Artificial glowworm swarm optimization algorithm for 0-1 knapsack problem%0-1背包问题的萤火虫群优化算法
程魁; 马良
2013-01-01
根据群集智能优化原理,给出了一种基于萤火虫寻优思想的新算法——萤火虫群优化算法,并针对0-1背包问题进行求解.经仿真实验并与蜂群算法、蚁群算法和微粒群算法进行了比较,获得了满意的结果,这说明了算法在0-1背包问题求解上的有效性和具有更快的收敛速度,拓展了萤火虫群优化算法的应用领域.%According to the principle of swarm intelligence, this paper proposed a new optimization algorithm based on the ideas of glowworms;the glowworm swarm optimization(GSO) algorithm to solve the 0-1 knapsack problem. Through the numerical simulations , it compared with that of artificial bee colony algorithm, ant colony optimization algorithm and particle swarm optimization. And it obtains the satisfactory results,which show the validity and effectiveness of the algorithm,expands the applications of GSO.
Stolpe, Mathias
2004-01-01
linear or as convex quadratic mixed 0-1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design......-state heat conduction and linear elasticity....
无
2000-01-01
In this article, we propose sharpening the gain of the chaotic annealing neural network to solve 0- 1 constrained optimization problem. During the chaotic annealing, the gain of the neurons gradually increases and finally arrives at a large value. This strategy can accelerate the convergence of the network to the binary state and keep the satisfaction of the constrains. The simulations, which take the knapsack problems as examples,demonstrate that the approach is efficient both in approximating the global solution and the number of iterations.
Emergence of robust solutions to 0-1 optimization problems in multi-agent systems
formation principles in engineering by designing multi-agent systems with appropriate interactions. By extracting selection processes as one of the main principles of pattern formation, we bridge the gap between detailed knowledge of self-organization in complex systems in natural science and its...... constructive application in engineering. The approach is demonstrated by giving two examples: First, time-dependent robot-target assignment problems with several autonomous robots and several targets are considered as model of flexible manufacturing systems. Each manufacturing target has to be served...... in a given time interval by one and only one robot and the total working costs have to be minimized (or total profits maximized). A specifically constructed dynamical system approach (coupled selection equations) is used which is based on pattern formation principles and results in fault resistant and robust...
Chaotic Neural Network Technique for "0-1" Programming Problems
王秀宏; 乔清理; 王正欧
2003-01-01
0-1 programming is a special case of the integer programming, which is commonly encountered in many optimization problems. Neural network and its general energy function are presented for 0-1 optimization problem. Then,the 0-1 optimization problems are solved by a neural network model with transient chaotic dynamics (TCNN). Numerical simulations of two typical 0-1 optimization problems show that TCNN can overcome HNN's main drawbacks that it suffers from the local minimum and can search for the global optimal solutions in to solveing 0-1 optimization problems.
薛峰; 陈刚; 高尚
2011-01-01
The classical particle swarm optimization is a powerful method to find the minimum of a numerical function,on a continuous definition domain. The particle swarm optimization algorithm combine the ideal of the genetic algorithm is recommended to solve 0-1 integer programming problem. All the 6 hybrid particle swarm optimization algorithms are proved effective. Especially the hybrid particle swarm optimization algorithm with across strategy A and mutation strategy C is a simple and effective better algorithm than others. It can easily be modified for any combinatorial problem for which we have no good specialized algorithm.%经典的粒子群是一个有效的寻找连续函数极值的方法,结合遗传算法的思想提出的混合粒子群算法来解决0-1整数规划问题,经过比较测试,6种混合粒子群算法的效果都比较好,特别交叉策略A和变异策略C的混合粒子群算法是最好的且简单有效的算法.对于目前还没有好的解法的组合优化问题,很容易地修改此算法就可解决.
Simulated Annealing for the 0/1 Multidimensional Knapsack Problem
Fubin Qian; Rui Ding
2007-01-01
In this paper a simulated annealing (SA) algorithm is presented for the 0/1 multidimensional knapsack problem. Problem-specific knowledge is incorporated in the algorithm description and evaluation of parameters in order to look into the performance of finite-time implementations of SA. Computational results show that SA performs much better than a genetic algorithm in terms of solution time, whilst having a modest loss of solution quality.
Linearization of multi-objective multi-quadratic 0-1 programming problems
Shifali Bhargava
2014-03-01
Full Text Available A linearization technique is developed for multi-objective multi-quadratic 0-1 programming problems with linear and quadratic constraints to reduce it to multi-objective linear mixed 0-1 programming problems. The method proposed in this paper needs only O (kn additional continuous variables where k is the number of quadratic constraints and n is the number of initial 0-1 variables. Keywords: Knapsack Constraint, Linearization, Multi-Objective, Multi-Quadratic, Optimal Solution.
Quantum Immune Clonal Selection Algorithm for Multi-objective 0/1 Knapsack Problems
Based on the concept and principles of quantum computing and the principle of the immune clonal selection, a new algorithm for multi-objective 0/1 knapsack problems is introduced. In the algorithm, for the novel representation, qubit antibodies in the antibody population are updated by applying a new chaos update strategy. A quantitative metric is used for testing the convergence to the Pareto-optimal front. Simulation results on the 0/1 knapsack problems show that the new algorithm, in most cases, is more effective. (general)
An Improved Hybrid Encoding Cuckoo Search Algorithm for 0-1 Knapsack Problems
Yanhong Feng; Ke Jia; Yichao He
2014-01-01
Cuckoo search (CS) is a new robust swarm intelligence method that is based on the brood parasitism of some cuckoo species. In this paper, an improved hybrid encoding cuckoo search algorithm (ICS) with greedy strategy is put forward for solving 0-1 knapsack problems. First of all, for solving binary optimization problem with ICS, based on the idea of individual hybrid encoding, the cuckoo search over a continuous space is transformed into the synchronous evolution search over discrete space....
This paper considers a bi-criteria general 0-1 random fuzzy programming problem based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problem is not well-defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goals for objectives, and considering the maximization of the aspiration level for total profit and the degree of necessity that the objective function's value satisfies the fuzzy goal, the main problem is transformed into a deterministic equivalent problem. Furthermore, by using the assumption that each random variable is distributed according to a normal distribution, the problem is equivalently transformed into a basic 0-1 programming problem, and the efficient strict solution method to find an optimal solution is constructed.
A Novel Harmony Search Algorithm Based on Teaching-Learning Strategies for 0-1 Knapsack Problems
Shouheng Tuo; Longquan Yong; Fang’an Deng
2014-01-01
To enhance the performance of harmony search (HS) algorithm on solving the discrete optimization problems, this paper proposes a novel harmony search algorithm based on teaching-learning (HSTL) strategies to solve 0-1 knapsack problems. In the HSTL algorithm, firstly, a method is presented to adjust dimension dynamically for selected harmony vector in optimization procedure. In addition, four strategies (harmony memory consideration, teaching-learning strategy, local pitch adjusting, and rand...
An improved hybrid encoding cuckoo search algorithm for 0-1 knapsack problems.
Feng, Yanhong; Jia, Ke; He, Yichao
2014-01-01
Cuckoo search (CS) is a new robust swarm intelligence method that is based on the brood parasitism of some cuckoo species. In this paper, an improved hybrid encoding cuckoo search algorithm (ICS) with greedy strategy is put forward for solving 0-1 knapsack problems. First of all, for solving binary optimization problem with ICS, based on the idea of individual hybrid encoding, the cuckoo search over a continuous space is transformed into the synchronous evolution search over discrete space. Subsequently, the concept of confidence interval (CI) is introduced; hence, the new position updating is designed and genetic mutation with a small probability is introduced. The former enables the population to move towards the global best solution rapidly in every generation, and the latter can effectively prevent the ICS from trapping into the local optimum. Furthermore, the greedy transform method is used to repair the infeasible solution and optimize the feasible solution. Experiments with a large number of KP instances show the effectiveness of the proposed algorithm and its ability to achieve good quality solutions. PMID:24527026
Optimal obstacle control problem
ZHU Li; LI Xiu-hua; GUO Xing-ming
2008-01-01
In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality. Existence, uniqueness and regularity of the optimal control problem are established. In addition, the approximation of the optimal obstacle problem is also studied.
A Novel Genetic Algorithm using Helper Objectives for the 0-1 Knapsack Problem
He, Jun; He, Feidun; Dong, Hongbin
2014-01-01
The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms are well suited for solving the knapsack problem and they find reasonably good solutions quickly. A naturally arising question is whether genetic algorithms are able to find solutions as good as approximation algorithms do. This paper presents a novel multi-o...
Yanhong Feng; Gai-Ge Wang; Qingjiang Feng; Xiang-Jun Zhao
2014-01-01
An effective hybrid cuckoo search algorithm (CS) with improved shuffled frog-leaping algorithm (ISFLA) is put forward for solving 0-1 knapsack problem. First of all, with the framework of SFLA, an improved frog-leap operator is designed with the effect of the global optimal information on the frog leaping and information exchange between frog individuals combined with genetic mutation with a small probability. Subsequently, in order to improve the convergence speed and enhance the exploitatio...
Yanhong Feng; Gai-Ge Wang; Qingjiang Feng; Xiang-Jun Zhao
2014-01-01
An effective hybrid cuckoo search algorithm (CS) with improved shuffled frog-leaping algorithm (ISFLA) is put forward for solving 0-1 knapsack problem. First of all, with the framework of SFLA, an improved frog-leap operator is designed with the effect of the global optimal information on the frog leaping and information exchange between frog individuals combined with genetic mutation with a small probability. Subsequently, in order to improve the ...
Convergence of Optimization Problems
K. Jeyalakshmi
2012-03-01
Full Text Available In this paper we consider a general optimization problem (OP and study the convergence and approximation of optimal values and optimal solutions to changes in the cost function and the set of feasible solutions. We consider the convergence optimization problems under the familiar notion of uniform convergence. We do not assume the convexity of the functions involved. Instead we consider a class of functions whose directional derivatives are convex. They are known as locally convex functions or following Craven and Mond nearly convex functions. We given necessary preliminaries and we prove that a sequence of locally convex optimization problems converge to a locally convex problem. We also prove that uniform convergence of locally convex optimization problems implies epi-graph convergence of the problems. Even though for simplicity we have taken locally convex functions, the results given here can be proved for locally Lipchitz functions also.
Solving the 0/1 Knapsack Problem by a Biomolecular DNA Computer
Hassan Taghipour
2013-01-01
Full Text Available Solving some mathematical problems such as NP-complete problems by conventional silicon-based computers is problematic and takes so long time. DNA computing is an alternative method of computing which uses DNA molecules for computing purposes. DNA computers have massive degrees of parallel processing capability. The massive parallel processing characteristic of DNA computers is of particular interest in solving NP-complete and hard combinatorial problems. NP-complete problems such as knapsack problem and other hard combinatorial problems can be easily solved by DNA computers in a very short period of time comparing to conventional silicon-based computers. Sticker-based DNA computing is one of the methods of DNA computing. In this paper, the sticker based DNA computing was used for solving the 0/1 knapsack problem. At first, a biomolecular solution space was constructed by using appropriate DNA memory complexes. Then, by the application of a sticker-based parallel algorithm using biological operations, knapsack problem was resolved in polynomial time.
Design optimization of a 0.1-ton/day active magnetic regenerative hydrogen liquefier
Zhang, L.; Sherif, S. A.; DeGregoria, A. J.; Zimm, C. B.; Veziroglu, T. N.
2000-04-01
A design optimization procedure of a 0.1-ton/day active magnetic regenerative (AMR) hydrogen liquefier model is described. The liquefier is proposed for the industrial liquid hydrogen market with overall efficiency being the primary measure of performance. This performance is described here in terms of particle size, bed length, and inter-stage temperature. Efficiency comparable to larger gas cycle plants is predicted. The magnetic liquefier may be modified to operate as a two-stage magnetic refrigerator between 77 and 20 K with high efficiency. The paper describes an optimization method as applied to the design of a two-stage AMR hydrogen liquefier and presents the associated results. A five-parameter optimization process is performed since there are five changeable parameters; the low- and high-stage particle sizes, the low- and high-stage bed lengths, and the inter-stage temperature. Model results are presented and compared with experimental results of an actual liquefier.
Bee Colony Algorithm for the Multi-objective 0-1 Programming Problem%多目标0-1规划问题的蜂群算法
韩燕燕; 马良; 赵小强
2012-01-01
In order to solve the multi-objective 0-1 programming problem with linear constrains, we present a new intelligent optimization algorithm--bee colony algorithm. The algorithm is coded and implemented on microcomputer through aseries of numerical tests. Comparisons with genetic algorithm, ant colony optimization algorithm and cellular ant colony algorithm show that the bee colony algorithm can get more pareto solutions to the multi-objective 0-1 programming problem. And the effectiveness of the Bee Colony Algorithm is validated.%针对多目标0-1规划问题,本文给出一种新型的智能优化算法——蜂群算法进行求解,并通过实例验证,与遗传算法、蚁群算法和元胞蚁群算法作了相应比较.就多目标0-1规划问题而言,蜂群算法能得到更多的Pareto解,说明了蜂群算法在解决该类问题上的有效性.
Yanhong Feng
2014-01-01
Full Text Available An effective hybrid cuckoo search algorithm (CS with improved shuffled frog-leaping algorithm (ISFLA is put forward for solving 0-1 knapsack problem. First of all, with the framework of SFLA, an improved frog-leap operator is designed with the effect of the global optimal information on the frog leaping and information exchange between frog individuals combined with genetic mutation with a small probability. Subsequently, in order to improve the convergence speed and enhance the exploitation ability, a novel CS model is proposed with considering the specific advantages of Lévy flights and frog-leap operator. Furthermore, the greedy transform method is used to repair the infeasible solution and optimize the feasible solution. Finally, numerical simulations are carried out on six different types of 0-1 knapsack instances, and the comparative results have shown the effectiveness of the proposed algorithm and its ability to achieve good quality solutions, which outperforms the binary cuckoo search, the binary differential evolution, and the genetic algorithm.
Feng, Yanhong; Wang, Gai-Ge; Feng, Qingjiang; Zhao, Xiang-Jun
2014-01-01
An effective hybrid cuckoo search algorithm (CS) with improved shuffled frog-leaping algorithm (ISFLA) is put forward for solving 0-1 knapsack problem. First of all, with the framework of SFLA, an improved frog-leap operator is designed with the effect of the global optimal information on the frog leaping and information exchange between frog individuals combined with genetic mutation with a small probability. Subsequently, in order to improve the convergence speed and enhance the exploitation ability, a novel CS model is proposed with considering the specific advantages of Lévy flights and frog-leap operator. Furthermore, the greedy transform method is used to repair the infeasible solution and optimize the feasible solution. Finally, numerical simulations are carried out on six different types of 0-1 knapsack instances, and the comparative results have shown the effectiveness of the proposed algorithm and its ability to achieve good quality solutions, which outperforms the binary cuckoo search, the binary differential evolution, and the genetic algorithm. PMID:25404940
求解0-1背包问题的二进制狼群算法%A binary wolf pack algorithm for solving 0-1 knapsack problem
吴虎胜; 张凤鸣; 战仁军; 汪送; 张超
2014-01-01
狼群算法（wolf pack algorithm，WPA）源于狼群在捕食及其猎物分配中所体现的群体智能，已被成功应用于复杂函数求解。在此基础上，通过定义运动算子，对人工狼位置、步长和智能行为重新进行二进制编码设计，提出了一种解决离散空间组合优化问题的二进制狼群算法（binary wolf pack algorithm，BWPA）。该算法保留了狼群算法基于职责分工的协作式搜索特性，选取离散空间的经典问题---0-1背包问题进行仿真实验，具体通过10组经典的背包问题算例和 BWPA 算法与经典的二进制粒子群算法、贪婪遗传算法、量子遗传算法在求解3组高维背包问题时的对比计算，例证了算法具有相对更好的稳定性和全局寻优能力。%The wolf pack algorithm (WPA),inspired by swarm intelligence of wolf pack in their prey hun-ting behaviors and distribution mode,has been proposed and successfully applied in complex function optimiza-tion problems.Based on the designing of the move operator,the artificial wolves’position,step-length and in-telligent behaviors are redesigned by binary coding,and a binary wolf pack algorithm (BWPA)is proposed to solve combinatorial optimization problems in discrete spaces.BWPA preserves the feature of cooperative search-ing based on job distribution of the wolf pack and is applied to 10 classic 0-1 knapsack problems.Moreover,the 3 high-dimensional 0-1 knapsack problems are tested.All results show that BWPA has better global convergence and computational robustness and outperforms the binary particle swarm optimization algorithm,the greedy genetic al-gorithm and the quantum genetic algorithm,especially for high-dimensional knapsack problems.
Decomposition Approaches for Optimization Problems
Kinable, Joris
2014-01-01
This dissertation encompasses the development of decomposition approaches for a variety of both real-world and fundamental optimization problems. Many optimization problems comprise of multiple interconnected subproblems, often rendering them too large or too complicated to solve as a single integral problem. Decomposition approaches are required to deal with these problems efficiently. By decomposing a problem into multiple subproblems, efficient dedicated procedures can be employed to solve...
A Problem on Optimal Transportation
Cechlarova, Katarina
2005-01-01
Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…
Topology optimization for acoustic problems
Dühring, Maria Bayard
In this paper a method to control acoustic properties in a room with topology optimization is presented. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized by distribution of material in a design domain along the ceiling in 2D and 3D. Nice 0-1 designs...
About an optimal visiting problem
Bagagiolo, Fabio; Benetton, Michela
2010-01-01
In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous "Traveling Salesman Problem" and brings all its computational diculties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equat...
求解0-1背包问题的改进混合遗传算法%Improved Hybrid Genetic Algorithm for Solving 0-1 Knapsack Problem
刘寒冰; 张亚娟
2015-01-01
针对一种混合遗传算法所采用的贪心变换法的不足，给出了一种改进的贪心修正法；并基于稳态复制的策略，对遗传算法的选择操作进行改进，给出了随机选择操作。在此基础上，提出了一种改进的混合遗传算法，并将新算法用于解决大规模的0-1背包问题，通过实例将新算法与 HGA 算法进行实验对比分析，并研究了变异概率对新算法性能的影响。实验结果表明新算法收敛速度快，寻优能力强。%An improved greedy correction method is advanced for overcome the flaw of greedy transform method adopted by hybrid genetic algorithm (HGA). And based on steady state reproduction strategy, the choice method of random selection is advanced. These new methods are combined with genetic algorithm to propose a high-efficient hybrid genetic algorithm (IHGA), and new algorithm was used to solve large-scale 0-1 knapsack problem. By many simulation experiments, IHGA algorithm is compared with HGA algorithm, and how the mutation probability affect the performance of the new algorithm has been studied. The experimental results show that the new algorithm has higher convergent speed and better optimization capability.
Topology optimization of flow problems
Gersborg, Allan Roulund
2007-01-01
This thesis investigates how to apply topology optimization using the material distribution technique to steady-state viscous incompressible flow problems. The target design applications are fluid devices that are optimized with respect to minimizing the energy loss, characteristic properties of...... dominated transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the thesis gives a proof-of-concept for the application of the method within fluid dynamic problems and it remains of interest for the design of microfluidic devices. Furthermore, the thesis contributes...... community. Although the study of the FVM is carried out using a simple heat conduction problem, the work illuminates and discusses the technicalities of employing the FVM in connection with topology optimization. Finally, parallelized solution methods are investigated using the high performance computing...
About an Optimal Visiting Problem
Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it; Benetton, Michela [Unversita di Trento, Dipartimento di Matematica (Italy)
2012-02-15
In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous 'Traveling Salesman Problem' and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equation. We introduce some 'external' variables, one per target, which keep in memory whether the corresponding target is already visited or not, and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton-Jacobi equation turns out to be discontinuous.
Well-posed optimization problems
Dontchev, Asen L
1993-01-01
This book presents in a unified way the mathematical theory of well-posedness in optimization. The basic concepts of well-posedness and the links among them are studied, in particular Hadamard and Tykhonov well-posedness. Abstract optimization problems as well as applications to optimal control, calculus of variations and mathematical programming are considered. Both the pure and applied side of these topics are presented. The main subject is often introduced by heuristics, particular cases and examples. Complete proofs are provided. The expected knowledge of the reader does not extend beyond textbook (real and functional) analysis, some topology and differential equations and basic optimization. References are provided for more advanced topics. The book is addressed to mathematicians interested in optimization and related topics, and also to engineers, control theorists, economists and applied scientists who can find here a mathematical justification of practical procedures they encounter.
Optimization and geophysical inverse problems
Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F.; Gill, P.; Heinkenschloss, M.; Johnson, L.; McEvilly, T.; More, J.; Newman, G.; Oldenburg, D.; Parker, P.; Porto, B.; Sen, M.; Torczon, V.; Vasco, D.; Woodward, N.B.
2000-10-01
A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness
Vidal, Rene Victor Valqui
1994-01-01
The paper studies the problem of determining the number and dimensions of sizes of apparel so as to maximize profits. It develops a simple one-variable bisection search algorithm that gives the optimal solution. An example is solved interactively using a Macintosh LC and Math CAD, a mathematical...
The Duality on Vector Optimization Problems
HUANG Long-guang
2012-01-01
Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.
Stability Analysis for Stochastic Optimization Problems
无
2007-01-01
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
On Alternative Optimal Solutions to Linear Fractional Optimization Problems
ShengjiaXue
2004-01-01
The structure of the optimal solution set is derived for linear fractional optimization problems with the representation theorem of polyhedral sets．And the computational procedure in determining all optimal solutions is also given．
Some Undecidable Problems on Approximability of NP Optimization Problems
黄雄
1996-01-01
In this paper some undecidable problems on approximability of NP optimization problems are investigated.In particular,the following problems are all undecidable:(1) Given an NP optimization problem,is it approximable in polynomial time?(2)For any polynomial-time computable function r(n),given a polynomial time approximable NP optimization problem,has it a polynomial-time approximation algorithm with approximation performance ratio r(n) (r(n)-approximable)?(3)For any polynomial-time computable functions r(n),r'(n),where r'(n)
Applying optimization software libraries to engineering problems
Healy, M. J.
1984-01-01
Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.
Optimization of Uncertainty Features for Transportation Problems
Eggenberg, Niklaus; Salani, Matteo; Bierlaire, Michel
2008-01-01
In this work we present the concept of Uncertainty Feature Optimization (UFO), an optimization framework to handle problems due to noisy data. We show that UFO is an extension of standard methods as robust optimization and stochastic optimization and we show that the method can be used when no information of the data uncertainty sets is available. We present a proof of concept for the multiple knapsack problem and we show applications to some routing problems: vehicle routing with stochastic ...
CASE STUDY IN OPTIMAL TELEVISION ADVERTS SELECTION AS KNAPSACK PROBLEM
E. Ivokhin
2014-06-01
Full Text Available In this research paper, we shall consider the application of classical 0-1 knapsack problem with a single constraint to selection of television advertisements at critical periods such as prime time news, news adjacencies, break in news and peak times using the WINQSB software. In the end of this paper we shall formulate the task of investigation of the post optimality solution of optimal Television Adverts Selection with respect to time allocated for every group adverts.
Nonessential Functionals in Multiobjective Optimal Control Problems
Malinowska, A. B.; Torres, D. F. M.
2006-01-01
We address the problem of obtaining well-defined criteria for multiobjective optimal control systems. Necessary and sufficient conditions for an optimal control functional to be nonessential are proved. The results provide effective tools for determining nonessential objectives in vector-valued optimal control problems.
Artificial Ant Species on Solving Optimization Problems
Pintea, Camelia-M.
2013-01-01
During the last years several ant-based techniques were involved to solve hard and complex optimization problems. The current paper is a short study about the influence of artificial ant species in solving optimization problems. There are studied the artificial Pharaoh Ants, Lasius Niger and also artificial ants with no special specificity used commonly in Ant Colony Optimization.
Ant colony optimization in continuous problem
YU Ling; LIU Kang; LI Kaishi
2007-01-01
Based on the analysis of the basic ant colony optimization and optimum problem in a continuous space,an ant colony optimization (ACO) for continuous problem is constructed and discussed. The algorithm is efficient and beneficial to the study of the ant colony optimization in a continuous space.
On Optimizing the Satisfiability (SAT) Problem
GU Jun; GU Qianping; DU Dingzhu
1999-01-01
The satisfiability(SAT) problem is abasic problem in computing theory. Presently, an active area of researchon SAT problem is to design efficient optimization algorithms forfinding a solution for a satisfiable CNF formula. A newformulation, the Universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real spacehas been developed. Many optimization techniques,such as the steepest descent method, Newton's method, and thecoordinate descent method, can be used to solve the Universal SAT problem. In this paper, we prove that, when the initial solution issufficiently close to the optimal solution, the steepest descent methodhas a linear convergence ratio β<1, Newton's method has aconvergence ratio of order two, and the convergence ratio of thecoordinate descent method is approximately (1-β/m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the Universal SAT problem is alsopresented in this paper.
Multiple optimal solutions to a sort of nonlinear optimization problem
Xue Shengjia
2007-01-01
The optimization problem is considered in which the objective function is pseudolinear(both pseudoconvex and pseudoconcave) and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions ( ifthe uniqueness condition is not satisfied ) are provided. Finally, an illustrative example is also given.
Global optimization in inverse problem of scatterometry
Afraites, Lekbir; Hazart, Jérôme; Schiavone, Patrick
2009-01-01
International audience In the current work, we consider the inverse problem in scatterometry which consists in determining the feature shape from an experimental ellipsometric signature. The reformulation of the given nonlinear identification problem was considered as a parametric optimization problem using the Least Square criterion. In this work, a design procedure for global robust optimization is developed using Kriging and global optimization approaches. Robustness is determined by Kr...
Ant Colony Optimization and Hypergraph Covering Problems
Pat, Ankit
2011-01-01
Ant Colony Optimization (ACO) is a very popular metaheuristic for solving computationally hard combinatorial optimization problems. Runtime analysis of ACO with respect to various pseudo-boolean functions and different graph based combinatorial optimization problems has been taken up in recent years. In this paper, we investigate the runtime behavior of an MMAS*(Max-Min Ant System) ACO algorithm on some well known hypergraph covering problems that are NP-Hard. In particular, we have addressed the Minimum Edge Cover problem, the Minimum Vertex Cover problem and the Maximum Weak- Independent Set problem. The influence of pheromone values and heuristic information on the running time is analysed. The results indicate that the heuristic information has greater impact towards improving the expected optimization time as compared to pheromone values. For certain instances of hypergraphs, we show that the MMAS* algorithm gives a constant order expected optimization time when the dominance of heuristic information is ...
Constrained Graph Optimization: Interdiction and Preservation Problems
Schild, Aaron V [Los Alamos National Laboratory
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
A Mathematical Optimization Problem in Bioinformatics
Heyer, Laurie J.
2008-01-01
This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…
Particle swarm optimization for complex nonlinear optimization problems
Alexandridis, Alex; Famelis, Ioannis Th.; Tsitouras, Charalambos
2016-06-01
This work presents the application of a technique belonging to evolutionary computation, namely particle swarm optimization (PSO), to complex nonlinear optimization problems. To be more specific, a PSO optimizer is setup and applied to the derivation of Runge-Kutta pairs for the numerical solution of initial value problems. The effect of critical PSO operational parameters on the performance of the proposed scheme is thoroughly investigated.
Optimal transportation problems with free Dirichlet regions
Buttazzo, Giuseppe; Oudet, Edouard; Stepanov, E.
2002-01-01
A Dirichlet region for an optimal mass transportation problem is, roughly speaking, a zone in which the transportation cost is vanishing. We study the optimal transportation problem with an unknown Dirichlet region S which varies in the class of closed connected subsets having prescribed 1-dimensional Hausdorff measure. We show the existence of an optimal Sopt and study some of its geometrical properties. We also present numerical computations which show the shape of Sopt in some model examples.
Fast Solvers of Fredholm Optimal Control Problems
Mario; Borzì
2010-01-01
The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.
Optimization problems on the Sierpinski gasket
Marek Galewski
2016-04-01
Full Text Available We investigate the existence of an optimal process for such an optimal control problem in which the dynamics is given by the Dirichlet problem driven by weak Laplacian on the Sierpinski gasket. To accomplish this task using a direct variational approach with no global growth conditions on the nonlinear term, we consider the existence of solutions, their uniqueness and their dependence on a functional parameter for mentioned Dirichlet problem. This allows us to prove that the optimal control problem admits at least one solution.
Topology Optimization for Convection Problems
Alexandersen, Joe
2011-01-01
.This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...
Algorithms and Models For Combinatorial Optimization Problems
Fernandes Muritiba, Albert Einstein
2010-01-01
In this thesis we present some combinatorial optimization problems, suggest models and algorithms for their effective solution. For each problem,we give its description, followed by a short literature review, provide methods to solve it and, finally, present computational results and comparisons with previous works to show the effectiveness of the proposed approaches. The considered problems are: the Generalized Traveling Salesman Problem (GTSP), the Bin Packing Problem with Conflicts(BPPC) a...
Binary Cockroach Swarm Optimization for Combinatorial Optimization Problem
Ibidun Christiana Obagbuwa
2016-09-01
Full Text Available The Cockroach Swarm Optimization (CSO algorithm is inspired by cockroach social behavior. It is a simple and efficient meta-heuristic algorithm and has been applied to solve global optimization problems successfully. The original CSO algorithm and its variants operate mainly in continuous search space and cannot solve binary-coded optimization problems directly. Many optimization problems have their decision variables in binary. Binary Cockroach Swarm Optimization (BCSO is proposed in this paper to tackle such problems and was evaluated on the popular Traveling Salesman Problem (TSP, which is considered to be an NP-hard Combinatorial Optimization Problem (COP. A transfer function was employed to map a continuous search space CSO to binary search space. The performance of the proposed algorithm was tested firstly on benchmark functions through simulation studies and compared with the performance of existing binary particle swarm optimization and continuous space versions of CSO. The proposed BCSO was adapted to TSP and applied to a set of benchmark instances of symmetric TSP from the TSP library. The results of the proposed Binary Cockroach Swarm Optimization (BCSO algorithm on TSP were compared to other meta-heuristic algorithms.
Ant Colony Optimization for Capacity Problems
Tad Gonsalves
2015-01-01
Full Text Available This paper deals with the optimization of the capac ity of a terminal railway station using the Ant Colony Optimization algorithm. The capacity of the terminal station is defined as the number of trains that depart from the station in un it interval of time. The railway capacity optimization problem is framed as a typical symmetr ical Travelling Salesman Problem (TSP, with the TSP nodes representing the train arrival / departure events and the TSP total cost representing the total time-interval of the schedul e. The application problem is then optimized using the ACO algorithm. The simulation experiments validate the formulation of the railway capacity problem as a TSP and the ACO algorithm pro duces optimal solutions superior to those produced by the domain experts.
On the Ramified Optimal Allocation Problem
Xia, Qinglan
2011-01-01
This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and efficiently designed transport systems of branching structures. The ramified allocation problem aims at finding an optimal allocation plan as well as an associated optimal allocation path to minimize overall cost of transporting commodity from factories to households. This problem differentiates itself from existing ramified transportation literature in that the distribution of production among factories is not fixed but endogenously determined as observed in many allocation practices. It's shown that due to the transport economy of scale in ramified transportation, each optimal allocation plan corresponds equivalently to an optimal assignment map from households to factories. This optimal assignment map provides a natural partition of both households and allocation paths. We...
Optimization and inverse problems in electromagnetism
Wiak, Sławomir
2003-01-01
From 12 to 14 September 2002, the Academy of Humanities and Economics (AHE) hosted the workshop "Optimization and Inverse Problems in Electromagnetism". After this bi-annual event, a large number of papers were assembled and combined in this book. During the workshop recent developments and applications in optimization and inverse methodologies for electromagnetic fields were discussed. The contributions selected for the present volume cover a wide spectrum of inverse and optimal electromagnetic methodologies, ranging from theoretical to practical applications. A number of new optimal and inverse methodologies were proposed. There are contributions related to dedicated software. Optimization and Inverse Problems in Electromagnetism consists of three thematic chapters, covering: -General papers (survey of specific aspects of optimization and inverse problems in electromagnetism), -Methodologies, -Industrial Applications. The book can be useful to students of electrical and electronics engineering, computer sci...
Topology optimization of wave-propagation problems
Jensen, Jakob Søndergaard; Sigmund, Ole
Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures....
Topology optimization for transient heat transfer problems
Zeidan, Said; Sigmund, Ole; Lazarov, Boyan Stefanov
-stepping scheme. A PCM can efficiently absorb heat while keeping its temperature nearly unchanged [8]. The use of PCM ine.g. electronics [9] and mechanics [10], yields improved performance and lower costs depending on a.o., the spatial distribution of PCM.The considered problem consists in optimizing......The focus of this work is on passive control of transient heat transfer problems using the topology optimization (TopOpt) method [1]. The goal is to find distributions of a limited amount of phase change material (PCM), within a given design domain, which optimizes the heat energy storage [2]. Our...... aim is to obtain manufacturable designs [3] as well as demonstrating TopOpt for mixed multiphysics problems [4].TopOpt provides material distributions in a given design domain, optimized with respect to a given objective and satisfying a set of constraints. Originating in static mechanical problems...
Servo Problem within Fuel Consumption Optimization
Suzdaleva, Evgenia; Nagy, Ivan; Pavelková, Lenka; Mlynářová, Tereza
Columbo: IASTED, 2012, s. 100-107. ISBN 978-0-88986-941-7. [The IASTED International Conference on Engineering and Applied Science. Columbo (LK), 27.12.2012-29.12.2012] R&D Projects: GA TA ČR TA01030123 Keywords : control * servo problem * fuel consumption optimization Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/2013/AS/suzdaleva-servo problem within fuel consumption optimization.pdf
Problem of detecting inclusions by topological optimization
I. Faye
2014-01-01
Full Text Available In this paper we propose a new method to detect inclusions. The proposed method is based on shape and topological optimization tools. In fact after presenting the problem, we use topologication optimization tools to detect inclusions in the domain. Numerical results are presented.
Generalized Benders’ Decomposition for topology optimization problems
Munoz Queupumil, Eduardo Javier; Stolpe, Mathias
2011-01-01
This article considers the non-linear mixed 0–1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders’ Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness...
An improved group search optimizer for mechanical design optimization problems
Hai Shen; Yunlong Zhu; Ben Niu; Q.H. Wu
2009-01-01
This paper presents an improved group search optimizer (iGSO) for solving mechanical design optimization problems.In the pro-posed algorithm,subpopulations and a co-operation evolutionary strategy were adopted to improve the global search capability and convergence performance.The iGSO is evaluated on two optimization problems of classical mechanical design:spring and pressure vessel.The experimental results are analyzed in comparison with those reported in the literatures.The results show that iGSO has much better convergence performance and is easier to implement in comparison with other existing evolutionary algorithms.
An optimal design problem in wave propagation
Bellido, J.C.; Donoso, Alberto
2007-01-01
We consider an optimal design problem in wave propagation proposed in Sigmund and Jensen (Roy. Soc. Lond. Philos. Trans. Ser. A 361:1001-1019, 2003) in the one-dimensional situation: Given two materials at our disposal with different elastic Young modulus and different density, the problem consis...... prove also the existence of classical solutions in certain cases....
Belief Propagation Algorithm for Portfolio Optimization Problems.
Shinzato, Takashi; Yasuda, Muneki
2015-01-01
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm. PMID:26305462
Topology optimization of Channel flow problems
Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.
2005-01-01
]. Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity--driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost...... sensitivities. Our target application is optimal layout design of channels in fluid network systems. Using concepts borrowed from topology optimization of compliant mechanisms in solid mechanics, we introduce a method for the synthesis of fluidic components, such as switches, diodes, etc....
Sensitivity analysis in optimization and reliability problems
The paper starts giving the main results that allow a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. In particular, general results are given for non-linear programming, and closed formulas for linear programming problems are supplied. Next, the methods are applied to a collection of civil engineering reliability problems, which includes a bridge crane, a retaining wall and a composite breakwater. Finally, the sensitivity analysis formulas are extended to calculus of variations problems and a slope stability problem is used to illustrate the methods
The \\infty eigenvalue problem and a problem of optimal transportation
Champion, Thierry; De Pascale, Luigi; Jimenez, Chloé
2008-01-01
The so-called eigenvalues and eigenfunctions of the infinite Laplacian $\\Delta_\\infty$ are defined through an asymptotic study of that of the usual $p$-Laplacian $\\Delta_p$, this brings to a characterization via a non-linear eigenvalue problem for a PDE satisfied in the viscosity sense. In this paper, we obtain an other characterization of the first eigenvalue via a problem of optimal transportation, and recover properties of the first eigenvalue and corresponding positive eigenfunctions.
Solving constrained optimization problems with hybrid particle swarm optimization
Zahara, Erwie; Hu, Chia-Hsin
2008-11-01
Constrained optimization problems (COPs) are very important in that they frequently appear in the real world. A COP, in which both the function and constraints may be nonlinear, consists of the optimization of a function subject to constraints. Constraint handling is one of the major concerns when solving COPs with particle swarm optimization (PSO) combined with the Nelder-Mead simplex search method (NM-PSO). This article proposes embedded constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, as a special operator in NM-PSO for dealing with constraints. Experiments using 13 benchmark problems are explained and the NM-PSO results are compared with the best known solutions reported in the literature. Comparison with three different meta-heuristics demonstrates that NM-PSO with the embedded constraint operator is extremely effective and efficient at locating optimal solutions.
On ε-optimality conditions for multiobjective fractional optimization problems
Kim Gwi
2011-01-01
Full Text Available Abstract A multiobjective fractional optimization problem (MFP, which consists of more than two fractional objective functions with convex numerator functions and convex denominator functions, finitely many convex constraint functions, and a geometric constraint set, is considered. Using parametric approach, we transform the problem (MFP into the non-fractional multiobjective convex optimization problem (NMCP v with parametric v ∈ ℝ p , and then give the equivalent relation between (weakly ε-efficient solution of (MFP and (weakly -efficient solution of . Using the equivalent relations, we obtain ε-optimality conditions for (weakly ε-efficient solution for (MFP. Furthermore, we present examples illustrating the main results of this study. 2000 Mathematics Subject Classification: 90C30, 90C46.
Graph optimization problems on a Bethe lattice
de Oliveira, Mário J.
1989-01-01
The p-partitioning and p-coloring problems on a Bethe lattice of coordination number z are analyzed. It is shown that these two NP-complete optimization problems turn out to be equivalent to finding the ground-state energy of p-state Potts models with frustration. Numerical calculation of the cost function of both problems are carried out for several values of z and p. In the case of p=2 the results are identical to those obtained by Mézard and Parisi for the case of the bipartitioning problem. A numerical upper bound to the chromatic number is found for several values of z.
Quantum optimization and maximum clique problems
Yatsenko, Vitaliy A.; Pardalos, Panos M.; Chiarini, Bruno H.
2004-08-01
This paper describes a new approach to global optimization and control uses geometric methods and modern quantum mathematics. Polynomial extremal problems (PEP) are considered. PEP constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. A general approach to optimization based on quantum holonomic computing algorithms and instanton mechanism. An optimization method based on geometric Lie - algebraic structures on Grassmann manifolds and related with Lax type flows is proposed. Making use of the differential geometric techniques it is shown that associated holonomy groups properly realizing quantum computation can be effectively found concerning polynomial problems. Two examples demonstrating calculation aspects of holonomic quantum computer and maximum clique problems in very large graphs, are considered in detail.
Statistical Physics of Hard Optimization Problems
Zdeborová, Lenka
2008-01-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the NP-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system ...
The inverse problem of the optimal regulator.
Yokoyama, R.; Kinnen, E.
1972-01-01
The inverse problem of the optimal regulator is considered for a general class of multi-input systems with integral-type performance indices. A new phase variable canonical form is shown to be convenient for this analysis. The advantage of the canonical form is to separate the state variables into subvectors of directly controlled, indirectly controlled, and uncontrollable components. Necessary and sufficient conditions for optimized performance indices are given. With the nonlinearities of the system restricted to functions of the directly controlled state variables, additional results are developed about the nonnegative property of optimized loss functions.
Singularity Theory for Nonlinear Optimization Problems
Casti, J.L.
1987-01-01
Techniques from the theory of singularities of smooth mappings are employed to study the reduction of nonlinear optimization problems to simpler forms. It is shown how singularity theory ideas can be used to: (1) reduce the decision-space dimensionality; (2) transform the constraint space to simpler form for primal algorithms; (3) provide sensitivity analysis.
Topology Optimization for Transient Wave Propagation Problems
Matzen, René
The study of elastic and optical waves together with intensive material research has revolutionized everyday as well as cutting edge technology in very tangible ways within the last century. Therefore it is important to continue the investigative work towards improving existing as well as innovate...... optimization problems from nano-photonics: First, an optical taper [P1] and a notch filter [P2] - both optimized by energy maximization. The last two cases demonstrate pulse shaping and delay in one [P3] and two [P5] dimensions. Whereas the test problem in [P3] is rather academic, the example considered in [P5......] optimizes structures that accommodate non-dispersive slow light, with important applications for optical buffering devices....
Topology optimization of fluid mechanics problems
Gersborg-Hansen, Allan
While topology optimization for solid continuum structures have been studied for about 20 years and for the special case of trusses for many more years, topology optimization of fluid mechanics problems is more recent. Borrvall and Petersson [1] is the seminal reference for topology optimization......D Navier-Stokes equation as well as an example with convection dominated transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the present work gives a proof-of-concept for the application of the method within fluid mechanics problems and it remains of...... using the material distribution technique with an underlying partial differential equation describing the fluid motion. The mathematical basis of departure is the incompressible Stokes equation with an extra absorption term which allows for material interpolation between Stokes flow and a model of Darcy...
Optimization problems arising in robust stability theory
Polyak, B.
1994-12-31
Robustness is one of the main topics in modern control theory. We consider one aspect of the theme - robust stability analysis under parametric uncertainty. It deals with stability problems for linear time-invariant differential or difference equations with uncertainties in their coefficients. Various optimization problems concerning {open_quotes}the largest{close_quotes} admissible uncertainty naturally arise. Examples: (1) Find the largest cube inscribed in stability domain; (2) Find the box with the largest volume preserving stability; (3) Describe a boundary of a two-dimensional image of a box under linear or nonlinear transformation; (4) Find a sum or a project of sets on a complex plane, e.g., find a product of n discs. These problems require new duality results and new necessary conditions of optimality.
Using combinatorial problem decomposition for optimizing plutonium inventory management
Plutonium Inventory Management Optimization can be modeled as a very large 0-1 linear program. To solve it, problem decomposition is necessary, since other classic techniques are not efficient for such a size. The first decomposition consists in favoring constraints that are the most difficult to reach and variables that have the highest influence on the cost: fortunately, both correspond to stock output decisions. The second decomposition consists in mixing continuous linear program solving and integer linear program solving. Besides, the first decisions to be taken are systematically favored, for they are based on data considered to be sure, when data supporting later decisions in known with less accuracy and confidence. (author)
Enhanced Bee Colony Algorithm for Complex Optimization Problems
S.Suriya; R. Deepalakshmi; S.Suresh kannan; Dr.S.P.SHANTHARAJAH
2012-01-01
Optimization problems are considered to be one kind of NP hard problems. Usually heuristic approaches are found to provide solutions for NP hard problems. There are a plenty of heuristic algorithmsavailable to solve optimization problems namely: Ant Colony Optimization, Particle Swarm Optimization, Bee Colony Optimization, etc. The basic Bee Colony algorithm, a population based search algorithm, is analyzed to be a novel tool for complex optimization problems. The algorithm mimics the food fo...
基于蜂群遗传算法的0-1背包问题%The O-1 Knapsack Problem Based on the Bee-Swarm Genetic Algorithm
吴迪; 姜永增; 宋广军
2011-01-01
针对0-1背包问题,本文提出了基于蜂群遗传算法的优化求解方案.该算法包括两个种群,一个主要用于全局搜索,另一个主要用于局部搜索;每个个体采用二进制编码;采用最优个体交叉策略;对当前解的处理措施是将还未装入背包且性价比最好的物品装进背包,直至不能装为止;不符合约束条件的解采用诱变因子指导变异处理;遗传算子包括单点交叉算子、简单变异算子、主动进化算子和抑制算子.本算法充分发挥了遗传算法的群体搜索和全局收敛的特性,快速地并行搜索,有效地克服了经典遗传算法容易陷入局部最优问题.数值实验表明,该算法在求解0-1背包问题中取得了较好的效果,同样可以应用于其它的组合优化问题.%This paper presents a bee-swarm genetic algorithm for the 0-1 knapsack problem.There are two populations, one for global search, and the other for local search.Each individual adopts the binary code.Only the best one can crossover.The strategy of managing the feasible solution is to enclose the goods which is out of the knapsack and cost-effective, until no goods can be put into.The solution which does not accord with the constraint condition mutates under the instruction of mutagens.The genetic operators include order crossover operator, two-block-exchange mutation operator and restraint operator.The method sufficiently takes the advantage of the genetic algorithm such as group search and global convergence in order to have a quick parallel search, which efficiently overcomes the problem of local optimization.The experimental results show that the bee swarm genetic algorithm is efficient in solving the 0-1 Knapsack problem, and is also suitable for other combinatorial optimization problems.
Statistical physics of hard optimization problems
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfy ability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named ”locked” constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfy ability.
Statistical physics of hard optimization problems
Zdeborová, Lenka
2009-06-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.
Evolutionary strategies for solving optimization problems
Ebeling, Werner; Reimann, Axel; Molgedey, Lutz
We will give a survey of applications of thermodynamically and biologically oriented evolutionary strategies for optimization problems. Primarily, we investigate the solution of discrete optimization problems, most of combinatorial type, using a certain class of coupled differential equations. The problem is to find the minimum on a large set of real numbers (the potential) Ui, defined on the integer set i = 1 ...s, where s is an extremely large nu mber. The stationary states of the system correspond to relative optima on the discrete set. First, several elementary evolutionary strategies are described by simple deterministic equations, leading to a high-dimensional system of coupled differential equations. The known equations for thermodynamic search processes and for simple models of biological evolution are unified by defining a two-parameter family of equations which embed both cases. The unified equations model mixed Boltzmann/Darwin- strategies including basic elements of thermodynamical and biological evolution as well. In a next step a master equation model in the occupation number space is defined. We investigate the transition probabilities and the convergence properties using tools from the theory of stochastic processes. Several examples are analyzed. In particular we study the optimization of theoretical model sequences with simple valuation rules. In order to demonstrate that the strategies developed here may also be used to investigate realistic problems we present an example application to RNA folding (search for a minimum free energy configuration).
On problem of optimization under incomplete information
Volf, Petr
Karviná : Silesian University in Opava, School of Business Administration in Karviná, 2012 - (Ramík, J.; Stavárek, D.), s. 968-973 ISBN 978-80-7248-779-0. [30th International Conference Mathematical Methods in Economics 2012. Karviná (CZ), 11.09.2012-13.09.2012] R&D Projects: GA ČR GAP402/10/0956 Institutional support: RVO:67985556 Keywords : optimization * censored data * Fisher information * product-limit estimate Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2012/SI/volf-on problem of optimization under incomplete information.pdf
On Optimal Harvesting Problems in Random Environments
Song, Qingshuo; Zhu, Chao
2010-01-01
This paper investigates the optimal harvesting strategy for a single species living in random environments, whose growth is given by a regime-switching diffusion. Harvesting is introduced as a stochastic control. The objective is to find a harvesting strategy which maximizes the expected total discounted income from harvesting up to extinction. This is a singular stochastic control problem, with both the extinction time and harvesting policy depending on the initial condition. Consequently one no longer obtains continuity of the value function for free using the standard arguments as those in regular or singular stochastic control problems. This paper provides a sufficient condition under which the continuity of the value function is obtained. Further, we show that the value function is a viscosity solution of a coupled system of quasi-variational inequalities. A verification theorem is also established. Based upon the verification theorem, we explicitly construct an $\\varepsilon$-optimal harvesting strategy ...
Hierarchical optimization for neutron scattering problems
Bao, Feng; Archibald, Rick; Bansal, Dipanshu; Delaire, Olivier
2016-06-01
We present a scalable optimization method for neutron scattering problems that determines confidence regions of simulation parameters in lattice dynamics models used to fit neutron scattering data for crystalline solids. The method uses physics-based hierarchical dimension reduction in both the computational simulation domain and the parameter space. We demonstrate for silicon that after a few iterations the method converges to parameters values (interatomic force-constants) computed with density functional theory simulations.
The optimization (ALARA) problem: A direct formulation
An alternative method to that set out by the International Commission on Radiological Protection (ICRP) for implementing the optimization (ALARA) principle of radiation protection is proposed. The method follows directly from the basic dose limitation system and naturally integrates the three components of the system. An essential feature of the method is that 'all exposures' is taken to mean 'each and every one' rather than the 'sum of individual doses', as in the usual method using the collective dose concept. The method draws on established techniques from optimization theory and those aspects of micro-economic theory which form the basis of cost-benefit analysis. The method takes separate account of both the direct costs to the community of the effects of radiation exposures and each individual's 'risk-benefit' attitudes to radiation exposures. The conundrum concerning the 'value of a life' turns out to be operationally and quantitatively irrelevant. Various constraints including the dose limits, economic and social constraints and natural physical constraints are included in the method which leads directly to a standard form problem in mathematical programming. A practical advantage of the method is that it is conceptually consistent with the operational methods used and judgements made regularly by health physicists and radiation safety officers. While the proposed method allows an optimization problem to be readily specified, it does require some familiarity with optimization solution techniques in larger applications. (author). 15 refs, 2 figs
Optimization problems for switched systems with impulsive control
Junhao HU; Huayou WANG; Xinzhi LIU; Bin LIU
2005-01-01
By using Impulsive Maximum Principal and three stage optimization method,this paper discusses optimization problems for linear impulsive switched systems with hybrid controls,which includes continuous control and impulsive control.The linear quadratic optimization problems without constraints such as optimal hybrid control,optimal stability and optimal switching instants are addressed in detail.These results are applicable to optimal control problems in economics,mechanics,and management.
Optimal control problem for the extended Fisher–Kolmogorov equation
Ning Duan
2016-02-01
In this paper, the optimal control problem for the extended Fisher–Kolmogorov equation is studied. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved and the optimality system is established.
A novel metaheuristic for continuous optimization problems: Virus optimization algorithm
Liang, Yun-Chia; Rodolfo Cuevas Juarez, Josue
2016-01-01
A novel metaheuristic for continuous optimization problems, named the virus optimization algorithm (VOA), is introduced and investigated. VOA is an iteratively population-based method that imitates the behaviour of viruses attacking a living cell. The number of viruses grows at each replication and is controlled by an immune system (a so-called 'antivirus') to prevent the explosive growth of the virus population. The viruses are divided into two classes (strong and common) to balance the exploitation and exploration effects. The performance of the VOA is validated through a set of eight benchmark functions, which are also subject to rotation and shifting effects to test its robustness. Extensive comparisons were conducted with over 40 well-known metaheuristic algorithms and their variations, such as artificial bee colony, artificial immune system, differential evolution, evolutionary programming, evolutionary strategy, genetic algorithm, harmony search, invasive weed optimization, memetic algorithm, particle swarm optimization and simulated annealing. The results showed that the VOA is a viable solution for continuous optimization.
Optimization of Pr0.9Ca0.1MnO3 thin ﬁlms with varying in-situ oxygen annealing treatments
Paturi P.
2013-01-01
Full Text Available The inﬂuence of in situ oxygen annealings on narrow electronic bandwidth Pr0.9Ca0.1MnO3 ﬁlms are investigated in the complex phase separation region. Measurements by x-ray diffractometry and SQUID magnetometry reveal that relatively high deposition temperature at 700 °C relaxes the lattice by twin boundaries while the lower deposition temperature at 500 °C with higher post-annealing temperature of 700 °C relaxes the substrate induced strain via oxygen absorption and makes the ﬁlm structure more homogeneous. This behaviour is clearly supported by the decrease of ferromagnetic ordering due to decrease of Mn3+ ions in ﬁlms oxygen annealed at high temperatures and this phenomenon is widely discussed with the models of double-exchange interaction, trapping of carriers in the oxygen vacancies and formation of magnetic polarons. The results show unambiguously that because the oxygen content tailors many physical properties dramatically, the annealing treatments are in very important role when optimizing these materials for future applications.
Statistical Physics of Hard Optimization Problems
Zdeborová, Lenka
2008-01-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the NP-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this thesis is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied co...
Optimal Planning and Problem-Solving
Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg
2008-01-01
CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.
The Replica Method in Optimization Problems.
Liao, Wuwell W.
In this thesis I discuss the application of the replica method in combinatorial optimization problems. In particular, I study certain graph-partitioning problems. One problem that I consider is the following. We are given a set of vertices V = (V_1,V_2,ldots V_{N}), with N even, and a set of edges E = {(V_{i},V _{j})i not= j}. Let each edge be connected with probability P. The bipartitioning problem is to divide V into two parts of equal size, in such a way as to minimize the number of edges N _{c} connecting these two parts. We are interested in the behavior of N_{c }/N, averaged over all possible configurations of edges in the limit N --> infty , as a function of the connectivity alpha = NP. When alpha is finite, the problem is shown to be similar, but not identical, to the mean field theory of a spin glass with finite connectivity. The replica-symmetric solution is derived. It is shown to be consistent with exact results for the infinite cluster obtained by P. Erdos.
Properties of solutions of optimization problems for set functions
Slawomir Dorosiewicz
2001-01-01
Full Text Available A definition of a special class of optimization problems with set functions is given. The existence of optimal solutions and first-order optimality conditions are proved. This case of optimal problems can be transformed to standard mixed problems of mathematical programming in Euclidean space. It makes possible the applications of various algorithms for these optimization problems for finding conditional extrema of set functions.
Single-Phase Optimal Odd PWM Problem
Kujan, Petr; Hromčík, M.; Šebek, M.
Piscataway : IEEE, 2008, s. 371-378. ISBN 978-1-4244-1767-4; ISBN 978-1-4244-1766-7. [The 34th Annual Conference of the IEEEE Industrial Electronics Society. Orlando (US), 10.12.2008-13.12.2008] R&D Projects: GA MŠk(CZ) 1M0567; GA ČR(CZ) GA102/08/0186 Grant ostatní: GA MŠk(CZ) LA300 Institutional research plan: CEZ:AV0Z10750506 Keywords : Optimal PWM problem * selected harmonics elimination * Newton identities Subject RIV: BC - Control Systems Theory
Linux software for large topology optimization problems
evolving product, which allows a parallel solution of the PDE, it lacks the important feature that the matrix-generation part of the computations is localized to each processor. This is well-known to be critical for obtaining a useful speedup on a Linux cluster and it motivates the search for a COMSOL......-like package for large topology optimization problems. One candidate for such software is developed for Linux by Sandia Nat’l Lab in the USA being the Sundance system. Sundance also uses a symbolic representation of the PDE and a scalable numerical solution is achieved by employing the underlying Trilinos...
Finite Volumes Discretization of Topology Optimization Problems
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout......-physics setting. In fact, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are...
A Novel Cat Swarm Optimization Algorithm for Unconstrained Optimization Problems
Meysam Orouskhani
2013-10-01
Full Text Available Cat Swarm Optimization (CSO is one of the new swarm intelligence algorithms for finding the best global solution. Because of complexity, sometimes the pure CSO takes a long time to converge and cannot achieve the accurate solution. For solving this problem and improving the convergence accuracy level, we propose a new improved CSO namely ‘Adaptive Dynamic Cat Swarm Optimization’. First, we add a new adaptive inertia weight to velocity equation and then use an adaptive acceleration coefficient. Second, by using the information of two previous/next dimensions and applying a new factor, we reach to a new position update equation composing the average of position and velocity information. Experimental results for six test functions show that in comparison with the pure CSO, the proposed CSO can takes a less time to converge and can find the best solution in less iteration.
Mathematical programming methods for large-scale topology optimization problems
Rojas Labanda, Susana
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......This thesis investigates new optimization methods for structural topology optimization problems. The aim of topology optimization is finding the optimal design of a structure. The physical problem is modelled as a nonlinear optimization problem. This powerful tool was initially developed......, 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...
Enhanced Bee Colony Algorithm for Complex Optimization Problems
S.Suriya
2012-01-01
Full Text Available Optimization problems are considered to be one kind of NP hard problems. Usually heuristic approaches are found to provide solutions for NP hard problems. There are a plenty of heuristic algorithmsavailable to solve optimization problems namely: Ant Colony Optimization, Particle Swarm Optimization, Bee Colony Optimization, etc. The basic Bee Colony algorithm, a population based search algorithm, is analyzed to be a novel tool for complex optimization problems. The algorithm mimics the food foraging behavior of swarmsof honey bees. This paper deals with a modified fitness function of Bee Colony algorithm. The effect of problem dimensionality on the performance of the algorithms will be investigated. This enhanced Bee Colony Optimization will be evaluated based on the well-known benchmark problems. The testing functions like Rastrigin, Rosenbrock, Ackley, Griewank and Sphere are used to evaluavate the performance of the enhanced Bee Colony algorithm. The simulation will be developed on MATLAB.
Artificial Bee Colony Optimization for Multiobjective Quadratic Assignment Problem
Eleyan, Haytham Mohammed
2015-01-01
ABSTRACT: Excellent ability of swarm intelligence can be used to solve multi-objective combinatorial optimization problems. Bee colony algorithms are new swarm intelligence techniques inspired from the smart behaviors of real honeybees in their foraging behavior. Artificial bee colony optimization algorithm has recently been applied for difficult real-valued and combinational optimization problems. Multiobjective quadratic assignment problem (mQAP) is a well-known and hard combinational optim...
Matheuristics for robust optimization: application to real-world problems
Toklu, Nihat Engin; Gambardella, Luca Maria; Montemanni, Roberto
2014-01-01
In the field of optimization, the perspective that the problem data are subject to uncertainty is gaining more and more interest. The uncertainty in an optimization problem represents the measurement errors during the phase of collecting data, or unforeseen changes in the environment while implementing the optimal solution in practice. When the uncertainty is ignored, an optimal solution according to the mathematical model can turn out to be far from optimal, or even infeasible in realit...
Group search optimizer for the mobile location management problem.
Wang, Dan; Xiong, Congcong; Huang, Wei
2014-01-01
We propose a diversity-guided group search optimizer-based approach for solving the location management problem in mobile computing. The location management problem, which is to find the optimal network configurations of management under the mobile computing environment, is considered here as an optimization problem. The proposed diversity-guided group search optimizer algorithm is realized with the aid of diversity operator, which helps alleviate the premature convergence problem of group search optimizer algorithm, a successful optimization algorithm inspired by the animal behavior. To address the location management problem, diversity-guided group search optimizer algorithm is exploited to optimize network configurations of management by minimizing the sum of location update cost and location paging cost. Experimental results illustrate the effectiveness of the proposed approach. PMID:25180199
A STABILITY THEOREM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS
M.H. Farag
2004-01-01
This paper presents the stability of difference approximations of an optimal control problem for a quasilinear parabolic equation with controls in the coefficients, boundary conditions and additional restrictions. The optimal control problem has been convered to one of the optimization problem using a penalty function technique. The difference approximations problem for the considered problem is obtained. The estimations of stability of the solution of difference approximations problem are proved. The stability estimation of the solution of difference approximations problem by the controls is obtained.
Fuchun Huang
2012-05-01
Full Text Available In this paper we address and advocate the sensor location problems and advocate them as test problems of nonsmooth optimization. These problems have easy-to-understand practical meaning and importance, easy to be even randomly generated, and the solutions can be displayed visually on a 2-dimensional plane. For testing some nonsmooth optimization solvers, we present a very simple sensor location problem of two sensors for four objects with the optimal solutions known by theoretical analysis. We tested several immediately ready-to-use optimization solvers on this problem and found that optimization solvers MATLAB’s ga( and VicSolver’s UNsolver can solve the problem, while some other optimization solvers like Excel solver, Dr Frank Vanden Berghen’s CONDOR, R’s optim(, and MATLAB’s fminunc( cannot solve the problem.
Hierarchical control based on Hopfield network for nonseparable optimization problems
无
2005-01-01
The nonseparable optimization control problem is considered, where the overall objective function is not of an additive form with respect to subsystems. Since there exists the problem that computation is very slow when using iterative algorithms in multiobjective optimization, Hopfield optimization hierarchical network based on IPM is presented to overcome such slow computation difficulty. Asymptotic stability of this Hopfield network is proved and its equilibrium point is the optimal point of the original problem. The simulation shows that the net is effective to deal with the optimization control problem for large-scale nonseparable steady state systems.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems
Existence of optimal nonanticipating controls in piecewise deterministic control problems
Seierstad, Atle
2008-01-01
Abstract Optimal nonanticipating controls are shown to exist in nonautonomous piecewise deterministic control problems with hard terminal restrictions. The assumptions needed are completely analogous to those needed to obtain optimal controls in deterministic control problems. The proof is based on well-known results on existence of deterministic optimal controls.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
Time optimal control problems for some non-smooth systems
Lou, Hongwei; Wen, Junjie; Xu, Yashan
2013-01-01
Time optimal control problems for some non-smooth systems in general form are considered. The non-smoothness is caused by singularity. It is proved that Pontryagin's maximum principle holds for at least one optimal relaxed control. Thus, Pontryagin's maximum principle holds when the optimal classical control is a unique optimal relaxed control. By constructing an auxiliary controlled system which admits the original optimal classical control as its unique optimal relaxed control, one get a ch...
Immune Algorithm for Solving the Optimization Problems of Computer Communication Networks
无
2000-01-01
The basic problem in optimizing communication networks is to assign a proper circuit for each origindestination pair in networks so as to minimize the average network delay, and the network optimal route selection model is a multi-constrained 0-1 nonlinear programming problem. In this paper, a new stochastic optimization algorithm, Immune Algorithm, is applied to solve the optimization problem in communication networks. And the backbone network vBNS is chosen to illustrate the technique of evaluating delay in a virtual network. At last, IA is compared with the optimization method in communication networks based on Genetic Algorithm, and the result shows that IA is better than GA in global optimum finding.
Fuchun Huang
2012-01-01
In this paper we address and advocate the sensor location problems and advocate them as test problems of nonsmooth optimization. These problems have easy-to-understand practical meaning and importance, easy to be even randomly generated, and the solutions can be displayed visually on a 2-dimensional plane. For testing some nonsmooth optimization solvers, we present a very simple sensor location problem of two sensors for four objects with the optimal solutions known by theoretical analysis. W...
Optimization, Randomized Approximability, and Boolean Constraint Satisfaction Problems
Yamakami, Tomoyuki
2011-01-01
We give a unified treatment to optimization problems that can be expressed in the form of nonnegative-real-weighted Boolean constraint satisfaction problems. Creignou, Khanna, Sudan, Trevisan, and Williamson studied the complexity of approximating their optimal solutions whose optimality is measured by the sums of outcomes of constraints. To explore a wider range of optimization constraint satisfaction problems, following an early work of Marchetti-Spaccamela and Romano, we study the case where the optimality is measured by products of constraints' outcomes. We completely classify those problems into three categories: PO problems, NPO-hard problems, and intermediate problems that lie between the former two categories. To prove this trichotomy theorem, we analyze characteristics of nonnegative-real-weighted constraints using a variant of the notion of T-constructibility developed earlier for complex-weighted counting constraint satisfaction problems.
Enhanced ant colony optimization for multiscale problems
Hu, Nan; Fish, Jacob
2016-03-01
The present manuscript addresses the issue of computational complexity of optimizing nonlinear composite materials and structures at multiple scales. Several solutions are detailed to meet the enormous computational challenge of optimizing nonlinear structures at multiple scales including: (i) enhanced sampling procedure that provides superior performance of the well-known ant colony optimization algorithm, (ii) a mapping-based meshing of a representative volume element that unlike unstructured meshing permits sensitivity analysis on coarse meshes, and (iii) a multilevel optimization procedure that takes advantage of possible weak coupling of certain scales. We demonstrate the proposed optimization procedure on elastic and inelastic laminated plates involving three scales.
Solving a Class of Non-Smooth Optimal Control Problems
M. H. Noori Skandari
2013-06-01
Full Text Available In this paper, we first propose a new generalized derivative for non-smooth functions and then we utilize this generalized derivative to convert a class of non-smooth optimal control problem to the corresponding smooth form. In the next step, we apply the discretization method to approximate the obtained smooth problem to the nonlinear programming problem. Finally, by solving the last problem, we obtain an approximate optimal solution for main problem.
On Optimal Solutions of Decision Problems with Imperfect Recall
Ambrus-Lakatos, Lorand
1999-01-01
In this paper, I study decision theory in the presence of imperfect recall. I use an extension of the standard strategy concept for the analysis of extensive form games in order to examine the range of imperfect recall problems for which there exists an optimal solution. Optimality is assessed in terms of perfect recall problems associated to their corresponding imperfect recall problems.
Optimal problem of cost function for the linear neutral systems
Yong Han Kang; Jong Yeoul Park
2001-01-01
We study the optimal control problem of a system governed by linear neutral type in Hilbert space X. We investigate optimal condition for quadratic cost function and as applications, we give some examples.
CAI, Dapeng
2008-01-01
We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to the finite horizon problems is optimal for the infinite horizon problems under the overtaking criterion.
Solving Multiobjective Optimization Problems Using Artificial Bee Colony Algorithm
Beiwei Zhang; Hanning Chen; Yunlong Zhu; Wenping Zou
2011-01-01
Multiobjective optimization has been a difficult problem and focus for research in fields of science and engineering. This paper presents a novel algorithm based on artificial bee colony (ABC) to deal with multi-objective optimization problems. ABC is one of the most recently introduced algorithms based on the intelligent foraging behavior of a honey bee swarm. It uses less control parameters, and it can be efficiently used for solving multimodal and multidimensional optimization problems. Ou...
An ant colony optimization algorithm for job shop scheduling problem
Edson Flórez; Wilfredo Gómez; MSc. Lola Bautista
2013-01-01
The nature has inspired several metaheuristics, outstanding among these is Ant Colony Optimization (ACO), which have proved to be very effective and efficient in problems of high complexity (NP-hard) in combinatorial optimization. This paper describes the implementation of an ACO model algorithm known as Elitist Ant System (EAS), applied to a combinatorial optimization problem called Job Shop Scheduling Problem (JSSP). We propose a method that seeks to reduce delays designating th...
Neural networks learning as a multiobjective optimal control problem
Krawczak, Maciej
1997-01-01
The supervised learning process of multilayer feedforward neural networks can be considered as a class of multi-objective, multi-stage optimal control problem. An iterative parametric minimax method is proposed in which the original optimization problem is embedded into a weighted minimax formulation. The resulting auxiliary parametric optimization problems at the lower level have simple structures that are readily tackled by efficient solution methods, such as the dynamic programming or the ...
Topology optimization problems with design-dependent sets of constraints
Schou, Marie-Louise Højlund
large scale. We find the global optimal solution to the stress constrained topology optimization problem using discrete design variables. The problem is solved using a parallel cut-and-branch method. The cuts include information about the mathematical structure of our problems and also their physics....... The method shows particularly good speedup because of the added cuts. The study of stress constrained topology optimization problem using continuous design variables constitute the main part of this thesis. Primarily we study the problem reformulated into standard form via the Mathematical Program...... of the stress constrained topology optimization problem. It further produces a feasible design. If the upper and lower bounds are far apart, then one should invest in attacking the stress constrained structural topology optimization problem. Otherwise one can use the obtained feasible design....
LDRD Final Report: Global Optimization for Engineering Science Problems
HART,WILLIAM E.
1999-12-01
For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD ''Global Optimization for Engineering Science Problems'' was the development of new robust and efficient optimization algorithms that can be used to find globally optimal solutions to complex optimization problems. This SAND report summarizes the technical accomplishments of this LDRD, discusses lessons learned and describes open research issues.
Identification and optimization problems in plasma physics
Parameter identification of the current in a tokamak plasma is studied. Plasma equilibrium in a vacuum container with a diaphragm is analyzed. A variable metric method with reduced optimization with nonlinear equality constraints; and a quasi-Newton reduced optimization method with constraints giving priority to restoration are presented
K. Lenin; B.Ravindranath Reddy; M. Surya Kalavathi
2013-01-01
Reactive Power Optimization is a complex combinatorial optimization problem involving non-linear function having multiple local minima, non-linear and discontinuous constrains. This paper presents Cooperative Multiple Particle Swarm Optimization (CMPSO) and Spatial Extended Particle Swarm Optimization (SEPSO) in trying to overcome the Problem of premature convergence. CMPSO and SEPSO are applied to Reactive Power Optimization problem and are evaluated on standard IEEE 30Bus System. The resu...
ISOGEOMETRIC SHAPE OPTIMIZATION FOR ELECTROMAGNETIC SCATTERING PROBLEMS
Nguyen, D. M.; Evgrafov, Anton; Gravesen, Jens
2012-01-01
We consider the benchmark problem of magnetic energy density enhancement in a small spatial region by varying the shape of two symmetric conducting scatterers. We view this problem as a prototype for a wide variety of geometric design problems in electromagnetic applications. Our approach for...
Xu Zhang; En-min Feng
2004-01-01
This paper studies the two-dimensional layout optimization problem.An optimization model with performance constraints is presented.The layout problem is partitioned intofinite subproblems in terms of graph theory,in such a way of that each subproblem overcomes its on-o inature optimal variable.A minimax problem is constructed that is locally equivalent to each subproblem.By using this minimax problem,we present the optimality function for every subproblem and prove that the first order necessary optimality condition is satisfied at a point if and only if this point is a zero of optimality function.
Advances in bio-inspired computing for combinatorial optimization problems
Pintea, Camelia-Mihaela
2013-01-01
Advances in Bio-inspired Combinatorial Optimization Problems' illustrates several recent bio-inspired efficient algorithms for solving NP-hard problems.Theoretical bio-inspired concepts and models, in particular for agents, ants and virtual robots are described. Large-scale optimization problems, for example: the Generalized Traveling Salesman Problem and the Railway Traveling Salesman Problem, are solved and their results are discussed.Some of the main concepts and models described in this book are: inner rule to guide ant search - a recent model in ant optimization, heterogeneous sensitive a
Fuzzy Optimal Solution to Fuzzy Transportation Problem: A New Approach
S. Mohanaselvi
2012-03-01
Full Text Available In this paper we propose a new algorithm for the initial fuzzy feasible solution to a fully fuzzy transportation problem. Then by using fuzzy version of modified distribution method, we obtain the fuzzy optimal solution for the fully fuzzy transportation problem without converting to a classical transportation problem. A numerical example is provided to illustrate the proposed algorithm. It can be seen that the proposed algorithm gives a better fuzzy optimal solution to the given fuzzy transportation problem.
Implementation of Travelling Salesman Problem Using ant Colony Optimization
Gaurav Singh,
2014-04-01
Full Text Available Within the Artificial Intelligence community, there is great need for fast and accurate traversal algorithms, specifically those that find a path from a start to goal with minimum cost. Cost can be distance, time, money, energy, etc. Travelling salesman problem (TSP is a combinatorial optimization problem. TSP is the most intensively studied problem in the area of optimization. Ant colony optimization (ACO is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. There have been many efforts in the past to provide time efficient solutions for the problem, both exact and approximate. This paper demonstrates the implementation of TSP using ant colony optimization(ACO.The solution to this problem enjoys wide applicability in a variety of practical fields.TSP in its purest form has several applications such as planning, logistics, and manufacture of microchips, military and traffic.
Optimization on photoelectric detection based on stacked La0.9Sr0.1MnO3-δ/LaAlO3-δ multijunctions
Three multijunctions consisting of La0.9Sr0.1MnO3-δ and LaAlO3-δ on Si substrate have been fabricated under different oxygen pressures by laser molecular beam epitaxy. They exhibit nonlinear and rectifying current-voltage characteristics and evident photocurrent response to He-Ne laser illumination. Experimental results indicate that the periodically stacked multijunction grown under lower oxygen pressure shows a better rectification behavior and a higher photocurrent. The photovoltaic responsivities of the multijunctions are enhanced greatly at reverse bias and are much higher than that of a similarly grown single p-n junction. Based on the band structure of the multilayers, a possible mechanism of the photovoltaic process was proposed. A high photovoltage responsivity of 168.6 mV/mW has been achieved at - 6 V bias; this demonstrates the potential of the present multijunction configuration for photodetectors operating at room temperature.
Topology Optimization in wave-propagation and flow problems
Sigmund, Ole; Jensen, Jakob Søndergaard; Gersborg-Hansen, A.; Haber, R.
We discuss recent extensions of the topology optimization method to wave-propagation and flow problems. More specifically, we optimize material distribution in scalar wave propagation problems modelled by Helmholtz equation. Moreover, we investigate the influence of the inertia term on the optima...
On two formulations of an optimal insulation problem
Munoz, Eduardo; Allaire, Gregoire; Bendsøe, Martin P.
problem is more in the realm of shape design, or rather, it is similar to optimal design of support conditions for structures. In both cases mathematical programming is used, but for the shape design case it is applied to the non-linear analysis problems that arise when the optimal design is explicitly...
Ant Colony Optimization and the Minimum Cut Problem
Kötzing, Timo; Lehre, Per Kristian; Neumann, Frank;
2010-01-01
Ant Colony Optimization (ACO) is a powerful metaheuristic for solving combinatorial optimization problems. With this paper we contribute to the theoretical understanding of this kind of algorithm by investigating the classical minimum cut problem. An ACO algorithm similar to the one that was proved...
SolveDB: Integrating Optimization Problem Solvers Into SQL Databases
Siksnys, Laurynas; Pedersen, Torben Bach
2016-01-01
-based syntax for optimization problems, (2) an extensible infrastructure for integrating different solvers, and (3) query optimization techniques to achieve the best execution performance and/or result quality. Extensive experiments with the PostgreSQL-based implementation show that SolveDB is a versatile tool...... workflows that are cumbersome, complex, inefficient, and error-prone. In this paper, we present SolveDB - a DBMS for optimization applications. SolveDB supports solvers for different problem classes and offers seamless data management and optimization problem solving in a pure SQL-based setting. This allows...
Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem
Chen, Wei
2015-07-01
In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.
Sufficient conditions for Lagrange, Mayer, and Bolza optimization problems
Boltyanski V.
2001-01-01
Full Text Available The Maximum Principle [2,13] is a well known necessary condition for optimality. This condition, generally, is not sufficient. In [3], the author proved that if there exists regular synthesis of trajectories, the Maximum Principle also is a sufficient condition for time-optimality. In this article, we generalize this result for Lagrange, Mayer, and Bolza optimization problems.
Optimal Control Problems for Nonlinear Variational Evolution Inequalities
Eun-Young Ju
2013-01-01
Full Text Available We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.
Support method for solving an optimal xenon shutdown problem
Since the discovering of the maximum principle by Pontriagin in 1956, methods for solving optimal control problems have been developed fast. There are the efforts to solve an optimal problem of transient process in a nuclear reactor using its ideas. However, the classical maximum principle does not show how to construct an optimal control or suboptimal control with a given exactness. We exploit mainly in the present work the ideas of the support method proposed by Gabasov and Kirillova for linear systems, in order to solve an optimal control problem for non-linear systems. The constructive maximum principle for non-linear dynamic systems with controllable structure received by us in this paper is new result. The ε - maximum principle is used for receiving an 7-phase ε - optimal control of optimal xenon shutdown problem. (author)
Optimization of VI/II pressure ratio in ZnTe growth on GaAs(0 0 1) by molecular beam epitaxy
ZnTe epilayers were grown on GaAs(0 0 1) substrates by molecular beam epitaxy (MBE) at different VI/II beam equivalent pressure (BEP) ratios (RVI/II) in a wide range of 0.96-11 with constant Zn flux. Based on in situ reflection high-energy electron diffraction (RHEED) observation, two-dimensional (2D) growth mode can be formed by increasing the RVI/II to 2.8. The Te/Zn pressure ratios lower than 4.0 correspond to Zn-rich growth state, while the ratios over 6.4 correspond to Te-rich one. The Zn sticking coefficient at various VI/II ratios are derived by the growth rate measurement. The ZnTe epilayer grown at a RVI/II of 6.4 displays the narrowest full-width at half-maximum (FWHM) of double-crystal X-ray rocking curve (DCXRC) for (0 0 4) reflection. Atomic force microscopy (AFM) characterization shows that the grain size enlarges drastically with the RVI/II. The surface root-mean-square (RMS) roughness decreases firstly, attains a minimum of 1.14 nm at a RVI/II of 4.0 and then increases at higher ratios. It is suggested that the most suitable RVI/II be controlled between 4.0 and 6.4 in order to grow high-quality ZnTe epitaxial thin films.
Optimal Sum-Rate of the Vector Gaussian CEO Problem
Ekrem, Ersen
2012-01-01
We study the vector Gaussian CEO problem, and obtain the optimal sum-rate that attains any given distortion. We show that the evaluation of the Berger-Tung inner bound with jointly Gaussian auxiliary random variables is optimal. We prove this optimality result by using channel enhancement in conjunction with a recent outer bound for the rate-distortion region of the vector Gaussian CEO problem.
The structure of optimal parameters for image restoration problems
de los Reyes, J. C.; Sch?nlieb, C. B.; Valkonen, T.
2015-01-01
We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general type of regulariser is considered, which encompasses total variation (TV), total generalized variation (TGV) and infimal-convolution total variation (ICTV). We prove that under certain conditions on the given data optimal parameters derived by bilevel optim...
OPTIMAL CONTROL PROBLEM OF SOME DIFFERENTIAL INCLUSION AND APPROXIMATION
DEBINSKA-NAGORSKA A.
2002-01-01
Full Text Available In this paper we present the optimal control problem governed by a variational inclusion with the monotone operator and a quadratic costfunctional. We apply standart Galerkin method to the approximation of the problem. After giving some results on the existance of optimal control we shall prove the existance of weak condensation points of a set of solution of approximate problems. Each of these points is a solution of the initial optimization problem. Finally we shall give a simple example using the obtaned results.
3D Topology optimization of Stokes flow problems
Gersborg-Hansen, Allan; Dammann, Bernd
energy efficient devices for 2D Stokes flow. Creeping flow problems are described by the Stokes equations which model very viscous fluids at macro scales or ordinary fluids at very small scales. The latter gives the motivation for topology optimization problems based on the Stokes equations being a model......The present talk is concerned with the application of topology optimization to creeping flow problems in 3D. This research is driven by the fact that topology optimization has proven very successful as a tool in academic and industrial design problems. Success stories are reported from such diverse...
K. Lenin
2013-03-01
Full Text Available Reactive Power Optimization is a complex combinatorial optimization problem involving non-linear function having multiple local minima, non-linear and discontinuous constrains. This paper presents Attractive and repulsive Particle Swarm Optimization (ARPSO and Random Virus Algorithm (RVA in trying to overcome the Problem of premature convergence. RVA and ARPSO is applied to Reactive Power Optimization problem and is evaluated on standard IEEE 30Bus System. The results show that RVA prevents premature convergence to high degree but still keeps a rapid convergence. It gives best solution when compared to Attractive and repulsive Particle Swarm Optimization (ARPSO and Particle Swarm Optimization (PSO.
Treating the Future Equally: Solving Undiscounted Infinite Horizon Optimization Problems
Cai, Dapeng; Nitta, Gyoshin
2007-01-01
Infinite horizon optimization problems accompany two perplexities. First, the infinite series of utility sequences may diverge. Second, boundary conditions at the infinite terminal time may not be rigorously expressed. In this paper, we show that under two fairly general conditions, the limit of the solution to the undiscounted finite horizon problem is optimal among feasible paths for the undiscounted infinite horizon problem, in the sense of the overtaking criterion. Applied to a simple Ram...
Fuzzy Optimal Solution to Fuzzy Transportation Problem: A New Approach
S. Mohanaselvi; K. Ganesan
2012-01-01
In this paper we propose a new algorithm for the initial fuzzy feasible solution to a fully fuzzy transportation problem. Then by using fuzzy version of modified distribution method, we obtain the fuzzy optimal solution for the fully fuzzy transportation problem without converting to a classical transportation problem. A numerical example is provided to illustrate the proposed algorithm. It can be seen that the proposed algorithm gives a better fuzzy optimal solution to the given fuzzy transp...
Convalesce Optimization for Input Allocation Problem Using Hybrid Genetic Algorithm
Mamta Madan; Sushila Madan
2010-01-01
Problem statement: The purpose of this study was to describe categories of hybrid genetic algorithm and validate that the hybrid genetic algorithm converges to the optimal solution rather than a near optimal solution so that Hybrid Genetic algorithms can be used to solve real world problems and receive significant interest. Approach: We implemented the input allocation problem for a manufacturing unit firstly with pure genetic algorithm using Matlab's GA tool and then compared the results wit...
Remarks on a benchmark nonlinear constrained optimization problem
Luo Yazhong; Lei Yongjun; Tang Guojin
2006-01-01
Remarks on a benchmark nonlinear constrained optimization problem are made. Due to a citation error, two absolutely different results for the benchmark problem are obtained by independent researchers. Parallel simulated annealing using simplex method is employed in our study to solve the benchmark nonlinear constrained problem with mistaken formula and the best-known solution is obtained, whose optimality is testified by the Kuhn-Tucker conditions.
Global solutions to general polynomial benchmark optimization problems
Zhou, Xiaojun
2012-01-01
The goal of this paper is to solve a class of high-order polynomial benchmark optimization problems, including the Goldstein-Price problem and the Three Hump Camel Back problem. By using a generalized canonical duality theory, we are able to transform the nonconvex primal problems to concave dual problems over convex domain(without duality gap), which can be solved easily to obtain global solutions.
Optimization Problems in Supply Chain Management
Romero Morales, Dolores
2000-01-01
textabstractMaria Dolores Romero Morales was born on Augustus 5th, 1971, in Sevilla (Spain). She studied Mathematics at University of Sevilla from 1989 to 1994 and specialized in Statistics and Operations Research. She wrote her Master's thesis on Global Optimization in Location Theory under the supervision of Dr. Emilio Carrizosa Priego and Dr. Eduardo Conde S?nchez. During the academic year 1995-1996 she was assistant professor at the department of Mathematics of the Business School, Univer...
Localization and Optimization Problems for Camera Networks
Borra, Domenica
2013-01-01
In the framework of networked control systems, we focus on networks of autonomous PTZ cameras. A large set of cameras communicating each other through a network is a widely used architecture in application areas like video surveillance, tracking and motion. First, we consider relative localization in sensor networks, and we tackle the issue of investigating the error propagation, in terms of the mean error on each component of the optimal estimator of the position vector. The relative error i...
Portfolio optimization and the random magnet problem
Rosenow, B.; Plerou, V.; Gopikrishnan, P.; Stanley, H. E.
2002-08-01
Diversification of an investment into independently fluctuating assets reduces its risk. In reality, movements of assets are mutually correlated and therefore knowledge of cross-correlations among asset price movements are of great importance. Our results support the possibility that the problem of finding an investment in stocks which exposes invested funds to a minimum level of risk is analogous to the problem of finding the magnetization of a random magnet. The interactions for this "random magnet problem" are given by the cross-correlation matrix C of stock returns. We find that random matrix theory allows us to make an estimate for C which outperforms the standard estimate in terms of constructing an investment which carries a minimum level of risk.
Dentcheva, Darinka; Ruszczynski, Andrzej
2003-01-01
We consider a new class of optimization problems involving stochastic dominance constraints of second order. We develop a new splitting approach to these models, optimality conditions and duality theory. These results are used to construct special decomposition methods.
Constraint Optimization for Highly Constrained Logistic Problems
Mochnacs, Maria Kinga; Tanaka, Meang Akira; Nyborg, Anders;
This report investigates whether propagators combined with branch and bound algorithm are suitable for solving the storage area stowage problem within reasonable time. The approach has not been attempted before and experiments show that the implementation was not capable of solving the storage ar...
TWO OPTIMAL CONTROL PROBLEMS IN CANCER CHEMOTHERAPY WITH DRUG RESISTANCE
Werner Krabs
2012-01-01
Full Text Available We investigate two well-known basic optimal control problems forchemotherapeutic cancer treatment modified by introducing a timedependent “resistance factor”. This factor should be responsible for the effect of the drug resistance of tumor cells on the dynamical growth for the tumor. Both optimal control problems have common pointwise but different integral constraints on the control. We show that in both models the usually practised bang-bang control is optimal if the resistance is sufficiently strong. Further, we discuss different optimal strategies in both models for general resistance.
Path Optimization Algorithm For Network Problems Using Job Sequencing Technique
Punit Kumar Singh
2012-06-01
Full Text Available The job sequencing technique is used to determine an optimal sequence. It performs a series of jobs by a number of specific orders so that it calculates the optimal cost. In this paper, we propose a novel approach to find an optimal path from source to destination by taking advantage of job sequencing technique. Wehave used n jobs m machine sequencing technique and this is divided into n jobs 2 machine problems. Using Johnson’s sequencing rule, we solved the problem and obtained the (n-1 sub sequences of the route. Using the proposed algorithm, we calculated the optimal sequence, which leads to the shortest path of the network.
Optimality conditions for the numerical solution of optimization problems with PDE constraints :
Aguilo Valentin, Miguel Alejandro [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ridzal, Denis [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2014-03-01
A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.
H-Optimal Control in Coefficients for Dirichlet Parabolic Problems
I. G. Balanenko
2010-01-01
Full Text Available In the paper the Dirichlet optimal control problem associated with a linear parabolic equation the coefficients of which we take as controls in L1(Ω has been studied. Since equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, it is shown that the optimal control problem in the coefficients can be stated in different settings depending on the choice of the class of admissible solutions. Using the direct method in the Calculus of Variations, the solvability of the above optimal control problems in the so-called class of inadmissible solutions has been discussed.
A capped optimal stopping problem for the maximum process
Kyprianou, Andreas E
2012-01-01
This paper concerns an optimal stopping problem driven by the running maximum of a spectrally negative Levy process X. More precisely, we are interested in capped versions of the American lookback optimal stopping problem, which has its origins in mathematical finance, and provide semi-explicit solutions in terms of scale functions. The optimal stopping boundary is characterised by an ordinary first-order differential equation involving scale functions and, in particular, changes according to the path variation of X. Furthermore, we will link these capped problems to Peskir's maximality principle.
OPTIMIZATION OF PRODUCTION PROBLEMS USING MATHEMATICAL PROGRAMMING
Romuald Szopa; Bogdan Marczyk
2011-01-01
In production activity, starting manufacturing of a new product involves taking a particular risk. Therefore, the need arises for investigating the rational basis for starting such projects. This process should begin from the verification of the opportunities of reaching the expected effects of the new production. One of the methods of solving the complex problems is mathematical programming, whose utility was demonstrated with an example of a manufacturing enterprise.
Reducibility of joint relay positioning and flow optimization problem
Thakur, Mohit; Médard, Muriel
2012-01-01
This paper shows how to reduce the otherwise hard joint relay positioning and flow optimization problem into a sequence a two simpler decoupled problems. We consider a class of wireless multicast hypergraphs mainly characterized by their hyperarc rate functions, that are increasing and convex in power, and decreasing in distance between the transmit node and the farthest end node of the hyperarc. The set-up consists of a single multicast flow session involving a source, multiple destinations and a relay that can be positioned freely. The first problem formulates the relay positioning problem in a purely geometric sense, and once the optimal relay position is obtained the second problem addresses the flow optimization. Furthermore, we present simple and efficient algorithms to solve these problems.
Integrating packing and distribution problems and optimization through mathematical programming
Fabio Miguel; Mariano Frutos; Fernando Tohmé; Máximo Méndez
2016-01-01
This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP) problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Proble...
The Tactical Berth Allocation Problem: integrated optimization in container terminals
Vacca, Ilaria; Salani, Matteo; Bierlaire, Michel
2010-01-01
In the context of container terminal operations, the simultaneous optimization of decision problems that are usually solved hierarchically by terminal's planners represents nowadays a promising research trend. In this talk we introduce the Tactical Berth Allocation Problem (TBAP), that deals with the integration of the berth allocation problem (BAP) and the quay crane assignment problem (QCAP). The objective is to schedule incoming ships over a time horizon, assigning them a berthing position...
Gradient Gene Algorithm: a Fast Optimization Method to MST Problem
无
2001-01-01
The extension of Minimum Spanning Tree(MST) problem is an NP hardproblem which does not exit a polynomial time algorithm. In this paper, a fast optimizat ion method on MST problem--the Gradient Gene Algorithm is introduced. Compar ed with other evolutionary algorithms on MST problem, it is more advanced: firstly, very simple and easy to realize; then, efficient and accurate; finally general on other combination optimization problems.
Finding Multiple Optimal Solutions to Optimal Load Distribution Problem in Hydropower Plant
Xinhao Jiang; Ximing Cai; Pan Liu; Tri-Dung Nguyen
2012-01-01
Optimal load distribution (OLD) among generator units of a hydropower plant is a vital task for hydropower generation scheduling and management. Traditional optimization methods for solving this problem focus on finding a single optimal solution. However, many practical constraints on hydropower plant operation are very difficult, if not impossible, to be modeled, and the optimal solution found by those models might be of limited practical uses. This motivates us to find multiple optimal solu...
Ant Colony Algorithm for the Weighted Item Layout Optimization Problem
Xu, Yi-Chun; Liu, Yong; Xiao, Ren-Bin; Amos, Martyn
2010-01-01
This paper discusses the problem of placing weighted items in a circular container in two-dimensional space. This problem is of great practical significance in various mechanical engineering domains, such as the design of communication satellites. Two constructive heuristics are proposed, one for packing circular items and the other for packing rectangular items. These work by first optimizing object placement order, and then optimizing object positioning. Based on these heuristics, an ant colony optimization (ACO) algorithm is described to search first for optimal positioning order, and then for the optimal layout. We describe the results of numerical experiments, in which we test two versions of our ACO algorithm alongside local search methods previously described in the literature. Our results show that the constructive heuristic-based ACO performs better than existing methods on larger problem instances.
Direct Multiple Shooting Optimization with Variable Problem Parameters
Whitley, Ryan J.; Ocampo, Cesar A.
2009-01-01
Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.
Universal fast gradient method for stochastic composit optimization problems
Gasnikov, Alexander; Nesterov, Yurii
2016-01-01
We propose a new simple variant of Fast Gradient Method that requires only one projection per iteration. We called this method Triangle Method (TM) because it has a corresponding geometric description. We generalize TM for convex and strictly convex composite optimization problems. Then we propose Universal Triangle Method (UTM) for convex and strictly convex composite optimization problems (see Yu. Nesterov, Math. Program. 2015. for more details about what is Universal Fast Gradient Method)....
Complicated problem solution techniques in optimal parameter searching
An algorithm is presented of a global search for numerical solution of multidimentional multiextremal multicriteria optimization problems with complicated constraints. A boundedness of object characteristic changes is assumed at restricted changes of its parameters (Lipschitz condition). The algorithm was realized as a computer code. The algorithm was realized as a computer code. The programme was used to solve in practice the different applied optimization problems. 10 refs.; 3 figs
Issues related to topology optimization of snap-through problems
Lindgaard, Esben; Dahl, Jonas
2012-01-01
This work focuses on issues related to topology optimization of static geometrically nonlinear structures experiencing snap-through behaviour. Different compliance and buckling criterion functions are studied and applied to topology optimization of a point loaded curved beam problem with the aim ...
A Cooperative Coevolutionary Cuckoo Search Algorithm for Optimization Problem
Hongqing Zheng; Yongquan Zhou
2013-01-01
Taking inspiration from an organizational evolutionary algorithm for numerical optimization, this paper designs a kind of dynamic population and combining evolutionary operators to form a novel algorithm, a cooperative coevolutionary cuckoo search algorithm (CCCS), for solving both unconstrained, constrained optimization and engineering problems. A population of this algorithm consists of organizations, and an organization consists of dynamic individuals. In experiments, fifteen unconstrained...
borealis - A generalized global update algorithm for Boolean optimization problems
Zhu, Zheng; Katzgraber, Helmut G
2016-01-01
Optimization problems with Boolean variables that fall into the nondeterministic polynomial (NP) class are of fundamental importance in computer science, mathematics, physics and industrial applications. Most notably, solving constraint-satisfaction problems, which are related to spin-glass-like Hamiltonians in physics, remains a difficult numerical task. As such, there has been great interest in designing efficient heuristics to solve these computationally difficult problems. Inspired by parallel tempering Monte Carlo in conjunction with the rejection-free isoenergetic cluster algorithm developed for Ising spin glasses, we present a generalized global update optimization heuristic that can be applied to different NP-complete problems with Boolean variables. The global cluster updates allow for a wide-spread sampling of phase space, thus considerably speeding up optimization. By carefully tuning the pseudo-temperature (needed to randomize the configurations) of the problem, we show that the method can efficie...
Exact solution for an optimal impermeable parachute problem
Lupu, Mircea; Scheiber, Ernest
2002-10-01
In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.
An object-oriented toolbox for studying optimization problems
Deng, H. Lydia; Gouveia, Wences; Scales, John
The CWP Object-Oriented Optimization Library (COOOL) is a collection of C++ classes for studying and solving optimization problems. It was developed using the freely available GNU compiler gcc. The library contains the basic building blocks for the efficient design of numerical linear algebra and optimization software; it also comes with a variety of unconstrained optimization algorithms and test objective functions drawn from our own research. The only requirement for using one of the optimization methods is that a simple model of communication be followed. This allows us to use exactly the same code to optimize functions tailored for a variety of hardware, no matter what programming language is used. Further, since we have provided class libraries containing building blocks for general purpose optimization and numerical linear algebra software, the development of new algorithms should be greatly aided. COOOL is now freely available via anonymous ftp at
Time discretization and quantization methods for optimal multiple switching problem
Paul, Gassiat; Kharroubi, Idris; Pham, Huyen
2011-01-01
In this paper, we study probabilistic numerical methods based on optimal quantization algorithms for computing the solution to optimal multiple switching problems with regime-dependent state process. We first consider a discrete-time approximation of the optimal switching problem, and analyze its rate of convergence. Given a time step $h$, the error is in general of order $(h \\log(1/h))^{1/2}$, and of order $h^{1/2}$ when the switching costs do not depend on the state process. We next propose...
On some fundamental properties of structural topology optimization problems
Stolpe, Mathias
2010-01-01
We study some fundamental mathematical properties of discretized structural topology optimization problems. Either compliance is minimized with an upper bound on the volume of the structure, or volume is minimized with an upper bound on the compliance. The design variables are either continuous o...... presented examples can be used as teaching material in graduate and undergraduate courses on structural topology optimization.......We study some fundamental mathematical properties of discretized structural topology optimization problems. Either compliance is minimized with an upper bound on the volume of the structure, or volume is minimized with an upper bound on the compliance. The design variables are either continuous or...
Optimization problem for gas centrifuge and local separation efficiency
Application of the ideal centrifuge theory to the numerical calculation and optimization of gas centrifuge and correct choice of local optimum criterion for the problems of numeric optimization is considered. Centrifuge with optimum circulation within rotor is used in reference to ideal one. Separation theory based on the radius-mean method is developed in the work. The error of choosing optimum criterion associated with the direct transfer of the ideal cascade theory available to literature is analyzed for the problems of the numerical optimization of centrifuge
SMMH - A Parallel Heuristic for Combinatorial Optimization Problems
The process of finding one or more optimal solutions for answering combinatorial optimization problems bases itself on the use of algorithms instances. Those instances usually have to explore a very large search spaces. Heuristics search focusing on the use of High-Order Hopfield neural networks is a largely deployed technique for very large search space. It can be established a very powerful analogy towards the dynamics evolution of a physics spin-glass system while minimizing its own energy and the energy function of the network. This paper presents a new approach for solving combinatorial optimization problems through parallel simulations, based on a High-Order Hopfield neural network using MPI specification
SMMH--A Parallel Heuristic for Combinatorial Optimization Problems
The process of finding one or more optimal solutions for answering combinatorial optimization problems bases itself on the use of algorithms instances. Those instances usually have to explore a very large search spaces. Heuristics search focusing on the use of High-Order Hopfield neural networks is a largely deployed technique for very large search space. It can be established a very powerful analogy towards the dynamics evolution of a physics spin-glass system while minimizing its own energy and the energy function of the network. This paper presents a new approach for solving combinatorial optimization problems through parallel simulations, based on a High-Order Hopfield neural network using MPI specification
The Transport Problem utilized for Machines Optimal Allocation
Olga-Ioana Amariei
2015-07-01
Full Text Available The present paper presents an optimal allocation mode of the machines in a manner to maximize the profit. Starting from provided data – time standard, technical itineraries, production volume, working regime and continuing with the determined ones – duration, necessary number of machines, unit profit, the problem became a maximization transport problem
Strong Duality and Optimality Conditions for Generalized Equilibrium Problems
D. H. Fang
2013-01-01
Full Text Available We consider a generalized equilibrium problem involving DC functions. By using the properties of the epigraph of the conjugate functions, some sufficient and/or necessary conditions for the weak and strong duality results and optimality conditions for generalized equilibrium problems are provided.
Continuity for vector optimization problems with equilibrium constraints
WU; Yunan
2004-01-01
The concept of vector optimization problems with equilibrium constraints (VOPEC) is introduced. By using the continuity results of the approximate solution set to the equilibrium problem, we obtain the same results of the marginal map and the approximate value in VOPEC (ε) for vector-valued mapping.
Reverse convex problems: an approach based on optimality conditions
Ider Tseveendorj
2006-01-01
Full Text Available We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.
Fusion Global-Local-Topology Particle Swarm Optimization for Global Optimization Problems
Zahra Beheshti; Siti Mariyam Shamsuddin; Sarina Sulaiman
2014-01-01
In recent years, particle swarm optimization (PSO) has been extensively applied in various optimization problems because of its structural and implementation simplicity. However, the PSO can sometimes find local optima or exhibit slow convergence speed when solving complex multimodal problems. To address these issues, an improved PSO scheme called fusion global-local-topology particle swarm optimization (FGLT-PSO) is proposed in this study. The algorithm employs both global and local topologi...
Yan Sun; Maoxiang Lang
2015-01-01
Purpose: The purpose of study is to solve the multi-modal transportation routing planning problem that aims to select an optimal route to move a consignment of goods from its origin to its destination through the multi-modal transportation network. And the optimization is from two viewpoints including cost and time. Design/methodology/approach: In this study, a bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. ...
Social interaction as a heuristic for combinatorial optimization problems
Fontanari, Jose F
2010-01-01
We investigate the performance of a variant of Axelrod's model for dissemination of culture - the Adaptive Culture Heuristic (ACH) - on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size $F$ by a Boolean Binary Perceptron. In this heuristic, $N$ agents, characterized by binary strings of length $F$ which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents' strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable $F/N^{1/4}$ so that the number of agen...
Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer
Rosenberg, Gili; Haghnegahdar, Poya; Goddard, Phil; Carr, Peter; Wu, Kesheng; de Prado, Marcos Lopez
2016-09-01
We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multi-period portfolio optimization problem we solve is significantly harder than the continuous variable problem. We present insight into how results may be improved using suitable software enhancements, and why current quantum annealing technology limits the size of problem that can be successfully solved today. The formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques.
Optimal Component Lumping: problem formulation and solution techniques
Lin, Bao; Leibovici, Claude F.; Jørgensen, Sten Bay
2008-01-01
This paper presents a systematic method for optimal lumping of a large number of components in order to minimize the loss of information. In principle, a rigorous composition-based model is preferable to describe a system accurately. However, computational intensity and numerical issues restrict...... commonly used to determine the lumping scheme. Given an objective function defined with a linear weighting rule, an optimal lumping problem is formulated as a mixed integer nonlinear programming (MINLP) problem both in discrete and in continuous settings. A reformulation of the original problem is also...
Numerical methods for solving terminal optimal control problems
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
Large scale optimization algorithms : applications to solution of inverse problems
Repetti, Audrey
2015-01-01
An efficient approach for solving an inverse problem is to define the recovered signal/image as a minimizer of a penalized criterion which is often split in a sum of simpler functions composed with linear operators. In the situations of practical interest, these functions may be neither convex nor smooth. In addition, large scale optimization problems often have to be faced. This thesis is devoted to the design of new methods to solve such difficult minimization problems, while paying attenti...
A New Fenchel Dual Problem in Vector Optimization
Radu Ioan Boţ; Anca Dumitru; Gert Wanka
2009-04-01
We introduce a new Fenchel dual for vector optimization problems inspired by the form of the Fenchel dual attached to the scalarized primal multiobjective problem. For the vector primal-dual pair we prove weak and strong duality. Furthermore, we recall two other Fenchel-type dual problems introduced in the past in the literature, in the vector case, and make a comparison among all three duals. Moreover, we show that their sets of maximal elements are equal.
Traveling Transportation Problem Optimization by Adaptive Current Search Method
Supaporn Suwannarongsri
2014-05-01
Full Text Available The adaptive current search (ACS is one of the novel metaheuristic optimization search techniques proposed for solving the combinatorial optimization problems. This paper aimed to present the application of the ACS to optimize the real-world traveling transportation problems (TTP of a specific car factory. The total distance of the selected TTP is performed as the objective function to be minimized in order to decrease the vehicle’s energy. To perform its effectiveness, four real-world TTP problems are conducted. Results obtained by the ACS are compared with those obtained by genetic algorithm (GA, tabu search (TS and current search (CS. As results, the ACS can provide very satisfactory solutions superior to other algorithms. The minimum total distance and the minimum vehicle’s energy of all TTP problems can be achieved by the ACS with the distant error of no longer than 3.05%.
RAHMANI, Shima; NIASATI, Mohsen
2015-01-01
The gravitational search algorithm is one of the new heuristic search optimization methods which are based on gravity law. Despite having high capability, this approach suffers from low search speed duo to lack of memory. To overcome this problem, the particle swarm optimization method has been used. Therefore, in this paper, hybrid particle swarm optimization and gravitational search algorithm has been used to find the solution of optimal power flow. Performance of the proposed method has be...
Wang, Gengsheng; Xu, Yashan
2011-01-01
This paper presents an equivalence theorem for three different kinds of optimal control problems, which are optimal target control problems, optimal norm control problems and optimal time control problems. Controlled systems in this study are internally controlled heat equations. With the aid of this theorem, we establish an optimal norm feedback law and build up two algorithms for optimal norms (together with optimal norm controls) and optimal time (along with optimal time controls), respect...
Finding the optimal values of some of the variables in SAT or MAX-SAT problems
Hammer, P.
1994-12-31
The properties of weak and strong persistency are introduced for SAT and MAX-SAT problems. These properties allow the detection of partial 0-1 assignments which can be extended to (optimal) solutions of these problems. A polytope is associated with any SAT or MAX-SAT problem, and it is shown that it has half-integral vertices. Furthermore, it is shown that the integer components of any of the vertices of this polytope have a weak persistency property, generalizing on the 1975 result of Nemhauser and Trotter. When applied to a MAX-2-SAT problem, along with a network flow calculation based on the roof-duality approach introduced by Hammer, Hansen, and Simeone in 1984, this technique yields a 3/4-approximation of the MAX-2-SAT problem.
CAI, Dapeng
2008-01-01
We aim to generalize the results of Cai and Nitta (2007) by allowing both the utility and production function to depend on time. We also consider an additional intertemporal optimality criterion. We clarify the conditions under which the limit of the solutions for the finite horizon problems is optimal among all attainable paths for the infinite horizon problems under the overtaking criterion, as well as the conditions under which such a limit is the unique optimum under the sum-of-utilities criterion. The results are applied to a parametric example of the one-sector growth model to examine the impacts of discounting on optimal paths.
Integrating packing and distribution problems and optimization through mathematical programming
Fabio Miguel
2016-06-01
Full Text Available This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW, which is a variant of the Travelling Salesman Problem (again a NP-Hard problem with extra constraints. Here we model those two problems in a single framework and use an evolutionary meta-heuristics to solve them jointly. Furthermore, we use data from a real world company as a test-bed for the method introduced here.
Finding Multiple Optimal Solutions to Optimal Load Distribution Problem in Hydropower Plant
Xinhao Jiang
2012-05-01
Full Text Available Optimal load distribution (OLD among generator units of a hydropower plant is a vital task for hydropower generation scheduling and management. Traditional optimization methods for solving this problem focus on finding a single optimal solution. However, many practical constraints on hydropower plant operation are very difficult, if not impossible, to be modeled, and the optimal solution found by those models might be of limited practical uses. This motivates us to find multiple optimal solutions to the OLD problem, which can provide more flexible choices for decision-making. Based on a special dynamic programming model, we use a modified shortest path algorithm to produce multiple solutions to the problem. It is shown that multiple optimal solutions exist for the case study of China’s Geheyan hydropower plant, and they are valuable for assessing the stability of generator units, showing the potential of reducing occurrence times of units across vibration areas.
Reliability optimization problems with multiple constraints under fuzziness
Gupta, Neha; Haseen, Sanam; Bari, Abdul
2016-06-01
In reliability optimization problems diverse situation occurs due to which it is not always possible to get relevant precision in system reliability. The imprecision in data can often be represented by triangular fuzzy numbers. In this manuscript, we have considered different fuzzy environment for reliability optimization problem of redundancy. We formulate a redundancy allocation problem for a hypothetical series-parallel system in which the parameters of the system are fuzzy. Two different cases are then formulated as non-linear programming problem and the fuzzy nature is defuzzified into crisp problems using three different defuzzification methods viz. ranking function, graded mean integration value and α-cut. The result of the methods is compared at the end of the manuscript using a numerical example.
Russian Doll Search for solving Constraint Optimization problems
Verfaillie, G.; Lemaitre, M. [CERT/ONERA, Toulouse (France); Schiex, T. [INRA, Castanet Tolosan (France)
1996-12-31
If the Constraint Satisfaction framework has been extended to deal with Constraint Optimization problems, it appears that optimization is far more complex than satisfaction. One of the causes of the inefficiency of complete tree search methods, like Depth First Branch and Bound, lies in the poor quality of the lower bound on the global valuation of a partial assignment, even when using Forward Checking techniques. In this paper, we introduce the Russian Doll Search algorithm which replaces one search by n successive searches on nested subproblems (n being the number of problem variables), records the results of each search and uses them later, when solving larger subproblems, in order to improve the lower bound on the global valuation of any partial assignment. On small random problems and on large real scheduling problems, this algorithm yields surprisingly good results, which greatly improve as the problems get more constrained and the bandwidth of the used variable ordering diminishes.
Turnpike theory of continuous-time linear optimal control problems
Zaslavski, Alexander J
2015-01-01
Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems. The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands. Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integran...
Optimal stability polynomials for numerical integration of initial value problems
Ketcheson, David I.
2013-01-08
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step size and corresponding method for a given problem when the spectrum of the initial value problem is known. The problem is expressed in terms of a general least deviation feasibility problem. Its solution is obtained by a new fast, accurate, and robust algorithm based on convex optimization techniques. Global convergence of the algorithm is proven in the case that the order of approximation is one and in the case that the spectrum encloses a starlike region. Examples demonstrate the effectiveness of the proposed algorithm even when these conditions are not satisfied.
Nearly Optimal Solution for Restricted Euclidean Bottleneck Steiner Tree Problem
Zimao Li
2014-04-01
Full Text Available A variation of the traditional Steiner tree problem, the bottleneck Steiner tree problem is considered in this paper, which asks to find a Steiner tree for n terminals with at most k Steiner points such that the length of the longest edge in the tree is minimized. The problem has applications in the design of WDM optical networks, design of wireless communication networks and reconstruction of phylogenetic tree in biology. We study a restricted version of the bottleneck Steiner tree problem in the Euclidean plane which requires that only degree-2 Steiner points are possibly adjacent in the optimal solution. The problem is known to be MAX-SNP hard and cannot be approximated within unless P=NP, we propose a nearly optimal randomized polynomial time approximation algorithm with performance ratio +e, where e is a positive number.
Integrated network design and scheduling problems : optimization algorithms and applications.
Nurre, Sarah G.; Carlson, Jeffrey J.
2014-01-01
We consider the class of integrated network design and scheduling problems. These problems focus on selecting and scheduling operations that will change the characteristics of a network, while being speci cally concerned with the performance of the network over time. Motivating applications of INDS problems include infrastructure restoration after extreme events and building humanitarian distribution supply chains. While similar models have been proposed, no one has performed an extensive review of INDS problems from their complexity, network and scheduling characteristics, information, and solution methods. We examine INDS problems under a parallel identical machine scheduling environment where the performance of the network is evaluated by solving classic network optimization problems. We classify that all considered INDS problems as NP-Hard and propose a novel heuristic dispatching rule algorithm that selects and schedules sets of arcs based on their interactions in the network. We present computational analysis based on realistic data sets representing the infrastructures of coastal New Hanover County, North Carolina, lower Manhattan, New York, and a realistic arti cial community CLARC County. These tests demonstrate the importance of a dispatching rule to arrive at near-optimal solutions during real-time decision making activities. We extend INDS problems to incorporate release dates which represent the earliest an operation can be performed and exible release dates through the introduction of specialized machine(s) that can perform work to move the release date earlier in time. An online optimization setting is explored where the release date of a component is not known.
Particle swarm as optimization tool in complex nuclear engineering problems
Due to its low computational cost, gradient-based search techniques associated to linear programming techniques are being used as optimization tools. These techniques, however, when applied to multimodal search spaces, can lead to local optima. When finding solutions for complex multimodal domains, random search techniques are being used with great efficacy. In this work we exploit the swarm optimization algorithm search power capacity as an optimization tool for the solution of complex high dimension and multimodal search spaces of nuclear problems. Due to its easy and natural representation of high dimension domains, the particle swarm optimization was applied with success for the solution of complex nuclear problems showing its efficacy in the search of solutions in high dimension and complex multimodal spaces. In one of these applications it enabled a natural and trivial solution in a way not obtained with other methods confirming the validity of its application. (author)
Algorithms and theoretical topics on selected combinatorial optimization problems
Kaveh, Arman
2010-01-01
We study the Quadratic Assignment Problem (QAP), Three Dimensional Assignment Problem (3AP) and Quadratic Three Dimensional Assignment Problem (Q3AP), which combines aspects of both QAP and 3AP. The three problems are known to be NP-hard. We propose new algorithms for obtaining near optimal solutions of QAP and 3AP and present computational results. Our algorithms obtain improved solutions in some benchmark instances of QAP and 3AP. We also discuss theoretical results on 3AP and Q3AP such as ...
PARALLEL HYBRID METHODS USED IN OPTIMIZATION PROBLEMS SOLVING
Ionut BALAN
2014-12-01
Full Text Available This paper presents different models of hybrid algorithms that can be run on parallel architectures being used in optimization problems solving. In these models we used several techniques: genetic algorithms, ant colony and tabu search. Optimization problems can achieve a high degree of complexity, which is the main reason for the necessity of using of these methods in such incursions. With their cooperation, we tried to obtain satisfactory results in much better running time than the sequential versions. These models have been run using various parallel configurations on a cluster cores, which belong to „Stefan cel Mare” University. The results obtained for these models were compared with each other and with the results obtained for models described in other personal papers. The paper highlights the advantages of the parallel hybrid cooperation in solving of complex optimization problems. This paper is structured in four chapters: Introduction, Cooperative heterogeneous model, Cooperative hybrid models and Conclusions.
Optimal reinsurance/investment problems for general insurance models
Liu, Yuping; 10.1214/08-AAP582
2009-01-01
In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random measure, representing the randomness from the financial market and the insurance claims, respectively. The random safety loading and stochastic interest rates are allowed in the model so that the reserve process is non-Markovian in general. The insurance company can manage the reserves through both portfolios of the investment and a reinsurance policy to optimize a certain utility function, defined in a generic way. The main feature of the problem lies in the intrinsic constraint on the part of reinsurance policy, which is only proportional to the claim-size instead of the current level of reserve, and hence it is quite different from the optimal investment/consumption problem with constraints in finance. Necessary and sufficient conditions for both well posedness and solvability...
Adaptive double chain quantum genetic algorithm for constrained optimization problems
Kong Haipeng; Li Ni; Shen Yuzhong
2015-01-01
Optimization problems are often highly constrained and evolutionary algorithms (EAs) are effective methods to tackle this kind of problems. To further improve search efficiency and con-vergence rate of EAs, this paper presents an adaptive double chain quantum genetic algorithm (ADCQGA) for solving constrained optimization problems. ADCQGA makes use of double-individuals to represent solutions that are classified as feasible and infeasible solutions. Fitness (or evaluation) functions are defined for both types of solutions. Based on the fitness function, three types of step evolution (SE) are defined and utilized for judging evolutionary individuals. An adaptive rotation is proposed and used to facilitate updating individuals in different solutions. To further improve the search capability and convergence rate, ADCQGA utilizes an adaptive evolution process (AEP), adaptive mutation and replacement techniques. ADCQGA was first tested on a widely used benchmark function to illustrate the relationship between initial parameter values and the convergence rate/search capability. Then the proposed ADCQGA is successfully applied to solve other twelve benchmark functions and five well-known constrained engineering design problems. Multi-aircraft cooperative target allocation problem is a typical constrained optimization problem and requires efficient methods to tackle. Finally, ADCQGA is successfully applied to solving the target allocation problem.
Economic and Financial Problems via Multiobjective Stochastic Optimization
Kaňková, Vlasta
Jihlava: College of Polytechnics Jihlava, 2013 - (Vojáčková, H.) ISBN 978-80-87035-76-4. [International Conference on Mathematical Methods in Economics 2013 /31./. Jihlava (CZ), 11.09.2013-13.09.2013] R&D Projects: GA ČR GA13-14445S; GA ČR GAP402/11/0150 Institutional support: RVO:67985556 Keywords : stochastic multiobjective optimization problems * efficient solution * Wasserstein metric * L_1 norm * empirical estimates * Lipschitz property Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2013/E/kankova-economic and financial problems via multiobjective stochastic optimization.pdf
State-Constrained Optimal Control Problems of Impulsive Differential Equations
Forcadel, Nicolas, E-mail: forcadel@ceremade.dauphine.fr [Universite Paris-Dauphine, Ceremade (France); Rao Zhiping, E-mail: Zhiping.Rao@ensta-paristech.fr; Zidani, Hasnaa, E-mail: Hasnaa.Zidani@ensta-paristech.fr [ENSTA ParisTech and INRIA-Saclay, Equipe COMMANDS (France)
2013-08-01
The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption.
On some fundamental properties of structural topology optimization problems
Stolpe, Mathias
2009-01-01
, we illustrate that the optimal solutions to the considered problems in general are not symmetric even if the design domain, the external loads, and the boundary conditions are symmetric around an axis. The presented examples can be used as teaching material in graduate and undergraduate courses on......We study some fundamental mathematical properties of classical structural topology optimization problems. Either compliance is minimized with an upper bound on the volume of the structure, or volume is minimized with an upper bound on the compliance. The design variables are either continuous or 0...
On a Nonsmooth Vector Optimization Problem with Generalized Cone Invexity
Hehua Jiao
2012-01-01
Full Text Available By using Clarke’s generalized gradients we consider a nonsmooth vector optimization problem with cone constraints and introduce some generalized cone-invex functions called K-α-generalized invex, K-α-nonsmooth invex, and other related functions. Several sufficient optimality conditions and Mond-Weir type weak and converse duality results are obtained for this problem under the assumptions of the generalized cone invexity. The results presented in this paper generalize and extend the previously known results in this area.
Optimal control problems for impulsive systems with integral boundary conditions
Allaberen Ashyralyev
2013-03-01
Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
Topology optimization of 3D Stokes flow problems
Gersborg-Hansen, Allan; Sigmund, Ole; Bendsøe, Martin P.
The design of MEMS devices have benefitted from the topology optimization tool and complicated layout problems have been solved, see [1] for an overview. This research is aimed at micro fluidic devices known as micro-Total-Analysis-Systems (muTAS) where the main physical phenomena originate from...... examples relevant for optimal micro fluidic mixer design are shown where the design is planar - compliant with micro fabrication techniques - and where the designs are 3D. In addition issues related to the parallel solution of the linear algebra problems are discussed. The implementation uses the...
Application of clustering global optimization to thin film design problems.
Lemarchand, Fabien
2014-03-10
Refinement techniques usually calculate an optimized local solution, which is strongly dependent on the initial formula used for the thin film design. In the present study, a clustering global optimization method is used which can iteratively change this initial formula, thereby progressing further than in the case of local optimization techniques. A wide panel of local solutions is found using this procedure, resulting in a large range of optical thicknesses. The efficiency of this technique is illustrated by two thin film design problems, in particular an infrared antireflection coating, and a solar-selective absorber coating. PMID:24663856
An optimized finite-difference scheme for wave propagation problems
Zingg, D. W.; Lomax, H.; Jurgens, H.
1993-01-01
Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.
Global Sufficient Optimality Conditions for a Special Cubic Minimization Problem
Xiaomei Zhang
2012-01-01
Full Text Available We present some sufficient global optimality conditions for a special cubic minimization problem with box constraints or binary constraints by extending the global subdifferential approach proposed by V. Jeyakumar et al. (2006. The present conditions generalize the results developed in the work of V. Jeyakumar et al. where a quadratic minimization problem with box constraints or binary constraints was considered. In addition, a special diagonal matrix is constructed, which is used to provide a convenient method for justifying the proposed sufficient conditions. Then, the reformulation of the sufficient conditions follows. It is worth noting that this reformulation is also applicable to the quadratic minimization problem with box or binary constraints considered in the works of V. Jeyakumar et al. (2006 and Y. Wang et al. (2010. Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.
Infinite horizon optimal control problems with multiple thermostatic hybrid dynamics
Bagagiolo, Fabio; Danieli, Katia
2010-01-01
We study an optimal control problem for a hybrid system exhibiting several internal switching variables whose discrete evolutions are governed by some delayed thermostatic laws. By the dynamic programming technique we prove that the value function is the unique viscosity solution of a system of several Hamilton-Jacobi equations, suitably coupled. The method involves a contraction principle and some suitably adapted results for exit-time problems with discontinuous exit cost.
Optimizing Human Diet Problem Based on Price and Taste Using
Hossein EGHBALI; Mohammad Ali EGHBALI; Ali VAHIDIAN KAMYAD
2012-01-01
Low price and good taste of foods are regarded as two major factors for optimal human nutrition. Due to price fluctuations and taste diversity, these two factors cannot be certainly and determinately evaluated. This problem must be viewed from another perspective because of the uncertainty about the amount of nutrients per unit of foods and also diversity of people’s daily needs to receive them.This paper discusses human diet problem in fuzzy environment. The approach deals with multi-objecti...
A Multi-Objective Genetic Algorithm for Optimal Portfolio Problems
林丹; 赵瑞
2004-01-01
This paper concerns with modeling and design of an algorithm for the portfolio selection problems with fixed transaction costs and minimum transaction lots. A mean-variance model for the portfolio selection problem is proposed, and the model is formulated as a non-smooth and nonlinear integer programming problem with multiple objective functions. As it has been proven that finding a feasible solution to the problem only is already NP-hard, based on NSGA-II and genetic algorithm for numerical optimization of constrained problems (Genocop), a multi-objective genetic algorithm (MOGA) is designed to solve the model. Its features comprise integer encoding and corresponding operators, and special treatment of constraints conditions. It is illustrated via a numerical example that the genetic algorithm can efficiently solve portfolio selection models proposed in this paper. This approach offers promise for the portfolio problems in practice.
2014-01-01
A new local search technique is proposed and used to improve the performance of particle swarm optimization algorithms by addressing the problem of premature convergence. In the proposed local search technique, a potential particle position in the solution search space is collectively constructed by a number of randomly selected particles in the swarm. The number of times the selection is made varies with the dimension of the optimization problem and each selected particle donates the value i...
Optimal recombination in genetic algorithms for combinatorial optimization problems: Part II
Eremeev Anton V.
2014-01-01
Full Text Available This paper surveys results on complexity of the optimal recombination problem (ORP, which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. In Part II, we consider the computational complexity of ORPs arising in genetic algorithms for problems on permutations: the Travelling Salesman Problem, the Shortest Hamilton Path Problem and the Makespan Minimization on Single Machine and some other related problems. The analysis indicates that the corresponding ORPs are NP-hard, but solvable by faster algorithms, compared to the problems they are derived from.
Sahay Rishi R.
2013-01-01
Full Text Available A second order Mond-Weir type dual is presented for a non-differentiable multiobjective optimization problem with square root terms in the objective as well as in the constraints. Optimality and duality results are presented. Classes of generalized higher order η - bonvex and related functions are introduced to study the optimality and duality results. A fractional case is presented at the end.
Bonnans, J Frédéric; Dupuis, Xavier
2012-01-01
This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions.
THE TANGENT CONES ON CONSTRAINT QUALIFICATIONS IN OPTIMIZATION PROBLEMS
Huang Longguang
2008-01-01
This article proposes a few tangent cones, which are relative to the constraint qualifications of optimization problems. With the upper and lower directional derivatives of an objective function, the characteristics of cones on the constraint qualifications are presented. The interrelations among the constraint qualifications, a few cones involved,and level sets of upper and lower directional derivatives are derived.
Topology optimization of fluid-structure-interaction problems in poroelasticity
Andreasen, Casper Schousboe; Sigmund, Ole
2013-01-01
This paper presents a method for applying topology optimization to fluid-structure interaction problems in saturated poroelastic media. The method relies on a multiple-scale method applied to periodic media. The resulting model couples the Stokes flow in the pores of the structure with the...
On the One-Dimensional Optimal Switching Problem
Bayraktar, Erhan; Egami, Masahiko
2007-01-01
We explicitly solve the optimal switching problem for one-dimensional diffusions by directly employing the dynamic programming principle and the excessive characterization of the value function. The shape of the value function and the smooth fit principle then can be proved using the properties of concave functions.
Solution of the problem of optimal definition of hadron jets
Reviewed is a systematic theory that solves the problem of construction of an ideal definition of hadron jets. The theory does not contain arbitrary assumptions and is fully based on the first principle of mathematical statistics and quantum field theory. The obtained optimal jet definition enhancing the quality of experimental data processing in cases of precision measurements or a low signal/background ratio
A monotonic method for solving nonlinear optimal control problems
Salomon, Julien
2009-01-01
Initially introduced in the framework of quantum control, the so-called monotonic algorithms have shown excellent numerical results when dealing with various bilinear optimal control problems. This paper aims at presenting a unified formulation of such procedures and the intrinsic assumptions they require. In this framework, we prove the feasibility of the general algorithm. Finally, we explain how these assumptions can be relaxed.
Optimization problems with equilibrium constraints and their numerical solution
Kočvara, Michal; Outrata, Jiří
2004-01-01
Roč. 101, č. 1 (2004), s. 119-149. ISSN 0025-5610 R&D Projects: GA AV ČR IAA1075005 Grant ostatní: BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : optimization problems * MPEC * MPCC Subject RIV: BA - General Mathematics Impact factor: 1.016, year: 2004
Features for Exploiting Black-Box Optimization Problem Structure
Tierney, Kevin; Malitsky, Yuri; Abell, Tinus
2013-01-01
Black-box optimization (BBO) problems arise in numerous scientic and engineering applications and are characterized by compu- tationally intensive objective functions, which severely limit the number of evaluations that can be performed. We present a robust set of features that analyze the tness...
Scheduling Internal Audit Activities: A Stochastic Combinatorial Optimization Problem
Rossi, R.; Tarim, S.A.; Hnich, B.; Prestwich, S.; Karacaer, S.
2010-01-01
The problem of finding the optimal timing of audit activities within an organisation has been addressed by many researchers. We propose a stochastic programming formulation with Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) certainty-equivalent models. In experiments neithe
Reduced-Complexity Semidefinite Relaxations of Optimal Power Flow Problems
Andersen, Martin Skovgaard; Hansson, Anders; Vandenberghe, Lieven
2014-01-01
We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality constraints in the conversion, we obtain semidefinite relaxations that are computationally cheaper, but potentially weake...
An iterative scheme for solving the optimal transportation problem
Kitagawa, Jun
2012-01-01
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of iterations necessary for the scheme to terminate, in terms of the error tolerance and number of points in the support of the discrete target measure.
Topology optimization of mass distribution problems in Stokes flow
Gersborg-Hansen, Allan; Berggren, Martin; Dammann, Bernd
We consider topology optimization of mass distribution problems in 2D and 3D Stokes flow with the aim of designing devices that meet target outflow rates. For the purpose of validation, the designs have been post processed using the image processing tools available in FEMLAB. In turn, this has...
Lower bounding problems for stress constrained discrete structural topology optimization problems
Stolpe, Mathias; Stainko, Roman; Kocvara, Michal
2007-01-01
The multiple load structural topology design problem is modeled as a minimization of the weight of the structure subject to equilibrium constraints and restrictions on the local stresses and nodal displacements. The problem involves a large number of discrete design variables and is modeled as a ...... suitable for implementation in a nonlinear branch and bound framework for solving the considered class of problems to global optimality....
Rees algebras, Monomial Subrings and Linear Optimization Problems
Dupont, Luis A.
2010-06-01
In this thesis we are interested in studying algebraic properties of monomial algebras, that can be linked to combinatorial structures, such as graphs and clutters, and to optimization problems. A goal here is to establish bridges between commutative algebra, combinatorics and optimization. We study the normality and the Gorenstein property-as well as the canonical module and the a-invariant-of Rees algebras and subrings arising from linear optimization problems. In particular, we study algebraic properties of edge ideals and algebras associated to uniform clutters with the max-flow min-cut property or the packing property. We also study algebraic properties of symbolic Rees algebras of edge ideals of graphs, edge ideals of clique clutters of comparability graphs, and Stanley-Reisner rings.
Proposal of Evolutionary Simplex Method for Global Optimization Problem
Shimizu, Yoshiaki
To make an agile decision in a rational manner, role of optimization engineering has been notified increasingly under diversified customer demand. With this point of view, in this paper, we have proposed a new evolutionary method serving as an optimization technique in the paradigm of optimization engineering. The developed method has prospects to solve globally various complicated problem appearing in real world applications. It is evolved from the conventional method known as Nelder and Mead’s Simplex method by virtue of idea borrowed from recent meta-heuristic method such as PSO. Mentioning an algorithm to handle linear inequality constraints effectively, we have validated effectiveness of the proposed method through comparison with other methods using several benchmark problems.
Numerical methods for optimal control problems with state constraints
Pytlak, Radosław
1999-01-01
While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.
Optimizing investment fund allocation using vehicle routing problem framework
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita
2014-07-01
The objective of investment is to maximize total returns or minimize total risks. To determine the optimum order of investment, vehicle routing problem method is used. The method which is widely used in the field of resource distribution shares almost similar characteristics with the problem of investment fund allocation. In this paper we describe and elucidate the concept of using vehicle routing problem framework in optimizing the allocation of investment fund. To better illustrate these similarities, sectorial data from FTSE Bursa Malaysia is used. Results show that different values of utility for risk-averse investors generate the same investment routes.
An ant colony optimization method for generalized TSP problem
Jinhui Yang; Xiaohu Shi; Maurizio Marchese; Yanchun Liang
2008-01-01
Focused on a variation of the euclidean traveling salesman problem (TSP), namely, the generalized traveling salesman problem (GTSP), this paper extends the ant colony optimization method from TSP to this field. By considering the group influence, an improved method is further improved. To avoid locking into local minima, a mutation process and a local searching technique are also introduced into this method. Numerical results show that the proposed method can deal with the GTSP problems fairly well, and the developed mutation process and local search technique are effective.
Problem statement for optimal design of steel structures
Ginzburg Aleksandr Vital'evich
2014-07-01
Full Text Available The presented article considers the following complex of tasks. The main stages of the life cycle of a building construction with the indication of process entrance and process exit are described. Requirements imposed on steel constructions are considered. The optimum range of application for steel designs is specified, as well as merits and demerits of a design material. The nomenclature of metal designs is listed - the block diagram is constructed. Possible optimality criteria of steel designs, offered by various authors for various types of constructions are considered. It is established that most often the criterion of a minimum of design mass is accepted as criterion of optimality; more rarely - a minimum of the given expenses, a minimum of a design cost in business. In the present article special attention is paid to a type of objective function of optimization problem. It is also established that depending on the accepted optimality criterion, the use of different types of functions is possible. This complexity of objective function depends on completeness of optimality criterion application. In the work the authors consider the following objective functions: the mass of the main element of a design; objective function by criterion of factory cost; objective function by criterion of cost in business. According to these examples it can be seen that objective functions by the criteria of labor expenses for production of designs are generally non-linear, which complicates solving the optimization problem. Another important factor influencing the problem of optimal design solution for steel designs, which is analyzed, is account for operating restrictions. In the article 8 groups of restrictions are analyzed. Attempts to completely account for the parameters of objective function optimized by particular optimality criteria, taking into account all the operating restrictions, considerably complicates the problem of designing. For solving this
Accelerated optimization problem search using Bose-Einstein condensation
We investigate a computational device that harnesses the effects of Bose-Einstein condensation to accelerate the speed of finding the solution of optimization problems. Many computationally difficult problems, including NP-complete problems, can be formulated as a ground state search problem. In a Bose-Einstein condensate, below the critical temperature, bosonic particles have a natural tendency to accumulate in the ground state. Furthermore, the speed of attaining this configuration is enhanced as a result of final state stimulation. We propose a physical device that incorporates these basic properties of bosons into the optimization problem, such that an optimized solution is found by a simple cooling of the physical temperature of the device. Using a semiclassical model to calculate the equilibration time for reaching the ground state, we found that this can be sped up by a factor of N, where N is the boson number per site. This allows for the annealing times for reaching a particular error to be systematically decreased by increasing the boson number per site. (paper)
Optimal Stopping Rules For Some Blackjack Type Problems
Grzybowski, Andrzej Z.
2010-03-01
The paper deals with a class of optimal stopping problems having some features of blackjack type games. A decision maker observes sequentially the values of a finite sequence of non-negative random variables. After each observation he decides whether to stop or to continue. If he decides to stop, he obtains a payoff dependent on the sum of already observed values. The greater the sum, the more the decision maker gains, unless the sum exceeds a positive number T-a limit given in the problem. If so, the decision maker loses all or part of his payoff. A sufficient condition for existence of a simple optimal stopping rule for such problems is formulated. Then some special cases are considered in detail. Some numerical examples and practical questions are discussed as well.
Heuristic Optimization for the Discrete Virtual Power Plant Dispatch Problem
Petersen, Mette Kirschmeyer; Hansen, Lars Henrik; Bendtsen, Jan Dimon;
2014-01-01
Problem. First NP-completeness of the Discrete Virtual Power Plant Dispatch Problem is proved formally. We then proceed to develop tailored versions of the meta-heuristic algorithms Hill Climber and Greedy Randomized Adaptive Search Procedure (GRASP). The algorithms are tuned and tested on portfolios of...... varying sizes. We find that all the tailored algorithms perform satisfactorily in the sense that they are able to find sub-optimal, but usable, solutions to very large problems (on the order of 10 5 units) at computation times on the scale of just 10 seconds, which is far beyond the capabilities of the...... optimal algorithms we have tested. In particular, GRASP Sorted shows the most promising performance, as it is able to find solutions that are both agile (sorted) and well balanced, and consistently yields the best numerical performance among the developed algorithms....
Solving Optimization Problems by the Spatial Public Goods Game
Javarone, Marco Alberto
2016-01-01
We introduce a method based on the spatial Public Goods Game for solving optimization tasks. In particular, we focus on the Traveling Salesman Problem, i.e., a problem whose search space exponentially grows increasing the number of cities, then becoming NP-hard. The proposed method considers a population whose agents are provided with a random solution to the given problem. Then, agents interact by playing the Public Goods Game using the fitness of their solution as currency of the game. In doing so, agents with better solutions provide higher contributions, while agents with lower ones tend to imitate the solution of richer agents to increase their fitness. Numerical simulations show that the proposed method allows to compute exact solutions, and suboptimal ones, in the considered search spaces. As result, beyond to propose a new heuristic for combinatorial optimization tasks, our work aims to highlight the potentiality of evolutionary game theory outside its current horizons.
Statistical physics of hard combinatorial optimization: Vertex cover problem
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems. (topical review - statistical physics and complex systems)
Optimal Parallel Algorithm for the Knapsack Problem Without Memory Conflicts
Ken-Li Li; Ren-Fa Li; Qing-Hua Li
2004-01-01
The knapsack problem is well known to be NP-complete. Due to its importance in cryptosystem and in number theory, in the past two decades, much effort has been made in order to find techniques that could lead to practical algorithms with reasonable running time. This paper proposes a new parallel algorithm for the knapsack problem where the optimal merging algorithm is adopted. The proposed algorithm is based on an EREW-SIMD machine with shared memory. It is proved that the proposed algorithm is both optimal and the first without memory conflicts algorithm for the knapsack problem. The comparisons of algorithm performance show that it is an improvement over the past researches.
A Cooperative Coevolutionary Cuckoo Search Algorithm for Optimization Problem
Hongqing Zheng
2013-01-01
Full Text Available Taking inspiration from an organizational evolutionary algorithm for numerical optimization, this paper designs a kind of dynamic population and combining evolutionary operators to form a novel algorithm, a cooperative coevolutionary cuckoo search algorithm (CCCS, for solving both unconstrained, constrained optimization and engineering problems. A population of this algorithm consists of organizations, and an organization consists of dynamic individuals. In experiments, fifteen unconstrained functions, eleven constrained functions, and two engineering design problems are used to validate the performance of CCCS, and thorough comparisons are made between the CCCS and the existing approaches. The results show that the CCCS obtains good performance in the solution quality. Moreover, for the constrained problems, the good performance is obtained by only incorporating a simple constraint handling technique into the CCCS. The results show that the CCCS is quite robust and easy to use.
Belief propagation : an asymptotically optimal algorithm for the random assignment problem
Salez, Justin; Shah, Devavrat
2009-01-01
The random assignment problem asks for the minimum-cost perfect matching in the complete $n\\times n$ bipartite graph $\\Knn$ with i.i.d. edge weights, say uniform on $[0,1]$. In a remarkable work by Aldous (2001), the optimal cost was shown to converge to $\\zeta(2)$ as $n\\to\\infty$, as conjectured by M\\'ezard and Parisi (1987) through the so-called cavity method. The latter also suggested a non-rigorous decentralized strategy for finding the optimum, which turned out to be an instance of the B...
Discrete particle swarm optimization algorithm for solving optimal sensor deployment problem
Rapaić Milan R.
2008-01-01
Full Text Available This paper addresses the Optimal Sensor Deployment Problem (OSDP. The goal is to maximize the probability of target detection, with simultaneous cost minimization. The problem is solved by the Discrete PSO (DPSO algorithm, a novel modification of the PSO algorithm, originally presented in the current paper. DPSO is general-purpose optimizer well suited for conducting search within a discrete search space. Its applicability is not limited to OSDP, it can be used to solve any combinatorial and integer programming problem. The effectiveness of the DPSO in solving OSDP was demonstrated on several examples.
Stability, Optimality and Manipulation in Matching Problems with Weighted Preferences
Maria Silvia Pini
2013-11-01
Full Text Available The stable matching problem (also known as the stable marriage problem is a well-known problem of matching men to women, so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools or, more generally, to any two-sided market. In the classical stable marriage problem, both men and women express a strict preference order over the members of the other sex, in a qualitative way. Here, we consider stable marriage problems with weighted preferences: each man (resp., woman provides a score for each woman (resp., man. Such problems are more expressive than the classical stable marriage problems. Moreover, in some real-life situations, it is more natural to express scores (to model, for example, profits or costs rather than a qualitative preference ordering. In this context, we define new notions of stability and optimality, and we provide algorithms to find marriages that are stable and/or optimal according to these notions. While expressivity greatly increases by adopting weighted preferences, we show that, in most cases, the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem. We also consider the manipulability properties of the procedures that return such stable marriages. While we know that all procedures are manipulable by modifying the preference lists or by truncating them, here, we consider if manipulation can occur also by just modifying the weights while preserving the ordering and avoiding truncation. It turns out that, by adding weights, in some cases, we may increase the possibility of manipulating, and this cannot be avoided by any reasonable restriction on the weights.
Particle Swarm Optimization Applied to the Economic Dispatch Problem
Rafik Labdani
2006-06-01
Full Text Available This paper presents solution of optimal power flow (OPF problem of a power system via a simple particle swarm optimization (PSO algorithm. The objective is to minimize the fuel cost and keep the power outputs of generators, bus voltages, shunt capacitors/reactors and transformers tap-setting in their secure limits.The effectiveness of PSO was compared to that of OPF by MATPOWER. The potential and superiority of PSO have been demonstrated through the results of IEEE 30-bus system
Optimization of Multiple Vehicle Routing Problems using Approximation Algorithms
Nallusamy, R; K. Duraiswamy,; Dhanalaksmi, R.; P. Parthiban
2010-01-01
This paper deals with generating of an optimized route for multiple Vehicle routing Problems (mVRP). We used a methodology of clustering the given cities depending upon the number of vehicles and each cluster is allotted to a vehicle. k- Means clustering algorithm has been used for easy clustering of the cities. In this way the mVRP has been converted into VRP which is simple in computation compared to mVRP. After clustering, an optimized route is generated for each vehicle in its allotted cl...
Multiresolution strategies for the numerical solution of optimal control problems
Jain, Sachin
There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a
Heuristic versus statistical physics approach to optimization problems
Optimization is a crucial ingredient of many calculation schemes in science and engineering. In this paper we assess several classes of methods: heuristic algorithms, methods directly relying on statistical physics such as the mean-field method and simulated annealing; and Hopfield-type neural networks and genetic algorithms partly related to statistical physics. We perform the analysis for three types of problems: (1) the Travelling Salesman Problem, (2) vector quantization, and (3) traffic control problem in multistage interconnection network. In general, heuristic algorithms perform better (except for genetic algorithms) and much faster but have to be specific for every problem. The key to improving the performance could be to include heuristic features into general purpose statistical physics methods. (author)
Optimizing Human Diet Problem Based on Price and Taste Using
Hossein EGHBALI
2012-07-01
Full Text Available Low price and good taste of foods are regarded as two major factors for optimal human nutrition. Due to price fluctuations and taste diversity, these two factors cannot be certainly and determinately evaluated. This problem must be viewed from another perspective because of the uncertainty about the amount of nutrients per unit of foods and also diversity of people’s daily needs to receive them.This paper discusses human diet problem in fuzzy environment. The approach deals with multi-objective fuzzy linear programming problem using a fuzzy programming technique for its solution. By prescribing a diet merely based on crisp data, some ofthe realities are neglected. For the same reason, we dealt with human diet problem through fuzzy approach. Results indicated uncertainty about factors of nutrition diet -including taste and price, amount of nutrients and their intake- would affect diet quality, making the proposed diet more realistic.
Tunneling and Speedup in Permutation-Invariant Quantum Optimization Problem
Albash, Tameem
Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via the quantum adiabatic algorithm. Restricting ourselves to qubit-permutation invariant problems, we show that tunneling in these problems can be understood using the semi-classical potential derived from the spin-coherent path integral formalism. Using this, we show that the class of problems that fall under Reichardt's bound (1), i.e., have a constant gap and hence can be efficiently solved using the quantum adiabatic algorithm, do not exhibit tunneling in the large system-size limit. We proceed to construct problems that do not fall under Reichardt's bound but numerically have a constant gap and do exhibit tunneling. However, perhaps counter-intuitively, tunneling does not provide the most efficient mechanism for finding the solution to these problems. Instead, an evolution involving a sequence of diabatic transitions through many avoided level-crossings, involving no tunneling, is optimal and outperforms tunneling in the adiabatic regime. In yet another twist, we show that in this case, classical spin-vector dynamics is as efficient as the diabatic quantum evolution (2).
RECIPES FOR BUILDING THE DUAL OF CONIC OPTIMIZATION PROBLEM
Diah Chaerani
2010-08-01
Full Text Available Building the dual of the primal problem of Conic Optimization (CO isa very important step to make the ¯nding optimal solution. In many cases a givenproblem does not have the simple structure of CO problem (i.e., minimizing a linearfunction over an intersection between a±ne space and convex cones but there areseveral conic constraints and sometimes also equality constraints. In this paper wedeal with the question how to form the dual problem in such cases. We discuss theanswer by considering several conic constraints with or without equality constraints.The recipes for building the dual of such cases is formed in standard matrix forms,such that it can be used easily on the numerical experiment. Special attention isgiven to dual development of special classes of CO problems, i.e., conic quadraticand semide¯nite problems. In this paper, we also brie°y present some preliminariestheory on CO as an introduction to the main topic
Rigorous location of phase transitions in hard optimization problems.
Achlioptas, Dimitris; Naor, Assaf; Peres, Yuval
2005-06-01
It is widely believed that for many optimization problems, no algorithm is substantially more efficient than exhaustive search. This means that finding optimal solutions for many practical problems is completely beyond any current or projected computational capacity. To understand the origin of this extreme 'hardness', computer scientists, mathematicians and physicists have been investigating for two decades a connection between computational complexity and phase transitions in random instances of constraint satisfaction problems. Here we present a mathematically rigorous method for locating such phase transitions. Our method works by analysing the distribution of distances between pairs of solutions as constraints are added. By identifying critical behaviour in the evolution of this distribution, we can pinpoint the threshold location for a number of problems, including the two most-studied ones: random k-SAT and random graph colouring. Our results prove that the heuristic predictions of statistical physics in this context are essentially correct. Moreover, we establish that random instances of constraint satisfaction problems have solutions well beyond the reach of any analysed algorithm. PMID:15944693
A NOTE ON IRREVERSIBLE INVESTMENT, HEDGING AND OPTIMAL CONSUMPTION PROBLEMS
VICKY HENDERSON; DAVID HOBSON
2006-01-01
A canonical problem in real option pricing, as described in the classic text of Dixit and Pindyck [2], is to determine the optimal time to invest at a fixed cost, to receive in return a stochastic cashflow. In this paper we are interested in this problem in an incomplete market where the cashflow is not spanned by the traded assets. We follow the formulation in Miao and Wang [21]; our contribution is to show that significant progress can be made in solving the Hamilton-Jacobi-Bellman equation...
A matrix product state method for solving combinatorial optimization problems
Pelton, S. S.; Chamon, C.; Mucciolo, E. R.
2015-03-01
We present a method based on a matrix product state representation to solve combinatorial optimization problems. All constraints are met by mapping Boolean gates into projection operators and applying operators sequentially. The method provides exact solutions with high success probability, even in the case of frustrated systems. The computational cost of the method is controlled by the maximum relative entropy of the system. Results of numerical simulations for several types of problems will be shown and discussed. NSF Grants CCF-1116590 and CCF-1117241.
Reactive Robustness and Integrated Approaches for Railway Optimization Problems
Haahr, Jørgen Thorlund
journeys helps the driver to drive efficiently and enhances robustness in a realistic (dynamic) environment. Four international scientific prizes have been awarded for distinct parts of the research during the course of this PhD project. The first prize was awarded for work during the \\2014 RAS Problem...... Solving Competition", where a freight yard optimization problem was considered. The second junior (PhD) prize was awared for the work performed in the \\ROADEF/EURO Challenge 2014: Trains don't vanish!", where the planning of rolling stock movements at a large station was considered. An honorable mention...... (and second place) was awarded in recognition for excellent work in the \\Discrete Optimization Challenge", where the aim was to minimize energy consumption in timetables. Finally, a second place was awarded in the \\2015 RAS Student Paper Award", where a comparison of solution methods for planning...
Efficient Intelligent Optimized Algorithm for Dynamic Vehicle Routing Problem
Jiangqing Wang
2011-11-01
Full Text Available In order to solve the dynamic vehicle routing problem (DVRP containing both dynamic network environment and real-time customer requests, an efficient intelligent optimized algorithm called IOA is proposed in this paper, which takes advantages of both global searching ability of evolutionary algorithms and local searching capability of ant colony algorithm. The proposed IOA incorporates ant colony algorithm for exploration and evolutionary algorithm for exploitation, and uses real-time information during the optimization process. In order to discuss the performance of the proposed algorithm, a mixed integral programming model for DVRP is formulated, and benchmark functions are constructed. Detailed simulation results and comparisons with the existed work show that the proposed IOA algorithm can achieve a higher performance gain, and is well suited to problems containing dynamic network environment and real-time customer requests.
MODIFIED GENETIC ALGORITHM APPLIED TO SOLVE PRODUCT FAMILY OPTIMIZATION PROBLEM
CHEN Chunbao; WANG Liya
2007-01-01
The product family design problem solved by evolutionary algorithms is discussed. A successfiil product family design method should achieve an optimal tradeoff among a set of competing objectives, which involves maximizing conunonality across the family of products and optimizing the performances of each product in the family. A 2-level chromosome structured genetic algorithm (2LCGA) is proposed to solve this dass of problems and its performance is analyzed in comparing its results with those obtained with other methods. By interpreting the chromosome as a 2-level linear structure, the variable commonality genetic algorithm (GA) is constructed to vary the amount of platform commonality and automatically searches across varying levels of commonality for the platform while trying to resolve the tradeoff between commonality and individual product performance within the product family during optimization process. By incorporating a commonality assessing index to the problem formulation, the 2LCGA optimize the product platform and its corresponding family of products in a single stage, which can yield improvements in the overall performance of the product family compared with two-stage approaches (the first stage involves determining the best settings for the platform variables and values of unique variables are found for each product in the second stage). The scope of the algorithm is also expanded by introducing a classification mechanism to allow multiple platforms to be considered during product family optimization, offering opportunities for superior overall design by more efficacious tradeoffs between commonality and performance. The effectiveness of 2LCGA is demonstrated through the design of a family of universal electric motors and comparison against previous results.
Evolutionary multiobjective optimization of the multi-location transshipment problem
Belgasmi, Nabil; Ghédira, Khaled; 10.1007/s12351-008-0015-5
2011-01-01
We consider a multi-location inventory system where inventory choices at each location are centrally coordinated. Lateral transshipments are allowed as recourse actions within the same echelon in the inventory system to reduce costs and improve service level. However, this transshipment process usually causes undesirable lead times. In this paper, we propose a multiobjective model of the multi-location transshipment problem which addresses optimizing three conflicting objectives: (1) minimizing the aggregate expected cost, (2) maximizing the expected fill rate, and (3) minimizing the expected transshipment lead times. We apply an evolutionary multiobjective optimization approach using the strength Pareto evolutionary algorithm (SPEA2), to approximate the optimal Pareto front. Simulation with a wide choice of model parameters shows the different trades-off between the conflicting objectives.
Radio interferometric gain calibration as a complex optimization problem
Smirnov, Oleg
2015-01-01
Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss-Newton, Levenberg-Marquardt, etc.) into the domain of complex functions of a complex variable. This employs a formalism called the Wirtinger derivative, and derives a full-complex Jacobian counterpart to the conventional real Jacobian. We apply these developments to the problem of radio interferometric gain calibration, and show how the general complex Jacobian formalism, when combined with conventional optimization approaches, yields a whole new family of calibration algorithms, including those for the polarized and direction-dependent gain regime. We further extend the Wirtinger calculus to an operator-based matrix calculus for describing the polarized calibration regime. Using approximate matrix inversion results in computationally efficient implementations; we show that some recently proposed calibration algorithms such as StefCal and peeling can be understood...
Sequential laminates in multiple-state optimal design problems
2006-01-01
Full Text Available In the study of optimal design related to stationary diffusion problems with multiple-state equations, the description of the set H = { ( Aa 1 , ... , Aa m : A ∈ K ( θ } for given vectors a 1 , ... , a m ∈ ℝ d ( m < d is crucial. K ( θ denotes all composite materials (in the sense of homogenisation theory with given local proportion θ of the first material. We prove that the boundary of H is attained by sequential laminates of rank at most m with matrix phase α I and core β I ( α < β . Examples showing that the information on the rank of optimal laminate cannot be improved, as well as the fact that sequential laminates with matrix phase α I are preferred to those with matrix phase β I , are presented. This result can significantly reduce the complexity of optimality conditions, with obvious impact on numerical treatment, as demonstrated in a simple numerical example.
Multiobjective Stochastic OptimizationProblems with Probability Constraints
Kaňková, Vlasta
Olomouc: Palacký University, Olomouc, 2014. ISBN 978-80-244-4209-9. [MME 2014. International Conference Mathematical Methods in Economics /32./. Olomouc (CZ), 10.09.2014-12.09.2014] R&D Projects: GA ČR GA13-14445S Institutional support: RVO:67985556 Keywords : Stochastic multiobjective optimization problems * (properly) efficient solution * Wasserstein metric * stability * empirical estimates Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2014/E/kankova-0433604.pdf
Optimal Decision Making Method for Multi Criteria Problems
Roghayeh Zamani; Pirayeh Yousefi
2013-01-01
Decision making is one of the essential and important fieldsnowadays, by integrating decision making on multi criteria and fuzzy logic, there will be a satisfactory theoretical framework for system evaluation. There exist several methods for multi parametric decision making. In this paper we will introduce a new way and optimal method for multi parametric problems by taking Fuzzy AHP method into consideration. In this method, it is planned to calculate the weight of criteria by the help of AH...
Optimal non-adaptive solutions for the counterfeit coin problem
Nguyen, C. Thach
2015-01-01
We give optimal solutions to all versions of the popular counterfeit coin problem obtained by varying whether (i) we know if the counterfeit coin is heavier or lighter than the genuine ones, (ii) we know if the counterfeit coin exists, (iii) we have access to additional genuine coins, and (iv) we need to determine if the counterfeit coin is heavier or lighter than the genuine ones. Moreover, our solutions are non-adaptive.
Parareal in time intermediate targets methods for optimal control problem
Maday, Yvon; Salomon, Julien
2012-01-01
In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets that gives rise to independent sub-problems that can be solved in parallel. This method can be coupled with the parareal in time algorithm. Numerical experiments show the efficiency of our method.
Shape optimization for Stokes problem with threshold slip
Haslinger, J.; Stebel, Jan; Taoufik, S.
2014-01-01
Roč. 59, č. 6 (2014), s. 631-652. ISSN 0862-7940 R&D Projects: GA ČR GA201/09/0917; GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985840 Keywords : Stokes problem * friction boundary condition * shape optimization Subject RIV: BA - General Mathematics Impact factor: 0.400, year: 2014 http://link.springer.com/article/10.1007%2Fs10492-014-0077-z
Artificial Fish School Algorithm Applied in a Combinatorial Optimization Problem
Yun Cai
2010-01-01
An improved artificial fish swarm algorithm (AFSA) for solving a combinatorial optimization problem—a berth allocation problem (BAP), which was formulated. Its objective is to minimize the turnaround time of vessels at container terminals so as to improve operation efficiency customer satisfaction. An adaptive artificial fish swarm algorithm was proposed to solve it. Firstly, the basic principle and the algorithm design of the AFSA were introduced. Then, for a test case, computational experim...
Optimizing Distribution Problems using WinQSB Software
Daniel Mihai Amariei
2015-07-01
Full Text Available In the present paper we are presenting a problem of distribution using the Network Modeling Module of the WinQSB software, were we have 5 athletes which we must assign the optimal sample, function of the obtained time, so as to obtain the maximum output of the athletes. Also we analyzed the case of an accident of 2 athletes, the coupling of 3 athletes with 5 various athletic events causing the maximum coupling, done using the Hungarian algorithm.
Non-concave and behavioural optimal portfolio choice problems
Meireles Rodrigues, Andrea Sofia; Rodrigues, Andrea
2014-01-01
Our aim is to examine the problem of optimal asset allocation for investors exhibiting a behaviour in the face of uncertainty which is not consistent with the usual axioms of Expected Utility Theory. This thesis is divided into two main parts. In the first one, comprising Chapter II, we consider an arbitrage-free discrete-time financial model and an investor whose risk preferences are represented by a possibly nonconcave utility function (defined on the non-negative half-line only...
Optimization of Multiple Vehicle Routing Problems Using Approximation Algorithms
R. Nallusamy
2009-12-01
Full Text Available This paper deals with generating of an optimized route for multiple Vehicle routing Problems (mVRP. We used a methodology of clustering the given cities depending upon the number of vehicles and eachcluster is allotted to a vehicle. k- Means clustering algorithm has been used for easy clustering of the cities. In this way the mVRP has been converted into VRP which is simple in computation compared to mVRP. After clustering, an optimized route is generated for each vehicle in its allotted cluster. Once the clustering had been done and after the cities were allocated to the various vehicles, each cluster/tour was taken as an individual Vehicle Routing problem and the steps of Genetic Algorithm were applied to the cluster and iterated to obtain the most optimal value of the distance after convergence takes place. After the application of the variousheuristic techniques, it was found that the Genetic algorithm gave a better result and a more optimal tour for mVRPs in short computational time than other Algorithms due to the extensive search and constructive nature of the algorithm.
Guaranteed Discrete Energy Optimization on Large Protein Design Problems.
Simoncini, David; Allouche, David; de Givry, Simon; Delmas, Céline; Barbe, Sophie; Schiex, Thomas
2015-12-01
In Computational Protein Design (CPD), assuming a rigid backbone and amino-acid rotamer library, the problem of finding a sequence with an optimal conformation is NP-hard. In this paper, using Dunbrack's rotamer library and Talaris2014 decomposable energy function, we use an exact deterministic method combining branch and bound, arc consistency, and tree-decomposition to provenly identify the global minimum energy sequence-conformation on full-redesign problems, defining search spaces of size up to 10(234). This is achieved on a single core of a standard computing server, requiring a maximum of 66GB RAM. A variant of the algorithm is able to exhaustively enumerate all sequence-conformations within an energy threshold of the optimum. These proven optimal solutions are then used to evaluate the frequencies and amplitudes, in energy and sequence, at which an existing CPD-dedicated simulated annealing implementation may miss the optimum on these full redesign problems. The probability of finding an optimum drops close to 0 very quickly. In the worst case, despite 1,000 repeats, the annealing algorithm remained more than 1 Rosetta unit away from the optimum, leading to design sequences that could differ from the optimal sequence by more than 30% of their amino acids. PMID:26610100
Solving nonlinear equality constrained multiobjective optimization problems using neural networks.
Mestari, Mohammed; Benzirar, Mohammed; Saber, Nadia; Khouil, Meryem
2015-10-01
This paper develops a neural network architecture and a new processing method for solving in real time, the nonlinear equality constrained multiobjective optimization problem (NECMOP), where several nonlinear objective functions must be optimized in a conflicting situation. In this processing method, the NECMOP is converted to an equivalent scalar optimization problem (SOP). The SOP is then decomposed into several-separable subproblems processable in parallel and in a reasonable time by multiplexing switched capacitor circuits. The approach which we propose makes use of a decomposition-coordination principle that allows nonlinearity to be treated at a local level and where coordination is achieved through the use of Lagrange multipliers. The modularity and the regularity of the neural networks architecture herein proposed make it suitable for very large scale integration implementation. An application to the resolution of a physical problem is given to show that the approach used here possesses some advantages of the point of algorithmic view, and provides processes of resolution often simpler than the usual techniques. PMID:25647664
Parallel particle swarm optimization algorithm in nuclear problems
Particle Swarm Optimization (PSO) is a population-based metaheuristic (PBM), in which solution candidates evolve through simulation of a simplified social adaptation model. Putting together robustness, efficiency and simplicity, PSO has gained great popularity. Many successful applications of PSO are reported, in which PSO demonstrated to have advantages over other well-established PBM. However, computational costs are still a great constraint for PSO, as well as for all other PBMs, especially in optimization problems with time consuming objective functions. To overcome such difficulty, parallel computation has been used. The default advantage of parallel PSO (PPSO) is the reduction of computational time. Master-slave approaches, exploring this characteristic are the most investigated. However, much more should be expected. It is known that PSO may be improved by more elaborated neighborhood topologies. Hence, in this work, we develop several different PPSO algorithms exploring the advantages of enhanced neighborhood topologies implemented by communication strategies in multiprocessor architectures. The proposed PPSOs have been applied to two complex and time consuming nuclear engineering problems: reactor core design and fuel reload optimization. After exhaustive experiments, it has been concluded that: PPSO still improves solutions after many thousands of iterations, making prohibitive the efficient use of serial (non-parallel) PSO in such kind of realworld problems; and PPSO with more elaborated communication strategies demonstrated to be more efficient and robust than the master-slave model. Advantages and peculiarities of each model are carefully discussed in this work. (author)
Mohammad-Reza Askari
2015-01-01
Abstract This paper introduces a new stochastic optimization framework based bat algorithm BA to solve the optimal distribution feeder reconfiguration DFR as well as the shunt capacitor placement and sizing in the distribution systems. The objective functions to be investigated are minimization of the active power losses and minimization of the total network costs an. In order to consider the uncertainties of the active and reactive loads in the problem point estimate method PEM with 2m schem...
Issues and Strategies in Solving Multidisciplinary Optimization Problems
Patnaik, Surya
2013-01-01
Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the
Yan Sun
2015-09-01
Full Text Available Purpose: The purpose of study is to solve the multi-modal transportation routing planning problem that aims to select an optimal route to move a consignment of goods from its origin to its destination through the multi-modal transportation network. And the optimization is from two viewpoints including cost and time. Design/methodology/approach: In this study, a bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. Minimizing the total transportation cost and the total transportation time are set as the optimization objectives of the model. In order to balance the benefit between the two objectives, Pareto optimality is utilized to solve the model by gaining its Pareto frontier. The Pareto frontier of the model can provide the multi-modal transportation operator (MTO and customers with better decision support and it is gained by the normalized normal constraint method. Then, an experimental case study is designed to verify the feasibility of the model and Pareto optimality by using the mathematical programming software Lingo. Finally, the sensitivity analysis of the demand and supply in the multi-modal transportation organization is performed based on the designed case. Findings: The calculation results indicate that the proposed model and Pareto optimality have good performance in dealing with the bi-objective optimization. The sensitivity analysis also shows the influence of the variation of the demand and supply on the multi-modal transportation organization clearly. Therefore, this method can be further promoted to the practice. Originality/value: A bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. The Pareto frontier based sensitivity analysis of the demand and supply in the multi-modal transportation organization is performed based on the designed case.
Guo-Qiang Zeng
2014-01-01
Full Text Available As a novel evolutionary optimization method, extremal optimization (EO has been successfully applied to a variety of combinatorial optimization problems. However, the applications of EO in continuous optimization problems are relatively rare. This paper proposes an improved real-coded population-based EO method (IRPEO for continuous unconstrained optimization problems. The key operations of IRPEO include generation of real-coded random initial population, evaluation of individual and population fitness, selection of bad elements according to power-law probability distribution, generation of new population based on uniform random mutation, and updating the population by accepting the new population unconditionally. The experimental results on 10 benchmark test functions with the dimension N=30 have shown that IRPEO is competitive or even better than the recently reported various genetic algorithm (GA versions with different mutation operations in terms of simplicity, effectiveness, and efficiency. Furthermore, the superiority of IRPEO to other evolutionary algorithms such as original population-based EO, particle swarm optimization (PSO, and the hybrid PSO-EO is also demonstrated by the experimental results on some benchmark functions.
Jianli Ding
2013-03-01
Full Text Available In this study, we set the average taxi time of flight as the objective of the gate and runway assignment problem. We present a gate and runway combinatorial optimization model with several restrictions such as restrictions of gate and runway time, type of aircraft and service. We design a Discrete Particle Swarm Optimization (DPSO algorithm to solve this problem. Inspired by the genetic algorithm and combined with the neighborhood search, we propose a new location update strategy. Finally, numerical experiments were carried out on two cases where gate supplication is adequate and it’s not, experimental results show that the discrete particle swarm algorithm achieved very good results.
APPLYING PARTICLE SWARM OPTIMIZATION TO JOB-SHOP SCHEDULING PROBLEM
Xia Weijun; Wu Zhiming; Zhang Wei; Yang Genke
2004-01-01
A new heuristic algorithm is proposed for the problem of finding the minimum makespan in the job-shop scheduling problem. The new algorithm is based on the principles of particle swarm optimization (PSO). PSO employs a collaborative population-based search, which is inspired by the social behavior of bird flocking. It combines local search (by self experience) and global search (by neighboring experience), possessing high search efficiency. Simulated annealing (SA) employs certain probability to avoid becoming trapped in a local optimum and the search process can be controlled by the cooling schedule. By reasonably combining these two different search algorithms, a general, fast and easily implemented hybrid optimization algorithm, named HPSO, is developed. The effectiveness and efficiency of the proposed PSO-based algorithm are demonstrated by applying it to some benchmark job-shop scheduling problems and comparing results with other algorithms in literature. Comparing results indicate that PSO-based algorithm is a viable and effective approach for the job-shop scheduling problem.
On convex optimization problems in quantum information theory
Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is usually impossible. As inspired by earlier investigations into the relative entropy of entanglement (REE) (Miranowicz and Ishizaka 2008 Phys. Rev. A 78 032310), we introduce a general method to solve the converse problem rather than find explicit solutions. That is, given a matrix in a convex set, we determine a family of convex functions that are minimized at this point. This method allows us find explicit formulae for the REE and the Rains bound, two well-known upper bounds on the distillable entanglement, and yields interesting information about these quantities, such as the fact that they coincide in the case where at least one subsystem of a multipartite state is a qubit. (paper)
Multiobjective Optimization Problem of Multireservoir System in Semiarid Areas
Z. J. Chen
2013-01-01
Full Text Available With the increasing scarcity of water resources, the growing importance of the optimization operation of the multireservoir system in water resources development, utilization, and management is increasingly evident. Some of the existing optimization methods are inadequate in applicability and effectiveness. Therefore, we need further research in how to enhance the applicability and effectiveness of the algorithm. On the basis of the research of the multireservoir system’s operating parameters in the Urumqi River basin, we establish a multiobjective optimization problem (MOP model of water resources development, which meets the requirements of water resources development. In the mathematical model, the domestic water consumption is the biggest, the production of industry and agricultural is the largest, the gross output value of industry and agricultural is the highest, and the investment of the water development is the minimum. We use the weighted variable-step shuffled frog leaping algorithm (SFLA to resolve it, which satisfies the constraints. Through establishing the test function and performance metrics, we deduce the evolutionary algorithms, which suit for solving MOP of the scheduling, and realize the multiobjective optimization of the multireservoir system. After that, using the fuzzy theory, we convert the competitive multiobjective function into single objective problem of maximum satisfaction, which is the only solution. A feasible solution is provided to resolve the multiobjective scheduling optimization of multireservoir system in the Urumqi River basin. It is the significance of the layout of production, the regional protection of ecological environment, and the sufficient and rational use of natural resources, in Urumqi and the surrounding areas.
Optimization of Capacitated Vehicle Routing Problem by Nested Particle Swarm Optimization
Karuppusamy Kanthavel
2011-01-01
Full Text Available Problem statement: Vehicle routing problem determines the optimum route for each vehicle as a sequence of visiting cities. The problem has been defined as NP-hard and exact solution is relatively difficult to achieve for real time large scale models. Though several attempts to solve the problem were made in the literature, new approaches may be tried to solve the problem to further reduce computational efforts. Approach: In this context this study focuses on maximum utilization of loading capacity and determines the optimum set of vehicle routes for Capacitated Vehicle Routing Problem (CVRP by a Nested Particle Swarm Optimization (NPSO technique. The algorithm is implemented as Master PSO and slave PSO for the identification of candidate list and route sequence in nested form to optimize the model. Results: Benchmarking data set of capacitated vehicle routing is considered for the evaluations. The total distance of set vehicle route obtained by the new approach is compared with the best known solution and other existing techniques. Conclusions/Recommendations: The NPSO produces significant results and computational performance than the existing PSO algorithms. This newly proposed NPSO algorithm develops the vehicle schedule without any local optimization technique.
A Memetic Algorithm for Global Optimization of Multimodal Nonseparable Problems.
Zhang, Geng; Li, Yangmin
2016-06-01
It is a big challenging issue of avoiding falling into local optimum especially when facing high-dimensional nonseparable problems where the interdependencies among vector elements are unknown. In order to improve the performance of optimization algorithm, a novel memetic algorithm (MA) called cooperative particle swarm optimizer-modified harmony search (CPSO-MHS) is proposed in this paper, where the CPSO is used for local search and the MHS for global search. The CPSO, as a local search method, uses 1-D swarm to search each dimension separately and thus converges fast. Besides, it can obtain global optimum elements according to our experimental results and analyses. MHS implements the global search by recombining different vector elements and extracting global optimum elements. The interaction between local search and global search creates a set of local search zones, where global optimum elements reside within the search space. The CPSO-MHS algorithm is tested and compared with seven other optimization algorithms on a set of 28 standard benchmarks. Meanwhile, some MAs are also compared according to the results derived directly from their corresponding references. The experimental results demonstrate a good performance of the proposed CPSO-MHS algorithm in solving multimodal nonseparable problems. PMID:26292352
A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems
Yong WANG; Zixing CAI
2009-01-01
In the real-world applications, most optimization problems are subject to different types of constraints. These problems are known as constrained optimization problems (COPs). Solving COPs is a very important area in the optimization field. In this paper, a hybrid multi-swarm particle swarm optimization (HMPSO) is proposed to deal with COPs. This method adopts a parallel search operator in which the current swarm is partitioned into several subswarms and particle swarm optimization (PSO) is severed as the search engine for each sub-swarm. Moreover, in order to explore more promising regions of the search space, differential evolution (DE) is incorporated to improve the personal best of each particle. First, the method is tested on 13 benchmark test functions and compared with three stateof-the-art approaches. The simulation results indicate that the proposed HMPSO is highly competitive in solving the 13 benchmark test functions. Afterward, the effectiveness of some mechanisms proposed in this paper and the effect of the parameter setting were validated by various experiments. Finally, HMPSO is further applied to solve 24 benchmark test functions collected in the 2006 IEEE Congress on Evolutionary Computation (CEC2006) and the experimental results indicate that HMPSO is able to deal with 22 test functions.
Adjoint optimization of natural convection problems: differentially heated cavity
Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.
2016-06-01
Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7 ) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here
Qilin Wang
2011-01-01
Full Text Available Some new properties are obtained for generalized second-order contingent (adjacent epiderivatives of set-valued maps. By employing the generalized second-order adjacent epiderivatives, necessary and sufficient conditions of Benson proper efficient solutions are given for set-valued optimization problems. The results obtained improve the corresponding results in the literature.
On the local structure of optimal measures in the multi-marginal optimal transportation problem
Pass, Brendan, Department Of Mathematics
2010-01-01
We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension of the support of the solution.
On the robust optimization to the uncertain vaccination strategy problem
In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented
Study on ant colony optimization for fuel loading pattern problem
Modified ant colony optimization (ACO) was applied to the in-core fuel loading pattern (LP) optimization problem to minimize the power peaking factor (PPF) in the modeled 1/4 symmetry PWR core. Loading order was found to be important in ACO. Three different loading orders with and without the adjacent effect between fuel assemblies (FAs) were compared, and it was found that the loading order from the central core is preferable because many selections of FAs to be inserted are available in the core center region. LPs were determined from pheromone trail and heuristic information, which is a priori knowledge based on the feature of the problem. Three types of heuristic information were compared to obtain the desirable performance of searching LPs with low PPF. Moreover, mutation operation, such as the genetic algorithm (GA), was introduced into the ACO algorithm to avoid searching similar LPs because heuristic information used in ACO tends to localize the searching space in the LP problem. The performance of ACO with some improvement was compared with those of simulated annealing and GA. In conclusion, good performance can be achieved by setting proper heuristic information and mutation operation parameter in ACO. (author)
Artificial Fish School Algorithm Applied in a Combinatorial Optimization Problem
Yun Cai
2010-11-01
Full Text Available An improved artificial fish swarm algorithm (AFSA for solving a combinatorial optimization problem—a berth allocation problem (BAP, which was formulated. Its objective is to minimize the turnaround time of vessels at container terminals so as to improve operation efficiency customer satisfaction. An adaptive artificial fish swarm algorithm was proposed to solve it. Firstly, the basic principle and the algorithm design of the AFSA were introduced. Then, for a test case, computational experiments explored the effect of algorithm parameters on the convergence of the algorithm. Experimental results verified the validity and feasibility of the proposed algorithm with rational parameters, and show that the algorithm has better convergence performance than genetic algorithm (GA and ant colony optimization (ACO.
Optimal tests for the two-sample spherical location problem
Ley, Christophe; Verdebout, Thomas
2012-01-01
We tackle the classical two-sample spherical location problem for directional data by having recourse to the Le Cam methodology, habitually used in classical "linear" multivariate analysis. More precisely we construct locally and asymptotically optimal (in the maximin sense) parametric tests, which we then turn into semi-parametric ones in two distinct ways. First, by using a studentization argument; this leads to so-called pseudo-FvML tests. Second, by resorting to the invariance principle; this leads to efficient rank-based tests. Within each construction, the semi-parametric tests inherit optimality under a given distribution (the FvML in the first case, any rotationally symmetric one in the second) from their parametric counterparts and also improve on the latter by being valid under the whole class of rotationally symmetric distributions. Asymptotic relative efficiencies are calculated and the finite-sample behavior of the proposed tests is investigated by means of a Monte Carlo simulation.
Rao, R. V.; Savsani, V. J.; Balic, J.
2012-12-01
An efficient optimization algorithm called teaching-learning-based optimization (TLBO) is proposed in this article to solve continuous unconstrained and constrained optimization problems. The proposed method is based on the effect of the influence of a teacher on the output of learners in a class. The basic philosophy of the method is explained in detail. The algorithm is tested on 25 different unconstrained benchmark functions and 35 constrained benchmark functions with different characteristics. For the constrained benchmark functions, TLBO is tested with different constraint handling techniques such as superiority of feasible solutions, self-adaptive penalty, ɛ-constraint, stochastic ranking and ensemble of constraints. The performance of the TLBO algorithm is compared with that of other optimization algorithms and the results show the better performance of the proposed algorithm.
An optimization algorithm inspired by musical composition in constrained optimization problems
Roman Anselmo Mora-Gutiérrez
2013-12-01
Full Text Available Many real-world problems can be expressed as an instance of the constrained nonlinear optimization problem (CNOP. This problem has a set of constraints specifies the feasible solution space. In the last years several algorithms have been proposed and developed for tackling CNOP. In this paper, we present a cultural algorithm for constrained optimization, which is an adaptation of “Musical Composition Method” or MCM, which was proposed in [33] by Mora et al. We evaluated and analyzed the performance of MCM on five test cases benchmark of the CNOP. Numerical results were compared to evolutionary algorithm based on homomorphous mapping [23], Artificial Immune System [9] and anti-culture population algorithm [39]. The experimental results demonstrate that MCM significantly improves the global performances of the other tested metaheuristics on same of benchmark functions.
Empirical Estimates in Economic and Financial Optimization Problems
Houda, Michal; Kaňková, Vlasta
2012-01-01
Roč. 19, č. 29 (2012), s. 50-69. ISSN 1212-074X R&D Projects: GA ČR GAP402/10/1610; GA ČR GAP402/11/0150; GA ČR GAP402/10/0956 Institutional research plan: CEZ:AV0Z10750506 Keywords : stochastic programming * empirical estimates * moment generating functions * stability * Wasserstein metric * L1-norm * Lipschitz property * consistence * convergence rate * normal distribution * Pareto distribution * Weibull distribution * distribution tails * simulation Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2012/E/houda-empirical estimates in economic and financial optimization problems.pdf
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
Wolf Search Algorithm for Solving Optimal Reactive Power Dispatch Problem
Kanagasabai Lenin; B.Ravindhranath Reddy; M.Surya Kalavathi
2015-01-01
This paper presents a new bio-inspired heuristic optimization algorithm called the Wolf Search Algorithm (WSA) for solving the multi-objective reactive power dispatch problem. Wolf Search algorithm is a new bio – inspired heuristic algorithm which based on wolf preying behaviour. The way wolves search for food and survive by avoiding their enemies has been imitated to formulate the algorithm for solving the reactive power dispatches. And the speciality of wolf is possessing both individual...
Combining Multiple Strategies for Multiarmed Bandit Problems and Asymptotic Optimality
Hyeong Soo Chang
2015-01-01
Full Text Available This brief paper provides a simple algorithm that selects a strategy at each time in a given set of multiple strategies for stochastic multiarmed bandit problems, thereby playing the arm by the chosen strategy at each time. The algorithm follows the idea of the probabilistic ϵt-switching in the ϵt-greedy strategy and is asymptotically optimal in the sense that the selected strategy converges to the best in the set under some conditions on the strategies in the set and the sequence of {ϵt}.
Topology optimization of 3D Stokes flow problems
Gersborg-Hansen, Allan
test problems only. The motivation for considering topology optimization in 3D Stokes flow originates from micro fluidic systems. At small scales the Stokes equations are a reasonable mathematical model to use for the fluid behavior. Physically Stokes flow is an exotic inertia free flow, which in...... setting of standard analysis software which enables a credible performance check relevant before design manufacturing. Note that this requires a proper interpretation of a computed design used to generate a body fitted mesh. In addition issues related to the parallel solution of the linear algebra...
Enhanced ant colony optimization for inventory routing problem
Wong, Lily; Moin, Noor Hasnah
2015-10-01
The inventory routing problem (IRP) integrates and coordinates two important components of supply chain management which are transportation and inventory management. We consider a one-to-many IRP network for a finite planning horizon. The demand for each product is deterministic and time varying as well as a fleet of capacitated homogeneous vehicles, housed at a depot/warehouse, delivers the products from the warehouse to meet the demand specified by the customers in each period. The inventory holding cost is product specific and is incurred at the customer sites. The objective is to determine the amount of inventory and to construct a delivery routing that minimizes both the total transportation and inventory holding cost while ensuring each customer's demand is met over the planning horizon. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (best integer) for each instance considered. We propose an enhanced ant colony optimization (ACO) to solve the problem and the built route is improved by using local search. The computational experiments demonstrating the effectiveness of our approach is presented.
Approximation Algorithms for Optimal Decision Trees and Adaptive TSP Problems
Gupta, Anupam; Nagarajan, Viswanath; Ravi, R
2010-01-01
We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any particular disease, what is a good adaptive strategy to perform these tests to minimize the expected cost to identify the disease? We settle the approximability of this problem by giving a tight $O(\\log m)$-approximation algorithm. We also consider a more substantial generalization, the Adaptive TSP problem. Given an underlying metric space, a random subset $S$ of cities is drawn from a known distribution, but $S$ is initially unknown to us--we get information about whether any city is in $S$ only when we visit the city in question. What is a good adaptive way of visiting all the cities in the random subset $S$ while minimizing the expected distance traveled? For this problem, we give the first poly-logarithmic approximation, and show that this algorithm is best possible unless w...
Analysis of optimal and near-optimal continuous-thrust transfer problems in general circular orbit
Kéchichian, Jean A.
2009-09-01
A pair of practical problems in optimal continuous-thrust transfer in general circular orbit is analyzed within the context of analytic averaging for rapid computations leading to near-optimal solutions. The first problem addresses the minimum-time transfer between inclined circular orbits by proposing an analytic solution based on a split-sequence strategy in which the equatorial inclination and node controls are done separately by optimally selecting the intermediate orbit size at the sequence switch point that results in the minimum-time transfer. The consideration of the equatorial inclination and node state variables besides the orbital velocity variable is needed to further account for the important J2 perturbation that precesses the orbit plane during the transfer, unlike the thrust-only case in which it is sufficient to consider the relative inclination and velocity variables thus reducing the dimensionality of the system equations. Further extensions of the split-sequence strategy with analytic J2 effect are thus possible for equal computational ease. The second problem addresses the maximization of the equatorial inclination in fixed time by adopting a particular thrust-averaging scheme that controls only the inclination and velocity variables, leaving the node at the mercy of the J2 precession, providing robust fast-converging codes that lead to efficient near-optimal solutions. Example transfers for both sets of problems are solved showing near-optimal features as far as transfer time is concerned, by directly comparing the solutions to "exact" purely numerical counterparts that rely on precision integration of the raw unaveraged system dynamics with continuously varying thrust vector orientation in three-dimensional space.
Mohammad-Reza Askari
2015-07-01
Full Text Available Abstract This paper introduces a new stochastic optimization framework based bat algorithm BA to solve the optimal distribution feeder reconfiguration DFR as well as the shunt capacitor placement and sizing in the distribution systems. The objective functions to be investigated are minimization of the active power losses and minimization of the total network costs an. In order to consider the uncertainties of the active and reactive loads in the problem point estimate method PEM with 2m scheme is employed as the stochastic tool. The feasibility and good performance of the proposed method are examined on the IEEE 69-bus test system.
Modified Monkey Optimization Algorithm for Solving Optimal Reactive Power Dispatch Problem
Kanagasabai Lenin
2015-04-01
Full Text Available In this paper, a novel approach Modified Monkey optimization (MMO algorithm for solving optimal reactive power dispatch problem has been presented. MMO is a population based stochastic meta-heuristic algorithm and it is inspired by intelligent foraging behaviour of monkeys. This paper improves both local leader and global leader phases. The proposed (MMO algorithm has been tested in standard IEEE 30 bus test system and simulation results show the worthy performance of the proposed algorithm in reducing the real power loss.
Applying dynamic programming to a gas-lift optimization problem
Camponogara, Eduardo; Nakashima, Paulo H.R. [Santa Catarina Univ., Florianopolis (Brazil). Dept. de Automacao e Sistemas]. E-mails: camponog@das.ufsc.br; phrn@das.ufsc.br
2003-07-01
The ever-increasing demand for nonrenewable resources and the pressure from stockholders are two forces pressing the oil industry for higher efficiency. The opportunities for advances abound in all sectors of the industry, in particular production processes in gas-lift oil wells, which are often favored to draw oil from high-depth reservoirs. Of concern in this paper is the task of distributing the limited supply of gas to the wells so as to induce an optimal oil production. Narrowing this task to the steady-state response of the wells gives rise to the gas-lift optimization problem, whose variables decide which wells should be active as well as the gas-injection and whose objective is profit maximization. The paper elaborates on a few properties of the problem and delivers a dynamic programming algorithm to find approximate solutions. The effectiveness of the algorithm was demonstrated by contrasting its solutions against upper bounds obtained with continuous relaxation. As closure, the paper outlines a few directions for future research. (author)
Solving the Traveling Salesman's Problem Using the African Buffalo Optimization.
Odili, Julius Beneoluchi; Mohmad Kahar, Mohd Nizam
2016-01-01
This paper proposes the African Buffalo Optimization (ABO) which is a new metaheuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills, and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman's Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation, and good memory of its previous personal exploits as well as tapping from the herd's collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive. PMID:26880872
无
2006-01-01
This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
An optimal iterative solver for the Stokes problem
Wathen, A. [Univ. of Bristol (United Kingdom); Silvester, D.
1994-12-31
Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal solver for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.
A program package for solving nonlinear optimization problems
For the solution of nonlinear optimization problems, sixteen programs have been prepared and tested on FACOM M200 computer. A set of auxiliary programs has also been equipped to facilitate the use of this program package, with the main stress on the reduction of the effort that is required for the preparation of the main program. An attempt has been made to unify the input/output format as far as possible throughout the auxiliary programs. The programs have been classified broadly into two categories according to whether it can treat the problems with constraints or not. Moreover, from the viewpoint of the characteristics of the solution techniques, the programs that can be used only for the problems without constraints have been sub-divided into the following three classes; the first class involves only the objective function values themselves, the second involves the values of the objective function and their first partial derivatives, and the last involves the second partial derivatives as well. In order to make this program package available to various users, the explanation on the calculational procedure, the meaning of the arguments in the calling sequence of each program and the instructions about input data requirements of each auxiliary program have been presented together with the sample input/output listings. (author)
Problems of future energy market planning and optimization
Problems of future energy supply in the form, which is demanded - heat, liquid fuel, electricity - are described. There are several factors, which probably could be studied separately: technology and its sustain ability with respect to the raw materials resources, long time for capacity construction, for some form of energy even absence of sufficiently deep technology knowledge and model of prices. Prices are specially peculiar problem - they could be very different from the standard approach (investment, operation and maintenance, fuel, profit), if there are market instabilities and you are not able to supply market by the demanded amount form of energy with the consequences on production. Expected effect will be jump in prices or regulated supply to equalize supply and use. Such situation will be until the new capacities are put into operation or new technologies of production are established - it could be time about ten or more years and this can completely change our standard consideration of profit. The main profit will be to avoid losses and unemployment. Also concept of local or domestic raw material resources could be changed - in the free market your resources will be sold to those paying more. Probable development of energy market is described in the article and special attention is devoted to the nuclear energy, which not only consume, but also produce raw material and how to proceed to avoid crises in supply. Contemporary understanding of the problem does not enable to formulate it strictly as mathematical optimization task (Authors)
Harish Garg
2013-01-01
The present work investigates the reliability optimization problem of the repairable industrial systems by utilizing uncertain, limited, and imprecise data. In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting objectives. Moreover, data collected or available for the systems are vague, ambiguous, qualitative, and imprecise in nature due to various practical constraints and hence creat...
Hifza Afaq
2011-05-01
Full Text Available The multi objective optimization problems can be found in various fields such as finance, automobile design, aircraft design, path optimization etc. This paper reviews some of the existing literature on multi objective optimization problems and some of the existing Swarm Intelligence (SI based techniques to solve these problems. The objective of this paper is to provide a starting point to the multi objective optimization problems to the reader.
Hifza Afaq; Sanjay Saini
2011-01-01
The multi objective optimization problems can be found in various fields such as finance, automobile design, aircraft design, path optimization etc. This paper reviews some of the existing literature on multi objective optimization problems and some of the existing Swarm Intelligence (SI) based techniques to solve these problems. The objective of this paper is to provide a starting point to the multi objective optimization problems to the reader.
Kui-Ting CHEN; Yijun Dai; Ke Fan; Takaaki Baba
2015-01-01
Capacitated vehicle routing problem with pickups and deliveries (CVRPPD) is one of the most challenging combinatorial optimization problems which include goods delivery/pickup optimization, vehicle number optimization, routing path optimization and transportation cost minimization. The conventional particle swarm optimization (PSO) is difficult to find an optimal solution of the CVRPPD due to its simple search strategy. A PSO with adaptive multi-swarm strategy (AMSPSO) is proposed to solve th...
Using a finite horizon numerical optimisation method for a periodic optimal control problem
Azzato, Jeffrey D.; Krawczyk, Jacek
2007-01-01
Computing a numerical solution to a periodic optimal control problem is difficult. A method of approximating a solution to a given (stochastic) optimal control problem using Markov chains was developed in [3]. This paper describes an attempt at applying this method to a periodic optimal control problem introduced in [2].
Wolf Search Algorithm for Solving Optimal Reactive Power Dispatch Problem
Kanagasabai Lenin
2015-03-01
Full Text Available This paper presents a new bio-inspired heuristic optimization algorithm called the Wolf Search Algorithm (WSA for solving the multi-objective reactive power dispatch problem. Wolf Search algorithm is a new bio – inspired heuristic algorithm which based on wolf preying behaviour. The way wolves search for food and survive by avoiding their enemies has been imitated to formulate the algorithm for solving the reactive power dispatches. And the speciality of wolf is possessing both individual local searching ability and autonomous flocking movement and this special property has been utilized to formulate the search algorithm .The proposed (WSA algorithm has been tested on standard IEEE 30 bus test system and simulation results shows clearly about the good performance of the proposed algorithm .
Human opinion dynamics: An inspiration to solve complex optimization problems
Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P.; Kapur, Pawan
2013-10-01
Human interactions give rise to the formation of different kinds of opinions in a society. The study of formations and dynamics of opinions has been one of the most important areas in social physics. The opinion dynamics and associated social structure leads to decision making or so called opinion consensus. Opinion formation is a process of collective intelligence evolving from the integrative tendencies of social influence with the disintegrative effects of individualisation, and therefore could be exploited for developing search strategies. Here, we demonstrate that human opinion dynamics can be utilised to solve complex mathematical optimization problems. The results have been compared with a standard algorithm inspired from bird flocking behaviour and the comparison proves the efficacy of the proposed approach in general. Our investigation may open new avenues towards understanding the collective decision making.
An Optimized and Scalable Eigensolver for Sequences of Eigenvalue Problems
Berljafa, Mario; Di Napoli, Edoardo
2014-01-01
In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution of one problem fosters the initialization of the next. In addition, some eigenproblem sequences show a connection between the solutions of adjacent eigenproblems. Whenever is possible to unravel the existence of such a connection, the eigenproblem sequence is said to be a correlated. When facing with a sequence of correlated eigenproblems the current strategy amounts to solving each eigenproblem in isolation. We propose a novel approach which exploits such correlation through the use of an eigensolver based on subspace iteration and accelerated with Chebyshev polynomials (ChFSI). The resulting eigensolver, is optimized by minimizing the number of matvec multiplications and parallelized using the Elemental library framework. Numerical results shows that ChFSI achieves excell...
Zhang, Y.
2013-01-01
This paper builds up two equivalence theorems for different kinds of optimal control problems of internally controlled Schr\\"{o}dinger equations. The first one concerns with the equivalence of the minimal norm and the minimal time control problems. (The minimal time control problems are also called the first type of optimal time control problems.) The targets of the aforementioned two kinds of problems are the origin of the state space. The second one deals with the equivalence of three optim...
Optimal Rapid Restart of Heuristic Methods of NP Hard Problems
侯越先; 王芳
2004-01-01
Many heuristic search methods exhibit a remarkable variability in the time required to solve some particular problem instances. Their cost distributions are often heavy-tailed. It has been demonstrated that, in most cases, rapid restart (RR) method can prominently suppress the heavy-tailed nature of the instances and improve computation efficiency. However, it is usually time-consuming to check whether an algorithm on a specific instance is heavy-tailed or not. Moreover, if the heavy-tailed distribution is confirmed and the RR method is relevant, an optimal RR threshold should be chosen to facilitate the RR mechanism. In this paper, an approximate approach is proposed to quickly check whether an algorithm on a specific instance is heavy-tailed or not.The method is realized by means of calculating the maximal Lyapunov exponent of its generic running trace.Then a statistical formula to estimate the optimal RR threshold is educed. The method is based on common nonparametric estimation, e. g. , Kernel estimation. Two heuristic methods are selected to verify our method. The experimental results are consistent with the theoretical consideration perfectly.
Evolution of the passive harmonic filters optimization problem in industrial power systems
Cabral-Leite, Jandecy; Pérez-Abril, Ignacio; Santos-Azevedo, Manoel Socorro; de Lima-Tostes, Maria Emilia; Holanda-Bezerra, Ubiratan
2014-01-01
Several authors have treated the optimization of passive filters in electric distribution systems. Optimization methods like: sequential quadratic programming (SQP), simulated annealing (SA), differential evolution (DE), artificial neural networks (ANN), particle swarm optimization (PSO), genetic algorithm (GA), etc., have been employed for optimizing certain configurations of passive filters. These optimization methods have been employed to solve several formulations of the problem of the pr...
AN ADAPTIVE MEMBRANE ALGORITHM FOR SOLVING COMBINATORIAL OPTIMIZATION PROBLEMS
Juanjuan HE; Jianhua XIAO; Zehui SHAO
2014-01-01
Membrane algorithms (MAs), which inherit from P systems, constitute a new parallel and distribute framework for approximate computation. In the paper, a membrane algorithm is proposed with the improvement that the involved parameters can be adaptively chosen. In the algorithm, some membranes can evolve dynamically during the computing process to specify the values of the requested parameters. The new algorithm is tested on a well-known combinatorial optimization problem, the travelling salesman problem. The em-pirical evidence suggests that the proposed approach is efficient and reliable when dealing with 11 benchmark instances, particularly obtaining the best of the known solutions in eight instances. Compared with the genetic algorithm, simulated annealing algorithm, neural net-work and a fine-tuned non-adaptive membrane algorithm, our algorithm performs better than them. In practice, to design the airline network that minimize the total routing cost on the CAB data with twenty-five US cities, we can quickly obtain high quality solutions using our algorithm.
Optimal Control Approaches to the Aggregate Production Planning Problem
Yasser A. Davizón
2015-12-01
Full Text Available In the area of production planning and control, the aggregate production planning (APP problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.
Solving Large-Scale Optimization Problems Related to Bell's Theorem
Gondzio, Jacek; Hall, J A Julian; Laskowski, Wiesław; Żukowski, Marek
2014-01-01
Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth description of a method of testing the existence of such models, which involves two levels of optimization: a higher-level non-linear task and a lower-level linear programming (LP) task. The article compares the performances of the existing implementation of the method, where the LPs are solved with the simplex method, and our new implementation, where the LPs are solved with a matrix-free interior point method. We describe in detail how the latter can be applied to our problem, discuss the basic scenario and possible improvements and how they impact on overall performance. Significant performance advantage of the matrix-free interior point method over the simplex method is confirmed by extensive computational results. The new method is able to solve problems which are orders of ma...
Zi-you Gao; Tian-de Guo; Guo-ping He; Fang Wu
2002-01-01
In this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations having a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQPtype algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.
A modified teaching–learning based optimization for multi-objective optimal power flow problem
Highlights: • A new modified teaching–learning based algorithm is proposed. • A self-adaptive wavelet mutation strategy is used to enhance the performance. • To avoid reaching a large repository size, a fuzzy clustering technique is used. • An efficiently smart population selection is utilized. • Simulations show the superiority of this algorithm compared with other ones. - Abstract: In this paper, a modified teaching–learning based optimization algorithm is analyzed to solve the multi-objective optimal power flow problem considering the total fuel cost and total emission of the units. The modified phase of the optimization algorithm utilizes a self-adapting wavelet mutation strategy. Moreover, a fuzzy clustering technique is proposed to avoid extremely large repository size besides a smart population selection for the next iteration. These techniques make the algorithm searching a larger space to find the optimal solutions while speed of the convergence remains good. The IEEE 30-Bus and 57-Bus systems are used to illustrate performance of the proposed algorithm and results are compared with those in literatures. It is verified that the proposed approach has better performance over other techniques
Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem
无
2006-01-01
Capacitated vehicle routing problem (CVRP) is an NP-hard problem. For large-scale problems, it is quite difficult to achieve an optimal solution with traditional optimization methods due to the high computational complexity. A new hybrid approximation algorithm is developed in this work to solve the problem. In the hybrid algorithm, discrete particle swarm optimization (DPSO) combines global search and local search to search for the optimal results and simulated annealing (SA) uses certain probability to avoid being trapped in a local optimum. The computational study showed that the proposed algorithm is a feasible and effective approach for capacitated vehicle routing problem, especially for large scale problems.
Using Bee Colony Optimization to Solve the Task Scheduling Problem in Homogenous Systems
Vahid Arabnejad; Ali Moeini; Nasrollah Moghadam
2011-01-01
Bee colony optimization (BCO) is one of the most recent algorithms in swarm intelligence that can be used in optimization problems this algorithm is based on the intelligent behavior of honey bees in foraging process. In this paper bee colony optimization is applied to solve the task scheduling problem which tasks have dependency with each other. Scheduling of tasks that represents by directed acyclic graph is a NP-complete problem. The main purpose of this problem is obtaining the minimum sc...
Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
The Fighter Problem: Optimal Allocation of a Discrete Commodity
Bartroff, Jay
2011-01-01
The Fighter problem with discrete ammunition is studied. An aircraft (fighter) equipped with $n$ anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which follows a homogeneous Poisson process with known intensity. If $j$ of the $n$ missiles are spent at an encounter they destroy an enemy plane with probability $a(j)$, where $a(0) = 0 $ and $\\{a(j)\\}$ is a known, strictly increasing concave sequence, e.g., $a(j) = 1-q^j, \\; \\, 0 < q < 1$. If the enemy is not destroyed, the enemy shoots the fighter down with known probability $1-u$, where $0 \\le u \\le 1$. The goal of the fighter is to shoot down as many enemy airplanes as possible during a given time period $[0, T]$. Let $K (n, t)$ be the smallest optimal number of missiles to be used at a present encounter, when the fighter has flying time $t$ remaining and $n$ missiles remaining. Three seemingly obvious properties of $K(n, t)$ have been conjectured: [A] The closer to the destination, the more of the $n$ missiles one should use, ...
ZHANG DE-TAO
2009-01-01
In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations.
A Risk-Sensitive Portfolio Optimization Problem with Fixed Incomes Securities
Goel, Mayank
2007-01-01
We discuss a class of risk-sensitive portfolio optimization problems. We consider the portfolio optimization model investigated by Nagai in 2003. The model by its nature can include fixed income securities as well in the portfolio. Under fairly general conditions, we prove the existence of optimal portfolio in both finite and infinite horizon problems.
Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples
Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control
Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)
2015-04-15
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.
A PROBLEM OF FINDING AN OPTIMAL STRUCTURE OF HEAT SUPPLY NETWORKS
V.N.Melkumov; Kuznetsov, I. S.; A. V. Loboda
2012-01-01
Problem statement. A mathematical model of heat supply network structure that takes into accountnetwork construction costs and profit obtained from heat consumers has been considered. Adirect solution of the heating network optimization problem based on profit is complicated by thecombinatorial nature of this problem. That is why development of the methods which allow tosolve this optimization problem in acceptable computation time is an actual problem.Results. A mathematical model of heat su...
2014-01-01
We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.
Vorozheikin, A.; Gonchar, T.; Panfilov, I.; Sopov, E.; Sopov, S.
2009-01-01
A new algorithm for the solution of complex constrained optimization problems based on the probabilistic genetic algorithm with optimal solution prediction is proposed. The efficiency investigation results in comparison with standard genetic algorithm are presented.
Weifeng Wang
2014-01-01
Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.
V. Selvi
2012-06-01
Full Text Available - SI is a computational and collective behavioral metaphor that is used for solving problems. The problems can be solved by SI by taking ants, termites, bees and wasps as an example. The application of SI algorithm are ACO, PSO and ABC which have been already applied to solve real world optimization problems in engineering. ACO is a member of SI in which ACO is inspired by the behaviour of ant colonies and it constitutes some metaheuristic optimization. ACO’s aim is to search for an optimal path with the help of graph. In PSO, a solution of continuous optimization problems can be solved , because PSO is population based stochastic optimization techniques for the solution of continuous optimization problem. In ABC the solution for the problem is found with help of foraging behaviour of honey bees. It is also swarm based meta heuristic algorithm. This paper presents the experimental verification of ACO and EACO.
2014-01-01
We consider an optimal control problem subject to the terminal state equality constraint and continuous inequality constraints on the control and the state. By using the control parametrization method used in conjunction with a time scaling transform, the constrained optimal control problem is approximated by an optimal parameter selection problem with the terminal state equality constraint and continuous inequality constraints on the control and the state. On this basis, a simple exact penal...
Chaudhuri, Arindam
2013-01-01
We present a dynamic algorithm for solving the Longest Common Subsequence Problem using Ant Colony Optimization Technique. The Ant Colony Optimization Technique has been applied to solve many problems in Optimization Theory, Machine Learning and Telecommunication Networks etc. In particular, application of this theory in NP-Hard Problems has a remarkable significance. Given two strings, the traditional technique for finding Longest Common Subsequence is based on Dynamic Programming which cons...
Optimization and Robustness in Planning and Scheduling Problems. Application to Container Terminals
RODRÍGUEZ MOLINS, MARIO
2015-01-01
Despite the continuous evolution in computers and information technology, real-world combinatorial optimization problems are NP-problems, in particular in the domain of planning and scheduling. Thus, although exact techniques from the Operations Research (OR) field, such as Linear Programming, could be applied to solve optimization problems, they are difficult to apply in real-world scenarios since they usually require too much computational time, i.e: an optimized solution is ...
Model Guided Sampling Optimization for Low-dimensional Problems
Bajer, L. (Lukáš); Holeňa, M. (Martin)
2015-01-01
Optimization of very expensive black-box functions requires utilization of maximum information gathered by the process of optimization. Model Guided Sampling Optimization (MGSO) forms a more robust alternative to Jones’ Gaussian-process-based EGO algorithm. Instead of EGO’s maximizing expected improvement, the MGSO uses sampling the probability of improvement which is shown to be helpful against trapping in local minima. Further, the MGSO can reach close-to-optimum solutions faster than stand...
Swaidan, Waleeda; Hussin, Amran
2015-10-01
Most direct methods solve finite time horizon optimal control problems with nonlinear programming solver. In this paper, we propose a numerical method for solving nonlinear optimal control problem with state and control inequality constraints. This method used quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a quadratic programming problem. The linear inequality constraints for trajectories variables are converted to quadratic programming constraint by using Haar wavelet collocation method. The proposed method has been applied to solve Optimal Control of Multi-Item Inventory Model. The accuracy of the states, controls and cost can be improved by increasing the Haar wavelet resolution.
Tang Zhili; Dong Jun
2009-01-01
complete and complete decisions of the leader and followers respectively. Several design examples illustrate the efficiency of the coupling algorithms for multi-criterion aerodynamic design optimization problems.
Optimization of casting process based on the theory of inventive problem solving
Liu Feng; Yang Yi; Li Xionglong
2011-01-01
Optimization of casting process involves the adjustment of parameters as well as the improvement of process schemes and measures. This paper proposes a new method based on the Theory of Inventive Problem Solving (TRIZ) for casting process optimization, and realizes the idea of applying TRIZ to optimize the casting process of a magnesium alloy intake manifold. By this method, the casting process is optimized so as to remove the shrinkage pores. The successful optimization of casting process de...
陆娟; 肖敏; 卢丽丽
2011-01-01
通过单因素试验(培养基用水、碳源、氮源、培养温度和培养基初始pH值)和正交试验对地农芽孢杆菌(Bacillus licheniformis)8-37-0-1发酵产生Levan果聚糖的培养基组成及培养条件进行优化,采用苯酚-硫酸法测定多糖含量.结果表明:以蔗糖100g/L、牛肉膏1.0g/L、酵母粉0.6g/L、K2HPO4 3.0g/L、KH2PO4 3.0g/L、NaCl 1.0g/L、MgSO4·7H2O 0.2g/L、FeSO4·7H2O 0.001g/L,自来水配制,培养基初始pH5.0,30℃培养8-37-0-1菌株24h,Levan果聚糖产量达到最高值41.7g/L,约是未优化时的5.0倍.
Implicit optimality criterion for convex SIP problem with box constrained index set
Kostyukova, O. I.; Tchemisova, T. V.
2012-01-01
We consider a convex problem of Semi-Infinite Programming (SIP) with multidimensional index set. In study of this problem we apply the approach suggested in [20] for convex SIP problems with one-dimensional index sets and based on the notions of immobile indices and their immobility orders. For the problem under consideration we formulate optimality conditions that are explicit and have the form of criterion. We compare this criterion with other known optimality conditions for ...
Sandal, Leif Kristoffer; Berge, Gerhard
2001-01-01
Dynamic optimization problems covers a great class of problems in management science and technology. The classical problem formulations being the variational approach as in classical mechanics, like Hamilton's principle and the optimal control theory in economics as the Pontryagin's maximum principle. In this account we start with a general problem formulation as an alternative to an approach based on solving differential equations. We focus on creating an analytical environment aimed at deri...
Magnússon, Sindri; Chathuranga Weeraddana, Pradeep; Fischione, Carlo
2014-01-01
The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial, though their global optimality is not guaranteed. Existing semi-definite programming relaxation based approaches are restricted to OPF problems where zero duality holds. In this paper, an efficient novel method to address the general nonconvex OPF problem is...
Stability, Optimality and Manipulation in Matching Problems with Weighted Preferences
Maria Silvia Pini; Francesca Rossi; K. Brent Venable; Toby Walsh
2013-01-01
The stable matching problem (also known as the stable marriage problem) is a well-known problem of matching men to women, so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools or, more generally, to any two-sided market. In the classical stable marriage problem, both men and women express a strict preference order over...
Uniqueness and Monge solutions in the multi-marginal optimal transportation problem
Pass, Brendan, Department Of Mathematics
2010-01-01
We study a multi-marginal optimal transportation problem. Under certain conditions on the cost function and the first marginal, we prove that the solution to the relaxed, Kantorovich version of the problem induces a solution to the Monge problem and that the solutions to both problems are unique.
Stochastic Constriction Cockroach Swarm Optimization for Multidimensional Space Function Problems
Obagbuwa, I. C,; A. O. Adewumi; A. A. Adebiyi
2014-01-01
The effect of stochastic constriction on cockroach swarm optimization (CSO) algorithm performance was examined in this paper. A stochastic constriction cockroach swarm optimization (SCCSO) algorithm is proposed. A stochastic constriction factor is introduced into CSO algorithm for swarm stability enhancement; control cockroach movement from one position to another while searching for solution to avoid explosion; enhanced local and global searching capabilities. SCCSO performance was tested th...
Sparse optimization for inverse problems in atmospheric modelling
Adam, Lukáš; Branda, Martin
2016-01-01
Roč. 79, č. 3 (2016), s. 256-266. ISSN 1364-8152 R&D Projects: GA MŠk(CZ) 7F14287 Institutional support: RVO:67985556 Keywords : Inverse modelling * Sparse optimization * Integer optimization * Least squares * European tracer experiment * Free Matlab codes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.420, year: 2014 http://library.utia.cas.cz/separaty/2016/MTR/adam-0457037.pdf
Vocational Education Network Optimization Program Implementation Problems and Solutions
Šīna, Inga
2015-01-01
The aim of the paper is to analyze two-year results of the optimization programs of vocational school network and vocational education balancing solutions in the European Social Fund project " Improvement of national qualification system, vocational education contents and co-operation among the bodies involved in vocational education." The topic is of particular importance as the prestige of vocational education is low, the school network optimization yielded no results and vocational trainin...
2010-04-01
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2010-04-01
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28 CFR 0.1 - Organizational units.
2010-07-01
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2010-04-01
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Existence of optimal controls for singular control problems with state constraints
Budhiraja, Amarjit; Ross, Kevin
2007-01-01
We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for Brownian control problems \\citehar, associated with a broad family of stochastic networks, follows as a consequence.
Solving Continuous-Time Optimal-Control Problems with a Spreadsheet.
Naevdal, Eric
2003-01-01
Explains how optimal control problems can be solved with a spreadsheet, such as Microsoft Excel. Suggests the method can be used by students, teachers, and researchers as a tool to find numerical solutions for optimal control problems. Provides several examples that range from simple to advanced. (JEH)
Jingtao Shi
2013-01-01
Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
Jingtao Shi; Zhiyong Yu
2013-01-01
This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
无
2000-01-01
The performance of analytical derivative and sparse matrix techniques applied to a traditional densesequential quadratic programming(SQP) is studied, and the strategy utilizing those techniques is also presented. Computational results on two typicalchemical optimization problems demonstrate significant enhancement in efficiency, which shows this strategy ispromising and suitable for large-scale process optimization problems.
钟卫涛; 邵之江; 张余岳; 钱积新
2000-01-01
The performance of analytical derivative and sparse matrix techniques applied to a traditional dense sequential quadratic programming (SQP) is studied, and the strategy utilizing those techniques is also presented.Computational results on two typical chemical optimization problems demonstrate significant enhancement in efficiency, which shows this strategy is promising and suitable for large-scale process optimization problems.
Kreuzer, Christian; Schedensack, Mira
2014-01-01
We extend the ideas of Diening, Kreuzer, and Stevenson [Instance optimality of the adaptive maximum strategy, Found. Comput. Math. (2015)], from conforming approximations of the Poisson problem to nonconforming Crouzeix-Raviart approximations of the Poisson and the Stokes problem in 2D. As a consequence, we obtain instance optimality of an AFEM with a modified maximum marking strategy.
The vector-valued measure defined by the well-posed linear boundary value problems is discussed. The maximum principle of the optimal control problem with non-convex constraint is proved by using the vector-valued measure. Especially, the necessary conditions of the optimal control of elliptic systems is derived without the convexity of the control domain and the cost function. (author)
Improving the efficiency of solving discrete optimization problems: The case of VRP
Belov, A.; Slastnikov, S.
2016-02-01
Paper is devoted constructing efficient metaheuristics algorithms for discrete optimization problems. Particularly, we consider vehicle routing problem applying original ant colony optimization method to solve it. Besides, some parts of algorithm are separated for parallel computing. Some experimental results are performed to compare the efficiency of these methods.
Sidky, Emil Y; Pan, Xiaochuan
2011-01-01
The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in the article, and several CP algorithm instances for many optimization problems relevant to CT are explicitly derived. An example application modeling breast CT with low-intensity X-ray illumination is presented.
Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan
2012-01-01
The primal–dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1–26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for...... the purpose of designing iterative image reconstruction algorithms for CT. The primal–dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example...... application modeling breast CT with low-intensity x-ray illumination is presented....
A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems
Ali, Hegagi M.; Pereira, Fernando Lobo; Gama, Sílvio M. A.
2016-09-01
In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo sense. We use a new approach to prove necessary conditions of optimality in the form of Pontryagin maximum principle for fractional nonlinear optimal control problems. Moreover, a new method based on a generalization of the Mittag-Leffler function is used to solving this class of fractional optimal control problems. A simple example is provided to illustrate the effectiveness of our main result.
A parallel clustered dynamic programming algorithm for discrete time optimal control problems
Optimal control of dynamical systems is a problem that arises in many areas of engineering and physical science. Due to the special structure of optimal control problems, currently there is no parallel algorithm that can solve optimal control problems efficiently on computers with a large number of processors. In this paper, we will introduce a new optimal control algorithm that permits massively parallel processing. The proposed algorithm, called Cluster Dynamic Programming, is a combination of two efficient serial algorithms, differential dynamic programming and a stagewise Newton's method. Parallel numerical results on an Intel iPSC/860 will be presented
Qu Chiwen
2016-01-01
Full Text Available The standard cuckoo search algorithm is of low accuracy and easy to fall into local optimal value in the later evolution. In this paper, an improved cuckoo algorithm is proposed. Dynamic change of parameter of probability is introduced to improve the convergence speed. Complex method is quoted to improve the capabilities of local search algorithm. A non-fixed multi-segment mapping penalty function is adopted to realize constraint processing algorithms. The results of the optimization problem constrained by standard test functions and two engineering design show that this algorithm is effective for solving constrained optimization problems and suitable for engineering design and other constrained optimization problems.
Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance
Bonnard, B; Glaser, S J; Lapert, M; Sugny, D; Zhang, Y
2012-01-01
The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.
稻垣, 陽介; イナガキ, ヨウスケ; Yousuke, Inagaki
2007-01-01
The efficiency of Monte Carlo simulated annealing algorithm based on the generalized statistics of Tsallis (GSA) is compared with conventional simulated annealing (CSA) based on Boltzmann-Gibbs statistics. Application to the discrete-time optimal growth problem demonstrates that the replacement of CSA by GSA has the potential to speed up optimizations with no loss of accuracy in finding optimal policy function.
Global solutions to a class of CEC benchmark constrained optimization problems
Zhou, Xiaojun
2012-01-01
This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Global optimality condition based on canonical duality theory is derived. Integrating the dual solutions with the KKT conditions, we are able to obtain the approximate solutions or global solutions easily.
Newton-type method for the variational discretization of topology optimization problems
Evgrafov, Anton
We present a locally quadratically convergent optimization algorithm for solving topology optimization problems. The distinguishing feature of the algorithm is to treat the design as a smooth function of the state and not vice versa as in the traditional nested approach to topology optimization, ...
Ghoniem, Ahmed
2007-01-01
This dissertation addresses the development of enhanced formulations for minimax and mixed-integer programming models for certain industrial and logistical systems, along with the design and implementation of efficient algorithmic strategies. We first examine the general class of minimax mixed-integer 0-1 problems of the type that frequently arise in decomposition approaches and in a variety of location and scheduling problems. We conduct an extensive polyhedral analysis of this problem in o...
This work focuses on the usage the Artificial Intelligence technique Particle Swarm Optimization (PSO) to optimize the fuel recharge at a nuclear reactor. This is a combinatorial problem, in which the search of the best feasible solution is done by minimizing a specific objective function. However, in this first moment it is possible to compare the fuel recharge problem with the Traveling Salesman Problem (TSP), since both of them are combinatorial, with one advantage: the evaluation of the TSP objective function is much more simple. Thus, the proposed methods have been applied to two TSPs: Oliver 30 and Rykel 48. In 1995, KENNEDY and EBERHART presented the PSO technique to optimize non-linear continued functions. Recently some PSO models for discrete search spaces have been developed for combinatorial optimization. Although all of them having different formulation from the ones presented here. In this paper, we use the PSO theory associated with to the Random Keys (RK)model, used in some optimizations with Genetic Algorithms. The Particle Swarm Optimization with Random Keys (PSORK) results from this association, which combines PSO and RK. The adaptations and changings in the PSO aim to allow the usage of the PSO at the nuclear fuel recharge. This work shows the PSORK being applied to the proposed combinatorial problem and the obtained results. (author)
Second-order cone programming formulations for a class of problems in structural optimization
Makrodimopoulos, A.; A. Bhaskar; Keane, A.J.
2010-01-01
This paper provides efficient and easy to implement formulations for two problems in structural optimization as second-order cone programming (SOCP) problems based on the minimum compliance method and derived using the principle of complementary energy. In truss optimization both single and multiple loads (where we optimize the worst-case compliance) are considered. By using a heuristic which is based on the SOCP duality we can consider a simple ground structure and...
Optimization problem of radiation protection for site work based on genetic algorithm
In this paper, Genetic Algorithm is applied for optimizing the temporary shielding plan of pipes when a valve needs to be repaired in the field of radiation protection. Firstly, the mathematical model of the radiation dose for shielding of two pipes is established, and then the model is converted to a constrained combinational optimization problem The Genetic Algorithm is used to solve this optimization problem. The experimental results show that the Genetic Algorithm can give an accurate complete radiation protection scheme. (authors)
Muhammad Farhan Ausaf; Liang Gao; Xinyu Li; Ghiath Al Aqel
2015-01-01
Process planning and scheduling are two important components of a manufacturing setup. It is important to integrate them to achieve better global optimality and improved system performance. To find optimal solutions for integrated process planning and scheduling (IPPS) problem, numerous algorithm-based approaches exist. Most of these approaches try to use existing meta-heuristic algorithms for solving the IPPS problem. Although these approaches have been shown to be effective in optimizing th...
Optimization of travel salesman problem using the ant colony system and Greedy search
In this paper we present some results obtained during the development of optimization systems that can be used to design refueling and patterns of control rods in a BWR. These systems use ant colonies and Greedy search. The first phase of this project is to be familiar with these optimization techniques applied to the problem of travel salesman problem (TSP). The utility of TSP study is that, like the refueling design and pattern design of control rods are problems of combinative optimization. Even, the similarity with the problem of the refueling design is remarkable. It is presented some results for the TSP with the 32 state capitals of Mexico country. (Author)
Solving stress constrained problems in topology and material optimization
Kočvara, Michal; Stingl, M.
2012-01-01
Roč. 46, č. 1 (2012), s. 1-15. ISSN 1615-147X R&D Projects: GA AV ČR IAA100750802 Grant ostatní: EU FP6(XE) 30717 Institutional research plan: CEZ:AV0Z10750506 Institutional support: RVO:67985556 Keywords : Topology optimization * Material Optimization * Stress based design * Nonlinear semidefinite programming Subject RIV: BA - General Mathematics Impact factor: 1.728, year: 2012 http://library.utia.cas.cz/separaty/2013/MTR/kocvara-0421362.pdf
Optimal improvement of graphs related to nuclear safeguards problems
This report develops the methodology for optimally improving graphs related to nuclear safeguards issues. In particular, given a fixed number of dollars, the report provides a method for optimally allocating such dollars over the arcs of a weighted graph (the weights vary as a function of dollars spent on arcs) so as to improve the system effectiveness measure which is the shortest of all shortest paths to several targets. Arc weights can be either clock times or detection probabilities and the algorithm does not explicitly consider all paths to the targets
Transportation problem by Monalisha\\'s approximation method for optimal solution (mamos
Monalisha Pattnaik
2015-09-01
Full Text Available Background: This paper finds initial basic feasible solution and optimal solution to the transportation problem by using MAM's (Monalisha's Approximation Method. Methods: Using the concept of comparison of the transportation problem by other methods of solution, the paper introduces a very effective method in terms of cost and time for solving these problems. This paper extends transportation problem by using different method of obtaining both initial basic feasible solution and optimal solution simultaneously other than existing methods. Results and conclusions: It is presented a cost saving and less time consuming and accurate method for obtaining the best optimal solution of the transportation problem . With the problem assumptions, the optimal solution can still be theoretically solved using the existing methods. Finally, numerical examples and sensitivity analysis are presented to illustrate the effectiveness of the theoretical results, and to gain additional managerial insights.
Optimization of the variational basis in the three body problem
The procedure of variational oscillator basis optimization is proposed to the calculation the energy spectra of three body systems. The hierarchy of basis functions is derived and energies of ground and excited states for three gravitating particles is obtained with high accuracy. 12 refs
Some Results on Optimal Dividend Problem in Two Risk Models
Shuaiqi Zhang
2010-12-01
Full Text Available The compound Poisson risk model and the compound Poisson risk model perturbed by diffusion are considered in the presence of a dividend barrier with solvency constraints. Moreover, it extends the known result due to [1]. Ref. [1] finds the optimal dividend policy is of a barrier type for a jump-diffusion model with exponentially distributed jumps. In this paper, it turns out that there can be two different solutions depending on the model’s parameters. Furthermore, an interesting result is given: the proportional transaction cost has no effect on the dividend barrier. The objective of the corporation is to maximize the cumulative expected discounted dividends payout with solvency constraints before the time of ruin. It is well known that under some reasonable assumptions, optimal dividend strategy is a barrier strategy, i.e., there is a level b_{1}(b_{2} so that whenever surplus goes above the level b_{1}(b_{2}, the excess is paid out as dividends. However, the optimal level b_{1}(b_{2} may be unacceptably low from a solvency point of view. Therefore, some constraints should imposed on an insurance company such as to pay out dividends unless the surplus has reached a level b^{1}_{c}>b_{1}(b^2_{c}>b_{2} . We show that in this case a barrier strategy at b^{1}_{c}(b^2_{c} is optimal.
Why Scientists Chase Big Problems: Individual Strategy and Social Optimality
Bergstrom, Carl T; Song, Yangbo
2016-01-01
Scientists pursue collective knowledge, but they also seek personal recognition from their peers. When scientists decide whether or not to work on a big new problem, they weigh the potential rewards of a major discovery against the costs of setting aside other projects. These self-interested choices can potentially spread researchers across problems in an efficient manner, but efficiency is not guaranteed. We use simple economic models to understand such decisions and their collective consequences. Academic science differs from industrial R&D in that academics often share partial solutions to gain reputation. This convention of Open Science is thought to accelerate collective discovery, but we find that it need not do so. The ability to share partial results influences which scientists work on a particular problem; consequently, Open Science can slow down the solution of a problem if it deters entry by important actors.
Strongly Polynomial Primal-Dual Algorithms for Concave Cost Combinatorial Optimization Problems
Magnanti, Thomas L
2012-01-01
We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge counterpart is a well-studied combinatorial optimization problem. Our technique preserves constant factor approximation ratios, as well as ratios that depend only on certain problem parameters, and exact algorithms yield exact algorithms. Using our technique, we obtain a new 1.61-approximation algorithm for the concave cost facility location problem. For inventory problems, we obtain a new exact algorithm for the economic lot-sizing problem with general concave ordering costs, and a 4-approximation algorithm for the joint replenishment problem with general concave individual ordering costs.
Why Scientists Chase Big Problems: Individual Strategy and Social Optimality
Bergstrom, Carl T.; Foster, Jacob G.; Song, Yangbo
2016-01-01
Scientists pursue collective knowledge, but they also seek personal recognition from their peers. When scientists decide whether or not to work on a big new problem, they weigh the potential rewards of a major discovery against the costs of setting aside other projects. These self-interested choices can potentially spread researchers across problems in an efficient manner, but efficiency is not guaranteed. We use simple economic models to understand such decisions and their collective consequ...
Grammatical evolution hyper-heuristic for combinatorial optimization problems
Sabar, Nasar; Ayob, Masri; Kendall, Graham; Qu, Rong
2013-01-01
Designing generic problem solvers that perform well across a diverse set of problems is a challenging task. In this work, we propose a hyper-heuristic framework to automatically generate an effective and generic solution method by utilizing grammatical evolution. In the proposed framework, grammatical evolution is used as an online solver builder, which takes several heuristic components (e.g., different acceptance criteria and different neighborhood structures) as inputs and evolves template...
Value-At-Risk Optimal Policies for Revenue Management Problems
Koenig, M; Meissner, J
2010-01-01
Consider a single-leg dynamic revenue management problem with fare classes controlled by capacity in a risk-averse setting. The revenue management strategy aims at limiting the down-side risk, and in particular, value-at-risk. A value-at-risk optimised policy offers an advantage when considering applications which do not allow for a large number of reiterations. They allow for specifying a confidence level regarding undesired scenarios. We state the underlying problem as a Markov decision pro...
An Optimal Stopping Problem in Dynamic Fuzzy Systems with Fuzzy Rewards
Yoshida, Yuji
1995-01-01
This paper deals with an optimal stopping problem in dynamic fuzzy systems with fuzzy rewards, and shows that the optimal discounted fuzzy reward is characterized by a unique solution of a fuzzy relational equation. We define a fuzzy expectation with a density given by fuzzy goals and we estimate discounted fuzzy rewads by the fuzzy expectation. This paper characterizes the optimal fuzzy expected value and gives an optimal stopping time.
Zhang, Gexiang; Cheng, Jixiang; Gheorghe, Marian; Research Group on Natural Computing (Universidad de Sevilla) (Coordinador)
2010-01-01
This paper proposes an approximate optimization algorithm combining P systems with ant colony optimization, called ACOPS, to solve traveling salesman prob- lems, which are well-known and extensively studied NP-complete combinatorial optimization problems. ACOPS uses the pheromone model and pheromone update rules defined by ant colony optimization algorithms, and the hierarchical membrane structure and transformation/communication rules of P systems. First, the parameter setting of...
Kamil, Anton A.; Adli Mustafa; Khlipah Ibrahim
2009-01-01
Problem statement: The most important character within optimization problem is the uncertainty of the future returns. Approach: To handle such problems, we utilized probabilistic methods alongside with optimization techniques. We developed single stage and two stage stochastic programming with recourse. The models were developed for risk adverse investors and the objective of the stochastic programming models is to minimize the maximum downside semi deviation. We used the so-called Here-and-N...
Chebyshev Finite Difference Method for Solving Constrained Quadratic Optimal Control Problems
M Maleki; M. Dadkhah Tirani
2011-01-01
. In this paper the Chebyshev finite difference method is employed for finding the approximate solution of time varying constrained optimal control problems. This approach consists of reducing the optimal control problem to a nonlinear mathematical programming problem. To this end, the collocation points (Chebyshev Gauss-Lobatto nodes) are introduced then the state and control variables are approximated using special Chebyshev series with unknown parameters. The performan...
A distributed approach to the optimal powerow flow problem and its privacy properties
Magnússon, Sindri
2013-01-01
In this thesis we address the optimal power flow (OPF) problem, where the goal is to find an optimal operating point of an electric network, which agrees to laws of physics and other physical limitations of the network. Traditionally the OPF problem has only been solved in the transmission network, which is responsible for transmitting the electricity from the power plants to cities. But with the introduction of the smart grid, the OPF problem has become relevant, not only in transmission net...
On relaxation of state-constrained optimal control problem in coefficients for biharmonic equation
P. I. Kogut
2015-01-01
Full Text Available We study a Dirichlet optimal control problem for biharmonic equation withcontrol and state constraints. The coecient of the biharmonic operator, the weightu, we take as a control in L1(Ω. We discuss the relaxation approach and show thatsome optimal solutions to the original problem can be attained in the limit byoptimal solutions of some extremal problem for variational inequality with a specialpenalized cost functional.
A viscosity solution approach to the Monge-Ampere formulation of the Optimal Transportation Problem
Benamou, Jean-David; Froese, Brittany D.; Oberman, Adam M.
2012-01-01
In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently led to significant theoretical results as well as applications in diverse areas. Numerical solution techniques for the OT problem remain underdeveloped. The solution is obtained by solving the second boundary value problem for the MA equation, a fully nonlinear elliptic partial differential equation (PDE). Instead o...
Optimal solution of investment problems via linear parabolic equations generated by Kalman filter
Dokuchaev, Nikolai
2008-01-01
We consider optimal investment problems for a diffusion market model with non-observable random drifts that evolve as an Ito's process. Admissible strategies do not use direct observations of the market parameters, but rather use historical stock prices. For a non-linear problem with a general performance criterion, the optimal portfolio strategy is expressed via the solution of a scalar minimization problem and a linear parabolic equation with coefficients generated by the Kalman filter.
帅斌; 赵佳虹
2011-01-01
An improved multi-objective 0-1 mixed-integer linear programming model for the location routing problem in hazardous waste logistics was proposed, in which the optimization objectives are to minimize total costs and risks, and the constraints include waste types and treatment technologies, capacity and operation costs of treatment centers. A TOPSIS ( technique for order preference by similarity to an ideal solution) algorithm was designed to solve this multi-objective model. The feasibility and advantage of the proposed model was demonstrated through a representative example taken from literature. Comparing with an exiting model, the proposed model reduced the risk by 7. 69％ at the expense of a little rise in cost by 0. 70％ .%为了解决危险废物回收、加工和处理中心选址问题,确定加工技术类别、安排危险废物和废物残余车辆运输路径,将回收环节纳入危险废物物流系统,考虑废物类型与加工技术的多样性、中心运营费用、废物与加工技术的相容性以及中心能力富余量约束,以费用和风险最小化为优化目标,建立了危险废物物流系统的改进多目标0-1混合整数线性规划模型.采用TOPSIS(technique for order preference by similarity to an ideal solution)方法求解模型.结果表明,与现有模型相比,本文模型的多目标优化方案以增加0.70%的费用为代价,将风险降低7.69%.
Pintu Das
2015-09-01
Full Text Available Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. The paper aims to give computational algorithm to solve a multi-objective non-linear programming problem (MONLPP using neutrosophic optimization method. The proposed method is for solving MONLPP with single valued neutrosophic data. We made a comparative study of optimal solution between intuitionistic fuzzy and neutrosophic optimization technique. The developed algorithm has been illustrated by a numerical example. Finally, optimal riser design problem is presented as an application of such technique.
ϵ-Duality Theorems for Convex Semidefinite Optimization Problems with Conic Constraints
Gue Myung Lee
2010-01-01
Full Text Available A convex semidefinite optimization problem with a conic constraint is considered. We formulate a Wolfe-type dual problem for the problem for its ϵ-approximate solutions, and then we prove ϵ-weak duality theorem and ϵ-strong duality theorem which hold between the problem and its Wolfe type dual problem. Moreover, we give an example illustrating the duality theorems.
Optimization approaches for treating nuclear power plant problems
Electricity generation is the process of generating electric energy from other forms of energy. There are many technologies that can be and are used to generate electricity. One of these technologies is the nuclear power. A nuclear power plant (NPP) is a thermal power station in which the heat source is one or more nuclear reactors. As in a conventional thermal power station the heat is used to generate steam which drives a steam turbine connected to a generator which produces electricity. As of February 2nd, 2012, there were 439 nuclear power plants in operation through the world. NPP are usually considered to be base load stations, which are best suited to constant power output. The thesis consists of five chapters: Chapter I presents a survey on some important concepts of the NPP problems. Chapter II introduces the economic future of nuclear power. It presents nuclear energy scenarios beyond 2015, market potential for electricity generation to 2030 and economics of new plant construction. Chapter III presents a reliability centered problem of power plant preventive maintenance scheduling. NPP preventive maintenance scheduling problem with fuzzy parameters in the constraints is solved. A case study is provided to demonstrate the efficiency of proposed model. A comparison study between the deterministic case and fuzzy case for the problem of concern is carried out. Chapter IV introduces a fuzzy approach to the generation expansion planning problem (GEP) in a multiobjective environment. The GEP problem as an integer programming model with fuzzy parameters in the constraints is formulated. A parametric study is carried out for the GEP problem. A case study is provided to demonstrate the efficiency of our proposed model. A comparison study between our approach and the deterministic one is made. Chapter V is concerned with the conclusions arrived in carrying out this thesis and gives some suggestions for further research.
Optimization and Reliability Problems in Structural Design of Wind Turbines
Sørensen, John Dalsgaard
2007-01-01
Reliability-based cost-benefit optimization formulations for wind turbines are presented. Some of the improtant aspects for stochastic modeling of loads, strengths and models uncertainties for wind turbines are described. Single wind turbines and wind turbines in wind farms with wake effects are...... discussed. Limit state equations are presented for fatigue limit states and for ultimate limit states with extreme wind load, and illustrated by bending failure. Illustrative examples are presented, and as a part of the results optimal reliability levels are obtained which corresponds to an annual...... reliability index equal to 3. An example with fatigue failure indicates that the reliability level is almost the same for single wind turbines and for wind turbines in wind farms if the wake effects are modeled equivalently in the design equation and the limit state equation....
Solving function optimization problems with the immune principle
左兴权; 李士勇
2004-01-01
Adaptive immune evolutionary algorithm is proposed based on the principle of adaptive immune response. Two new algorithm parameters of expansion radius and mutation radius are defined to construct a small neighborhood and a large neighborhood, then expansion and mutation operations are designed to search the local and global regions of solution space simultaneously by using the two neighborhoods, thus, two-level neighborhood search mechanism is realized. The degree of the diversity in the population is described with the average Euclideandistance among all individuals, and it is used to adjust algorithm parameters adaptively to accelerate convergence and avoid getting stuck at local optima. The algorithm is proved to be convergent and its optimization principle is analyzed. The experiment results of multi-modal function optimization show that the algorithm is effective.
Optimal anisotropic three-phase conducting composites: Plane problem
Cherkaev, Andrej
2010-01-01
The paper establishes tight lower bound for effective conductivity tensor $K_*$ of two-dimensional three-phase conducting anisotropic composites and defines optimal microstructures. It is assumed that three materials are mixed with fixed volume fractions and that the conductivity of one of the materials is infinite. The bound expands the Hashin-Shtrikman and Translation bounds to multiphase structures, it is derived using the technique of {\\em localized polyconvexity} that is a combination of Translation method and additional inequalities on the fields in the materials; similar technique was used by Nesi (1995) and Cherkaev (2009) for isotropic multiphase composites. This paper expands the bounds to the anisotropic composites. The lower bound of conductivity (G-closure) is a piece-wise analytic function of eigenvalues of $K_*$, that depends only on conductivities of components and their volume fractions. Also, we find optimal microstructures that realize the bounds, developing the technique suggested earlier ...
Solving the optimal PWM problem for odd symmetry waveforms
Kujan, Petr; Hromčík, Martin; Šebek, Michael
Laxenburg: IFAC, 2008, s. 8672-8677. ISBN 978-3-902661-00-5. [The 17th IFAC World Congress. Seoul (KR), 06.07.2008-11.07.2008] R&D Projects: GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10750506 Keywords : Polynomial methods * optimal PWM * selected harmonics elimination * Newton identities * Pade approximation * orthogonal polynomials * composite power sums Subject RIV: BC - Control Systems Theory
Solving nonconvex SDP problems of structural optimization with stability control
Kočvara, Michal; Stingl, M.
2004-01-01
Roč. 19, č. 5 (2004), s. 595-609. ISSN 1055-6788 R&D Projects: GA AV ČR IAA1075005 Grant ostatní: BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : structural optimization * stability control * nonconvex semidefinite programming Subject RIV: BA - General Mathematics Impact factor: 0.273, year: 2004
Optimization methods for inverse problems with energy norm
Hrtus, Rostislav; Haslinger, Jaroslav; Blaheta, Radim
Ostrava : VŠB-TUO, 2014 - (Krátký, M.; Dvorský, J.; Moravec, P.), s. 484-489 ISBN 978-80-248-3458-0. [WOFEX 2014 - Ph.D. Workshop of Faculty of Electrical Engineering and Computer Science. Ostrava (CZ), 09.09.2014-09.09.2014] Institutional support: RVO:68145535 Keywords : optimization methods * parameter distribution * Newton methods Subject RIV: BA - General Mathematics
Existence in optimal control problems of certain Fredholm integral equations
Roubíček, Tomáš; Schmidt, W. H.
2001-01-01
Roč. 30, č. 3 (2001), s. 303-322. ISSN 0324-8569 R&D Projects: GA AV ČR IAA1075005; GA ČR GA201/00/0768; GA MŠk 11320007 Institutional research plan: AV0Z1075907 Keywords : optimal control * integral equation * Young measures Subject RIV: BA - General Mathematics Impact factor: 0.154, year: 2001
Optimization methods for inverse problems with energy norm
Hrtus, Rostislav; Haslinger, Jaroslav; Blaheta, Radim
Ostrava: VŠB-TUO, 2014 - (Krátký, M.; Dvorský, J.; Moravec, P.), s. 484-489 ISBN 978-80-248-3458-0. [WOFEX 2014 - Ph.D. Workshop of Faculty of Electrical Engineering and Computer Science. Ostrava (CZ), 09.09.2014-09.09.2014] Institutional support: RVO:68145535 Keywords : optimization methods * parameter distribution * Newton methods Subject RIV: BA - General Mathematics
An Optimization Problem for Predicting the Maximal Effect of Degradation of Mechanical Structures
Achtziger, W.; Bendsøe, Martin P.; Taylor, J. E.
2000-01-01
gives insight in terms of a mechanical interpretation of the optimization problem. We derive an equivalent convex problem formulation and a convex dual problem, and for dyadic matrices A(i) a quadratic programming problem formulation is developed. A nontrivial numerical example is included, based on the......This paper deals with a nonlinear nonconvex optimization problem that models prediction of degradation in discrete or discretized mechanical structures. The mathematical difficulty lies in equality constraints of the form Σ(i=1)(m) 1/yi A(i) x=b, where A(i) are symmetric and positive semidefinite...
Andreica, Mugurel Ionut
2010-01-01
In this paper we present novel algorithmic solutions for several resource processing and data transfer multicriteria optimization problems. The results of most of the presented techniques are strategies which solve the considered problems (almost) optimally. Thus, the developed algorithms construct intelligent strategies which can be implemented by agents in specific situations. All the described solutions make use of the properties of the considered problems and, thus, they are not applicable to a very general class of problems. However, by considering the specific details of each problem, we were able to obtain very efficient results.
Asymptotic Optimality Theory For Decentralized Sequential Multihypothesis Testing Problems
Wang, Yan
2010-01-01
The Bayesian formulation of sequentially testing $M \\ge 3$ hypotheses is studied in the context of a decentralized sensor network system. In such a system, local sensors observe raw observations and send quantized sensor messages to a fusion center which makes a final decision when stopping taking observations. Asymptotically optimal decentralized sequential tests are developed from a class of "two-stage" tests that allows the sensor network system to make a preliminary decision in the first stage and then optimize each local sensor quantizer accordingly in the second stage. It is shown that the optimal local quantizer at each local sensor in the second stage can be defined as a maximin quantizer which turns out to be a randomization of at most $M-1$ unambiguous likelihood quantizers (ULQ). We first present in detail our results for the system with a single sensor and binary sensor messages, and then extend to more general cases involving any finite alphabet sensor messages, multiple sensors, or composite hyp...
Optimal stopping problems for the maximum process with upper and lower caps
Ott, Curdin
2011-01-01
This paper concerns optimal stopping problems driven by a spectrally negative L\\'evy process $X$. More precisely, we are interested in modifications of the Shepp-Shiryaev optimal stopping problem (also known as Russian optimal stopping problem). First, we consider a capped version of the latter and provide the solution explicitly in terms of scale function. In particular, the optimal stopping boundary is characterised by an ordinary differential equation involving scale function and changes according to the path variation of $X$. Secondly, in the spirit of the work of Shepp, Shiryaev and Sulem (2002), we consider a modification of the capped version of the Shepp-Shiryaev optimal stopping problem in the sense that the decision to stop has to be made before the process $X$ falls below a given level.
Müller, Stefan; Regensburger, Georg; Steuer, Ralf
2014-04-21
The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In particular, the total enzymatic capacity for cellular metabolism is limited by finite resources that are shared between all enzymes, such as cytosolic space, energy expenditure for amino-acid synthesis, or micro-nutrients. While extensive work has been done to study constrained optimization problems based only on stoichiometric information, mathematical results that characterize the optimal flux in kinetic metabolic networks are still scarce. Here, we study constrained enzyme allocation problems with general kinetics, using the theory of oriented matroids. We give a rigorous proof for the fact that optimal solutions of the non-linear optimization problem are elementary flux modes. This finding has significant consequences for our understanding of optimality in metabolic networks as well as for the identification of metabolic switches and the computation of optimal flux distributions in kinetic metabolic networks. PMID:24295962
A HIGH PERFORMANCE OPTIMIZATION TECHNIQUE FOR POLE BALANCING PROBLEM
Bahadır KARASULU
2008-02-01
Full Text Available High performance computing techniques can be used effectively for solution of the complex scientific problems. Pole balancing problem is a basic benchmark tool of robotic field, which is an important field of Artificial Intelligence research areas. In this study, a solution is developed for pole balancing problem using Artificial Neural Network (ANN and high performance computation technique. Algorithm, that basis of the Reinforcement Learning method which is used to find the force of pole's balance, is transfered to parallel environment. In Implementation, C is preferred as programming language and Message Passing Interface (MPI is used for parallel computation technique. Self–Organizing Map (SOM ANN model's neurons (artificial neural nodes and their weights are distributed to six processors of a server computer which equipped with each quad core processor (total 24 processors. In this way, performance values are obtained for different number of artificial neural nodes. Success of method based on results is discussed.
Optimization of the imported air express cargo distribution problem
Hwang, T.L.
2013-03-01
Full Text Available This study examines the delivering network of imported air express cargo as an integrated multi-depot vehicle routing problem. Integrated multi-depot vehicle routing problem attempts to decide which service centers should be used and how much freight should be unloaded in each service center. The role of an exchange point which is allowing the delivery vans and shuttles to exchange imported and exported goods is also addressed. Test results demonstrate the feasibility of the four models so these are highly promising for use in a diverse array of applications, such as in home delivery and reverse logistics.
Some optimal control problems of multistate equations appearing in fluid mechanics
This work deals with two optimal control problems associated to the steady-state Navier-Stokes equations. The state of the system is the velocity of the fluid and the controls are the body forces or the heat flux on the boundary. In the second case the Navier-Stokes equations are coupled with the stationary heat equation. The control problems consist in minimizing a cost functional involving the turbulence. Some control constraints can be added to the problem. Existence of an optimal control is proved and some optimality conditions are derived. In both problems the relation control-state is multi-valued and therefore the derivation of the optimality conditions is not obvious. To overcome this difficulty, we introduce an approximate family of optimal control problems governed by a well posed linear elliptic system, we obtain the optimality conditions for these problems and then we pass to the limit. The approach followed in this study can be used in the numerical resolution of the optimal control problem. (Author). 13 refs
A Collection of Challenging Optimization Problems in Science, Engineering and Economics
Mehta, Dhagash
2015-01-01
Function optimization and finding simultaneous solutions of a system of nonlinear equations (SNE) are two closely related and important optimization problems. However, unlike in the case of function optimization in which one is required to find the global minimum and sometimes local minima, a database of challenging SNEs where one is required to find stationary points (extrama and saddle points) is not readily available. In this article, we initiate building such a database of important SNE (which also includes related function optimization problems), arising from Science, Engineering and Economics. After providing a short review of the most commonly used mathematical and computational approaches to find solutions of such systems, we provide a preliminary list of challenging problems by writing the Mathematical formulation down, briefly explaning the origin and importance of the problem and giving a short account on the currently known results, for each of the problems. We anticipate that this database will n...
Multiphysics field analysis and multiobjective design optimization: a benchmark problem
di Barba, P.; Doležel, Ivo; Karban, P.; Kůs, P.; Mach, F.; Mognaschi, M. E.; Savini, A.
2014-01-01
Roč. 22, č. 7 (2014), s. 1214-1225. ISSN 1741-5977 R&D Projects: GA ČR(CZ) GAP102/11/0498 Institutional support: RVO:61388998 Keywords : coupled-field problems * finite-element analysis * hp-FEM adaptation Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 0.868, year: 2014
De Vincenzo, Ilario; Carbone, Giuseppe
2016-01-01
A large number of optimization algorithms have been developed by researchers to solve a variety of complex problems in operations management area. We present a novel optimization algorithm belonging to the class of swarm intelligence optimization methods. The algorithm mimics the decision making process of human groups and exploits the dynamics of this process as an optimization tool for combinatorial problems. In order to achieve this aim, a continuous-time Markov process is proposed to describe the behavior of a population of socially interacting agents, modelling how humans in a group modify their opinions driven by self-interest and consensus seeking. As in the case of a collection of spins, the dynamics of such a system is characterized by a phase transition from low to high values of the overall consenus (magnetization). We recognize this phase transition as being associated with the emergence of a collective superior intelligence of the population. While this state being active, a cooling schedule is a...
Global optimization for overall HVAC systems - Part I problem formulation and analysis
This paper presents the global optimization technologies for overall heating, ventilating and air conditioning (HVAC) systems. The objective function of global optimization and constraints are formulated based on mathematical models of the major components. All these models are associated with power consumption components and heat exchangers for transferring cooling load. The characteristics of all the major components are briefly introduced by models, and the interactions between them are analyzed and discussed to show the complications of the problem. According to the characteristics of the operating components, the complicated original optimization problem for overall HVAC systems is transformed and simplified into a compact form ready for optimization
Optimal capital structure: Problems with the Harvard and Damodaran Approaches
Fernadez, Pablo
2002-01-01
In this paper we will present an analysis of the optimal capital structure using two examples: one proposed by the Harvard Business School and the other proposed by Damodaran. First, we highlight certain inconsistencies in the debt and equity costs assumed by the Harvard Business School note from a number of viewpoints. We calculate the incremental cost of debt implied in Harvard's note and we find also inconsistencies: surprisingly, the last two debt increments have a cost of 14.75% and 18.5...
Optimization problems of the third edge-connectivity of graphs
WANG; Yingqian
2006-01-01
The third edge-connectivity λ3(G) of a graph G is defined as the minimum cardinality over all sets of edges, if any, whose deletion disconnects G and each component of the resulting graph has at least 3 vertices. An upper bound has been established for λ3(G) whenever λ3(G) is well-defined. This paper first introduces two combinatorial optimization concepts, that is, maximality and superiority, of λ3(G), and then proves the Ore type sufficient conditions for G to be maximally and super third edge-connected. These concepts and results are useful in network reliability analysis.
Model Guided Sampling Optimization for Low-Dimensional Problems
Bajer, Lukáš; Holeňa, Martin
Lisbon: Scitepress, 2015 - (Loiseau, S.; Filipe, J.; Duval, J.; van den Herik, J.), s. 451-456 ISBN 978-989-758-074-1. [ICAART 2015. International Conference on Agents and Artificial Intelligence /7./. Lisbon (PT), 10.01.2015-12.01.2015] R&D Projects: GA ČR GAP202/10/1333; GA ČR GA13-17187S Institutional support: RVO:67985807 Keywords : black-box Optimization * Gaussian Process * Surrogate Modelling * EGO Subject RIV: IN - Informatics, Computer Science
Model Guided Sampling Optimization for Low-Dimensional Problems
Bajer, Lukáš; Holeňa, Martin
Lisbon : Scitepress, 2015 - (Loiseau, S.; Filipe, J.; Duval, J.; van den Herik, J.), s. 451-456 ISBN 978-989-758-074-1. [ICAART 2015. International Conference on Agents and Artificial Intelligence /7./. Lisbon (PT), 10.01.2015-12.01.2015] R&D Projects: GA ČR GAP202/10/1333; GA ČR GA13-17187S Institutional support: RVO:67985807 Keywords : black-box Optimization * Gaussian Process * Surrogate Modelling * EGO Subject RIV: IN - Informatics, Computer Science
Selvi, V; Dr. R. Umarani
2012-01-01
- SI is a computational and collective behavioral metaphor that is used for solving problems. The problems can be solved by SI by taking ants, termites, bees and wasps as an example. The application of SI algorithm are ACO, PSO and ABC which have been already applied to solve real world optimization problems in engineering. ACO is a member of SI in which ACO is inspired by the behaviour of ant colonies and it constitutes some metaheuristic optimization. ACO’s aim is to search for an optimal p...
Fish School Search Algorithm for Solving Optimal Reactive Power Dispatch Problem
K. Lenin
2013-01-01
Full Text Available This paper presents an algorithm for solving the multi-objective reactive power dispatch problem in a power system. Modal analysis of the system is used for static voltage stability assessment. Loss minimization and maximization of voltage stability margin are taken as the objectives. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. This paper presents fish school search a novel method of swarm intelligence for solving above problem. Fish school search Algorithm, which was inspired by the natural schooling behaviours of fish, a powerful stochastic optimization technique has been utilised to solve the reactive power optimization problem.
Optimization of the drayage problem using exact methods
Reinhardt, Line Blander; Pisinger, David; Spoorendonk, Simon;
2016-01-01
Major liner shipping companies offer pre- and end-haulage as part of a door-to-door service, but unfortunately pre- and end-haulage is frequently one of the major bottlenecks in efficient liner shipping due to the lack of coordination between customers.In this paper, we apply techniques from...... vehicle routing problems to schedule pre- and end-haulage of containers, and perform tests on data from a major liner shipping company. The paper considers several versions of the scheduling problem such as having multiple empty container depots, and having to balance the empty container depot levels. The...... balancing empty container storage level at depots, are considered. Computational results are reported on real-life data from a major liner shipping company....
SOLVING TRUST REGION PROBLEM IN LARGE SCALE OPTIMIZATION
Bing-sheng He
2000-01-01
This paper presents a new method for solving the basic problem in the “model trust region” approach to large scale minimization: Compute a vector x such that 1/2xTHx + cTx = min, subject to the constraint ‖x‖2≤a. The method is a combination of the CG method and a projection and contraction (PC) method. The first (CG) method with x0 = 0 as the start point either directly offers a solution of the problem, or--as soon as the norm of the iterate greater than a, --it gives a suitable starting point and a favourable choice of a crucial scaling parameter in the second (PC) method. Some numerical examples are given, which indicate that the method is applicable.
Optimal calculational schemes for solving multigroup photon transport problem
A scheme of complex algorithm for solving multigroup equation of radiation transport is suggested. The algorithm is based on using the method of successive collisions, the method of forward scattering and the spherical harmonics method, and is realized in the FORAP program (FORTRAN, BESM-6 computer). As an example the results of calculating reactor photon transport in water are presented. The considered algorithm being modified may be used for solving neutron transport problems
Stochastic optimization models for a single-sink transportation problem
Maggioni, Francesca; Kaut, Michal; Bertazzi, Luca
2008-01-01
In this paper we study a single-sink transportation problem in which the production capacity of the suppliers and the demand of the single customer are stochastic. Shipments are performed by capacitated vehicles, which have to be booked in advance, before the realization of the production capacity and the demand. Once the production capacity and the demand are revealed, there is an option to cancel some of the booked vehicles against a cancellation fee. If the quantity shipped from the suppli...
Solving inverse problems in imaging using robust and regularized optimization
Gonzalez Gonzalez, Adriana
2016-01-01
Digital images play an important role in human life since they allow observing, analyzing, studying and characterizing the world surrounding us. Their use is ubiquitous in many applications such as medicine, biology, astronomy and industrial manufacture. Nonetheless, the desired digital images are often not available and need to be recovered from corrupted, incomplete and/or indirect observations. Determining the unknown image from the available observations is called an inverse problem. In t...
The berth allocation problem: Optimizing vessel arrival time
Mihalis M Golias; Georgios K Saharidis; Maria Boile; Sotirios Theofanis; Ierapetritou, Marianthi G.
2009-01-01
The berth scheduling problem deals with the assignment of vessels to berths in a marine terminal, with the objective to maximize the ocean carriers’ satisfaction (minimize delays) and/or minimize the terminal operator's costs. In the existing literature, two main assumptions are made regarding the status of a vessel: (a) either all vessels to be served are already in the port before the planning period starts, or (b) they are scheduled to arrive after the planning period starts. The latter ca...
Quantum Field Theory in (0 + 1) Dimensions
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
A genetic algorithm approach to optimization for the radiological worker allocation problem
The worker allocation optimization problem in radiological facilities inevitably involves various types of requirements and constraints relevant to radiological protection and labor management. Some of these goals and constraints are not amenable to a rigorous mathematical formulation. Conventional methods for this problem rely heavily on sophisticated algebraic or numerical algorithms, which cause difficulties in the search for optimal solutions in the search space of worker allocation optimization problems. Genetic algorithms (GAB) are stochastic search algorithms introduced by J. Holland in the 1970s based on ideas and techniques from genetic and evolutionary theories. The most striking characteristic of GAs is the large flexibility allowed in the formulation of the optimal problem and the process of the search for the optimal solution. In the formulation, it is not necessary to define the optimal problem in rigorous mathematical terms, as required in the conventional methods. Furthermore, by designing a model of evolution for the optimal search problem, the optimal solution can be sought efficiently with computational simple manipulations without highly complex mathematical algorithms. We reported a GA approach to the worker allocation problem in radiological facilities in the previous study. In this study, two types of hard constraints were employed to reduce the huge search space, where the optimal solution is sought in such a way as to satisfy as many of soft constraints as possible. It was demonstrated that the proposed evolutionary method could provide the optimal solution efficiently compared with conventional methods. However, although the employed hard constraints could localize the search space into a very small region, it brought some complexities in the designed genetic operators and demanded additional computational burdens. In this paper, we propose a simplified evolutionary model with less restrictive hard constraints and make comparisons between
EXISTENCE OF 0-1 UNIVERSAL MINIMAL TOTAL DOMINATING FUNCTIONS
FANG Qizhi
2004-01-01
In this paper, we study the existence of 0-1 universal minimal total dominating functions in a graph. We establish a formulation of linear inequalities to characterize universal minimal total dominating functions and show that for a kind of graphs whose adjacent matrices are balanced, the existence of universal minimal total dominating functions coincides with that of 0-1 ones. It is also proved that for general graphs, the problem of testing the existence of 0-1 universal minimal total dominating functions is NP-hard.
ZHANG Rong; LIU Xing
2004-01-01
Using the Stackelberg differential games(SDG) theory, we quantitatively study a problem of optimal intertemporal investment and tax rate design. Under some appropriate assumptions, the open-loop Stackelberg equilibrium solutions are obtained. Equilibrium solutions show that: 1. The optimal strategies derived from differential game and unilateral optimal control approaches are different; 2. It is not always the best strategy for the government to use a constant tax rate over the whole time period; 3. The admissible size of tax rate adjustment may have great effect on the government's optimal strategy; 4.SDG approach has no significant effect on the firm's optimal investment strategy.
The Goh necessary optimality conditions for the Mayer problem with control constraints
Frankowska, Hélène; Tonon, Daniela
2013-01-01
The well known Goh second order necessary optimality conditions in optimal control theory concern singular optimal controls taking values in the interior of a set of controls U. In this paper we investigate these conditions for the Mayer problem when U is a convex polytope or a closed subset of class C2 for an integrable optimal control u( ) that may take values in the boundary of U. This is indeed a frequent situation in optimal control and for this reason the understanding of this issue is ...
Kim, Yong Yook
2004-01-01
The objective of this work was to employ artificial neural networks (NN) to solve inverse problems in different engineering fields, overcoming various obstacles in applying NN to different problems and benefiting from the experience of solving different types of inverse problems. The inverse problems investigated are: 1) damage detection in structures, 2) detection of an anomaly in a light-diffusive medium, such as human tissue using optical imaging, 3) structural optimization of fiber optic ...
Learning from Data as an Optimization and Inverse Problem
Kůrková, Věra
Heidelberg: Springer, 2012 - (Madani, K.; Correia, A.; Rosa, A.; Filipe, J.), s. 361-372. (Studies in Computational Intelligence. 399). ISBN 978-3-642-27533-3. ISSN 1860-949X. [IJCCI 2010. International Joint Conference on Computational Intelligence. Valencia (ES), 24.10.2010-26.10.2010] R&D Projects: GA ČR GAP202/11/1368 Institutional research plan: CEZ:AV0Z10300504 Keywords : learning from data * minimization of empirical error * inverse problems * reproducing kernel Hilbert spaces Subject RIV: IN - Informatics, Computer Science
A new evolutionary algorithm with LQV learning for combinatorial problems optimization
Genetic algorithms are biologically motivated adaptive systems which have been used, with good results, for combinatorial problems optimization. In this work, a new learning mode, to be used by the population-based incremental learning algorithm, has the aim to build a new evolutionary algorithm to be used in optimization of numerical problems and combinatorial problems. This new learning mode uses a variable learning rate during the optimization process, constituting a process known as proportional reward. The development of this new algorithm aims its application in the optimization of reload problem of PWR nuclear reactors, in order to increase the useful life of the nuclear fuel. For the test, two classes of problems are used: numerical problems and combinatorial problems. Due to the fact that the reload problem is a combinatorial problem, the major interest relies on the last class. The results achieved with the tests indicate the applicability of the new learning mode, showing its potential as a developing tool in the solution of reload problem. (author)
Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer
Miele, A.; Basapur, V. K.
1984-01-01
The maneuver considered in the present investigation involves the coplanar transfer of a spacecraft from a high earth orbit (HEO) to a low earth orbit (LEO). HEO can be a geosynchronous earth orbit (GEO). The basic concept utilized involves the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. The considered type of flight is also called synergetic space flight. With respect to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The Bolza problem of optimal control is stated, and the first-order optimality conditions for this problem are given. The one-arc approach, the two-arc approach, and the three-subarc approach are discussed. Attention is given to the Chebyshev problem of optimal control, details concerning aeroassisted orbital transfer (AOT), AOT optimization problems, and numerical experiments.
G. Kondrat'ev
1999-12-01
Full Text Available In this article some ideas of Hamilton mechanics and differential-algebraic Geometry are used to exact definition of the potential function (Bellman-Lyapunov function in the optimal stabilization problem of smooth finite-dimensional systems.
On the Limit Matrix Obtained in the Homogenization of an Optimal Control Problem
S Kesavan; M Rajesh
2002-05-01
A new formulation for the limit matrix occurring in the cost functional of an optimal control problem on homogenization is obtained. It is used to obtain an upper bound for this matrix (in the sense of positive definite matrices).
An adaptive ant colony system algorithm for continuous-space optimization problems
李艳君; 吴铁军
2003-01-01
Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates. Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved.
An adaptive ant colony system algorithm for continuous-space optimization problems
李艳君; 吴铁军
2003-01-01
Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates.Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved.
G. Kondrat'ev
1999-10-01
Full Text Available In this article some ideas of Hamilton mechanics and differential-algebraic Geometry are used to exact definition of the potential function (Bellman-Lyapunov function in the optimal stabilization problem of smooth finite-dimensional systems.
GLOBAL OPTIMIZATION OF PUMP CONFIGURATION PROBLEM USING EXTENDED CROWDING GENETIC ALGORITHM
Zhang Guijun; Wu Tihua; Ye Rong
2004-01-01
An extended crowding genetic algorithm (ECGA) is introduced for solving optimal pump configuration problem,which was presented by T.Westerlund in 1994.This problem has been found to be non-convex,and the objective function contained several local optima and global optimality could not be ensured by all the traditional MINLP optimization method.The concepts of species conserving and composite encoding are introduced to crowding genetic algorithm (CGA) for maintain the diversity of population more effectively and coping with the continuous and/or discrete variables in MINLP problem.The solution of three-levels pump configuration got from DICOPT++ software (OA algorithm) is also given.By comparing with the solutions obtained from DICOPT++,ECP method,and MIN-MIN method,the ECGA algorithm proved to be very effective in finding the global optimal solution of multi-levels pump configuration via using the problem-specific information.
Implementation of genetic algorithm technique for solving ROP detector layout optimization problem
The regional overpower protection (ROP) systems protect CANDU® reactors against overpower in the fuel that could reduce the safety margin-to-dryout. The overpower could originate from localized power peaking within the core or a general increase in the core power level. The design of the detector layout for the ROP systems is a challenging discrete optimization problem. In recent years, two algorithms have been developed to find a quasi-optimal solution to this detector layout optimization problem. Both of these algorithms utilize the simulated annealing (SA) algorithm as their optimization engine. In the present paper, an alternative optimization algorithm, namely the genetic algorithm (GA), has been implemented as the optimization engine. The implementation is done within the ADORE algorithm. Based on this preliminary studies performed on four different sizes of ROP system, it has been demonstrated that the GA technique is able to produce good results. (author)
Liang, J J; Song, H; B. Y. Qu; Liu, Z. F.
2014-01-01
In path planning problems, the most important task is to find a suitable collision-free path which satisfies some certain criteria (the shortest path length, security, feasibility, smoothness, and so on), so defining a suitable curve to describe path is essential. Three different commonly used curves are compared and discussed based on their performance on solving a set of path planning problems. Dynamic multiswarm particle swarm optimizer is employed to optimize the necessary parameters for ...
On the smooth-fit property for one-dimensional optimal switching problem
Pham, Huyen
2004-01-01
This paper studies the problem of optimal switching for one-dimensional diffusion, which may be regarded as sequential optimal stopping problem with changes of regimes. The resulting dynamic programming principle leads to a system of variational inequa-lities, and the state space is divided into continuation regions and switching regions. By means of viscosity solutions approach, we prove the smoot-fit $C^1$ property of the value functions.
Application of Particle Swarm Optimization Algorithm in the Heating System Planning Problem
Rong-Jiang Ma; Nan-Yang Yu; Jun-Yi Hu
2013-01-01
Based on the life cycle cost (LCC) approach, this paper presents an integral mathematical model and particle swarm optimization (PSO) algorithm for the heating system planning (HSP) problem. The proposed mathematical model minimizes the cost of heating system as the objective for a given life cycle time. For the particularity of HSP problem, the general particle swarm optimization algorithm was improved. An actual case study was calculated to check its feasibility in practical use. The result...
2014-01-01
For SLA-aware service composition problem (SSC), an optimization model for this algorithm is built, and a hybrid multiobjective discrete particle swarm optimization algorithm (HMDPSO) is also proposed in this paper. According to the characteristic of this problem, a particle updating strategy is designed by introducing crossover operator. In order to restrain particle swarm’s premature convergence and increase its global search capacity, the swarm diversity indicator is introduced and a parti...
New algorithms for some NP-optimization problems by DNA computing
无
2002-01-01
There are lots of DNA computation models now. The model developed by Martyn Amos' group is special in its error-resistant property, but unfortunately, its computational power is limited and cannot solve optimization problems efficiently. In this paper, some new methods have been introduced to enlarge the computational power of this model. And based on these new methods, several DNA algorithms have been designed to solve some NP-optimization problems such as minimal vertex cover, maximal clique and MAX-3SAT.
Km. Shweta; Alka Singh
2013-01-01
Ant Colony optimization has proved suitable to solve a wide range of combinatorial optimization(or NP-hard) problems as the Travelling Salesman Problem (TSP). The first step of ACO algorithm is to setthe parameters that drive the algorithm. The parameter has an important impact on the performance of theant colony algorithm. The basic parameters that are used in ACO algorithms are; the relative importance (orweight) of pheromone, the relative importance of heuristics value, initial pheromone v...
UFO: Uncertainty Feature Optimization, an Implicit Paradigm for Problems with Noisy Data
Eggenberg, Niklaus; Salani, Matteo; Bierlaire, Michel
2008-01-01
Optimization problems due to noisy data solved using stochastic programming or robust optimization approaches require the explicit characterization of an uncertainty set U that models the nature of the noise. Such approaches depend on the modeling of the uncertainty set and suffer from an erroneous estimation of the noise. In this paper, we introduce a framework that considers the uncertain data implicitly. We define the concept of Uncertainty Features (UF), which are problem-specific struct...
Hartmann, Alexander K
2005-01-01
A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics. The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary
Manapova, Aigul
2016-08-01
We consider optimal control problems for second order elliptic equations with non-self-adjoint operators-convection-diffusion problems. Control processes are described by semi-linear convection-diffusion equation with discontinuous data and solutions (states) subject to the boundary interface conditions of imperfect type (i.e., problems with a jump of the coefficients and the solution on the interface; the jump of the solution is proportional to the normal component of the flux). Controls are involved in the coefficients of diffusion and convective transfer. We prove differentiability and Lipshitz continuity of the cost functional, depending on a state of the system and a control. The calculation of the gradients uses the numerical solutions of direct problems for the state and adjoint problems.
Holzer, S.; Wagner, M.; A Sheikholeslami; Karner, M.; Span, G.; Grasser, T.; Selberherr, S.
2006-01-01
We present the capabilities of our optimization framework in conjunction with typical applications for thermal problems. Our software package supports a wide rage of simulators and optimization strategies to improve electronic devices in terms of speed, reliability, efficiency, and to reduce thermal degradation due to mechanical influences. Moreover, we show several optimization examples, where we succeeded to extract electro-thermal material and process parameters. These new material paramet...
Opposition-Based Barebones Particle Swarm for Constrained Nonlinear Optimization Problems
Hui Wang
2012-01-01
This paper presents a modified barebones particle swarm optimization (OBPSO) to solve constrained nonlinear optimization problems. The proposed approach OBPSO combines barebones particle swarm optimization (BPSO) and opposition-based learning (OBL) to improve the quality of solutions. A novel boundary search strategy is used to approach the boundary between the feasible and infeasible search region. Moreover, an adaptive penalty method is employed to handle constraints. To verify the performa...
Ant Colony Optimization ACO For The Traveling Salesman Problem TSP Using Partitioning
Alok Bajpai; Raghav Yadav
2015-01-01
Abstract An ant colony optimization is a technique which was introduced in 1990s and which can be applied to a variety of discrete combinatorial optimization problem and to continuous optimization. The ACO algorithm is simulated with the foraging behavior of the real ants to find the incremental solution constructions and to realize a pheromone laying-and-following mechanism. This pheromone is the indirect communication among the ants. In this paper we introduces the partitioning technique ba...
An Interpretation of the Gini Coefficient in a Stiglitz Two-Type Optimal Tax Problem
Rasmussen, Bo Sandemann
2014-01-01
In a two-type Stiglitz (1982) model of optimal non-linear taxation it is shown that when the utility function relating to consumption is logaritmic the shadow price of the incentive constraint relating to the optimal tax problem exactly equals the Gini coefficient of the second-best optimal income...... workers reveal that also in these cases the desired degree of income redistribution is positively correlated with the shadow prices of the incentive constraints....
A Simulation-Based Optimization Approach for Integrated Port Resource Allocation Problem
Ilati, Gholamreza; Sheikholeslami, Abdorreza; Hassannayebi, Erfan
2014-01-01
Todays, due to the rapid increase in shipping volumes, the container terminals are faced with the challenge to cope with these increasing demands. To handle this challenge, it is crucial to use flexible and efficient optimization approach in order to decrease operating cost. In this paper, a simulation-based optimization approach is proposed to construct a near-optimal berth allocation plan integrated with a plan for tug assignment and for resolution of the quay crane re-allocation problem. ...
MPI parallel programming of mixed integer optimization problems using CPLEX with COIN-OR
Aldasoro Marcellan, Unai; Garín Martín, María Araceli; Merino Maestre, María; Pérez Sainz de Rozas, Gloria
2012-01-01
The aim of this technical report is to present some detailed explanations in order to help to understand and use the Message Passing Interface (MPI) parallel programming for solving several mixed integer optimization problems. We have developed a C++ experimental code that uses the IBM ILOG CPLEX optimizer within the COmputational INfrastructure for Operations Research (COIN-OR) and MPI parallel computing for solving the optimization models under UNIX-like systems. The computational experienc...
Predatory Search Strategy Based on Swarm Intelligence for Continuous Optimization Problems
Wang, J. W.; H. F. Wang; Ip, W. H.; Furuta, K; Kanno, T.; Zhang, W. J.
2013-01-01
We propose an approach to solve continuous variable optimization problems. The approach is based on the integration of predatory search strategy (PSS) and swarm intelligence technique. The integration is further based on two newly defined concepts proposed for the PSS, namely, “restriction” and “neighborhood,” and takes the particle swarm optimization (PSO) algorithm as the local optimizer. The PSS is for the switch of exploitation and exploration (in particular by the adjustment of neighborh...
Possibility of application of optimization methods to solve problems in mining
Mijalkovski, Stojance; Doneva, Blagica; Karanakova Stefanovska, Radmila
2009-01-01
This paper presents a brief analysis of multi-criteria optimization, as a possibility for application in mining, in solving a problem. Multi-criteria decision can be applied in an optimum choice of mining method unearthed, the optimal choice of transport means, etc. In applying multi - criteria decision, most of the criteria according which will be select the most optimal alternative, can be taken into account.
Mathematical optimization model of avionics complexation problem on early stage of designing
V.M. Vorobyov
2006-01-01
Full Text Available The article is the sequel of another one of this digest of authors “Approximate optimization solution by Pareto of discrete extremal problem of complexation of new generation avionics” and its development in the direction of creating optimization model and organization under synthesis of avionics structure.
A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet
Boualem Djehiche
2014-01-01
a two-mode optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy.
A new solving procedure by m-M calculus for problems of constrained optimization
Prešić Slaviša
2007-01-01
Full Text Available In this paper we state two procedures for constrained optimization based on the concepts of m-M Calculus. The first procedure is called basic and the second is called quick solving procedure. The quick solving procedure is very effective. It can also be applied to problems of unconstrained optimization. .
Analysis and formulation of a class of complex dynamic optimization problems
Kameswaran, Shivakumar
The Direct Transcription approach, also known as the direct simultaneous approach, is a widely used solution strategy for the solution of dynamic optimization problems involving differential-algebraic equations (DAEs). Direct transcription refers to the procedure of approximating the infinite dimensional problem by a finite dimensional one, which is then solved using a nonlinear programming (NLP) solver tailored to large-scale problems. Systems governed by partial differential equations (PDEs) can also be handled by spatially discretizing the PDEs to convert them to a system of DAEs. The objective of this thesis is firstly to ensure that direct transcription using Radau collocation is provably correct, and secondly to widen the applicability of the direct simultaneous approach to a larger class of dynamic optimization and optimal control problems (OCPs). This thesis aims at addressing these issues using rigorous theoretical tools and/or characteristic examples, and at the same time use the results for solving large-scale industrial applications to realize the benefits. The first part of this work deals with the analysis of convergence rates for direct transcription of unconstrained and final-time equality constrained optimal control problems. The problems are discretized using collocation at Radau points. Convergence is analyzed from an NLP/matrix-algebra perspective, which enables the prediction of the conditioning of the direct transcription NLP as the mesh size becomes finer. Several convergence results are presented along with tests on numerous example problems. These convergence results lead to an adjoint estimation procedure given the Lagrange multipliers for the large-scale NLP. The work also reveals the role of process control concepts such as controllability on the convergence analysis, and provides a very important link between control and optimization inside the framework of dynamic optimization. As an effort to extend the applicability of the direct
New Meta-Heuristic for Combinatorial Optimization Problems:Intersection Based Scaling
Peng Zou; Zhi Zhou; Ying-Yu Wan; Guo-Liang Chen; Jun Gu
2004-01-01
Combinatorial optimization problems are found in many application fields such as computer science, engineering and economy. In this paper, a new efficient meta-heuristic, Intersection-Based Scaling (IBS for abbreviation),is proposed and it can be applied to the combinatorial optimization problems. The main idea of IBS is to scale the size of the instance based on the intersection of some local optima, and to simplify the search space by extracting the intersection from the instance, which makes the search more efficient. The combination of IBS with some local search heuristics of different combinatorial optimization problems such as Traveling Salesman Problem (TSP) and Graph Partitioning Problem (GPP) is studied, and comparisons are made with some of the best heuristic algorithms and meta-heuristic algorithms. It is found that it has significantly improved the performance of existing local search heuristics and significantly outperforms the known best algorithms.
Using Bee Colony Optimization to Solve the Task Scheduling Problem in Homogenous Systems
Vahid Arabnejad
2011-09-01
Full Text Available Bee colony optimization (BCO is one of the most recent algorithms in swarm intelligence that can be used in optimization problems this algorithm is based on the intelligent behavior of honey bees in foraging process. In this paper bee colony optimization is applied to solve the task scheduling problem which tasks have dependency with each other. Scheduling of tasks that represents by directed acyclic graph is a NP-complete problem. The main purpose of this problem is obtaining the minimum schedule length that is called make-span. To realize the performance of BCO in this problem, the obtained results are presented and compared with the most successful methods such as Ant colony system, Tabu search and simulate annealing. The comparison shows that BCO produces the solutions in a different way and it is still among the bests.
Multigrid one shot methods for optimal control problems: Infinite dimensional control
Arian, Eyal; Taasan, Shlomo
1994-01-01
The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.
Deterministic Time-inconsistent Optimal Control Problems - an Essentially Cooperative Approach
Jiong-min YONG
2012-01-01
A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations.To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control,a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced.Under certain conditions,it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem,which is the value function of a time-consistent optimal control problem.Moreover,it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.
OpenMP Dual Population Genetic Algorithm for Solving Constrained Optimization Problems
A. J. Umbarkar
2015-01-01
Full Text Available Dual Population Genetic Algorithm is an effective optimization algorithm that provides additional diversity to the main population. It deals with the premature convergence problem as well as the diversity problem associated with Genetic Algorithm. But dual population introduces additional search space that increases time required to find an optimal solution. This large scale search space problem can be easily solved using all available cores of current age multi-core processors. Experiments are conducted on the problem set of CEC 2006 constrained optimization problems. Results of Sequential DPGA and OpenMP DPGA are compared on the basis of accuracy and run time. OpenMP DPGA gives speed up in execution.
Evaluation of Genetic Algorithm Concepts using Model Problems. Part 1; Single-Objective Optimization
Holst, Terry L.; Pulliam, Thomas H.
2003-01-01
A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.
Conceptual design optimization of rectilinear building frames: A knapsack problem approach
Sharafi, Pezhman; Teh, Lip H.; Hadi, Muhammad N. S.
2015-10-01
This article presents an automated technique for preliminary layout (conceptual design) optimization of rectilinear, orthogonal building frames in which the shape of the building plan, the number of bays and the size of unsupported spans are variables. It adopts the knapsack problem as the applied combinatorial optimization problem, and describes how the conceptual design optimization problem can be generally modelled as the unbounded multi-constraint multiple knapsack problem. It discusses some special cases, which can be modelled more efficiently as the single knapsack problem, the multiple-choice knapsack problem or the multiple knapsack problem. A knapsack contains sub-rectangles that define the floor plan and the location of columns. Particular conditions or preferences for the conceptual design can be incorporated as constraints on the knapsacks and/or sub-rectangles. A bi-objective knapsack problem is defined with the aim of obtaining a conceptual design having minimum cost and maximum plan regularity (minimum structural eccentricity). A multi-objective ant colony algorithm is formulated to solve the combinatorial optimization problem. A numerical example is included to demonstrate the application of the present method and the robustness of the algorithm.
Bonnans, J. Frederic; Hermant, Audrey
2006-01-01
The paper deals with optimal control problems with only one control variable and one state constraint, of arbitrary order. We consider the case of finitely many boundary arcs and touch times. We obtain a no-gap theory of second-order conditions, allowing to characterize second-order quadratic growth.
Evaluation of Genetic Algorithm Concepts Using Model Problems. Part 2; Multi-Objective Optimization
Holst, Terry L.; Pulliam, Thomas H.
2003-01-01
A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.
Maurer, Helmut; Osmolovskii, Nikolai,
2013-01-01
We study optimal control problems with a two-sided mixed control-state constraint and assume that the control variable appears linearly in both the system dynamics and constraints. By defining the control-state constraint as a new control variable, the optimal control problem is transformed into an optimal control problem with simple bounds on the new control variable. In view of Pontryagin's Minimum Principle, optimal controls of the transformed problem are concatenations of bang-bang or sin...
Selecting radiotherapy dose distributions by means of constrained optimization problems.
Alfonso, J C L; Buttazzo, G; García-Archilla, B; Herrero, M A; Núñez, L
2014-05-01
The main steps in planning radiotherapy consist in selecting for any patient diagnosed with a solid tumor (i) a prescribed radiation dose on the tumor, (ii) bounds on the radiation side effects on nearby organs at risk and (iii) a fractionation scheme specifying the number and frequency of therapeutic sessions during treatment. The goal of any radiotherapy treatment is to deliver on the tumor a radiation dose as close as possible to that selected in (i), while at the same time conforming to the constraints prescribed in (ii). To this day, considerable uncertainties remain concerning the best manner in which such issues should be addressed. In particular, the choice of a prescription radiation dose is mostly based on clinical experience accumulated on the particular type of tumor considered, without any direct reference to quantitative radiobiological assessment. Interestingly, mathematical models for the effect of radiation on biological matter have existed for quite some time, and are widely acknowledged by clinicians. However, the difficulty to obtain accurate in vivo measurements of the radiobiological parameters involved has severely restricted their direct application in current clinical practice.In this work, we first propose a mathematical model to select radiation dose distributions as solutions (minimizers) of suitable variational problems, under the assumption that key radiobiological parameters for tumors and organs at risk involved are known. Second, by analyzing the dependence of such solutions on the parameters involved, we then discuss the manner in which the use of those minimizers can improve current decision-making processes to select clinical dosimetries when (as is generally the case) only partial information on model radiosensitivity parameters is available. A comparison of the proposed radiation dose distributions with those actually delivered in a number of clinical cases strongly suggests that solutions of our mathematical model can be
Optimization-based decision support systems for planning problems in processing industries
Claassen, G.D.H.
2014-01-01
Summary Optimization-based decision support systems for planning problems in processing industries Nowadays, efficient planning of material flows within and between supply chains is of vital importance and has become one of the most challenging problems for decision support in practice. The tremendo
Biswas, Md. Haider Ali; de Pinho, Maria do Rosario
2013-01-01
Here we derive a nonsmooth maximum principle for optimal control problems with both state and mixed constraints. Crucial to our development is a convexity assumption on the "velocity set". The approach consists of applying known penalization techniques for state constraints together with recent results for mixed constrained problems.