International Nuclear Information System (INIS)
Sekine, Jun
2006-01-01
The dual optimization problem for the exponential hedging problem is addressed with a cone constraint. Without boundedness conditions on the terminal payoff and the drift of the Ito-type controlled process, the backward stochastic differential equation, which has a quadratic growth term in the drift, is derived as a necessary and sufficient condition for optimality via a variational method and dynamic programming. Further, solvable situations are given, in which the value and the optimizer are expressed in closed forms with the help of the Clark-Haussmann-Ocone formula
Goldengorin, Boris; Vink, Marius de
1999-01-01
The Data-Correcting Algorithm (DCA) corrects the data of a hard problem instance in such a way that we obtain an instance of a well solvable special case. For a given prescribed accuracy of the solution, the DCA uses a branch and bound scheme to make sure that the solution of the corrected instance
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…
Firefly Mating Algorithm for Continuous Optimization Problems
Directory of Open Access Journals (Sweden)
Amarita Ritthipakdee
2017-01-01
Full Text Available This paper proposes a swarm intelligence algorithm, called firefly mating algorithm (FMA, for solving continuous optimization problems. FMA uses genetic algorithm as the core of the algorithm. The main feature of the algorithm is a novel mating pair selection method which is inspired by the following 2 mating behaviors of fireflies in nature: (i the mutual attraction between males and females causes them to mate and (ii fireflies of both sexes are of the multiple-mating type, mating with multiple opposite sex partners. A female continues mating until her spermatheca becomes full, and, in the same vein, a male can provide sperms for several females until his sperm reservoir is depleted. This new feature enhances the global convergence capability of the algorithm. The performance of FMA was tested with 20 benchmark functions (sixteen 30-dimensional functions and four 2-dimensional ones against FA, ALC-PSO, COA, MCPSO, LWGSODE, MPSODDS, DFOA, SHPSOS, LSA, MPDPGA, DE, and GABC algorithms. The experimental results showed that the success rates of our proposed algorithm with these functions were higher than those of other algorithms and the proposed algorithm also required fewer numbers of iterations to reach the global optima.
Optimal management with hybrid dynamics : The shallow lake problem
Reddy, P.V.; Schumacher, Hans; Engwerda, Jacob; Camlibel, M.K.; Julius, A.A.; Pasumarthy, R.
2015-01-01
In this article we analyze an optimal management problem that arises in ecological economics using hybrid systems modeling. First, we introduce a discounted autonomous infinite horizon hybrid optimal control problem and develop few tools to analyze the necessary conditions for optimality. Next,
A note on the depth function of combinatorial optimization problems
Woeginger, G.J.
2001-01-01
In a recent paper [Discrete Appl. Math. 43 (1993) 115–129], Kern formulates two conjectures on the relationship between the computational complexity of computing the depth function of a discrete optimization problem and the computational complexity of solving this optimization problem to optimality.
MO-FG-CAMPUS-TeP3-04: Deliverable Robust Optimization in IMPT Using Quadratic Objective Function
Energy Technology Data Exchange (ETDEWEB)
Shan, J; Liu, W; Bues, M; Schild, S [Mayo Clinic Arizona, Phoenix, AZ (United States)
2016-06-15
Purpose: To find and evaluate the way of applying deliverable MU constraints into robust spot intensity optimization in Intensity-Modulated- Proton-Therapy (IMPT) to prevent plan quality and robustness from degrading due to machine deliverable MU-constraints. Methods: Currently, the influence of the deliverable MU-constraints is retrospectively evaluated by post-processing immediately following optimization. In this study, we propose a new method based on the quasi-Newton-like L-BFGS-B algorithm with which we turn deliverable MU-constraints on and off alternatively during optimization. Seven patients with two different machine settings (small and large spot size) were planned with both conventional and new methods. For each patient, three kinds of plans were generated — conventional non-deliverable plan (plan A), conventional deliverable plan with post-processing (plan B), and new deliverable plan (plan C). We performed this study with both realistic (small) and artificial (large) deliverable MU-constraints. Results: With small minimum MU-constraints considered, new method achieved a slightly better plan quality than conventional method (D95% CTV normalized to the prescription dose: 0.994[0.992∼0.996] (Plan C) vs 0.992[0.986∼0.996] (Plan B)). With large minimum MU constraints considered, results show that the new method maintains plan quality while plan quality from the conventional method is degraded greatly (D95% CTV normalized to the prescription dose: 0.987[0.978∼0.994] (Plan C) vs 0.797[0.641∼1.000] (Plan B)). Meanwhile, plan robustness of these two method’s results is comparable. (For all 7 patients, CTV DVH band gap at D95% normalized to the prescription dose: 0.015[0.005∼0.043] (Plan C) vs 0.012[0.006∼0.038] (Plan B) with small MU-constraints and 0.019[0.009∼0.039] (Plan C) vs 0.030[0.015∼0.041] (Plan B) with large MU-constraints) Conclusion: Positive correlation has been found between plan quality degeneration and magnitude of
MO-FG-CAMPUS-TeP3-04: Deliverable Robust Optimization in IMPT Using Quadratic Objective Function
International Nuclear Information System (INIS)
Shan, J; Liu, W; Bues, M; Schild, S
2016-01-01
Purpose: To find and evaluate the way of applying deliverable MU constraints into robust spot intensity optimization in Intensity-Modulated- Proton-Therapy (IMPT) to prevent plan quality and robustness from degrading due to machine deliverable MU-constraints. Methods: Currently, the influence of the deliverable MU-constraints is retrospectively evaluated by post-processing immediately following optimization. In this study, we propose a new method based on the quasi-Newton-like L-BFGS-B algorithm with which we turn deliverable MU-constraints on and off alternatively during optimization. Seven patients with two different machine settings (small and large spot size) were planned with both conventional and new methods. For each patient, three kinds of plans were generated — conventional non-deliverable plan (plan A), conventional deliverable plan with post-processing (plan B), and new deliverable plan (plan C). We performed this study with both realistic (small) and artificial (large) deliverable MU-constraints. Results: With small minimum MU-constraints considered, new method achieved a slightly better plan quality than conventional method (D95% CTV normalized to the prescription dose: 0.994[0.992∼0.996] (Plan C) vs 0.992[0.986∼0.996] (Plan B)). With large minimum MU constraints considered, results show that the new method maintains plan quality while plan quality from the conventional method is degraded greatly (D95% CTV normalized to the prescription dose: 0.987[0.978∼0.994] (Plan C) vs 0.797[0.641∼1.000] (Plan B)). Meanwhile, plan robustness of these two method’s results is comparable. (For all 7 patients, CTV DVH band gap at D95% normalized to the prescription dose: 0.015[0.005∼0.043] (Plan C) vs 0.012[0.006∼0.038] (Plan B) with small MU-constraints and 0.019[0.009∼0.039] (Plan C) vs 0.030[0.015∼0.041] (Plan B) with large MU-constraints) Conclusion: Positive correlation has been found between plan quality degeneration and magnitude of
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao
2015-01-01
be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution
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.
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.
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Toward solving the sign problem with path optimization method
Mori, Yuto; Kashiwa, Kouji; Ohnishi, Akira
2017-12-01
We propose a new approach to circumvent the sign problem in which the integration path is optimized to control the sign problem. We give a trial function specifying the integration path in the complex plane and tune it to optimize the cost function which represents the seriousness of the sign problem. We call it the path optimization method. In this method, we do not need to solve the gradient flow required in the Lefschetz-thimble method and then the construction of the integration-path contour arrives at the optimization problem where several efficient methods can be applied. In a simple model with a serious sign problem, the path optimization method is demonstrated to work well; the residual sign problem is resolved and precise results can be obtained even in the region where the global sign problem is serious.
An optimal design problem in wave propagation
DEFF Research Database (Denmark)
Bellido, J.C.; Donoso, Alberto
2007-01-01
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...... also the existence of classical solutions in certain cases....
Identification and optimization problems in plasma physics
International Nuclear Information System (INIS)
Gilbert, J.C.
1986-06-01
Parameter identification of the current in a tokamak plasma is studied. Plasma equilibrium in a vacuum container with a diaphragm is analyzed. A variable metric method with reduced optimization with nonlinear equality constraints; and a quasi-Newton reduced optimization method with constraints giving priority to restoration are presented [fr
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.
Optimal solutions for routing problems with profits
Archetti, C.; Bianchessi, N.; Speranza, M. G.
2013-01-01
In this paper, we present a branch-and-price algorithm to solve two well-known vehicle routing problems with profits, the Capacitated Team Orienteering Problem and the Capacitated Profitable Tour Problem. A restricted master heuristic is applied at each node of the branch-and-bound tree in order to
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...
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 Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem
Directory of Open Access Journals (Sweden)
Mio Horai
2016-01-01
Full Text Available We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.
Gravitation and quadratic forms
International Nuclear Information System (INIS)
Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha
2017-01-01
The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.
Gravitation and quadratic forms
Energy Technology Data Exchange (ETDEWEB)
Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)
2017-03-31
The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.
Large-scale sequential quadratic programming algorithms
Energy Technology Data Exchange (ETDEWEB)
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
The optimal solution of a non-convex state-dependent LQR problem and its applications.
Directory of Open Access Journals (Sweden)
Xudan Xu
Full Text Available This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR problem, in which the control penalty weighting matrix [Formula: see text] in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting [Formula: see text]. It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting [Formula: see text], in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions.
Frequency response as a surrogate eigenvalue problem in topology optimization
DEFF Research Database (Denmark)
Andreassen, Erik; Ferrari, Federico; Sigmund, Ole
2018-01-01
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...
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.
Sufficient conditions for Lagrange, Mayer, and Bolza optimization problems
Directory of Open Access Journals (Sweden)
Boltyanski V.
2001-01-01
Full Text Available The Maximum Principle [2,13] is a well known necessary condition for optimality. This condition, generally, is not sufficient. In [3], the author proved that if there exists regular synthesis of trajectories, the Maximum Principle also is a sufficient condition for time-optimality. In this article, we generalize this result for Lagrange, Mayer, and Bolza optimization problems.
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.
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 present talk is concerned with the application of topology optimization to creeping flow problems in 3D. This research is driven by the fact that topology optimization has proven very successful as a tool in academic and industrial design problems. Success stories are reported from such diverse...
Fuzzy Random λ-Mean SAD Portfolio Selection Problem: An Ant Colony Optimization Approach
Thakur, Gour Sundar Mitra; Bhattacharyya, Rupak; Mitra, Swapan Kumar
2010-10-01
To reach the investment goal, one has to select a combination of securities among different portfolios containing large number of securities. Only the past records of each security do not guarantee the future return. As there are many uncertain factors which directly or indirectly influence the stock market and there are also some newer stock markets which do not have enough historical data, experts' expectation and experience must be combined with the past records to generate an effective portfolio selection model. In this paper the return of security is assumed to be Fuzzy Random Variable Set (FRVS), where returns are set of random numbers which are in turn fuzzy numbers. A new λ-Mean Semi Absolute Deviation (λ-MSAD) portfolio selection model is developed. The subjective opinions of the investors to the rate of returns of each security are taken into consideration by introducing a pessimistic-optimistic parameter vector λ. λ-Mean Semi Absolute Deviation (λ-MSAD) model is preferred as it follows absolute deviation of the rate of returns of a portfolio instead of the variance as the measure of the risk. As this model can be reduced to Linear Programming Problem (LPP) it can be solved much faster than quadratic programming problems. Ant Colony Optimization (ACO) is used for solving the portfolio selection problem. ACO is a paradigm for designing meta-heuristic algorithms for combinatorial optimization problem. Data from BSE is used for illustration.
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
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.
Topology optimization of fluid-structure-interaction problems in poroelasticity
DEFF Research Database (Denmark)
Andreasen, Casper Schousboe; Sigmund, Ole
2013-01-01
This paper presents a method for applying topology optimization to fluid-structure interaction problems in saturated poroelastic media. The method relies on a multiple-scale method applied to periodic media. The resulting model couples the Stokes flow in the pores of the structure with the deform...... by topology optimization in order to optimize the performance of a shock absorber and test the pressure loading capabilities and optimization of an internally pressurized lid. © 2013 Published by Elsevier B.V....
Some Optimization Problems for p-Laplacian Type Equations
International Nuclear Information System (INIS)
Del Pezzo, L. M.; Fernandez Bonder, J.
2009-01-01
In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional over some admissible class of loads f where u is the (unique) solution to the problem -Δ p u+ vertical bar u vertical bar p-2 u=0 in Ω with vertical bar ∇u vertical bar p-2 u ν =f on ∂Ω
From combinatorial optimization to real algebraic geometry and back
Directory of Open Access Journals (Sweden)
Janez Povh
2014-12-01
Full Text Available In this paper, we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to the quadratic assignment problem. We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The latter formulation enables a hierarchy of approximations which rely on results from polynomial optimization, a sub-eld of real algebraic geometry.
A Global Optimization Algorithm for Sum of Linear Ratios Problem
Yuelin Gao; Siqiao Jin
2013-01-01
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 c...
Constraint interface preconditioning for topology optimization problems
Czech Academy of Sciences Publication Activity Database
Kočvara, Michal; Loghin, D.; Turner, J.
2016-01-01
Roč. 38, č. 1 (2016), A128-A145 ISSN 1064-8275 R&D Projects: GA AV ČR IAA100750802 Grant - others:European Commission - EC(XE) 313781 Institutional support: RVO:67985556 Keywords : topology optimization * domain decomposition * Newton-Krylov Subject RIV: BA - General Mathematics Impact factor: 2.195, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/kocvara-0460325.pdf
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.
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...
Optimal Wafer Cutting in Shuttle Layout Problems
DEFF Research Database (Denmark)
Nisted, Lasse; Pisinger, David; Altman, Avri
2011-01-01
. The shuttle layout problem is frequently solved in two phases: first, a floorplan of the shuttle is generated. Then, a cutting plan is found which minimizes the overall number of wafers needed to satisfy the demand of each die type. Since some die types require special production technologies, only compatible...
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...
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)
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)
Solving Multiobjective Optimization Problems Using Artificial Bee Colony Algorithm
Directory of Open Access Journals (Sweden)
Wenping Zou
2011-01-01
Full Text Available Multiobjective optimization has been a difficult problem and focus for research in fields of science and engineering. This paper presents a novel algorithm based on artificial bee colony (ABC to deal with multi-objective optimization problems. ABC is one of the most recently introduced algorithms based on the intelligent foraging behavior of a honey bee swarm. It uses less control parameters, and it can be efficiently used for solving multimodal and multidimensional optimization problems. Our algorithm uses the concept of Pareto dominance to determine the flight direction of a bee, and it maintains nondominated solution vectors which have been found in an external archive. The proposed algorithm is validated using the standard test problems, and simulation results show that the proposed approach is highly competitive and can be considered a viable alternative to solve multi-objective optimization problems.
Still, Georg J.; Ahmed, F.
The paper deals with the simple but important problem of maximizing a (nonconvex) quadratic function on the unit simplex. This program is directly related to the concept of evolutionarily stable strategies (ESS) in biology. We discuss this relation and study optimality conditions, stability and
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.
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.
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 ......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...
Topology optimization for acoustic-structure interaction problems
DEFF Research Database (Denmark)
Yoon, Gil Ho; Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
We propose a gradient based topology optimization algorithm for acoustic-structure (vibro-acoustic) interaction problems without an explicit interfacing boundary representation. In acoustic-structure interaction problems, the pressure field and the displacement field are governed by the Helmholtz...... to subdomain interfaces evolving during the optimization process. In this paper, we propose to use a mixed finite element formulation with displacements and pressure as primary variables (u/p formulation) which eliminates the need for explicit boundary representation. In order to describe the Helmholtz......-dimensional acoustic-structure interaction problems are optimized to show the validity of the proposed method....
Linear-quadratic control and quadratic differential forms for multidimensional behaviors
Napp, D.; Trentelman, H.L.
2011-01-01
This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look
A Variant of the Topkis-Veinott Method for Solving Inequality Constrained Optimization Problems
International Nuclear Information System (INIS)
Birge, J. R.; Qi, L.; Wei, Z.
2000-01-01
In this paper we give a variant of the Topkis-Veinott method for solving inequality constrained optimization problems. This method uses a linearly constrained positive semidefinite quadratic problem to generate a feasible descent direction at each iteration. Under mild assumptions, the algorithm is shown to be globally convergent in the sense that every accumulation point of the sequence generated by the algorithm is a Fritz-John point of the problem. We introduce a Fritz-John (FJ) function, an FJ1 strong second-order sufficiency condition (FJ1-SSOSC), and an FJ2 strong second-order sufficiency condition (FJ2-SSOSC), and then show, without any constraint qualification (CQ), that (i) if an FJ point z satisfies the FJ1-SSOSC, then there exists a neighborhood N(z) of z such that, for any FJ point y element of N(z) {z } , f 0 (y) ≠ f 0 (z) , where f 0 is the objective function of the problem; (ii) if an FJ point z satisfies the FJ2-SSOSC, then z is a strict local minimum of the problem. The result (i) implies that the entire iteration point sequence generated by the method converges to an FJ point. We also show that if the parameters are chosen large enough, a unit step length can be accepted by the proposed algorithm
Optimization algorithms and applications
Arora, Rajesh Kumar
2015-01-01
Choose the Correct Solution Method for Your Optimization ProblemOptimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs. The book covers both gradient and stochastic methods as solution techniques for unconstrained and constrained optimization problems. It discusses the conjugate gradient method, Broyden-Fletcher-Goldfarb-Shanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible direc
Dickmann, M
2015-01-01
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in
Comparison of optimal design methods in inverse problems
International Nuclear Information System (INIS)
Banks, H T; Holm, K; Kappel, F
2011-01-01
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)
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).
New Exact Penalty Functions for Nonlinear Constrained Optimization Problems
Directory of Open Access Journals (Sweden)
Bingzhuang Liu
2014-01-01
Full Text Available For two kinds of nonlinear constrained optimization problems, we propose two simple penalty functions, respectively, by augmenting the dimension of the primal problem with a variable that controls the weight of the penalty terms. Both of the penalty functions enjoy improved smoothness. Under mild conditions, it can be proved that our penalty functions are both exact in the sense that local minimizers of the associated penalty problem are precisely the local minimizers of the original constrained problem.
An optimal control approach to manpower planning problem
Directory of Open Access Journals (Sweden)
H. W. J. Lee
2001-01-01
Full Text Available A manpower planning problem is studied in this paper. The model includes scheduling different types of workers over different tasks, employing and terminating different types of workers, and assigning different types of workers to various trainning programmes. The aim is to find an optimal way to do all these while keeping the time-varying demand for minimum number of workers working on each different tasks satisfied. The problem is posed as an optimal discrete-valued control problem in discrete time. A novel numerical scheme is proposed to solve the problem, and an illustrative example is provided.
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....
Optimal stability polynomials for numerical integration of initial value problems
Ketcheson, David I.; Ahmadia, Aron
2013-01-01
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step
Infinite-horizon optimal control problems in economics
Energy Technology Data Exchange (ETDEWEB)
Aseev, Sergei M; Besov, Konstantin O; Kryazhimskii, Arkadii V
2012-04-30
This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the 'standard' limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices. Bibliography: 53 titles.
An inverse optimal control problem in the electrical discharge ...
Indian Academy of Sciences (India)
Marin Gostimirovic
2018-05-10
May 10, 2018 ... Keywords. EDM process; discharge energy; heat source parameters; inverse problem; optimization. 1. Introduction .... ation, thermal modeling of the EDM process would become ..... simulation of die-sinking EDM. CIRP Ann.
Infinite-horizon optimal control problems in economics
International Nuclear Information System (INIS)
Aseev, Sergei M; Besov, Konstantin O; Kryazhimskii, Arkadii V
2012-01-01
This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the 'standard' limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices. Bibliography: 53 titles.
An Optimal Linear Coding for Index Coding Problem
Pezeshkpour, Pouya
2015-01-01
An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding problem is presented. The coding is proved to be the optimal solution from the linear perspective and can be easily utilize for any number of messages. The importance of this work is lying mostly on the usage of the presented coding in the groupcast index coding ...
Complicated problem solution techniques in optimal parameter searching
International Nuclear Information System (INIS)
Gergel', V.P.; Grishagin, V.A.; Rogatneva, E.A.; Strongin, R.G.; Vysotskaya, I.N.; Kukhtin, V.V.
1992-01-01
An algorithm is presented of a global search for numerical solution of multidimentional multiextremal multicriteria optimization problems with complicated constraints. A boundedness of object characteristic changes is assumed at restricted changes of its parameters (Lipschitz condition). The algorithm was realized as a computer code. The algorithm was realized as a computer code. The programme was used to solve in practice the different applied optimization problems. 10 refs.; 3 figs
Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications
2015-06-24
WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Arizona State University School of Mathematical & Statistical Sciences 901 S...SUPPLEMENTARY NOTES 14. ABSTRACT The major goals of this project were completed: the exact solution of previously unsolved challenging combinatorial optimization... combinatorial optimization problem, the Directional Sensor Problem, was solved in two ways. First, heuristically in an engineering fashion and second, exactly
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....
Ellis, John; Sueiro, Maria
2014-01-01
Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.
On some fundamental properties of structural topology optimization problems
DEFF Research Database (Denmark)
Stolpe, Mathias
2010-01-01
We study some fundamental mathematical properties of discretized structural topology optimization problems. Either compliance is minimized with an upper bound on the volume of the structure, or volume is minimized with an upper bound on the compliance. The design variables are either continuous o....... The presented examples can be used as teaching material in graduate and undergraduate courses on structural topology optimization....
STATEMENT OF THE OPTIMIZATION PROBLEM OF CARBON PRODUCTS PRODUCTION
Directory of Open Access Journals (Sweden)
O. A. Zhuchenko
2016-08-01
Full Text Available The paper formulated optimization problem formulation production of carbon products. The analysis of technical and economic parameters that can be used to optimize the production of carbonaceous products had been done by the author. To evaluate the efficiency of the energy-intensive production uses several technical and economic indicators. In particular, the specific cost, productivity, income and profitability of production. Based on a detailed analysis had been formulated optimality criterion that takes into account the technological components of profitability. The components in detail the criteria and the proposed method of calculating non-trivial, one of them - the production cost of each product. When solving the optimization problem of technological modes of production into account constraints on the variables are optimized. Thus, restrictions may be expressed on the number of each product produced. Have been formulated the method of calculating the cost per unit of product. Attention is paid to the quality indices of finished products as an additional constraint in the optimization problem. As a result have been formulated the general problem of optimizing the production of carbon products, which includes the optimality criterion and restrictions.
SolveDB: Integrating Optimization Problem Solvers Into SQL Databases
DEFF Research Database (Denmark)
Siksnys, Laurynas; Pedersen, Torben Bach
2016-01-01
for optimization problems, (2) an extensible infrastructure for integrating different solvers, and (3) query optimization techniques to achieve the best execution performance and/or result quality. Extensive experiments with the PostgreSQL-based implementation show that SolveDB is a versatile tool offering much...
Effective Teaching of Economics: A Constrained Optimization Problem?
Hultberg, Patrik T.; Calonge, David Santandreu
2017-01-01
One of the fundamental tenets of economics is that decisions are often the result of optimization problems subject to resource constraints. Consumers optimize utility, subject to constraints imposed by prices and income. As economics faculty, instructors attempt to maximize student learning while being constrained by their own and students'…
Problems in determining the optimal use of road safety measures
DEFF Research Database (Denmark)
Elvik, Rune
2014-01-01
for intervention that ensures maximum safety benefits. The third problem is how to develop policy options to minimise the risk of indivisibilities and irreversible choices. The fourth problem is how to account for interaction effects between road safety measures when determining their optimal use. The fifth......This paper discusses some problems in determining the optimal use of road safety measures. The first of these problems is how best to define the baseline option, i.e. what will happen if no new safety measures are introduced. The second problem concerns choice of a method for selection of targets...... problem is how to obtain the best mix of short-term and long-term measures in a safety programme. The sixth problem is how fixed parameters for analysis, including the monetary valuation of road safety, influence the results of analyses. It is concluded that it is at present not possible to determine...
Random Matrix Approach for Primal-Dual Portfolio Optimization Problems
Tada, Daichi; Yamamoto, Hisashi; Shinzato, Takashi
2017-12-01
In this paper, we revisit the portfolio optimization problems of the minimization/maximization of investment risk under constraints of budget and investment concentration (primal problem) and the maximization/minimization of investment concentration under constraints of budget and investment risk (dual problem) for the case that the variances of the return rates of the assets are identical. We analyze both optimization problems by the Lagrange multiplier method and the random matrix approach. Thereafter, we compare the results obtained from our proposed approach with the results obtained in previous work. Moreover, we use numerical experiments to validate the results obtained from the replica approach and the random matrix approach as methods for analyzing both the primal and dual portfolio optimization problems.
Huang, Hui; Ning, Jixian
2017-01-01
Prederivatives play an important role in the research of set optimization problems. First, we establish several existence theorems of prederivatives for γ -paraconvex set-valued mappings in Banach spaces with [Formula: see text]. Then, in terms of prederivatives, we establish both necessary and sufficient conditions for the existence of Pareto minimal solution of set optimization problems.
ON THE OPTIMAL CONTROL OF A PROBLEM OF ENVIRONMENTAL POLLUTION
Directory of Open Access Journals (Sweden)
José Dávalos Chuquipoma
2016-06-01
Full Text Available This article is studied the optimal control of distributed parameter systems applied to an environmental pollution problem. The model consists of a differential equation partial parabolic modeling of a pollutant transport in a fluid. The model is considered the speed with which the pollutant spreads in the environment and degradation that suffers the contaminant by the presence of a factor biological inhibitor, which breaks the contaminant at a rate that is not dependent on space and time. Using the method of Lagrange multipliers is possible to prove the existence solving the problem of control and obtaining optimality conditions for optimal control.
DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers
Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro
2016-10-01
This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.
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.
Strong Duality and Optimality Conditions for Generalized Equilibrium Problems
Directory of Open Access Journals (Sweden)
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.
Optimization of the solution of the problem of scheduling theory ...
African Journals Online (AJOL)
This article describes the genetic algorithm used to solve the problem related to the scheduling theory. A large number of different methods is described in the scientific literature. The main issue that faced the problem in question is that it is necessary to search the optimal solution in a large search space for the set of ...
orthogonal and scaling transformations of quadratic functions
African Journals Online (AJOL)
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functions of sub-problems of various nonlinear programming problems that employ methods such as sequential quadratic programming and trust-region methods (Sorensen, 1982; Eldersveld,. 1991; Nocedal and Wright, 1999). Various problems in Algebra, Functional Analysis,. Analytic Geometry and Computational Mathe-.
Global Optimization for Bus Line Timetable Setting Problem
Directory of Open Access Journals (Sweden)
Qun Chen
2014-01-01
Full Text Available This paper defines bus timetables setting problem during each time period divided in terms of passenger flow intensity; it is supposed that passengers evenly arrive and bus runs are set evenly; the problem is to determine bus runs assignment in each time period to minimize the total waiting time of passengers on platforms if the number of the total runs is known. For such a multistage decision problem, this paper designed a dynamic programming algorithm to solve it. Global optimization procedures using dynamic programming are developed. A numerical example about bus runs assignment optimization of a single line is given to demonstrate the efficiency of the proposed methodology, showing that optimizing buses’ departure time using dynamic programming can save computational time and find the global optimal solution.
An intutionistic fuzzy optimization approach to vendor selection problem
Directory of Open Access Journals (Sweden)
Prabjot Kaur
2016-09-01
Full Text Available Selecting the right vendor is an important business decision made by any organization. The decision involves multiple criteria and if the objectives vary in preference and scope, then nature of decision becomes multiobjective. In this paper, a vendor selection problem has been formulated as an intutionistic fuzzy multiobjective optimization where appropriate number of vendors is to be selected and order allocated to them. The multiobjective problem includes three objectives: minimizing the net price, maximizing the quality, and maximizing the on time deliveries subject to supplier's constraints. The objection function and the demand are treated as intutionistic fuzzy sets. An intutionistic fuzzy set has its ability to handle uncertainty with additional degrees of freedom. The Intutionistic fuzzy optimization (IFO problem is converted into a crisp linear form and solved using optimization software Tora. The advantage of IFO is that they give better results than fuzzy/crisp optimization. The proposed approach is explained by a numerical example.
Willigenburg, van L.G.; Koning, de W.L.
2013-01-01
Two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria, called the optimal compensation problem. One describes the matrix valued white stochastic
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.
Introduction to optimal control theory
International Nuclear Information System (INIS)
Agrachev, A.A.
2002-01-01
These are lecture notes of the introductory course in Optimal Control theory treated from the geometric point of view. Optimal Control Problem is reduced to the study of controls (and corresponding trajectories) leading to the boundary of attainable sets. We discuss Pontryagin Maximum Principle, basic existence results, and apply these tools to concrete simple optimal control problems. Special sections are devoted to the general theory of linear time-optimal problems and linear-quadratic problems. (author)
ON PROBLEM OF REGIONAL WAREHOUSE AND TRANSPORT INFRASTRUCTURE OPTIMIZATION
Directory of Open Access Journals (Sweden)
I. Yu. Miretskiy
2017-01-01
Full Text Available The article suggests an approach of solving the problem of warehouse and transport infrastructure optimization in a region. The task is to determine the optimal capacity and location of the support network of warehouses in the region, as well as power, composition and location of motor fleets. Optimization is carried out using mathematical models of a regional warehouse network and a network of motor fleets. These models are presented as mathematical programming problems with separable functions. The process of finding the optimal solution of problems is complicated due to high dimensionality, non-linearity of functions, and the fact that a part of variables are constrained to integer, and some variables can take values only from a discrete set. Given the mentioned above complications search for an exact solution was rejected. The article suggests an approximate approach to solving problems. This approach employs effective computational schemes for solving multidimensional optimization problems. We use the continuous relaxation of the original problem to obtain its approximate solution. An approximately optimal solution of continuous relaxation is taken as an approximate solution of the original problem. The suggested solution method implies linearization of the obtained continuous relaxation and use of the separable programming scheme and the scheme of branches and bounds. We describe the use of the simplex method for solving the linearized continuous relaxation of the original problem and the specific moments of the branches and bounds method implementation. The paper shows the finiteness of the algorithm and recommends how to accelerate process of finding a solution.
Integrating packing and distribution problems and optimization through mathematical programming
Directory of Open Access Journals (Sweden)
Fabio Miguel
2016-06-01
Full Text Available This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW, which is a variant of the Travelling Salesman Problem (again a NP-Hard problem with extra constraints. Here we model those two problems in a single framework and use an evolutionary meta-heuristics to solve them jointly. Furthermore, we use data from a real world company as a test-bed for the method introduced here.
Ghosh, D.; Sierksma, G.
2000-01-01
Sensitivity analysis of e-optimal solutions is the problem of calculating the range within which a problem parameter may lie so that the given solution re-mains e-optimal. In this paper we study the sensitivity analysis problem for e-optimal solutions tocombinatorial optimization problems with
Finding Multiple Optimal Solutions to Optimal Load Distribution Problem in Hydropower Plant
Directory of Open Access Journals (Sweden)
Xinhao Jiang
2012-05-01
Full Text Available Optimal load distribution (OLD among generator units of a hydropower plant is a vital task for hydropower generation scheduling and management. Traditional optimization methods for solving this problem focus on finding a single optimal solution. However, many practical constraints on hydropower plant operation are very difficult, if not impossible, to be modeled, and the optimal solution found by those models might be of limited practical uses. This motivates us to find multiple optimal solutions to the OLD problem, which can provide more flexible choices for decision-making. Based on a special dynamic programming model, we use a modified shortest path algorithm to produce multiple solutions to the problem. It is shown that multiple optimal solutions exist for the case study of China’s Geheyan hydropower plant, and they are valuable for assessing the stability of generator units, showing the potential of reducing occurrence times of units across vibration areas.
SOLVING ENGINEERING OPTIMIZATION PROBLEMS WITH THE SWARM INTELLIGENCE METHODS
Directory of Open Access Journals (Sweden)
V. Panteleev Andrei
2017-01-01
Full Text Available An important stage in problem solving process for aerospace and aerostructures designing is calculating their main charac- teristics optimization. The results of the four constrained optimization problems related to the design of various technical systems: such as determining the best parameters of welded beams, pressure vessel, gear, spring are presented. The purpose of each task is to minimize the cost and weight of the construction. The object functions in optimization practical problem are nonlinear functions with a lot of variables and a complex layer surface indentations. That is why using classical approach for extremum seeking is not efficient. Here comes the necessity of using such methods of optimization that allow to find a near optimal solution in acceptable amount of time with the minimum waste of computer power. Such methods include the methods of Swarm Intelligence: spiral dy- namics algorithm, stochastic diffusion search, hybrid seeker optimization algorithm. The Swarm Intelligence methods are designed in such a way that a swarm consisting of agents carries out the search for extremum. In search for the point of extremum, the parti- cles exchange information and consider their experience as well as the experience of population leader and the neighbors in some area. To solve the listed problems there has been designed a program complex, which efficiency is illustrated by the solutions of four applied problems. Each of the considered applied optimization problems is solved with all the three chosen methods. The ob- tained numerical results can be compared with the ones found in a swarm with a particle method. The author gives recommenda- tions on how to choose methods parameters and penalty function value, which consider inequality constraints.
Turnpike theory of continuous-time linear optimal control problems
Zaslavski, Alexander J
2015-01-01
Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems. The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands. Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integran...
A coherent Ising machine for 2000-node optimization problems
Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki
2016-11-01
The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.
Optimal stability polynomials for numerical integration of initial value problems
Ketcheson, David I.
2013-01-08
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step size and corresponding method for a given problem when the spectrum of the initial value problem is known. The problem is expressed in terms of a general least deviation feasibility problem. Its solution is obtained by a new fast, accurate, and robust algorithm based on convex optimization techniques. Global convergence of the algorithm is proven in the case that the order of approximation is one and in the case that the spectrum encloses a starlike region. Examples demonstrate the effectiveness of the proposed algorithm even when these conditions are not satisfied.
Salcedo-Sanz, S.; Del Ser, J.; Landa-Torres, I.; Gil-López, S.; Portilla-Figueras, J. A.
2014-01-01
This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems. PMID:25147860
Optimal recombination in genetic algorithms for combinatorial optimization problems: Part I
Directory of Open Access Journals (Sweden)
Eremeev Anton V.
2014-01-01
Full Text Available This paper surveys results on complexity of the optimal recombination problem (ORP, which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We consider efficient reductions of the ORPs, allowing to establish polynomial solvability or NP-hardness of the ORPs, as well as direct proofs of hardness results. Part I presents the basic principles of optimal recombination with a survey of results on Boolean Linear Programming Problems. Part II (to appear in a subsequent issue is devoted to the ORPs for problems which are naturally formulated in terms of search for an optimal permutation.
Nonlinear dynamics of quadratically cubic systems
International Nuclear Information System (INIS)
Rudenko, O V
2013-01-01
We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)
Bound constrained quadratic programming via piecewise
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.
1999-01-01
of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive......We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...
Particle swarm as optimization tool in complex nuclear engineering problems
International Nuclear Information System (INIS)
Medeiros, Jose Antonio Carlos Canedo
2005-06-01
Due to its low computational cost, gradient-based search techniques associated to linear programming techniques are being used as optimization tools. These techniques, however, when applied to multimodal search spaces, can lead to local optima. When finding solutions for complex multimodal domains, random search techniques are being used with great efficacy. In this work we exploit the swarm optimization algorithm search power capacity as an optimization tool for the solution of complex high dimension and multimodal search spaces of nuclear problems. Due to its easy and natural representation of high dimension domains, the particle swarm optimization was applied with success for the solution of complex nuclear problems showing its efficacy in the search of solutions in high dimension and complex multimodal spaces. In one of these applications it enabled a natural and trivial solution in a way not obtained with other methods confirming the validity of its application. (author)
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard
2015-05-04
In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).
Parallel and Cooperative Particle Swarm Optimizer for Multimodal Problems
Directory of Open Access Journals (Sweden)
Geng Zhang
2015-01-01
Full Text Available Although the original particle swarm optimizer (PSO method and its related variant methods show some effectiveness for solving optimization problems, it may easily get trapped into local optimum especially when solving complex multimodal problems. Aiming to solve this issue, this paper puts forward a novel method called parallel and cooperative particle swarm optimizer (PCPSO. In case that the interacting of the elements in D-dimensional function vector X=[x1,x2,…,xd,…,xD] is independent, cooperative particle swarm optimizer (CPSO is used. Based on this, the PCPSO is presented to solve real problems. Since the dimension cannot be split into several lower dimensional search spaces in real problems because of the interacting of the elements, PCPSO exploits the cooperation of two parallel CPSO algorithms by orthogonal experimental design (OED learning. Firstly, the CPSO algorithm is used to generate two locally optimal vectors separately; then the OED is used to learn the merits of these two vectors and creates a better combination of them to generate further search. Experimental studies on a set of test functions show that PCPSO exhibits better robustness and converges much closer to the global optimum than several other peer algorithms.
Optimal Control Problems for Partial Differential Equations on Reticulated Domains
Kogut, Peter I
2011-01-01
In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for gradu
Intelligent discrete particle swarm optimization for multiprocessor task scheduling problem
Directory of Open Access Journals (Sweden)
S Sarathambekai
2017-03-01
Full Text Available Discrete particle swarm optimization is one of the most recently developed population-based meta-heuristic optimization algorithm in swarm intelligence that can be used in any discrete optimization problems. This article presents a discrete particle swarm optimization algorithm to efficiently schedule the tasks in the heterogeneous multiprocessor systems. All the optimization algorithms share a common algorithmic step, namely population initialization. It plays a significant role because it can affect the convergence speed and also the quality of the final solution. The random initialization is the most commonly used method in majority of the evolutionary algorithms to generate solutions in the initial population. The initial good quality solutions can facilitate the algorithm to locate the optimal solution or else it may prevent the algorithm from finding the optimal solution. Intelligence should be incorporated to generate the initial population in order to avoid the premature convergence. This article presents a discrete particle swarm optimization algorithm, which incorporates opposition-based technique to generate initial population and greedy algorithm to balance the load of the processors. Make span, flow time, and reliability cost are three different measures used to evaluate the efficiency of the proposed discrete particle swarm optimization algorithm for scheduling independent tasks in distributed systems. Computational simulations are done based on a set of benchmark instances to assess the performance of the proposed algorithm.
Solving Unconstrained Global Optimization Problems via Hybrid Swarm Intelligence Approaches
Directory of Open Access Journals (Sweden)
Jui-Yu Wu
2013-01-01
Full Text Available Stochastic global optimization (SGO algorithms such as the particle swarm optimization (PSO approach have become popular for solving unconstrained global optimization (UGO problems. The PSO approach, which belongs to the swarm intelligence domain, does not require gradient information, enabling it to overcome this limitation of traditional nonlinear programming methods. Unfortunately, PSO algorithm implementation and performance depend on several parameters, such as cognitive parameter, social parameter, and constriction coefficient. These parameters are tuned by using trial and error. To reduce the parametrization of a PSO method, this work presents two efficient hybrid SGO approaches, namely, a real-coded genetic algorithm-based PSO (RGA-PSO method and an artificial immune algorithm-based PSO (AIA-PSO method. The specific parameters of the internal PSO algorithm are optimized using the external RGA and AIA approaches, and then the internal PSO algorithm is applied to solve UGO problems. The performances of the proposed RGA-PSO and AIA-PSO algorithms are then evaluated using a set of benchmark UGO problems. Numerical results indicate that, besides their ability to converge to a global minimum for each test UGO problem, the proposed RGA-PSO and AIA-PSO algorithms outperform many hybrid SGO algorithms. Thus, the RGA-PSO and AIA-PSO approaches can be considered alternative SGO approaches for solving standard-dimensional UGO problems.
Krohling, Renato A; Coelho, Leandro dos Santos
2006-12-01
In this correspondence, an approach based on coevolutionary particle swarm optimization to solve constrained optimization problems formulated as min-max problems is presented. In standard or canonical particle swarm optimization (PSO), a uniform probability distribution is used to generate random numbers for the accelerating coefficients of the local and global terms. We propose a Gaussian probability distribution to generate the accelerating coefficients of PSO. Two populations of PSO using Gaussian distribution are used on the optimization algorithm that is tested on a suite of well-known benchmark constrained optimization problems. Results have been compared with the canonical PSO (constriction factor) and with a coevolutionary genetic algorithm. Simulation results show the suitability of the proposed algorithm in terms of effectiveness and robustness.
Heuristic Optimization for the Discrete Virtual Power Plant Dispatch Problem
DEFF Research Database (Denmark)
Petersen, Mette Kirschmeyer; Hansen, Lars Henrik; Bendtsen, Jan Dimon
2014-01-01
We consider a Virtual Power Plant, which is given the task of dispatching a fluctuating power supply to a portfolio of flexible consumers. The flexible consumers are modeled as discrete batch processes, and the associated optimization problem is denoted the Discrete Virtual Power Plant Dispatch...... Problem. First NP-completeness of the Discrete Virtual Power Plant Dispatch Problem is proved formally. We then proceed to develop tailored versions of the meta-heuristic algorithms Hill Climber and Greedy Randomized Adaptive Search Procedure (GRASP). The algorithms are tuned and tested on portfolios...... of varying sizes. We find that all the tailored algorithms perform satisfactorily in the sense that they are able to find sub-optimal, but usable, solutions to very large problems (on the order of 10 5 units) at computation times on the scale of just 10 seconds, which is far beyond the capabilities...
Solving optimization problems by the public goods game
Javarone, Marco Alberto
2017-09-01
We introduce a method based on the Public Goods Game for solving optimization tasks. In particular, we focus on the Traveling Salesman Problem, i.e. a NP-hard problem whose search space exponentially grows increasing the number of cities. The proposed method considers a population whose agents are provided with a random solution to the given problem. In doing so, agents interact by playing the Public Goods Game using the fitness of their solution as currency of the game. Notably, agents with better solutions provide higher contributions, while those with lower ones tend to imitate the solution of richer agents for increasing their fitness. Numerical simulations show that the proposed method allows to compute exact solutions, and suboptimal ones, in the considered search spaces. As result, beyond to propose a new heuristic for combinatorial optimization problems, our work aims to highlight the potentiality of evolutionary game theory beyond its current horizons.
Ojalehto, Vesa; Podkopaev, Dmitry; Miettinen, Kaisa
2015-01-01
We generalize the applicability of interactive methods for solving computationally demanding, that is, time-consuming, multiobjective optimization problems. For this purpose we propose a new agent assisted interactive algorithm. It employs a computationally inexpensive surrogate problem and four different agents that intelligently update the surrogate based on the preferences specified by a decision maker. In this way, we decrease the waiting times imposed on the decision maker du...
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2016-01-01
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Dynamic Vehicle Routing Problems with Enhanced Ant Colony Optimization
Directory of Open Access Journals (Sweden)
Haitao Xu
2018-01-01
Full Text Available As we all know, there are a great number of optimization problems in the world. One of the relatively complicated and high-level problems is the vehicle routing problem (VRP. Dynamic vehicle routing problem (DVRP is a major variant of VRP, and it is closer to real logistic scene. In DVRP, the customers’ demands appear with time, and the unserved customers’ points must be updated and rearranged while carrying out the programming paths. Owing to the complexity and significance of the problem, DVRP applications have grabbed the attention of researchers in the past two decades. In this paper, we have two main contributions to solving DVRP. Firstly, DVRP is solved with enhanced Ant Colony Optimization (E-ACO, which is the traditional Ant Colony Optimization (ACO fusing improved K-means and crossover operation. K-means can divide the region with the most reasonable distance, while ACO using crossover is applied to extend search space and avoid falling into local optimum prematurely. Secondly, several new evaluation benchmarks are proposed, which can objectively and comprehensively estimate the proposed method. In the experiment, the results for different scale problems are compared to those of previously published papers. Experimental results show that the algorithm is feasible and efficient.
Groenwold, A.A.; Etman, L.F.P.
2008-01-01
We study the classical topology optimization problem, in which minimum compliance is sought, subject to linear constraints. Using a dual statement, we propose two separable and strictly convex subproblems for use in sequential approximate optimization (SAO) algorithms.Respectively, the subproblems
Optimal recombination in genetic algorithms for combinatorial optimization problems: Part II
Directory of Open Access Journals (Sweden)
Eremeev Anton V.
2014-01-01
Full Text Available This paper surveys results on complexity of the optimal recombination problem (ORP, which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. In Part II, we consider the computational complexity of ORPs arising in genetic algorithms for problems on permutations: the Travelling Salesman Problem, the Shortest Hamilton Path Problem and the Makespan Minimization on Single Machine and some other related problems. The analysis indicates that the corresponding ORPs are NP-hard, but solvable by faster algorithms, compared to the problems they are derived from.
Optimization problems with equilibrium constraints and their numerical solution
Czech Academy of Sciences Publication Activity Database
Kočvara, Michal; Outrata, Jiří
Roč. 101 , č. 1 (2004), s. 119-149 ISSN 0025-5610 R&D Projects: GA AV ČR IAA1075005 Grant - others:BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : optimization problems * MPEC * MPCC Subject RIV: BA - General Mathematics Impact factor: 1.016, year: 2004
Scenario tree generation and multi-asset financial optimization problems
DEFF Research Database (Denmark)
Geyer, Alois; Hanke, Michael; Weissensteiner, Alex
2013-01-01
We compare two popular scenario tree generation methods in the context of financial optimization: moment matching and scenario reduction. Using a simple problem with a known analytic solution, moment matching-when ensuring absence of arbitrage-replicates this solution precisely. On the other hand...
Optimal portfolio selection for general provisioning and terminal wealth problems
van Weert, K.; Dhaene, J.; Goovaerts, M.
2010-01-01
In Dhaene et al. (2005), multiperiod portfolio selection problems are discussed, using an analytical approach to find optimal constant mix investment strategies in a provisioning or a savings context. In this paper we extend some of these results, investigating some specific, real-life situations.
Optimal portfolio selection for general provisioning and terminal wealth problems
van Weert, K.; Dhaene, J.; Goovaerts, M.
2009-01-01
In Dhaene et al. (2005), multiperiod portfolio selection problems are discussed, using an analytical approach to find optimal constant mix investment strategies in a provisioning or savings context. In this paper we extend some of these results, investigating some specific, real-life situations. The
New preconditioned conjugate gradient algorithms for nonlinear unconstrained optimization problems
International Nuclear Information System (INIS)
Al-Bayati, A.; Al-Asadi, N.
1997-01-01
This paper presents two new predilection conjugate gradient algorithms for nonlinear unconstrained optimization problems and examines their computational performance. Computational experience shows that the new proposed algorithms generally imp lone the efficiency of Nazareth's [13] preconditioned conjugate gradient algorithm. (authors). 16 refs., 1 tab
Landsman, Zinoviy
2008-10-01
We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see sciencedirect.com/science/journal/03770427>, articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.
Proposal of Evolutionary Simplex Method for Global Optimization Problem
Shimizu, Yoshiaki
To make an agile decision in a rational manner, role of optimization engineering has been notified increasingly under diversified customer demand. With this point of view, in this paper, we have proposed a new evolutionary method serving as an optimization technique in the paradigm of optimization engineering. The developed method has prospects to solve globally various complicated problem appearing in real world applications. It is evolved from the conventional method known as Nelder and Mead’s Simplex method by virtue of idea borrowed from recent meta-heuristic method such as PSO. Mentioning an algorithm to handle linear inequality constraints effectively, we have validated effectiveness of the proposed method through comparison with other methods using several benchmark problems.
Redundant interferometric calibration as a complex optimization problem
Grobler, T. L.; Bernardi, G.; Kenyon, J. S.; Parsons, A. R.; Smirnov, O. M.
2018-05-01
Observations of the redshifted 21 cm line from the epoch of reionization have recently motivated the construction of low-frequency radio arrays with highly redundant configurations. These configurations provide an alternative calibration strategy - `redundant calibration' - and boost sensitivity on specific spatial scales. In this paper, we formulate calibration of redundant interferometric arrays as a complex optimization problem. We solve this optimization problem via the Levenberg-Marquardt algorithm. This calibration approach is more robust to initial conditions than current algorithms and, by leveraging an approximate matrix inversion, allows for further optimization and an efficient implementation (`redundant STEFCAL'). We also investigated using the preconditioned conjugate gradient method as an alternative to the approximate matrix inverse, but found that its computational performance is not competitive with respect to `redundant STEFCAL'. The efficient implementation of this new algorithm is made publicly available.
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
Optimizing investment fund allocation using vehicle routing problem framework
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita
2014-07-01
The objective of investment is to maximize total returns or minimize total risks. To determine the optimum order of investment, vehicle routing problem method is used. The method which is widely used in the field of resource distribution shares almost similar characteristics with the problem of investment fund allocation. In this paper we describe and elucidate the concept of using vehicle routing problem framework in optimizing the allocation of investment fund. To better illustrate these similarities, sectorial data from FTSE Bursa Malaysia is used. Results show that different values of utility for risk-averse investors generate the same investment routes.
Essays on variational approximation techniques for stochastic optimization problems
Deride Silva, Julio A.
This dissertation presents five essays on approximation and modeling techniques, based on variational analysis, applied to stochastic optimization problems. It is divided into two parts, where the first is devoted to equilibrium problems and maxinf optimization, and the second corresponds to two essays in statistics and uncertainty modeling. Stochastic optimization lies at the core of this research as we were interested in relevant equilibrium applications that contain an uncertain component, and the design of a solution strategy. In addition, every stochastic optimization problem relies heavily on the underlying probability distribution that models the uncertainty. We studied these distributions, in particular, their design process and theoretical properties such as their convergence. Finally, the last aspect of stochastic optimization that we covered is the scenario creation problem, in which we described a procedure based on a probabilistic model to create scenarios for the applied problem of power estimation of renewable energies. In the first part, Equilibrium problems and maxinf optimization, we considered three Walrasian equilibrium problems: from economics, we studied a stochastic general equilibrium problem in a pure exchange economy, described in Chapter 3, and a stochastic general equilibrium with financial contracts, in Chapter 4; finally from engineering, we studied an infrastructure planning problem in Chapter 5. We stated these problems as belonging to the maxinf optimization class and, in each instance, we provided an approximation scheme based on the notion of lopsided convergence and non-concave duality. This strategy is the foundation of the augmented Walrasian algorithm, whose convergence is guaranteed by lopsided convergence, that was implemented computationally, obtaining numerical results for relevant examples. The second part, Essays about statistics and uncertainty modeling, contains two essays covering a convergence problem for a sequence
Ordinal optimization and its application to complex deterministic problems
Yang, Mike Shang-Yu
1998-10-01
We present in this thesis a new perspective to approach a general class of optimization problems characterized by large deterministic complexities. Many problems of real-world concerns today lack analyzable structures and almost always involve high level of difficulties and complexities in the evaluation process. Advances in computer technology allow us to build computer models to simulate the evaluation process through numerical means, but the burden of high complexities remains to tax the simulation with an exorbitant computing cost for each evaluation. Such a resource requirement makes local fine-tuning of a known design difficult under most circumstances, let alone global optimization. Kolmogorov equivalence of complexity and randomness in computation theory is introduced to resolve this difficulty by converting the complex deterministic model to a stochastic pseudo-model composed of a simple deterministic component and a white-noise like stochastic term. The resulting randomness is then dealt with by a noise-robust approach called Ordinal Optimization. Ordinal Optimization utilizes Goal Softening and Ordinal Comparison to achieve an efficient and quantifiable selection of designs in the initial search process. The approach is substantiated by a case study in the turbine blade manufacturing process. The problem involves the optimization of the manufacturing process of the integrally bladed rotor in the turbine engines of U.S. Air Force fighter jets. The intertwining interactions among the material, thermomechanical, and geometrical changes makes the current FEM approach prohibitively uneconomical in the optimization process. The generalized OO approach to complex deterministic problems is applied here with great success. Empirical results indicate a saving of nearly 95% in the computing cost.
Indian Academy of Sciences (India)
[G] Giannessi F, Theorems of alternative, quadratic programs and complementarity problems, in: Variational Inequalities and Complementarity Problems (eds) R W Cottle, F Giannessi and J L Lions (New York: Wiley) (1980) pp. 151±186. [K1] Kazmi K R, Existence of solutions for vector optimization, Appl. Math. Lett. 9 (1996).
Statistical physics of hard combinatorial optimization: Vertex cover problem
Zhao, Jin-Hua; Zhou, Hai-Jun
2014-07-01
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.
Exact cancellation of quadratic divergences in top condensation models
International Nuclear Information System (INIS)
Blumhofer, A.
1995-01-01
We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))
Particle Swarm Optimization and Uncertainty Assessment in Inverse Problems
Directory of Open Access Journals (Sweden)
José L. G. Pallero
2018-01-01
Full Text Available Most inverse problems in the industry (and particularly in geophysical exploration are highly underdetermined because the number of model parameters too high to achieve accurate data predictions and because the sampling of the data space is scarce and incomplete; it is always affected by different kinds of noise. Additionally, the physics of the forward problem is a simplification of the reality. All these facts result in that the inverse problem solution is not unique; that is, there are different inverse solutions (called equivalent, compatible with the prior information that fits the observed data within similar error bounds. In the case of nonlinear inverse problems, these equivalent models are located in disconnected flat curvilinear valleys of the cost-function topography. The uncertainty analysis consists of obtaining a representation of this complex topography via different sampling methodologies. In this paper, we focus on the use of a particle swarm optimization (PSO algorithm to sample the region of equivalence in nonlinear inverse problems. Although this methodology has a general purpose, we show its application for the uncertainty assessment of the solution of a geophysical problem concerning gravity inversion in sedimentary basins, showing that it is possible to efficiently perform this task in a sampling-while-optimizing mode. Particularly, we explain how to use and analyze the geophysical models sampled by exploratory PSO family members to infer different descriptors of nonlinear uncertainty.
Global Optimization of Nonlinear Blend-Scheduling Problems
Directory of Open Access Journals (Sweden)
Pedro A. Castillo Castillo
2017-04-01
Full Text Available The scheduling of gasoline-blending operations is an important problem in the oil refining industry. This problem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but also non-convex nonlinear behavior, due to the blending of various materials with different quality properties. In this work, a global optimization algorithm is proposed to solve a previously published continuous-time mixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimization, the distribution problem, and several important operational features and constraints. The algorithm employs piecewise McCormick relaxation (PMCR and normalized multiparametric disaggregation technique (NMDT to compute estimates of the global optimum. These techniques partition the domain of one of the variables in a bilinear term and generate convex relaxations for each partition. By increasing the number of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates of the global solution. The algorithm is compared to two commercial global solvers and two heuristic methods by solving four examples from the literature. Results show that the proposed global optimization algorithm performs on par with commercial solvers but is not as fast as heuristic approaches.
Stability, Optimality and Manipulation in Matching Problems with Weighted Preferences
Directory of Open Access Journals (Sweden)
Maria Silvia Pini
2013-11-01
Full Text Available The stable matching problem (also known as the stable marriage problem is a well-known problem of matching men to women, so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools or, more generally, to any two-sided market. In the classical stable marriage problem, both men and women express a strict preference order over the members of the other sex, in a qualitative way. Here, we consider stable marriage problems with weighted preferences: each man (resp., woman provides a score for each woman (resp., man. Such problems are more expressive than the classical stable marriage problems. Moreover, in some real-life situations, it is more natural to express scores (to model, for example, profits or costs rather than a qualitative preference ordering. In this context, we define new notions of stability and optimality, and we provide algorithms to find marriages that are stable and/or optimal according to these notions. While expressivity greatly increases by adopting weighted preferences, we show that, in most cases, the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem. We also consider the manipulability properties of the procedures that return such stable marriages. While we know that all procedures are manipulable by modifying the preference lists or by truncating them, here, we consider if manipulation can occur also by just modifying the weights while preserving the ordering and avoiding truncation. It turns out that, by adding weights, in some cases, we may increase the possibility of manipulating, and this cannot be avoided by any reasonable restriction on the weights.
Multiresolution strategies for the numerical solution of optimal control problems
Jain, Sachin
There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a
Optimizing Human Diet Problem Based on Price and Taste Using
Directory of Open Access Journals (Sweden)
Hossein EGHBALI
2012-07-01
Full Text Available Low price and good taste of foods are regarded as two major factors for optimal human nutrition. Due to price fluctuations and taste diversity, these two factors cannot be certainly and determinately evaluated. This problem must be viewed from another perspective because of the uncertainty about the amount of nutrients per unit of foods and also diversity of people’s daily needs to receive them.This paper discusses human diet problem in fuzzy environment. The approach deals with multi-objective fuzzy linear programming problem using a fuzzy programming technique for its solution. By prescribing a diet merely based on crisp data, some ofthe realities are neglected. For the same reason, we dealt with human diet problem through fuzzy approach. Results indicated uncertainty about factors of nutrition diet -including taste and price, amount of nutrients and their intake- would affect diet quality, making the proposed diet more realistic.
Heuristic versus statistical physics approach to optimization problems
International Nuclear Information System (INIS)
Jedrzejek, C.; Cieplinski, L.
1995-01-01
Optimization is a crucial ingredient of many calculation schemes in science and engineering. In this paper we assess several classes of methods: heuristic algorithms, methods directly relying on statistical physics such as the mean-field method and simulated annealing; and Hopfield-type neural networks and genetic algorithms partly related to statistical physics. We perform the analysis for three types of problems: (1) the Travelling Salesman Problem, (2) vector quantization, and (3) traffic control problem in multistage interconnection network. In general, heuristic algorithms perform better (except for genetic algorithms) and much faster but have to be specific for every problem. The key to improving the performance could be to include heuristic features into general purpose statistical physics methods. (author)
Directory of Open Access Journals (Sweden)
Weixing Su
2017-03-01
Full Text Available There are many dynamic optimization problems in the real world, whose convergence and searching ability is cautiously desired, obviously different from static optimization cases. This requires an optimization algorithm adaptively seek the changing optima over dynamic environments, instead of only finding the global optimal solution in the static environment. This paper proposes a novel comprehensive learning artificial bee colony optimizer (CLABC for optimization in dynamic environments problems, which employs a pool of optimal foraging strategies to balance the exploration and exploitation tradeoff. The main motive of CLABC is to enrich artificial bee foraging behaviors in the ABC model by combining Powell’s pattern search method, life-cycle, and crossover-based social learning strategy. The proposed CLABC is a more bee-colony-realistic model that the bee can reproduce and die dynamically throughout the foraging process and population size varies as the algorithm runs. The experiments for evaluating CLABC are conducted on the dynamic moving peak benchmarks. Furthermore, the proposed algorithm is applied to a real-world application of dynamic RFID network optimization. Statistical analysis of all these cases highlights the significant performance improvement due to the beneficial combination and demonstrates the performance superiority of the proposed algorithm.
Su, Weixing; Chen, Hanning; Liu, Fang; Lin, Na; Jing, Shikai; Liang, Xiaodan; Liu, Wei
2017-03-01
There are many dynamic optimization problems in the real world, whose convergence and searching ability is cautiously desired, obviously different from static optimization cases. This requires an optimization algorithm adaptively seek the changing optima over dynamic environments, instead of only finding the global optimal solution in the static environment. This paper proposes a novel comprehensive learning artificial bee colony optimizer (CLABC) for optimization in dynamic environments problems, which employs a pool of optimal foraging strategies to balance the exploration and exploitation tradeoff. The main motive of CLABC is to enrich artificial bee foraging behaviors in the ABC model by combining Powell's pattern search method, life-cycle, and crossover-based social learning strategy. The proposed CLABC is a more bee-colony-realistic model that the bee can reproduce and die dynamically throughout the foraging process and population size varies as the algorithm runs. The experiments for evaluating CLABC are conducted on the dynamic moving peak benchmarks. Furthermore, the proposed algorithm is applied to a real-world application of dynamic RFID network optimization. Statistical analysis of all these cases highlights the significant performance improvement due to the beneficial combination and demonstrates the performance superiority of the proposed algorithm.
RECIPES FOR BUILDING THE DUAL OF CONIC OPTIMIZATION PROBLEM
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Diah Chaerani
2010-08-01
Full Text Available Building the dual of the primal problem of Conic Optimization (CO isa very important step to make the ¯nding optimal solution. In many cases a givenproblem does not have the simple structure of CO problem (i.e., minimizing a linearfunction over an intersection between a±ne space and convex cones but there areseveral conic constraints and sometimes also equality constraints. In this paper wedeal with the question how to form the dual problem in such cases. We discuss theanswer by considering several conic constraints with or without equality constraints.The recipes for building the dual of such cases is formed in standard matrix forms,such that it can be used easily on the numerical experiment. Special attention isgiven to dual development of special classes of CO problems, i.e., conic quadraticand semide¯nite problems. In this paper, we also brie°y present some preliminariestheory on CO as an introduction to the main topic
On the MSE Performance and Optimization of Regularized Problems
Alrashdi, Ayed
2016-11-01
The amount of data that has been measured, transmitted/received, and stored in the recent years has dramatically increased. So, today, we are in the world of big data. Fortunately, in many applications, we can take advantages of possible structures and patterns in the data to overcome the curse of dimensionality. The most well known structures include sparsity, low-rankness, block sparsity. This includes a wide range of applications such as machine learning, medical imaging, signal processing, social networks and computer vision. This also led to a specific interest in recovering signals from noisy compressed measurements (Compressed Sensing (CS) problem). Such problems are generally ill-posed unless the signal is structured. The structure can be captured by a regularizer function. This gives rise to a potential interest in regularized inverse problems, where the process of reconstructing the structured signal can be modeled as a regularized problem. This thesis particularly focuses on finding the optimal regularization parameter for such problems, such as ridge regression, LASSO, square-root LASSO and low-rank Generalized LASSO. Our goal is to optimally tune the regularizer to minimize the mean-squared error (MSE) of the solution when the noise variance or structure parameters are unknown. The analysis is based on the framework of the Convex Gaussian Min-max Theorem (CGMT) that has been used recently to precisely predict performance errors.
A concept for global optimization of topology design problems
DEFF Research Database (Denmark)
Stolpe, Mathias; Achtziger, Wolfgang; Kawamoto, Atsushi
2006-01-01
We present a concept for solving topology design problems to proven global optimality. We propose that the problems are modeled using the approach of simultaneous analysis and design with discrete design variables and solved with convergent branch and bound type methods. This concept is illustrated...... on two applications. The first application is the design of stiff truss structures where the bar areas are chosen from a finite set of available areas. The second considered application is simultaneous topology and geometry design of planar articulated mechanisms. For each application we outline...
Analytic semigroups and optimal regularity in parabolic problems
Lunardi, Alessandra
2012-01-01
The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in p
Topology optimization of coated structures and material interface problems
DEFF Research Database (Denmark)
Clausen, Anders; Aage, Niels; Sigmund, Ole
2015-01-01
This paper presents a novel method for including coated structures and prescribed material interface properties into the minimum compliance topology optimization problem. Several elements of the method are applicable to a broader range of interface problems. The approach extends the standard SIMP......-step filtering/projection approach. The modeled coating thickness is derived analytically, and the coating is shown to be accurately controlled and applied in a highly uniform manner over the structure. An alternative interpretation of the model is to perform single-material design for additive manufacturing...
An Elite Decision Making Harmony Search Algorithm for Optimization Problem
Directory of Open Access Journals (Sweden)
Lipu Zhang
2012-01-01
Full Text Available This paper describes a new variant of harmony search algorithm which is inspired by a well-known item “elite decision making.” In the new algorithm, the good information captured in the current global best and the second best solutions can be well utilized to generate new solutions, following some probability rule. The generated new solution vector replaces the worst solution in the solution set, only if its fitness is better than that of the worst solution. The generating and updating steps and repeated until the near-optimal solution vector is obtained. Extensive computational comparisons are carried out by employing various standard benchmark optimization problems, including continuous design variables and integer variables minimization problems from the literature. The computational results show that the proposed new algorithm is competitive in finding solutions with the state-of-the-art harmony search variants.
Shape optimization for Stokes problem with threshold slip
Czech Academy of Sciences Publication Activity Database
Haslinger, J.; Stebel, Jan; Taoufik, S.
2014-01-01
Roč. 59, č. 6 (2014), s. 631-652 ISSN 0862-7940 R&D Projects: GA ČR GA201/09/0917; GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985840 Keywords : Stokes problem * friction boundary condition * shape optimization Subject RIV: BA - General Mathematics Impact factor: 0.400, year: 2014 http://link.springer.com/article/10.1007%2Fs10492-014-0077-z
Optimizing Distribution Problems using WinQSB Software
Directory of Open Access Journals (Sweden)
Daniel Mihai Amariei
2015-07-01
Full Text Available In the present paper we are presenting a problem of distribution using the Network Modeling Module of the WinQSB software, were we have 5 athletes which we must assign the optimal sample, function of the obtained time, so as to obtain the maximum output of the athletes. Also we analyzed the case of an accident of 2 athletes, the coupling of 3 athletes with 5 various athletic events causing the maximum coupling, done using the Hungarian algorithm.
Integrals of Motion for Discrete-Time Optimal Control Problems
Torres, Delfim F. M.
2003-01-01
We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the discrete time Lagrangian and discrete time control system. As corollaries, results for first-order and higher-order discrete problems of the calculus of variations are obtained.
A fractional optimal control problem for maximizing advertising efficiency
Igor Bykadorov; Andrea Ellero; Stefania Funari; Elena Moretti
2007-01-01
We propose an optimal control problem to model the dynamics of the communication activity of a firm with the aim of maximizing its efficiency. We assume that the advertising effort undertaken by the firm contributes to increase the firm's goodwill and that the goodwill affects the firm's sales. The aim is to find the advertising policies in order to maximize the firm's efficiency index which is computed as the ratio between "outputs" and "inputs" properly weighted; the outputs are represented...
Tokenplan: A Planner for Both Satisfaction and Optimization Problem
Meiller, Yannick; Fabiani, Patrick
2001-01-01
Tokenplan is a planner based on the use of Petri nets. Its main feature is the flexibility it offers in the way it builds the planning graph. The Fifth International Conference on Artificial Intelligence Planning and Scheduling planning competition validated its behavior with a graphplan-like behavior. The next step is to demonstrate the benefits we expect from our planner in planning problems involving optimization and uncertainty handling.
Heuristics for NP-hard optimization problems - simpler is better!?
Directory of Open Access Journals (Sweden)
Žerovnik Janez
2015-11-01
Full Text Available We provide several examples showing that local search, the most basic metaheuristics, may be a very competitive choice for solving computationally hard optimization problems. In addition, generation of starting solutions by greedy heuristics should be at least considered as one of very natural possibilities. In this critical survey, selected examples discussed include the traveling salesman, the resource-constrained project scheduling, the channel assignment, and computation of bounds for the Shannon capacity.
Ananiev, Sergey
2006-01-01
The paper demonstrates the equivalence between the optimality criteria (OC) method, initially proposed by Bendsoe & Kikuchi for topology optimization problem, and the projected gradient method. The equivalence is shown using Hestenes definition of Lagrange multipliers. Based on this development, an alternative formulation of the Karush-Kuhn-Tucker (KKT) condition is suggested. Such reformulation has some advantages, which will be also discussed in the paper. For verification purposes the modi...
Guaranteed Discrete Energy Optimization on Large Protein Design Problems.
Simoncini, David; Allouche, David; de Givry, Simon; Delmas, Céline; Barbe, Sophie; Schiex, Thomas
2015-12-08
In Computational Protein Design (CPD), assuming a rigid backbone and amino-acid rotamer library, the problem of finding a sequence with an optimal conformation is NP-hard. In this paper, using Dunbrack's rotamer library and Talaris2014 decomposable energy function, we use an exact deterministic method combining branch and bound, arc consistency, and tree-decomposition to provenly identify the global minimum energy sequence-conformation on full-redesign problems, defining search spaces of size up to 10(234). This is achieved on a single core of a standard computing server, requiring a maximum of 66GB RAM. A variant of the algorithm is able to exhaustively enumerate all sequence-conformations within an energy threshold of the optimum. These proven optimal solutions are then used to evaluate the frequencies and amplitudes, in energy and sequence, at which an existing CPD-dedicated simulated annealing implementation may miss the optimum on these full redesign problems. The probability of finding an optimum drops close to 0 very quickly. In the worst case, despite 1,000 repeats, the annealing algorithm remained more than 1 Rosetta unit away from the optimum, leading to design sequences that could differ from the optimal sequence by more than 30% of their amino acids.
Parallel particle swarm optimization algorithm in nuclear problems
International Nuclear Information System (INIS)
Waintraub, Marcel; Pereira, Claudio M.N.A.; Schirru, Roberto
2009-01-01
Particle Swarm Optimization (PSO) is a population-based metaheuristic (PBM), in which solution candidates evolve through simulation of a simplified social adaptation model. Putting together robustness, efficiency and simplicity, PSO has gained great popularity. Many successful applications of PSO are reported, in which PSO demonstrated to have advantages over other well-established PBM. However, computational costs are still a great constraint for PSO, as well as for all other PBMs, especially in optimization problems with time consuming objective functions. To overcome such difficulty, parallel computation has been used. The default advantage of parallel PSO (PPSO) is the reduction of computational time. Master-slave approaches, exploring this characteristic are the most investigated. However, much more should be expected. It is known that PSO may be improved by more elaborated neighborhood topologies. Hence, in this work, we develop several different PPSO algorithms exploring the advantages of enhanced neighborhood topologies implemented by communication strategies in multiprocessor architectures. The proposed PPSOs have been applied to two complex and time consuming nuclear engineering problems: reactor core design and fuel reload optimization. After exhaustive experiments, it has been concluded that: PPSO still improves solutions after many thousands of iterations, making prohibitive the efficient use of serial (non-parallel) PSO in such kind of realworld problems; and PPSO with more elaborated communication strategies demonstrated to be more efficient and robust than the master-slave model. Advantages and peculiarities of each model are carefully discussed in this work. (author)
Robust Optimization Model for Production Planning Problem under Uncertainty
Directory of Open Access Journals (Sweden)
Pembe GÜÇLÜ
2017-01-01
Full Text Available Conditions of businesses change very quickly. To take into account the uncertainty engendered by changes has become almost a rule while planning. Robust optimization techniques that are methods of handling uncertainty ensure to produce less sensitive results to changing conditions. Production planning, is to decide from which product, when and how much will be produced, with a most basic definition. Modeling and solution of the Production planning problems changes depending on structure of the production processes, parameters and variables. In this paper, it is aimed to generate and apply scenario based robust optimization model for capacitated two-stage multi-product production planning problem under parameter and demand uncertainty. With this purpose, production planning problem of a textile company that operate in İzmir has been modeled and solved, then deterministic scenarios’ and robust method’s results have been compared. Robust method has provided a production plan that has higher cost but, will result close to feasible and optimal for most of the different scenarios in the future.
Directory of Open Access Journals (Sweden)
Yan Sun
2015-09-01
Full Text Available Purpose: The purpose of study is to solve the multi-modal transportation routing planning problem that aims to select an optimal route to move a consignment of goods from its origin to its destination through the multi-modal transportation network. And the optimization is from two viewpoints including cost and time. Design/methodology/approach: In this study, a bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. Minimizing the total transportation cost and the total transportation time are set as the optimization objectives of the model. In order to balance the benefit between the two objectives, Pareto optimality is utilized to solve the model by gaining its Pareto frontier. The Pareto frontier of the model can provide the multi-modal transportation operator (MTO and customers with better decision support and it is gained by the normalized normal constraint method. Then, an experimental case study is designed to verify the feasibility of the model and Pareto optimality by using the mathematical programming software Lingo. Finally, the sensitivity analysis of the demand and supply in the multi-modal transportation organization is performed based on the designed case. Findings: The calculation results indicate that the proposed model and Pareto optimality have good performance in dealing with the bi-objective optimization. The sensitivity analysis also shows the influence of the variation of the demand and supply on the multi-modal transportation organization clearly. Therefore, this method can be further promoted to the practice. Originality/value: A bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. The Pareto frontier based sensitivity analysis of the demand and supply in the multi-modal transportation organization is performed based on the designed case.
Directory of Open Access Journals (Sweden)
Guo-Qiang Zeng
2014-01-01
Full Text Available As a novel evolutionary optimization method, extremal optimization (EO has been successfully applied to a variety of combinatorial optimization problems. However, the applications of EO in continuous optimization problems are relatively rare. This paper proposes an improved real-coded population-based EO method (IRPEO for continuous unconstrained optimization problems. The key operations of IRPEO include generation of real-coded random initial population, evaluation of individual and population fitness, selection of bad elements according to power-law probability distribution, generation of new population based on uniform random mutation, and updating the population by accepting the new population unconditionally. The experimental results on 10 benchmark test functions with the dimension N=30 have shown that IRPEO is competitive or even better than the recently reported various genetic algorithm (GA versions with different mutation operations in terms of simplicity, effectiveness, and efficiency. Furthermore, the superiority of IRPEO to other evolutionary algorithms such as original population-based EO, particle swarm optimization (PSO, and the hybrid PSO-EO is also demonstrated by the experimental results on some benchmark functions.
Issues and Strategies in Solving Multidisciplinary Optimization Problems
Patnaik, Surya
2013-01-01
Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the
International Nuclear Information System (INIS)
Hardiyanti, Y; Haekal, M; Waris, A; Haryanto, F
2016-01-01
This research compares the quadratic optimization program on Intensity Modulated Radiation Therapy Treatment Planning (IMRTP) with the Computational Environment for Radiotherapy Research (CERR) software. We assumed that the number of beams used for the treatment planner was about 9 and 13 beams. The case used the energy of 6 MV with Source Skin Distance (SSD) of 100 cm from target volume. Dose calculation used Quadratic Infinite beam (QIB) from CERR. CERR was used in the comparison study between Gauss Primary threshold method and Gauss Primary exponential method. In the case of lung cancer, the threshold variation of 0.01, and 0.004 was used. The output of the dose was distributed using an analysis in the form of DVH from CERR. The maximum dose distributions obtained were on the target volume (PTV) Planning Target Volume, (CTV) Clinical Target Volume, (GTV) Gross Tumor Volume, liver, and skin. It was obtained that if the dose calculation method used exponential and the number of beam 9. When the dose calculation method used the threshold and the number of beam 13, the maximum dose distributions obtained were on the target volume PTV, GTV, heart, and skin. (paper)
Guises and disguises of quadratic divergences
Energy Technology Data Exchange (ETDEWEB)
Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)
2014-12-15
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Eigenfunctions of quadratic hamiltonians in Wigner representation
International Nuclear Information System (INIS)
Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.
1984-01-01
Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail
Topology Optimization for Wave Propagation Problems with Experimental Validation
DEFF Research Database (Denmark)
Christiansen, Rasmus Ellebæk
designed using the proposed method is provided. A novel approach for designing meta material slabs with selectively tuned negative refractive behavior is outlined. Numerical examples demonstrating the behavior of a slab under different conditions is provided. Results from an experimental studydemonstrating...... agreement with numerical predictions are presented. Finally an approach for designing acoustic wave shaping devices is treated. Three examples of applications are presented, a directional sound emission device, a wave splitting device and a flat focusing lens. Experimental results for the first two devices......This Thesis treats the development and experimental validation of density-based topology optimization methods for wave propagation problems. Problems in the frequency regime where design dimensions are between approximately one fourth and ten wavelengths are considered. All examples treat problems...
Orthogonal and Scaling Transformations of Quadratic Functions with ...
African Journals Online (AJOL)
In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...
An Efficient Optimization Method for Solving Unsupervised Data Classification Problems
Directory of Open Access Journals (Sweden)
Parvaneh Shabanzadeh
2015-01-01
Full Text Available Unsupervised data classification (or clustering analysis is one of the most useful tools and a descriptive task in data mining that seeks to classify homogeneous groups of objects based on similarity and is used in many medical disciplines and various applications. In general, there is no single algorithm that is suitable for all types of data, conditions, and applications. Each algorithm has its own advantages, limitations, and deficiencies. Hence, research for novel and effective approaches for unsupervised data classification is still active. In this paper a heuristic algorithm, Biogeography-Based Optimization (BBO algorithm, was adapted for data clustering problems by modifying the main operators of BBO algorithm, which is inspired from the natural biogeography distribution of different species. Similar to other population-based algorithms, BBO algorithm starts with an initial population of candidate solutions to an optimization problem and an objective function that is calculated for them. To evaluate the performance of the proposed algorithm assessment was carried on six medical and real life datasets and was compared with eight well known and recent unsupervised data classification algorithms. Numerical results demonstrate that the proposed evolutionary optimization algorithm is efficient for unsupervised data classification.
On the degeneracy of the IMRT optimization problem
International Nuclear Information System (INIS)
Alber, M.; Meedt, G.; Nuesslin, F.; Reemtsen, R.
2002-01-01
One approach to the computation of photon IMRT treatment plans is the formulation of an optimization problem with an objective function that derives from an objective density. An investigation of the second-order properties of such an objective function in a neighborhood of the minimizer opens an intuitive access to many traits of this approach. A general finding is that only a small subset of the parameter space has nonzero curvature, while the objective function is entirely flat in a neighborhood of the minimizer in most directions. The dimension of the subspace of vanishing curvature serves as a measure for the degeneracy of the solution. This finding is important both for algorithm design and evaluation of the mathematical model of clinical intuition, expressed by the objective function. The structure of the subspace of great curvature is found to be imposed on the problem by conflicts between objectives of target and critical structures. These conflicts and their corresponding modes of resolution form a common trait between all reasonable treatment plans of a given case. The high degree of degeneracy makes the use of a conjugate gradient optimization algorithm particularly favorable since the number of iterations to convergence is equivalent to the number of different eigenvalues of the curvature tensor and is hence independent from the number of optimization parameters. A high level of degeneracy of the fluence profiles implies that it should be possible to stipulate further delivery-related conditions without causing severe deterioration of the dose distribution
Quadratic Hedging of Basis Risk
Directory of Open Access Journals (Sweden)
Hardy Hulley
2015-02-01
Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.
International Nuclear Information System (INIS)
2005-01-01
Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces
Directory of Open Access Journals (Sweden)
Vivek Patel
2012-08-01
Full Text Available Nature inspired population based algorithms is a research field which simulates different natural phenomena to solve a wide range of problems. Researchers have proposed several algorithms considering different natural phenomena. Teaching-Learning-based optimization (TLBO is one of the recently proposed population based algorithm which simulates the teaching-learning process of the class room. This algorithm does not require any algorithm-specific control parameters. In this paper, elitism concept is introduced in the TLBO algorithm and its effect on the performance of the algorithm is investigated. The effects of common controlling parameters such as the population size and the number of generations on the performance of the algorithm are also investigated. The proposed algorithm is tested on 35 constrained benchmark functions with different characteristics and the performance of the algorithm is compared with that of other well known optimization algorithms. The proposed algorithm can be applied to various optimization problems of the industrial environment.
Directory of Open Access Journals (Sweden)
Firat Evirgen
2016-04-01
Full Text Available In this paper, a class of Nonlinear Programming problem is modeled with gradient based system of fractional order differential equations in Caputo's sense. To see the overlap between the equilibrium point of the fractional order dynamic system and theoptimal solution of the NLP problem in a longer timespan the Multistage Variational İteration Method isapplied. The comparisons among the multistage variational iteration method, the variationaliteration method and the fourth order Runge-Kutta method in fractional and integer order showthat fractional order model and techniques can be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programming problems.
Energy Technology Data Exchange (ETDEWEB)
Ohori, T.; Yamamoto, H.; Setsu, Nenso; Watanabe, K. (Hokkaido Inst. of Technology, Hokkaido (Japan))
1994-04-20
The accelerated approximate solution of combinatorial optimization problems by symmetry integrating hopfield neural network (NN) has been applied to many combinatorial problems such as the traveling salesman problem, the network planning problem, etc. However, the hopfield NN converges to local minimum solutions very slowly. In this paper, a general inclination model composed by introducing an accelerated parameter to the hopfield model is proposed, and it has been shown that the acceleration parameter can make the model converge to the local minima more quickly. Moreover, simulation experiments for random quadratic combinatorial problems with two and twenty-five variables were carried out. The results show that the acceleration of convergence makes the attraction region of the local minimum change and the accuracy of solution worse. If an initial point is selected around the center of unit hyper cube, solutions with high accuracy not affected by the acceleration parameter can be obtained. 9 refs., 8 figs., 3 tabs.
On the robust optimization to the uncertain vaccination strategy problem
International Nuclear Information System (INIS)
Chaerani, D.; Anggriani, N.; Firdaniza
2014-01-01
In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented
On the robust optimization to the uncertain vaccination strategy problem
Energy Technology Data Exchange (ETDEWEB)
Chaerani, D., E-mail: d.chaerani@unpad.ac.id; Anggriani, N., E-mail: d.chaerani@unpad.ac.id; Firdaniza, E-mail: d.chaerani@unpad.ac.id [Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Padjadjaran Indonesia, Jalan Raya Bandung Sumedang KM 21 Jatinangor Sumedang 45363 (Indonesia)
2014-02-21
In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.
Study on ant colony optimization for fuel loading pattern problem
International Nuclear Information System (INIS)
Kishi, Hironori; Kitada, Takanori
2013-01-01
Modified ant colony optimization (ACO) was applied to the in-core fuel loading pattern (LP) optimization problem to minimize the power peaking factor (PPF) in the modeled 1/4 symmetry PWR core. Loading order was found to be important in ACO. Three different loading orders with and without the adjacent effect between fuel assemblies (FAs) were compared, and it was found that the loading order from the central core is preferable because many selections of FAs to be inserted are available in the core center region. LPs were determined from pheromone trail and heuristic information, which is a priori knowledge based on the feature of the problem. Three types of heuristic information were compared to obtain the desirable performance of searching LPs with low PPF. Moreover, mutation operation, such as the genetic algorithm (GA), was introduced into the ACO algorithm to avoid searching similar LPs because heuristic information used in ACO tends to localize the searching space in the LP problem. The performance of ACO with some improvement was compared with those of simulated annealing and GA. In conclusion, good performance can be achieved by setting proper heuristic information and mutation operation parameter in ACO. (author)
Spectral Analysis of Large Finite Element Problems by Optimization Methods
Directory of Open Access Journals (Sweden)
Luca Bergamaschi
1994-01-01
Full Text Available Recently an efficient method for the solution of the partial symmetric eigenproblem (DACG, deflated-accelerated conjugate gradient was developed, based on the conjugate gradient (CG minimization of successive Rayleigh quotients over deflated subspaces of decreasing size. In this article four different choices of the coefficient βk required at each DACG iteration for the computation of the new search direction Pk are discussed. The “optimal” choice is the one that yields the same asymptotic convergence rate as the CG scheme applied to the solution of linear systems. Numerical results point out that the optimal βk leads to a very cost effective algorithm in terms of CPU time in all the sample problems presented. Various preconditioners are also analyzed. It is found that DACG using the optimal βk and (LLT−1 as a preconditioner, L being the incomplete Cholesky factor of A, proves a very promising method for the partial eigensolution. It appears to be superior to the Lanczos method in the evaluation of the 40 leftmost eigenpairs of five finite element problems, and particularly for the largest problem, with size equal to 4560, for which the speed gain turns out to fall between 2.5 and 6.0, depending on the eigenpair level.
PID controller tuning using metaheuristic optimization algorithms for benchmark problems
Gholap, Vishal; Naik Dessai, Chaitali; Bagyaveereswaran, V.
2017-11-01
This paper contributes to find the optimal PID controller parameters using particle swarm optimization (PSO), Genetic Algorithm (GA) and Simulated Annealing (SA) algorithm. The algorithms were developed through simulation of chemical process and electrical system and the PID controller is tuned. Here, two different fitness functions such as Integral Time Absolute Error and Time domain Specifications were chosen and applied on PSO, GA and SA while tuning the controller. The proposed Algorithms are implemented on two benchmark problems of coupled tank system and DC motor. Finally, comparative study has been done with different algorithms based on best cost, number of iterations and different objective functions. The closed loop process response for each set of tuned parameters is plotted for each system with each fitness function.
Using combinatorial problem decomposition for optimizing plutonium inventory management
International Nuclear Information System (INIS)
Niquil, Y.; Gondran, M.; Voskanian, A.; Paris-11 Univ., 91 - Orsay
1997-03-01
Plutonium Inventory Management Optimization can be modeled as a very large 0-1 linear program. To solve it, problem decomposition is necessary, since other classic techniques are not efficient for such a size. The first decomposition consists in favoring constraints that are the most difficult to reach and variables that have the highest influence on the cost: fortunately, both correspond to stock output decisions. The second decomposition consists in mixing continuous linear program solving and integer linear program solving. Besides, the first decisions to be taken are systematically favored, for they are based on data considered to be sure, when data supporting later decisions in known with less accuracy and confidence. (author)
Macroscopic relationship in primal-dual portfolio optimization problem
Shinzato, Takashi
2018-02-01
In the present paper, using a replica analysis, we examine the portfolio optimization problem handled in previous work and discuss the minimization of investment risk under constraints of budget and expected return for the case that the distribution of the hyperparameters of the mean and variance of the return rate of each asset are not limited to a specific probability family. Findings derived using our proposed method are compared with those in previous work to verify the effectiveness of our proposed method. Further, we derive a Pythagorean theorem of the Sharpe ratio and macroscopic relations of opportunity loss. Using numerical experiments, the effectiveness of our proposed method is demonstrated for a specific situation.
Topology optimization of 3D Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Sigmund, Ole; Bendsøe, Martin P.
fluid mechanics. In future practice a muTAS could be used by doctors, engineers etc. as a hand held device with short reaction time that provides on-site analysis of a flowing substance such as blood, polluted water or similar. Borrvall and Petersson [2] paved the road for using the topology...... particular at micro scales since they are easily manufacturable and maintenance free. Here we consider topology optimization of 3D Stokes flow problems which is a reasonable fluid model to use at small scales. The presentation elaborates on effects caused by 3D fluid modelling on the design. Numerical...
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
Empirical Estimates in Economic and Financial Optimization Problems
Czech Academy of Sciences Publication Activity Database
Houda, Michal; Kaňková, Vlasta
2012-01-01
Roč. 19, č. 29 (2012), s. 50-69 ISSN 1212-074X R&D Projects: GA ČR GAP402/10/1610; GA ČR GAP402/11/0150; GA ČR GAP402/10/0956 Institutional research plan: CEZ:AV0Z10750506 Keywords : stochastic programming * empirical estimates * moment generating functions * stability * Wasserstein metric * L1-norm * Lipschitz property * consistence * convergence rate * normal distribution * Pareto distribution * Weibull distribution * distribution tails * simulation Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2012/E/houda-empirical estimates in economic and financial optimization problems.pdf
Keulen, van T.A.C.; Gillot, J.; Jager, de A.G.; Steinbuch, M.
2014-01-01
This paper presents a numerical solution for scalar state constrained optimal control problems. The algorithm rewrites the constrained optimal control problem as a sequence of unconstrained optimal control problems which can be solved recursively as a two point boundary value problem. The solution
A Monarch Butterfly Optimization for the Dynamic Vehicle Routing Problem
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Shifeng Chen
2017-09-01
Full Text Available The dynamic vehicle routing problem (DVRP is a variant of the Vehicle Routing Problem (VRP in which customers appear dynamically. The objective is to determine a set of routes that minimizes the total travel distance. In this paper, we propose a monarch butterfly optimization (MBO algorithm to solve DVRPs, utilizing a greedy strategy. Both migration operation and the butterfly adjusting operator only accept the offspring of butterfly individuals that have better fitness than their parents. To improve performance, a later perturbation procedure is implemented, to maintain a balance between global diversification and local intensification. The computational results indicate that the proposed technique outperforms the existing approaches in the literature for average performance by at least 9.38%. In addition, 12 new best solutions were found. This shows that this proposed technique consistently produces high-quality solutions and outperforms other published heuristics for the DVRP.
Reactive Robustness and Integrated Approaches for Railway Optimization Problems
DEFF Research Database (Denmark)
Haahr, Jørgen Thorlund
journeys helps the driver to drive efficiently and enhances robustness in a realistic (dynamic) environment. Four international scientific prizes have been awarded for distinct parts of the research during the course of this PhD project. The first prize was awarded for work during the \\2014 RAS Problem...... to absorb or withstand unexpected events such as delays. Making robust plans is central in order to maintain a safe and timely railway operation. This thesis focuses on reactive robustness, i.e., the ability to react once a plan is rendered infeasible in operation due to disruptions. In such time...... Solving Competition", where a freight yard optimization problem was considered. The second junior (PhD) prize was awared for the work performed in the \\ROADEF/EURO Challenge 2014: Trains don't vanish!", where the planning of rolling stock movements at a large station was considered. An honorable mention...
Optimization method for an evolutional type inverse heat conduction problem
International Nuclear Information System (INIS)
Deng Zuicha; Yu Jianning; Yang Liu
2008-01-01
This paper deals with the determination of a pair (q, u) in the heat conduction equation u t -u xx +q(x,t)u=0, with initial and boundary conditions u(x,0)=u 0 (x), u x vertical bar x=0 =u x vertical bar x=1 =0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced
Optimization method for an evolutional type inverse heat conduction problem
Deng, Zui-Cha; Yu, Jian-Ning; Yang, Liu
2008-01-01
This paper deals with the determination of a pair (q, u) in the heat conduction equation u_t-u_{xx}+q(x,t)u=0, with initial and boundary conditions u(x,0)=u_0(x),\\qquad u_x|_{x=0}=u_x|_{x=1}=0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced.
Quadratic spatial soliton interactions
Jankovic, Ladislav
Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30
A DE-Based Scatter Search for Global Optimization Problems
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Kun Li
2015-01-01
Full Text Available This paper proposes a hybrid scatter search (SS algorithm for continuous global optimization problems by incorporating the evolution mechanism of differential evolution (DE into the reference set updated procedure of SS to act as the new solution generation method. This hybrid algorithm is called a DE-based SS (SSDE algorithm. Since different kinds of mutation operators of DE have been proposed in the literature and they have shown different search abilities for different kinds of problems, four traditional mutation operators are adopted in the hybrid SSDE algorithm. To adaptively select the mutation operator that is most appropriate to the current problem, an adaptive mechanism for the candidate mutation operators is developed. In addition, to enhance the exploration ability of SSDE, a reinitialization method is adopted to create a new population and subsequently construct a new reference set whenever the search process of SSDE is trapped in local optimum. Computational experiments on benchmark problems show that the proposed SSDE is competitive or superior to some state-of-the-art algorithms in the literature.
Enhanced ant colony optimization for inventory routing problem
Wong, Lily; Moin, Noor Hasnah
2015-10-01
The inventory routing problem (IRP) integrates and coordinates two important components of supply chain management which are transportation and inventory management. We consider a one-to-many IRP network for a finite planning horizon. The demand for each product is deterministic and time varying as well as a fleet of capacitated homogeneous vehicles, housed at a depot/warehouse, delivers the products from the warehouse to meet the demand specified by the customers in each period. The inventory holding cost is product specific and is incurred at the customer sites. The objective is to determine the amount of inventory and to construct a delivery routing that minimizes both the total transportation and inventory holding cost while ensuring each customer's demand is met over the planning horizon. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (best integer) for each instance considered. We propose an enhanced ant colony optimization (ACO) to solve the problem and the built route is improved by using local search. The computational experiments demonstrating the effectiveness of our approach is presented.
Quadratic Interpolation and Linear Lifting Design
Directory of Open Access Journals (Sweden)
Joel Solé
2007-03-01
Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.
Directory of Open Access Journals (Sweden)
Mohammad-Reza Askari
2015-07-01
Full Text Available Abstract This paper introduces a new stochastic optimization framework based bat algorithm BA to solve the optimal distribution feeder reconfiguration DFR as well as the shunt capacitor placement and sizing in the distribution systems. The objective functions to be investigated are minimization of the active power losses and minimization of the total network costs an. In order to consider the uncertainties of the active and reactive loads in the problem point estimate method PEM with 2m scheme is employed as the stochastic tool. The feasibility and good performance of the proposed method are examined on the IEEE 69-bus test system.
Modified Monkey Optimization Algorithm for Solving Optimal Reactive Power Dispatch Problem
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Kanagasabai Lenin
2015-04-01
Full Text Available In this paper, a novel approach Modified Monkey optimization (MMO algorithm for solving optimal reactive power dispatch problem has been presented. MMO is a population based stochastic meta-heuristic algorithm and it is inspired by intelligent foraging behaviour of monkeys. This paper improves both local leader and global leader phases. The proposed (MMO algorithm has been tested in standard IEEE 30 bus test system and simulation results show the worthy performance of the proposed algorithm in reducing the real power loss.
A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
Energy Technology Data Exchange (ETDEWEB)
Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)
2017-06-15
We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.
Simultaneous Optimization of Tallies in Difficult Shielding Problems
International Nuclear Information System (INIS)
Peplow, Douglas E.; Evans, Thomas M.; Wagner, John C.
2008-01-01
Monte Carlo is quite useful for calculating specific quantities in complex transport problems. Many variance reduction strategies have been developed that accelerate Monte Carlo calculations for specific tallies. However, when trying to calculate multiple tallies or a mesh tally, users have had to accept different levels of relative uncertainty among the tallies or run separate calculations optimized for each individual tally. To address this limitation, an extension of the CADIS (Consistent Adjoint Driven Importance Sampling) method, which is used for difficult source/detector problems, has been developed to optimize several tallies or the cells of a mesh tally simultaneously. The basis for this method is the development of an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. This method utilizes the results of a forward discrete ordinates solution, which may be based on a quick, coarse-mesh calculation, to develop a forward-weighted source for the adjoint calculation. The importance map and the biased source computed from the adjoint flux are then used in the forward Monte Carlo calculation to obtain approximately uniform relative uncertainties for the desired tallies. This extension is called forward-weighted CADIS, or FW-CADIS
Quadratic soliton self-reflection at a quadratically nonlinear interface
Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai
2003-11-01
The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.
A revisit to quadratic programming with fuzzy parameters
International Nuclear Information System (INIS)
Liu, S.-T.
2009-01-01
Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.
Directory of Open Access Journals (Sweden)
Rashad O. Mastaliev
2016-12-01
Full Text Available The optimal control problem of nonlinear stochastic systems which mathematical model is given by Ito stochastic differential equation with delay argument is considered. Assuming that the concerned region is open for the control by the first and the second variation (classical sense of the quality functional we obtain the necessary optimality condition of the first and the second order. In the particular case we receive the stochastic analog of the Legendre—Clebsch condition and some constructively verified conclusions from the second order necessary condition. We investigate the Legendre–Clebsch conditions for the degeneration case and obtain the necessary conditions of optimality for a special control, in the classical sense.
National Research Council Canada - National Science Library
Khoo, Wai
1999-01-01
.... These problems model stochastic portfolio optimization problems (SPOPs) which assume deterministic unit weight, and normally distributed unit return with known mean and variance for each item type...
A Framework for Constrained Optimization Problems Based on a Modified Particle Swarm Optimization
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Biwei Tang
2016-01-01
Full Text Available This paper develops a particle swarm optimization (PSO based framework for constrained optimization problems (COPs. Aiming at enhancing the performance of PSO, a modified PSO algorithm, named SASPSO 2011, is proposed by adding a newly developed self-adaptive strategy to the standard particle swarm optimization 2011 (SPSO 2011 algorithm. Since the convergence of PSO is of great importance and significantly influences the performance of PSO, this paper first theoretically investigates the convergence of SASPSO 2011. Then, a parameter selection principle guaranteeing the convergence of SASPSO 2011 is provided. Subsequently, a SASPSO 2011-based framework is established to solve COPs. Attempting to increase the diversity of solutions and decrease optimization difficulties, the adaptive relaxation method, which is combined with the feasibility-based rule, is applied to handle constraints of COPs and evaluate candidate solutions in the developed framework. Finally, the proposed method is verified through 4 benchmark test functions and 2 real-world engineering problems against six PSO variants and some well-known methods proposed in the literature. Simulation results confirm that the proposed method is highly competitive in terms of the solution quality and can be considered as a vital alternative to solve COPs.
PARETO OPTIMAL SOLUTIONS FOR MULTI-OBJECTIVE GENERALIZED ASSIGNMENT PROBLEM
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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.
Problems of future energy market planning and optimization
International Nuclear Information System (INIS)
Vladimir Lelek; David Jaluvka
2007-01-01
Problems of future energy supply in the form, which is demanded - heat, liquid fuel, electricity - are described. There are several factors, which probably could be studied separately: technology and its sustain ability with respect to the raw materials resources, long time for capacity construction, for some form of energy even absence of sufficiently deep technology knowledge and model of prices. Prices are specially peculiar problem - they could be very different from the standard approach (investment, operation and maintenance, fuel, profit), if there are market instabilities and you are not able to supply market by the demanded amount form of energy with the consequences on production. Expected effect will be jump in prices or regulated supply to equalize supply and use. Such situation will be until the new capacities are put into operation or new technologies of production are established - it could be time about ten or more years and this can completely change our standard consideration of profit. The main profit will be to avoid losses and unemployment. Also concept of local or domestic raw material resources could be changed - in the free market your resources will be sold to those paying more. Probable development of energy market is described in the article and special attention is devoted to the nuclear energy, which not only consume, but also produce raw material and how to proceed to avoid crises in supply. Contemporary understanding of the problem does not enable to formulate it strictly as mathematical optimization task (Authors)
Automated bond order assignment as an optimization problem.
Dehof, Anna Katharina; Rurainski, Alexander; Bui, Quang Bao Anh; Böcker, Sebastian; Lenhof, Hans-Peter; Hildebrandt, Andreas
2011-03-01
Numerous applications in Computational Biology process molecular structures and hence strongly rely not only on correct atomic coordinates but also on correct bond order information. For proteins and nucleic acids, bond orders can be easily deduced but this does not hold for other types of molecules like ligands. For ligands, bond order information is not always provided in molecular databases and thus a variety of approaches tackling this problem have been developed. In this work, we extend an ansatz proposed by Wang et al. that assigns connectivity-based penalty scores and tries to heuristically approximate its optimum. In this work, we present three efficient and exact solvers for the problem replacing the heuristic approximation scheme of the original approach: an A*, an ILP and an fixed-parameter approach (FPT) approach. We implemented and evaluated the original implementation, our A*, ILP and FPT formulation on the MMFF94 validation suite and the KEGG Drug database. We show the benefit of computing exact solutions of the penalty minimization problem and the additional gain when computing all optimal (or even suboptimal) solutions. We close with a detailed comparison of our methods. The A* and ILP solution are integrated into the open-source C++ LGPL library BALL and the molecular visualization and modelling tool BALLView and can be downloaded from our homepage www.ball-project.org. The FPT implementation can be downloaded from http://bio.informatik.uni-jena.de/software/.
Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints
Kmet', Tibor; Kmet'ová, Mária
2009-09-01
A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.
Quadratic brackets from symplectic forms
International Nuclear Information System (INIS)
Alekseev, Anton Yu.; Todorov, Ivan T.
1994-01-01
We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
Computation of optimal transport and related hedging problems via penalization and neural networks
Eckstein, Stephan; Kupper, Michael
2018-01-01
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. We present numerical examples from optimal transport, martingale optimal transport, portfolio optimization under uncertainty and generative adversa...
Electrical Discharge Platinum Machining Optimization Using Stefan Problem Solutions
Directory of Open Access Journals (Sweden)
I. B. Stavitskiy
2015-01-01
Full Text Available The article presents the theoretical study results of platinum workability by electrical discharge machining (EDM, based on the solution of the thermal problem of moving the boundary of material change phase, i.e. Stefan problem. The problem solution enables defining the surface melt penetration of the material under the heat flow proceeding from the time of its action and the physical properties of the processed material. To determine the rational EDM operating conditions of platinum the article suggests relating its workability with machinability of materials, for which the rational EDM operating conditions are, currently, defined. It is shown that at low densities of the heat flow corresponding to the finishing EDM operating conditions, the processing conditions used for steel 45 are appropriate for platinum machining; with EDM at higher heat flow densities (e.g. 50 GW / m2 for this purpose copper processing conditions are used; at the high heat flow densities corresponding to heavy roughing EDM it is reasonable to use tungsten processing conditions. The article also represents how the minimum width of the current pulses, at which platinum starts melting and, accordingly, the EDM process becomes possible, depends on the heat flow density. It is shown that the processing of platinum is expedient at a pulse width corresponding to the values, called the effective pulse width. Exceeding these values does not lead to a substantial increase in removal of material per pulse, but considerably reduces the maximum repetition rate and therefore, the EDM capacity. The paper shows the effective pulse width versus the heat flow density. It also presents the dependences of the maximum platinum surface melt penetration and the corresponding pulse width on the heat flow density. Results obtained using solutions of the Stephen heat problem can be used to optimize EDM operating conditions of platinum machining.
Wolf Search Algorithm for Solving Optimal Reactive Power Dispatch Problem
Directory of Open Access Journals (Sweden)
Kanagasabai Lenin
2015-03-01
Full Text Available This paper presents a new bio-inspired heuristic optimization algorithm called the Wolf Search Algorithm (WSA for solving the multi-objective reactive power dispatch problem. Wolf Search algorithm is a new bio – inspired heuristic algorithm which based on wolf preying behaviour. The way wolves search for food and survive by avoiding their enemies has been imitated to formulate the algorithm for solving the reactive power dispatches. And the speciality of wolf is possessing both individual local searching ability and autonomous flocking movement and this special property has been utilized to formulate the search algorithm .The proposed (WSA algorithm has been tested on standard IEEE 30 bus test system and simulation results shows clearly about the good performance of the proposed algorithm .
Using combinatorial problem decomposition for optimizing plutonium inventory management
Energy Technology Data Exchange (ETDEWEB)
Niquil, Y.; Gondran, M. [Electricite de France (EDF), 92 - Clamart (France). Direction des Etudes et Recherches; Voskanian, A. [Electricite de France (EDF), 92 - Clamart (France). Direction des Etudes et Recherches]|[Paris-11 Univ., 91 - Orsay (France). Lab. de Recherche en Informatique
1997-03-01
Plutonium Inventory Management Optimization can be modeled as a very large 0-1 linear program. To solve it, problem decomposition is necessary, since other classic techniques are not efficient for such a size. The first decomposition consists in favoring constraints that are the most difficult to reach and variables that have the highest influence on the cost: fortunately, both correspond to stock output decisions. The second decomposition consists in mixing continuous linear program solving and integer linear program solving. Besides, the first decisions to be taken are systematically favored, for they are based on data considered to be sure, when data supporting later decisions in known with less accuracy and confidence. (author) 7 refs.
Fractional and multivariable calculus model building and optimization problems
Mathai, A M
2017-01-01
This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...
Energy Technology Data Exchange (ETDEWEB)
Liu, X; Belcher, AH; Wiersma, R [The University of Chicago, Chicago, IL (United States)
2016-06-15
Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimization and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre-iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases. Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built-in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also
Optimal consumption—portfolio problem with CVaR constraints
International Nuclear Information System (INIS)
Zhang, Qingye; Gao, Yan
2016-01-01
The optimal portfolio selection is a fundamental issue in finance, and its two most important ingredients are risk and return. Merton's pioneering work in dynamic portfolio selection emphasized only the expected utility of the consumption and the terminal wealth. To make the optimal portfolio strategy be achievable, risk control over bankruptcy during the investment horizon is an indispensable ingredient. So, in this paper, we consider the consumption-portfolio problem coupled with a dynamic risk control. More specifically, different from the existing literature, we impose a dynamic relative CVaR constraint on it. By the stochastic dynamic programming techniques, we derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation. Moreover, by the Lagrange multiplier method, the closed form solution is provided when the utility function is a logarithmic one. At last, an illustrative empirical study is given. The results show the distinct difference of the portfolio strategies with and without the CVaR constraints: the proportion invested in the risky assets is reduced over time with CVaR constraint instead of being constant without CVaR constraints. This can provide a good decision-making reference for the investors.
Optimal Control Approaches to the Aggregate Production Planning Problem
Directory of Open Access Journals (Sweden)
Yasser A. Davizón
2015-12-01
Full Text Available In the area of production planning and control, the aggregate production planning (APP problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.
On quadratic residue codes and hyperelliptic curves
Directory of Open Access Journals (Sweden)
David Joyner
2008-01-01
Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2003-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
A modified teaching–learning based optimization for multi-objective optimal power flow problem
International Nuclear Information System (INIS)
Shabanpour-Haghighi, Amin; Seifi, Ali Reza; Niknam, Taher
2014-01-01
Highlights: • A new modified teaching–learning based algorithm is proposed. • A self-adaptive wavelet mutation strategy is used to enhance the performance. • To avoid reaching a large repository size, a fuzzy clustering technique is used. • An efficiently smart population selection is utilized. • Simulations show the superiority of this algorithm compared with other ones. - Abstract: In this paper, a modified teaching–learning based optimization algorithm is analyzed to solve the multi-objective optimal power flow problem considering the total fuel cost and total emission of the units. The modified phase of the optimization algorithm utilizes a self-adapting wavelet mutation strategy. Moreover, a fuzzy clustering technique is proposed to avoid extremely large repository size besides a smart population selection for the next iteration. These techniques make the algorithm searching a larger space to find the optimal solutions while speed of the convergence remains good. The IEEE 30-Bus and 57-Bus systems are used to illustrate performance of the proposed algorithm and results are compared with those in literatures. It is verified that the proposed approach has better performance over other techniques
Yu, Xiang; Zhang, Xueqing
2017-01-01
Comprehensive learning particle swarm optimization (CLPSO) is a powerful state-of-the-art single-objective metaheuristic. Extending from CLPSO, this paper proposes multiswarm CLPSO (MSCLPSO) for multiobjective optimization. MSCLPSO involves multiple swarms, with each swarm associated with a separate original objective. Each particle's personal best position is determined just according to the corresponding single objective. Elitists are stored externally. MSCLPSO differs from existing multiobjective particle swarm optimizers in three aspects. First, each swarm focuses on optimizing the associated objective using CLPSO, without learning from the elitists or any other swarm. Second, mutation is applied to the elitists and the mutation strategy appropriately exploits the personal best positions and elitists. Third, a modified differential evolution (DE) strategy is applied to some extreme and least crowded elitists. The DE strategy updates an elitist based on the differences of the elitists. The personal best positions carry useful information about the Pareto set, and the mutation and DE strategies help MSCLPSO discover the true Pareto front. Experiments conducted on various benchmark problems demonstrate that MSCLPSO can find nondominated solutions distributed reasonably over the true Pareto front in a single run.
Arasomwan, Martins Akugbe; Adewumi, Aderemi Oluyinka
2014-01-01
A new local search technique is proposed and used to improve the performance of particle swarm optimization algorithms by addressing the problem of premature convergence. In the proposed local search technique, a potential particle position in the solution search space is collectively constructed by a number of randomly selected particles in the swarm. The number of times the selection is made varies with the dimension of the optimization problem and each selected particle donates the value in the location of its randomly selected dimension from its personal best. After constructing the potential particle position, some local search is done around its neighbourhood in comparison with the current swarm global best position. It is then used to replace the global best particle position if it is found to be better; otherwise no replacement is made. Using some well-studied benchmark problems with low and high dimensions, numerical simulations were used to validate the performance of the improved algorithms. Comparisons were made with four different PSO variants, two of the variants implement different local search technique while the other two do not. Results show that the improved algorithms could obtain better quality solution while demonstrating better convergence velocity and precision, stability, robustness, and global-local search ability than the competing variants. PMID:24723827
Directory of Open Access Journals (Sweden)
R. Venkata Rao
2013-01-01
Full Text Available Teaching-Learning-based optimization (TLBO is a recently proposed population based algorithm, which simulates the teaching-learning process of the class room. This algorithm requires only the common control parameters and does not require any algorithm-specific control parameters. In this paper, the effect of elitism on the performance of the TLBO algorithm is investigated while solving unconstrained benchmark problems. The effects of common control parameters such as the population size and the number of generations on the performance of the algorithm are also investigated. The proposed algorithm is tested on 76 unconstrained benchmark functions with different characteristics and the performance of the algorithm is compared with that of other well known optimization algorithms. A statistical test is also performed to investigate the results obtained using different algorithms. The results have proved the effectiveness of the proposed elitist TLBO algorithm.
Directory of Open Access Journals (Sweden)
V. A. Baturin
2017-03-01
Full Text Available An optimal control problem for discrete systems is considered. A method of successive improvements along with its modernization based on the expansion of the main structures of the core algorithm about the parameter is suggested. The idea of the method is based on local approximation of attainability set, which is described by the zeros of the Bellman function in the special problem of optimal control. The essence of the problem is as follows: from the end point of the phase is required to find a path that minimizes functional deviations of the norm from the initial state. If the initial point belongs to the attainability set of the original controlled system, the value of the Bellman function equal to zero, otherwise the value of the Bellman function is greater than zero. For this special task Bellman equation is considered. The support approximation and Bellman equation are selected. The Bellman function is approximated by quadratic terms. Along the allowable trajectory, this approximation gives nothing, because Bellman function and its expansion coefficients are zero. We used a special trick: an additional variable is introduced, which characterizes the degree of deviation of the system from the initial state, thus it is obtained expanded original chain. For the new variable initial nonzero conditions is selected, thus obtained trajectory is lying outside attainability set and relevant Bellman function is greater than zero, which allows it to hold a non-trivial approximation. As a result of these procedures algorithms of successive improvements is designed. Conditions for relaxation algorithms and conditions for the necessary conditions of optimality are also obtained.
Optimal Monetary Policy Cooperation through State-Independent Contracts with Targets
DEFF Research Database (Denmark)
Jensen, Henrik
2000-01-01
Simple state-independent monetary institutions are shown to secure optimal cooperative policies in a stochastic, linear-quadratic two-country world with international policy spill-overs and national credibility problems. Institutions characterize delegation to independent central bankers facing...... quadratic performance related contracts punishing or rewarding deviations from primary and intermediate policy targets...
Binary classification posed as a quadratically constrained quadratic ...
Indian Academy of Sciences (India)
DEEPAK KUMAR
whether the particle is lying within the search space by car- rying out a check on the QCQP ... likely to go out of the search space are redeployed back to their previous ... problems such as optimization of sensor networks or col- laborative data ...
Schwarz and multilevel methods for quadratic spline collocation
Energy Technology Data Exchange (ETDEWEB)
Christara, C.C. [Univ. of Toronto, Ontario (Canada); Smith, B. [Univ. of California, Los Angeles, CA (United States)
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
A sequential quadratic programming algorithm using an incomplete solution of the subproblem
Energy Technology Data Exchange (ETDEWEB)
Murray, W. [Stanford Univ., CA (United States). Systems Optimization Lab.; Prieto, F.J. [Universidad `Carlos III` de Madrid (Spain). Dept. de Estadistica y Econometria
1993-05-01
We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact set.
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
Directory of Open Access Journals (Sweden)
Hailong Wang
2018-01-01
Full Text Available The backtracking search optimization algorithm (BSA is a population-based evolutionary algorithm for numerical optimization problems. BSA has a powerful global exploration capacity while its local exploitation capability is relatively poor. This affects the convergence speed of the algorithm. In this paper, we propose a modified BSA inspired by simulated annealing (BSAISA to overcome the deficiency of BSA. In the BSAISA, the amplitude control factor (F is modified based on the Metropolis criterion in simulated annealing. The redesigned F could be adaptively decreased as the number of iterations increases and it does not introduce extra parameters. A self-adaptive ε-constrained method is used to handle the strict constraints. We compared the performance of the proposed BSAISA with BSA and other well-known algorithms when solving thirteen constrained benchmarks and five engineering design problems. The simulation results demonstrated that BSAISA is more effective than BSA and more competitive with other well-known algorithms in terms of convergence speed.
Directory of Open Access Journals (Sweden)
Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
Optimal control problem for the extended Fisher–Kolmogorov equation
Indian Academy of Sciences (India)
by methods of optimal control, such as chemical engineering and vehicle ... ern optimal control theories and applied models are not only represented by .... Obviously, equation (2.5) is an ordinary differential equation and according to ODE.
A Risk-Sensitive Portfolio Optimization Problem with Fixed Incomes Securities
Goel, Mayank; Kumar, K. Suresh
2007-01-01
We discuss a class of risk-sensitive portfolio optimization problems. We consider the portfolio optimization model investigated by Nagai in 2003. The model by its nature can include fixed income securities as well in the portfolio. Under fairly general conditions, we prove the existence of optimal portfolio in both finite and infinite horizon problems.
Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control
Energy Technology Data Exchange (ETDEWEB)
Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)
2015-04-15
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.
Quadratic programming with fuzzy parameters: A membership function approach
International Nuclear Information System (INIS)
Liu, S.-T.
2009-01-01
Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.
Directory of Open Access Journals (Sweden)
Weifeng Wang
2014-01-01
Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.
Vorozheikin, A.; Gonchar, T.; Panfilov, I.; Sopov, E.; Sopov, S.
2009-01-01
A new algorithm for the solution of complex constrained optimization problems based on the probabilistic genetic algorithm with optimal solution prediction is proposed. The efficiency investigation results in comparison with standard genetic algorithm are presented.
Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function
Pearson, John W.; Stoll, Martin; Wathen, Andrew J.
2012-01-01
Optimal control problems with partial differential equations as constraints play an important role in many applications. The inclusion of bound constraints for the state variable poses a significant challenge for optimization methods. Our focus here
Gunter, Devon
2016-01-01
It is no easy feat to engage young people with abstract material as well as push them to greater depths of understanding. Add in the extra pressures of curriculum expectations and standards and the problem is exacerbated. Projects designed around standards and having multiple entry points clearly offer students the best opportunity to engage with…
Optimization of a bundle divertor for FED
International Nuclear Information System (INIS)
Hively, L.M.; Rothe, K.E.; Minkoff, M.
1982-01-01
Optimal double-T bundle divertor configurations have been obtained for the Fusion Engineering Device (FED). On-axis ripple is minimized, while satisfying a series of engineering constraints. The ensuing non-linear optimization problem is solved via a sequence of quadratic programming subproblems, using the VMCON algorithm. The resulting divertor designs are substantially improved over previous configurations
The Inverse Optimal Control Problem for a Three-Loop Missile Autopilot
Hwang, Donghyeok; Tahk, Min-Jea
2018-04-01
The performance characteristics of the autopilot must have a fast response to intercept a maneuvering target and reasonable robustness for system stability under the effect of un-modeled dynamics and noise. By the conventional approach, the three-loop autopilot design is handled by time constant, damping factor and open-loop crossover frequency to achieve the desired performance requirements. Note that the general optimal theory can be also used to obtain the same gain as obtained from the conventional approach. The key idea of using optimal control technique for feedback gain design revolves around appropriate selection and interpretation of the performance index for which the control is optimal. This paper derives an explicit expression, which relates the weight parameters appearing in the quadratic performance index to the design parameters such as open-loop crossover frequency, phase margin, damping factor, or time constant, etc. Since all set of selection of design parameters do not guarantee existence of optimal control law, explicit inequalities, which are named the optimality criteria for the three-loop autopilot (OC3L), are derived to find out all set of design parameters for which the control law is optimal. Finally, based on OC3L, an efficient gain selection procedure is developed, where time constant is set to design objective and open-loop crossover frequency and phase margin as design constraints. The effectiveness of the proposed technique is illustrated through numerical simulations.
A multilevel, level-set method for optimizing eigenvalues in shape design problems
International Nuclear Information System (INIS)
Haber, E.
2004-01-01
In this paper, we consider optimal design problems that involve shape optimization. The goal is to determine the shape of a certain structure such that it is either as rigid or as soft as possible. To achieve this goal we combine two new ideas for an efficient solution of the problem. First, we replace the eigenvalue problem with an approximation by using inverse iteration. Second, we use a level set method but rather than propagating the front we use constrained optimization methods combined with multilevel continuation techniques. Combining these two ideas we obtain a robust and rapid method for the solution of the optimal design problem
Optimization of lift gas allocation in a gas lifted oil field as non-linear optimization problem
Directory of Open Access Journals (Sweden)
Roshan Sharma
2012-01-01
Full Text Available Proper allocation and distribution of lift gas is necessary for maximizing total oil production from a field with gas lifted oil wells. When the supply of the lift gas is limited, the total available gas should be optimally distributed among the oil wells of the field such that the total production of oil from the field is maximized. This paper describes a non-linear optimization problem with constraints associated with the optimal distribution of the lift gas. A non-linear objective function is developed using a simple dynamic model of the oil field where the decision variables represent the lift gas flow rate set points of each oil well of the field. The lift gas optimization problem is solved using the emph'fmincon' solver found in MATLAB. As an alternative and for verification, hill climbing method is utilized for solving the optimization problem. Using both of these methods, it has been shown that after optimization, the total oil production is increased by about 4. For multiple oil wells sharing lift gas from a common source, a cascade control strategy along with a nonlinear steady state optimizer behaves as a self-optimizing control structure when the total supply of lift gas is assumed to be the only input disturbance present in the process. Simulation results show that repeated optimization performed after the first time optimization under the presence of the input disturbance has no effect in the total oil production.
Reduced order modeling in topology optimization of vibroacoustic problems
DEFF Research Database (Denmark)
Creixell Mediante, Ester; Jensen, Jakob Søndergaard; Brunskog, Jonas
2017-01-01
complex 3D parts. The optimization process can therefore become highly time consuming due to the need to solve a large system of equations at each iteration. Projection-based parametric Model Order Reduction (pMOR) methods have successfully been applied for reducing the computational cost of material......There is an interest in introducing topology optimization techniques in the design process of structural-acoustic systems. In topology optimization, the design space must be finely meshed in order to obtain an accurate design, which results in large numbers of degrees of freedom when designing...... or size optimization in large vibroacoustic models; however, new challenges are encountered when dealing with topology optimization. Since a design parameter per element is considered, the total number of design variables becomes very large; this poses a challenge to most existing pMOR techniques, which...
An Enhanced Memetic Algorithm for Single-Objective Bilevel Optimization Problems.
Islam, Md Monjurul; Singh, Hemant Kumar; Ray, Tapabrata; Sinha, Ankur
2017-01-01
Bilevel optimization, as the name reflects, deals with optimization at two interconnected hierarchical levels. The aim is to identify the optimum of an upper-level leader problem, subject to the optimality of a lower-level follower problem. Several problems from the domain of engineering, logistics, economics, and transportation have an inherent nested structure which requires them to be modeled as bilevel optimization problems. Increasing size and complexity of such problems has prompted active theoretical and practical interest in the design of efficient algorithms for bilevel optimization. Given the nested nature of bilevel problems, the computational effort (number of function evaluations) required to solve them is often quite high. In this article, we explore the use of a Memetic Algorithm (MA) to solve bilevel optimization problems. While MAs have been quite successful in solving single-level optimization problems, there have been relatively few studies exploring their potential for solving bilevel optimization problems. MAs essentially attempt to combine advantages of global and local search strategies to identify optimum solutions with low computational cost (function evaluations). The approach introduced in this article is a nested Bilevel Memetic Algorithm (BLMA). At both upper and lower levels, either a global or a local search method is used during different phases of the search. The performance of BLMA is presented on twenty-five standard test problems and two real-life applications. The results are compared with other established algorithms to demonstrate the efficacy of the proposed approach.
Diagnostic criteria for idiopathic inflammatory myopathies. Problems of their optimization
Directory of Open Access Journals (Sweden)
O. A. Antelava
2014-01-01
Full Text Available The paper deals with the problems of optimizing the diagnostic criteria for idiopathic inflammatory myopathies (IIM, a group of heterogeneous rare autoimmune diseases characterized by inflammatory lesion in the skeletal muscles. The representatives of this group are traditionally considered to be polymyositis (PM, dermatomyositis (DM, and inclusion-body myositis. The authors detail the history of classification criteria for IIM from those proposed by T.A. Medsger et al. (1970 relying on its clinical picture, laboratory data and instrumental findings, as well as the criteria (including the first introduced exclusion ones elaborated by A. Bohan and J.B. Peter in 1975, which remain fundamental in both clinical practice and researches. The basis for the clinical and serological criteria proposed by Y. Troyanov et al. (2005 for IIM is the identification of myositis-overlap syndromes. The classificational (subtype identification and therapeutic value of the criteria based on clinical and serological characteristics was supported by the Hungarian investigators A. Vancsa et al. (2010 who investigated the relationship between the clinical and therapeutic characteristics of IIM and positivity for myositis-specific and myositis-associated antibodies. The criteria developed by M.C. Dalakas (1991, 2003 are based on the specific immunopathological features of a histological pattern, which allow the differentiation of DM, PM, and inclusion-body myositis from other myopathic syndromes. The 2004 European Neuromuscular Center (ENMC criteria first identify necrotizing autoimmune myopathy and nonspecific myositis as individual subtypes. The serological classification of IIM, which is based onthe assessment of autoantibodies that play an important role in the pathogenesis of the disease, is of indubitable interest. There is an obvious need for the correct and timely diagnosis of both IIM as a whole and its subtypes in particular, which is complicated by
Stability in quadratic torsion theories
Energy Technology Data Exchange (ETDEWEB)
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2017-11-15
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
Stability in quadratic torsion theories
International Nuclear Information System (INIS)
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado
2017-01-01
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
Optimization of constrained multiple-objective reliability problems using evolutionary algorithms
International Nuclear Information System (INIS)
Salazar, Daniel; Rocco, Claudio M.; Galvan, Blas J.
2006-01-01
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
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.
Optimal Experimental Design for Large-Scale Bayesian Inverse Problems
Ghattas, Omar
2014-01-01
We develop a Bayesian framework for the optimal experimental design of the shock tube experiments which are being carried out at the KAUST Clean Combustion Research Center. The unknown parameters are the pre-exponential parameters and the activation
Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems
National Research Council Canada - National Science Library
Abramson, Mark A; Audet, Charles; Dennis, Jr, J. E
2004-01-01
.... This class combines and extends the Audet-Dennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPS-filter algorithms for general nonlinear constraints...
Sparse optimization for inverse problems in atmospheric modelling
Czech Academy of Sciences Publication Activity Database
Adam, Lukáš; Branda, Martin
2016-01-01
Roč. 79, č. 3 (2016), s. 256-266 ISSN 1364-8152 R&D Projects: GA MŠk(CZ) 7F14287 Institutional support: RVO:67985556 Keywords : Inverse modelling * Sparse optimization * Integer optimization * Least squares * European tracer experiment * Free Matlab codes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.404, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/adam-0457037.pdf
Augmented Lagrangian Method For Discretized Optimal Control ...
African Journals Online (AJOL)
In this paper, we are concerned with one-dimensional time invariant optimal control problem, whose objective function is quadratic and the dynamical system is a differential equation with initial condition .Since most real life problems are nonlinear and their analytical solutions are not readily available, we resolve to ...
Handelman's hierarchy for the maximum stable set problem
Laurent, M.; Sun, Z.
2014-01-01
The maximum stable set problem is a well-known NP-hard problem in combinatorial optimization, which can be formulated as the maximization of a quadratic square-free polynomial over the (Boolean) hypercube. We investigate a hierarchy of linear programming relaxations for this problem, based on a
OPTIM, Minimization of Band-Width of Finite Elements Problems
International Nuclear Information System (INIS)
Huart, M.
1977-01-01
1 - Nature of the physical problem solved: To minimize the band-width of finite element problems. 2 - Method of solution: A surface is constructed from the x-y-coordinates of each node using its node number as z-value. This surface consists of triangles. Nodes are renumbered in such a way as to minimize the surface area. 3 - Restrictions on the complexity of the problem: This program is applicable to 2-D problems. It is dimensioned for a maximum of 1000 elements
Resolution and optimization methods for tour planning problems
International Nuclear Information System (INIS)
Vasserot, Jean-Pierre
1976-12-01
The aim of this study is to describe computerized methods for the resolution of the computer supported tour planning problem. After a presentation of this problem in operational research, the different existing methods of resolution are reviewed with the different approaches which have led to their elaboration. Different critics and comparisons are made on these methods and some improvements and new procedures are proposed, some of them allowing to solve more general problems. Finally, the structure of such a program, made at the CII to solve this kind of problem under multiple constraints is analysed [fr
Directory of Open Access Journals (Sweden)
Susanta Dutta
2018-05-01
Full Text Available This paper presents an efficient quasi-oppositional chemical reaction optimization (QOCRO technique to find the feasible optimal solution of the multi objective optimal reactive power dispatch (RPD problem with flexible AC transmission system (FACTS device. The quasi-oppositional based learning (QOBL is incorporated in conventional chemical reaction optimization (CRO, to improve the solution quality and the convergence speed. To check the superiority of the proposed method, it is applied on IEEE 14-bus and 30-bus systems and the simulation results of the proposed approach are compared to those reported in the literature. The computational results reveal that the proposed algorithm has excellent convergence characteristics and is superior to other multi objective optimization algorithms. Keywords: Quasi-oppositional chemical reaction optimization (QOCRO, Reactive power dispatch (RPD, TCSC, SVC, Multi-objective optimization
Directory of Open Access Journals (Sweden)
Emmanuel Okewu
2017-10-01
Full Text Available The role of automation in sustainable development is not in doubt. Computerization in particular has permeated every facet of human endeavour, enhancing the provision of information for decision-making that reduces cost of operation, promotes productivity and socioeconomic prosperity and cohesion. Hence, a new field called information and communication technology for development (ICT4D has emerged. Nonetheless, the need to ensure environmentally friendly computing has led to this research study with particular focus on green computing in Africa. This is against the backdrop that the continent is feared to suffer most from the vulnerability of climate change and the impact of environmental risk. Using Nigeria as a test case, this paper gauges the green computing awareness level of Africans via sample survey. It also attempts to institutionalize green computing maturity model with a view to optimizing the level of citizens awareness amid inherent uncertainties like low bandwidth, poor network and erratic power in an emerging African market. Consequently, we classified the problem as a stochastic optimization problem and applied metaheuristic search algorithm to determine the best sensitization strategy. Although there are alternative ways of promoting green computing education, the metaheuristic search we conducted indicated that an online real-time solution that not only drives but preserves timely conversations on electronic waste (e-waste management and energy saving techniques among the citizenry is cutting edge. The authors therefore reviewed literature, gathered requirements, modelled the proposed solution using Universal Modelling Language (UML and developed a prototype. The proposed solution is a web-based multi-tier e-Green computing system that educates computer users on innovative techniques of managing computers and accessories in an environmentally friendly way. We found out that such a real-time web-based interactive forum does not
Quadratic forms for Feynman-Kac semigroups
International Nuclear Information System (INIS)
Hibey, Joseph L.; Charalambous, Charalambos D.
2006-01-01
Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions
New results for time reversed symplectic dynamic systems and quadratic functionals
Directory of Open Access Journals (Sweden)
Roman Simon Hilscher
2012-05-01
Full Text Available In this paper, we examine time scale symplectic (or Hamiltonian systems and the associated quadratic functionals which contain a forward shift in the time variable. Such systems and functionals have a close connection to Jacobi systems for calculus of variations and optimal control problems on time scales. Our results, among which we consider the Reid roundabout theorem, generalize the corresponding classical theory for time reversed discrete symplectic systems, as well as they complete the recently developed theory of time scale symplectic systems.
The linear ordering problem: an algorithm for the optimal solution ...
African Journals Online (AJOL)
In this paper we describe and implement an algorithm for the exact solution of the Linear Ordering problem. Linear Ordering is the problem of finding a linear order of the nodes of a graph such that the sum of the weights which are consistent with this order is as large as possible. It is an NP - Hard combinatorial optimisation ...
Features for Exploiting Black-Box Optimization Problem Structure
DEFF Research Database (Denmark)
Tierney, Kevin; Malitsky, Yuri; Abell, Tinus
2013-01-01
landscape of BBO problems and show how an algorithm portfolio approach can exploit these general, problem indepen- dent features and outperform the utilization of any single minimization search strategy. We test our methodology on data from the GECCO Workshop on BBO Benchmarking 2012, which contains 21...
Quadratic prediction of factor scores
Wansbeek, T
1999-01-01
Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic
On quadratic variation of martingales
Indian Academy of Sciences (India)
On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...
Quadratic divergences and dimensional regularisation
International Nuclear Information System (INIS)
Jack, I.; Jones, D.R.T.
1990-01-01
We present a detailed analysis of quadratic and quartic divergences in dimensionally regulated renormalisable theories. We perform explicit three-loop calculations for a general theory of scalars and fermions. We find that the higher-order quartic divergences are related to the lower-order ones by the renormalisation group β-functions. (orig.)
Robust optimization methods for chance constrained, simulation-based, and bilevel problems
Yanikoglu, I.
2014-01-01
The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty
Topology optimization of bounded acoustic problems using the hybrid finite element-wave based method
DEFF Research Database (Denmark)
Goo, Seongyeol; Wang, Semyung; Kook, Junghwan
2017-01-01
This paper presents an alternative topology optimization method for bounded acoustic problems that uses the hybrid finite element-wave based method (FE-WBM). The conventional method for the topology optimization of bounded acoustic problems is based on the finite element method (FEM), which...
International Nuclear Information System (INIS)
Xunjing, L.
1981-12-01
The vector-valued measure defined by the well-posed linear boundary value problems is discussed. The maximum principle of the optimal control problem with non-convex constraint is proved by using the vector-valued measure. Especially, the necessary conditions of the optimal control of elliptic systems is derived without the convexity of the control domain and the cost function. (author)
Optimal Stopping Problems Driven by Lévy Processes and Pasting Principles
Surya, B.A.
2007-01-01
Solving optimal stopping problems driven by Lévy processes has been a challenging task and has found many applications in modern theory of mathematical finance. For example situations in which optimal stopping typically arise include the problem of finding the arbitrage-free price of the American
Optimization methods for the Train Unit Shunting Problem
DEFF Research Database (Denmark)
Haahr, Jørgen Thorlund; Lusby, Richard Martin; Wagenaar, Joris Camiel
2017-01-01
We consider the Train Unit Shunting Problem, an important planning problem for passenger railway operators. This problem entails assigning train units from shunting yards to scheduled train services in such a way that the resulting operations are without conflicts. The problem arises at every...... shunting yard in the railway network and involves matching train units to arriving and departing train services as well as assigning the selected matchings to appropriate shunting yard tracks. We present an extensive comparison benchmark of multiple solution approaches for this problem, some of which...... are novel. In particular, we develop a constraint programming formulation, a column generation approach, and a randomized greedy heuristic. We compare and benchmark these approaches with two existing methods, a mixed integer linear program and a two-stage heuristic. The benchmark contains multiple real...
DEFF Research Database (Denmark)
Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan
2012-01-01
The primal–dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1–26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems...... for the purpose of designing iterative image reconstruction algorithms for CT. The primal–dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application...
de Klerk, E.; Laurent, M.
2011-01-01
The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization problems is known to converge finitely under some assumptions. [J. B. Lasserre, Convexity in semialgebraic geometry and polynomial optimization, SIAM J. Optim., 19 (2009), pp. 1995–2014]. We give a
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...
Wihartiko, F. D.; Wijayanti, H.; Virgantari, F.
2018-03-01
Genetic Algorithm (GA) is a common algorithm used to solve optimization problems with artificial intelligence approach. Similarly, the Particle Swarm Optimization (PSO) algorithm. Both algorithms have different advantages and disadvantages when applied to the case of optimization of the Model Integer Programming for Bus Timetabling Problem (MIPBTP), where in the case of MIPBTP will be found the optimal number of trips confronted with various constraints. The comparison results show that the PSO algorithm is superior in terms of complexity, accuracy, iteration and program simplicity in finding the optimal solution.
Optimal improvement of graphs related to nuclear safeguards problems
International Nuclear Information System (INIS)
Jacobsen, S.E.
1977-08-01
This report develops the methodology for optimally improving graphs related to nuclear safeguards issues. In particular, given a fixed number of dollars, the report provides a method for optimally allocating such dollars over the arcs of a weighted graph (the weights vary as a function of dollars spent on arcs) so as to improve the system effectiveness measure which is the shortest of all shortest paths to several targets. Arc weights can be either clock times or detection probabilities and the algorithm does not explicitly consider all paths to the targets
Iterative solution to the optimal poison management problem in pressurized water reactors
International Nuclear Information System (INIS)
Colletti, J.P.; Levine, S.H.; Lewis, J.B.
1983-01-01
A new method for solving the optimal poison management problem for a multiregion pressurized water reactor has been developed. The optimization objective is to maximize the end-of-cycle core excess reactivity for any given beginning-of-cycle fuel loading. The problem is treated as an optimal control problem with the region burnup and control absorber concentrations acting as the state and control variables, respectively. Constraints are placed on the power peaking, soluble boron concentration, and control absorber concentrations. The solution method consists of successive relinearizations of the system equations resulting in a sequence of nonlinear programming problems whose solutions converge to the desired optimal control solution. Application of the method to several test problems based on a simplified three-region reactor suggests a bang-bang optimal control strategy with the peak power location switching between the inner and outer regions of the core and the critical soluble boron concentration as low as possible throughout the cycle
Optimal resampling for the noisy OneMax problem
Liu, Jialin; Fairbank, Michael; Pérez-Liébana, Diego; Lucas, Simon M.
2016-01-01
The OneMax problem is a standard benchmark optimisation problem for a binary search space. Recent work on applying a Bandit-Based Random Mutation Hill-Climbing algorithm to the noisy OneMax Problem showed that it is important to choose a good value for the resampling number to make a careful trade off between taking more samples in order to reduce noise, and taking fewer samples to reduce the total computational cost. This paper extends that observation, by deriving an analytical expression f...
International Nuclear Information System (INIS)
Meneses, Anderson Alvarenga de Moura; Schirru, Roberto
2005-01-01
This work focuses on the usage the Artificial Intelligence technique Particle Swarm Optimization (PSO) to optimize the fuel recharge at a nuclear reactor. This is a combinatorial problem, in which the search of the best feasible solution is done by minimizing a specific objective function. However, in this first moment it is possible to compare the fuel recharge problem with the Traveling Salesman Problem (TSP), since both of them are combinatorial, with one advantage: the evaluation of the TSP objective function is much more simple. Thus, the proposed methods have been applied to two TSPs: Oliver 30 and Rykel 48. In 1995, KENNEDY and EBERHART presented the PSO technique to optimize non-linear continued functions. Recently some PSO models for discrete search spaces have been developed for combinatorial optimization. Although all of them having different formulation from the ones presented here. In this paper, we use the PSO theory associated with to the Random Keys (RK)model, used in some optimizations with Genetic Algorithms. The Particle Swarm Optimization with Random Keys (PSORK) results from this association, which combines PSO and RK. The adaptations and changings in the PSO aim to allow the usage of the PSO at the nuclear fuel recharge. This work shows the PSORK being applied to the proposed combinatorial problem and the obtained results. (author)
International Nuclear Information System (INIS)
Cao, Dingzhou; Murat, Alper; Chinnam, Ratna Babu
2013-01-01
This paper proposes a decomposition-based approach to exactly solve the multi-objective Redundancy Allocation Problem for series-parallel systems. Redundancy allocation problem is a form of reliability optimization and has been the subject of many prior studies. The majority of these earlier studies treat redundancy allocation problem as a single objective problem maximizing the system reliability or minimizing the cost given certain constraints. The few studies that treated redundancy allocation problem as a multi-objective optimization problem relied on meta-heuristic solution approaches. However, meta-heuristic approaches have significant limitations: they do not guarantee that Pareto points are optimal and, more importantly, they may not identify all the Pareto-optimal points. In this paper, we treat redundancy allocation problem as a multi-objective problem, as is typical in practice. We decompose the original problem into several multi-objective sub-problems, efficiently and exactly solve sub-problems, and then systematically combine the solutions. The decomposition-based approach can efficiently generate all the Pareto-optimal solutions for redundancy allocation problems. Experimental results demonstrate the effectiveness and efficiency of the proposed method over meta-heuristic methods on a numerical example taken from the literature.
Optimization of travel salesman problem using the ant colony system and Greedy search
International Nuclear Information System (INIS)
Esquivel E, J.; Ordonez A, A.; Ortiz S, J. J.
2008-01-01
In this paper we present some results obtained during the development of optimization systems that can be used to design refueling and patterns of control rods in a BWR. These systems use ant colonies and Greedy search. The first phase of this project is to be familiar with these optimization techniques applied to the problem of travel salesman problem (TSP). The utility of TSP study is that, like the refueling design and pattern design of control rods are problems of combinative optimization. Even, the similarity with the problem of the refueling design is remarkable. It is presented some results for the TSP with the 32 state capitals of Mexico country. (Author)
Optimal Component Lumping: problem formulation and solution techniques
DEFF Research Database (Denmark)
Lin, Bao; Leibovici, Claude F.; Jørgensen, Sten Bay
2008-01-01
This paper presents a systematic method for optimal lumping of a large number of components in order to minimize the loss of information. In principle, a rigorous composition-based model is preferable to describe a system accurately. However, computational intensity and numerical issues restrict ...
Optimization of the variational basis in the three body problem
International Nuclear Information System (INIS)
Simenog, I.V.; Pushkash, O.M.; Bestuzheva, A.B.
1995-01-01
The procedure of variational oscillator basis optimization is proposed to the calculation the energy spectra of three body systems. The hierarchy of basis functions is derived and energies of ground and excited states for three gravitating particles is obtained with high accuracy. 12 refs
Isogeometric Shape Optimization for Quasi-static and Transient Problems
Wang, Z.P.
2016-01-01
The recently developed isogeometric analysis (IGA) was aimed, from the start, at integrating computer aided design (CAD) and analysis. This synthesis of geometry and analysis has naturally led to renewed interest in developing structural shape optimization. The advantages of using isogeometric
Optimal infrastructure maintenance scheduling problem under budget uncertainty.
2010-05-01
This research addresses a general class of infrastructure asset management problems. Infrastructure : agencies usually face budget uncertainties that will eventually lead to suboptimal planning if : maintenance decisions are made without taking the u...
Directory of Open Access Journals (Sweden)
R. Berdysheva
1998-03-01
Full Text Available Lower bounds of stability, pseudostability and quasistability radii of lexicographic set in vector combinatorial problem on systems of subsets of finite set with partial criteria of more general kinds have been found.
Optimization Using Simulation of the Vehicle Routing Problem
Nayera E. El-Gharably; Khaled S. El-Kilany; Aziz E. El-Sayed
2013-01-01
A key element of many distribution systems is the routing and scheduling of vehicles servicing a set of customers. A wide variety of exact and approximate algorithms have been proposed for solving the vehicle routing problems (VRP). Exact algorithms can only solve relatively small problems of VRP, which is classified as NP-Hard. Several approximate algorithms have proven successful in finding a feasible solution not necessarily optimum. Although different parts of the pro...
Application of Fuzzy Optimization to the Orienteering Problem
Directory of Open Access Journals (Sweden)
Madhushi Verma
2015-01-01
Full Text Available This paper deals with the orienteering problem (OP which is a combination of two well-known problems (i.e., travelling salesman problem and the knapsack problem. OP is an NP-hard problem and is useful in appropriately modeling several challenging applications. As the parameters involved in these applications cannot be measured precisely, depicting them using crisp numbers is unrealistic. Further, the decision maker may be satisfied with graded satisfaction levels of solutions, which cannot be formulated using a crisp program. To deal with the above-stated two issues, we formulate the fuzzy orienteering problem (FOP and provide a method to solve it. Here we state the two necessary conditions of OP of maximizing the total collected score and minimizing the time taken to traverse a path (within the specified time bound as fuzzy goals and the remaining necessary conditions as crisp constraints. Using the max-min formulation of the fuzzy sets obtained from the fuzzy goals, we calculate the fuzzy decision sets (Z and Z∗ that contain the feasible paths and the desirable paths, respectively, along with the degrees to which they are acceptable. To efficiently solve large instances of FOP, we also present a parallel algorithm on CREW PRAM model.
Optimization approaches for treating nuclear power plant problems
International Nuclear Information System (INIS)
Abdelgoad, A.S.A.
2012-01-01
Electricity generation is the process of generating electric energy from other forms of energy. There are many technologies that can be and are used to generate electricity. One of these technologies is the nuclear power. A nuclear power plant (NPP) is a thermal power station in which the heat source is one or more nuclear reactors. As in a conventional thermal power station the heat is used to generate steam which drives a steam turbine connected to a generator which produces electricity. As of February 2nd, 2012, there were 439 nuclear power plants in operation through the world. NPP are usually considered to be base load stations, which are best suited to constant power output. The thesis consists of five chapters: Chapter I presents a survey on some important concepts of the NPP problems. Chapter II introduces the economic future of nuclear power. It presents nuclear energy scenarios beyond 2015, market potential for electricity generation to 2030 and economics of new plant construction. Chapter III presents a reliability centered problem of power plant preventive maintenance scheduling. NPP preventive maintenance scheduling problem with fuzzy parameters in the constraints is solved. A case study is provided to demonstrate the efficiency of proposed model. A comparison study between the deterministic case and fuzzy case for the problem of concern is carried out. Chapter IV introduces a fuzzy approach to the generation expansion planning problem (GEP) in a multiobjective environment. The GEP problem as an integer programming model with fuzzy parameters in the constraints is formulated. A parametric study is carried out for the GEP problem. A case study is provided to demonstrate the efficiency of our proposed model. A comparison study between our approach and the deterministic one is made. Chapter V is concerned with the conclusions arrived in carrying out this thesis and gives some suggestions for further research.
A note on fixed point optimality criteria for the location problem with arbitrary norms: Reply
DEFF Research Database (Denmark)
Juel, Henrik; Love, Robert F.
1983-01-01
The single-facility location problem in continuous space is considered, with distances given by arbitrary norms. When distances are Euclidean, for many practical problems the optimal location of the new facility coincides with one of the existing facilities. This property carries over to problems...... with generalized distances. In this paper a necessary and sufficient condition for the location of an existing facility to be the optimal location of the new facility is developed. Some computational examples using the condition are given....
Tunjo Perić; Željko Mandić
2017-01-01
This paper presents the production plan optimization in the metal industry considered as a multi-criteria programming problem. We first provided the definition of the multi-criteria programming problem and classification of the multicriteria programming methods. Then we applied two multi-criteria programming methods (the STEM method and the PROMETHEE method) in solving a problem of multi-criteria optimization production plan in a company from the metal industry. The obtained resul...
Solving dominance and potential optimality in imprecise multi-attribute additive problems
International Nuclear Information System (INIS)
Mateos, Alfonso; Jimenez, Antonio; Rios-Insua, Sixto
2003-01-01
We consider the multicriteria decision-making problem where there is partial information on decision maker preferences, represented by means of an imprecise multiattribute additive utility function, and where the consequences of the alternatives or strategies are also possibly imprecise. Under these circumstances we consider how useful problem-solving concepts, namely nondominated, potentially optimal, adjacent potentially optimal alternatives, can be analytically computed. Thus, the problem can be solved much more efficiently using the classical methodology of linear programming
Optimal Experimental Design for Large-Scale Bayesian Inverse Problems
Ghattas, Omar
2014-01-06
We develop a Bayesian framework for the optimal experimental design of the shock tube experiments which are being carried out at the KAUST Clean Combustion Research Center. The unknown parameters are the pre-exponential parameters and the activation energies in the reaction rate expressions. The control parameters are the initial mixture composition and the temperature. The approach is based on first building a polynomial based surrogate model for the observables relevant to the shock tube experiments. Based on these surrogates, a novel MAP based approach is used to estimate the expected information gain in the proposed experiments, and to select the best experimental set-ups yielding the optimal expected information gains. The validity of the approach is tested using synthetic data generated by sampling the PC surrogate. We finally outline a methodology for validation using actual laboratory experiments, and extending experimental design methodology to the cases where the control parameters are noisy.
Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers
Czech Academy of Sciences Publication Activity Database
Adam, Lukáš; Branda, Martin
2016-01-01
Roč. 170, č. 2 (2016), s. 419-436 ISSN 0022-3239 R&D Projects: GA ČR GA15-00735S Institutional support: RVO:67985556 Keywords : Chance constrained programming * Optimality conditions * Regularization * Algorithms * Free MATLAB codes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.289, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/adam-0460909.pdf
Problem statement for optimal design of steel structures
Ginzburg Aleksandr Vital'evich; Vasil'kin Andrey Aleksandrovich
2014-01-01
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 desi...