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)