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
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.
A Trust-region-based Sequential Quadratic Programming Algorithm
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....
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
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...
Frost, Susan A.; Bodson, Marc; Acosta, Diana M.
2009-01-01
The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.
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.
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.
Hashimoto, Hiroyuki; Takaguchi, Yusuke; Nakamura, Shizuka
Instability of calculation process and increase of calculation time caused by increasing size of continuous optimization problem remain the major issues to be solved to apply the technique to practical industrial systems. This paper proposes an enhanced quadratic programming algorithm based on interior point method mainly for improvement of calculation stability. The proposed method has dynamic estimation mechanism of active constraints on variables, which fixes the variables getting closer to the upper/lower limit on them and afterwards releases the fixed ones as needed during the optimization process. It is considered as algorithm-level integration of the solution strategy of active-set method into the interior point method framework. We describe some numerical results on commonly-used bench-mark problems called “CUTEr” to show the effectiveness of the proposed method. Furthermore, the test results on large-sized ELD problem (Economic Load Dispatching problems in electric power supply scheduling) are also described as a practical industrial application.
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).
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
Chen, Zheng; Mi, Chris Chunting; Xiong, Rui; Xu, Jun; You, Chenwen
2014-02-01
This paper introduces an online and intelligent energy management controller to improve the fuel economy of a power-split plug-in hybrid electric vehicle (PHEV). Based on analytic analysis between fuel-rate and battery current at different driveline power and vehicle speed, quadratic equations are applied to simulate the relationship between battery current and vehicle fuel-rate. The power threshold at which engine is turned on is optimized by genetic algorithm (GA) based on vehicle fuel-rate, battery state of charge (SOC) and driveline power demand. The optimal battery current when the engine is on is calculated using quadratic programming (QP) method. The proposed algorithm can control the battery current effectively, which makes the engine work more efficiently and thus reduce the fuel-consumption. Moreover, the controller is still applicable when the battery is unhealthy. Numerical simulations validated the feasibility of the proposed controller.
A Quadratically Convergent O(square root of nL-Iteration Algorithm for Linear Programming
National Research Council Canada - National Science Library
Ye, Y; Gueler, O; Tapia, Richard A; Zhang, Y
1991-01-01
...)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap...
Liu, Hua-Long; Liu, Hua-Dong
2014-10-01
Partial discharge (PD) in power transformers is one of the prime reasons resulting in insulation degradation and power faults. Hence, it is of great importance to study the techniques of the detection and localization of PD in theory and practice. The detection and localization of PD employing acoustic emission (AE) techniques, as a kind of non-destructive testing, plus due to the advantages of powerful capability of locating and high precision, have been paid more and more attention. The localization algorithm is the key factor to decide the localization accuracy in AE localization of PD. Many kinds of localization algorithms exist for the PD source localization adopting AE techniques including intelligent and non-intelligent algorithms. However, the existed algorithms possess some defects such as the premature convergence phenomenon, poor local optimization ability and unsuitability for the field applications. To overcome the poor local optimization ability and easily caused premature convergence phenomenon of the fundamental genetic algorithm (GA), a new kind of improved GA is proposed, namely the sequence quadratic programming-genetic algorithm (SQP-GA). For the hybrid optimization algorithm, SQP-GA, the sequence quadratic programming (SQP) algorithm which is used as a basic operator is integrated into the fundamental GA, so the local searching ability of the fundamental GA is improved effectively and the premature convergence phenomenon is overcome. Experimental results of the numerical simulations of benchmark functions show that the hybrid optimization algorithm, SQP-GA, is better than the fundamental GA in the convergence speed and optimization precision, and the proposed algorithm in this paper has outstanding optimization effect. At the same time, the presented SQP-GA in the paper is applied to solve the ultrasonic localization problem of PD in transformers, then the ultrasonic localization method of PD in transformers based on the SQP-GA is proposed. And
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.
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
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...
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
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.
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.
Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients
Directory of Open Access Journals (Sweden)
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.
Institute of Scientific and Technical Information of China (English)
黄静静; 商朋见; 王爱文
2011-01-01
将半定规划(Semidefinite Programming,SDP)的内点算法推广到二次半定规划(QuadraticSemidefinite Programming,QSDP),重点讨论了AHO搜索方向的产生方法.首先利用Wolfe对偶理论推导得到了求解二次半定规划的非线性方程组,利用牛顿法求解该方程组,得到了求解QSDP的内点算法的AHO搜索方向,证明了该搜索方向的存在唯一性,最后给出了求解二次半定规划的预估校正内点算法的具体步骤,并对基于不同搜索方向的内点算法进行了数值实验,结果表明基于NT方向的内点算法最为稳健.%This paper extends the interior point algorithm for solving Semidefinite Programming (SDP) to Quadratic Semidefinite Programming(QSDP) and especially discusses the generation of AHO search direction. Firstly, we derive the nonlinear equations for solving QSDP using Wolfe's dual theorem.The AHO search direction is got by applying Newton' s method to the equations. Then we prove the existence and uniqueness of the search direction, and give the detaied steps of predictor-corrector interior-point algorithm. At last, this paper provides a numerical comparison of the algoritms using three different search directions and suggests the algorithm using NT direction is the most robust.
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).
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.
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.
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
Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems
International Nuclear Information System (INIS)
Scott, D.S.; Ward, R.C.
1981-01-01
Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices
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.
A New GCD Algorithm for Quadratic Number Rings with Unique Factorization
DEFF Research Database (Denmark)
Agarwal, Saurabh; Frandsen, Gudmund Skovbjerg
2006-01-01
We present an algorithm to compute a greatest common divisor of two integers in a quadratic number ring that is a unique factorization domain. The algorithm uses bit operations in a ring of discriminant Δ. This appears to be the first gcd algorithm of complexity o(n 2) for any fixed non-Euclidean...
The quadratic speedup in Grover's search algorithm from the entanglement perspective
International Nuclear Information System (INIS)
Rungta, Pranaw
2009-01-01
We show that Grover's algorithm can be described as an iterative change of the bipartite entanglement, which leads to a necessary and sufficient condition for quadratic speedup. This allows us to reestablish, from the entanglement perspective, that Grover's search algorithm is the only optimal pure state search algorithm.
Fleming, P.
1983-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.
Binary GCD like Algorithms for Some Complex Quadratic Rings
DEFF Research Database (Denmark)
Agarwal, Saurabh; Frandsen, Gudmund Skovbjerg
2004-01-01
On the lines of the binary gcd algorithm for rational integers, algorithms for computing the gcd are presented for the ring of integers in where . Thus a binary gcd like algorithm is presented for a unique factorization domain which is not Euclidean (case d=-19). Together with the earlier known b...
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.
Quantum Algorithms for Weighing Matrices and Quadratic Residues
van Dam, Wim
2000-01-01
In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is ignificantly lower than the classical one. It is pointed out that this scheme captures both Bernstein & Vazirani's inner-product protocol, as well as Grover's search algorithm. In the second part of the ar...
Quadratic adaptive algorithm for solving cardiac action potential models.
Chen, Min-Hung; Chen, Po-Yuan; Luo, Ching-Hsing
2016-10-01
An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential. Copyright © 2016 Elsevier Ltd. All rights
Chang, Weng-Long
2012-03-01
Assume that n is a positive integer. If there is an integer such that M (2) ≡ C (mod n), i.e., the congruence has a solution, then C is said to be a quadratic congruence (mod n). If the congruence does not have a solution, then C is said to be a quadratic noncongruence (mod n). The task of solving the problem is central to many important applications, the most obvious being cryptography. In this article, we describe a DNA-based algorithm for solving quadratic congruence and factoring integers. In additional to this novel contribution, we also show the utility of our encoding scheme, and of the algorithm's submodules. We demonstrate how a variety of arithmetic, shifted and comparative operations, namely bitwise and full addition, subtraction, left shifter and comparison perhaps are performed using strands of DNA.
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.
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.
MM Algorithms for Geometric and Signomial Programming.
Lange, Kenneth; Zhou, Hua
2014-02-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.
Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm
Directory of Open Access Journals (Sweden)
Wei Xie
2007-01-01
Full Text Available A linear time-invariant (LTI output feedback controller is designed for a linear parameter-varying (LPV control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.
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
Fleming, P.
1985-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.
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.
Identify Beta-Hairpin Motifs with Quadratic Discriminant Algorithm Based on the Chemical Shifts.
Directory of Open Access Journals (Sweden)
Feng YongE
Full Text Available Successful prediction of the beta-hairpin motif will be helpful for understanding the of the fold recognition. Some algorithms have been proposed for the prediction of beta-hairpin motifs. However, the parameters used by these methods were primarily based on the amino acid sequences. Here, we proposed a novel model for predicting beta-hairpin structure based on the chemical shift. Firstly, we analyzed the statistical distribution of chemical shifts of six nuclei in not beta-hairpin and beta-hairpin motifs. Secondly, we used these chemical shifts as features combined with three algorithms to predict beta-hairpin structure. Finally, we achieved the best prediction, namely sensitivity of 92%, the specificity of 94% with 0.85 of Mathew's correlation coefficient using quadratic discriminant analysis algorithm, which is clearly superior to the same method for the prediction of beta-hairpin structure from 20 amino acid compositions in the three-fold cross-validation. Our finding showed that the chemical shift is an effective parameter for beta-hairpin prediction, suggesting the quadratic discriminant analysis is a powerful algorithm for the prediction of beta-hairpin.
Directory of Open Access Journals (Sweden)
Xuewen Mu
2015-01-01
quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.
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
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.
A Collision-Free G2 Continuous Path-Smoothing Algorithm Using Quadratic Polynomial Interpolation
Directory of Open Access Journals (Sweden)
Seong-Ryong Chang
2014-12-01
Full Text Available Most path-planning algorithms are used to obtain a collision-free path without considering continuity. On the other hand, a continuous path is needed for stable movement. In this paper, the searched path was converted into a G2 continuous path using the modified quadratic polynomial and membership function interpolation algorithm. It is simple, unique and provides a good geometric interpretation. In addition, a collision-checking and improvement algorithm is proposed. The collision-checking algorithm can check the collisions of a smoothed path. If collisions are detected, the collision improvement algorithm modifies the collision path to a collision-free path. The collision improvement algorithm uses a geometric method. This method uses the perpendicular line between a collision position and the collision piecewise linear path. The sub-waypoint is added, and the QPMI algorithm is applied again. As a result, the collision-smoothed path is converted into a collision-free smooth path without changing the continuity.
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,
Obstacle Avoidance for Redundant Manipulators Utilizing a Backward Quadratic Search Algorithm
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Tianjian Hu
2016-06-01
Full Text Available Obstacle avoidance can be achieved as a secondary task by appropriate inverse kinematics (IK resolution of redundant manipulators. Most prior literature requires the time-consuming determination of the closest point to the obstacle for every calculation step. Aiming at the relief of computational burden, this paper develops what is termed a backward quadratic search algorithm (BQSA as another option for solving IK problems in obstacle avoidance. The BQSA detects possible collisions based on the root property of a category of quadratic functions, which are derived from ellipse-enveloped obstacles and the positions of each link's end-points. The algorithm executes a backward search for possible obstacle collisions, from the end-effector to the base, and avoids obstacles by utilizing a hybrid IK scheme, incorporating the damped least-squares method, the weighted least-norm method and the gradient projection method. Some details of the hybrid IK scheme, such as values of the damped factor, weights and the clamping velocity, are discussed, along with a comparison of computational load between previous methods and BQSA. Simulations of a planar seven-link manipulator and a PUMA 560 robot verify the effectiveness of BQSA.
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.
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.
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
Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2018-06-01
In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.
Bandele, Samuel Oye; Adekunle, Adeyemi Suraju
2015-01-01
The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…
Algorithmic Principles of Mathematical Programming
Faigle, Ulrich; Kern, Walter; Still, Georg
2002-01-01
Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear
Energy Technology Data Exchange (ETDEWEB)
Chao, R.M.; Ko, S.H.; Lin, I.H. [Department of Systems and Naval Mechatronics Engineering, National Cheng Kung University, Tainan, Taiwan 701 (China); Pai, F.S. [Department of Electronic Engineering, National University of Tainan (China); Chang, C.C. [Department of Environment and Energy, National University of Tainan (China)
2009-12-15
The historically high cost of crude oil price is stimulating research into solar (green) energy as an alternative energy source. In general, applications with large solar energy output require a maximum power point tracking (MPPT) algorithm to optimize the power generated by the photovoltaic effect. This work aims to provide a stand-alone solution for solar energy applications by integrating a DC/DC buck converter to a newly developed quadratic MPPT algorithm along with its appropriate software and hardware. The quadratic MPPT method utilizes three previously used duty cycles with their corresponding power outputs. It approaches the maximum value by using a second order polynomial formula, which converges faster than the existing MPPT algorithm. The hardware implementation takes advantage of the real-time controller system from National Instruments, USA. Experimental results have shown that the proposed solar mechatronics system can correctly and effectively track the maximum power point without any difficulties. (author)
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.
Engwerda, Jacob
2015-01-01
This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to
Beams configuration design in target area with successive quadratic programming method
International Nuclear Information System (INIS)
Shi Zhiquan; Tan Jichun; Wei Xiaofeng; Man Jongzai; Zhang Xiaomin; Yuan Jing; Yuan Xiaodong
1998-01-01
The author describes the application of successive quadratic programming method (SQP) to design laser beam configuration in target area. Based on the requirement of ICF experiment physics, a math model of indirect-driver beam geometry is given. A 3D wire-frame is plotted, in which support lines represent 60 laser entireties and 240 turning points of support lines' segments stand for the spatial positions of reflectors
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
Fitting timeseries by continuous-time Markov chains: A quadratic programming approach
International Nuclear Information System (INIS)
Crommelin, D.T.; Vanden-Eijnden, E.
2006-01-01
Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows
An algorithm for the solution of dynamic linear programs
Psiaki, Mark L.
1989-01-01
The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation
DEFF Research Database (Denmark)
Huang, Shaojun; Wu, Qiuwei; Oren, Shmuel S.
2015-01-01
) calculates dynamic tariffs and publishes them to the aggregators, who make the optimal energy plans for the flexible demands. The DLMP through QP instead of linear programing as studied in previous literatures solves the multiple solution issue of the ag- gregator optimization which may cause......This paper presents the distribution locational mar- ginal pricing (DLMP) method through quadratic programming (QP) designed to alleviate the congestion that might occur in a distribution network with high penetration of flexible demands. In the DLMP method, the distribution system operator (DSO...
A high-performance Riccati based solver for tree-structured quadratic programs
DEFF Research Database (Denmark)
Frison, Gianluca; Kouzoupis, Dimitris; Diehl, Moritz
2017-01-01
the online solution of such problems challenging and the development of tailored solvers crucial. In this paper, an interior point method is presented that can solve Quadratic Programs (QPs) arising in multi-stage MPC efficiently by means of a tree-structured Riccati recursion and a high-performance linear...... algebra library. A performance comparison with code-generated and general purpose sparse QP solvers shows that the computation times can be significantly reduced for all problem sizes that are practically relevant in embedded MPC applications. The presented implementation is freely available as part...
Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach
International Nuclear Information System (INIS)
Catalao, J.P.S.; Pousinho, H.M.I.; Mendes, V.M.F.
2010-01-01
This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach.
Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach
Energy Technology Data Exchange (ETDEWEB)
Catalao, J.P.S.; Pousinho, H.M.I. [Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha (Portugal); Mendes, V.M.F. [Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emidio Navarro, 1950-062 Lisbon (Portugal)
2010-03-15
This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach. (author)
Quadratic-linear pattern in cancer fractional radiotherapy. Equations for a computering program
International Nuclear Information System (INIS)
Burgos, D.; Bullejos, J.; Garcia Puche, J.L.; Pedraza, V.
1990-01-01
Knowledge of equivalence between different tratment schemes with the same iso-effect is the essential thing in clinical cancer radiotherapy. For this purpose it is very useful the group of ideas derived from quadratic-linear pattern (Q-L) proposed in order to analyze cell survival curve to radiation. Iso-effect definition caused by several irradiation rules is done by extrapolated tolerance dose (ETD). Because equations for ETD are complex, a computering program have been carried out. In this paper, iso-effect equations for well defined therapeutic situations and flow diagram proposed for resolution, have been studied. (Author)
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
DEFF Research Database (Denmark)
Holzleitner, Ludwig
1996-01-01
, here the shape of two dimensional parts with different thickness areas will be optimized. As in the previos paper, a methodology for structural optimization using the commercial finite element package MSC/NASTRAN for structural analysis is described. Three different methods for design sensitivity......This work is closely connected to the paper: K.G. MAHMOUD, H.W. ENGL and HOLZLEITNER: "OPTIMUM STRUCTURAL DESIGN USING MSC/NASTRAN AND SEQUENTIAL QUADRATIC PROGRAMMING", Computers & Structures, Vol. 52, No. 3, pp. 437-447, (1994). In contrast to that paper, where thickness optimization is described...
Algorithm for programming function generators
International Nuclear Information System (INIS)
Bozoki, E.
1981-01-01
The present paper deals with a mathematical problem, encountered when driving a fully programmable μ-processor controlled function generator. An algorithm is presented to approximate a desired function by a set of straight segments in such a way that additional restrictions (hardware imposed) are also satisfied. A computer program which incorporates this algorithm and automatically generates the necessary input for the function generator for a broad class of desired functions is also described
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.
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
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.
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.
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.
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.
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.
Linear programming algorithms and applications
Vajda, S
1981-01-01
This text is based on a course of about 16 hours lectures to students of mathematics, statistics, and/or operational research. It is intended to introduce readers to the very wide range of applicability of linear programming, covering problems of manage ment, administration, transportation and a number of other uses which are mentioned in their context. The emphasis is on numerical algorithms, which are illustrated by examples of such modest size that the solutions can be obtained using pen and paper. It is clear that these methods, if applied to larger problems, can also be carried out on automatic (electronic) computers. Commercially available computer packages are, in fact, mainly based on algorithms explained in this book. The author is convinced that the user of these algorithms ought to be knowledgeable about the underlying theory. Therefore this volume is not merely addressed to the practitioner, but also to the mathematician who is interested in relatively new developments in algebraic theory and in...
Directory of Open Access Journals (Sweden)
Fakhruddin Wirakusuma
2017-01-01
Full Text Available Kebutuhan daya listrik saat ini meningkat pesat seiring dengan perkembangan teknologi. Peningkatan kebutuhan daya listrik ini bertolak belakang dengan menipisnya ketersediaan sumber energy minyak dan batu bara. Permasalahan ini berdampak pada ketahanan listrik nasional. Untuk memenuhi kebutuhan daya listrik yang besar dengan cakupan wilayah yang luas diperlukan pembangkit tersebar berskala kecil. Pembangkit tersebar ini diupayakan bersumber pada energi terbarukan untuk meminimalkan pemakaian dari sumber energy minyak dan batu bara lalu dihubungkan ke Micro Grid serta digunakan baterai sebagai power balance. Oleh karena banyaknya pembangkit tersebar dan penggunaan baterai maka penting untuk menentukan besarnya pembangkitan daya listrik yang optimal dari masing-masing pembangkit serta penggunaan baterai berdasarkan kapasitas yang optimal sehingga kebutuhan daya listrik dapat dipenuhi dengan biaya yang minimal tiap waktunya. Optimisasi ini dikenal dengan istilah Dynamic Economic Dispatch. Optimisasi ini sudah banyak dilakukan dilakukan dengan berbagai macam metode Artificial Intelligence. Pada penelitian ini, metode Artificial Intellegence yang diaplikasikan yakni Quadratic Programming. Metode ini diterapkan pada software MATLAB. Dengan metode tersebut, diketahui bahwa penggunaan baterai mampu mengurangi total biaya pembangkitan.
Guam Community Coral Reef Monitoring Program, Benthic Quadrat Surveys at Guam in 2013
National Oceanic and Atmospheric Administration, Department of Commerce — Guam community members gathered benthic cover data using a 0.25m2 quadrat with 6 intersecting points at each meter along a 25-meter transect. Members identified...
Dudik, Joshua M; Kurosu, Atsuko; Coyle, James L; Sejdić, Ervin
2015-04-01
Cervical auscultation with high resolution sensors is currently under consideration as a method of automatically screening for specific swallowing abnormalities. To be clinically useful without human involvement, any devices based on cervical auscultation should be able to detect specified swallowing events in an automatic manner. In this paper, we comparatively analyze the density-based spatial clustering of applications with noise algorithm (DBSCAN), a k-means based algorithm, and an algorithm based on quadratic variation as methods of differentiating periods of swallowing activity from periods of time without swallows. These algorithms utilized swallowing vibration data exclusively and compared the results to a gold standard measure of swallowing duration. Data was collected from 23 subjects that were actively suffering from swallowing difficulties. Comparing the performance of the DBSCAN algorithm with a proven segmentation algorithm that utilizes k-means clustering demonstrated that the DBSCAN algorithm had a higher sensitivity and correctly segmented more swallows. Comparing its performance with a threshold-based algorithm that utilized the quadratic variation of the signal showed that the DBSCAN algorithm offered no direct increase in performance. However, it offered several other benefits including a faster run time and more consistent performance between patients. All algorithms showed noticeable differentiation from the endpoints provided by a videofluoroscopy examination as well as reduced sensitivity. In summary, we showed that the DBSCAN algorithm is a viable method for detecting the occurrence of a swallowing event using cervical auscultation signals, but significant work must be done to improve its performance before it can be implemented in an unsupervised manner. Copyright © 2015 Elsevier Ltd. All rights reserved.
Quadratic third-order tensor optimization problem with quadratic constraints
Directory of Open Access Journals (Sweden)
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.
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.
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…
KENO-VI: A Monte Carlo Criticality Program with generalized quadratic geometry
International Nuclear Information System (INIS)
Hollenbach, D.F.; Petrie, L.M.; Landers, N.F.
1993-01-01
This report discusses KENO-VI which is a new version of the KENO monte Carlo Criticality Safety developed at Oak Ridge National Laboratory. The purpose of KENO-VI is to provide a criticality safety code similar to KENO-V.a that possesses a more general and flexible geometry package. KENO-VI constructs and processes geometry data as sets of quadratic equations. A lengthy set of simple, easy-to-use geometric functions, similar to those provided in KENO-V.a., and the ability to build more complex geometric shapes represented by sets of quadratic equations are the heart of the geometry package in KENO-VI. The code's flexibility is increased by allowing intersecting geometry regions, hexagonal as well as cuboidal arrays, and the ability to specify an array boundary that intersects the array
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.
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....
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
A new algorithm for generalized fractional programs
J.B.G. Frenk (Hans); A.I. Barros (Ana); S. Schaible; S. Zhang (Shuzhong)
1996-01-01
textabstractA new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type algorithm for generalized
Liao, Bolin; Zhang, Yunong; Jin, Long
2016-02-01
In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.
TEACHING ALGORITHMIZATION AND PROGRAMMING USING PYTHON LANGUAGE
Directory of Open Access Journals (Sweden)
M. Lvov
2014-07-01
Full Text Available The article describes requirements to educational programming languages and considers the use of Python as the first programming language. The issues of introduction of this programming language into teaching and replacing Pascal by Python are examined. The advantages of such approach are regarded. The comparison of popular programming languages is represented from the point of view of their convenience of use for teaching algorithmization and programming. Python supports lots of programming paradigms: structural, object-oriented, functional, imperative and aspect-oriented, and learning can be started without any preparation. There is one more advantage of the language: all algorithms are written easily and structurally in Python. Therefore, due to all mentioned above, it is possible to affirm that Python pretends to become a decent replacement for educational programming language PASCAL both at schools and on the first courses of higher education establishments.
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.
AES ALGORITHM IMPLEMENTATION IN PROGRAMMING LANGUAGES
Directory of Open Access Journals (Sweden)
Luminiţa DEFTA
2010-12-01
Full Text Available Information encryption represents the usage of an algorithm to convert an unknown message into an encrypted one. It is used to protect the data against unauthorized access. Protected data can be stored on a media device or can be transmitted through the network. In this paper we describe a concrete implementation of the AES algorithm in the Java programming language (available from Java Development Kit 6 libraries and C (using the OpenSSL library. AES (Advanced Encryption Standard is an asymmetric key encryption algorithm formally adopted by the U.S. government and was elected after a long process of standardization.
Liang, Lihua; Yuan, Jia; Zhang, Songtao; Zhao, Peng
2018-01-01
This work presents optimal linear quadratic regulator (LQR) based on genetic algorithm (GA) to solve the two degrees of freedom (2 DoF) motion control problem in head seas for wave piercing catamarans (WPC). The proposed LQR based GA control strategy is to select optimal weighting matrices (Q and R). The seakeeping performance of WPC based on proposed algorithm is challenged because of multi-input multi-output (MIMO) system of uncertain coefficient problems. Besides the kinematical constraint problems of WPC, the external conditions must be considered, like the sea disturbance and the actuators (a T-foil and two flaps) control. Moreover, this paper describes the MATLAB and LabVIEW software plats to simulate the reduction effects of WPC. Finally, the real-time (RT) NI CompactRIO embedded controller is selected to test the effectiveness of the actuators based on proposed techniques. In conclusion, simulation and experimental results prove the correctness of the proposed algorithm. The percentage of heave and pitch reductions are more than 18% in different high speeds and bad sea conditions. And the results also verify the feasibility of NI CompactRIO embedded controller.
Linear programming mathematics, theory and algorithms
1996-01-01
Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.
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
Indian Academy of Sciences (India)
polynomial) division have been found in Vedic Mathematics which are dated much before Euclid's algorithm. A programming language Is used to describe an algorithm for execution on a computer. An algorithm expressed using a programming.
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....
Dynamic programming algorithms for biological sequence comparison.
Pearson, W R; Miller, W
1992-01-01
Efficient dynamic programming algorithms are available for a broad class of protein and DNA sequence comparison problems. These algorithms require computer time proportional to the product of the lengths of the two sequences being compared [O(N2)] but require memory space proportional only to the sum of these lengths [O(N)]. Although the requirement for O(N2) time limits use of the algorithms to the largest computers when searching protein and DNA sequence databases, many other applications of these algorithms, such as calculation of distances for evolutionary trees and comparison of a new sequence to a library of sequence profiles, are well within the capabilities of desktop computers. In particular, the results of library searches with rapid searching programs, such as FASTA or BLAST, should be confirmed by performing a rigorous optimal alignment. Whereas rapid methods do not overlook significant sequence similarities, FASTA limits the number of gaps that can be inserted into an alignment, so that a rigorous alignment may extend the alignment substantially in some cases. BLAST does not allow gaps in the local regions that it reports; a calculation that allows gaps is very likely to extend the alignment substantially. Although a Monte Carlo evaluation of the statistical significance of a similarity score with a rigorous algorithm is much slower than the heuristic approach used by the RDF2 program, the dynamic programming approach should take less than 1 hr on a 386-based PC or desktop Unix workstation. For descriptive purposes, we have limited our discussion to methods for calculating similarity scores and distances that use gap penalties of the form g = rk. Nevertheless, programs for the more general case (g = q+rk) are readily available. Versions of these programs that run either on Unix workstations, IBM-PC class computers, or the Macintosh can be obtained from either of the authors.
Altin, Necmi
2018-05-01
An interval type-2 fuzzy logic controller-based maximum power point tracking algorithm and direct current-direct current (DC-DC) converter topology are proposed for photovoltaic (PV) systems. The proposed maximum power point tracking algorithm is designed based on an interval type-2 fuzzy logic controller that has an ability to handle uncertainties. The change in PV power and the change in PV voltage are determined as inputs of the proposed controller, while the change in duty cycle is determined as the output of the controller. Seven interval type-2 fuzzy sets are determined and used as membership functions for input and output variables. The quadratic boost converter provides high voltage step-up ability without any reduction in performance and stability of the system. The performance of the proposed system is validated through MATLAB/Simulink simulations. It is seen that the proposed system provides high maximum power point tracking speed and accuracy even for fast changing atmospheric conditions and high voltage step-up requirements.
Nonnegative constraint quadratic program technique to enhance the resolution of γ spectra
Li, Jinglun; Xiao, Wuyun; Ai, Xianyun; Chen, Ye
2018-04-01
Two concepts of the nonnegative least squares problem (NNLS) and the linear complementarity problem (LCP) are introduced for the resolution enhancement of the γ spectra. The respective algorithms such as the active set method and the primal-dual interior point method are applied to solve the above two problems. In mathematics, the nonnegative constraint results in the sparsity of the optimal solution of the deconvolution, and it is this sparsity that enhances the resolution. Finally, a comparison in the peak position accuracy and the computation time is made between these two methods and the boosted L_R and Gold methods.
A Sequential Quadratic Programming Algorithm Using an Incomplete Solution of the Subproblem
1990-09-01
Electr6nica e Inform’itica Industrial E.T.S. Ingenieros Industriales Universidad Polit6cnica, Madrid Technical Report SOL 90-12 September 1990 -Y...MURRAY* AND FRANCISCO J. PRIETOt *Systems Optimization Laboratory Department of Operations Research Stanford University tDept. de Automitica, Ingenieria
Directory of Open Access Journals (Sweden)
Riza Fahmi Andriyanto
2017-01-01
Full Text Available Kebutuhan akan energi listrik terus menigkat seiring dengan perkembangan teknologi. meningkatnya beban listrik ini harus diimbangi dengan penambahan daya yang dibangkitkan. Hal ini sangat berpengaruh pada penjadwalan unit pembangkit yang harus ditentukan dengan baik agar didapatkan pembangkitan yang optimal. Pada Tugas Akhir ini mengambil topik mengenai unit commitment dan economic dispatch dengan mempertimbangkan nilai dari batasan generator (ramp-rate. Metode yang digunakan adalah complete enumeration dengan forward dynamic programming pada unit commitment dan quadratic programming pada economic dispatch. Metode - metode tersebut diterapkan dalam pemrograman matlab sehingga dapat dijadikan suatu program perhitungan unit commitment dan economic dispatch dengan mempertimbangkan nilai batasan ramp-rate. Dengan metode tersebut, diharapkan permasalahan penjadwalan unit pembangkit dapat terselesaikan dengan baik dan optimal sehingga memperoleh total biaya pembangkitan yang ekonomis.
International Nuclear Information System (INIS)
Zhang Yunong; Li Zhan
2009-01-01
In this Letter, by following Zhang et al.'s method, a recurrent neural network (termed as Zhang neural network, ZNN) is developed and analyzed for solving online the time-varying convex quadratic-programming problem subject to time-varying linear-equality constraints. Different from conventional gradient-based neural networks (GNN), such a ZNN model makes full use of the time-derivative information of time-varying coefficient. The resultant ZNN model is theoretically proved to have global exponential convergence to the time-varying theoretical optimal solution of the investigated time-varying convex quadratic program. Computer-simulation results further substantiate the effectiveness, efficiency and novelty of such ZNN model and method.
A Superlinearly Convergent O(square root of nL)-Iteration Algorithm for Linear Programming
National Research Council Canada - National Science Library
Ye, Y; Tapia, Richard A; Zhang, Y
1991-01-01
.... We demonstrate that the modified algorithm maintains its O(square root of nL)-iteration complexity, while exhibiting superlinear convergence for general problems and quadratic convergence for nondegenerate 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…
PACE: A dynamic programming algorithm for hardware/software partitioning
DEFF Research Database (Denmark)
Knudsen, Peter Voigt; Madsen, Jan
1996-01-01
This paper presents the PACE partitioning algorithm which is used in the LYCOS co-synthesis system for partitioning control/dataflow graphs into hardware and software parts. The algorithm is a dynamic programming algorithm which solves both the problem of minimizing system execution time...
Dynamic Programming Algorithms in Speech Recognition
Directory of Open Access Journals (Sweden)
Titus Felix FURTUNA
2008-01-01
Full Text Available In a system of speech recognition containing words, the recognition requires the comparison between the entry signal of the word and the various words of the dictionary. The problem can be solved efficiently by a dynamic comparison algorithm whose goal is to put in optimal correspondence the temporal scales of the two words. An algorithm of this type is Dynamic Time Warping. This paper presents two alternatives for implementation of the algorithm designed for recognition of the isolated words.
Indian Academy of Sciences (India)
to as 'divide-and-conquer'. Although there has been a large effort in realizing efficient algorithms, there are not many universally accepted algorithm design paradigms. In this article, we illustrate algorithm design techniques such as balancing, greedy strategy, dynamic programming strategy, and backtracking or traversal of ...
Domí nguez, Luis F.; Pistikopoulos, Efstratios N.
2010-01-01
continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem
Energy Technology Data Exchange (ETDEWEB)
Enghauser, Michael [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-02-01
The goal of the Domestic Nuclear Detection Office (DNDO) Algorithm Improvement Program (AIP) is to facilitate gamma-radiation detector nuclide identification algorithm development, improvement, and validation. Accordingly, scoring criteria have been developed to objectively assess the performance of nuclide identification algorithms. In addition, a Microsoft Excel spreadsheet application for automated nuclide identification scoring has been developed. This report provides an overview of the equations, nuclide weighting factors, nuclide equivalencies, and configuration weighting factors used by the application for scoring nuclide identification algorithm performance. Furthermore, this report presents a general overview of the nuclide identification algorithm scoring application including illustrative examples.
Portfolio selection using genetic algorithms | Yahaya | International ...
African Journals Online (AJOL)
In this paper, one of the nature-inspired evolutionary algorithms – a Genetic Algorithms (GA) was used in solving the portfolio selection problem (PSP). Based on a real dataset from a popular stock market, the performance of the algorithm in relation to those obtained from one of the popular quadratic programming (QP) ...
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.
Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae
Rosu, Grigore; Havelund, Klaus
2001-01-01
The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.
Algorithms, The λ Calculus and Programming
Indian Academy of Sciences (India)
IAS Admin
developed a model to understand ... Hence the ¸ calculus also served as an alternate model ...... Practical programming using usual languages based on .... and return values as. 'answers'. This style of programming that emerges is therefore.
Bilevel programming problems theory, algorithms and applications to energy networks
Dempe, Stephan; Pérez-Valdés, Gerardo A; Kalashnykova, Nataliya; Kalashnikova, Nataliya
2015-01-01
This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.
A Partitioning and Bounded Variable Algorithm for Linear Programming
Sheskin, Theodore J.
2006-01-01
An interesting new partitioning and bounded variable algorithm (PBVA) is proposed for solving linear programming problems. The PBVA is a variant of the simplex algorithm which uses a modified form of the simplex method followed by the dual simplex method for bounded variables. In contrast to the two-phase method and the big M method, the PBVA does…
Primal-dual path-following algorithms for circular programming
Directory of Open Access Journals (Sweden)
Baha Alzalg
2017-06-01
Full Text Available Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003 3--51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan algebras associated with the circular cones to derive primal-dual path-following interior point algorithms for circular programming problems. We prove polynomial convergence of the proposed algorithms by showing that the circular logarithmic barrier is a strongly self-concordant barrier. The numerical examples show the path-following algorithms are simple and efficient.
A scalable parallel algorithm for multiple objective linear programs
Wiecek, Malgorzata M.; Zhang, Hong
1994-01-01
This paper presents an ADBASE-based parallel algorithm for solving multiple objective linear programs (MOLP's). Job balance, speedup and scalability are of primary interest in evaluating efficiency of the new algorithm. Implementation results on Intel iPSC/2 and Paragon multiprocessors show that the algorithm significantly speeds up the process of solving MOLP's, which is understood as generating all or some efficient extreme points and unbounded efficient edges. The algorithm gives specially good results for large and very large problems. Motivation and justification for solving such large MOLP's are also included.
A Programming Environment for Parallel Vision Algorithms
1990-04-11
industrial arm on the market , while the unique head was designed by Rochester’s Computer Science and Mechanical Engineering Departments. 9a 4.1 Introduction...R. Constraining-Unification and the Programming Language Unicorn . In Logic Programming, Functions, Relations, and Equations, Degroot and Lind- strom
Quantum algorithms for the ordered search problem via semidefinite programming
International Nuclear Information System (INIS)
Childs, Andrew M.; Landahl, Andrew J.; Parrilo, Pablo A.
2007-01-01
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log 2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for the ordered search problem in terms of a semidefinite program, we find quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log 605 N≅0.433 log 2 N queries, which improves upon the previously best known exact algorithm
Algorithms and programs for consequence diagram and fault tree construction
International Nuclear Information System (INIS)
Hollo, E.; Taylor, J.R.
1976-12-01
A presentation of algorithms and programs for consequence diagram and sequential fault tree construction that are intended for reliability and disturbance analysis of large systems. The system to be analyzed must be given as a block diagram formed by mini fault trees of individual system components. The programs were written in LISP programming language and run on a PDP8 computer with 8k words of storage. A description is given of the methods used and of the program construction and working. (author)
A Direct Heuristic Algorithm for Linear Programming
Indian Academy of Sciences (India)
Abstract. An (3) mathematically non-iterative heuristic procedure that needs no artificial variable is presented for solving linear programming problems. An optimality test is included. Numerical experiments depict the utility/scope of such a procedure.
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
Optimization of Algorithms Using Extensions of Dynamic Programming
AbouEisha, Hassan M.
2017-04-09
We study and answer questions related to the complexity of various important problems such as: multi-frontal solvers of hp-adaptive finite element method, sorting and majority. We advocate the use of dynamic programming as a viable tool to study optimal algorithms for these problems. The main approach used to attack these problems is modeling classes of algorithms that may solve this problem using a discrete model of computation then defining cost functions on this discrete structure that reflect different complexity measures of the represented algorithms. As a last step, dynamic programming algorithms are designed and used to optimize those models (algorithms) and to obtain exact results on the complexity of the studied problems. The first part of the thesis presents a novel model of computation (element partition tree) that represents a class of algorithms for multi-frontal solvers along with cost functions reflecting various complexity measures such as: time and space. It then introduces dynamic programming algorithms for multi-stage and bi-criteria optimization of element partition trees. In addition, it presents results based on optimal element partition trees for famous benchmark meshes such as: meshes with point and edge singularities. New improved heuristics for those benchmark meshes were ob- tained based on insights of the optimal results found by our algorithms. The second part of the thesis starts by introducing a general problem where different problems can be reduced to and show how to use a decision table to model such problem. We describe how decision trees and decision tests for this table correspond to adaptive and non-adaptive algorithms for the original problem. We present exact bounds on the average time complexity of adaptive algorithms for the eight elements sorting problem. Then bounds on adaptive and non-adaptive algorithms for a variant of the majority problem are introduced. Adaptive algorithms are modeled as decision trees whose depth
An online re-linearization scheme suited for Model Predictive and Linear Quadratic Control
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the equations for primal-dual interior-point quadratic programming problem solver used for MPC. The algorithm exploits the special structure of the MPC problem and is able to reduce the computational burden such that the computational burden scales with prediction...... horizon length in a linear way rather than cubic, which would be the case if the structure was not exploited. It is also shown how models used for design of model-based controllers, e.g. linear quadratic and model predictive, can be linearized both at equilibrium and non-equilibrium points, making...
AUTOMATION PROGRAM FOR RECOGNITION OF ALGORITHM SOLUTION OF MATHEMATIC TASK
Directory of Open Access Journals (Sweden)
Denis N. Butorin
2014-01-01
Full Text Available In the article are been describing technology for manage of testing task in computer program. It was found for recognition of algorithm solution of mathematic task. There are been justifi ed the using hierarchical structure for a special set of testing questions. Also, there has been presented the release of the described tasks in the computer program openSEE.
AUTOMATION PROGRAM FOR RECOGNITION OF ALGORITHM SOLUTION OF MATHEMATIC TASK
Denis N. Butorin
2014-01-01
In the article are been describing technology for manage of testing task in computer program. It was found for recognition of algorithm solution of mathematic task. There are been justifi ed the using hierarchical structure for a special set of testing questions. Also, there has been presented the release of the described tasks in the computer program openSEE.
Image Processing Algorithms in the Secondary School Programming Education
Gerják, István
2017-01-01
Learning computer programming for students of the age of 14-18 is difficult and requires endurance and engagement. Being familiar with the syntax of a computer language and writing programs in it are challenges for youngsters, not to mention that understanding algorithms is also a big challenge. To help students in the learning process, teachers…
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.
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 New Finite Continuation Algorithm for Linear Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa
1996-01-01
We describe a new finite continuation algorithm for linear programming. The dual of the linear programming problem with unit lower and upper bounds is formulated as an $\\ell_1$ minimization problem augmented with the addition of a linear term. This nondifferentiable problem is approximated...... by a smooth problem. It is shown that the minimizers of the smooth problem define a family of piecewise-linear paths as a function of a smoothing parameter. Based on this property, a finite algorithm that traces these paths to arrive at an optimal solution of the linear program is developed. The smooth...
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
Multiobjective Optimization Involving Quadratic Functions
Directory of Open Access Journals (Sweden)
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.
Optimisation in radiotherapy II: Programmed and inversion optimisation algorithms
International Nuclear Information System (INIS)
Ebert, M.
1997-01-01
This is the second article in a three part examination of optimisation in radiotherapy. The previous article established the bases of optimisation in radiotherapy, and the formulation of the optimisation problem. This paper outlines several algorithms that have been used in radiotherapy, for searching for the best irradiation strategy within the full set of possible strategies. Two principle classes of algorithm are considered - those associated with mathematical programming which employ specific search techniques, linear programming type searches or artificial intelligence - and those which seek to perform a numerical inversion of the optimisation problem, finishing with deterministic iterative inversion. (author)
Algorithmic Trading with Developmental and Linear Genetic Programming
Wilson, Garnett; Banzhaf, Wolfgang
A developmental co-evolutionary genetic programming approach (PAM DGP) and a standard linear genetic programming (LGP) stock trading systemare applied to a number of stocks across market sectors. Both GP techniques were found to be robust to market fluctuations and reactive to opportunities associated with stock price rise and fall, with PAMDGP generating notably greater profit in some stock trend scenarios. Both algorithms were very accurate at buying to achieve profit and selling to protect assets, while exhibiting bothmoderate trading activity and the ability to maximize or minimize investment as appropriate. The content of the trading rules produced by both algorithms are also examined in relation to stock price trend scenarios.
Linear Programming, the Simplex Algorithm and Simple Polytopes
Directory of Open Access Journals (Sweden)
Das Bhusan
2010-09-01
Full Text Available In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.
Domínguez, Luis F.
2010-12-01
This work introduces two algorithms for the solution of pure integer and mixed-integer bilevel programming problems by multiparametric programming techniques. The first algorithm addresses the integer case of the bilevel programming problem where integer variables of the outer optimization problem appear in linear or polynomial form in the inner problem. The algorithm employs global optimization techniques to convexify nonlinear terms generated by a reformulation linearization technique (RLT). A continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem appear in linear or polynomial forms in the inner problem. The algorithm relies on the use of global multiparametric mixed-integer programming techniques at the inner optimization level. In both algorithms, the multiparametric solutions obtained are embedded in the outer problem to form a set of single-level (M)(I)(N)LP problems - which are then solved to global optimality using standard fixed-point (global) optimization methods. Numerical examples drawn from the open literature are presented to illustrate the proposed algorithms. © 2010 Elsevier Ltd.
Factorization method of quadratic template
Kotyrba, Martin
2017-07-01
Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.
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]…
Indian Academy of Sciences (India)
algorithm design technique called 'divide-and-conquer'. One of ... Turtle graphics, September. 1996. 5. ... whole list named 'PO' is a pointer to the first element of the list; ..... Program for computing matrices X and Y and placing the result in C *).
Arc-Search Infeasible Interior-Point Algorithm for Linear Programming
Yang, Yaguang
2014-01-01
Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper proposes an alternative algorithm, arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by arc-search infeasible interior-point algorithm and Mehrotra's algorithm, that the propo...
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-.
Abejuela, Harmony Raylen; Osser, David N
2016-01-01
This revision of previous algorithms for the pharmacotherapy of generalized anxiety disorder was developed by the Psychopharmacology Algorithm Project at the Harvard South Shore Program. Algorithms from 1999 and 2010 and associated references were reevaluated. Newer studies and reviews published from 2008-14 were obtained from PubMed and analyzed with a focus on their potential to justify changes in the recommendations. Exceptions to the main algorithm for special patient populations, such as women of childbearing potential, pregnant women, the elderly, and those with common medical and psychiatric comorbidities, were considered. Selective serotonin reuptake inhibitors (SSRIs) are still the basic first-line medication. Early alternatives include duloxetine, buspirone, hydroxyzine, pregabalin, or bupropion, in that order. If response is inadequate, then the second recommendation is to try a different SSRI. Additional alternatives now include benzodiazepines, venlafaxine, kava, and agomelatine. If the response to the second SSRI is unsatisfactory, then the recommendation is to try a serotonin-norepinephrine reuptake inhibitor (SNRI). Other alternatives to SSRIs and SNRIs for treatment-resistant or treatment-intolerant patients include tricyclic antidepressants, second-generation antipsychotics, and valproate. This revision of the GAD algorithm responds to issues raised by new treatments under development (such as pregabalin) and organizes the evidence systematically for practical clinical application.
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
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 ...
Semi-definite Programming: methods and algorithms for energy management
International Nuclear Information System (INIS)
Gorge, Agnes
2013-01-01
The present thesis aims at exploring the potentialities of a powerful optimization technique, namely Semi-definite Programming, for addressing some difficult problems of energy management. We pursue two main objectives. The first one consists of using SDP to provide tight relaxations of combinatorial and quadratic problems. A first relaxation, called 'standard' can be derived in a generic way but it is generally desirable to reinforce them, by means of tailor-made tools or in a systematic fashion. These two approaches are implemented on different models of the Nuclear Outages Scheduling Problem, a famous combinatorial problem. We conclude this topic by experimenting the Lasserre's hierarchy on this problem, leading to a sequence of semi-definite relaxations whose optimal values tends to the optimal value of the initial problem. The second objective deals with the use of SDP for the treatment of uncertainty. We investigate an original approach called 'distributionally robust optimization', that can be seen as a compromise between stochastic and robust optimization and admits approximations under the form of a SDP. We compare the benefits of this method w.r.t classical approaches on a demand/supply equilibrium problem. Finally, we propose a scheme for deriving SDP relaxations of MISOCP and we report promising computational results indicating that the semi-definite relaxation improves significantly the continuous relaxation, while requiring a reasonable computational effort. SDP therefore proves to be a promising optimization method that offers great opportunities for innovation in energy management. (author)
Comparison of optimization algorithms in intensity-modulated radiation therapy planning
Kendrick, Rachel
Intensity-modulated radiation therapy is used to better conform the radiation dose to the target, which includes avoiding healthy tissue. Planning programs employ optimization methods to search for the best fluence of each photon beam, and therefore to create the best treatment plan. The Computational Environment for Radiotherapy Research (CERR), a program written in MATLAB, was used to examine some commonly-used algorithms for one 5-beam plan. Algorithms include the genetic algorithm, quadratic programming, pattern search, constrained nonlinear optimization, simulated annealing, the optimization method used in Varian EclipseTM, and some hybrids of these. Quadratic programing, simulated annealing, and a quadratic/simulated annealing hybrid were also separately compared using different prescription doses. The results of each dose-volume histogram as well as the visual dose color wash were used to compare the plans. CERR's built-in quadratic programming provided the best overall plan, but avoidance of the organ-at-risk was rivaled by other programs. Hybrids of quadratic programming with some of these algorithms seems to suggest the possibility of better planning programs, as shown by the improved quadratic/simulated annealing plan when compared to the simulated annealing algorithm alone. Further experimentation will be done to improve cost functions and computational time.
Swarm, genetic and evolutionary programming algorithms applied to multiuser detection
Directory of Open Access Journals (Sweden)
Paul Jean Etienne Jeszensky
2005-02-01
Full Text Available In this paper, the particles swarm optimization technique, recently published in the literature, and applied to Direct Sequence/Code Division Multiple Access systems (DS/CDMA with multiuser detection (MuD is analyzed, evaluated and compared. The Swarm algorithm efficiency when applied to the DS-CDMA multiuser detection (Swarm-MuD is compared through the tradeoff performance versus computational complexity, being the complexity expressed in terms of the number of necessary operations in order to reach the performance obtained through the optimum detector or the Maximum Likelihood detector (ML. The comparison is accomplished among the genetic algorithm, evolutionary programming with cloning and Swarm algorithm under the same simulation basis. Additionally, it is proposed an heuristics-MuD complexity analysis through the number of computational operations. Finally, an analysis is carried out for the input parameters of the Swarm algorithm in the attempt to find the optimum parameters (or almost-optimum for the algorithm applied to the MuD problem.
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.
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 ...
Gu, Huidong; Liu, Guowen; Wang, Jian; Aubry, Anne-Françoise; Arnold, Mark E
2014-09-16
A simple procedure for selecting the correct weighting factors for linear and quadratic calibration curves with least-squares regression algorithm in bioanalytical LC-MS/MS assays is reported. The correct weighting factor is determined by the relationship between the standard deviation of instrument responses (σ) and the concentrations (x). The weighting factor of 1, 1/x, or 1/x(2) should be selected if, over the entire concentration range, σ is a constant, σ(2) is proportional to x, or σ is proportional to x, respectively. For the first time, we demonstrated with detailed scientific reasoning, solid historical data, and convincing justification that 1/x(2) should always be used as the weighting factor for all bioanalytical LC-MS/MS assays. The impacts of using incorrect weighting factors on curve stability, data quality, and assay performance were thoroughly investigated. It was found that the most stable curve could be obtained when the correct weighting factor was used, whereas other curves using incorrect weighting factors were unstable. It was also found that there was a very insignificant impact on the concentrations reported with calibration curves using incorrect weighting factors as the concentrations were always reported with the passing curves which actually overlapped with or were very close to the curves using the correct weighting factor. However, the use of incorrect weighting factors did impact the assay performance significantly. Finally, the difference between the weighting factors of 1/x(2) and 1/y(2) was discussed. All of the findings can be generalized and applied into other quantitative analysis techniques using calibration curves with weighted least-squares regression algorithm.
Mohammad, Othman; Osser, David N
2014-01-01
This new algorithm for the pharmacotherapy of acute mania was developed by the Psychopharmacology Algorithm Project at the Harvard South Shore Program. The authors conducted a literature search in PubMed and reviewed key studies, other algorithms and guidelines, and their references. Treatments were prioritized considering three main considerations: (1) effectiveness in treating the current episode, (2) preventing potential relapses to depression, and (3) minimizing side effects over the short and long term. The algorithm presupposes that clinicians have made an accurate diagnosis, decided how to manage contributing medical causes (including substance misuse), discontinued antidepressants, and considered the patient's childbearing potential. We propose different algorithms for mixed and nonmixed mania. Patients with mixed mania may be treated first with a second-generation antipsychotic, of which the first choice is quetiapine because of its greater efficacy for depressive symptoms and episodes in bipolar disorder. Valproate and then either lithium or carbamazepine may be added. For nonmixed mania, lithium is the first-line recommendation. A second-generation antipsychotic can be added. Again, quetiapine is favored, but if quetiapine is unacceptable, risperidone is the next choice. Olanzapine is not considered a first-line treatment due to its long-term side effects, but it could be second-line. If the patient, whether mixed or nonmixed, is still refractory to the above medications, then depending on what has already been tried, consider carbamazepine, haloperidol, olanzapine, risperidone, and valproate first tier; aripiprazole, asenapine, and ziprasidone second tier; and clozapine third tier (because of its weaker evidence base and greater side effects). Electroconvulsive therapy may be considered at any point in the algorithm if the patient has a history of positive response or is intolerant of medications.
Mathematical models and algorithms for the computer program 'WOLF'
International Nuclear Information System (INIS)
Halbach, K.
1975-12-01
The computer program FLOW finds the nonrelativistic self- consistent set of two-dimensional ion trajectories and electric fields (including space charges from ions and electrons) for a given set of initial and boundary conditions for the particles and fields. The combination of FLOW with the optimization code PISA gives the program WOLF, which finds the shape of the emitter which is consistent with the plasma forming it, and in addition varies physical characteristics such as electrode position, shapes, and potentials so that some performance characteristics are optimized. The motivation for developing these programs was the desire to design optimum ion source extractor/accelerator systems in a systematic fashion. The purpose of this report is to explain and derive the mathematical models and algorithms which approximate the real physical processes. It serves primarily to document the computer programs. 10 figures
Indian Academy of Sciences (India)
will become clear in the next article when we discuss a simple logo like programming language. ... Rod B may be used as an auxiliary store. The problem is to find an algorithm which performs this task. ... No disks are moved from A to Busing C as auxiliary rod. • move _disk (A, C);. (No + l)th disk is moved from A to C directly ...
Applications and algorithms for mixed integer nonlinear programming
International Nuclear Information System (INIS)
Leyffer, Sven; Munson, Todd; Linderoth, Jeff; Luedtke, James; Miller, Andrew
2009-01-01
The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scientific applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......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...... 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...
DEFF Research Database (Denmark)
Atamtürk, Alper; Muller, Laurent Flindt; Pisinger, David
2013-01-01
Motivated by addressing probabilistic 0-1 programs we study the conic quadratic knapsack polytope with generalized upper bound (GUB) constraints. In particular, we investigate separating and extending GUB cover inequalities. We show that, unlike in the linear case, determining whether a cover can...... be extended with a single variable is NP-hard. We describe and compare a number of exact and heuristic separation and extension algorithms which make use of the structure of the constraints. Computational experiments are performed for comparing the proposed separation and extension algorithms...
Solution of quadratic matrix equations for free vibration analysis of structures.
Gupta, K. K.
1973-01-01
An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.
Dynamic Programming and Graph Algorithms in Computer Vision*
Felzenszwalb, Pedro F.; Zabih, Ramin
2013-01-01
Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting, since by carefully exploiting problem structure they often provide non-trivial guarantees concerning solution quality. In this paper we briefly review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo; the mid-level problem of interactive object segmentation; and the high-level problem of model-based recognition. PMID:20660950
Zhang, Yongjun; Lu, Zhixin
2017-10-01
Spectrum resources are very precious, so it is increasingly important to locate interference signals rapidly. Convex programming algorithms in wireless sensor networks are often used as localization algorithms. But in view of the traditional convex programming algorithm is too much overlap of wireless sensor nodes that bring low positioning accuracy, the paper proposed a new algorithm. Which is mainly based on the traditional convex programming algorithm, the spectrum car sends unmanned aerial vehicles (uses) that can be used to record data periodically along different trajectories. According to the probability density distribution, the positioning area is segmented to further reduce the location area. Because the algorithm only increases the communication process of the power value of the unknown node and the sensor node, the advantages of the convex programming algorithm are basically preserved to realize the simple and real-time performance. The experimental results show that the improved algorithm has a better positioning accuracy than the original convex programming algorithm.
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
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
Bonus algorithm for large scale stochastic nonlinear programming problems
Diwekar, Urmila
2015-01-01
This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...
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
Towards Merging Binary Integer Programming Techniques with Genetic Algorithms
Directory of Open Access Journals (Sweden)
Reza Zamani
2017-01-01
Full Text Available This paper presents a framework based on merging a binary integer programming technique with a genetic algorithm. The framework uses both lower and upper bounds to make the employed mathematical formulation of a problem as tight as possible. For problems whose optimal solutions cannot be obtained, precision is traded with speed through substituting the integrality constrains in a binary integer program with a penalty. In this way, instead of constraining a variable u with binary restriction, u is considered as real number between 0 and 1, with the penalty of Mu(1-u, in which M is a large number. Values not near to the boundary extremes of 0 and 1 make the component of Mu(1-u large and are expected to be avoided implicitly. The nonbinary values are then converted to priorities, and a genetic algorithm can use these priorities to fill its initial pool for producing feasible solutions. The presented framework can be applied to many combinatorial optimization problems. Here, a procedure based on this framework has been applied to a scheduling problem, and the results of computational experiments have been discussed, emphasizing the knowledge generated and inefficiencies to be circumvented with this framework in future.
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 LINEAR PROGRAMMING ALGORITHM FOR LEAST-COST SCHEDULING
Directory of Open Access Journals (Sweden)
AYMAN H AL-MOMANI
1999-12-01
Full Text Available In this research, some concepts of linear programming and critical path method are reviewed to describe recent modeling structures that have been of great value in analyzing extended planning horizon project time-cost trade-offs problems. A simplified representation of a small project and a linear programming model is formulated to represent this system. Procedures to solve these various problems formulations were cited and the final solution is obtained using LINDO program. The model developed represents many restrictions and management considerations of the project. It could be used by construction managers in a planning stage to explore numerous possible opportunities to the contractor and predict the effect of a decision on the construction to facilitate a preferred operating policy given different management objectives. An implementation using this method is shown to outperform several other techniques and a large class of test problems. Linear programming show that the algorithm is very promising in practice on a wide variety of time-cost trade-offs problems. This method is simple, applicable to a large network, and generates a shorter computational time at low cost, along with an increase in robustness.
Quaternion orders, quadratic forms, and Shimura curves
Alsina, Montserrat
2004-01-01
Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...
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…
Sub-quadratic decoding of one-point hermitian codes
DEFF Research Database (Denmark)
Nielsen, Johan Sebastian Rosenkilde; Beelen, Peter
2015-01-01
We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power...... decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities....
Toward a molecular programming language for algorithmic self-assembly
Patitz, Matthew John
Self-assembly is the process whereby relatively simple components autonomously combine to form more complex objects. Nature exhibits self-assembly to form everything from microscopic crystals to living cells to galaxies. With a desire to both form increasingly sophisticated products and to understand the basic components of living systems, scientists have developed and studied artificial self-assembling systems. One such framework is the Tile Assembly Model introduced by Erik Winfree in 1998. In this model, simple two-dimensional square 'tiles' are designed so that they self-assemble into desired shapes. The work in this thesis consists of a series of results which build toward the future goal of designing an abstracted, high-level programming language for designing the molecular components of self-assembling systems which can perform powerful computations and form into intricate structures. The first two sets of results demonstrate self-assembling systems which perform infinite series of computations that characterize computably enumerable and decidable languages, and exhibit tools for algorithmically generating the necessary sets of tiles. In the next chapter, methods for generating tile sets which self-assemble into complicated shapes, namely a class of discrete self-similar fractal structures, are presented. Next, a software package for graphically designing tile sets, simulating their self-assembly, and debugging designed systems is discussed. Finally, a high-level programming language which abstracts much of the complexity and tedium of designing such systems, while preventing many of the common errors, is presented. The summation of this body of work presents a broad coverage of the spectrum of desired outputs from artificial self-assembling systems and a progression in the sophistication of tools used to design them. By creating a broader and deeper set of modular tools for designing self-assembling systems, we hope to increase the complexity which is
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.
Empirical study of self-configuring genetic programming algorithm performance and behaviour
International Nuclear Information System (INIS)
KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" data-affiliation=" (Siberian State Aerospace University named after Academician M.F. Reshetnev 31 KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" >Semenkin, E; KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" data-affiliation=" (Siberian State Aerospace University named after Academician M.F. Reshetnev 31 KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" >Semenkina, M
2015-01-01
The behaviour of the self-configuring genetic programming algorithm with a modified uniform crossover operator that implements a selective pressure on the recombination stage, is studied over symbolic programming problems. The operator's probabilistic rates interplay is studied and the role of operator variants on algorithm performance is investigated. Algorithm modifications based on the results of investigations are suggested. The performance improvement of the algorithm is demonstrated by the comparative analysis of suggested algorithms on the benchmark and real world problems
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)
A new separation algorithm for the Boolean quadric and cut polytopes
DEFF Research Database (Denmark)
Sørensen, Michael Malmros; Letchford, Adam N.
2014-01-01
A separation algorithm is a procedure for generating cutting planes. Up to now, only a few polynomial-time separation algorithms were known for the Boolean quadric and cut polytopes. These polytopes arise in connection with zero–one quadratic programming and the max-cut problem, respectively. We...
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
A Primal-Dual Interior Point-Linear Programming Algorithm for MPC
DEFF Research Database (Denmark)
Edlund, Kristian; Sokoler, Leo Emil; Jørgensen, John Bagterp
2009-01-01
Constrained optimal control problems for linear systems with linear constraints and an objective function consisting of linear and l1-norm terms can be expressed as linear programs. We develop an efficient primal-dual interior point algorithm for solution of such linear programs. The algorithm...
A Functional Programming Approach to AI Search Algorithms
Panovics, Janos
2012-01-01
The theory and practice of search algorithms related to state-space represented problems form the major part of the introductory course of Artificial Intelligence at most of the universities and colleges offering a degree in the area of computer science. Students usually meet these algorithms only in some imperative or object-oriented language…
Maintenance of Process Control Algorithms based on Dynamic Program Slicing
DEFF Research Database (Denmark)
Hansen, Ole Fink; Andersen, Nils Axel; Ravn, Ole
2010-01-01
Today’s industrial control systems gradually lose performance after installation and must be regularly maintained by means of adjusting parameters and modifying the control algorithm, in order to regain high performance. Industrial control algorithms are complex software systems, and it is partic...
Portfolio optimization by using linear programing models based on genetic algorithm
Sukono; Hidayat, Y.; Lesmana, E.; Putra, A. S.; Napitupulu, H.; Supian, S.
2018-01-01
In this paper, we discussed the investment portfolio optimization using linear programming model based on genetic algorithms. It is assumed that the portfolio risk is measured by absolute standard deviation, and each investor has a risk tolerance on the investment portfolio. To complete the investment portfolio optimization problem, the issue is arranged into a linear programming model. Furthermore, determination of the optimum solution for linear programming is done by using a genetic algorithm. As a numerical illustration, we analyze some of the stocks traded on the capital market in Indonesia. Based on the analysis, it is shown that the portfolio optimization performed by genetic algorithm approach produces more optimal efficient portfolio, compared to the portfolio optimization performed by a linear programming algorithm approach. Therefore, genetic algorithms can be considered as an alternative on determining the investment portfolio optimization, particularly using linear programming models.
Directory of Open Access Journals (Sweden)
Tanwiwat Jaikuna
2017-02-01
Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.
National Oceanic and Atmospheric Administration, Department of Commerce — The Pacific Reef Assessment and Monitoring Program (Pacific RAMP), established by the Coral Reef Ecosystem Program (CREP) of the NOAA Pacific Islands Fisheries...
Probabilistic analysis algorithm for UA slope software program.
2013-12-01
A reliability-based computational algorithm for using a single row and equally spaced drilled shafts to : stabilize an unstable slope has been developed in this research. The Monte-Carlo simulation (MCS) : technique was used in the previously develop...
Optimization of Algorithms Using Extensions of Dynamic Programming
AbouEisha, Hassan M.
2017-01-01
of the thesis presents a novel model of computation (element partition tree) that represents a class of algorithms for multi-frontal solvers along with cost functions reflecting various complexity measures such as: time and space. It then introduces dynamic
A primal-dual exterior point algorithm for linear programming problems
Directory of Open Access Journals (Sweden)
Samaras Nikolaos
2009-01-01
Full Text Available The aim of this paper is to present a new simplex type algorithm for the Linear Programming Problem. The Primal - Dual method is a Simplex - type pivoting algorithm that generates two paths in order to converge to the optimal solution. The first path is primal feasible while the second one is dual feasible for the original problem. Specifically, we use a three-phase-implementation. The first two phases construct the required primal and dual feasible solutions, using the Primal Simplex algorithm. Finally, in the third phase the Primal - Dual algorithm is applied. Moreover, a computational study has been carried out, using randomly generated sparse optimal linear problems, to compare its computational efficiency with the Primal Simplex algorithm and also with MATLAB's Interior Point Method implementation. The algorithm appears to be very promising since it clearly shows its superiority to the Primal Simplex algorithm as well as its robustness over the IPM algorithm.
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.)
Dhage Iteration Method for Generalized Quadratic Functional Integral Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-01-01
Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.
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.
Indian Academy of Sciences (India)
ticians but also forms the foundation of computer science. Two ... with methods of developing algorithms for solving a variety of problems but ... applications of computers in science and engineer- ... numerical calculus are as important. We will ...
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...
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.)
Applying genetic algorithms for programming manufactoring cell tasks
Directory of Open Access Journals (Sweden)
Efredy Delgado
2005-05-01
Full Text Available This work was aimed for developing computational intelligence for scheduling a manufacturing cell's tasks, based manily on genetic algorithms. The manufacturing cell was modelled as beign a production-line; the makespan was calculated by using heuristics adapted from several libraries for genetic algorithms computed in C++ builder. Several problems dealing with small, medium and large list of jobs and machinery were resolved. The results were compared with other heuristics. The approach developed here would seem to be promising for future research concerning scheduling manufacturing cell tasks involving mixed batches.
A Stereo Dual-Channel Dynamic Programming Algorithm for UAV Image Stitching.
Li, Ming; Chen, Ruizhi; Zhang, Weilong; Li, Deren; Liao, Xuan; Wang, Lei; Pan, Yuanjin; Zhang, Peng
2017-09-08
Dislocation is one of the major challenges in unmanned aerial vehicle (UAV) image stitching. In this paper, we propose a new algorithm for seamlessly stitching UAV images based on a dynamic programming approach. Our solution consists of two steps: Firstly, an image matching algorithm is used to correct the images so that they are in the same coordinate system. Secondly, a new dynamic programming algorithm is developed based on the concept of a stereo dual-channel energy accumulation. A new energy aggregation and traversal strategy is adopted in our solution, which can find a more optimal seam line for image stitching. Our algorithm overcomes the theoretical limitation of the classical Duplaquet algorithm. Experiments show that the algorithm can effectively solve the dislocation problem in UAV image stitching, especially for the cases in dense urban areas. Our solution is also direction-independent, which has better adaptability and robustness for stitching images.
RSA Algorithm. Features of the C # Object Programming Implementation
Directory of Open Access Journals (Sweden)
Elena V. Staver
2012-08-01
Full Text Available Public-key algorithms depend on the encryption key and the decoding key, connected with the first one. For data public key encryption, the text is divided into blocks, each of which is represented as a number. To decrypt the message a secret key is used.
DEFF Research Database (Denmark)
Rong, Aiying; Hakonen, Henri; Lahdelma, Risto
2008-01-01
introduce in this paper the DP-RSC1 algorithm, which is a variant of the dynamic programming (DP) algorithm based on linear relaxation of the ON/OFF states of the units and sequential commitment of units one by one. The time complexity of DP-RSC1 is proportional to the number of generating units...
A DEEP CUT ELLIPSOID ALGORITHM FOR CONVEX-PROGRAMMING - THEORY AND APPLICATIONS
FRENK, JBG; GROMICHO, J; ZHANG, S
1994-01-01
This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent
Universal algorithms and programs for calculating the motion parameters in the two-body problem
Bakhshiyan, B. T.; Sukhanov, A. A.
1979-01-01
The algorithms and FORTRAN programs for computing positions and velocities, orbital elements and first and second partial derivatives in the two-body problem are presented. The algorithms are applicable for any value of eccentricity and are convenient for computing various navigation parameters.
Testing Algorithmic Skills in Traditional and Non-Traditional Programming Environments
Csernoch, Mária; Biró, Piroska; Máth, János; Abari, Kálmán
2015-01-01
The Testing Algorithmic and Application Skills (TAaAS) project was launched in the 2011/2012 academic year to test first year students of Informatics, focusing on their algorithmic skills in traditional and non-traditional programming environments, and on the transference of their knowledge of Informatics from secondary to tertiary education. The…
A Deep Cut Ellipsoid Algorithm for convex Programming: theory and Applications
Frenk, J.B.G.; Gromicho Dos Santos, J.A.; Zhang, S.
1994-01-01
This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent
A deep cut ellipsoid algorithm for convex programming : Theory and applications
J.B.G. Frenk (Hans); J.A.S. Gromicho (Joaquim); S. Zhang (Shuzhong)
1994-01-01
textabstractThis paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules
Algorithms and programs for processing of satellite data on ozone layer and UV radiation levels
International Nuclear Information System (INIS)
Borkovskij, N.B.; Ivanyukovich, V.A.
2012-01-01
Some algorithms and programs for automatic retrieving and processing ozone layer satellite data are discussed. These techniques are used for reliable short-term UV-radiation levels forecasting. (authors)
The Application Programming Interface (API) for Uncertainty Analysis, Sensitivity Analysis, and Parameter Estimation (UA/SA/PE API) tool development, here fore referred to as the Calibration, Optimization, and Sensitivity and Uncertainty Algorithms API (COSU-API), was initially d...
Indian Academy of Sciences (India)
algorithm that it is implicitly understood that we know how to generate the next natural ..... Explicit comparisons are made in line (1) where maximum and minimum is ... It can be shown that the function T(n) = 3/2n -2 is the solution to the above ...
Improved dynamic-programming-based algorithms for segmentation of masses in mammograms
International Nuclear Information System (INIS)
Dominguez, Alfonso Rojas; Nandi, Asoke K.
2007-01-01
In this paper, two new boundary tracing algorithms for segmentation of breast masses are presented. These new algorithms are based on the dynamic programming-based boundary tracing (DPBT) algorithm proposed in Timp and Karssemeijer, [S. Timp and N. Karssemeijer, Med. Phys. 31, 958-971 (2004)] The DPBT algorithm contains two main steps: (1) construction of a local cost function, and (2) application of dynamic programming to the selection of the optimal boundary based on the local cost function. The validity of some assumptions used in the design of the DPBT algorithm is tested in this paper using a set of 349 mammographic images. Based on the results of the tests, modifications to the computation of the local cost function have been designed and have resulted in the Improved-DPBT (IDPBT) algorithm. A procedure for the dynamic selection of the strength of the components of the local cost function is presented that makes these parameters independent of the image dataset. Incorporation of this dynamic selection procedure has produced another new algorithm which we have called ID 2 PBT. Methods for the determination of some other parameters of the DPBT algorithm that were not covered in the original paper are presented as well. The merits of the new IDPBT and ID 2 PBT algorithms are demonstrated experimentally by comparison against the DPBT algorithm. The segmentation results are evaluated with base on the area overlap measure and other segmentation metrics. Both of the new algorithms outperform the original DPBT; the improvements in the algorithms performance are more noticeable around the values of the segmentation metrics corresponding to the highest segmentation accuracy, i.e., the new algorithms produce more optimally segmented regions, rather than a pronounced increase in the average quality of all the segmented regions
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025
On Quadratic Variation of Martingales
Indian Academy of Sciences (India)
where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025
Orthogonality preserving infinite dimensional quadratic stochastic operators
International Nuclear Information System (INIS)
Akın, Hasan; Mukhamedov, Farrukh
2015-01-01
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators
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
DE and NLP Based QPLS Algorithm
Yu, Xiaodong; Huang, Dexian; Wang, Xiong; Liu, Bo
As a novel evolutionary computing technique, Differential Evolution (DE) has been considered to be an effective optimization method for complex optimization problems, and achieved many successful applications in engineering. In this paper, a new algorithm of Quadratic Partial Least Squares (QPLS) based on Nonlinear Programming (NLP) is presented. And DE is used to solve the NLP so as to calculate the optimal input weights and the parameters of inner relationship. The simulation results based on the soft measurement of diesel oil solidifying point on a real crude distillation unit demonstrate that the superiority of the proposed algorithm to linear PLS and QPLS which is based on Sequential Quadratic Programming (SQP) in terms of fitting accuracy and computational costs.
Optimal Control of Complex Systems Based on Improved Dual Heuristic Dynamic Programming Algorithm
Directory of Open Access Journals (Sweden)
Hui Li
2017-01-01
Full Text Available When applied to solving the data modeling and optimal control problems of complex systems, the dual heuristic dynamic programming (DHP technique, which is based on the BP neural network algorithm (BP-DHP, has difficulty in prediction accuracy, slow convergence speed, poor stability, and so forth. In this paper, a dual DHP technique based on Extreme Learning Machine (ELM algorithm (ELM-DHP was proposed. Through constructing three kinds of network structures, the paper gives the detailed realization process of the DHP technique in the ELM. The controller designed upon the ELM-DHP algorithm controlled a molecular distillation system with complex features, such as multivariability, strong coupling, and nonlinearity. Finally, the effectiveness of the algorithm is verified by the simulation that compares DHP and HDP algorithms based on ELM and BP neural network. The algorithm can also be applied to solve the data modeling and optimal control problems of similar complex systems.
Programming Deep Brain Stimulation for Parkinson's Disease: The Toronto Western Hospital Algorithms.
Picillo, Marina; Lozano, Andres M; Kou, Nancy; Puppi Munhoz, Renato; Fasano, Alfonso
2016-01-01
Deep brain stimulation (DBS) is an established and effective treatment for Parkinson's disease (PD). After surgery, a number of extensive programming sessions are performed to define the most optimal stimulation parameters. Programming sessions mainly rely only on neurologist's experience. As a result, patients often undergo inconsistent and inefficient stimulation changes, as well as unnecessary visits. We reviewed the literature on initial and follow-up DBS programming procedures and integrated our current practice at Toronto Western Hospital (TWH) to develop standardized DBS programming protocols. We propose four algorithms including the initial programming and specific algorithms tailored to symptoms experienced by patients following DBS: speech disturbances, stimulation-induced dyskinesia and gait impairment. We conducted a literature search of PubMed from inception to July 2014 with the keywords "deep brain stimulation", "festination", "freezing", "initial programming", "Parkinson's disease", "postural instability", "speech disturbances", and "stimulation induced dyskinesia". Seventy papers were considered for this review. Based on the literature review and our experience at TWH, we refined four algorithms for: (1) the initial programming stage, and management of symptoms following DBS, particularly addressing (2) speech disturbances, (3) stimulation-induced dyskinesia, and (4) gait impairment. We propose four algorithms tailored to an individualized approach to managing symptoms associated with DBS and disease progression in patients with PD. We encourage established as well as new DBS centers to test the clinical usefulness of these algorithms in supplementing the current standards of care. Copyright © 2016 Elsevier Inc. All rights reserved.
A Dynamic Programming Algorithm for the k-Haplotyping Problem
Institute of Scientific and Technical Information of China (English)
Zhen-ping Li; Ling-yun Wu; Yu-ying Zhao; Xiang-sun Zhang
2006-01-01
The Minimum Fragments Removal (MFR) problem is one of the haplotyping problems: given a set of fragments, remove the minimum number of fragments so that the resulting fragments can be partitioned into k classes of non-conflicting subsets. In this paper, we formulate the k-MFR problem as an integer linear programming problem, and develop a dynamic programming approach to solve the k-MFR problem for both the gapless and gap cases.
Exploration Of Deep Learning Algorithms Using Openacc Parallel Programming Model
Hamam, Alwaleed A.
2017-03-13
Deep learning is based on a set of algorithms that attempt to model high level abstractions in data. Specifically, RBM is a deep learning algorithm that used in the project to increase it\\'s time performance using some efficient parallel implementation by OpenACC tool with best possible optimizations on RBM to harness the massively parallel power of NVIDIA GPUs. GPUs development in the last few years has contributed to growing the concept of deep learning. OpenACC is a directive based ap-proach for computing where directives provide compiler hints to accelerate code. The traditional Restricted Boltzmann Ma-chine is a stochastic neural network that essentially perform a binary version of factor analysis. RBM is a useful neural net-work basis for larger modern deep learning model, such as Deep Belief Network. RBM parameters are estimated using an efficient training method that called Contrastive Divergence. Parallel implementation of RBM is available using different models such as OpenMP, and CUDA. But this project has been the first attempt to apply OpenACC model on RBM.
Exploration Of Deep Learning Algorithms Using Openacc Parallel Programming Model
Hamam, Alwaleed A.; Khan, Ayaz H.
2017-01-01
Deep learning is based on a set of algorithms that attempt to model high level abstractions in data. Specifically, RBM is a deep learning algorithm that used in the project to increase it's time performance using some efficient parallel implementation by OpenACC tool with best possible optimizations on RBM to harness the massively parallel power of NVIDIA GPUs. GPUs development in the last few years has contributed to growing the concept of deep learning. OpenACC is a directive based ap-proach for computing where directives provide compiler hints to accelerate code. The traditional Restricted Boltzmann Ma-chine is a stochastic neural network that essentially perform a binary version of factor analysis. RBM is a useful neural net-work basis for larger modern deep learning model, such as Deep Belief Network. RBM parameters are estimated using an efficient training method that called Contrastive Divergence. Parallel implementation of RBM is available using different models such as OpenMP, and CUDA. But this project has been the first attempt to apply OpenACC model on RBM.
Implementing embedded artificial intelligence rules within algorithmic programming languages
Feyock, Stefan
1988-01-01
Most integrations of artificial intelligence (AI) capabilities with non-AI (usually FORTRAN-based) application programs require the latter to execute separately to run as a subprogram or, at best, as a coroutine, of the AI system. In many cases, this organization is unacceptable; instead, the requirement is for an AI facility that runs in embedded mode; i.e., is called as subprogram by the application program. The design and implementation of a Prolog-based AI capability that can be invoked in embedded mode are described. The significance of this system is twofold: Provision of Prolog-based symbol-manipulation and deduction facilities makes a powerful symbolic reasoning mechanism available to applications programs written in non-AI languages. The power of the deductive and non-procedural descriptive capabilities of Prolog, which allow the user to describe the problem to be solved, rather than the solution, is to a large extent vitiated by the absence of the standard control structures provided by other languages. Embedding invocations of Prolog rule bases in programs written in non-AI languages makes it possible to put Prolog calls inside DO loops and similar control constructs. The resulting merger of non-AI and AI languages thus results in a symbiotic system in which the advantages of both programming systems are retained, and their deficiencies largely remedied.
Indian Academy of Sciences (India)
of programs, illustrate a method of establishing the ... importance of methods of establishing the correctness of .... Thus, the proof will be different for each input ..... Formal methods are pivotal in the design, development, and maintenance of ...
Z-Q. Luo; J.F. Sturm; S. Zhang (Shuzhong)
1996-01-01
textabstractThis paper establishes the superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming under the assumptions that the semidefinite program has a strictly complementary primal-dual optimal solution and that the size of the central path
Förster, Michael
2014-01-01
Numerical programs often use parallel programming techniques such as OpenMP to compute the program's output values as efficient as possible. In addition, derivative values of these output values with respect to certain input values play a crucial role. To achieve code that computes not only the output values simultaneously but also the derivative values, this work introduces several source-to-source transformation rules. These rules are based on a technique called algorithmic differentiation. The main focus of this work lies on the important reverse mode of algorithmic differentiation. The inh
Moore, J H
1995-06-01
A genetic algorithm for instrumentation control and optimization was developed using the LabVIEW graphical programming environment. The usefulness of this methodology for the optimization of a closed loop control instrument is demonstrated with minimal complexity and the programming is presented in detail to facilitate its adaptation to other LabVIEW applications. Closed loop control instruments have variety of applications in the biomedical sciences including the regulation of physiological processes such as blood pressure. The program presented here should provide a useful starting point for those wishing to incorporate genetic algorithm approaches to LabVIEW mediated optimization of closed loop control instruments.
Linear Quadratic Controller with Fault Detection in Compact Disk Players
DEFF Research Database (Denmark)
Vidal, Enrique Sanchez; Hansen, K.G.; Andersen, R.S.
2001-01-01
The design of the positioning controllers in Optical Disk Drives are today subjected to a trade off between an acceptable suppression of external disturbances and an acceptable immunity against surfaces defects. In this paper an algorithm is suggested to detect defects of the disk surface combined...... with an observer and a Linear Quadratic Regulator. As a result, the mentioned trade off is minimized and the playability of the tested compact disk player is considerably enhanced....
A Note on 5-bit Quadratic Permutations’ Classification
Božilov, Dušan; Bilgin, Begül; Sahin, Hacı Ali
2017-01-01
Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees of their inverses, together with multiplicative complexity and existence of uniform threshold reali...
Adaptive Dynamic Programming for Control Algorithms and Stability
Zhang, Huaguang; Luo, Yanhong; Wang, Ding
2013-01-01
There are many methods of stable controller design for nonlinear systems. In seeking to go beyond the minimum requirement of stability, Adaptive Dynamic Programming for Control approaches the challenging topic of optimal control for nonlinear systems using the tools of adaptive dynamic programming (ADP). The range of systems treated is extensive; affine, switched, singularly perturbed and time-delay nonlinear systems are discussed as are the uses of neural networks and techniques of value and policy iteration. The text features three main aspects of ADP in which the methods proposed for stabilization and for tracking and games benefit from the incorporation of optimal control methods: • infinite-horizon control for which the difficulty of solving partial differential Hamilton–Jacobi–Bellman equations directly is overcome, and proof provided that the iterative value function updating sequence converges to the infimum of all the value functions obtained by admissible control law sequences; • finite-...
Geometric Semantic Genetic Programming Algorithm and Slump Prediction
Xu, Juncai; Shen, Zhenzhong; Ren, Qingwen; Xie, Xin; Yang, Zhengyu
2017-01-01
Research on the performance of recycled concrete as building material in the current world is an important subject. Given the complex composition of recycled concrete, conventional methods for forecasting slump scarcely obtain satisfactory results. Based on theory of nonlinear prediction method, we propose a recycled concrete slump prediction model based on geometric semantic genetic programming (GSGP) and combined it with recycled concrete features. Tests show that the model can accurately p...
Coherent states for quadratic Hamiltonians
International Nuclear Information System (INIS)
Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes
2011-01-01
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...
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
Nagy, Ivan
2017-01-01
This book provides a general theoretical background for constructing the recursive Bayesian estimation algorithms for mixture models. It collects the recursive algorithms for estimating dynamic mixtures of various distributions and brings them in the unified form, providing a scheme for constructing the estimation algorithm for a mixture of components modeled by distributions with reproducible statistics. It offers the recursive estimation of dynamic mixtures, which are free of iterative processes and close to analytical solutions as much as possible. In addition, these methods can be used online and simultaneously perform learning, which improves their efficiency during estimation. The book includes detailed program codes for solving the presented theoretical tasks. Codes are implemented in the open source platform for engineering computations. The program codes given serve to illustrate the theory and demonstrate the work of the included algorithms.
A chaos-based evolutionary algorithm for general nonlinear programming problems
International Nuclear Information System (INIS)
El-Shorbagy, M.A.; Mousa, A.A.; Nasr, S.M.
2016-01-01
In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs.
Maze solving algorithm and its programs using Z-80 assembler language for a robot
Energy Technology Data Exchange (ETDEWEB)
Takeno, J; Mukaidono, M
1982-01-01
In the first part the formation of a maze problem is introduced and the outline of this algorithm to solve a maze is explained in the second part. The third part describes the detail of this program, and the final part shows the program which has been developed using Z-80 assembler language. This program has portability for other robots using Z-80 microprocessors. 7 references.
Hosfelt, Diane Duros
2015-01-01
Threats from the internet, particularly malicious software (i.e., malware) often use cryptographic algorithms to disguise their actions and even to take control of a victim's system (as in the case of ransomware). Malware and other threats proliferate too quickly for the time-consuming traditional methods of binary analysis to be effective. By automating detection and classification of cryptographic algorithms, we can speed program analysis and more efficiently combat malware. This thesis wil...
A linear programming algorithm to test for jamming in hard-sphere packings
International Nuclear Information System (INIS)
Donev, Aleksandar; Torquato, Salvatore.; Stillinger, Frank H.; Connelly, Robert
2004-01-01
Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B 105 (2001)], a classification scheme of jammed packings into hierarchical categories of locally, collectively and strictly jammed configurations has been proposed. They suggest that these jamming categories can be tested using numerical algorithms that analyze an equivalent contact network of the packing under applied displacements, but leave the design of such algorithms as a future task. In this work, we present a rigorous and practical algorithm to assess whether an ideal hard-sphere packing in two or three dimensions is jammed according to the aforementioned categories. The algorithm is based on linear programming and is applicable to regular as well as random packings of finite size with hard-wall and periodic boundary conditions. If the packing is not jammed, the algorithm yields representative multi-particle unjamming motions. Furthermore, we extend the jamming categories and the testing algorithm to packings with significant interparticle gaps. We describe in detail two variants of the proposed randomized linear programming approach to test for jamming in hard-sphere packings. The first algorithm treats ideal packings in which particles form perfect contacts. Another algorithm treats the case of jamming in packings with significant interparticle gaps. This extended algorithm allows one to explore more fully the nature of the feasible particle displacements. We have implemented the algorithms and applied them to ordered as well as random packings of circular disks and spheres with periodic boundary conditions. Some representative results for large disordered disk and sphere packings are given, but more robust and efficient implementations as well as further applications (e.g., non-spherical particles) are anticipated for the future
AbouEisha, Hassan M.; Moshkov, Mikhail; Calo, Victor M.; Paszynski, Maciej; Goik, Damian; Jopek, Konrad
2014-01-01
In this paper we present a dynamic programming algorithm for finding optimal elimination trees for computational grids refined towards point or edge singularities. The elimination tree is utilized to guide the multi-frontal direct solver algorithm
A Branch-and-Bound Algorithm Embedded with DCA for DC Programming
Directory of Open Access Journals (Sweden)
Meihua Wang
2012-01-01
Full Text Available The special importance of Difference of Convex (DC functions programming has been recognized in recent studies on nonconvex optimization problems. In this work, a class of DC programming derived from the portfolio selection problems is studied. The most popular method applied to solve the problem is the Branch-and-Bound (B&B algorithm. However, “the curse of dimensionality” will affect the performance of the B&B algorithm. DC Algorithm (DCA is an efficient method to get a local optimal solution. It has been applied to many practical problems, especially for large-scale problems. A B&B-DCA algorithm is proposed by embedding DCA into the B&B algorithms, the new algorithm improves the computational performance and obtains a global optimal solution. Computational results show that the proposed B&B-DCA algorithm has the superiority of the branch number and computational time than general B&B. The nice features of DCA (inexpensiveness, reliability, robustness, globality of computed solutions, etc. provide crucial support to the combined B&B-DCA for accelerating the convergence of B&B.
A backtracking algorithm for the stream AND-parallel execution of logic programs
Energy Technology Data Exchange (ETDEWEB)
Somogyi, Z.; Ramamohanarao, K.; Vaghani, J. (Univ. of Melbourne, Parkville (Australia))
1988-06-01
The authors present the first backtracking algorithm for stream AND-parallel logic programs. It relies on compile-time knowledge of the data flow graph of each clause to let it figure out efficiently which goals to kill or restart when a goal fails. This crucial information, which they derive from mode declarations, was not available at compile-time in any previous stream AND-parallel system. They show that modes can increase the precision of the backtracking algorithm, though their algorithm allows this precision to be traded off against overhead on a procedure-by-procedure and call-by-call basis. The modes also allow their algorithm to handle efficiently programs that manipulate partially instantiated data structures and an important class of programs with circular dependency graphs. On code that does not need backtracking, the efficiency of their algorithm approaches that of the committed-choice languages; on code that does need backtracking its overhead is comparable to that of the independent AND-parallel backtracking algorithms.
Quadratic reactivity fuel cycle model
International Nuclear Information System (INIS)
Lewins, J.D.
1985-01-01
For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper
Development and validation of an online interactive, multimedia wound care algorithms program.
Beitz, Janice M; van Rijswijk, Lia
2012-01-01
To provide education based on evidence-based and validated wound care algorithms we designed and implemented an interactive, Web-based learning program for teaching wound care. A mixed methods quantitative pilot study design with qualitative components was used to test and ascertain the ease of use, validity, and reliability of the online program. A convenience sample of 56 RN wound experts (formally educated, certified in wound care, or both) participated. The interactive, online program consists of a user introduction, interactive assessment of 15 acute and chronic wound photos, user feedback about the percentage correct, partially correct, or incorrect algorithm and dressing choices and a user survey. After giving consent, participants accessed the online program, provided answers to the demographic survey, and completed the assessment module and photographic test, along with a posttest survey. The construct validity of the online interactive program was strong. Eighty-five percent (85%) of algorithm and 87% of dressing choices were fully correct even though some programming design issues were identified. Online study results were consistently better than previously conducted comparable paper-pencil study results. Using a 5-point Likert-type scale, participants rated the program's value and ease of use as 3.88 (valuable to very valuable) and 3.97 (easy to very easy), respectively. Similarly the research process was described qualitatively as "enjoyable" and "exciting." This digital program was well received indicating its "perceived benefits" for nonexpert users, which may help reduce barriers to implementing safe, evidence-based care. Ongoing research using larger sample sizes may help refine the program or algorithms while identifying clinician educational needs. Initial design imperfections and programming problems identified also underscored the importance of testing all paper and Web-based programs designed to educate health care professionals or guide
Optimized programming algorithm for cylindrical and directional deep brain stimulation electrodes.
Anderson, Daria Nesterovich; Osting, Braxton; Vorwerk, Johannes; Dorval, Alan D; Butson, Christopher R
2018-04-01
Deep brain stimulation (DBS) is a growing treatment option for movement and psychiatric disorders. As DBS technology moves toward directional leads with increased numbers of smaller electrode contacts, trial-and-error methods of manual DBS programming are becoming too time-consuming for clinical feasibility. We propose an algorithm to automate DBS programming in near real-time for a wide range of DBS lead designs. Magnetic resonance imaging and diffusion tensor imaging are used to build finite element models that include anisotropic conductivity. The algorithm maximizes activation of target tissue and utilizes the Hessian matrix of the electric potential to approximate activation of neurons in all directions. We demonstrate our algorithm's ability in an example programming case that targets the subthalamic nucleus (STN) for the treatment of Parkinson's disease for three lead designs: the Medtronic 3389 (four cylindrical contacts), the direct STNAcute (two cylindrical contacts, six directional contacts), and the Medtronic-Sapiens lead (40 directional contacts). The optimization algorithm returns patient-specific contact configurations in near real-time-less than 10 s for even the most complex leads. When the lead was placed centrally in the target STN, the directional leads were able to activate over 50% of the region, whereas the Medtronic 3389 could activate only 40%. When the lead was placed 2 mm lateral to the target, the directional leads performed as well as they did in the central position, but the Medtronic 3389 activated only 2.9% of the STN. This DBS programming algorithm can be applied to cylindrical electrodes as well as novel directional leads that are too complex with modern technology to be manually programmed. This algorithm may reduce clinical programming time and encourage the use of directional leads, since they activate a larger volume of the target area than cylindrical electrodes in central and off-target lead placements.
Directory of Open Access Journals (Sweden)
Daniil S. Chivilikhin
2014-11-01
Full Text Available The procedure of testing traditionally used in software engineering cannot guarantee program correctness; therefore verification is used at the excess requirements to programs reliability. Verification makes it possible to check certain properties of programs in all possible computational states; however, this process is very complex. In the model checking method a model of the program is built (often, manually and requirements in terms of temporal logic are formulated. Such temporal properties of the model can be checked automatically. The main issue in this framework is the gap between the program and its model. Automata-based programming paradigm gives the possibility to overcome this limitation. In this paradigm, program logic is represented using finite-state machines. The advantage of finite-state machines is that their models can be constructed automatically. The paper deals with the application of mutation-based ant colony optimization algorithm to the problem of finite-state machine construction from their specification, defined by test scenarios and temporal properties. The presented approach has been tested on the elevator doors control problem as well as on randomly generated data. Obtained results show the ant colony algorithm is two-three times faster than the previously used genetic algorithm. The proposed approach can be recommended for inferring control programs for critical systems.
Programming Deep Brain Stimulation for Tremor and Dystonia: The Toronto Western Hospital Algorithms.
Picillo, Marina; Lozano, Andres M; Kou, Nancy; Munhoz, Renato Puppi; Fasano, Alfonso
2016-01-01
Deep brain stimulation (DBS) is an effective treatment for essential tremor (ET) and dystonia. After surgery, a number of extensive programming sessions are performed, mainly relying on neurologist's personal experience as no programming guidelines have been provided so far, with the exception of recommendations provided by groups of experts. Finally, fewer information is available for the management of DBS in ET and dystonia compared with Parkinson's disease. Our aim is to review the literature on initial and follow-up DBS programming procedures for ET and dystonia and integrate the results with our current practice at Toronto Western Hospital (TWH) to develop standardized DBS programming protocols. We conducted a literature search of PubMed from inception to July 2014 with the keywords "balance", "bradykinesia", "deep brain stimulation", "dysarthria", "dystonia", "gait disturbances", "initial programming", "loss of benefit", "micrographia", "speech", "speech difficulties" and "tremor". Seventy-six papers were considered for this review. Based on the literature review and our experience at TWH, we refined three algorithms for management of ET, including: (1) initial programming, (2) management of balance and speech issues and (3) loss of stimulation benefit. We also depicted algorithms for the management of dystonia, including: (1) initial programming and (2) management of stimulation-induced hypokinesia (shuffling gait, micrographia and speech impairment). We propose five algorithms tailored to an individualized approach to managing ET and dystonia patients with DBS. We encourage the application of these algorithms to supplement current standards of care in established as well as new DBS centers to test the clinical usefulness of these algorithms in supplementing the current standards of care. Copyright © 2016 Elsevier Inc. All rights reserved.
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.
Nuclear power reactor analysis, methods, algorithms and computer programs
International Nuclear Information System (INIS)
Matausek, M.V
1981-01-01
Full text: For a developing country buying its first nuclear power plants from a foreign supplier, disregarding the type and scope of the contract, there is a certain number of activities which have to be performed by local stuff and domestic organizations. This particularly applies to the choice of the nuclear fuel cycle strategy and the choice of the type and size of the reactors, to bid parameters specification, bid evaluation and final safety analysis report evaluation, as well as to in-core fuel management activities. In the Nuclear Engineering Department of the Boris Kidric Institute of Nuclear Sciences (NET IBK) the continual work is going on, related to the following topics: cross section and resonance integral calculations, spectrum calculations, generation of group constants, lattice and cell problems, criticality and global power distribution search, fuel burnup analysis, in-core fuel management procedures, cost analysis and power plant economics, safety and accident analysis, shielding problems and environmental impact studies, etc. The present paper gives the details of the methods developed and the results achieved, with the particular emphasis on the NET IBK computer program package for the needs of planning, construction and operation of nuclear power plants. The main problems encountered so far were related to small working team, lack of large and powerful computers, absence of reliable basic nuclear data and shortage of experimental and empirical results for testing theoretical models. Some of these difficulties have been overcome thanks to bilateral and multilateral cooperation with developed countries, mostly through IAEA. It is the authors opinion, however, that mutual cooperation of developing countries, having similar problems and similar goals, could lead to significant results. Some activities of this kind are suggested and discussed. (author)
Algorithms and programming tools for image processing on the MPP:3
Reeves, Anthony P.
1987-01-01
This is the third and final report on the work done for NASA Grant 5-403 on Algorithms and Programming Tools for Image Processing on the MPP:3. All the work done for this grant is summarized in the introduction. Work done since August 1986 is reported in detail. Research for this grant falls under the following headings: (1) fundamental algorithms for the MPP; (2) programming utilities for the MPP; (3) the Parallel Pascal Development System; and (4) performance analysis. In this report, the results of two efforts are reported: region growing, and performance analysis of important characteristic algorithms. In each case, timing results from MPP implementations are included. A paper is included in which parallel algorithms for region growing on the MPP is discussed. These algorithms permit different sized regions to be merged in parallel. Details on the implementation and peformance of several important MPP algorithms are given. These include a number of standard permutations, the FFT, convolution, arbitrary data mappings, image warping, and pyramid operations, all of which have been implemented on the MPP. The permutation and image warping functions have been included in the standard development system library.
Quadratically convergent MCSCF scheme using Fock operators
International Nuclear Information System (INIS)
Das, G.
1981-01-01
A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations
Geometrical and Graphical Solutions of Quadratic Equations.
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Quadratic Lagrangians and Legendre transformation
International Nuclear Information System (INIS)
Magnano, G.
1988-01-01
In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor
Parallelizing Gene Expression Programming Algorithm in Enabling Large-Scale Classification
Directory of Open Access Journals (Sweden)
Lixiong Xu
2017-01-01
Full Text Available As one of the most effective function mining algorithms, Gene Expression Programming (GEP algorithm has been widely used in classification, pattern recognition, prediction, and other research fields. Based on the self-evolution, GEP is able to mine an optimal function for dealing with further complicated tasks. However, in big data researches, GEP encounters low efficiency issue due to its long time mining processes. To improve the efficiency of GEP in big data researches especially for processing large-scale classification tasks, this paper presents a parallelized GEP algorithm using MapReduce computing model. The experimental results show that the presented algorithm is scalable and efficient for processing large-scale classification tasks.
Algorithm Building and Learning Programming Languages Using a New Educational Paradigm
Jain, Anshul K.; Singhal, Manik; Gupta, Manu Sheel
2011-08-01
This research paper presents a new concept of using a single tool to associate syntax of various programming languages, algorithms and basic coding techniques. A simple framework has been programmed in Python that helps students learn skills to develop algorithms, and implement them in various programming languages. The tool provides an innovative and a unified graphical user interface for development of multimedia objects, educational games and applications. It also aids collaborative learning amongst students and teachers through an integrated mechanism based on Remote Procedure Calls. The paper also elucidates an innovative method for code generation to enable students to learn the basics of programming languages using drag-n-drop methods for image objects.
Energy Technology Data Exchange (ETDEWEB)
Kim, Jung Min; Kim, Dae Sup; Hong, Dong Ki; Back, Geum Mun; Kwak, Jung Won [Dept. of Radiation Oncology, , Seoul (Korea, Republic of)
2012-03-15
There was a problem with using MU verification programs for the reasons that there were errors of MU when using MU verification programs based on Pencil Beam Convolution (PBC) Algorithm with radiation treatment plans around lung using Analytical Anisotropic Algorithm (AAA). On this study, we studied the methods that can verify the calculated treatment plans using AAA. Using Eclipse treatment planning system (Version 8.9, Varian, USA), for each 57 fields of 7 cases of Lung Stereotactic Body Radiation Therapy (SBRT), we have calculated using PBC and AAA with dose calculation algorithm. By developing MU of established plans, we compared and analyzed with MU of manual calculation programs. We have analyzed relationship between errors and 4 variables such as field size, lung path distance of radiation, Tumor path distance of radiation, effective depth that can affect on errors created from PBC algorithm and AAA using commonly used programs. Errors of PBC algorithm have showned 0.2{+-}1.0% and errors of AAA have showned 3.5{+-}2.8%. Moreover, as a result of analyzing 4 variables that can affect on errors, relationship in errors between lung path distance and MU, connection coefficient 0.648 (P=0.000) has been increased and we could calculate MU correction factor that is A.E=L.P 0.00903+0.02048 and as a result of replying for manual calculation program, errors of 3.5{+-}2.8% before the application has been decreased within 0.4{+-}2.0%. On this study, we have learned that errors from manual calculation program have been increased as lung path distance of radiation increases and we could verified MU of AAA with a simple method that is called MU correction factor.
International Nuclear Information System (INIS)
Kim, Jung Min; Kim, Dae Sup; Hong, Dong Ki; Back, Geum Mun; Kwak, Jung Won
2012-01-01
There was a problem with using MU verification programs for the reasons that there were errors of MU when using MU verification programs based on Pencil Beam Convolution (PBC) Algorithm with radiation treatment plans around lung using Analytical Anisotropic Algorithm (AAA). On this study, we studied the methods that can verify the calculated treatment plans using AAA. Using Eclipse treatment planning system (Version 8.9, Varian, USA), for each 57 fields of 7 cases of Lung Stereotactic Body Radiation Therapy (SBRT), we have calculated using PBC and AAA with dose calculation algorithm. By developing MU of established plans, we compared and analyzed with MU of manual calculation programs. We have analyzed relationship between errors and 4 variables such as field size, lung path distance of radiation, Tumor path distance of radiation, effective depth that can affect on errors created from PBC algorithm and AAA using commonly used programs. Errors of PBC algorithm have showned 0.2±1.0% and errors of AAA have showned 3.5±2.8%. Moreover, as a result of analyzing 4 variables that can affect on errors, relationship in errors between lung path distance and MU, connection coefficient 0.648 (P=0.000) has been increased and we could calculate MU correction factor that is A.E=L.P 0.00903+0.02048 and as a result of replying for manual calculation program, errors of 3.5±2.8% before the application has been decreased within 0.4±2.0%. On this study, we have learned that errors from manual calculation program have been increased as lung path distance of radiation increases and we could verified MU of AAA with a simple method that is called MU correction factor.
Theoretical and algorithmic advances in multi-parametric programming and control
Pistikopoulos, Efstratios N.; Dominguez, Luis; Panos, Christos; Kouramas, Konstantinos; Chinchuluun, Altannar
2012-01-01
This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system. © 2012 Springer-Verlag.
Theoretical and algorithmic advances in multi-parametric programming and control
Pistikopoulos, Efstratios N.
2012-04-21
This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system. © 2012 Springer-Verlag.
International Nuclear Information System (INIS)
Stefaniak, B.
2002-01-01
As described earlier, a dedicated computer program was developed for quantitative evaluation of regional lung perfusion defects, visualized by pulmonary scintigraphy. The correctness of the basic assumptions accepted to construct the algorithms and of the all program functions needed to be checked, before application of the program into the clinical routine. The aim of this study was to verified the program using various software instruments and physical models. Evaluation of the proposed method was performed using software procedures, physical lung phantom, and selected lung image.The reproducibility of lung regions, defined by the program was found excellent. No significant distortion of registered data was observed after ROI transformation into the circle and retransformation into the original shape. The obtained results comprised parametric presentation of activity defects as well as a set of numerical indices which defined extent and intensity of decreased counts density. Among these indices PD2 and DM* were proved the most suitable for the above purposes. The obtained results indicate that the algorithms used for the program construction were correct and suitable for the aim of the study. The above algorithms enable function under study to be presented graphically with true imaging of activity distribution, as well as numerical indices, defining extent and intensity of activity defects to calculated. (author)
Quadratic independence of coordinate functions of certain ...
Indian Academy of Sciences (India)
... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.
Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...
African Journals Online (AJOL)
Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...
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
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...
A multithreaded parallel implementation of a dynamic programming algorithm for sequence comparison.
Martins, W S; Del Cuvillo, J B; Useche, F J; Theobald, K B; Gao, G R
2001-01-01
This paper discusses the issues involved in implementing a dynamic programming algorithm for biological sequence comparison on a general-purpose parallel computing platform based on a fine-grain event-driven multithreaded program execution model. Fine-grain multithreading permits efficient parallelism exploitation in this application both by taking advantage of asynchronous point-to-point synchronizations and communication with low overheads and by effectively tolerating latency through the overlapping of computation and communication. We have implemented our scheme on EARTH, a fine-grain event-driven multithreaded execution and architecture model which has been ported to a number of parallel machines with off-the-shelf processors. Our experimental results show that the dynamic programming algorithm can be efficiently implemented on EARTH systems with high performance (e.g., speedup of 90 on 120 nodes), good programmability and reasonable cost.
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
The genetic algorithm for the nonlinear programming of water pollution control system
Energy Technology Data Exchange (ETDEWEB)
Wei, J.; Zhang, J. [China University of Geosciences (China)
1999-08-01
In the programming of water pollution control system the combined method of optimization with simulation is used generally. It is not only laborious in calculation, but also the global optimum of the obtained solution is guaranteed difficult. In this paper, the genetic algorithm (GA) used in the nonlinear programming of water pollution control system is given, by which the preferred conception for the programming of waste water system is found in once-through operation. It is more succinct than the conventional method and the global optimum of the obtained solution could be ensured. 6 refs., 4 figs., 3 tabs.
Algorithms and programming tools for image processing on the MPP, part 2
Reeves, Anthony P.
1986-01-01
A number of algorithms were developed for image warping and pyramid image filtering. Techniques were investigated for the parallel processing of a large number of independent irregular shaped regions on the MPP. In addition some utilities for dealing with very long vectors and for sorting were developed. Documentation pages for the algorithms which are available for distribution are given. The performance of the MPP for a number of basic data manipulations was determined. From these results it is possible to predict the efficiency of the MPP for a number of algorithms and applications. The Parallel Pascal development system, which is a portable programming environment for the MPP, was improved and better documentation including a tutorial was written. This environment allows programs for the MPP to be developed on any conventional computer system; it consists of a set of system programs and a library of general purpose Parallel Pascal functions. The algorithms were tested on the MPP and a presentation on the development system was made to the MPP users group. The UNIX version of the Parallel Pascal System was distributed to a number of new sites.
Correlation signatures of wet soils and snows. [algorithm development and computer programming
Phillips, M. R.
1972-01-01
Interpretation, analysis, and development of algorithms have provided the necessary computational programming tools for soil data processing, data handling and analysis. Algorithms that have been developed thus far, are adequate and have been proven successful for several preliminary and fundamental applications such as software interfacing capabilities, probability distributions, grey level print plotting, contour plotting, isometric data displays, joint probability distributions, boundary mapping, channel registration and ground scene classification. A description of an Earth Resources Flight Data Processor, (ERFDP), which handles and processes earth resources data under a users control is provided.
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.
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
Penalty dynamic programming algorithm for dim targets detection in sensor systems.
Huang, Dayu; Xue, Anke; Guo, Yunfei
2012-01-01
In order to detect and track multiple maneuvering dim targets in sensor systems, an improved dynamic programming track-before-detect algorithm (DP-TBD) called penalty DP-TBD (PDP-TBD) is proposed. The performances of tracking techniques are used as a feedback to the detection part. The feedback is constructed by a penalty term in the merit function, and the penalty term is a function of the possible target state estimation, which can be obtained by the tracking methods. With this feedback, the algorithm combines traditional tracking techniques with DP-TBD and it can be applied to simultaneously detect and track maneuvering dim targets. Meanwhile, a reasonable constraint that a sensor measurement can originate from one target or clutter is proposed to minimize track separation. Thus, the algorithm can be used in the multi-target situation with unknown target numbers. The efficiency and advantages of PDP-TBD compared with two existing methods are demonstrated by several simulations.
Directory of Open Access Journals (Sweden)
Diamantidis A. C.
2004-01-01
Full Text Available In this study, the buffer allocation problem (BAP in homogeneous, asymptotically reliable serial production lines is considered. A known aggregation method, given by Lim, Meerkov, and Top (1990, for the performance evaluation (i.e., estimation of throughput of this type of production lines when the buffer allocation is known, is used as an evaluative method in conjunction with a newly developed dynamic programming (DP algorithm for the BAP. The proposed algorithm is applied to production lines where the number of machines is varying from four up to a hundred machines. The proposed algorithm is fast because it reduces the volume of computations by rejecting allocations that do not lead to maximization of the line's throughput. Numerical results are also given for large production lines.
Directory of Open Access Journals (Sweden)
M. Abdul-Niby
2016-04-01
Full Text Available The Traveling Salesman Problem (TSP is an integer programming problem that falls into the category of NP-Hard problems. As the problem become larger, there is no guarantee that optimal tours will be found within reasonable computation time. Heuristics techniques, like genetic algorithm and simulating annealing, can solve TSP instances with different levels of accuracy. Choosing which algorithm to use in order to get a best solution is still considered as a hard choice. This paper suggests domain reduction as a tool to be combined with any meta-heuristic so that the obtained results will be almost the same. The hybrid approach of combining domain reduction with any meta-heuristic encountered the challenge of choosing an algorithm that matches the TSP instance in order to get the best results.
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
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
Directory of Open Access Journals (Sweden)
Tautz Diethard
2002-03-01
Full Text Available Abstract Background The identification of species or species groups with specific oligo-nucleotides as molecular signatures is becoming increasingly popular for bacterial samples. However, it shows also great promise for other small organisms that are taxonomically difficult to tract. Results We have devised here an algorithm that aims to find the optimal probes for any given set of sequences. The program requires only a crude alignment of these sequences as input and is optimized for performance to deal also with very large datasets. The algorithm is designed such that the position of mismatches in the probes influences the selection and makes provision of single nucleotide outloops. Program implementations are available for Linux and Windows.
Directory of Open Access Journals (Sweden)
Stanimirović Ivan
2009-01-01
Full Text Available We introduce a heuristic method for the single resource constrained project scheduling problem, based on the dynamic programming solution of the knapsack problem. This method schedules projects with one type of resources, in the non-preemptive case: once started an activity is not interrupted and runs to completion. We compare the implementation of this method with well-known heuristic scheduling method, called Minimum Slack First (known also as Gray-Kidd algorithm, as well as with Microsoft Project.
Schur Stability Regions for Complex Quadratic Polynomials
Cheng, Sui Sun; Huang, Shao Yuan
2010-01-01
Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)
Quadratic Functionals with General Boundary Conditions
International Nuclear Information System (INIS)
Dosla, Z.; Dosly, O.
1997-01-01
The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions
ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME INCLUDING POLARIZATION
Energy Technology Data Exchange (ETDEWEB)
Chen, Bin; Maddumage, Prasad [Research Computing Center, Department of Scientific Computing, Florida State University, Tallahassee, FL 32306 (United States); Kantowski, Ronald; Dai, Xinyu; Baron, Eddie, E-mail: bchen3@fsu.edu [Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019 (United States)
2015-05-15
Active galactic nuclei (AGNs) and quasars are important astrophysical objects to understand. Recently, microlensing observations have constrained the size of the quasar X-ray emission region to be of the order of 10 gravitational radii of the central supermassive black hole. For distances within a few gravitational radii, light paths are strongly bent by the strong gravity field of the central black hole. If the central black hole has nonzero angular momentum (spin), then a photon’s polarization plane will be rotated by the gravitational Faraday effect. The observed X-ray flux and polarization will then be influenced significantly by the strong gravity field near the source. Consequently, linear gravitational lensing theory is inadequate for such extreme circumstances. We present simple algorithms computing the strong lensing effects of Kerr black holes, including the effects on polarization. Our algorithms are realized in a program “KERTAP” in two versions: MATLAB and Python. The key ingredients of KERTAP are a graphic user interface, a backward ray-tracing algorithm, a polarization propagator dealing with gravitational Faraday rotation, and algorithms computing observables such as flux magnification and polarization angles. Our algorithms can be easily realized in other programming languages such as FORTRAN, C, and C++. The MATLAB version of KERTAP is parallelized using the MATLAB Parallel Computing Toolbox and the Distributed Computing Server. The Python code was sped up using Cython and supports full implementation of MPI using the “mpi4py” package. As an example, we investigate the inclination angle dependence of the observed polarization and the strong lensing magnification of AGN X-ray emission. We conclude that it is possible to perform complex numerical-relativity related computations using interpreted languages such as MATLAB and Python.
ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME INCLUDING POLARIZATION
International Nuclear Information System (INIS)
Chen, Bin; Maddumage, Prasad; Kantowski, Ronald; Dai, Xinyu; Baron, Eddie
2015-01-01
Active galactic nuclei (AGNs) and quasars are important astrophysical objects to understand. Recently, microlensing observations have constrained the size of the quasar X-ray emission region to be of the order of 10 gravitational radii of the central supermassive black hole. For distances within a few gravitational radii, light paths are strongly bent by the strong gravity field of the central black hole. If the central black hole has nonzero angular momentum (spin), then a photon’s polarization plane will be rotated by the gravitational Faraday effect. The observed X-ray flux and polarization will then be influenced significantly by the strong gravity field near the source. Consequently, linear gravitational lensing theory is inadequate for such extreme circumstances. We present simple algorithms computing the strong lensing effects of Kerr black holes, including the effects on polarization. Our algorithms are realized in a program “KERTAP” in two versions: MATLAB and Python. The key ingredients of KERTAP are a graphic user interface, a backward ray-tracing algorithm, a polarization propagator dealing with gravitational Faraday rotation, and algorithms computing observables such as flux magnification and polarization angles. Our algorithms can be easily realized in other programming languages such as FORTRAN, C, and C++. The MATLAB version of KERTAP is parallelized using the MATLAB Parallel Computing Toolbox and the Distributed Computing Server. The Python code was sped up using Cython and supports full implementation of MPI using the “mpi4py” package. As an example, we investigate the inclination angle dependence of the observed polarization and the strong lensing magnification of AGN X-ray emission. We conclude that it is possible to perform complex numerical-relativity related computations using interpreted languages such as MATLAB and Python
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.
Radiotherapy treatment planning linear-quadratic radiobiology
Chapman, J Donald
2015-01-01
Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....
Directory of Open Access Journals (Sweden)
Paru Patrawalla
Full Text Available Identification and characterization of asthma phenotypes are challenging due to disease complexity and heterogeneity. The Severe Asthma Research Program (SARP used unsupervised cluster analysis to define 5 phenotypically distinct asthma clusters that they replicated using 3 variables in a simplified algorithm. We evaluated whether this simplified SARP algorithm could be used in a separate and diverse urban asthma population to recreate these 5 phenotypic clusters.The SARP simplified algorithm was applied to adults with asthma recruited to the New York University/Bellevue Asthma Registry (NYUBAR to classify patients into five groups. The clinical phenotypes were summarized and compared.Asthma subjects in NYUBAR (n = 471 were predominantly women (70% and Hispanic (57%, which were demographically different from the SARP population. The clinical phenotypes of the five groups generated by the simplified SARP algorithm were distinct across groups and distributed similarly to those described for the SARP population. Groups 1 and 2 (6 and 63%, respectively had predominantly childhood onset atopic asthma. Groups 4 and 5 (20% were older, with the longest duration of asthma, increased symptoms and exacerbations. Group 4 subjects were the most atopic and had the highest peripheral eosinophils. Group 3 (10% had the least atopy, but included older obese women with adult-onset asthma, and increased exacerbations.Application of the simplified SARP algorithm to the NYUBAR yielded groups that were phenotypically distinct and useful to characterize disease heterogeneity. Differences across NYUBAR groups support phenotypic variation and support the use of the simplified SARP algorithm for classification of asthma phenotypes in future prospective studies to investigate treatment and outcome differences between these distinct groups.Clinicaltrials.gov NCT00212537.
International Nuclear Information System (INIS)
Matyushenko, N.N.; Titov, Yu.G.
1982-01-01
Programs of atom coordinate generation and space symmetry groups in a form of equivalent point systems are presented. Programs of generation and coordinate output from an on-line storage are written in the FORTRAN language for the ES computer. They may be used in laboratories specialized in studying atomic structure and material properties, in colleges and by specialists in other fields of physics and chemistry
Dose calculation algorithm for the Department of Energy Laboratory Accreditation Program
International Nuclear Information System (INIS)
Moscovitch, M.; Tawil, R.A.; Thompson, D.; Rhea, T.A.
1991-01-01
The dose calculation algorithm for a symmetric four-element LiF:Mg,Ti based thermoluminescent dosimeter is presented. The algorithm is based on the parameterization of the response of the dosimeter when exposed to both pure and mixed fields of various types and compositions. The experimental results were then used to develop the algorithm as a series of empirical response functions. Experiments to determine the response of the dosimeter and to test the dose calculation algorithm were performed according to the standard established by the Department of Energy Laboratory Accreditation Program (DOELAP). The test radiation fields include: 137 Cs gamma rays, 90 Sr/ 90 Y and 204 Tl beta particles, low energy photons of 20-120 keV and moderated 252 Cf neutron fields. The accuracy of the system has been demonstrated in an official DOELAP blind test conducted at Sandia National Laboratory. The test results were well within DOELAP tolerance limits. The results of this test are presented and discussed
Comparison between dynamic programming and genetic algorithm for hydro unit economic load dispatch
Directory of Open Access Journals (Sweden)
Bin Xu
2014-10-01
Full Text Available The hydro unit economic load dispatch (ELD is of great importance in energy conservation and emission reduction. Dynamic programming (DP and genetic algorithm (GA are two representative algorithms for solving ELD problems. The goal of this study was to examine the performance of DP and GA while they were applied to ELD. We established numerical experiments to conduct performance comparisons between DP and GA with two given schemes. The schemes included comparing the CPU time of the algorithms when they had the same solution quality, and comparing the solution quality when they had the same CPU time. The numerical experiments were applied to the Three Gorges Reservoir in China, which is equipped with 26 hydro generation units. We found the relation between the performance of algorithms and the number of units through experiments. Results show that GA is adept at searching for optimal solutions in low-dimensional cases. In some cases, such as with a number of units of less than 10, GA's performance is superior to that of a coarse-grid DP. However, GA loses its superiority in high-dimensional cases. DP is powerful in obtaining stable and high-quality solutions. Its performance can be maintained even while searching over a large solution space. Nevertheless, due to its exhaustive enumerating nature, it costs excess time in low-dimensional cases.
Fast intersection detection algorithm for PC-based robot off-line programming
Fedrowitz, Christian H.
1994-11-01
This paper presents a method for fast and reliable collision detection in complex production cells. The algorithm is part of the PC-based robot off-line programming system of the University of Siegen (Ropsus). The method is based on a solid model which is managed by a simplified constructive solid geometry model (CSG-model). The collision detection problem is divided in two steps. In the first step the complexity of the problem is reduced in linear time. In the second step the remaining solids are tested for intersection. For this the Simplex algorithm, which is known from linear optimization, is used. It computes a point which is common to two convex polyhedra. The polyhedra intersect, if such a point exists. Regarding the simplified geometrical model of Ropsus the algorithm runs also in linear time. In conjunction with the first step a resultant collision detection algorithm is found which requires linear time in all. Moreover it computes the resultant intersection polyhedron using the dual transformation.
A Constraint programming-based genetic algorithm for capacity output optimization
Directory of Open Access Journals (Sweden)
Kate Ean Nee Goh
2014-10-01
Full Text Available Purpose: The manuscript presents an investigation into a constraint programming-based genetic algorithm for capacity output optimization in a back-end semiconductor manufacturing company.Design/methodology/approach: In the first stage, constraint programming defining the relationships between variables was formulated into the objective function. A genetic algorithm model was created in the second stage to optimize capacity output. Three demand scenarios were applied to test the robustness of the proposed algorithm.Findings: CPGA improved both the machine utilization and capacity output once the minimum requirements of a demand scenario were fulfilled. Capacity outputs of the three scenarios were improved by 157%, 7%, and 69%, respectively.Research limitations/implications: The work relates to aggregate planning of machine capacity in a single case study. The constraints and constructed scenarios were therefore industry-specific.Practical implications: Capacity planning in a semiconductor manufacturing facility need to consider multiple mutually influenced constraints in resource availability, process flow and product demand. The findings prove that CPGA is a practical and an efficient alternative to optimize the capacity output and to allow the company to review its capacity with quick feedback.Originality/value: The work integrates two contemporary computational methods for a real industry application conventionally reliant on human judgement.
A Hybrid Genetic Programming Algorithm for Automated Design of Dispatching Rules.
Nguyen, Su; Mei, Yi; Xue, Bing; Zhang, Mengjie
2018-06-04
Designing effective dispatching rules for production systems is a difficult and timeconsuming task if it is done manually. In the last decade, the growth of computing power, advanced machine learning, and optimisation techniques has made the automated design of dispatching rules possible and automatically discovered rules are competitive or outperform existing rules developed by researchers. Genetic programming is one of the most popular approaches to discovering dispatching rules in the literature, especially for complex production systems. However, the large heuristic search space may restrict genetic programming from finding near optimal dispatching rules. This paper develops a new hybrid genetic programming algorithm for dynamic job shop scheduling based on a new representation, a new local search heuristic, and efficient fitness evaluators. Experiments show that the new method is effective regarding the quality of evolved rules. Moreover, evolved rules are also significantly smaller and contain more relevant attributes.
Game-based programming towards developing algorithmic thinking skills in primary education
Directory of Open Access Journals (Sweden)
Hariklia Tsalapatas
2012-06-01
Full Text Available This paper presents cMinds, a learning intervention that deploys game-based visual programming towards building analytical, computational, and critical thinking skills in primary education. The proposed learning method exploits the structured nature of programming, which is inherently logical and transcends cultural barriers, towards inclusive learning that exposes learners to algorithmic thinking. A visual programming environment, entitled ‘cMinds Learning Suite’, has been developed aimed for classroom use. Feedback from the deployment of the learning methods and tools in classrooms in several European countries demonstrates elevated learner motivation for engaging in logical learning activities, fostering of creativity and an entrepreneurial spirit, and promotion of problem-solving capacity
A Mixed Integer Programming Poultry Feed Ration Optimisation Problem Using the Bat Algorithm
Directory of Open Access Journals (Sweden)
Godfrey Chagwiza
2016-01-01
Full Text Available In this paper, a feed ration problem is presented as a mixed integer programming problem. An attempt to find the optimal quantities of Moringa oleifera inclusion into the poultry feed ration was done and the problem was solved using the Bat algorithm and the Cplex solver. The study used findings of previous research to investigate the effects of Moringa oleifera inclusion in poultry feed ration. The results show that the farmer is likely to gain US$0.89 more if Moringa oleifera is included in the feed ration. Results also show superiority of the Bat algorithm in terms of execution time and number of iterations required to find the optimum solution as compared with the results obtained by the Cplex solver. Results revealed that there is a significant economic benefit of Moringa oleifera inclusion into the poultry feed ration.
Cabaret, S; Coppier, H; Rachid, A; Barillère, R; CERN. Geneva. IT Department
2007-01-01
The GCS (Gas Control System) project team at CERN uses a Model Driven Approach with a Framework - UNICOS (UNified Industrial COntrol System) - based on PLC (Programming Language Controller) and SCADA (Supervisory Control And Data Acquisition) technologies. The first' UNICOS versions were able to provide a PID (Proportional Integrative Derivative) controller whereas the Gas Systems required more advanced control strategies. The MultiController is a new UNICOS object which provides the following advanced control algorithms: Smith Predictor, PFC (Predictive Function Control), RST* and GPC (Global Predictive Control). Its design is based on a monolithic entity with a global structure definition which is able to capture the desired set of parameters of any specific control algorithm supported by the object. The SCADA system -- PVSS - supervises the MultiController operation. The PVSS interface provides users with supervision faceplate, in particular it links any MultiController with recipes: the GCS experts are ab...
Algorithms and programs for evaluating fault trees with multi-state components
International Nuclear Information System (INIS)
Wickenhaeuser, A.
1989-07-01
Part 1 and 2 of the report contain a summary overview of methods and algorithms for the solution of fault tree analysis problems. The following points are treated in detail: Treatment of fault tree components with more than two states. Acceleration of the solution algorithms. Decomposition and modularization of extensive systems. Calculation of the structural function and the exact occurrence probability. Treatment of statistical dependencies. A flexible tool to be employed in solving these problems is the method of forming Boolean variables with restrictions. In this way, components with more than two states can be treated, the possibilities of forming modules expanded, and statistical dependencies treated. Part 3 contains descriptions of the MUSTAFA, MUSTAMO, PASPI, and SIMUST computer programs based on these methods. (orig./HP) [de
Quadratic Finite Element Method for 1D Deterministic Transport
International Nuclear Information System (INIS)
Tolar, D R Jr.; Ferguson, J M
2004-01-01
In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ((und r)) and angular ((und (Omega))) dependences on the angular flux ψ(und r),(und (Omega))are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of ψ(und r),(und (Omega)). Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable (μ) in developing the one-dimensional (1D) spherical geometry S N equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S N algorithms
Design of reinforced areas of concrete column using quadratic polynomials
Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.
2017-11-01
Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.
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
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...
Reactor Network Synthesis Using Coupled Genetic Algorithm with the Quasi-linear Programming Method
Soltani, H.; Shafiei, S.; Edraki, J.
2016-01-01
This research is an attempt to develop a new procedure for the synthesis of reactor networks (RNs) using a genetic algorithm (GA) coupled with the quasi-linear programming (LP) method. The GA is used to produce structural configuration, whereas continuous variables are handled using a quasi-LP formulation for finding the best objective function. Quasi-LP consists of LP together with a search loop to find the best reactor conversions (xi), as well as split and recycle ratios (yi). Quasi-LP rep...
Semi-Supervised Half-Quadratic Nonnegative Matrix Factorization for Face Recognition
Alghamdi, Masheal M.
2014-05-01
Face recognition is a challenging problem in computer vision. Difficulties such as slight differences between similar faces of different people, changes in facial expressions, light and illumination condition, and pose variations add extra complications to the face recognition research. Many algorithms are devoted to solving the face recognition problem, among which the family of nonnegative matrix factorization (NMF) algorithms has been widely used as a compact data representation method. Different versions of NMF have been proposed. Wang et al. proposed the graph-based semi-supervised nonnegative learning (S2N2L) algorithm that uses labeled data in constructing intrinsic and penalty graph to enforce separability of labeled data, which leads to a greater discriminating power. Moreover the geometrical structure of labeled and unlabeled data is preserved through using the smoothness assumption by creating a similarity graph that conserves the neighboring information for all labeled and unlabeled data. However, S2N2L is sensitive to light changes, illumination, and partial occlusion. In this thesis, we propose a Semi-Supervised Half-Quadratic NMF (SSHQNMF) algorithm that combines the benefits of S2N2L and the robust NMF by the half- quadratic minimization (HQNMF) algorithm.Our algorithm improves upon the S2N2L algorithm by replacing the Frobenius norm with a robust M-Estimator loss function. A multiplicative update solution for our SSHQNMF algorithmis driven using the half- 4 quadratic (HQ) theory. Extensive experiments on ORL, Yale-A and a subset of the PIE data sets for nine M-estimator loss functions for both SSHQNMF and HQNMF algorithms are investigated, and compared with several state-of-the-art supervised and unsupervised algorithms, along with the original S2N2L algorithm in the context of classification, clustering, and robustness against partial occlusion. The proposed algorithm outperformed the other algorithms. Furthermore, SSHQNMF with Maximum Correntropy
Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong
2018-05-19
In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.
Penalty Dynamic Programming Algorithm for Dim Targets Detection in Sensor Systems
Directory of Open Access Journals (Sweden)
Yunfei Guo
2012-04-01
Full Text Available In order to detect and track multiple maneuvering dim targets in sensor systems, an improved dynamic programming track-before-detect algorithm (DP-TBD called penalty DP-TBD (PDP-TBD is proposed. The performances of tracking techniques are used as a feedback to the detection part. The feedback is constructed by a penalty term in the merit function, and the penalty term is a function of the possible target state estimation, which can be obtained by the tracking methods. With this feedback, the algorithm combines traditional tracking techniques with DP-TBD and it can be applied to simultaneously detect and track maneuvering dim targets. Meanwhile, a reasonable constraint that a sensor measurement can originate from one target or clutter is proposed to minimize track separation. Thus, the algorithm can be used in the multi-target situation with unknown target numbers. The efficiency and advantages of PDP-TBD compared with two existing methods are demonstrated by several simulations.
A depth-first search algorithm to compute elementary flux modes by linear programming.
Quek, Lake-Ee; Nielsen, Lars K
2014-07-30
The decomposition of complex metabolic networks into elementary flux modes (EFMs) provides a useful framework for exploring reaction interactions systematically. Generating a complete set of EFMs for large-scale models, however, is near impossible. Even for moderately-sized models (linear programming (LP) to enumerate EFMs in an exhaustive fashion. Constraints can be introduced to directly generate a subset of EFMs satisfying the set of constraints. The depth-first search algorithm has a constant memory overhead. Using flux constraints, a large LP problem can be massively divided and parallelized into independent sub-jobs for deployment into computing clusters. Since the sub-jobs do not overlap, the approach scales to utilize all available computing nodes with minimal coordination overhead or memory limitations. The speed of the algorithm was comparable to efmtool, a mainstream Double Description method, when enumerating all EFMs; the attrition power gained from performing flux feasibility tests offsets the increased computational demand of running an LP solver. Unlike the Double Description method, the algorithm enables accelerated enumeration of all EFMs satisfying a set of constraints.
An Analysis of OpenACC Programming Model: Image Processing Algorithms as a Case Study
Directory of Open Access Journals (Sweden)
M. J. Mišić
2014-06-01
Full Text Available Graphics processing units and similar accelerators have been intensively used in general purpose computations for several years. In the last decade, GPU architecture and organization changed dramatically to support an ever-increasing demand for computing power. Along with changes in hardware, novel programming models have been proposed, such as NVIDIA’s Compute Unified Device Architecture (CUDA and Open Computing Language (OpenCL by Khronos group. Although numerous commercial and scientific applications have been developed using these two models, they still impose a significant challenge for less experienced users. There are users from various scientific and engineering communities who would like to speed up their applications without the need to deeply understand a low-level programming model and underlying hardware. In 2011, OpenACC programming model was launched. Much like OpenMP for multicore processors, OpenACC is a high-level, directive-based programming model for manycore processors like GPUs. This paper presents an analysis of OpenACC programming model and its applicability in typical domains like image processing. Three, simple image processing algorithms have been implemented for execution on the GPU with OpenACC. The results were compared with their sequential counterparts, and results are briefly discussed.
International Nuclear Information System (INIS)
Miller, I.; Roman, K.
1979-12-01
In order to perform studies of the influence of regional groundwater flow systems on the long-term performance of potential high-level nuclear waste repositories, it was determined that an adequate computer model would have to consider the full three-dimensional flow system. Golder Associates' SOLTR code, while three-dimensional, has an overly simple algorithm for simulating the passage of radionuclides from one aquifier to another above or below it. Part 1 of this report describes the algorithm developed to provide SOLTR with an improved capability for simulating interaquifer transport
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.
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)
Cascaded Quadratic Soliton Compression in Waveguide Structures
DEFF Research Database (Denmark)
Guo, Hairun
between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...
On orthogonality preserving quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
On orthogonality preserving quadratic stochastic operators
International Nuclear Information System (INIS)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-01-01
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too
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
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
Multi-objective genetic algorithm for solving N-version program design problem
International Nuclear Information System (INIS)
Yamachi, Hidemi; Tsujimura, Yasuhiro; Kambayashi, Yasushi; Yamamoto, Hisashi
2006-01-01
N-version programming (NVP) is a programming approach for constructing fault tolerant software systems. Generally, an optimization model utilized in NVP selects the optimal set of versions for each module to maximize the system reliability and to constrain the total cost to remain within a given budget. In such a model, while the number of versions included in the obtained solution is generally reduced, the budget restriction may be so rigid that it may fail to find the optimal solution. In order to ameliorate this problem, this paper proposes a novel bi-objective optimization model that maximizes the system reliability and minimizes the system total cost for designing N-version software systems. When solving multi-objective optimization problem, it is crucial to find Pareto solutions. It is, however, not easy to obtain them. In this paper, we propose a novel bi-objective optimization model that obtains many Pareto solutions efficiently. We formulate the optimal design problem of NVP as a bi-objective 0-1 nonlinear integer programming problem. In order to overcome this problem, we propose a Multi-objective genetic algorithm (MOGA), which is a powerful, though time-consuming, method to solve multi-objective optimization problems. When implementing genetic algorithm (GA), the use of an appropriate genetic representation scheme is one of the most important issues to obtain good performance. We employ random-key representation in our MOGA to find many Pareto solutions spaced as evenly as possible along the Pareto frontier. To pursue improve further performance, we introduce elitism, the Pareto-insertion and the Pareto-deletion operations based on distance between Pareto solutions in the selection process. The proposed MOGA obtains many Pareto solutions along the Pareto frontier evenly. The user of the MOGA can select the best compromise solution among the candidates by controlling the balance between the system reliability and the total cost
Multi-objective genetic algorithm for solving N-version program design problem
Energy Technology Data Exchange (ETDEWEB)
Yamachi, Hidemi [Department of Computer and Information Engineering, Nippon Institute of Technology, Miyashiro, Saitama 345-8501 (Japan) and Department of Production and Information Systems Engineering, Tokyo Metropolitan Institute of Technology, Hino, Tokyo 191-0065 (Japan)]. E-mail: yamachi@nit.ac.jp; Tsujimura, Yasuhiro [Department of Computer and Information Engineering, Nippon Institute of Technology, Miyashiro, Saitama 345-8501 (Japan)]. E-mail: tujimr@nit.ac.jp; Kambayashi, Yasushi [Department of Computer and Information Engineering, Nippon Institute of Technology, Miyashiro, Saitama 345-8501 (Japan)]. E-mail: yasushi@nit.ac.jp; Yamamoto, Hisashi [Department of Production and Information Systems Engineering, Tokyo Metropolitan Institute of Technology, Hino, Tokyo 191-0065 (Japan)]. E-mail: yamamoto@cc.tmit.ac.jp
2006-09-15
N-version programming (NVP) is a programming approach for constructing fault tolerant software systems. Generally, an optimization model utilized in NVP selects the optimal set of versions for each module to maximize the system reliability and to constrain the total cost to remain within a given budget. In such a model, while the number of versions included in the obtained solution is generally reduced, the budget restriction may be so rigid that it may fail to find the optimal solution. In order to ameliorate this problem, this paper proposes a novel bi-objective optimization model that maximizes the system reliability and minimizes the system total cost for designing N-version software systems. When solving multi-objective optimization problem, it is crucial to find Pareto solutions. It is, however, not easy to obtain them. In this paper, we propose a novel bi-objective optimization model that obtains many Pareto solutions efficiently. We formulate the optimal design problem of NVP as a bi-objective 0-1 nonlinear integer programming problem. In order to overcome this problem, we propose a Multi-objective genetic algorithm (MOGA), which is a powerful, though time-consuming, method to solve multi-objective optimization problems. When implementing genetic algorithm (GA), the use of an appropriate genetic representation scheme is one of the most important issues to obtain good performance. We employ random-key representation in our MOGA to find many Pareto solutions spaced as evenly as possible along the Pareto frontier. To pursue improve further performance, we introduce elitism, the Pareto-insertion and the Pareto-deletion operations based on distance between Pareto solutions in the selection process. The proposed MOGA obtains many Pareto solutions along the Pareto frontier evenly. The user of the MOGA can select the best compromise solution among the candidates by controlling the balance between the system reliability and the total cost.
Quadratic mass relations in topological bootstrap theory
International Nuclear Information System (INIS)
Jones, C.E.; Uschersohn, J.
1980-01-01
From the requirement of reality of discontinuities of scattering amplitudes at the spherical level of the topological bootstrap theory, a large number of mass relations for hadrons is derived. Quadratic mass formulas for the symmetry-breaking pattern of both mesons and baryon is obtained and their relation to conventional models of symmetry breaking is briefly discussed
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...
Fundamental quadratic variational principle underlying general relativity
International Nuclear Information System (INIS)
Atkins, W.K.
1983-01-01
The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed
Investigating Students' Mathematical Difficulties with Quadratic Equations
O'Connor, Bronwyn Reid; Norton, Stephen
2016-01-01
This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…
Commuting quantum traces for quadratic algebras
International Nuclear Information System (INIS)
Nagy, Zoltan; Avan, Jean; Doikou, Anastasia; Rollet, Genevieve
2005-01-01
Consistent tensor products on auxiliary spaces, hereafter denoted 'fusion procedures', and commuting transfer matrices are defined for general quadratic algebras, nondynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures then yield integer-indexed families of commuting Hamiltonians
Park, Sang Cheol; Leader, Joseph Ken; Tan, Jun; Lee, Guee Sang; Kim, Soo Hyung; Na, In Seop; Zheng, Bin
2011-01-01
Objective this article presents a new computerized scheme that aims to accurately and robustly separate left and right lungs on CT examinations. Methods we developed and tested a method to separate the left and right lungs using sequential CT information and a guided dynamic programming algorithm using adaptively and automatically selected start point and end point with especially severe and multiple connections. Results the scheme successfully identified and separated all 827 connections on the total 4034 CT images in an independent testing dataset of CT examinations. The proposed scheme separated multiple connections regardless of their locations, and the guided dynamic programming algorithm reduced the computation time to approximately 4.6% in comparison with the traditional dynamic programming and avoided the permeation of the separation boundary into normal lung tissue. Conclusions The proposed method is able to robustly and accurately disconnect all connections between left and right lungs and the guided dynamic programming algorithm is able to remove redundant processing. PMID:21412104
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.
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....
AbouEisha, Hassan M.
2014-06-06
In this paper we present a dynamic programming algorithm for finding optimal elimination trees for computational grids refined towards point or edge singularities. The elimination tree is utilized to guide the multi-frontal direct solver algorithm. Thus, the criterion for the optimization of the elimination tree is the computational cost associated with the multi-frontal solver algorithm executed over such tree. We illustrate the paper with several examples of optimal trees found for grids with point, isotropic edge and anisotropic edge mixed with point singularity. We show the comparison of the execution time of the multi-frontal solver algorithm with results of MUMPS solver with METIS library, implementing the nested dissection algorithm.
Osser, David N; Roudsari, Mohsen Jalali; Manschreck, Theo
2013-01-01
This article is an update of the algorithm for schizophrenia from the Psychopharmacology Algorithm Project at the Harvard South Shore Program. A literature review was conducted focusing on new data since the last published version (1999-2001). The first-line treatment recommendation for new-onset schizophrenia is with amisulpride, aripiprazole, risperidone, or ziprasidone for four to six weeks. In some settings the trial could be shorter, considering that evidence of clear improvement with antipsychotics usually occurs within the first two weeks. If the trial of the first antipsychotic cannot be completed due to intolerance, try another until one of the four is tolerated and given an adequate trial. There should be evidence of bioavailability. If the response to this adequate trial is unsatisfactory, try a second monotherapy. If the response to this second adequate trial is also unsatisfactory, and if at least one of the first two trials was with risperidone, olanzapine, or a first-generation (typical) antipsychotic, then clozapine is recommended for the third trial. If neither trial was with any these three options, a third trial prior to clozapine should occur, using one of those three. If the response to monotherapy with clozapine (with dose adjusted by using plasma levels) is unsatisfactory, consider adding risperidone, lamotrigine, or ECT. Beyond that point, there is little solid evidence to support further psychopharmacological treatment choices, though we do review possible options.
Directory of Open Access Journals (Sweden)
Chenlu Miao
2016-01-01
Full Text Available Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP, which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard problem. Consequently, using traditional methods to solve such problems is difficult. Genetic algorithms (GAs have great value in solving BLP problems, and many studies have designed GAs to solve BLP problems; however, such GAs are typically designed for special cases that do not involve MINLBLP with one or multiple followers. Therefore, we propose a bilevel GA to solve these particular MINLBLP problems, which are widely used in product family problems. We give numerical examples to demonstrate the effectiveness of the proposed algorithm. In addition, a reducer family case study is examined to demonstrate practical applications of the proposed BLGA.
Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras
Escobar-Ruiz, Mauricio A.; Kalnins, Ernest G.; Miller, Willar, Jr.; Subag, Eyal
2017-03-01
Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra {so}(4,C) to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of {e}(2,C) and {so}(3,C) and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.
DEFF Research Database (Denmark)
Rong, Aiying; Hakonen, Henri; Lahdelma, Risto
2009-01-01
efficiency of the plants. We introduce in this paper the DRDP-RSC algorithm, which is a dynamic regrouping based dynamic programming (DP) algorithm based on linear relaxation of the ON/OFF states of the units, sequential commitment of units in small groups. Relaxed states of the plants are used to reduce...... the dimension of the UC problem and dynamic regrouping is used to improve the solution quality. Numerical results based on real-life data sets show that this algorithm is efficient and optimal or near-optimal solutions with very small optimality gap are obtained....
DEFF Research Database (Denmark)
Sokoler, Leo Emil; Frison, Gianluca; Skajaa, Anders
2015-01-01
We develop an efficient homogeneous and self-dual interior-point method (IPM) for the linear programs arising in economic model predictive control of constrained linear systems with linear objective functions. The algorithm is based on a Riccati iteration procedure, which is adapted to the linear...... system of equations solved in homogeneous and self-dual IPMs. Fast convergence is further achieved using a warm-start strategy. We implement the algorithm in MATLAB and C. Its performance is tested using a conceptual power management case study. Closed loop simulations show that 1) the proposed algorithm...
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)
Coherent states of systems with quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica
2015-06-15
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Coherent states of systems with quadratic Hamiltonians
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.
2015-01-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
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.''
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
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.
Temporal quadratic expansion nodal Green's function method
International Nuclear Information System (INIS)
Liu Cong; Jing Xingqing; Xu Xiaolin
2000-01-01
A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method
Joux, Antoine
2009-01-01
Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applic
Walking solitons in quadratic nonlinear media
Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru
1996-01-01
We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed
Quadratic Term Structure Models in Discrete Time
Marco Realdon
2006-01-01
This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...
Least Squares Problems with Absolute Quadratic Constraints
Directory of Open Access Journals (Sweden)
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.
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 Comparative Analysis of Quadratics Unit in Singaporean, Turkish and IBDP Mathematics Textbooks
Directory of Open Access Journals (Sweden)
Reyhan Sağlam
2012-12-01
Full Text Available The purpose of this study was to analyze and compare the contents of the chapters on quadratics in three mathematics textbooks selected from Turkey, Singapore, and the International Baccalaureate Diploma Program (IBDP through content analysis. The analysis of mathematical content showed that the three textbooks have different approaches and priorities in terms of the positions of chapters and weights of the quadratics units, and the time allocated to them within the respective curricular programs. It was also found that the Turkish textbook covers a greater number of learning outcomes targeted for quadratics among the three mathematics syllabi, showing a detailed treatment of the topic compared to the other two textbooks.Key Words: Content analysis, international comparative studies, mathematics textbooks
Quadratic tracer dynamical models tobacco growth
International Nuclear Information System (INIS)
Qiang Jiyi; Hua Cuncai; Wang Shaohua
2011-01-01
In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)
Graphical Solution of the Monic Quadratic Equation with Complex Coefficients
Laine, A. D.
2015-01-01
There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…
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.
System network planning expansion using mathematical programming, genetic algorithms and tabu search
International Nuclear Information System (INIS)
Sadegheih, A.; Drake, P.R.
2008-01-01
In this paper, system network planning expansion is formulated for mixed integer programming, a genetic algorithm (GA) and tabu search (TS). Compared with other optimization methods, GAs are suitable for traversing large search spaces, since they can do this relatively rapidly and because the use of mutation diverts the method away from local minima, which will tend to become more common as the search space increases in size. GA's give an excellent trade off between solution quality and computing time and flexibility for taking into account specific constraints in real situations. TS has emerged as a new, highly efficient, search paradigm for finding quality solutions to combinatorial problems. It is characterized by gathering knowledge during the search and subsequently profiting from this knowledge. The attractiveness of the technique comes from its ability to escape local optimality. The cost function of this problem consists of the capital investment cost in discrete form, the cost of transmission losses and the power generation costs. The DC load flow equations for the network are embedded in the constraints of the mathematical model to avoid sub-optimal solutions that can arise if the enforcement of such constraints is done in an indirect way. The solution of the model gives the best line additions and also provides information regarding the optimal generation at each generation point. This method of solution is demonstrated on the expansion of a 10 bus bar system to 18 bus bars. Finally, a steady-state genetic algorithm is employed rather than generational replacement, also uniform crossover is used
Zheng, Shijie; Zhang, Nan; Xia, Yanjun; Wang, Hongtao
2014-03-01
A new heuristic strategy for the non-uniform strain profile reconstruction along Fiber Bragg Gratings is proposed in this paper, which is based on the modified transfer matrix and Genetic Programming(GP) algorithm. The present method uses Genetic Programming to determine the applied strain field as a function of position along the fiber length. The structures that undergo adaptation in genetic programming are hierarchical structures which are different from that of conventional genetic algorithm operating on strings. GP regress the strain profile function which matches the 'measured' spectrum best and makes space resolution of strain reconstruction arbitrarily high, or even infinite. This paper also presents an experimental verification of the reconstruction of non-homogeneous strain fields using GP. The results are compared with numerical calculations of finite element method. Both the simulation examples and experimental results demonstrate that Genetic Programming can effectively reconstruct continuous profile expression along the whole FBG, and greatly improves its computational efficiency and accuracy.
STRUCTURE OPTIMIZATION OF RESERVATION BY PRECISE QUADRATIC REGULARIZATION
Directory of Open Access Journals (Sweden)
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.
International Nuclear Information System (INIS)
Kobayashi, Fujio; Yamaguchi, Shoichiro
1985-01-01
Fundamental studies have been made on the application of mathematical programming to the reconstruction of tomographic images from projections of a small number of views without requiring any circular symmetry nor periodicity. Linear programming and quadratic programming were applied to minimize the quadratic sum of the residue and to finally obtain optimized reconstruction images. The mathematical algorithms were verified by the method of computer simulation, and the relationship between the number of picture elements and the number of iterations necessary for convergence was also investigated. The methods of linear programming and quadratic programming require fairly simple mathematical procedures, and strict solutions can be obtained within a finite number of iterations. Their only draw back is the requirement of a large quantity of computer memory. But this problem will be desolved by the advent of large fast memory devices in the near future. (Aoki, K.)
2-Phase NSGA II: An Optimized Reward and Risk Measurements Algorithm in Portfolio Optimization
Directory of Open Access Journals (Sweden)
Seyedeh Elham Eftekharian
2017-11-01
Full Text Available Portfolio optimization is a serious challenge for financial engineering and has pulled down special attention among investors. It has two objectives: to maximize the reward that is calculated by expected return and to minimize the risk. Variance has been considered as a risk measure. There are many constraints in the world that ultimately lead to a non–convex search space such as cardinality constraint. In conclusion, parametric quadratic programming could not be applied and it seems essential to apply multi-objective evolutionary algorithm (MOEA. In this paper, a new efficient multi-objective portfolio optimization algorithm called 2-phase NSGA II algorithm is developed and the results of this algorithm are compared with the NSGA II algorithm. It was found that 2-phase NSGA II significantly outperformed NSGA II algorithm.
Parallel Integer Factorization Using Quadratic Forms
National Research Council Canada - National Science Library
McMath, Stephen S
2005-01-01
.... In 1975, Daniel Shanks used class group infrastructure to modify the Morrison-Brillhart algorithm and develop Square Forms Factorization, but he never published his work on this algorithm or provided...
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
A heuristic algorithm to approximate dynamic program of a novel new product development process
Directory of Open Access Journals (Sweden)
Hamed Fazlollahtabar
2016-01-01
Full Text Available We are concerned with a new product development (NPD network in digital environment in which the aim is to find integrated attributes for value added purposes. Different views exist for new product development. Here, the effective factors are categorized into customers, competitors and the company’s own past experience. Also, various attributes are considered for the development of a product. Thus, using digital data of attributes, the optimal set of attributes is chosen for user in the new product development. Regarding the multi stage decision making process of the customer, competitor and company’s own past experience, we develop a multi-dimensional dynamic program as a useful tool for multi stage decision making. To counteract the dynamism of the digital data in different time periods, two concepts of state and policy direction are introduced to determine the cost of moving through the stages of the proposed NPD digital network. Since the space requirements and value function computations become impractical for even moderate size, we approximate the optimal value function developing a heuristic algorithm.
Fuzzy bilevel programming with multiple non-cooperative followers: model, algorithm and application
Ke, Hua; Huang, Hu; Ralescu, Dan A.; Wang, Lei
2016-04-01
In centralized decision problems, it is not complicated for decision-makers to make modelling technique selections under uncertainty. When a decentralized decision problem is considered, however, choosing appropriate models is no longer easy due to the difficulty in estimating the other decision-makers' inconclusive decision criteria. These decision criteria may vary with different decision-makers because of their special risk tolerances and management requirements. Considering the general differences among the decision-makers in decentralized systems, we propose a general framework of fuzzy bilevel programming including hybrid models (integrated with different modelling methods in different levels). Specially, we discuss two of these models which may have wide applications in many fields. Furthermore, we apply the proposed two models to formulate a pricing decision problem in a decentralized supply chain with fuzzy coefficients. In order to solve these models, a hybrid intelligent algorithm integrating fuzzy simulation, neural network and particle swarm optimization based on penalty function approach is designed. Some suggestions on the applications of these models are also presented.
Urselmann, Maren; Emmerich, Michael T. M.; Till, Jochen; Sand, Guido; Engell, Sebastian
2007-07-01
Engineering optimization often deals with large, mixed-integer search spaces with a rigid structure due to the presence of a large number of constraints. Metaheuristics, such as evolutionary algorithms (EAs), are frequently suggested as solution algorithms in such cases. In order to exploit the full potential of these algorithms, it is important to choose an adequate representation of the search space and to integrate expert-knowledge into the stochastic search operators, without adding unnecessary bias to the search. Moreover, hybridisation with mathematical programming techniques such as mixed-integer programming (MIP) based on a problem decomposition can be considered for improving algorithmic performance. In order to design problem-specific EAs it is desirable to have a set of design guidelines that specify properties of search operators and representations. Recently, a set of guidelines has been proposed that gives rise to so-called Metric-based EAs (MBEAs). Extended by the minimal moves mutation they allow for a generalization of EA with self-adaptive mutation strength in discrete search spaces. In this article, a problem-specific EA for process engineering task is designed, following the MBEA guidelines and minimal moves mutation. On the background of the application, the usefulness of the design framework is discussed, and further extensions and corrections proposed. As a case-study, a two-stage stochastic programming problem in chemical batch process scheduling is considered. The algorithm design problem can be viewed as the choice of a hierarchical decision structure, where on different layers of the decision process symmetries and similarities can be exploited for the design of minimal moves. After a discussion of the design approach and its instantiation for the case-study, the resulting problem-specific EA/MIP is compared to a straightforward application of a canonical EA/MIP and to a monolithic mathematical programming algorithm. In view of the
Hougardy, Stefan
2016-01-01
Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.
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)
Energy Technology Data Exchange (ETDEWEB)
Strout, Michelle [Colorado State Univ., Fort Collins, CO (United States)
2015-08-15
Programming parallel machines is fraught with difficulties: the obfuscation of algorithms due to implementation details such as communication and synchronization, the need for transparency between language constructs and performance, the difficulty of performing program analysis to enable automatic parallelization techniques, and the existence of important "dusty deck" codes. The SAIMI project developed abstractions that enable the orthogonal specification of algorithms and implementation details within the context of existing DOE applications. The main idea is to enable the injection of small programming models such as expressions involving transcendental functions, polyhedral iteration spaces with sparse constraints, and task graphs into full programs through the use of pragmas. These smaller, more restricted programming models enable orthogonal specification of many implementation details such as how to map the computation on to parallel processors, how to schedule the computation, and how to allocation storage for the computation. At the same time, these small programming models enable the expression of the most computationally intense and communication heavy portions in many scientific simulations. The ability to orthogonally manipulate the implementation for such computations will significantly ease performance programming efforts and expose transformation possibilities and parameter to automated approaches such as autotuning. At Colorado State University, the SAIMI project was supported through DOE grant DE-SC3956 from April 2010 through August 2015. The SAIMI project has contributed a number of important results to programming abstractions that enable the orthogonal specification of implementation details in scientific codes. This final report summarizes the research that was funded by the SAIMI project.
International Nuclear Information System (INIS)
Tao Ganqiang; Yu Qing; Xiao Xiao
2011-01-01
Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)
Linear programming foundations and extensions
Vanderbei, Robert J
2001-01-01
Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail. Moreover, Linear Programming: Foundations and Extensions underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied: -The two-phase simplex method; -The primal-dual simplex method; -The path-following interior-point method; -The homogeneous self-dual methods. In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex m...
International Nuclear Information System (INIS)
Yang, H.T.; Chen, S.L.
1989-01-01
A multi-objective optimization approach to generation expansion planning is presented. The approach is designed by adding a new multi-criteria decision (MCD) procedure to the conventional algorithm which combines dynamic programming with production simulation method. The MCD procedure can help decision makers weight the relative importance of multiple attributes associated with the decision alternatives, and find the near-best compromise solution efficiently at each optimization step of the conventional algorithm. Practical application of proposed approach to feasibility evaluation of the fourth nuclear power plant of Tawian is also presented, demonstrating the effectiveness and limitations of the approach
Directory of Open Access Journals (Sweden)
Linlin Gao
2015-11-01
Full Text Available From the perspective of vehicle dynamics, the four-wheel independent steering vehicle dynamics stability control method is studied, and a four-wheel independent steering varying parameter linear quadratic regulator control system is proposed with the help of expert control method. In the article, a four-wheel independent steering linear quadratic regulator controller for model following purpose is designed first. Then, by analyzing the four-wheel independent steering vehicle dynamic characteristics and the influence of linear quadratic regulator control parameters on control performance, a linear quadratic regulator control parameter adjustment strategy based on vehicle steering state is proposed to achieve the adaptive adjustment of linear quadratic regulator control parameters. In addition, to further improve the control performance, the proposed varying parameter linear quadratic regulator control system is optimized by genetic algorithm. Finally, simulation studies have been conducted by applying the proposed control system to the 8-degree-of-freedom four-wheel independent steering vehicle dynamics model. The simulation results indicate that the proposed control system has better performance and robustness and can effectively improve the stability and steering safety of the four-wheel independent steering vehicle.
Phase space eigenfunctions of multidimensional quadratic Hamiltonians
International Nuclear Information System (INIS)
Dodonov, V.V.; Man'ko, V.I.
1986-01-01
We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)
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
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...
National Oceanic and Atmospheric Administration, Department of Commerce — The Pacific Reef Assessment and Monitoring Program (Pacific RAMP), established by the Coral Reef Ecosystem Division of the NOAA Pacific Islands Fisheries Science...
Zhang, Huaguang; Jiang, He; Luo, Chaomin; Xiao, Geyang
2017-10-01
In this paper, we investigate the nonzero-sum games for a class of discrete-time (DT) nonlinear systems by using a novel policy iteration (PI) adaptive dynamic programming (ADP) method. The main idea of our proposed PI scheme is to utilize the iterative ADP algorithm to obtain the iterative control policies, which not only ensure the system to achieve stability but also minimize the performance index function for each player. This paper integrates game theory, optimal control theory, and reinforcement learning technique to formulate and handle the DT nonzero-sum games for multiplayer. First, we design three actor-critic algorithms, an offline one and two online ones, for the PI scheme. Subsequently, neural networks are employed to implement these algorithms and the corresponding stability analysis is also provided via the Lyapunov theory. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our proposed approach.
Quadratic residues and non-residues selected topics
Wright, Steve
2016-01-01
This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
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.))
Distance matrices and quadratic embedding of graphs
Directory of Open Access Journals (Sweden)
Nobuaki Obata
2018-04-01
Full Text Available A connected graph is said to be of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a graph to be of QE class are derived from the point of view of graph operations. For a quantitative criterion the QE constant is introduced and concrete examples are shown with explicit calculation. If the distance matrix admits a constant row sum, the QE constant coincides with the second largest eigenvalue of the distance matrix. The QE constants are determined for all graphs on $n$ vertices with $n\\le5$, among which two are not of QE class.
Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers
International Nuclear Information System (INIS)
Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.
2005-01-01
The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules
Gain scheduled linear quadratic control for quadcopter
Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.
2017-12-01
This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.
Charged black holes in quadratic gravity
International Nuclear Information System (INIS)
Matyjasek, Jerzy; Tryniecki, Dariusz
2004-01-01
Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. The obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit the exact location of the (degenerate) event horizon is given by r + =|e|. Similarly to the classical Reissner-Nordstroem solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for boundary conditions of the second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed
A ''quadratized'' augmented plane wave method
International Nuclear Information System (INIS)
Smrcka, L.
1982-02-01
The exact radial solution inside the muffin-tin sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term. Making use of it the energy independent augmented plane waves are formed which lead to the secular equations linear in energy. The method resembles the currently used linearized APW method but yields higher accuracy. The analysis of solution inside one muffin-tin sphere shows that the eigenvalue error is proportional to (E-E 0 ) 6 as compared with (E-E 0 ) 4 for LAPW. The error of eigenfunctions is (E-E 0 ) 3 ((E-E 0 ) 2 for LAPW). These conclusions are confirmed by direct numerical calculation of band structure of Cu and Al. (author)
Quadratic gravity in first order formalism
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Enrique; Anero, Jesus; Gonzalez-Martin, Sergio, E-mail: enrique.alvarez@uam.es, E-mail: jesusanero@gmail.com, E-mail: sergio.gonzalez.martin@uam.es [Departamento de Física Teórica and Instituto de Física Teórica (IFT-UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid (Spain)
2017-10-01
We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than 1/ p {sup 2}. The drawback is of course that the parameter space of the theory is too big, so that in many cases will be far away from a theory of gravity alone. In order to analyze this issue, the interaction between external sources was examined in some detail. We find that this interaction is conveyed mainly by propagation of the three-index connection field. At any rate the theory as it stands is in the conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated by quantum corrections.
van Otterlo, Martijn
2017-01-01
Ethics of algorithms is an emerging topic in various disciplines such as social science, law, and philosophy, but also artificial intelligence (AI). The value alignment problem expresses the challenge of (machine) learning values that are, in some way, aligned with human requirements or values. In this paper I argue for looking at how humans have formalized and communicated values, in professional codes of ethics, and for exploring declarative decision-theoretic ethical programs (DDTEP) to fo...
Programming Non-Trivial Algorithms in the Measurement Based Quantum Computation Model
Energy Technology Data Exchange (ETDEWEB)
Alsing, Paul [United States Air Force Research Laboratory, Wright-Patterson Air Force Base; Fanto, Michael [United States Air Force Research Laboratory, Wright-Patterson Air Force Base; Lott, Capt. Gordon [United States Air Force Research Laboratory, Wright-Patterson Air Force Base; Tison, Christoper C. [United States Air Force Research Laboratory, Wright-Patterson Air Force Base
2014-01-01
We provide a set of prescriptions for implementing a quantum circuit model algorithm as measurement based quantum computing (MBQC) algorithm1, 2 via a large cluster state. As means of illustration we draw upon our numerical modeling experience to describe a large graph state capable of searching a logical 8 element list (a non-trivial version of Grover's algorithm3 with feedforward). We develop several prescriptions based on analytic evaluation of cluster states and graph state equations which can be generalized into any circuit model operations. Such a resulting cluster state will be able to carry out the desired operation with appropriate measurements and feed forward error correction. We also discuss the physical implementation and the analysis of the principal 3-qubit entangling gate (Toffoli) required for a non-trivial feedforward realization of an 8-element Grover search algorithm.
A unified framework of descent algorithms for nonlinear programs and variational inequalities
International Nuclear Information System (INIS)
Patriksson, M.
1993-01-01
We present a framework of algorithms for the solution of continuous optimization and variational inequality problems. In the general algorithm, a search direction finding auxiliary problems is obtained by replacing the original cost function with an approximating monotone cost function. The proposed framework encompasses algorithm classes presented earlier by Cohen, Dafermos, Migdalas, and Tseng, and includes numerous descent and successive approximation type methods, such as Newton methods, Jacobi and Gauss-Siedel type decomposition methods for problems defined over Cartesian product sets, and proximal point methods, among others. The auxiliary problem of the general algorithm also induces equivalent optimization reformulation and descent methods for asymmetric variational inequalities. We study the convergence properties of the general algorithm when applied to unconstrained optimization, nondifferentiable optimization, constrained differentiable optimization, and variational inequalities; the emphasis of the convergence analyses is placed on basic convergence results, convergence using different line search strategies and truncated subproblem solutions, and convergence rate results. This analysis offer a unification of known results; moreover, it provides strengthenings of convergence results for many existing algorithms, and indicates possible improvements of their realizations. 482 refs
A superlinear interior points algorithm for engineering design optimization
Herskovits, J.; Asquier, J.
1990-01-01
We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.
Pattern Nulling of Linear Antenna Arrays Using Backtracking Search Optimization Algorithm
Directory of Open Access Journals (Sweden)
Kerim Guney
2015-01-01
Full Text Available An evolutionary method based on backtracking search optimization algorithm (BSA is proposed for linear antenna array pattern synthesis with prescribed nulls at interference directions. Pattern nulling is obtained by controlling only the amplitude, position, and phase of the antenna array elements. BSA is an innovative metaheuristic technique based on an iterative process. Various numerical examples of linear array patterns with the prescribed single, multiple, and wide nulls are given to illustrate the performance and flexibility of BSA. The results obtained by BSA are compared with the results of the following seventeen algorithms: particle swarm optimization (PSO, genetic algorithm (GA, modified touring ant colony algorithm (MTACO, quadratic programming method (QPM, bacterial foraging algorithm (BFA, bees algorithm (BA, clonal selection algorithm (CLONALG, plant growth simulation algorithm (PGSA, tabu search algorithm (TSA, memetic algorithm (MA, nondominated sorting GA-2 (NSGA-2, multiobjective differential evolution (MODE, decomposition with differential evolution (MOEA/D-DE, comprehensive learning PSO (CLPSO, harmony search algorithm (HSA, seeker optimization algorithm (SOA, and mean variance mapping optimization (MVMO. The simulation results show that the linear antenna array synthesis using BSA provides low side-lobe levels and deep null levels.
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...
An Extended Quadratic Frobenius Primality Test with Average and Worst Case Error Estimates
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg
2003-01-01
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....
An Extended Quadratic Frobenius Primality Test with Average- and Worst-Case Error Estimate
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg
2006-01-01
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....
An Extended Quadratic Frobenius Primality Test with Average Case Error Estimates
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg
2001-01-01
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....
Rey, Martin P.; Pontzen, Andrew
2018-02-01
Recent work has studied the interplay between a galaxy's history and its observable properties using `genetically modified' cosmological zoom simulations. The approach systematically generates alternative histories for a halo, while keeping its cosmological environment fixed. Applications to date altered linear properties of the initial conditions, such as the mean overdensity of specified regions; we extend the formulation to include quadratic features, such as local variance, that determines the overall importance of smooth accretion relative to mergers in a galaxy's history. We introduce an efficient algorithm for this new class of modification and demonstrate its ability to control the variance of a region in a one-dimensional toy model. Outcomes of this work are twofold: (i) a clarification of the formulation of genetic modifications and (ii) a proof of concept for quadratic modifications leading the way to a forthcoming implementation in cosmological simulations.
Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares
Orr, Jeb S.
2012-01-01
A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed
Methods of using the quadratic assignment problem solution
Directory of Open Access Journals (Sweden)
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.
Noise-induced chaos in a quadratically nonlinear oscillator
International Nuclear Information System (INIS)
Gan Chunbiao
2006-01-01
The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system
Programming Algorithms of load balancing with HA-Proxy in HTTP services
Directory of Open Access Journals (Sweden)
José Teodoro Mejía Viteri
2018-02-01
Full Text Available The access to the public and private services through the web gains daily protagonism, and sometimes they must support amounts of requests that a team can not process, so there are solutions that use algorithms that allow to distribute the load of requests of a web application in several equipment; the objective of this work is to perform an analysis of load balancing scheduling algorithms through the HA-Proxy tool, and deliver an instrument that identifies the load distribution algorithm to be used and the technological infrastructure, to largely cover implementation. The information used for this work is based on a bibliographic analysis, eld study and implementation of the different load balancing algorithms in equipment, where the distribution and its performance will be analyzed. The incorporation of this technology to the management of services on the web, improves availability, helps business continuity and through the different forms of distribution of the requests of the algorithms that can be implemented in HA-Proxy to provide those responsible for information technology systems with a view of their advantages and disadvantages.
Directory of Open Access Journals (Sweden)
Scott Hazelhurst
2010-11-01
Full Text Available The level of detail and precision that appears in the experimental methodology section computer science papers is usually much less than in natural science disciplines. This is partially justified by different nature of experiments. The experimental evidence presented here shows that the time taken by the same algorithm varies so significantly on different CPUs that without knowing the exact model of CPU, it is difficult to compare the results. This is placed in context by analysing a cross-section of experimental results reported in the literature. The reporting of experimental results is sometimes insufficient to allow experiments to be replicated, and in some case is insufficient to support the claims made for the algorithms. New standards for reporting on algorithms results are suggested.
THE ALGORITHM AND PROGRAM OF M-MATRICES SEARCH AND STUDY
Directory of Open Access Journals (Sweden)
Y. N. Balonin
2013-05-01
Full Text Available The algorithm and software for search and study of orthogonal bases matrices – minimax matrices (M-matrix are considered. The algorithm scheme is shown, comments on calculation blocks are given, and interface of the MMatrix software system developed with participation of the authors is explained. The results of the universal algorithm work are presented as Hadamard matrices, Belevitch matrices (C-matrices, conference matrices and matrices of even and odd orders complementary and closely related to those ones by their properties, in particular, the matrix of the 22-th order for which there is no C-matrix. Examples of portraits for alternative matrices of the 255-th and the 257-th orders are given corresponding to the sequences of Mersenne and Fermat numbers. A new way to get Hadamard matrices is explained, different from the previously known procedures based on iterative processes and calculations of Lagrange symbols, with theoretical and practical meaning.
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 ...
Quadratic Twists of Rigid Calabi–Yau Threefolds Over
DEFF Research Database (Denmark)
Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko
2013-01-01
of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...
Approximate *-derivations and approximate quadratic *-derivations on C*-algebras
Directory of Open Access Journals (Sweden)
Park Choonkil
2011-01-01
Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.
Effects of Classroom Instruction on Students' Understanding of Quadratic Equations
Vaiyavutjamai, Pongchawee; Clements, M. A.
2006-01-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…
Analysis of Students' Error in Learning of Quadratic Equations
Zakaria, Effandi; Ibrahim; Maat, Siti Mistima
2010-01-01
The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…
Sketching the General Quadratic Equation Using Dynamic Geometry Software
Stols, G. H.
2005-01-01
This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…
Tangent Lines without Derivatives for Quadratic and Cubic Equations
Carroll, William J.
2009-01-01
In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)
Visualising the Roots of Quadratic Equations with Complex Coefficients
Bardell, Nicholas S.
2014-01-01
This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…
Sparse Covariance Matrix Estimation by DCA-Based Algorithms.
Phan, Duy Nhat; Le Thi, Hoai An; Dinh, Tao Pham
2017-11-01
This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods.
An approach of traffic signal control based on NLRSQP algorithm
Zou, Yuan-Yang; Hu, Yu
2017-11-01
This paper presents a linear program model with linear complementarity constraints (LPLCC) to solve traffic signal optimization problem. The objective function of the model is to obtain the minimization of total queue length with weight factors at the end of each cycle. Then, a combination algorithm based on the nonlinear least regression and sequence quadratic program (NLRSQP) is proposed, by which the local optimal solution can be obtained. Furthermore, four numerical experiments are proposed to study how to set the initial solution of the algorithm that can get a better local optimal solution more quickly. In particular, the results of numerical experiments show that: The model is effective for different arrival rates and weight factors; and the lower bound of the initial solution is, the better optimal solution can be obtained.
Group leaders optimization algorithm
Daskin, Anmer; Kais, Sabre
2011-03-01
We present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique which is designed into a group architecture. To demonstrate the efficiency of the method, a standard suite of single and multi-dimensional optimization functions along with the energies and the geometric structures of Lennard-Jones clusters are given as well as the application of the algorithm on quantum circuit design problems. We show that as an improvement over previous methods, the algorithm scales as N 2.5 for the Lennard-Jones clusters of N-particles. In addition, an efficient circuit design is shown for a two-qubit Grover search algorithm which is a quantum algorithm providing quadratic speedup over the classical counterpart.
International Nuclear Information System (INIS)
Baginyan, S.A.; Govorun, N.N.; Tkhang, T.L.; Shigaev, V.N.
1982-01-01
Software development minimum guidance system for measuring pictures of bubble chamber on the base of a scanner (HPD) and special hardware processor (SHP) is described. The algorithm of selective filter is proposed. The local software structure and functional specifications of its major parts are described. Some examples of processing picture from HBC-1 (JINR) are also presented
International Nuclear Information System (INIS)
Machnes, S.; Sander, U.; Glaser, S. J.; Schulte-Herbrueggen, T.; Fouquieres, P. de; Gruslys, A.; Schirmer, S.
2011-01-01
For paving the way to novel applications in quantum simulation, computation, and technology, increasingly large quantum systems have to be steered with high precision. It is a typical task amenable to numerical optimal control to turn the time course of pulses, i.e., piecewise constant control amplitudes, iteratively into an optimized shape. Here, we present a comparative study of optimal-control algorithms for a wide range of finite-dimensional applications. We focus on the most commonly used algorithms: GRAPE methods which update all controls concurrently, and Krotov-type methods which do so sequentially. Guidelines for their use are given and open research questions are pointed out. Moreover, we introduce a unifying algorithmic framework, DYNAMO (dynamic optimization platform), designed to provide the quantum-technology community with a convenient matlab-based tool set for optimal control. In addition, it gives researchers in optimal-control techniques a framework for benchmarking and comparing newly proposed algorithms with the state of the art. It allows a mix-and-match approach with various types of gradients, update and step-size methods as well as subspace choices. Open-source code including examples is made available at http://qlib.info.
Directory of Open Access Journals (Sweden)
MASOUM, M. A. S.
2011-05-01
Full Text Available This paper presents a genetic algorithm (GA to maximize total system social welfare and alleviate congestion by best placement and sizing of TCSC device, in a double-sided auction market. To introduce more accurate modeling, the valve loading effects is incorporated to the conventional quadratic smooth generator cost curves. By adding the valve point effect, the model presents nondifferentiable and nonconvex regions that challenge most gradient-based optimization algorithms. In addition, quadratic consumer benefit functions integrated in the objective function to guarantee that locational marginal prices charged at the demand buses is less than or equal to DisCos benefit, earned by selling that power to retail customers. The proposed approach makes use of the genetic algorithm to optimal schedule GenCos, DisCos and TCSC location and size, while the Newton-Raphson algorithm minimizes the mismatch of the power flow equations. Simulation results on the modified IEEE 14-bus and 30-bus test systems (with/without line flow constraints, before and after the compensation are used to examine the impact of TCSC on the total system social welfare improvement. Several cases are considered to test and validate the consistency of detecting best solutions. Simulation results are compared to solutions obtained by sequential quadratic programming (SQP approaches.
Are ghost surfaces quadratic-flux-minimizing?
International Nuclear Information System (INIS)
Hudson, S.R.; Dewar, R.L.
2009-01-01
Two candidates for 'almost-invariant' toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, ∫A.dl. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other 11/2 degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.
Securing Digital Audio using Complex Quadratic Map
Suryadi, MT; Satria Gunawan, Tjandra; Satria, Yudi
2018-03-01
In This digital era, exchanging data are common and easy to do, therefore it is vulnerable to be attacked and manipulated from unauthorized parties. One data type that is vulnerable to attack is digital audio. So, we need data securing method that is not vulnerable and fast. One of the methods that match all of those criteria is securing the data using chaos function. Chaos function that is used in this research is complex quadratic map (CQM). There are some parameter value that causing the key stream that is generated by CQM function to pass all 15 NIST test, this means that the key stream that is generated using this CQM is proven to be random. In addition, samples of encrypted digital sound when tested using goodness of fit test are proven to be uniform, so securing digital audio using this method is not vulnerable to frequency analysis attack. The key space is very huge about 8.1×l031 possible keys and the key sensitivity is very small about 10-10, therefore this method is also not vulnerable against brute-force attack. And finally, the processing speed for both encryption and decryption process on average about 450 times faster that its digital audio duration.
Paino, A.; Keller, J.; Popescu, M.; Stone, K.
2014-06-01
In this paper we present an approach that uses Genetic Programming (GP) to evolve novel feature extraction algorithms for greyscale images. Our motivation is to create an automated method of building new feature extraction algorithms for images that are competitive with commonly used human-engineered features, such as Local Binary Pattern (LBP) and Histogram of Oriented Gradients (HOG). The evolved feature extraction algorithms are functions defined over the image space, and each produces a real-valued feature vector of variable length. Each evolved feature extractor breaks up the given image into a set of cells centered on every pixel, performs evolved operations on each cell, and then combines the results of those operations for every cell using an evolved operator. Using this method, the algorithm is flexible enough to reproduce both LBP and HOG features. The dataset we use to train and test our approach consists of a large number of pre-segmented image "chips" taken from a Forward Looking Infrared Imagery (FLIR) camera mounted on the hood of a moving vehicle. The goal is to classify each image chip as either containing or not containing a buried object. To this end, we define the fitness of a candidate solution as the cross-fold validation accuracy of the features generated by said candidate solution when used in conjunction with a Support Vector Machine (SVM) classifier. In order to validate our approach, we compare the classification accuracy of an SVM trained using our evolved features with the accuracy of an SVM trained using mainstream feature extraction algorithms, including LBP and HOG.
Buaria, D.; Yeung, P. K.
2017-12-01
A new parallel algorithm utilizing a partitioned global address space (PGAS) programming model to achieve high scalability is reported for particle tracking in direct numerical simulations of turbulent fluid flow. The work is motivated by the desire to obtain Lagrangian information necessary for the study of turbulent dispersion at the largest problem sizes feasible on current and next-generation multi-petaflop supercomputers. A large population of fluid particles is distributed among parallel processes dynamically, based on instantaneous particle positions such that all of the interpolation information needed for each particle is available either locally on its host process or neighboring processes holding adjacent sub-domains of the velocity field. With cubic splines as the preferred interpolation method, the new algorithm is designed to minimize the need for communication, by transferring between adjacent processes only those spline coefficients determined to be necessary for specific particles. This transfer is implemented very efficiently as a one-sided communication, using Co-Array Fortran (CAF) features which facilitate small data movements between different local partitions of a large global array. The cost of monitoring transfer of particle properties between adjacent processes for particles migrating across sub-domain boundaries is found to be small. Detailed benchmarks are obtained on the Cray petascale supercomputer Blue Waters at the University of Illinois, Urbana-Champaign. For operations on the particles in a 81923 simulation (0.55 trillion grid points) on 262,144 Cray XE6 cores, the new algorithm is found to be orders of magnitude faster relative to a prior algorithm in which each particle is tracked by the same parallel process at all times. This large speedup reduces the additional cost of tracking of order 300 million particles to just over 50% of the cost of computing the Eulerian velocity field at this scale. Improving support of PGAS models on
Qiu, J. P.; Niu, D. X.
Micro-grid is one of the key technologies of the future energy supplies. Take economic planning. reliability, and environmental protection of micro grid as a basis for the analysis of multi-strategy objective programming problems for micro grid which contains wind power, solar power, and battery and micro gas turbine. Establish the mathematical model of each power generation characteristics and energy dissipation. and change micro grid planning multi-objective function under different operating strategies to a single objective model based on AHP method. Example analysis shows that in combination with dynamic ant mixed genetic algorithm can get the optimal power output of this model.
Cochran, D. R.; Ishikawa, M. K.; Paulson, R. E.; Ramsey, H. R.
1975-01-01
A user guide for the Programming Language for Allocation and Network Scheduling (PLANS) is presented. Information is included for the construction of PLANS programs. The basic philosophy of PLANS is discussed, and access and update reference techniques are described along with the use of tree structures.
Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART
Hodyss, D.; Anderson, J. L.; Collins, N.; Campbell, W. F.; Reinecke, P. A.
2017-12-01
Many Ensemble-Based Kalman ltering (EBKF) algorithms process the observations serially. Serial observation processing views the data assimilation process as an iterative sequence of scalar update equations. What is useful about this data assimilation algorithm is that it has very low memory requirements and does not need complex methods to perform the typical high-dimensional inverse calculation of many other algorithms. Recently, the push has been towards the prediction, and therefore the assimilation of observations, for regions and phenomena for which high-resolution is required and/or highly nonlinear physical processes are operating. For these situations, a basic hypothesis is that the use of the EBKF is sub-optimal and performance gains could be achieved by accounting for aspects of the non-Gaussianty. To this end, we develop here a new component of the Data Assimilation Research Testbed [DART] to allow for a wide-variety of users to test this hypothesis. This new version of DART allows one to run several variants of the EBKF as well as several variants of the quadratic polynomial lter using the same forecast model and observations. Dierences between the results of the two systems will then highlight the degree of non-Gaussianity in the system being examined. We will illustrate in this work the differences between the performance of linear versus quadratic polynomial regression in a hierarchy of models from Lorenz-63 to a simple general circulation model.
Parallel Algorithm for Incremental Betweenness Centrality on Large Graphs
Jamour, Fuad Tarek; Skiadopoulos, Spiros; Kalnis, Panos
2017-01-01
: they either require excessive memory (i.e., quadratic to the size of the input graph) or perform unnecessary computations rendering them prohibitively slow. We propose iCentral; a novel incremental algorithm for computing betweenness centrality in evolving
On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables
Al-Naffouri, Tareq Y.
2015-10-30
© 2015 IEEE. In this work, we propose a unified approach to evaluating the CDF and PDF of indefinite quadratic forms in Gaussian random variables. Such a quantity appears in many applications in communications, signal processing, information theory, and adaptive filtering. For example, this quantity appears in the mean-square-error (MSE) analysis of the normalized least-meansquare (NLMS) adaptive algorithm, and SINR associated with each beam in beam forming applications. The trick of the proposed approach is to replace inequalities that appear in the CDF calculation with unit step functions and to use complex integral representation of the the unit step function. Complex integration allows us then to evaluate the CDF in closed form for the zero mean case and as a single dimensional integral for the non-zero mean case. Utilizing the saddle point technique allows us to closely approximate such integrals in non zero mean case. We demonstrate how our approach can be extended to other scenarios such as the joint distribution of quadratic forms and ratios of such forms, and to characterize quadratic forms in isotropic distributed random variables.We also evaluate the outage probability in multiuser beamforming using our approach to provide an application of indefinite forms in communications.
Benhalouche, Fatima Zohra; Karoui, Moussa Sofiane; Deville, Yannick; Ouamri, Abdelaziz
2017-04-01
This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.
Projection of curves on B-spline surfaces using quadratic reparameterization
Yang, Yijun
2010-09-01
Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the projected curve and the original curve is controlled under the user-specified distance tolerance. The projected curve is T-G 1 continuous, where T is the user-specified angle tolerance. Examples are given to show the performance of our algorithm. © 2010 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Mishra Vinod
2016-01-01
Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.
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...
Jihong, Qu
2014-01-01
Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision. PMID:24895663
Ren, Kun; Jihong, Qu
2014-01-01
Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision.
2008-09-22
function essentially binary • Value function measures cost to go – Solution of Eikonal equation – Gradient determines optimal control typical laser...of nodes – Dijkstra’s algorithm is essentially unchanged • Continuous space – Static HJ PDE no longer reduces to the Eikonal equation – Gradient of ϑ...bounded: ||·||1 • If action is bounded in ||·||p, then value function is solution of “ Eikonal ” equation ||ϑ(x)||p* = c(x) in the dual norm p* – p = 1
A Sequential Convex Semidefinite Programming Algorithm for Multiple-Load Free Material Optimization
Czech Academy of Sciences Publication Activity Database
Stingl, M.; Kočvara, Michal; Leugering, G.
2009-01-01
Roč. 20, č. 1 (2009), s. 130-155 ISSN 1052-6234 R&D Projects: GA AV ČR IAA1075402 Grant - others:commision EU(XE) EU-FP6-30717 Institutional research plan: CEZ:AV0Z10750506 Keywords : structural optimization * material optimization * semidefinite programming * sequential convex programming Subject RIV: BA - General Mathematics Impact factor: 1.429, year: 2009
2017-02-19
new high-school STEM program in robotics. The program utilizes state -of-the- art sensors and embedded computers for mobile robotics. These...software. Students do not engage in hardware design or development. They are given a hardware kit that includes state -of-the- art sensors and... Engineering and Computer Science (under course number 6.141) and the Department of Aeronautics and Astronautics (under course number 16.405). Let us
Zenil, Hector
2018-02-18
To extract and learn representations leading to generative mechanisms from data, especially without making arbitrary decisions and biased assumptions, is a central challenge in most areas of scientific research particularly in connection to current major limitations of influential topics and methods of machine and deep learning as they have often lost sight of the model component. Complex data is usually produced by interacting sources with different mechanisms. Here we introduce a parameter-free model-based approach, based upon the seminal concept of Algorithmic Probability, that decomposes an observation and signal into its most likely algorithmic generative mechanisms. Our methods use a causal calculus to infer model representations. We demonstrate the method ability to distinguish interacting mechanisms and deconvolve them, regardless of whether the objects produce strings, space-time evolution diagrams, images or networks. We numerically test and evaluate our method and find that it can disentangle observations from discrete dynamic systems, random and complex networks. We think that these causal inference techniques can contribute as key pieces of information for estimations of probability distributions complementing other more statistical-oriented techniques that otherwise lack model inference capabilities.
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.
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.
Quadratic Sieve integer factorization using Hadoop
Ghebregiorgish, Semere Tsehaye
2012-01-01
Master's thesis in Computer Science Integer factorization problem is one of the most important parts in the world of cryptography. The security of the widely-used public-key cryptographic algorithm, RSA [1], and the Blum Blum Shub cryptographic pseudorandom number generator [2] heavily depend on the presumed difficulty of factoring a number to its prime constituents. As the size of the number to be factored gets larger, the difficulty of the problem increases enormously. Thi...
Integrable Hamiltonian systems and interactions through quadratic constraints
International Nuclear Information System (INIS)
Pohlmeyer, K.
1975-08-01
Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de
A perturbative solution for gravitational waves in quadratic gravity
International Nuclear Information System (INIS)
Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de
2003-01-01
We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin
Accurate nonlocal theory for cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey
2007-01-01
We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....
Resolving Actuator Redundancy - Control Allocation vs. Linear Quadratic Control
Härkegård, Ola
2004-01-01
When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give...
Quadratic measurement and conditional state preparation in an optomechanical system
DEFF Research Database (Denmark)
A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.
2014-01-01
We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....
Scale-Invariant Rotating Black Holes in Quadratic Gravity
Directory of Open Access Journals (Sweden)
Guido Cognola
2015-07-01
Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
Staff turnover in hotels : exploring the quadratic and linear relationships.
Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.
2015-01-01
The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....
On wave-packet dynamics in a decaying quadratic potential
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Henriksen, Niels Engholm
1997-01-01
We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....
The stability of quadratic-reciprocal functional equation
Song, Aimin; Song, Minwei
2018-04-01
A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.
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....
Hu, T C
2002-01-01
Newly enlarged, updated second edition of a valuable text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discusses binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. 153 black-and-white illus. 23 tables.Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9
An inertia-free filter line-search algorithm for large-scale nonlinear programming
Energy Technology Data Exchange (ETDEWEB)
Chiang, Nai-Yuan; Zavala, Victor M.
2016-02-15
We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection via symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.
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.
Directory of Open Access Journals (Sweden)
Oleksandr B. Yashchyk
2016-05-01
Full Text Available The article discusses the importance of studying the notion of algorithm and its formal specification using Turing machines. In the article it was identified the basic hypothesis of the theory of algorithms for Turing as well as reviewed scientific research of modern scientists devoted to this issue and found the main principles of the Turing machine as an abstract mathematical model. The process of forming information competencies components, information culture and students` logical thinking development with the inclusion of the topic “Study and Application of Turing machine as Universal Algorithm Executor” in the course of Informatics was analyzed.
Sağlam, Reyhan
2012-01-01
Ankara : The Program of Curriculum and Instruction, Bilkent University, 2012. Thesis (Master's) -- Bilkent University, 2012. Includes bibliographical references leaves 110-118. The purpose of this study was to analyze and compare the chapters on quadratics in three mathematics textbooks selected from Turkey, Singapore, and the International Baccalaureate Diploma Programme (IBDP) in terms of content, organization, and presentation style through content analysis. The analys...
Sastry, Kumara Narasimha
2007-03-01
Effective and efficient rnultiscale modeling is essential to advance both the science and synthesis in a, wide array of fields such as physics, chemistry, materials science; biology, biotechnology and pharmacology. This study investigates the efficacy and potential of rising genetic algorithms for rnultiscale materials modeling and addresses some of the challenges involved in designing competent algorithms that solve hard problems quickly, reliably and accurately. In particular, this thesis demonstrates the use of genetic algorithms (GAs) and genetic programming (GP) in multiscale modeling with the help of two non-trivial case studies in materials science and chemistry. The first case study explores the utility of genetic programming (GP) in multi-timescaling alloy kinetics simulations. In essence, GP is used to bridge molecular dynamics and kinetic Monte Carlo methods to span orders-of-magnitude in simulation time. Specifically, GP is used to regress symbolically an inline barrier function from a limited set of molecular dynamics simulations to enable kinetic Monte Carlo that simulate seconds of real time. Results on a non-trivial example of vacancy-assisted migration on a surface of a face-centered cubic (fcc) Copper-Cobalt (CuxCo 1-x) alloy show that GP predicts all barriers with 0.1% error from calculations for less than 3% of active configurations, independent of type of potentials used to obtain the learning set of barriers via molecular dynamics. The resulting method enables 2--9 orders-of-magnitude increase in real-time dynamics simulations taking 4--7 orders-of-magnitude less CPU time. The second case study presents the application of multiobjective genetic algorithms (MOGAs) in multiscaling quantum chemistry simulations. Specifically, MOGAs are used to bridge high-level quantum chemistry and semiempirical methods to provide accurate representation of complex molecular excited-state and ground-state behavior. Results on ethylene and benzene---two common
QUADrATiC: scalable gene expression connectivity mapping for repurposing FDA-approved therapeutics.
O'Reilly, Paul G; Wen, Qing; Bankhead, Peter; Dunne, Philip D; McArt, Darragh G; McPherson, Suzanne; Hamilton, Peter W; Mills, Ken I; Zhang, Shu-Dong
2016-05-04
Gene expression connectivity mapping has proven to be a powerful and flexible tool for research. Its application has been shown in a broad range of research topics, most commonly as a means of identifying potential small molecule compounds, which may be further investigated as candidates for repurposing to treat diseases. The public release of voluminous data from the Library of Integrated Cellular Signatures (LINCS) programme further enhanced the utilities and potentials of gene expression connectivity mapping in biomedicine. We describe QUADrATiC ( http://go.qub.ac.uk/QUADrATiC ), a user-friendly tool for the exploration of gene expression connectivity on the subset of the LINCS data set corresponding to FDA-approved small molecule compounds. It enables the identification of compounds for repurposing therapeutic potentials. The software is designed to cope with the increased volume of data over existing tools, by taking advantage of multicore computing architectures to provide a scalable solution, which may be installed and operated on a range of computers, from laptops to servers. This scalability is provided by the use of the modern concurrent programming paradigm provided by the Akka framework. The QUADrATiC Graphical User Interface (GUI) has been developed using advanced Javascript frameworks, providing novel visualization capabilities for further analysis of connections. There is also a web services interface, allowing integration with other programs or scripts. QUADrATiC has been shown to provide an improvement over existing connectivity map software, in terms of scope (based on the LINCS data set), applicability (using FDA-approved compounds), usability and speed. It offers potential to biological researchers to analyze transcriptional data and generate potential therapeutics for focussed study in the lab. QUADrATiC represents a step change in the process of investigating gene expression connectivity and provides more biologically-relevant results than
A review on quantum search algorithms
Giri, Pulak Ranjan; Korepin, Vladimir E.
2017-12-01
The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It is evident from the early invented quantum algorithms such as Deutsch's algorithm, Deutsch-Jozsa algorithm and its variation as Bernstein-Vazirani algorithm, Simon algorithm, Shor's algorithms, etc. Quantum parallelism also significantly speeds up the database search algorithm, which is important in computer science because it comes as a subroutine in many important algorithms. Quantum database search of Grover achieves the task of finding the target element in an unsorted database in a time quadratically faster than the classical computer. We review Grover's quantum search algorithms for a singe and multiple target elements in a database. The partial search algorithm of Grover and Radhakrishnan and its optimization by Korepin called GRK algorithm are also discussed.
Chenlu Miao; Gang Du; Yi Xia; Danping Wang
2016-01-01
Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP) to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP), which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard pr...
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.
Ravi, Keerthi Sravan; Potdar, Sneha; Poojar, Pavan; Reddy, Ashok Kumar; Kroboth, Stefan; Nielsen, Jon-Fredrik; Zaitsev, Maxim; Venkatesan, Ramesh; Geethanath, Sairam
2018-03-11
To provide a single open-source platform for comprehensive MR algorithm development inclusive of simulations, pulse sequence design and deployment, reconstruction, and image analysis. We integrated the "Pulseq" platform for vendor-independent pulse programming with Graphical Programming Interface (GPI), a scientific development environment based on Python. Our integrated platform, Pulseq-GPI, permits sequences to be defined visually and exported to the Pulseq file format for execution on an MR scanner. For comparison, Pulseq files using either MATLAB only ("MATLAB-Pulseq") or Python only ("Python-Pulseq") were generated. We demonstrated three fundamental sequences on a 1.5 T scanner. Execution times of the three variants of implementation were compared on two operating systems. In vitro phantom images indicate equivalence with the vendor supplied implementations and MATLAB-Pulseq. The examples demonstrated in this work illustrate the unifying capability of Pulseq-GPI. The execution times of all the three implementations were fast (a few seconds). The software is capable of user-interface based development and/or command line programming. The tool demonstrated here, Pulseq-GPI, integrates the open-source simulation, reconstruction and analysis capabilities of GPI Lab with the pulse sequence design and deployment features of Pulseq. Current and future work includes providing an ISMRMRD interface and incorporating Specific Absorption Ratio and Peripheral Nerve Stimulation computations. Copyright © 2018 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Tzolakis, G.; Papanikolaou, P.; Kolokotronis, D.; Samaras, N.; Tourlidakis, A.; Tomboulides, A.
2012-01-01
Since most of the world's electric energy production is mainly based on fossil fuels and need for better efficiency of the energy conversion systems is imminent, mathematical programming algorithms were applied for the simulation and optimization of a detailed model of an existing lignite-fired power plant in Kozani, Greece (KARDIA IV). The optimization of its overall thermal efficiency, using as control variables the mass flow rates of the steam turbine extractions and the fuel consumption, was performed with the use of the simulation and optimization software gPROMS. The power plant components' mathematical models were imported in software by the authors and the results showed that further increase to the overall thermal efficiency of the plant can be achieved (a 0.55% absolute increase) through reduction of the HP turbine's and increase of the LP turbine's extractions mass flow rates and the parallel reduction of the fuel consumption by 2.05% which also results to an equivalent reduction of the greenhouse gasses. The setup of the mathematical model and the flexibility of gPROMS, make this software applicable to various power plants. - Highlights: ► Modeling and simulation of the flue gases circuit of a specific plant. ► Designing of modules in gPROMS FO (Foreign Objects). ► Simulation of the complete detailed plant with gPROMS. ► Optimization using a non-linear optimization algorithm of the plant's efficiency.
Directory of Open Access Journals (Sweden)
Jiekun Song
2016-01-01
Full Text Available Harmonious development of 3Es (economy-energy-environment system is the key to realize regional sustainable development. The structure and components of 3Es system are analyzed. Based on the analysis of causality diagram, GDP and industrial structure are selected as the target parameters of economy subsystem, energy consumption intensity is selected as the target parameter of energy subsystem, and the emissions of COD, ammonia nitrogen, SO2, and NOX and CO2 emission intensity are selected as the target parameters of environment system. Fixed assets investment of three industries, total energy consumption, and investment in environmental pollution control are selected as the decision variables. By regarding the parameters of 3Es system optimization as fuzzy numbers, a fuzzy chance-constrained goal programming (FCCGP model is constructed, and a hybrid intelligent algorithm including fuzzy simulation and genetic algorithm is proposed for solving it. The results of empirical analysis on Shandong province of China show that the FCCGP model can reflect the inherent relationship and evolution law of 3Es system and provide the effective decision-making support for 3Es system optimization.
Directory of Open Access Journals (Sweden)
Widasari Edita Rosana
2018-01-01
Full Text Available Sidoarjo mudflow or known as Lapindo mudflow erupted since 2006. The Sidoarjo mudflow is located in Sidoarjo City, East Java, Indonesia. The mudflow-affected area has high air pollution level and high health risk. Therefore, in this paper was implemented a system that can categorize the level of air pollution into several categories. The air quality index can be categorized using fuzzy logic algorithm based on the concentration of air pollutant parameters in the mudflow-affected area. Furthermore, Dataflow programming is used to process the fuzzy logic algorithm. Based on the result, the measurement accuracy of the air quality index in the mudflow-affected area has an accuracy rate of 93.92% in Siring Barat, 93.34% in Mindi, and 95.96% in Jatirejo. The methane concentration is passes the standard quality even though the air quality index is safe. Hence, the area is indicated into Hazardous level. In addition, Mindi has highest and stable methane concentration. It means that Mindi has high-risk air pollution.
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....
ALGORITHMS FOR THE PROGRAMMING OF FOOTWEAR SOLES MOULDS ON WORKING POSTS OF INJECTION MACHINES
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LUCA Cornelia
2014-05-01
Full Text Available The moulds stock necessary for realization in rhythmically conditions, a certain volume of footwear soles depends on some criterions such as: the range of soles for footwear volume daily realized, the sizes structure of those soles for footwear and, respectively, the sizes tally, the technological cycle for an used mould depending on the equipment efficiency, the provide necessity of spare moulds, the using and fixing conditions etc. From the efficiency point of view, the equipments may have two working posts, or more working posts (always, an even number, as 6, 12, 24, 40 posts. Footwear soles manufacturing takes into account the percentage distribution of the size numbers of the size series. When o portative assembly is used for the manufacturing of the footwear soles using the injection with “n” working posts, it is very important an optimum distribution of the working posts. The disadvantages of these equipments are the situations of the no equilibrium programming of the moulds, so that, in one time, some working posts spread out of the work. The paper presents some practical and theoretical solutions for moulds stock programming in portative assembly for footwear soles injection, so that an optimum equilibrium degree of the working posts will obtain
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.
Comparison between linear quadratic and early time dose models
International Nuclear Information System (INIS)
Chougule, A.A.; Supe, S.J.
1993-01-01
During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs
A Branch and Bound Algorithm for a Class of Biobjective Mixed Integer Programs
DEFF Research Database (Denmark)
Stidsen, Thomas Riis; Andersen, Kim Allan; Dammann, Bernd
2014-01-01
there is the complicating factor that some of the variables are required to be integral. The resulting class of problems is named multiobjective mixed integer programming (MOMIP) problems. Solving these kinds of optimization problems exactly requires a method that can generate the whole set of nondominated points (the...... Pareto-optimal front). In this paper, we first give a survey of the newly developed branch and bound methods for solving MOMIP problems. After that, we propose a new branch and bound method for solving a subclass of MOMIP problems, where only two objectives are allowed, the integer variables are binary......, and one of the two objectives has only integer variables. The proposed method is able to find the full set of nondominated points. It is tested on a large number of problem instances, from six different classes of MOMIP problems. The results reveal that the developed biobjective branch and bound method...
The quadratic reciprocity law a collection of classical proofs
Baumgart, Oswald
2015-01-01
This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.
Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems
International Nuclear Information System (INIS)
Marquette, Ian
2011-01-01
There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.
Directory of Open Access Journals (Sweden)
Luman Zhao
2015-01-01
Full Text Available A thrust allocation method was proposed based on a hybrid optimization algorithm to efficiently and dynamically position a semisubmersible drilling rig. That is, the thrust allocation was optimized to produce the generalized forces and moment required while at the same time minimizing the total power consumption under the premise that forbidden zones should be taken into account. An optimization problem was mathematically formulated to provide the optimal thrust allocation by introducing the corresponding design variables, objective function, and constraints. A hybrid optimization algorithm consisting of a genetic algorithm and a sequential quadratic programming (SQP algorithm was selected and used to solve this problem. The proposed method was evaluated by applying it to a thrust allocation problem for a semisubmersible drilling rig. The results indicate that the proposed method can be used as part of a cost-effective strategy for thrust allocation of the rig.
Large N saddle formulation of quadratic building block theories
International Nuclear Information System (INIS)
Halpern, M.B.
1980-01-01
I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)
Remarks on second-order quadratic systems in algebras
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Art Sagle
2017-10-01
Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.
Quantum tomography and classical propagator for quadratic quantum systems
International Nuclear Information System (INIS)
Man'ko, O.V.
1999-03-01
The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)
New robust chaotic system with exponential quadratic term
International Nuclear Information System (INIS)
Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)
Subgroups of class groups of algebraic quadratic function fields
International Nuclear Information System (INIS)
Wang Kunpeng; Zhang Xianke
2001-09-01
Ideal class groups H(K) of algebraic quadratic function fields K are studied, by using mainly the theory of continued fractions of algebraic functions. Properties of such continued fractions are discussed first. Then a necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, this criterion condition holds true for both real and imaginary fields K. Furthermore, several series of function fields K, including real, inertia imaginary, as well as ramified imaginary quadratic function fields, are given, and their class groups H(K) are proved to contain cyclic subgroups of order n. (author)
Jackson, M A
1982-01-01
The programmer's task is often taken to be the construction of algorithms, expressed in hierarchical structures of procedures: this view underlies the majority of traditional programming languages, such as Fortran. A different view is appropriate to a wide class of problem, perhaps including some problems in High Energy Physics. The programmer's task is regarded as having three main stages: first, an explicit model is constructed of the reality with which the program is concerned; second, thi...
Synthesis of concentric circular antenna arrays using dragonfly algorithm
Babayigit, B.
2018-05-01
Due to the strong non-linear relationship between the array factor and the array elements, concentric circular antenna array (CCAA) synthesis problem is challenging. Nature-inspired optimisation techniques have been playing an important role in solving array synthesis problems. Dragonfly algorithm (DA) is a novel nature-inspired optimisation technique which is based on the static and dynamic swarming behaviours of dragonflies in nature. This paper presents the design of CCAAs to get low sidelobes using DA. The effectiveness of the proposed DA is investigated in two different (with and without centre element) cases of two three-ring (having 4-, 6-, 8-element or 8-, 10-, 12-element) CCAA design. The radiation pattern of each design cases is obtained by finding optimal excitation weights of the array elements using DA. Simulation results show that the proposed algorithm outperforms the other state-of-the-art techniques (symbiotic organisms search, biogeography-based optimisation, sequential quadratic programming, opposition-based gravitational search algorithm, cat swarm optimisation, firefly algorithm, evolutionary programming) for all design cases. DA can be a promising technique for electromagnetic problems.
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...
Heim, Catherine; Cole, Elaine; West, Anita; Tai, Nigel; Brohi, Karim
2016-09-01
Quality improvement (QI) programs have shown to reduce preventable mortality in trauma care. Detailed review of all trauma deaths is a time and resource consuming process and calculated probability of survival (Ps) has been proposed as audit filter. Review is limited on deaths that were 'expected to survive'. However no Ps-based algorithm has been validated and no study has examined elements of preventability associated with deaths classified as 'expected'. The objective of this study was to examine whether trauma performance review can be streamlined using existing mortality prediction tools without missing important areas for improvement. We conducted a retrospective study of all trauma deaths reviewed by our trauma QI program. Deaths were classified into non-preventable, possibly preventable, probably preventable or preventable. Opportunities for improvement (OPIs) involve failure in the process of care and were classified into clinical and system deviations from standards of care. TRISS and PS were used for calculation of probability of survival. Peer-review charts were reviewed by a single investigator. Over 8 years, 626 patients were included. One third showed elements of preventability and 4% were preventable. Preventability occurred across the entire range of the calculated Ps band. Limiting review to unexpected deaths would have missed over 50% of all preventability issues and a third of preventable deaths. 37% of patients showed opportunities for improvement (OPIs). Neither TRISS nor PS allowed for reliable identification of OPIs and limiting peer-review to patients with unexpected deaths would have missed close to 60% of all issues in care. TRISS and PS fail to identify a significant proportion of avoidable deaths and miss important opportunities for process and system improvement. Based on this, all trauma deaths should be subjected to expert panel review in order to aim at a maximal output of performance improvement programs. Copyright © 2016 Elsevier
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Narong Wichapa
2018-01-01
Full Text Available Infectious waste disposal remains one of the most serious problems in the medical, social and environmental domains of almost every country. Selection of new suitable locations and finding the optimal set of transport routes for a fleet of vehicles to transport infectious waste material, location routing problem for infectious waste disposal, is one of the major problems in hazardous waste management. Determining locations for infectious waste disposal is a difficult and complex process, because it requires combining both intangible and tangible factors. Additionally, it depends on several criteria and various regulations. This facility location problem for infectious waste disposal is complicated, and it cannot be addressed using any stand-alone technique. Based on a case study, 107 hospitals and 6 candidate municipalities in Upper-Northeastern Thailand, we considered criteria such as infrastructure, geology and social & environmental criteria, evaluating global priority weights using the fuzzy analytical hierarchy process (Fuzzy AHP. After that, a new multi-objective facility location problem model which hybridizes fuzzy AHP and goal programming (GP, namely the HGP model, was tested. Finally, the vehicle routing problem (VRP for a case study was formulated, and it was tested using a hybrid genetic algorithm (HGA which hybridizes the push forward insertion heuristic (PFIH, genetic algorithm (GA and three local searches including 2-opt, insertion-move and interexchange-move. The results show that both the HGP and HGA can lead to select new suitable locations and to find the optimal set of transport routes for vehicles delivering infectious waste material. The novelty of the proposed methodologies, HGP, is the simultaneous combination of relevant factors that are difficult to interpret and cost factors in order to determine new suitable locations, and HGA can be applied to determine the transport routes which provide a minimum number of vehicles
Energy Technology Data Exchange (ETDEWEB)
Wichapa, Narong; Khokhajaikiat, Porntep
2017-07-01
Disposal of infectious waste remains one of the most serious problems in the social and environmental domains of almost every nation. Selection of new suitable locations and finding the optimal set of transport routes to transport infectious waste, namely location routing problem for infectious waste disposal, is one of the major problems in hazardous waste management. Design/methodology/approach: Due to the complexity of this problem, location routing problem for a case study, forty hospitals and three candidate municipalities in sub-Northeastern Thailand, was divided into two phases. The first phase is to choose suitable municipalities using hybrid fuzzy goal programming model which hybridizes the fuzzy analytic hierarchy process and fuzzy goal programming. The second phase is to find the optimal routes for each selected municipality using hybrid genetic algorithm which hybridizes the genetic algorithm and local searches including 2-Opt-move, Insertion-move and ?-interchange-move. Findings: The results indicate that the hybrid fuzzy goal programming model can guide the selection of new suitable municipalities, and the hybrid genetic algorithm can provide the optimal routes for a fleet of vehicles effectively. Originality/value: The novelty of the proposed methodologies, hybrid fuzzy goal programming model, is the simultaneous combination of both intangible and tangible factors in order to choose new suitable locations, and the hybrid genetic algorithm can be used to determine the optimal routes which provide a minimum number of vehicles and minimum transportation cost under the actual situation, efficiently.
International Nuclear Information System (INIS)
Wichapa, Narong; Khokhajaikiat, Porntep
2017-01-01
Disposal of infectious waste remains one of the most serious problems in the social and environmental domains of almost every nation. Selection of new suitable locations and finding the optimal set of transport routes to transport infectious waste, namely location routing problem for infectious waste disposal, is one of the major problems in hazardous waste management. Design/methodology/approach: Due to the complexity of this problem, location routing problem for a case study, forty hospitals and three candidate municipalities in sub-Northeastern Thailand, was divided into two phases. The first phase is to choose suitable municipalities using hybrid fuzzy goal programming model which hybridizes the fuzzy analytic hierarchy process and fuzzy goal programming. The second phase is to find the optimal routes for each selected municipality using hybrid genetic algorithm which hybridizes the genetic algorithm and local searches including 2-Opt-move, Insertion-move and ?-interchange-move. Findings: The results indicate that the hybrid fuzzy goal programming model can guide the selection of new suitable municipalities, and the hybrid genetic algorithm can provide the optimal routes for a fleet of vehicles effectively. Originality/value: The novelty of the proposed methodologies, hybrid fuzzy goal programming model, is the simultaneous combination of both intangible and tangible factors in order to choose new suitable locations, and the hybrid genetic algorithm can be used to determine the optimal routes which provide a minimum number of vehicles and minimum transportation cost under the actual situation, efficiently.
Directory of Open Access Journals (Sweden)
Narong Wichapa
2017-11-01
Originality/value: The novelty of the proposed methodologies, hybrid fuzzy goal programming model, is the simultaneous combination of both intangible and tangible factors in order to choose new suitable locations, and the hybrid genetic algorithm can be used to determine the optimal routes which provide a minimum number of vehicles and minimum transportation cost under the actual situation, efficiently.
Decentralized linear quadratic power system stabilizers for multi ...
Indian Academy of Sciences (India)
Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
ON WEIGHTED GENERALIZED FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS
Directory of Open Access Journals (Sweden)
E. L. Shishkina
2016-12-01
Full Text Available In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with the Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with the Bessel operator.
Feedback nash equilibria for linear quadratic descriptor differential games
Engwerda, J.C.; Salmah, S.
2012-01-01
In this paper, we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a
Initial post dynamic buckling of a quadratic-cubic column ...
African Journals Online (AJOL)
In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains ...
Quadratic algebras in the noncommutative integration method of wave equation
International Nuclear Information System (INIS)
Varaksin, O.L.
1995-01-01
The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras
Propagator of a time-dependent unbound quadratic Hamiltonian system
International Nuclear Information System (INIS)
Yeon, K.H.; Kim, H.J.; Um, C.I.; George, T.F.; Pandey, L.N.
1996-01-01
The propagator for a time-dependent unbound quadratic Hamiltonian system is explicitly evaluated using the path integral method. Two time-invariant quantities of the system are found where these invariants determine whether or not the system is bound. Several examples are considered to illustrate that the propagator obtained for the unbound systems is correct
On Fredholm-Stieltjes quadratic integral equation with supremum
International Nuclear Information System (INIS)
Darwish, M.A.
2007-08-01
We prove an existence theorem of monotonic solutions for a quadratic integral equation of Fredholm-Stieltjes type in C[0,1]. The concept of measure of non-compactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof. (author)
Quadratic theory and feedback controllers for linear time delay systems
International Nuclear Information System (INIS)
Lee, E.B.
1976-01-01
Recent research on the design of controllers for systems having time delays is discussed. Results for the ''open loop'' and ''closed loop'' designs will be presented. In both cases results for minimizing a quadratic cost functional are given. The usefulness of these results is not known, but similar results for the non-delay case are being routinely applied. (author)
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
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
Quadratic Poisson brackets compatible with an algebra structure
Balinsky, A. A.; Burman, Yu.
1994-01-01
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.
On misclassication probabilities of linear and quadratic classiers ...
African Journals Online (AJOL)
We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: ...
Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games
Engwerda, J.C.; Salmah, Y.
2010-01-01
In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a
A Unified Approach to Teaching Quadratic and Cubic Equations.
Ward, A. J. B.
2003-01-01
Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)
Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions
Leyendekkers, J. V.; Shannon, A. G.
2004-01-01
An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.
Visualising the Complex Roots of Quadratic Equations with Real Coefficients
Bardell, Nicholas S.
2012-01-01
The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…