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Sample records for 0-1 optimization problems

  1. Glowworm Swarm Optimization for solving 0/1 Knapsack Problem%求解0/1背包问题的萤火虫算法

    程春英

    2015-01-01

    In this paper, the glowworm dwarm optimization was applied to solve the small-scale 0/1 knapsack problem, using basic idea of glowworm swarm optimization , analyze the 0/1 knapsack problem, Through the items for 10、20 and 50 knapsack problem to carry on the simulation experiment, The experimental results show that the algorithm in solving the small-scale 0/1 knapsack problem is feasible.%该文将萤火虫算法应用于求解小规模0/1背包问题,利用基本萤火虫算法的求解思想,对0/1背包问题进行分析,通过对物品数为10、25和50的背包问题进行了仿真实验,实验结果表明该算法在解决小规模0/1背包问题是可行的。

  2. 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.

  3. On the reformulation of topology optimization problems as linear or convex quadratic mixed 0-1 programs

    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...

  4. 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......Nature shows us in our daily life how robust, flexible and optimal self-organized modular constructions work in complex physical, chemical and biological systems, which successfully adapt to new and unexpected situations. A promising strategy is therefore to use such self-organization and pattern...... 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...

  5. 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.

  6. Solving Multi-Objective 0-1 Programming Problem by Artificial Glowworm Swarm Optimization Algorithm%多目标0-1规划的萤火虫算法

    程魁; 马良

    2013-01-01

    针对于多目标0-1规划问题,给出一种新型的智能优化算法一萤火虫优化算法对其进行求解,并在计算机上予以实现.经一系列算例测试,并与其它智能算法 进行比较,算法能获得较多的非劣解,表明算法可行有效,可求解实际应用中的相应问题.

  7. DNA computation model to solve 0-1 programming problem.

    Zhang, Fengyue; Yin, Zhixiang; Liu, Bo; Xu, Jin

    2004-01-01

    0-1 programming problem is an important problem in opsearch with very widespread applications. In this paper, a new DNA computation model utilizing solution-based and surface-based methods is presented to solve the 0-1 programming problem. This model contains the major benefits of both solution-based and surface-based methods; including vast parallelism, extraordinary information density and ease of operation. The result, verified by biological experimentation, revealed the potential of DNA computation in solving complex programming problem.

  8. 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.

  9. Optimization Problems

    Yaping Hu

    2015-01-01

    the nonsmooth convex optimization problem. First, by using Moreau-Yosida regularization, we convert the original objective function to a continuously differentiable function; then we use approximate function and gradient values of the Moreau-Yosida regularization to substitute the corresponding exact values in the algorithm. The global convergence is proved under suitable assumptions. Numerical experiments are presented to show the effectiveness of this algorithm.

  10. Approximating the 0-1 Multiple Knapsack Problem with Agent Decomposition and Market Negotiation

    Smolinski, B.

    1999-09-03

    The 0-1 multiple knapsack problem appears in many domains from financial portfolio management to cargo ship stowing. Methods for solving it range from approximate algorithms, such as greedy algorithms, to exact algorithms, such as branch and bound. Approximate algorithms have no bounds on how poorly they perform and exact algorithms can suffer from exponential time and space complexities with large data sets. This paper introduces a market model based on agent decomposition and market auctions for approximating the 0-1 multiple knapsack problem, and an algorithm that implements the model (M(x)). M(x) traverses the solution space rather than getting caught in a local maximum, overcoming an inherent problem of many greedy algorithms. The use of agents ensures that infeasible solutions are not considered while traversing the solution space and that traversal of the solution space is not just random, but is also directed. M(x) is compared to a bound and bound algorithm (BB) and a simple greedy algorithm with a random shuffle (G(x)). The results suggest that M(x) is a good algorithm for approximating the 0-1 Multiple Knapsack problem. M(x) almost always found solutions that were close to optimal in a fraction of the time it took BB to run and with much less memory on large test data sets. M(x) usually performed better than G(x) on hard problems with correlated data.

  11. A Thermodynamical Selection-Based Discrete Differential Evolution for the 0-1 Knapsack Problem

    Zhaolu Guo

    2014-11-01

    Full Text Available Many problems in business and engineering can be modeled as 0-1 knapsack problems. However, the 0-1 knapsack problem is one of the classical NP-hard problems. Therefore, it is valuable to develop effective and efficient algorithms for solving 0-1 knapsack problems. Aiming at the drawbacks of the selection operator in the traditional differential evolution (DE, we present a novel discrete differential evolution (TDDE for solving 0-1 knapsack problem. In TDDE, an enhanced selection operator inspired by the principle of the minimal free energy in thermodynamics is employed, trying to balance the conflict between the selective pressure and the diversity of population to some degree. An experimental study is conducted on twenty 0-1 knapsack test instances. The comparison results show that TDDE can gain competitive performance on the majority of the test instances.

  12. 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.

  13. Solving Multidimensional 0-1 Knapsack Problem by P Systems with Input and Active Membranes

    2004-01-01

    P systems are parallel molecular computing models based on pro- cessing multisets of objects in cell-like membrane structures. In this paper we give a membrane algorithm to multidimensional 0-1 knapsack problem in lin- ear time by recognizer P systems with input and with active membranes using 2-division. This algorithm can also be modi¯ed to solve general 0-1 integer programming problem.

  14. The general form of 0-1 programming problem based on DNA computing.

    ZhiXiang, Yin; Fengyue, Zhang; Jin, Xu

    2003-06-01

    DNA computing is a novel method of solving a class of intractable computational problems, in which the computing speeds up exponentially with the problem size. Up to now, many accomplishments have been made to improve its performance and increase its reliability. In this paper, we solved the general form of 0-1 programming problem with fluorescence labeling techniques based on surface chemistry by attempting to apply DNA computing to a programming problem. Our method has some significant advantages such as simple encoding, low cost, and short operating time.

  15. An Effective Hybrid Cuckoo Search Algorithm with Improved Shuffled Frog Leaping Algorithm for 0-1 Knapsack Problems

    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 ...

  16. 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.

  17. 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.

  18. Effects of MOEA Temporally Switching Pareto Partial Dominance on Many-objective 0/1 Knapsack Problems

    Sato, Hiroyuki; Aguirre, Hernán E.; Kiyoshi, Tanaka

    In this work, we propose a novel multi-objective evolutionary algorithm (MOEA) which improves search performance of MOEA especially for many-objective combinatorial optimization problems. Pareto dominance based MOEAs such as NSGA-II and SPEA2 meet difficulty to rank solutions in the population noticeably deteriorating search performance as we increase the number of objectives. In the proposed method, we rank solutions by calculating Pareto partial dominance between solutions using r objective functions selected from m objective functions to induce appropriate selection pressure in many-objective optimization by Pareto-based MOEA. Also, we temporally switch r objective functions among mCr combinations in every interval generations Ig to optimize all of the objective functions throughout the entire evolution process. In this work, we use many-objective 0/1 knapsack problems to show the search performance of the proposed method and analyze its evolution behavior. Simulation results show that there is an optimum value for the number of objective functions r to be considered for the calculation of Pareto partial dominance and the interval (generation numbers) Ig to maximize the entire search performance. Also, the search performance of the proposed method is superior to recent state-of-the-art MOEAs, i.e., IBEA, CDAS and MSOPS. Furthermore, we show that the computational time of the proposed method is much less than IBEA, CDAS and MSOPS, and comparative or sometimes less than NSGA-II.

  19. An Effective Hybrid Cuckoo Search Algorithm with Improved Shuffled Frog Leaping Algorithm for 0-1 Knapsack Problems

    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.

  20. An effective hybrid cuckoo search algorithm with improved shuffled frog leaping algorithm for 0-1 knapsack problems.

    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.

  1. 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.

  2. Cargo Revenue Management: Bid-Prices for a 0-1 Multi Knapsack Problem

    K. Pak; R. Dekker (Rommert)

    2004-01-01

    textabstractRevenue management is the practice of selecting those customers that generate the maximum revenue from a fixed and perishable capacity. Cargo revenue management differs from the well-known passenger revenue management problem by the fact that its capacity constraint is 2-dimensional, i.e

  3. Class and Home Problems: Optimization Problems

    Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard

    2011-01-01

    Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…

  4. PcapDB: Search Optimized Packet Capture, Version 0.1.0.0

    2016-11-04

    PcapDB is a packet capture system designed to optimize the captured data for fast search in the typical (network incident response) use case. The technology involved in this software has been submitted via the IDEAS system and has been filed as a provisional patent. It includes the following primary components: capture: The capture component utilizes existing capture libraries to retrieve packets from network interfaces. Once retrieved the packets are passed to additional threads for sorting into flows and indexing. The sorted flows and indexes are passed to other threads so that they can be written to disk. These components are written in the C programming language. search: The search components provide a means to find relevant flows and the associated packets. A search query is parsed and represented as a search tree. Various search commands, written in C, are then used resolve this tree into a set of search results. The tree generation and search execution management components are written in python. interface: The PcapDB web interface is written in Python on the Django framework. It provides a series of pages, API's, and asynchronous tasks that allow the user to manage the capture system, perform searches, and retrieve results. Web page components are written in HTML,CSS and Javascript.

  5. Solving Optimal Timing Problems Elegantly

    Todorova, Tamara

    2013-01-01

    Few textbooks in mathematical economics cover optimal timing problems. Those which cover them do it scantly or in a rather clumsy way, making it hard for students to understand and apply the concept of optimal time in new contexts. Discussing the plentiful illustrations of optimal timing problems, we present an elegant and simple method of solving them. Whether the present value function is exponential or logarithmic, a convenient way to solve it is to convert the base to the exponential numb...

  6. Topology optimization for acoustic problems

    Dühring, Maria Bayard

    2006-01-01

    In this paper a method to control acoustic properties in a room with topology optimization is presented. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized by distribution of material in a design domain along the ceiling in 2D and 3D. Nice 0-1 design...

  7. Optimal Revascularization Strategy on Medina 0,1,0 Left Main Bifurcation Lesions in Type 2 Diabetes

    Zheng, Xuwei; Peng, Hongyu; Zhao, Donghui; Ma, Qin; Fu, Kun; Chen, Guo

    2016-01-01

    Aim. Diabetes mellitus (DM) is a major risk factor for cardiovascular disease. The implications of a diagnosis of DM are as severe as the diagnosis of coronary artery disease. For many patients with complex coronary artery disease, optimal revascularization strategy selection and optimal medical therapy are equally important. In this study, we compared the hemodynamic results of different stenting techniques for Medina 0,1,0 left main bifurcation lesions. Methods. We use idealized left main bifurcation models and computational fluid dynamics analysis to evaluate hemodynamic parameters which are known to affect the risk of restenosis and thrombosis at stented bifurcation. The surface integrals of time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) at bifurcation site were quantified. Results. Crossover stenting without final kissing balloon angioplasty provided the most favorable hemodynamic results (integrated values of TAWSS = 2.96 × 10−4 N, OSI = 4.75 × 10−6 m2) with bifurcation area subjected to OSI values >0.25, >0.35, and >0.45 calculated as 0.39 mm2, 0.06 mm2, and 0 mm2, respectively. Conclusion. Crossover stenting only offers hemodynamic advantages over other stenting techniques for Medina 0,1,0 left main bifurcation lesions and large bifurcation angle is associated with unfavorable flow profiles. PMID:27777957

  8. Optimal Revascularization Strategy on Medina 0,1,0 Left Main Bifurcation Lesions in Type 2 Diabetes

    Xuwei Zheng

    2016-01-01

    Full Text Available Aim. Diabetes mellitus (DM is a major risk factor for cardiovascular disease. The implications of a diagnosis of DM are as severe as the diagnosis of coronary artery disease. For many patients with complex coronary artery disease, optimal revascularization strategy selection and optimal medical therapy are equally important. In this study, we compared the hemodynamic results of different stenting techniques for Medina 0,1,0 left main bifurcation lesions. Methods. We use idealized left main bifurcation models and computational fluid dynamics analysis to evaluate hemodynamic parameters which are known to affect the risk of restenosis and thrombosis at stented bifurcation. The surface integrals of time-averaged wall shear stress (TAWSS and oscillatory shear index (OSI at bifurcation site were quantified. Results. Crossover stenting without final kissing balloon angioplasty provided the most favorable hemodynamic results (integrated values of TAWSS = 2.96 × 10−4 N, OSI = 4.75 × 10−6 m2 with bifurcation area subjected to OSI values >0.25, >0.35, and >0.45 calculated as 0.39 mm2, 0.06 mm2, and 0 mm2, respectively. Conclusion. Crossover stenting only offers hemodynamic advantages over other stenting techniques for Medina 0,1,0 left main bifurcation lesions and large bifurcation angle is associated with unfavorable flow profiles.

  9. Evolution Strategies in Optimization Problems

    Cruz, Pedro A F

    2007-01-01

    Evolution Strategies are inspired in biology and part of a larger research field known as Evolutionary Algorithms. Those strategies perform a random search in the space of admissible functions, aiming to optimize some given objective function. We show that simple evolution strategies are a useful tool in optimal control, permitting to obtain, in an efficient way, good approximations to the solutions of some recent and challenging optimal control problems.

  10. Topology Optimization for Convection Problems

    Alexandersen, Joe

    2011-01-01

    This report deals with the topology optimization of convection problems.That is, the aim of the project is to develop, implement and examine topology optimization of purely thermal and coupled thermomechanical problems,when the design-dependent eects of convection are taken into consideration.......This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...

  11. 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...... 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....... Although the study of the FVM is carried out using a simple heat conduction problem, the work illuminates and discusses the technicalities of employing the FVM in connection with topology optimization. Finally, parallelized solution methods are investigated using the high performance computing facility...

  12. 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

  13. On the optimal sizing problem

    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 ...

  14. 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.

  15. Creep performance of Zr-1Nb-0.75Sn-0.1Fe cladding tubes with optimized Sn content

    Kim, Won Nyeon; Choi, Yong; Hong, Sun Ig

    2014-12-01

    Creep properties of stress-relieved Zr-1Nb-0.75Sn-0.1Fe alloy with a lower Sn content were studied. Zr-1Nb-0.75Sn-0.1Fe alloy was found to have stress exponents of 6-7, independent of stress level, unlike Zr-1Nb-1Sn-0.1Fe alloy, in which the transition of stress exponent with increase of stress was observed. The constancy of stress exponent, without the transition observed in Zr-1Nb-0.75Sn-0.1Fe alloy with lower Sn content, is associated with the decrease of Sn atoms. The activation energies for creep deformation were calculated to be between 210 and 260 kJ/mol for the Zr-1Nb-0.75Sn-0.1Fe alloy with a lower Sn content. The slightly smaller creep activation energy in Zr-1Nb-0.75Sn-0.1Fe, compared with that of Zr-1Nb-1Sn-0.1Fe alloy, is thought to be attributed to the lower Sn content. The creep data obtained at different temperatures and stress fell close to a single line, suggesting the creep life of Zr-1Nb-0.75Sn-0.1Fe alloy with a lower Sn content is well expressed by the Larson-Miller Parameter.

  16. Optimization in HIV screening problems

    Lev Abolnikov

    2003-01-01

    Full Text Available In this article, the authors use both deterministic and stochastic approaches to the analysis of some optimization problems that arise in the group (“pool” HIV screening practice. Two kinds of testing policies are considered. For the first kind, group-individual testing, the optimal size of the group that should be selected for testing is found. For more general group-subgroup testing procedure the authors develop a numerical algorithm for finding the sequence of successively selected subgroups that minimizes the total cost of testing. Assuming that both arriving and testing processes have a random nature, the authors suggest a stochastic model in which the optimal size of the group in the group-individual testing procedure is found by using methods of queueing theory.

  17. 格雷码混合遗传算法求解0-1背包问题%Gray coded hybrid genetic algorithm for 0-1 knapsack problem

    王则林; 吴志健

    2012-01-01

    This paper gave an athematic mode of 0-1 knapsack problem,and modified the binary coding to establish a gray coded hybrid genetic algorithm used greedy algorithm to handle with the constraint conditions, And this paper proposed a value density operator to the individual, which could improve the search effciency, used the elitism mechanism to accelerate the convergence process, The numerical experiment proves the affectivity of the algorithm.%给出0-1背包问题的数学模型,修改传统二进制编码为格雷码混合遗传算法,使用贪心算法来解决约束问题,对每个个体使用价值密度来衡量,提高了算法搜索效率,同时使用精英保留机制来加速算法收敛的速度.最后通过数值实验证明了算法的有效性.

  18. 克隆选择免疫遗传算法对高维0/1背包问题应用%Immune genetic algorithm based on clonal selection and its application to 0/1 knapsack problem

    武慧虹; 钱淑渠; 徐志丹

    2013-01-01

    There are some problems such as slow convergence and easy stagnation in local optima when using Genetic Algorithms ( GA) to solve high-dimensional knapsack problem. To overcome those shortcomings, a bio-inspired clonal selection immune genetic algorithm was developed to solve knapsack problem with high dimension. In the algorithm, the antibody was binary coded and the affinity of antibody was designed based on its density;in addition, the population was divided into feasible and infeasible population, and the feasible antibodies were cloned dynamically and mutated to produce the offspring population, meanwhile the infeasible antibodies were repaired towards the feasibility. The simulation experiments on the four kinds of 0/1 knapsack problem with high dimension and comparison with ETGA, RIGA and ISGA demonstrate that the proposed algorithm has better ability in handling constraints and more rapid convergence.%针对遗传算法求解高维背包问题收敛速度慢、易于陷入局部最优的缺点,基于生物免疫系统克隆选择原理,提出一种克隆选择免疫遗传算法.该算法中抗体采用二进制编码,通过抗体浓度设计抗体亲和力,进化群分离为可行群和非可行群,进化过程仅可行抗体动态克隆和突变,非可行抗体经修复算子获可行抗体.数值实验中,选取三种著名的算法用于四种高维的背包问题求解,结果表明:所提算法较其他算法具有更强的约束处理能力和快速收敛的效果.

  19. Stability Analysis for Stochastic Optimization Problems

    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.

  20. 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.

  1. 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)optimization problem,is it r'(n)-approximable?

  2. Examples of Systems of Functions Being Riesz Bases in L_{2}(0,1). Application to a Nonlinear Boundary Value Problem

    Zhidkov, P E

    2001-01-01

    We establish examples of systems of functions being Riesz bases in L_{2}(0,1). We then apply this result to improve a theorem presented in [9] showing that an arbitrary "standard" system of solutions of a nonlinear boundary value problem, normalized to 1 in the same space, is a Riesz basis in this space. The proofs in this work are quite elementary.

  3. 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......–1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality....

  4. 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.

  5. 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.

  6. 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.

  7. Evolutionary computation for dynamic optimization problems

    Yao, Xin

    2013-01-01

    This book provides a compilation on the state-of-the-art and recent advances of evolutionary computation for dynamic optimization problems. The motivation for this book arises from the fact that many real-world optimization problems and engineering systems are subject to dynamic environments, where changes occur over time. Key issues for addressing dynamic optimization problems in evolutionary computation, including fundamentals, algorithm design, theoretical analysis, and real-world applications, are presented. "Evolutionary Computation for Dynamic Optimization Problems" is a valuable reference to scientists, researchers, professionals and students in the field of engineering and science, particularly in the areas of computational intelligence, nature- and bio-inspired computing, and evolutionary computation.

  8. Optimal impulse control problems and linear programming.

    Bauso, D.

    2009-01-01

    Optimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation in real-time problems. We do this by using a paradigm borrowed from the Operations Research field. As main result, ...

  9. 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 ...

  10. 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…

  11. Topology optimization of wave-propagation problems

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2006-01-01

    Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures.......Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures....

  12. Metaheuristic optimization of acoustic inverse problems.

    van Leijen, A.V.; Rothkrantz, L.; Groen, F.

    2011-01-01

    Swift solving of geoacoustic inverse problems strongly depends on the application of a global optimization scheme. Given a particular inverse problem, this work aims to answer the questions how to select an appropriate metaheuristic search strategy, and how to configure it for optimal performance. F

  13. Problem Solving through an Optimization Problem in Geometry

    Poon, Kin Keung; Wong, Hang-Chi

    2011-01-01

    This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

  14. 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.

  15. 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.

  16. 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...

  17. 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...

  18. Dynamic consistency for Stochastic Optimal Control problems

    Carpentier, Pierre; Cohen, Guy; De Lara, Michel; Girardeau, Pierre

    2010-01-01

    For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step $t_0$, the decision maker formulates an optimization problem that yields optimal decision rules for all the forthcoming time step $t_0, t_1, ..., T$; at the next time step $t_1$, he is able to formulate a new optimization problem starting at time $t_1$ that yields a new sequence of optimal decision rules. This process can be continued until final time $T$ is reached. A family of optimization problems formulated in this way is said to be time consistent if the optimal strategies obtained when solving the original problem remain optimal for all subsequent problems. The notion of time consistency, well-known in the field of Economics, has been recently introduced in the context of risk measures, notably by Artzner et al. (2007) and studied in the Stochastic Programming framework by Shapiro (2009) and for Markov Decision Processes...

  19. Optimal control problems with switching points

    Seywald, Hans

    1991-09-01

    An overview is presented of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

  20. Chemical reaction optimization for solving shortest common supersequence problem.

    Khaled Saifullah, C M; Rafiqul Islam, Md

    2016-10-01

    Shortest common supersequence (SCS) is a classical NP-hard problem, where a string to be constructed that is the supersequence of a given string set. The SCS problem has an enormous application of data compression, query optimization in the database and different bioinformatics activities. Due to NP-hardness, the exact algorithms fail to compute SCS for larger instances. Many heuristics and meta-heuristics approaches were proposed to solve this problem. In this paper, we propose a meta-heuristics approach based on chemical reaction optimization, CRO_SCS that is designed inspired by the nature of the chemical reactions. For different optimization problems like 0-1 knapsack, quadratic assignment, global numeric optimization problems CRO algorithm shows very good performance. We have redesigned the reaction operators and a new reform function to solve the SCS problem. The outcomes of the proposed CRO_SCS algorithm are compared with those of the enhanced beam search (IBS_SCS), deposition and reduction (DR), ant colony optimization (ACO) and artificial bee colony (ABC) algorithms. The length of supersequence, execution time and standard deviation of all related algorithms show that CRO_SCS gives better results on the average than all other algorithms.

  1. Vector Broadcast Channels: Optimal Threshold Selection Problem

    Samarasinghe, Tharaka; Evans, Jamie

    2011-01-01

    Threshold feedback policies are well known and provably rate-wise optimal selective feedback techniques for communication systems requiring partial channel state information (CSI). However, optimal selection of thresholds at mobile users to maximize information theoretic data rates subject to feedback constraints is an open problem. In this paper, we focus on the optimal threshold selection problem, and provide a solution for this problem for finite feedback systems. Rather surprisingly, we show that using the same threshold values at all mobile users is not always a rate-wise optimal feedback strategy, even for a system with identical users experiencing statistically the same channel conditions. By utilizing the theory of majorization, we identify an underlying Schur-concave structure in the rate function and obtain sufficient conditions for a homogenous threshold feedback policy to be optimal. Our results hold for most fading channel models, and we illustrate an application of our results to familiar Raylei...

  2. Geoengineering as an optimization problem

    Ban-Weiss, George A; Caldeira, Ken, E-mail: georgebw@stanford.edu [Department of Global Ecology, Carnegie Institution for Science, 260 Panama Street, Stanford, CA 94305 (United States)

    2010-07-15

    There is increasing evidence that Earth's climate is currently warming, primarily due to emissions of greenhouse gases from human activities, and Earth has been projected to continue warming throughout this century. Scientists have begun to investigate the potential for geoengineering options for reducing surface temperatures and whether such options could possibly contribute to environmental risk reduction. One proposed method involves deliberately increasing aerosol loading in the stratosphere to scatter additional sunlight to space. Previous modeling studies have attempted to predict the climate consequences of hypothetical aerosol additions to the stratosphere. These studies have shown that this method could potentially reduce surface temperatures, but could not recreate a low-CO{sub 2} climate in a high-CO{sub 2} world. In this study, we attempt to determine the latitudinal distribution of stratospheric aerosols that would most closely achieve a low-CO{sub 2} climate despite high CO{sub 2} levels. Using the NCAR CAM3.1 general circulation model, we find that having a stratospheric aerosol loading in polar regions higher than that in tropical regions leads to a temperature distribution that is more similar to the low-CO{sub 2} climate than that yielded by a globally uniform loading. However, such polar weighting of stratospheric sulfate tends to degrade the degree to which the hydrological cycle is restored, and thus does not markedly contribute to improved recovery of a low-CO{sub 2} climate. In the model, the optimal latitudinally varying aerosol distributions diminished the rms zonal mean land temperature change from a doubling of CO{sub 2} by 94% and the rms zonal mean land precipitation minus evaporation change by 74%. It is important to note that this idealized study represents a first attempt at optimizing the engineering of climate using a general circulation model; uncertainties are high and not all processes that are important in reality are

  3. OPTIMAL CONTROL PROBLEM FOR PARABOLIC VARIATIONAL INEQUALITIES

    汪更生

    2001-01-01

    This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations.The maximum principle and some kind of approximate controllability are studied.

  4. Linux software for large topology optimization problems

    Recently the commercial finite element tool-box COMSOL has proven to be an excellent platform for development of the topology optimization method, teaching and other multi-physics modeling problems. This is mainly due to COMSOL’s flexibility and symbolic infrastructure which puts focus on the mod......Recently the commercial finite element tool-box COMSOL has proven to be an excellent platform for development of the topology optimization method, teaching and other multi-physics modeling problems. This is mainly due to COMSOL’s flexibility and symbolic infrastructure which puts focus......-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...... library. This talk investigates the efficiency of Sundance for large topology optimization problems....

  5. An optimal hostage rescue problem

    Shi, Fengbo

    2000-01-01

    We propose the following mathematical model of optinal reacue problems concerning hostage.Suppose i persons are taken as hostages at any given point in time t,and we have to make a decision on attempting either rescue or no resuce. Let p be the probability of a hostage being killed in a rescue attempt,and let s be the probability of criminal(s) surrendering up to the following point in time if no rescue attempt is made.Futher,let g and r be the probabilities of a hostage being,respectively,ki...

  6. Topology optimization for transient heat transfer problems

    Zeidan, Said; Sigmund, Ole; Lazarov, Boyan Stefanov

    The focus of this work is on passive control of transient heat transfer problems using the topology optimization (TopOpt) method [1]. The goal is to find distributions of a limited amount of phase change material (PCM), within a given design domain, which optimizes the heat energy storage [2]. Our...

  7. A Problem-Oriented Mathematical Optimization Course

    Wenger, Robert B.; Rhyner, Charles R.

    1977-01-01

    This article describes a one-semester junior and senior level course in applied mathematical optimization for undergraduates which provides the opportunity to test models by doing numerical experiments and to learn to use computer subroutines for solving optimization problems. (MN)

  8. 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.

  9. 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 consists...... of finding the best distributions of the two initial materials in a rod in order to minimize the vibration energy in the structure under periodic loading of driving frequency Omega. We comment on relaxation and optimality conditions, and perform numerical simulations of the optimal configurations. We prove...

  10. Variable Expansion Techniques for Decomposable Optimization Problems

    2011-03-05

    meration or dynamic programming. Recall the edge partition problem studied by Taskin et al. above in reference 7. (Z. Caner Taskin was supported by the...Stochastic Integer Program- ming, August 2009 August 2009. 12 2. Z. Caner Taskin, Algorithms for Solving Multi-Level Optimization Problems with Dis

  11. Shape flows for spectral optimization problems

    Bucur, Dorin; Stefanelli, Ulisse

    2011-01-01

    We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the evolution of {\\it capacitary measures} with respect to the $\\gamma$-convergence dissipation distance and with the evolution of domains in spectral optimization problems.

  12. 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...... function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical...... 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....

  13. Better relaxations of classical discrete optimization problems.

    Lancia, Giuseppe; Konjevod, Goran; Carr, Robert D.; Parehk, Ojas

    2008-08-01

    A mathematical program is an optimization problem expressed as an objective function of multiple variables subject to set of constraints. When the optimization problem has specific structure, the problem class usually has a special name. A linear program is the optimization of a linear objective function subject to linear constraints. An integer program is a linear program where some of the variables must take only integer values. A semidefinite program is a linear program where the variables are arranged in a matrix and for all feasible solutions, this matrix must be positive semidefinite. There are general-purpose solvers for each of these classes of mathematical program. There are usually many ways to express a problem as a correct, say, linear program. However, equivalent formulations can have significantly different practical tractability. In this poster, we present new formulations for two classic discrete optimization problems, maximum cut (max cut) and the graphical traveling salesman problem (GTSP), that are significantly stronger, and hence more computationally tractable, than any previous formulations of their class. Both partially answer longstanding open theoretical questions in polyhedral combinatorics.

  14. A simple convex optimization problem with many applications

    Vidal, Rene Victor Valqui

    1994-01-01

    This paper presents an algorithm for the solution of a simple convex optimization problem. This problem is a generalization of several other optimization problems which have applications to resource allocation, optimal capacity expansion, and vehicle scheduling. The algorithm is based...

  15. 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...... as for vectorial elastic wave propagation problems using finite element analysis [P2], [P4]. The concept is implemented in a parallel computing code that includes efficient techniques for performing gradient based topology optimization. Using the developed computational framework the thesis considers four...... 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...

  16. Trajectory metaheuristic algorithms to optimize problems combinatorics

    Natalia Alancay

    2016-12-01

    Full Text Available The application of metaheuristic algorithms to optimization problems has been very important during the last decades. The main advantage of these techniques is their flexibility and robustness, which allows them to be applied to a wide range of problems. In this work we concentrate on metaheuristics based on Simulated Annealing, Tabu Search and Variable Neighborhood Search trajectory whose main characteristic is that they start from a point and through the exploration of the neighborhood vary the current solution, forming a trajectory. By means of the instances of the selected combinatorial problems, a computational experimentation is carried out that illustrates the behavior of the algorithmic methods to solve them. The main objective of this work is to perform the study and comparison of the results obtained for the selected trajectories metaheuristics in its application for the resolution of a set of academic problems of combinatorial optimization.

  17. Solving global optimization problems on GPU cluster

    Barkalov, Konstantin; Gergel, Victor; Lebedev, Ilya

    2016-06-01

    The paper contains the results of investigation of a parallel global optimization algorithm combined with a dimension reduction scheme. This allows solving multidimensional problems by means of reducing to data-independent subproblems with smaller dimension solved in parallel. The new element implemented in the research consists in using several graphic accelerators at different computing nodes. The paper also includes results of solving problems of well-known multiextremal test class GKLS on Lobachevsky supercomputer using tens of thousands of GPU cores.

  18. Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

    Wang, Di; Kleinberg, Robert D

    2009-11-28

    Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.

  19. Shape Optimization Problems with Internal Constraint

    Bucur, Dorin; Velichkov, Bozhidar

    2011-01-01

    We consider shape optimization problems with internal inclusion constraints, of the form $$\\min\\big\\{J(\\Omega)\\ :\\ \\Dr\\subset\\Omega\\subset\\R^d,\\ |\\Omega|=m\\big\\},$$ where the set $\\Dr$ is fixed, possibly unbounded, and $J$ depends on $\\Omega$ via the spectrum of the Dirichlet Laplacian. We analyze the existence of a solution and its qualitative properties, and rise some open questions.

  20. Modelling Robust Design Problems via Conic Optimization

    Chaerani, D.

    2006-01-01

    This thesis deals with optimization problems with uncertain data. Uncertainty here means that the data is not known exactly at the time when its solution has to be determined. In many models the uncertainty is ignored and a representative nominal value of the data is used. The uncertainty may be due

  1. Optimal Wafer Cutting in Shuttle Layout Problems

    Nisted, Lasse; Pisinger, David; Altman, Avri

    2011-01-01

    A major cost in semiconductor manufacturing is the generation of photo masks which are used to produce the dies. When producing smaller series of chips it can be advantageous to build a shuttle mask (or multi-project wafer) to share the startup costs by placing different dies on the same mask. Th...... problem becomes a maximum vertex-weighted clique problem in which each clique consists of cutting compatible dies. The resulting branch-and-price algorithm is able to solve realistic cutting problems to optimality in a couple of seconds....

  2. Topology optimization of fluid mechanics problems

    Gersborg-Hansen, Allan

    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......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......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...

  3. Maximum process problems in optimal control theory

    Goran Peskir

    2005-01-01

    Full Text Available Given a standard Brownian motion (Btt≥0 and the equation of motion dXt=vtdt+2dBt, we set St=max0≤s≤tXs and consider the optimal control problem supvE(Sτ−Cτ, where c>0 and the supremum is taken over all admissible controls v satisfying vt∈[μ0,μ1] for all t up to τ=inf{t>0|Xt∉(ℓ0,ℓ1} with μ0g∗(St, where s↦g∗(s is a switching curve that is determined explicitly (as the unique solution to a nonlinear differential equation. The solution found demonstrates that the problem formulations based on a maximum functional can be successfully included in optimal control theory (calculus of variations in addition to the classic problem formulations due to Lagrange, Mayer, and Bolza.

  4. 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.

  5. 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 ...

  6. 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.

  7. Mesh refinement strategy for optimal control problems

    Paiva, Luis Tiago; Fontes, Fernando,

    2013-01-01

    International audience; Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform node...

  8. Tractable problems in optimal decentralized control

    Rotkowitz, Michael Charles

    2005-07-01

    This thesis considers the problem of constructing optimal decentralized controllers. The problem is formulated as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. The notion of quadratic invariance of a constraint set with respect to a system is defined. It is shown that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback. It is further shown that if the constraint set has this property, this allows the constrained minimum-norm problem to be solved via convex programming. These results are developed in a very general framework, and are shown to hold for continuous-time systems, discrete-time systems, or operators on Banach spaces, for stable or unstable plants, and for the minimization of any norm. The utility of these results is then demonstrated on some specific constraint classes. An explicit test is derived for sparsity constraints on a controller to be quadratically invariant, and thus amenable to convex synthesis. Symmetric synthesis is also shown to be quadratically invariant. The problem of control over networks with delays is then addressed as another constraint class. Multiple subsystems are considered, each with its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. It is shown that if the communication delays are less than the propagation delays, then the associated constraints are quadratically invariant, and thus optimal controllers can be synthesized. We further show that this result still holds in the presence of computational delays. This thesis unifies the few previous results on specific tractable decentralized control problems, identifies broad and useful classes of new solvable problems, and delineates the largest known class of convex problems in decentralized control.

  9. 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.

  10. Distributed Algorithms for Optimal Power Flow Problem

    Lam, Albert Y S; Tse, David

    2011-01-01

    Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real time. With some special network structure, e.g. trees, the problem has been shown to have a zero duality gap and the convex dual problem yields the optimal solution. In this paper, we propose a primal and a dual algorithm to coordinate the smaller subproblems decomposed from the convexified OPF. We can arrange the subproblems to be solved sequentially and cumulatively in a central node or solved in parallel in distributed nodes. We test the algorithms on IEEE radial distribution test feeders, some random tree-structured networks, and the IEEE transmission system benchmarks. Simulation results show that the computation time can be improved dramatically with our algorithms over the centralized approach of solving the problem without decomposition, especially in tree-structured...

  11. Solving Optimization Problems via Vortex Optimization Algorithm and Cognitive Development Optimization Algorithm

    Ahmet Demir

    2017-01-01

    Full Text Available In the fields which require finding the most appropriate value, optimization became a vital approach to employ effective solutions. With the use of optimization techniques, many different fields in the modern life have found solutions to their real-world based problems. In this context, classical optimization techniques have had an important popularity. But after a while, more advanced optimization problems required the use of more effective techniques. At this point, Computer Science took an important role on providing software related techniques to improve the associated literature. Today, intelligent optimization techniques based on Artificial Intelligence are widely used for optimization problems. The objective of this paper is to provide a comparative study on the employment of classical optimization solutions and Artificial Intelligence solutions for enabling readers to have idea about the potential of intelligent optimization techniques. At this point, two recently developed intelligent optimization algorithms, Vortex Optimization Algorithm (VOA and Cognitive Development Optimization Algorithm (CoDOA, have been used to solve some multidisciplinary optimization problems provided in the source book Thomas' Calculus 11th Edition and the obtained results have compared with classical optimization solutions. 

  12. 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.

  13. 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.

  14. Hybrid intelligent optimization methods for engineering problems

    Pehlivanoglu, Yasin Volkan

    The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and

  15. Difficulties in Evolutionary Multiobjective Optimization for Many-Objective Optimization Problems and Their Scalability Improvement Techniques

    Tsukamoto, Noritaka; Nojima, Yusuke; Ishibuchi, Hisao

    In this paper, we examine the behavior of evolutionary multiobjective optimization (EMO) algorithms to clarify the difficulties in their scalability to many-objective optimization problems. Whereas EMO algorithms usually work well on two-objective problems, it has also been reported that they do not work well on many-objective problems. First, we examine the behavior of the most well-known and frequently-used Pareto-based EMO algorithm (i. e. , NSGA-II) on many-objective 0/1 knapsack problems. Experimental results show that the search ability of NSGA-II is severely deteriorated by the increase in the number of objectives. This is because the selection pressure toward the Pareto front is severely weakened by the increase in the number of non-dominated solutions. Next we briefly review some approaches to the scalability improvement of EMO algorithms to many-objective problems. Then we examine their effects on the search ability of NSGA-II. Experimental results show that the improvement in the convergence of solutions to the Pareto front often leads to the decrease in their diversity.

  16. HREELS and photoemission study of GaSb( 1 0 0 )-(1×3) surfaces prepared by optimal atomic hydrogen cleaning

    Veal, T. D.; Lowe, M. J.; McConville, C. F.

    2002-03-01

    High-resolution electron-energy-loss spectroscopy (HREELS) and synchrotron-radiation photoemission spectroscopy (SRPES) have been used to study the Sb-stabilised GaSb(1 0 0)-(1×3) surface prepared by a two-stage low-temperature atomic hydrogen cleaning (AHC) procedure. The use of a maximum annealing temperature of 300 °C avoids the degradation of surface stoichiometry associated with higher annealing temperatures. After AHC at a sample temperature of 100 °C, SRPES results show that all Sb oxides have been removed and only a small amount of Ga oxide remains. Further AHC treatment at 300 °C results in a clean surface with a sharp (1×3) low energy electron diffraction pattern. SRPES results indicate that the surface stoichiometry is identical to that previously found for GaSb(1 0 0)-(1×3) prepared by in situ molecular beam epitaxy. Electron energy-dependent HREEL spectra exhibit a coupled plasmon-phonon mode which has been used to study the electronic structure of the near-surface region. Semi-classical dielectric theory simulations of the HREEL spectra of the clean GaSb(1 0 0)-(1×3) surface indicate no detectable electronic damage or dopant passivation results from the AHC treatment. Valence band SRPES indicates that the surface Fermi level is close to the valence band maximum, suggesting the presence of an inversion layer at the surface.

  17. Finite Volumes Discretization of Topology Optimization Problems

    Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

    of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout...... such a mature and versatile technique for discretiz- ing partial dierential equations in the form of conservation laws of varying types. Advantages of FVMs include the simplicity of implementation, their local conservation properties, and the ease of coupling various PDEs in a multi-physics setting. In fact......, FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly...

  18. Chemical Reaction Optimization for Max Flow Problem

    Reham Barham

    2016-08-01

    Full Text Available This study presents an algorithm for MaxFlow problem using "Chemical Reaction Optimization algorithm (CRO". CRO is a recently established meta-heuristics algorithm for optimization, inspired by the nature of chemical reactions. The main concern is to find the best maximum flow value at which the flow can be shipped from the source node to the sink node in a flow network without violating any capacity constraints in which the flow of each edge remains within the upper bound value of the capacity. The proposed MaxFlow-CRO algorithm is presented, analyzed asymptotically and experimental test is conducted. Asymptotic runtime is derived theoretically. The algorithm is implemented using JAVA programming language. Results show a good performance with a complexity of O(I E2, for I iterations and E edges. The number of iterations I in the algorithm, is an important factor that will affect the results obtained. As number of iterations is increased, best possible max-Flow value is obtained.

  19. Mesh refinement strategy for optimal control problems

    Paiva, L. T.; Fontes, F. A. C. C.

    2013-10-01

    Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.

  20. 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.

  1. Optimization of Teaching Model“2 .5+1 .0+1 .0”%“2.5+1.0+0.5”教学模式的优化

    方月梅; 郭建林; 肖文胜

    2015-01-01

    This paper analyzes implementation situation of the teaching pattern"2.5 +1.0 +1.0"among the environmental engineering majors and the existing problems .Four proposals have been put forward as follows:simplifying the courses in Phase "2.5",selecting targeted courses;strengthening the cultivation on practical ability of the professional teachers;strengthening the communication between mentors and interns;making full use of off-campus practice bases and strengthening communication to establish benign interaction relation-ship.Optimizing teaching mode"2.5 +1.0 +1.0"can be more in line with the practical talent training mode.%分析了环境工程专业“2.5+1.0+0.5”教学模式的实施现状及存在的主要问题,并针对相关问题提出了4个方面的建议:精简“2.5”阶段的课程,课程选择应具有针对性;加强专业教师实践能力的培养;加强指导教师与实习学生之间的沟通交流;充分发挥校外实习基地的作用,形成良性互动关系。旨在对“2.5+1.0+0.5”教学模式进行优化,使之更加符合环境工程专业应用型人才培养的需要。

  2. SolveDB: Integrating Optimization Problem Solvers Into SQL Databases

    Siksnys, Laurynas; Pedersen, Torben Bach

    2016-01-01

    Many real-world decision problems involve solving optimization problems based on data in an SQL database. Traditionally, solving such problems requires combining a DBMS with optimization software packages for each required class of problems (e.g. linear and constraint programming) -- leading...... to workflows that are cumbersome, complex, inefficient, and error-prone. In this paper, we present SolveDB - a DBMS for optimization applications. SolveDB supports solvers for different problem classes and offers seamless data management and optimization problem solving in a pure SQL-based setting. This allows...... for much simpler and more effective solutions of database-based optimization problems. SolveDB is based on the 3-level ANSI/SPARC architecture and allows formulating, solving, and analysing solutions of optimization problems using a single so-called solve query. SolveDB provides (1) an SQL-based syntax...

  3. 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.

  4. Hierarchical control based on Hopfield network for nonseparable optimization problems

    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.

  5. About one problem of optimal stabilization of linear compound systems

    Barseghyan V.R.

    2014-12-01

    Full Text Available The problem of optimal stabilization of linear compound system is investigated. Based on Lyapunov function method the method of building optimal stabilizing control action is suggested. The solution of the problem of optimal stabilization of a concrete compound system is given.

  6. 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.

  7. 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.

  8. Immune Algorithm for Solving the Optimization Problems of Computer Communication Networks

    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.

  9. Algorithmic Aspects of Several Data Transfer Service Optimization Problems

    Andreica, Mugurel Ionut; Ionescu, Florin; Andreica, Cristina Teodora

    2009-01-01

    Optimized data transfer services are highly demanded nowadays, due to the large amounts of data which are frequently being produced and accessed. In this paper we consider several data transfer service optimization problems (optimal server location in path networks, optimal packet sequencing and minimum makespan packet scheduling), for which we provide novel algorithmic solutions.

  10. Particle Swarm Optimization with Genetic Operators for Vehicle Routing Problem

    P. V. PURANIK

    2012-07-01

    Full Text Available Vehicle Routing Problem (VRP is to find shortest route thereby minimizing total cost. VRP is a NP-hard and Combinatorial optimization problem. Such problems increase exponentially with the problem size. Various derivative based optimization techniques are employed for optimization. Derivative based optimization techniques are difficult to evaluate. Therefore parallel search algorithm emerged to solve VRP. In this work, a particle swarm optimization (PSO algorithm and Genetic algorithm (GA with crossover and mutation operator are applied to two typical functions to deal with the problem of VRP efficiently using MATLAB software. Before solving VRP, optimization of functions using PSO and GA are checked. In this paper capacitate VRP with time window (CVRPTW is proposed. The computational result shows generation of input for VRP, optimization of Rastrigin function, Rosenbrock function using PSO and GA.

  11. Usage of the particle swarm optimization in problems of mechanics

    Hajžman M.

    2016-06-01

    Full Text Available This paper deals with the optimization method called particle swarm optimization and its usage in mechanics. Basic versions of the method is introduced and several improvements and modifications are applied for better convergence of the algorithms. The performance of the optimization algorithm implemented in an original in-house software is investigated by means of three basic and one complex problems of mechanics. The goal of the first problem is to find optimal parameters of a dynamic absorber of vibrations. The second problem is about the tunning of eigenfrequencies of beam bending vibrations. The third problem is to optimize parameters of a clamped beam with various segments. The last complex problem is the optimization of a tilting mechanism with multilevel control. The presented results show that the particle swarm optimization can be efficiently used in mechanical tasks.

  12. Replica analysis for the duality of the portfolio optimization problem

    Shinzato, Takashi

    2016-11-01

    In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.

  13. some notes on discount factor restrictions for dynamic optimization problems

    Gerhard Sorger

    2008-01-01

    We consider dynamic optimization problems on one-dimensional state spaces. Un- der standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation between the size of the discount factor of the dynamic optimization problem on the one hand and the properties of the dynamical system xt+1 = h(xt) on the other hand. The purpose of this paper is to survey...

  14. 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.

  15. An Effective Hybrid Optimization Algorithm for Capacitated Vehicle Routing Problem

    2006-01-01

    Capacitated vehicle routing problem (CVRP) is an important combinatorial optimization problem. However, it is quite difficult to achieve an optimal solution with the traditional optimization methods owing to the high computational complexity. A hybrid algorithm was developed to solve the problem, in which an artificial immune clonal algorithm (AICA) makes use of the global search ability to search the optimal results and simulated annealing (SA) algorithm employs certain probability to avoid becoming trapped in a local optimum. The results obtained from the computational study show that the proposed algorithm is a feasible and effective method for capacitated vehicle routing problem.

  16. The Model for Two-dimensional Layout Optimization Problem with Performance Constraints and Its Optimality Function

    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.

  17. 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

  18. 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...

  19. 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.

  20. A weak Hamiltonian finite element method for optimal control problems

    Hodges, Dewey H.; Bless, Robert R.

    1990-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  1. Weak Hamiltonian finite element method for optimal control problems

    Hodges, Dewey H.; Bless, Robert R.

    1991-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  2. Solving semi-infinite optimization problems with interior point techniques

    Stein, Oliver; Still, Georg

    2003-01-01

    We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads

  3. The study of cuckoo optimization algorithm for production planning problem

    Akbarzadeh, Afsane; Shadkam, Elham

    2015-01-01

    Constrained Nonlinear programming problems are hard problems, and one of the most widely used and common problems for production planning problem to optimize. In this study, one of the mathematical models of production planning is survey and the problem solved by cuckoo algorithm. Cuckoo Algorithm is efficient method to solve continues non linear problem. Moreover, mentioned models of production planning solved with Genetic algorithm and Lingo software and the results will compared. The Cucko...

  4. Quadratic 0-1 programming: Geometric methods and duality analysis

    Liu, Chunli

    The unconstraint quadratic binary problem (UBQP), as a classical combinatorial problem, finds wide applications in broad field and human activities including engineering, science, finance, etc. The NP-hardness of the combinatorial problems makes a great challenge to solve the ( UBQP). The main purpose of this research is to develop high performance solution method for solving (UBQP) via the geometric properties of the objective ellipse contour and the optimal solution. This research makes several contributions to advance the state-of-the-art of geometric approach of (UBQP). These contributions include both theoretical and numerical aspects as stated below. In part I of this dissertation, certain rich geometric properties hidden behind quadratic 0-1 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0-1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0-1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results. In part II of this dissertation, we present new results of the duality gap between the binary quadratic optimization problem and its Lagrangian dual. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the problem. We then characterize the zeroness of duality gap by the distance, delta, between the binary set and certain affine space C. Finally, we discuss a computational procedure of the distance delta. These results provide new insights into the duality gap and polynomial solvability of binary quadratic optimization problems.

  5. Metaheuristic Optimization: Algorithm Analysis and Open Problems

    2012-01-01

    Metaheuristic algorithms are becoming an important part of modern optimization. A wide range of metaheuristic algorithms have emerged over the last two decades, and many metaheuristics such as particle swarm optimization are becoming increasingly popular. Despite their popularity, mathematical analysis of these algorithms lacks behind. Convergence analysis still remains unsolved for the majority of metaheuristic algorithms, while efficiency analysis is equally challenging. In this paper, we i...

  6. An optimization approach for the satisfiability problem

    S. Noureddine

    2015-01-01

    Full Text Available We describe a new approach for solving the satisfiability problem by geometric programming. We focus on the theoretical background and give details of the algorithmic procedure. The algorithm is provably efficient as geometric programming is in essence a polynomial problem. The correctness of the algorithm is discussed. The version of the satisfiability problem we study is exact satisfiability with only positive variables, which is known to be NP-complete.

  7. Applications of Fitzpatrick functions for solving optimization problems

    Nashed, Z.; Raykov, I.

    2012-10-01

    This paper presents applications of Fitzparick functions to optimization problems. The main purpose of the present work is to introduce applications of the Fitzpatrick functions, involving their specific properties as the maximal monotonicity, or the proper, convex and lower semi-continuity, for solving optimization problems.

  8. Applications of Fitzpatrick functions for solving optimization problems II

    Nashed, Z.; Raykov, I.

    2015-10-01

    This paper is a continuation of the paper [8] and presents more applications of Fitzpatrick functions for solving optimization problems. The main purpose of the present work is to introduce some new properties of Fitzpatrick functions useful for solving optimization problems, using also their already presented specific properties, as the maximal monotonicity, proper, convex and lower semi-continuity.

  9. Optimization problems for fast AAM fitting in-the-wild

    Tzimiropoulos, Georgios; Pantic, Maja

    2013-01-01

    We describe a very simple framework for deriving the most-well known optimization problems in Active Appearance Models (AAMs), and most importantly for providing efficient solutions. Our formulation results in two optimization problems for fast and exact AAM fitting, and one new algorithm which has

  10. 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 prov...

  11. 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.

  12. 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.

  13. Optimal Component Lumping: problem formulation and solution techniques

    Lin, Bao; Leibovici, Claude F.; Jørgensen, Sten Bay

    2008-01-01

    to determine the lumping scheme. Given an objective function defined with a linear weighting rule, an optimal lumping problem is formulated as a mixed integer nonlinear programming (MINLP) problem both in discrete and in continuous settings. A reformulation of the original problem is also presented, which...... significantly reduces the number of independent variables. The application to a system with 144 components demonstrates that the optimal lumping problem can be efficiently solved with a stochastic optimization method, Tabu Search (TS) algorithm. The case study also reveals that the discrete formulation...

  14. Attractive and Repulsive Particle Swarm Optimization and Random Virus Algorithm for Solving Reactive Power Optimization Problem

    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.

  15. OPTIMIZATION OF CAPACITATED VEHICLE ROUTING PROBLEM USING PSO

    S.R.VENKATESAN

    2011-10-01

    Full Text Available This paper presents solution techniques for Capacitated Vehicle Routing Problem (CVRP using metaheuristics. Capacitated Vehicle Routing Problem is divided into set of customers called cluster, and find optimum travel distance of vehicle route. The CVRP is a combinatorial optimization problem; particle swarm optimization(PSO technique is adapted in this paper to solve this problem. The main problem is divided into subprograms/clusters and each subprogram is treated as travelling salesman problem and solved by usingparticle swarm optimization techniques (PSO. This paper presents a sweep, Clark and wright algorithm to form the clusters. This model is then solved by using a particle swarm optimization (PSO method to find optimum travel distance of vehicle route. Our analysis suggests that the proposed model enables users to establish route to serve all given customers with minimum distance of vehicles and maximum capacity.

  16. Improved Ant Colony Optimization for Seafood Product Delivery Routing Problem

    Baozhen Yao

    2014-02-01

    Full Text Available This paper deals with a real-life vehicle delivery routing problem, which is a seafood product delivery routing problem. Considering the features of the seafood product delivery routing problem, this paper formulated this problem as a multi-depot open vehicle routing problem. Since the multi-depot open vehicle routing problem is a very complex problem, a method is used to reduce the complexity of the problem by changing the multi-depot open vehicle routing problem into an open vehicle routing problem with a dummy central depot in this paper. Then, ant colony optimization is used to solve the problem. To improve the performance of the algorithm, crossover operation and some adaptive strategies are used. Finally, the computational results for the benchmark problems of the multi-depot vehicle routing problem indicate that the proposed ant colony optimization is an effective method to solve the multi-depot vehicle routing problem. Furthermore, the computation results of the seafood product delivery problem from Dalian, China also suggest that the proposed ant colony optimization is feasible to solve the seafood product delivery routing problem.

  17. Unconstrained Optimization Reformulations of Equilibrium Problems

    Li Ping ZHANG; Ji Ye HAN

    2009-01-01

    We generalize the D-gap function developed in the literature for variational inequalities to a general equilibrium problem (EP). Through the D-gap function,the equilibrium problem is cast as an unconstrained minimization problem. We give conditions under which any stationary point of the D-gap function is a solution of EP and conditions under which it provides a global error bound for EP. Finally,these results are applied to box-constrained EP and then weaker conditions are established to obtain the desired results for box-constrained EP.

  18. Problem optimalnih kartografskih projekcija : Problem of the optimal cartographic projections

    Krešimir Frankić

    2014-12-01

    Full Text Available Kartografske projekcije primjenjuju se za grafičko prikazivanje teritorija u sitnom mjerilu. Pravilnim izborom projekcije smanjuju se deformacije prikazanog teritorija, koji je omeđen graničnom linijom. U većini slučajeva ta granična linija nije neka matematički definirana krivulja, koja se najlakše prikazuje u obliku zatvorenog poligona. Optimalne kartografske projekcije, slijedeći neki definirani kriterij, trebale bi utvrditi konstante projekcije s najmanjim mogućim deformacijama. Airy-Kavrajski kriterij vodi direktno do optimizacije Euklidske norme, a to znači do metode najmanjih kvadrata. Brzi moderni kompjutori omogućuju jednostavnu optimizaciju bilo koje analitički definirane projekcije za teritorije čija granica se aproksimira konačnim nizom individualnih točaka. : Cartographic projections are basis for the graphical representation of various territories in small scale mapping. Proper selection of projection reduces the deformation of the presented territory, which is bounded by a boundary line. In most cases, this border line is not a mathematically defined curve, which is most easily displayed in the form of a closed polygon. The optimal cartographic projections based on a selected criterion of quality are those whose constants lead to the smallest value of the criterion. In the presented work it is recommended to use Airy-Kavrajski criterion whose minimization is actually minimization of the second Euclidean norm. The solution of optimal projections of various classes is reduced to the method of least squares. Fast modern computers enable the optimization of an arbitrary territory by evaluating the selected criterion in a finite number of points.

  19. 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.

  20. Moments of random sums and Robbins' problem of optimal stopping

    Gnedin, Alexander

    2011-01-01

    Robbins' problem of optimal stopping asks one to minimise the expected {\\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\\it value} of the stopped variable under the rule optimal in the sense of the rank, by embedding the problem in a much more general context of selection problems with the nonanticipation constraint lifted, and with the payoff growing like a power function of the rank.

  1. Optimization Problems in Supply Chain Management

    D. Romero Morales (Dolores)

    2000-01-01

    textabstractMaria Dolores Romero Morales was born on Augustus 5th, 1971, in Sevilla (Spain). She studied Mathematics at University of Sevilla from 1989 to 1994 and specialized in Statistics and Operations Research. She wrote her Master's thesis on Global Optimization in Location Theory under the sup

  2. Improved extremal optimization for the asymmetric traveling salesman problem

    Chen, Yu-Wang; Zhu, Yao-Jia; Yang, Gen-Ke; Lu, Yong-Zai

    2011-11-01

    This paper presents an improved extremal optimization (IEO) algorithm for solving the asymmetric traveling salesman problem (ATSP). At each update step, the IEO algorithm proceeds through two main steps: extremal dynamics and cooperative optimization. As an improvement of extremal optimization (EO), the IEO provides a general combinatorial optimization framework by emphasizing the step of cooperative optimization. In the paper, an effective cooperative optimization strategy with combination of greedy search and random walk is designed in terms of the microscopic characteristics of the ATSP solutions. Simulation results on a set of benchmark ATSP instances show that the proposed IEO algorithm provides satisfactory performance on computational effectiveness and efficiency.

  3. Optimal control problems related to the navigation channel engineering

    朱江; 曾庆存; 郭冬建; 刘卓

    1997-01-01

    The navigation channel engineering poses optimal control problems of how to find the optimal way of engineering such that the water depth of the channel is maximum under certain budget constraint, or the cost of me en-gineering is minimum while certain goals are achieved. These are typical control problems of distributed system gov erned by hydraulic/sedimentation models. The problems and methods of solutions are discussed Since the models, usually complicated, are nonlinear, they can be solved by solving a series of linear problems For linear problems the solutions are given. Thus the algorithms are simplified.

  4. The Uniqueness of Optimal Solution for Linear Programming Problem

    QuanlingWei; HongYan; JunWang

    2004-01-01

    This paper investigates an old problem in operations research, the uniqueness of the optimal solution to a linear programming problem. We discuss the problem on a general polyhedron, give some equivalent conditions for uniqueness testing. In addition, we discuss the implementation issues for linear programming based decision making procedures,which motivated this research.

  5. 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.

  6. Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems

    Vázquez, Luis

    2013-01-01

    Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems explores how Newton's equation for the motion of one particle in classical mechanics combined with finite difference methods allows creation of a mechanical scenario to solve basic problems in linear algebra and programming. The authors present a novel, unified numerical and mechanical approach and an important analysis method of optimization. This book also: Presents mechanical method for determining matrix singularity or non-independence of dimension and complexity Illustrates novel mathematical applications of classical Newton’s law Offers a new approach and insight to basic, standard problems Includes numerous examples and applications Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems is an ideal book for undergraduate and graduate students as well as researchers interested in linear problems and optimization, and nonlinear dynamics.      

  7. 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...

  8. Optimality conditions for the numerical solution of optimization problems with PDE constraints :

    Aguilo Valentin, Miguel Alejandro; Ridzal, Denis

    2014-03-01

    A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.

  9. A Numerical Embedding Method for Solving the Nonlinear Optimization Problem

    田保锋; 戴云仙; 孟泽红; 张建军

    2003-01-01

    A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.

  10. Checking for Optimal Solutions in Some NP-Complete Problems

    Bauer, Michel; Orland, Henri

    2005-09-01

    For some weighted NP-complete problems, checking whether a proposed solution is optimal is a nontrivial task. Such is the case for the traveling salesman problem, or the spin-glass problem in three dimensions. In this Letter, we consider the weighted tripartite matching problem, a well known NP-complete problem. We write mean-field finite temperature equations for this model and derive their zero temperature limit. We show that any solution of the zero temperature equations provides an exact absolute ground state of the system. As a consequence, we propose a criterion which can be checked in polynomial time, and such that given a putative optimal solution, if the criterion is satisfied, then the solution is indeed optimal. This criterion is generalized to a class of variants of the multiple traveling salesmen problems.

  11. Optimal Opinion Control: The Campaign Problem

    2015-01-01

    Opinion dynamics is nowadays a very common field of research. In this article we formulate and then study a novel, namely strategic perspective on such dynamics: There are the usual normal agents that update their opinions, for instance according the well-known bounded confidence mechanism. But, additionally, there is at least one strategic agent. That agent uses opinions as freely selectable strategies to get control on the dynamics: The strategic agent of our benchmark problem tries, during...

  12. Optimization problems related to zigzag pocket machining

    Arkin, E.M.; Held, M.; Smith, C.L. [State Univ. of New York, Stony Brook, NY (United States)

    1996-12-31

    A fundamental problem of manufacturing is to produce mechanical parts from billets by clearing areas within specified boundaries from the material. Based on a graph-theoretical formulation, the algorithmic handling of one particular machining problem {open_quote}zigzag pocket machining{close_quote} is investigated. We present a linear-time algorithm that ensures that no region of the pocket is machined repeatedly, thereby attempting to minimize the number of tool retractions required. This problem is shown to be NP-hard for pockets with holes. Our algorithm is a provable good in the sense that the machining path generated for a pocket with h holes requires at most 5. OPT+ 6 - h retractions, where OPT is the (unknown) minimum number of retractions required by any algorithm. The algorithm has been implemented, and practical tests for pockets without holes clearly showed that one can expect an approximation factor of about 1.5 for practical examples, rather than the factor 5 as proved by our analysis.

  13. Gradient Gene Algorithm: a Fast Optimization Method to MST Problem

    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.

  14. Comparison of optimal design methods in inverse problems

    Banks, H. T.; Holm, K.; Kappel, F.

    2011-07-01

    Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).

  15. On two formulations of an optimal insulation problem

    Munoz, Eduardo; Allaire, Gregoire; Bendsøe, Martin P.

    2007-01-01

    ; this 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......Two formulations for the design of the optimal insulation of a domain are investigated by computational means. The results illustrate the similarities and differences that result from the two approaches. One method is in the format of a topology design problem of distributing insulating material...... in a domain surrounding a non-design domain that is heated by a given heat-source; this problem is treated in both a relaxed format as well as a penalized material format. The other approach deals with the optimal distribution of a thin layer of insulation on the boundary of the non-design domain...

  16. Topology optimization of vibration and wave propagation problems

    Jensen, Jakob Søndergaard

    2007-01-01

    The method of topology optimization is a versatile method to determine optimal material layouts in mechanical structures. The method relies on, in principle, unlimited design freedom that can be used to design materials, structures and devices with significantly improved performance and sometimes...... novel functionality. This paper addresses basic issues in simulation and topology design of vibration and wave propagation problems. Steady-state and transient wave propagation problems are addressed and application examples for both cases are presented....

  17. Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems

    Zuliang Lu

    2011-01-01

    We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element ...

  18. Modified constrained differential evolution for solving nonlinear global optimization problems

    2013-01-01

    Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolut...

  19. Existence and approximation results for shape optimization problems in rotordynamics

    Strauß, Frank; Heuveline, Vincent; Schweizer, Ben

    2006-01-01

    We consider a shape optimization problem in rotordynamics where the mass of a rotor is minimized subject to constraints on the natural frequencies. Our analysis is based on a class of rotors described by a Rayleigh beam model including effects of rotary inertia and gyroscopic moments. The solution of the equation of motion leads to a generalized eigenvalue problem. The governing operators are non-symmetric due to the gyroscopic terms. We prove the existence of solutions for the optimization p...

  20. Fuzzy Inspired Hybrid Genetic Approach to Optimize Travelling Salesman Problem

    Bindu

    2012-06-01

    Full Text Available One of the category of algorithm Problems are basically exponential problems. These problems are basically exponential problems and take time to find the solution. In the present work we are optimising one of the common NP complete problem called Travelling Salesman Problem. In our work we have defined a genetic approach by combining fuzzy approach along with genetics. In this work we have implemented the modified DPX crossover to improve genetic approach. The work is implemented in MATLAB environment and obtained results shows the define approach has optimized the existing genetic algorithm results

  1. CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS

    WU Zhiyou; ZHANG Liansheng; BAI Fusheng; YANG Xinmin

    2004-01-01

    In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function,then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. Programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C. Programming problem using the existing algorithms about them.

  2. Test problem construction for single-objective bilevel optimization.

    Sinha, Ankur; Malo, Pekka; Deb, Kalyanmoy

    2014-01-01

    In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization. The construction procedure is flexible and allows its user to control the different complexities that are to be included in the test problems independently of each other. In addition to properties that control the difficulty in convergence, the procedure also allows the user to introduce difficulties caused by interaction of the two levels. As a companion to the test problem construction framework, the paper presents a standard test suite of 12 problems, which includes eight unconstrained and four constrained problems. Most of the problems are scalable in terms of variables and constraints. To provide baseline results, we have solved the proposed test problems using a nested bilevel evolutionary algorithm. The results can be used for comparison, while evaluating the performance of any other bilevel optimization algorithm. The code related to the paper may be accessed from the website http://bilevel.org .

  3. A Decision Support System for Solving Multiple Criteria Optimization Problems

    Filatovas, Ernestas; Kurasova, Olga

    2011-01-01

    In this paper, multiple criteria optimization has been investigated. A new decision support system (DSS) has been developed for interactive solving of multiple criteria optimization problems (MOPs). The weighted-sum (WS) approach is implemented to solve the MOPs. The MOPs are solved by selecting different weight coefficient values for the criteria…

  4. Comments on `A discrete optimal control problem for descriptor systems'

    Ravn, Hans

    1990-01-01

    In the above-mentioned work (see ibid., vol.34, p.177-81 (1989)), necessary and sufficient optimality conditions are derived for a discrete-time optimal problem, as well as other specific cases of implicit and explicit dynamic systems. The commenter corrects a mistake and demonstrates that there ...

  5. 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...

  6. Robust mixed 0-1 polynomial programming%鲁棒混合0-1多项式规划

    张建科

    2011-01-01

    针对含误差数据的混合0-1多项式优化问题,给出一种鲁棒优化方法,以提高其最优解的鲁棒性。该方法先将原问题转化为混合0-1线性规划,并在最坏情况下给出混合0-1线性规划的鲁棒对应模型,随后利用该鲁棒对应模型求解原优化问题。数值试验表明,该方法所求出的最优解具有良好的鲁棒性。%Considering that the data of a mixed 0-1 polynomial optimization problem are with error, a robust optimization method is proposed to improve the robustness of the problem's optimal solution. By the proposed method, the original problem is transformed into a missed 0-1 linear programming model firstly, then, in the worst case, a robust optimization counterpart is put forward, and finally, based on this corresponding robust optimization counterpart, the original problem can be solved. Numerical experiments show that the optimal solution worked out in this way is of good robustness.

  7. Optimal Solutions for the Temporal Precedence Problem

    Brodal, Gerth Stølting; Makris, Christos; Sioutas, Spyros;

    2002-01-01

    a in the structure, while the operation precedes (a,b) returns true iff element a was inserted before element b temporally. In [11] a solution was provided to the problem with worst-case time complexity O (log log n ) per operation and O(n log log n) space, where n is the number of elements inserted. It was also...... demonstrated that the precedes operation has a lower bound of Ω (log log n ) for the Pure Pointer Machine model of computation. In this paper we present two simple solutions with linear space and worst-case constant insertion time. In addition, we describe two algorithms that can handle the precedes (a...

  8. Phase optimization problems applications in wave field theory

    Bulatsyk, Olena O; Topolyuk, Yury P; Bulatsyk, Olena; Voitovich, Nikolai N

    2010-01-01

    This is the only book available in English language to consider inverse and optimization problems in which phase field distributions are used as optimizing functions. The mathematical technique used relates to nonlinear integral equations, with numerical methods developed and applied to concrete problems. Written by a team of outstanding and renowned experts in the field, this monograph will appeal to all those dealing with the investigation, design, and optimization of electromagnetic and acoustic radiating and transmitting devices and systems, while also being of interest to mathematicians w

  9. Upper Hölder continuity of parametric vector optimization problems

    Xian-Fu Hu

    2016-11-01

    Full Text Available Abstract This paper is concerned with upper Hölder continuity and Hölder calmness of a perturbed vector optimization problem. We establish some new sufficient conditions for upper Hölder continuity and Hölder calmness of the perturbed solution mappings and the perturbed optimal value mappings of a vector optimization problem under the case that the objective function and the feasible set are, respectively, perturbed by parameters. Our results generalize and extend the corresponding ones of Li and Li (Appl. Math. Comput. 232:908-918, 2014.

  10. 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.

  11. 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.

  12. Reverse convex problems: an approach based on optimality conditions

    Ider Tseveendorj

    2006-01-01

    We present some results concerning reverse convex problems. Global optimality conditions for the problems with a nonsmooth reverse convex constraint are established and convergence of an algorithm in the case of linear program with an additional quadratic reverse convex constraint is studied.

  13. Moments of random sums and Robbins' problem of optimal stopping

    Gnedin, A.V.; Iksanov, A.

    2011-01-01

    Robbins' problem of optimal stopping is that of minimising the expected rank of an observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the value of the stopped variable under the rule that yields the minimal expected rank, by embedding the problem in a much mor

  14. Study of optimal control problems for hybrid dynamical systems

    Gao Rui; Wang Lei; Wang Yuzhen

    2006-01-01

    From the viewpoint of continuous systems, optimal control problem is proposed for a class of controlled Hybrid dynamical systems. Then a mathematical method- HDS minimum principle is put forward, which can solve the above problem. The HDS minimum principle is proved by means of Ekeland's variational principle.

  15. AN ALGORITHM FOR CONTINUOUS TYPE OPTIMAL SPHERICALFACILITY LOCATION PROBLEM

    ZHANG Liping; WANG Changyu

    1999-01-01

    In this paper, we study the continuously spherical facilitylocation problem.(P)(minx∈S∫∫(x)=Ωφ(υ)cos-1(υTx)dΩ) We prove a hull property and optimality condition of the problem (P), andpropose an algorithm to solve (P). Global convergence is proved.

  16. 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.

  17. Multiplier methods for optimization problems with Lipschitzian derivatives

    Izmailov, A. F.; Kurennoy, A. S.

    2012-12-01

    Optimization problems for which the objective function and the constraints have locally Lipschitzian derivatives but are not assumed to be twice differentiable are examined. For such problems, analyses of the local convergence and the convergence rate of the multiplier (or the augmented Lagrangian) method and the linearly constraint Lagrangian method are given.

  18. Topology optimization for acoustic-structure interaction problems

    Yoon, Gil Ho; Jensen, Jakob Søndergaard; Sigmund, Ole

    2006-01-01

    We propose a gradient based topology optimization algorithm for acoustic-structure (vibro-acoustic) interaction problems without an explicit interfacing boundary representation. In acoustic-structure interaction problems, the pressure field and the displacement field are governed by the Helmholtz...

  19. OPTIMAL THICKNESS OF A CYLINDRICAL SHELL - AN OPTIMAL CONTROL PROBLEM IN LINEAR ELASTICITY THEORY

    Peter Nestler

    2013-01-01

    Full Text Available In this paper we discuss optimization problems for cylindrical tubeswhich are loaded by an applied force. This is a problem of optimal control in linear elasticity theory (shape optimization. We are looking for an optimal thickness minimizing the deflection (deformation of the tube under the influence of an external force. From basic equations of mechanics, we derive the equation of deformation. We apply the displacement approach from shell theory and make use of the hypotheses of Mindlin and Reissner. A corresponding optimal control problem is formulated and first order necessary conditions for the optimal solution (optimal thickness are derived. We present numerical examples which were solved by the finite element method.

  20. Fuzzy Multiobjective Reliability Optimization Problem of Industrial Systems Using Particle Swarm Optimization

    Harish Garg

    2013-01-01

    systems by utilizing uncertain, limited, and imprecise data. In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting objectives. Moreover, data collected or available for the systems are vague, ambiguous, qualitative, and imprecise in nature due to various practical constraints and hence create some difficulties in optimizing the design problems. To handle these problems, this work presents an interactive method for solving the fuzzy multiobjective optimization decision-making problem, which can be used for the optimization decision making of the reliability with two or more objectives. Based on the preference of the decision makers toward the objectives, fuzzy multi-objective optimization problem is converted into crisp optimization problem and then solved with evolutionary algorithm. The proposed approach has been applied to the decomposition unit of a urea fertilizer plant situated in the northern part of India producing 1500–2000 metric tons per day.

  1. Examining the Bernstein global optimization approach to optimal power flow problem

    Patil, Bhagyesh V.; Sampath, L. P. M. I.; Krishnan, Ashok; Ling, K. V.; Gooi, H. B.

    2016-10-01

    This work addresses a nonconvex optimal power flow problem (OPF). We introduce a `new approach' in the context of OPF problem based on the Bernstein polynomials. The applicability of the approach is studied on a real-world 3-bus power system. The numerical results obtained with this new approach for a 3-bus system reveal a satisfactory improvement in terms of optimality. The results are found to be competent with generic global optimization solvers BARON and COUENNE.

  2. Mathematical programming methods for large-scale topology optimization problems

    Rojas Labanda, Susana

    , and at the same time, reduce the number of function evaluations. Nonlinear optimization methods, such as sequential quadratic programming and interior point solvers, have almost not been embraced by the topology optimization community. Thus, this work is focused on the introduction of this kind of second...... 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...... structure of the problem. In both solvers, information of the exact Hessian is considered. A robust iterative method is implemented to efficiently solve large-scale linear systems. Both TopSQP and TopIP have successful results in terms of convergence, number of iterations, and objective function values...

  3. 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.

  4. Solving the Travelling Salesman Problem Using the Ant Colony Optimization

    Zuzana Čičková

    2011-12-01

    Full Text Available In this article, we study a possibility of solving the well-known Travelling Salesman Problem (TSP, which ranges among NP-hard problems, and offer a theoretical overview of some methods used for solving this problem. We discuss the Ant Colony Optimization (ACO, which belongs to the group of evolutionary techniques and presents the approach used in the application of ACO to the TSP. We study the impact of some control parameters by implementing this algorithm. The quality of the solution is compared with the optimal solution.

  5. 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 deform......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...... by topology optimization in order to optimize the performance of a shock absorber and test the pressure loading capabilities and optimization of an internally pressurized lid. © 2013 Published by Elsevier B.V....

  6. A Global Optimization Algorithm for Sum of Linear Ratios Problem

    Yuelin Gao

    2013-01-01

    Full Text Available We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

  7. 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.

  8. Open Vehicle Routing Problem by Ant Colony Optimization

    Er. Gurpreet Singh

    2014-01-01

    Full Text Available Vehicle routing problem (VRP is real-world combinatorial optimization problem which determine the optimal route of a vehicle. Generally, toprovide the efficientvehicle serving to the customer through different services by visiting the number of cities or stops. The VRP follows the Travelling Salesman Problem (TSP, in which each of vehicle visiting a set of cities such that every city is visited by exactly one vehicle only once. This work proposes the Ant Colony Optimization (ACO-TSP algorithm to eliminate the tour loop for Open Vehicle routing Problem (OVRP. A key aspect of this algorithm is to plan the routes of buses that must pick up and deliver the school students from various bus stops on time, especially in the case of far distance covered by the vehicle in a rural area and find out the efficient and safe vehicle route.

  9. TSP based Evolutionary optimization approach for the Vehicle Routing Problem

    Kouki, Zoulel; Chaar, Besma Fayech; Ksouri, Mekki

    2009-03-01

    Vehicle Routing and Flexible Job Shop Scheduling Problems (VRP and FJSSP) are two common hard combinatorial optimization problems that show many similarities in their conceptual level [2, 4]. It was proved for both problems that solving techniques like exact methods fail to provide good quality solutions in a reasonable amount of time when dealing with large scale instances [1, 5, 14]. In order to overcome this weakness, we decide in the favour of meta heuristics and we focalize on evolutionary algorithms that have been successfully used in scheduling problems [1, 5, 9]. In this paper we investigate the common properties of the VRP and the FJSSP in order to provide a new controlled evolutionary approach for the CVRP optimization inspired by the FJSSP evolutionary optimization algorithms introduced in [10].

  10. Optimal vehicle planning and the search tour problem

    Wettergren, Thomas A.; Bays, Matthew J.

    2016-05-01

    We describe a problem of optimal planning for unmanned vehicles and illustrate two distinct procedures for its solution. The problem under consideration, which we refer to as the search tour problem, involves the determination of multi-stage plans for unmanned vehicles conducting search operations. These types of problems are important in situations where the searcher has varying performance in different regions throughout the domain due to environmental complexity. The ability to provide robust planning for unmanned systems under difficult environmental conditions is critical for their use in search operations. The problem we consider consists of searches with variable times for each of the stages, as well as an additional degree of freedom for each stage to select from one of a finite set of operational configurations. As each combination of configuration and stage time leads to a different performance level, there is a need to determine the optimal configuration of these stages. When the complexity of constraints on total time, as well as resources expended at each stage for a given configuration, are added, the problem becomes one of non-trivial search effort allocation and numerical methods of optimization are required. We show two solution approaches for this numerical optimization problem. The first solution technique is to use a mixed-integer linear programming formulation, for which commercially available solvers can find optimal solutions in a reasonable amount of time. We use this solution as a baseline and compare against a new inner/outer optimization formulation. This inner/outer optimization compares favorably to the baseline solution, but is also amenable to adaptation as the search operation progresses. Numerical examples illustrate the utility of the approach for unmanned vehicle search planning.

  11. 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.

  12. Lessons Learned During Solutions of Multidisciplinary Design Optimization Problems

    Patnaik, Suna N.; Coroneos, Rula M.; Hopkins, Dale A.; Lavelle, Thomas M.

    2000-01-01

    Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. During solution of the multidisciplinary problems several issues were encountered. This paper lists four issues and discusses the strategies adapted for their resolution: (1) The optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. (2) Optimum solutions obtained were infeasible for aircraft and air-breathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. (3) Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. (4) The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through six problems: (1) design of an engine component, (2) synthesis of a subsonic aircraft, (3) operation optimization of a supersonic engine, (4) design of a wave-rotor-topping device, (5) profile optimization of a cantilever beam, and (6) design of a cvlindrical shell. The combined effort of designers and researchers can bring the optimization method from academia to industry.

  13. 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.

  14. Reactive Robustness and Integrated Approaches for Railway Optimization Problems

    Haahr, Jørgen Thorlund

    Solving Competition", where a freight yard optimization problem was considered. The second junior (PhD) prize was awared for the work performed in the \\ROADEF/EURO Challenge 2014: Trains don't vanish!", where the planning of rolling stock movements at a large station was considered. An honorable mention......Planning railway operations is not a simple task as it entails solving multiple interdependent optimization problems. These problems have been subject to study in the literature for the last few decades, and are still profoundly researched. The robustness of a plan or schedule denotes the ability...... a disruption the updated timetable may be impossible to realize due to the lack of rolling stock units at certain positions. It is important to avoid creating problems for later or subsequent planning stages. Several railway problems are studied in this thesis. The main contributions are summarized...

  15. A coherent Ising machine for 2000-node optimization problems

    Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki

    2016-11-01

    The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

  16. 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.

  17. Global optimization over linear constraint non-convex programming problem

    ZHANG Gui-Jun; WU Ti-Huan; YE Rong; YANG Hai-qing

    2005-01-01

    A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programmin g problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.

  18. 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...

  19. 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.

  20. The coral reefs optimization algorithm: a novel metaheuristic for efficiently solving optimization problems.

    Salcedo-Sanz, S; Del Ser, J; Landa-Torres, I; Gil-López, S; Portilla-Figueras, J A

    2014-01-01

    This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems.

  1. Ant colony optimization for solving university facility layout problem

    Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin

    2013-04-01

    Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ≤ 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).

  2. 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 ...

  3. 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...... optimization tool for micro fluidic design problems by considering design of energy efficient devices subjected to Stokes flow. Several researchers have elaborated on [2], however, this research has focused on 2D fluid modelling which limits the practical impact of the computed designs. This limitation...

  4. 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...

  5. Adaptive double chain quantum genetic algorithm for constrained optimization problems

    Kong Haipeng

    2015-02-01

    Full Text Available 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 convergence 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.

  6. 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.

  7. 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.

  8. Optimal Control Problems for Partial Differential Equations on Reticulated Domains

    Kogut, Peter I

    2011-01-01

    In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for gradu

  9. On the Optimal Controller for LTV Measurement Feedback Control Problem

    Ting GONG; Yu Feng LU

    2011-01-01

    In this paper, we consider the measurement feedback control problem for discrete linear time-varying systems within the framework of nest algebra consisting of causal and bounded linear operators. Based on the inner-outer factorization of operators, we reduce the control problem to a distance from a certain operator to a special subspace of a nest algebra and show the existence of the optimal LTV controller in two different ways: one via the characteristic of the subspace in question directly, the other via the duality theory. The latter also gives a new formula for computing the optimal cost.

  10. An Improved Particle Swarm Optimization for Traveling Salesman Problem

    Liu, Xinmei; Su, Jinrong; Han, Yan

    In allusion to particle swarm optimization being prone to get into local minimum, an improved particle swarm optimization algorithm is proposed. The algorithm draws on the thinking of the greedy algorithm to initialize the particle swarm. Two swarms are used to optimize synchronously. Crossover and mutation operators in genetic algorithm are introduced into the new algorithm to realize the sharing of information among swarms. We test the algorithm with Traveling Salesman Problem with 14 nodes and 30 nodes. The result shows that the algorithm can break away from local minimum earlier and it has high convergence speed and convergence ratio.

  11. Topology optimization problems for reflection and dissipation of elastic waves

    Jensen, Jakob Søndergaard

    2007-01-01

    This paper is devoted to topology optimization problems for elastic wave propagation. The objective of the study is to maximize the reflection or the dissipation in a finite slab of material for pressure and shear waves in a range of frequencies. The optimized designs consist of two or three...... material phases: a host material and scattering and/or absorbing inclusions. The capabilities of the optimization algorithm are demonstrated with two numerical examples in which the reflection and dissipation of ground-borne wave pulses are maximized....

  12. 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.

  13. Optimal Results and Numerical Simulations for Flow Shop Scheduling Problems

    Tao Ren

    2012-01-01

    Full Text Available This paper considers the m-machine flow shop problem with two objectives: makespan with release dates and total quadratic completion time, respectively. For Fm|rj|Cmax, we prove the asymptotic optimality for any dense scheduling when the problem scale is large enough. For Fm‖ΣCj2, improvement strategy with local search is presented to promote the performance of the classical SPT heuristic. At the end of the paper, simulations show the effectiveness of the improvement strategy.

  14. 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.

  15. MNP:A Class of NP Optimization Problems

    程歧; 朱洪

    1997-01-01

    A large class of NP optimization problems called MNP are studied.It is shown that Rmax(2)is in this class and some problems which are not likely in Rmax(2) are in this class.A new kind of reductions,SL-reductions,is defined to preserve approximability and nonapproximability,so it is a more general version of L-reductions and A-reductions.Then some complete problems of this class under SL-reductions are shown and it is proved that the max-clique problem is one of them.So all complete problems in this class are as difficult to approximate as the max-clique problem.

  16. Nonconvex continuous models for combinatorial optimization problems with application to satisfiability and node packing problems

    Warners, J.P.

    1997-01-01

    We show how a large class of combinatorial optimization problems can be reformulated as a nonconvex minimization problem over the unit hyper cube with continuous variables. No additional constraints are required; all constraints are incorporated in the n onconvex objective function, which is a polyn

  17. Trajectory and Population Metaheuristics applied to Combinatorial Optimization Problems

    Natalia Alancay

    2016-04-01

    Full Text Available In the world there are a multitude of everyday problems that require a solution that meets a set of requirements in the most appropriate way maximizing or minimizing a certain value. However, finding an optimal solution for certain optimization problems can be an incredibly difficult or an impossible task. This is because when a problem becomes large enough, we have to look through a huge number of possible solutions, the most efficient solution, that is, the one that has the lower cost. The ways to treat feasible solutions for their practical application are varied. One of the strategy that has gained a great acceptance and that has been getting an important formal body are the metaheuristics since it is established strategies to cross and explore the space of solutions of the problem usually generated in a random and iterative way. The main advantage of this technique is their flexibility and robustness, which allows them to be applied to a wide range of problems. In this work we focus on a metaheuristic based on Simulated Annealing trajectory and a population - based Cellular Genetic Algorithm with the objective of carrying out a study and comparison of the results obtained in its application for the resolution of a set of academic problems of combinatorial optimization.

  18. Combinatorial particle swarm optimization for solving blocking flowshop scheduling problem

    Mansour Eddaly

    2016-10-01

    Full Text Available This paper addresses to the flowshop scheduling problem with blocking constraints. The objective is to minimize the makespan criterion. We propose a hybrid combinatorial particle swarm optimization algorithm (HCPSO as a resolution technique for solving this problem. At the initialization, different priority rules are exploited. Experimental study and statistical analysis were performed to select the most adapted one for this problem. Then, the swarm behavior is tested for solving a combinatorial optimization problem such as a sequencing problem under constraints. Finally, an iterated local search algorithm based on probabilistic perturbation is sequentially introduced to the particle swarm optimization algorithm for improving the quality of solution. The computational results show that our approach is able to improve several best known solutions of the literature. In fact, 76 solutions among 120 were improved. Moreover, HCPSO outperforms the compared methods in terms of quality of solutions in short time requirements. Also, the performance of the proposed approach is evaluated according to a real-world industrial problem.

  19. 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.

  20. Evaluation of Direct Collocation Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem.

    De Groote, Friedl; Kinney, Allison L; Rao, Anil V; Fregly, Benjamin J

    2016-10-01

    Estimation of muscle forces during motion involves solving an indeterminate problem (more unknown muscle forces than joint moment constraints), frequently via optimization methods. When the dynamics of muscle activation and contraction are modeled for consistency with muscle physiology, the resulting optimization problem is dynamic and challenging to solve. This study sought to identify a robust and computationally efficient formulation for solving these dynamic optimization problems using direct collocation optimal control methods. Four problem formulations were investigated for walking based on both a two and three dimensional model. Formulations differed in the use of either an explicit or implicit representation of contraction dynamics with either muscle length or tendon force as a state variable. The implicit representations introduced additional controls defined as the time derivatives of the states, allowing the nonlinear equations describing contraction dynamics to be imposed as algebraic path constraints, simplifying their evaluation. Problem formulation affected computational speed and robustness to the initial guess. The formulation that used explicit contraction dynamics with muscle length as a state failed to converge in most cases. In contrast, the two formulations that used implicit contraction dynamics converged to an optimal solution in all cases for all initial guesses, with tendon force as a state generally being the fastest. Future work should focus on comparing the present approach to other approaches for computing muscle forces. The present approach lacks some of the major limitations of established methods such as static optimization and computed muscle control while remaining computationally efficient.

  1. MPCpy v0.1

    2017-01-24

    This software can be used to develop and test Model Predictive Control (MPC) algorithms with simulated buildings or deploy MPC in real buildings. This includes the gathering of exogenous data, training of simplified models, and control optimization.

  2. A Case Study to Test Mozaik for Different Optimization Problems

    Bekar, Kursat B [ORNL; Azmy, Yousry [North Carolina State University; Unlu, Kenan [Pennsylvania State University; BrenizerJr., Jack [Pennsylvania State University

    2009-01-01

    We present four different shape optimization problems based on the existing beam port facility of the Penn State Breazeale Reactor and their results obtained by the modular optimization code package, MOZAIK. Each model problem has a different beam tube configuration with the same optimization goal: to determine an optimal D2O moderator tank shape for the given beam tube arrangement that maximizes the thermal neutron beam intensity at the beam tube exit end. In this study, the power of the automated search process was demonstrated and its capabilities were tested. In addition, the performance of the beam port was analyzed using alternative beam tube arrangements. All alternative arrangements indicate that higher thermal neutron beam intensity can be obtained at the beam tube exit end using a smaller volume of D2O in the system than is used in the existing beam port configuration. Moreover, the results show that MOZAIK is ready for deployment to address shape optimization problems involving radiation transport in nuclear engineering applications.

  3. 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

  4. Philon's line generalized: an optimization problem from geometry

    Wetterling, W.W.E.

    1996-01-01

    Consider inn-dimensional Euclidean space the intersection of a convex cone and a hyperplane through a given point. The problem is to minimize the (n-1)-volume of this intersection. A geometric interpretation of the first-order optimality condition is given. The special casen=2 is known as a characte

  5. Approximated analytical solution to an Ebola optimal control problem

    Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.

    2016-11-01

    An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.

  6. Practical inventory routing: A problem definition and an optimization method

    Geiger, Martin Josef

    2011-01-01

    The global objective of this work is to provide practical optimization methods to companies involved in inventory routing problems, taking into account this new type of data. Also, companies are sometimes not able to deal with changing plans every period and would like to adopt regular structures for serving customers.

  7. 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 weaker...

  8. 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.

  9. On some fundamental properties of structural topology optimization problems

    Stolpe, Mathias

    2010-01-01

    convergence properties of penalization approaches based on material interpolation models. Furthermore, 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...

  10. Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

    Ben-Tal, A.; den Hertog, D.; De Waegenaere, A.M.B.; Melenberg, B.; Rennen, G.

    2011-01-01

    In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters contai

  11. 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.

  12. Heuristic Optimization for the Discrete Virtual Power Plant Dispatch Problem

    Petersen, Mette Kirschmeyer; Hansen, Lars Henrik; Bendtsen, Jan Dimon

    2014-01-01

    We consider a Virtual Power Plant, which is given the task of dispatching a fluctuating power supply to a portfolio of flexible consumers. The flexible consumers are modeled as discrete batch processes, and the associated optimization problem is denoted the Discrete Virtual Power Plant Dispatch P...

  13. 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...... landscape of BBO problems and show how an algorithm portfolio approach can exploit these general, problem indepen- dent features and outperform the utilization of any single minimization search strategy. We test our methodology on data from the GECCO Workshop on BBO Benchmarking 2012, which contains 21...

  14. Chebyshev-Legendre method for discretizing optimal control problems

    ZHANG Wen; MA He-ping

    2009-01-01

    In this paper, a numerical method for solving the optimal control (OC) problems is presented. The method is enlightened by the Chebyshev-Legendre (CL) method for solving the partial differential equations (PDEs). The Legen-dre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto (CGL) collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method.

  15. Efficient infill sampling for unconstrained robust optimization problems

    Rehman, Samee Ur; Langelaar, Matthijs

    2016-08-01

    A novel infill sampling criterion is proposed for efficient estimation of the global robust optimum of expensive computer simulation based problems. The algorithm is especially geared towards addressing problems that are affected by uncertainties in design variables and problem parameters. The method is based on constructing metamodels using Kriging and adaptively sampling the response surface via a principle of expected improvement adapted for robust optimization. Several numerical examples and an engineering case study are used to demonstrate the ability of the algorithm to estimate the global robust optimum using a limited number of expensive function evaluations.

  16. 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.

  17. 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.

  18. STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS

    2000-01-01

    This paper studies a stochastic linear quadratic optimal control problem (LQ problem, for short), for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. The authors introduce the stochastic Riccati equation for the LQ problem. This is a backward SDE with a complicated nonlinearity and a singularity. The local solvability of such a backward SDE is established, which by no means is obvious. For the case of deterministic coefficients, some further discussions on the Riccati equations have been carried out. Finally, an illustrative example is presented.

  19. Global Optimization Approach to Non-convex Problems

    LU Zi-fang; ZHENG Hui-li

    2004-01-01

    A new approach to find the global optimal solution of the special non-convex problems is proposed in this paper. The non-convex objective problem is first decomposed into two convex sub-problems. Then a generalized gradient is introduced to determine a search direction and the evolution equation is built to obtain a global minimum point. By the approach, we can prevent the search process from some local minima and search a global minimum point. Two numerical examples are given to prove the approach to be effective.

  20. Simulation Optimization of the Crossdock Door Assignment Problem

    Aickelin, Uwe

    2008-01-01

    The purpose of this report is to present the Crossdock Door Assignment Problem, which involves assigning destinations to outbound dock doors of Crossdock centres such that travel distance by material handling equipment is minimized. We propose a two fold solution; simulation and optimization of the simulation model simulation optimization. The novel aspect of our solution approach is that we intend to use simulation to derive a more realistic objective function and use Memetic algorithms to find an optimal solution. The main advantage of using Memetic algorithms is that it combines a local search with Genetic Algorithms. The Crossdock Door Assignment Problem is a new domain application to Memetic Algorithms and it is yet unknown how it will perform.

  1. Feedback Solution to Optimal Switching Problems With Switching Cost.

    Heydari, Ali

    2016-10-01

    The problem of optimal switching between nonlinear autonomous subsystems is investigated in this paper where the objective is not only bringing the states to close to the desired point, but also adjusting the switching pattern, in the sense of penalizing switching occurrences and assigning different preferences to utilization of different modes. The mode sequence is unspecified and a switching cost term is used in the cost function for penalizing each switching. It is shown that once a switching cost is incorporated, the optimal cost-to-go function depends on the subsystem which was active at the previous time step. Afterward, an approximate dynamic programming-based method is developed, which provides an approximation of the optimal solution to the problem in a feedback form and for different initial conditions. Finally, the performance of the method is analyzed through numerical examples.

  2. 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

  3. OPTIMIZING MULTIPLE TRAVELLING SALESMAN PROBLEM CONSIDERING THE ROAD CAPACITY

    Ranjana Ponraj

    2014-01-01

    Full Text Available The Multiple Travelling Salesman Problems (MTSP can be used in a wide range of discrete optimization problems. As the solution to this problem has wide applicability in many practical fields, this NP Hard problem highly raises the need for an efficient solution. The problem is determining a set of routes for the salesmen that jointly visit a set of given cities which are facing difficulty because of road congestion. Selection of proper route is based on the road capacity, which is the deciding factor in the opt vehicle usage. The objective of the study is to optimize the vehicle utilization and minimize the time of travel by salesman based on the road capacity. The solution to this problem is achieved in 3 steps; the first step is by assigning addresses to cities by Ad-assignment algorithm. The second step is by assigning cities and vehicles to salesman by Sl-assignment algorithm. The third step is by using Parallel Shortest Path Multiple Salesman (PSPMS algorithms to obtain the shortest path. The PSPMS algorithm runs in parallel for each salesman. The solutions to the problem are known to possess an exponential time complexity. From the result we observe that PSPMS is one of the best approximate algorithms used to solve MTSP.

  4. LGMS-FOA: An Improved Fruit Fly Optimization Algorithm for Solving Optimization Problems

    Dan Shan

    2013-01-01

    Full Text Available Recently, a new fruit fly optimization algorithm (FOA is proposed to solve optimization problems. In this paper, we empirically study the performance of FOA. Six different nonlinear functions are selected as testing functions. The experimental results illustrate that FOA cannot solve complex optimization problems effectively. In order to enhance the performance of FOA, an improved FOA (named LGMS-FOA is proposed. Simulation results and comparisons of LGMS-FOA with FOA and other metaheuristics show that LGMS-FOA can greatly enhance the searching efficiency and greatly improve the searching quality.

  5. Optimal Parallel Algorithm for the Knapsack Problem Without Memory Conflicts

    Ken-Li Li; Ren-Fa Li; Qing-Hua Li

    2004-01-01

    The knapsack problem is well known to be NP-complete. Due to its importance in cryptosystem and in number theory, in the past two decades, much effort has been made in order to find techniques that could lead to practical algorithms with reasonable running time. This paper proposes a new parallel algorithm for the knapsack problem where the optimal merging algorithm is adopted. The proposed algorithm is based on an EREW-SIMD machine with shared memory. It is proved that the proposed algorithm is both optimal and the first without memory conflicts algorithm for the knapsack problem. The comparisons of algorithm performance show that it is an improvement over the past researches.

  6. Solving Optimization Problems by the Spatial Public Goods Game

    Javarone, Marco Alberto

    2016-01-01

    We introduce a method based on the spatial Public Goods Game for solving optimization tasks. In particular, we focus on the Traveling Salesman Problem, i.e., a problem whose search space exponentially grows increasing the number of cities, then becoming NP-hard. The proposed method considers a population whose agents are provided with a random solution to the given problem. Then, agents interact by playing the Public Goods Game using the fitness of their solution as currency of the game. In doing so, agents with better solutions provide higher contributions, while agents with lower ones tend to imitate the solution of richer agents to increase their fitness. Numerical simulations show that the proposed method allows to compute exact solutions, and suboptimal ones, in the considered search spaces. As result, beyond to propose a new heuristic for combinatorial optimization tasks, our work aims to highlight the potentiality of evolutionary game theory outside its current horizons.

  7. A Cooperative Coevolutionary Cuckoo Search Algorithm for Optimization Problem

    Hongqing Zheng

    2013-01-01

    Full Text Available Taking inspiration from an organizational evolutionary algorithm for numerical optimization, this paper designs a kind of dynamic population and combining evolutionary operators to form a novel algorithm, a cooperative coevolutionary cuckoo search algorithm (CCCS, for solving both unconstrained, constrained optimization and engineering problems. A population of this algorithm consists of organizations, and an organization consists of dynamic individuals. In experiments, fifteen unconstrained functions, eleven constrained functions, and two engineering design problems are used to validate the performance of CCCS, and thorough comparisons are made between the CCCS and the existing approaches. The results show that the CCCS obtains good performance in the solution quality. Moreover, for the constrained problems, the good performance is obtained by only incorporating a simple constraint handling technique into the CCCS. The results show that the CCCS is quite robust and easy to use.

  8. Multicast Routing Problem Using Tree-Based Cuckoo Optimization Algorithm

    Mahmood Sardarpour

    2016-06-01

    Full Text Available The problem of QoS multicast routing is to find a multicast tree with the least expense/cost which would meet the limitations such as band width, delay and loss rate. This is a NP-Complete problem. To solve the problem of multicast routing, the entire routes from the source node to every destination node are often recognized. Then the routes are integrated and changed into a single multicast tree. But they are slow and complicated methods. The present paper introduces a new tree-based optimization method to overcome such weaknesses. The recommended method directly optimizes the multicast tree. Therefore a tree-based typology including several spanning trees is created which combines the trees two by two. For this purpose, the Cuckoo Algorithm is used which is proved to be well converged and makes quick calculations. The simulation conducted on different types of network typologies proved that it is a practical and influential algorithm.

  9. A free boundary approach to shape optimization problems.

    Bucur, D; Velichkov, B

    2015-09-13

    The analysis of shape optimization problems involving the spectrum of the Laplace operator, such as isoperimetric inequalities, has known in recent years a series of interesting developments essentially as a consequence of the infusion of free boundary techniques. The main focus of this paper is to show how the analysis of a general shape optimization problem of spectral type can be reduced to the analysis of particular free boundary problems. In this survey article, we give an overview of some very recent technical tools, the so-called shape sub- and supersolutions, and show how to use them for the minimization of spectral functionals involving the eigenvalues of the Dirichlet Laplacian, under a volume constraint.

  10. Topology optimization of 3D Stokes flow problems

    Gersborg-Hansen, Allan

    to different flow problems. However, this research has focused on 2D fluid modelling, which limits the practical impact of the computed designs. The explanation of the limitation is that the finite size domain used in topology optimization problems ensures that the velocity components couples, even for Stokes...... flow [3]. Furthermore, it is questionable if such a coupling can be captured by a 2D model especially in non-trivial geometries as typically seen in topology design. This statement is widely accepted in the fluid mechanics community, i.e. that planar fluid models are useful for academic test problems...... only. The motivation for considering topology optimization in 3D Stokes flow originates from micro fluidic systems. At small scales the Stokes equations are a reasonable mathematical model to use for the fluid behavior. Physically Stokes flow is an exotic inertia free flow, which in practice...

  11. A hybrid artificial bee colony optimization and quantum evolutionary algorithm for continuous optimization problems.

    Duan, Hai-Bin; Xu, Chun-Fang; Xing, Zhi-Hui

    2010-02-01

    In this paper, a novel hybrid Artificial Bee Colony (ABC) and Quantum Evolutionary Algorithm (QEA) is proposed for solving continuous optimization problems. ABC is adopted to increase the local search capacity as well as the randomness of the populations. In this way, the improved QEA can jump out of the premature convergence and find the optimal value. To show the performance of our proposed hybrid QEA with ABC, a number of experiments are carried out on a set of well-known Benchmark continuous optimization problems and the related results are compared with two other QEAs: the QEA with classical crossover operation, and the QEA with 2-crossover strategy. The experimental comparison results demonstrate that the proposed hybrid ABC and QEA approach is feasible and effective in solving complex continuous optimization problems.

  12. Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures

    Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Kobilarov, Marin

    2012-08-01

    Computing globally efficient solutions is a major challenge in optimal control of nonlinear dynamical systems. This work proposes a method combining local optimization and motion planning techniques based on exploiting inherent dynamical systems structures, such as symmetries and invariant manifolds. Prior to the optimal control, the dynamical system is analyzed for structural properties that can be used to compute pieces of trajectories that are stored in a motion planning library. In the context of mechanical systems, these motion planning candidates, termed primitives, are given by relative equilibria induced by symmetries and motions on stable or unstable manifolds of e.g. fixed points in the natural dynamics. The existence of controlled relative equilibria is studied through Lagrangian mechanics and symmetry reduction techniques. The proposed framework can be used to solve boundary value problems by performing a search in the space of sequences of motion primitives connected using optimized maneuvers. The optimal sequence can be used as an admissible initial guess for a post-optimization. The approach is illustrated by two numerical examples, the single and the double spherical pendula, which demonstrates its benefit compared to standard local optimization techniques.

  13. Performance investigation of multigrid optimization for DNS-based optimal control problems

    Nita, Cornelia; Vandewalle, Stefan; Meyers, Johan

    2016-11-01

    Optimal control theory in Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES) of turbulent flow involves large computational cost and memory overhead for the optimization of the controls. In this context, the minimization of the cost functional is typically achieved by employing gradient-based iterative methods such as quasi-Newton, truncated Newton or non-linear conjugate gradient. In the current work, we investigate the multigrid optimization strategy (MGOpt) in order to speed up the convergence of the damped L-BFGS algorithm for DNS-based optimal control problems. The method consists in a hierarchy of optimization problems defined on different representation levels aiming to reduce the computational resources associated with the cost functional improvement on the finest level. We examine the MGOpt efficiency for the optimization of an internal volume force distribution with the goal of reducing the turbulent kinetic energy or increasing the energy extraction in a turbulent wall-bounded flow; problems that are respectively related to drag reduction in boundary layers, or energy extraction in large wind farms. Results indicate that in some cases the multigrid optimization method requires up to a factor two less DNS and adjoint DNS than single-grid damped L-BFGS. The authors acknowledge support from OPTEC (OPTimization in Engineering Center of Excellence, KU Leuven, Grant No PFV/10/002).

  14. Ant Colony Optimization for Solving Solid Waste Collection Scheduling Problems

    Z. Ismail

    2009-01-01

    Full Text Available Problem statement: Southern Waste Management environment (SWM environment is a company responsible for the collection and disposal of solid waste for the city of Johor Bahru, a city with over one million populations. The company is implementing an integrated solid waste management system where it involved in the optimization of resources to ensure the effectiveness of its services. Formulating this real life problem into vehicle routing problem with stochastic demand model and using some designed algorithms to minimize operation cost of solid waste management. Approach: The implementation of Ant Colony Optimization (ACO for solving solid waste collection problem as a VRPSD model was described. A set of data modified from the well known 50 customers problems were used to find the route such that the expected traveling cost was minimized. The total cost was minimized by adopting a preventive restocking policy which was trading off the extra cost of returning to depot after a stock-out with the cost of returning depot for restocking before a stock-out actually occurs. For comparison purposes, Simulated Annealing (SA was used to generate the solution under the same condition. Results: For the problem size with 12 customers with vehicle capacity 10 units, both algorithms obtained the same best cost which is 69.4358 units. But the percentage deviations of averages from the associated best cost are 0.1322 and 0.7064 for ACS and SA. The results indicated that for all demand ranges, proposed ACO algorithm showed better performance than SA algorithm. Conclusion: SA was able to obtain good solutions for small ranges especially small size of problem. For ACS, it is always provide good results for all tested ranges and problems sizes of the tested problem.

  15. Stability, Optimality and Manipulation in Matching Problems with Weighted Preferences

    Maria Silvia Pini

    2013-11-01

    Full Text Available The stable matching problem (also known as the stable marriage problem is a well-known problem of matching men to women, so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools or, more generally, to any two-sided market. In the classical stable marriage problem, both men and women express a strict preference order over the members of the other sex, in a qualitative way. Here, we consider stable marriage problems with weighted preferences: each man (resp., woman provides a score for each woman (resp., man. Such problems are more expressive than the classical stable marriage problems. Moreover, in some real-life situations, it is more natural to express scores (to model, for example, profits or costs rather than a qualitative preference ordering. In this context, we define new notions of stability and optimality, and we provide algorithms to find marriages that are stable and/or optimal according to these notions. While expressivity greatly increases by adopting weighted preferences, we show that, in most cases, the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem. We also consider the manipulability properties of the procedures that return such stable marriages. While we know that all procedures are manipulable by modifying the preference lists or by truncating them, here, we consider if manipulation can occur also by just modifying the weights while preserving the ordering and avoiding truncation. It turns out that, by adding weights, in some cases, we may increase the possibility of manipulating, and this cannot be avoided by any reasonable restriction on the weights.

  16. Optimal convex correcting procedures in problems of high dimension

    Dokukin, A. A.; Senko, O. V.

    2011-09-01

    The properties of convex correcting procedures (CCPs) over sets of predictors are examined. It is shown that the minimization of the generalized error in a CCP is reduced to a quadratic programming problem. The conditions are studied under which a set of predictors cannot be reduced without degrading the accuracy of the corresponding optimal CCP. Experimental studies of the prognostic properties of CCPs for samples of one-dimensional linear regressions showed that CCP optimization can be an effective tool for regression variable selection.

  17. 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...... enabled an evaluation of the design with a body fitted mesh in a standard analysis software relevant in engineering practice prior to design manufacturing. This work investigates the proper choice of a maximum penalization value during the optimization process that ensures that the target outflow rates...

  18. Particle Swarm Optimization Applied to the Economic Dispatch Problem

    Rafik Labdani

    2006-06-01

    Full Text Available This paper presents solution of optimal power flow (OPF problem of a power system via a simple particle swarm optimization (PSO algorithm. The objective is to minimize the fuel cost and keep the power outputs of generators, bus voltages, shunt capacitors/reactors and transformers tap-setting in their secure limits.The effectiveness of PSO was compared to that of OPF by MATPOWER. The potential and superiority of PSO have been demonstrated through the results of IEEE 30-bus system

  19. Multiresolution strategies for the numerical solution of optimal control problems

    Jain, Sachin

    There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a

  20. Optimization of the electrochemical performance of a Ni/Ce0.9Gd0.1O2-δ-impregnated La0.57Sr0.15TiO3 anode in hydrogen

    Xia, Tian; Brüll, Annelise; Grimaud, Alexis; Fourcade, Sébastien; Mauvy, Fabrice; Zhao, Hui; Grenier, Jean-Claude; Bassat, Jean-Marc

    2014-09-01

    A-site deficient perovskite La0.57Sr0.15TiO3 (LSTO) materials are synthesized by a modified polyacrylamide gel route. X-ray diffraction pattern of LSTO indicates an orthorhombic structure. The thermal expansion coefficient of LSTO is 10.0 × 10-6 K-1 at 600 °C in 5%H2/Ar. LSTO shows an electrical conductivity of 2 S cm-1 at 600 °C in 3%H2O/H2. A new composite material, containing the porous LSTO backbone impregnated with small amounts of Ce0.9Gd0.1O2-δ (CGO) (3.4-8.3 wt.%) and Ni/Cu (2.0-6.3 wt.%), is investigated as an alternative anode for solid oxide fuel cells (SOFCs). Because of the substantial electro-catalytic activity of the fine and well-dispersed Ni particles on the surface of the ceramic framework, the polarization resistance of 6.3%Ni-8.3%CGO-LSTO anode reaches 0.73 Ω cm2 at 800 °C in 3%H2O/H2. In order to further improve the anodic performance, corn starch and carbon black are used as pore-formers to optimize the microstructure of anodes.

  1. RECIPES FOR BUILDING THE DUAL OF CONIC OPTIMIZATION PROBLEM

    Diah Chaerani

    2010-08-01

    Full Text Available Building the dual of the primal problem of Conic Optimization (CO isa very important step to make the ¯nding optimal solution. In many cases a givenproblem does not have the simple structure of CO problem (i.e., minimizing a linearfunction over an intersection between a±ne space and convex cones but there areseveral conic constraints and sometimes also equality constraints. In this paper wedeal with the question how to form the dual problem in such cases. We discuss theanswer by considering several conic constraints with or without equality constraints.The recipes for building the dual of such cases is formed in standard matrix forms,such that it can be used easily on the numerical experiment. Special attention isgiven to dual development of special classes of CO problems, i.e., conic quadraticand semide¯nite problems. In this paper, we also brie°y present some preliminariestheory on CO as an introduction to the main topic

  2. On the MSE Performance and Optimization of Regularized Problems

    Alrashdi, Ayed

    2016-11-01

    The amount of data that has been measured, transmitted/received, and stored in the recent years has dramatically increased. So, today, we are in the world of big data. Fortunately, in many applications, we can take advantages of possible structures and patterns in the data to overcome the curse of dimensionality. The most well known structures include sparsity, low-rankness, block sparsity. This includes a wide range of applications such as machine learning, medical imaging, signal processing, social networks and computer vision. This also led to a specific interest in recovering signals from noisy compressed measurements (Compressed Sensing (CS) problem). Such problems are generally ill-posed unless the signal is structured. The structure can be captured by a regularizer function. This gives rise to a potential interest in regularized inverse problems, where the process of reconstructing the structured signal can be modeled as a regularized problem. This thesis particularly focuses on finding the optimal regularization parameter for such problems, such as ridge regression, LASSO, square-root LASSO and low-rank Generalized LASSO. Our goal is to optimally tune the regularizer to minimize the mean-squared error (MSE) of the solution when the noise variance or structure parameters are unknown. The analysis is based on the framework of the Convex Gaussian Min-max Theorem (CGMT) that has been used recently to precisely predict performance errors.

  3. Constraint Algorithm for Extremals in Optimal Control Problems

    Barbero-Linan, Maria

    2007-01-01

    A characterization of different kinds of extremals of optimal control problems is given if we take an open control set. A well known constraint algorithm for implicit differential equations is adapted to the study of such problems. Some necessary conditions of Pontryagin's Maximum Principle determine the primary constraint submanifold for the algorithm. Some examples in the control literature, such as subRiemannian geometry and control-affine systems, are revisited to give, in a clear geometric way, a subset where the abnormal, normal and strict abnormal extremals stand.

  4. Novel electromagnetism-like mechanism method for multiobjective optimization problems

    Lixia Han,Shujuan Jiang,; Shaojiang Lan

    2015-01-01

    As a new-style stochastic algorithm, the electro-magnetism-like mechanism (EM) method gains more and more attention from many researchers in recent years. A novel model based on EM (NMEM) for multiobjective optimization problems is proposed, which regards the charge of al particles as the con-straints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the pro-posed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.

  5. Adaptive Uncertainty Resolution in Bayesian Combinatorial Optimization Problems

    Guha, Sudipto

    2008-01-01

    In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some objective function over the parameters) is significantly improved if some of these parameters can be probed or observed. In a resource constrained situation, deciding which parameters to observe in order to optimize system performance itself becomes an interesting and important optimization problem. This general problem is the focus of this paper. One of the most important considerations in this framework is whether adaptivity is required for the observations. Adaptive observations introduce blocking or sequential operations in the system whereas non-adaptive observations can be performed in parallel. One of the important questions in this regard is to characterize the benefit of adaptivity for probes and observation. We present general techniques for designing constant factor appr...

  6. A novel comprehensive learning artificial bee colony optimizer for dynamic optimization biological problems

    Weixing Su

    2017-03-01

    Full Text Available There are many dynamic optimization problems in the real world, whose convergence and searching ability is cautiously desired, obviously different from static optimization cases. This requires an optimization algorithm adaptively seek the changing optima over dynamic environments, instead of only finding the global optimal solution in the static environment. This paper proposes a novel comprehensive learning artificial bee colony optimizer (CLABC for optimization in dynamic environments problems, which employs a pool of optimal foraging strategies to balance the exploration and exploitation tradeoff. The main motive of CLABC is to enrich artificial bee foraging behaviors in the ABC model by combining Powell’s pattern search method, life-cycle, and crossover-based social learning strategy. The proposed CLABC is a more bee-colony-realistic model that the bee can reproduce and die dynamically throughout the foraging process and population size varies as the algorithm runs. The experiments for evaluating CLABC are conducted on the dynamic moving peak benchmarks. Furthermore, the proposed algorithm is applied to a real-world application of dynamic RFID network optimization. Statistical analysis of all these cases highlights the significant performance improvement due to the beneficial combination and demonstrates the performance superiority of the proposed algorithm.

  7. MODIFIED GENETIC ALGORITHM APPLIED TO SOLVE PRODUCT FAMILY OPTIMIZATION PROBLEM

    CHEN Chunbao; WANG Liya

    2007-01-01

    The product family design problem solved by evolutionary algorithms is discussed. A successfiil product family design method should achieve an optimal tradeoff among a set of competing objectives, which involves maximizing conunonality across the family of products and optimizing the performances of each product in the family. A 2-level chromosome structured genetic algorithm (2LCGA) is proposed to solve this dass of problems and its performance is analyzed in comparing its results with those obtained with other methods. By interpreting the chromosome as a 2-level linear structure, the variable commonality genetic algorithm (GA) is constructed to vary the amount of platform commonality and automatically searches across varying levels of commonality for the platform while trying to resolve the tradeoff between commonality and individual product performance within the product family during optimization process. By incorporating a commonality assessing index to the problem formulation, the 2LCGA optimize the product platform and its corresponding family of products in a single stage, which can yield improvements in the overall performance of the product family compared with two-stage approaches (the first stage involves determining the best settings for the platform variables and values of unique variables are found for each product in the second stage). The scope of the algorithm is also expanded by introducing a classification mechanism to allow multiple platforms to be considered during product family optimization, offering opportunities for superior overall design by more efficacious tradeoffs between commonality and performance. The effectiveness of 2LCGA is demonstrated through the design of a family of universal electric motors and comparison against previous results.

  8. Radio interferometric gain calibration as a complex optimization problem

    Smirnov, Oleg

    2015-01-01

    Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss-Newton, Levenberg-Marquardt, etc.) into the domain of complex functions of a complex variable. This employs a formalism called the Wirtinger derivative, and derives a full-complex Jacobian counterpart to the conventional real Jacobian. We apply these developments to the problem of radio interferometric gain calibration, and show how the general complex Jacobian formalism, when combined with conventional optimization approaches, yields a whole new family of calibration algorithms, including those for the polarized and direction-dependent gain regime. We further extend the Wirtinger calculus to an operator-based matrix calculus for describing the polarized calibration regime. Using approximate matrix inversion results in computationally efficient implementations; we show that some recently proposed calibration algorithms such as StefCal and peeling can be understood...

  9. Gradient of the Value Function in Parametric Convex Optimization Problems

    Baotić, Mato

    2016-01-01

    We investigate the computation of the gradient of the value function in parametric convex optimization problems. We derive general expression for the gradient of the value function in terms of the cost function, constraints and Lagrange multipliers. In particular, we show that for the strictly convex parametric quadratic program the value function is continuously differentiable at every point in the interior of feasible space for which the Linear Independent Constraint Qualification holds.

  10. First-order optimality condition of basis pursuit denoise problem

    朱玮; 舒适; 成礼智

    2014-01-01

    A new first-order optimality condition for the basis pursuit denoise (BPDN) problem is derived. This condition provides a new approach to choose the penalty param-eters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.

  11. Optimizing Distribution Problems using WinQSB Software

    Daniel Mihai Amariei

    2015-07-01

    Full Text Available In the present paper we are presenting a problem of distribution using the Network Modeling Module of the WinQSB software, were we have 5 athletes which we must assign the optimal sample, function of the obtained time, so as to obtain the maximum output of the athletes. Also we analyzed the case of an accident of 2 athletes, the coupling of 3 athletes with 5 various athletic events causing the maximum coupling, done using the Hungarian algorithm.

  12. Parareal in time intermediate targets methods for optimal control problem

    Maday, Yvon; Salomon, Julien

    2012-01-01

    In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets that gives rise to independent sub-problems that can be solved in parallel. This method can be coupled with the parareal in time algorithm. Numerical experiments show the efficiency of our method.

  13. Optimization of Multiple Vehicle Routing Problems Using Approximation Algorithms

    R. Nallusamy

    2009-12-01

    Full Text Available This paper deals with generating of an optimized route for multiple Vehicle routing Problems (mVRP. We used a methodology of clustering the given cities depending upon the number of vehicles and eachcluster is allotted to a vehicle. k- Means clustering algorithm has been used for easy clustering of the cities. In this way the mVRP has been converted into VRP which is simple in computation compared to mVRP. After clustering, an optimized route is generated for each vehicle in its allotted cluster. Once the clustering had been done and after the cities were allocated to the various vehicles, each cluster/tour was taken as an individual Vehicle Routing problem and the steps of Genetic Algorithm were applied to the cluster and iterated to obtain the most optimal value of the distance after convergence takes place. After the application of the variousheuristic techniques, it was found that the Genetic algorithm gave a better result and a more optimal tour for mVRPs in short computational time than other Algorithms due to the extensive search and constructive nature of the algorithm.

  14. Optimization of Multiple Vehicle Routing Problems using Approximation Algorithms

    Nallusamy, R; Dhanalaksmi, R; Parthiban, P

    2010-01-01

    This paper deals with generating of an optimized route for multiple Vehicle routing Problems (mVRP). We used a methodology of clustering the given cities depending upon the number of vehicles and each cluster is allotted to a vehicle. k- Means clustering algorithm has been used for easy clustering of the cities. In this way the mVRP has been converted into VRP which is simple in computation compared to mVRP. After clustering, an optimized route is generated for each vehicle in its allotted cluster. Once the clustering had been done and after the cities were allocated to the various vehicles, each cluster/tour was taken as an individual Vehicle Routing problem and the steps of Genetic Algorithm were applied to the cluster and iterated to obtain the most optimal value of the distance after convergence takes place. After the application of the various heuristic techniques, it was found that the Genetic algorithm gave a better result and a more optimal tour for mVRPs in short computational time than other Algorit...

  15. Overview: Applications of numerical optimization methods to helicopter design problems

    Miura, H.

    1984-01-01

    There are a number of helicopter design problems that are well suited to applications of numerical design optimization techniques. Adequate implementation of this technology will provide high pay-offs. There are a number of numerical optimization programs available, and there are many excellent response/performance analysis programs developed or being developed. But integration of these programs in a form that is usable in the design phase should be recognized as important. It is also necessary to attract the attention of engineers engaged in the development of analysis capabilities and to make them aware that analysis capabilities are much more powerful if integrated into design oriented codes. Frequently, the shortcoming of analysis capabilities are revealed by coupling them with an optimization code. Most of the published work has addressed problems in preliminary system design, rotor system/blade design or airframe design. Very few published results were found in acoustics, aerodynamics and control system design. Currently major efforts are focused on vibration reduction, and aerodynamics/acoustics applications appear to be growing fast. The development of a computer program system to integrate the multiple disciplines required in helicopter design with numerical optimization technique is needed. Activities in Britain, Germany and Poland are identified, but no published results from France, Italy, the USSR or Japan were found.

  16. Issues and Strategies in Solving Multidisciplinary Optimization Problems

    Patnaik, Surya

    2013-01-01

    Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the

  17. Bi-objective optimization for multi-modal transportation routing planning problem based on Pareto optimality

    Yan Sun

    2015-09-01

    Full Text Available Purpose: The purpose of study is to solve the multi-modal transportation routing planning problem that aims to select an optimal route to move a consignment of goods from its origin to its destination through the multi-modal transportation network. And the optimization is from two viewpoints including cost and time. Design/methodology/approach: In this study, a bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. Minimizing the total transportation cost and the total transportation time are set as the optimization objectives of the model. In order to balance the benefit between the two objectives, Pareto optimality is utilized to solve the model by gaining its Pareto frontier. The Pareto frontier of the model can provide the multi-modal transportation operator (MTO and customers with better decision support and it is gained by the normalized normal constraint method. Then, an experimental case study is designed to verify the feasibility of the model and Pareto optimality by using the mathematical programming software Lingo. Finally, the sensitivity analysis of the demand and supply in the multi-modal transportation organization is performed based on the designed case. Findings: The calculation results indicate that the proposed model and Pareto optimality have good performance in dealing with the bi-objective optimization. The sensitivity analysis also shows the influence of the variation of the demand and supply on the multi-modal transportation organization clearly. Therefore, this method can be further promoted to the practice. Originality/value: A bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. The Pareto frontier based sensitivity analysis of the demand and supply in the multi-modal transportation organization is performed based on the designed case.

  18. Ant Colony Optimization for Capacitated Vehicle Routing Problem

    H. V. Seow

    2012-01-01

    Full Text Available Problem statement: The Capacitated Vehicle Routing Problem (CVRP is a well-known combinatorial optimization problem which is concerned with the distribution of goods between the depot and customers. It is of economic importance to businesses as approximately 10-20% of the final cost of the goods is contributed by the transportation process. Approach: This problem was tackled using an Ant Colony Optimization (ACO combined with heuristic approaches that act as the route improvement strategies. The proposed ACO utilized a pheromone evaporation procedure of standard ant algorithm in order to introduce an evaporation rate that depends on the solutions found by the artificial ants. Results: Computational experiments were conducted on benchmark data set and the results obtained from the proposed algorithms shown that the application of combination of two different heuristics in the ACO had the capability to improve the ants’ solutions better than ACO embedded with only one heuristic. Conclusion: ACO with swap and 3-opt heuristic has the capability to tackle the CVRP with satisfactory solution quality and run time. It is a viable alternative for solving the CVRP.

  19. APPLYING PARTICLE SWARM OPTIMIZATION TO JOB-SHOP SCHEDULING PROBLEM

    Xia Weijun; Wu Zhiming; Zhang Wei; Yang Genke

    2004-01-01

    A new heuristic algorithm is proposed for the problem of finding the minimum makespan in the job-shop scheduling problem. The new algorithm is based on the principles of particle swarm optimization (PSO). PSO employs a collaborative population-based search, which is inspired by the social behavior of bird flocking. It combines local search (by self experience) and global search (by neighboring experience), possessing high search efficiency. Simulated annealing (SA) employs certain probability to avoid becoming trapped in a local optimum and the search process can be controlled by the cooling schedule. By reasonably combining these two different search algorithms, a general, fast and easily implemented hybrid optimization algorithm, named HPSO, is developed. The effectiveness and efficiency of the proposed PSO-based algorithm are demonstrated by applying it to some benchmark job-shop scheduling problems and comparing results with other algorithms in literature. Comparing results indicate that PSO-based algorithm is a viable and effective approach for the job-shop scheduling problem.

  20. Optimization of Pr(0.9)Ca(0.1)MnO(3) thin films and observation of coexisting spin-glass and ferromagnetic phases at low temperature.

    Svedberg, M; Majumdar, S; Huhtinen, H; Paturi, P; Granroth, S

    2011-09-28

    Optimization of thin films of small bandwidth manganite, Pr(1-x)Ca(x)MnO3 (for x = 0.1), and their magnetic properties are investigated. Using different pulsed laser deposition (PLD) conditions, several films were deposited from the stoichiometric target material on SrTiO3 (001) substrate and their thorough structural and magnetic characterizations were carried out using x-ray diffraction, atomic force microscopy, x-ray photoelectron spectroscopy (XPS), SQUID magnetometry and ac susceptibility measurements. A systematic investigation shows that irrespective of the growth temperature (between 550 and 750 °C), all the as-deposited films have twin boundaries and magnetic double phases. Post-annealing in partial or full oxygen pressure removes the extra phase and the twin boundaries. Zero-field-cooled magnetization data show an antiferromagnetic to paramagnetic transition at around 100 K whereas the field-cooled magnetization data exhibit a paramagnetic to ferromagnetic transition close to 120 K. However, depending on the oxygen treatments, the saturation magnetization and Curie temperature of the films change significantly. Redistribution of oxygen vacancies due to annealing treatments leading to a change in ratio of Mn3+ and Mn4+ in the films is observed from XPS measurements. Low temperature (below 100 K) dc magnetization of these films shows metamagnetic transition, high coercivity and irreversibility magnetizations, indicating the presence of a spin-glass phase at low temperature. The frequency dependent shift in spin-glass freezing temperature from ac susceptibility measurement confirms the coexistence of spin-glass and ferromagnetic phases in these samples at low temperature.

  1. Use of genetic algorithms for solving problems of optimal cutting

    Sergievskiy Maxim

    2016-01-01

    Full Text Available Cutting and packing problem is one of the most common optimization problem. Even a small space or material savings allow obtaining substantial advantages on an industrial scale. This paper proposes the genetic algorithm to solve this problem. It includes multipoint operators of crossing, mutation and selection. To use these operators, the special encoding of cutting card is applied, that can be transformed to the real coordinates by using decoder. This is a block typed decoder, which substitution strategy is “first-fit”. Efficiency of the solutions, obtained by the algorithm, depends on its parameters and on dimension of a task, but on average it decreases under the logarithmic law from dimension of a task. Temporary complexity of algorithm shows square dependence on the task dimension.

  2. Multiobjective Optimization Problem of Multireservoir System in Semiarid Areas

    Z. J. Chen

    2013-01-01

    Full Text Available With the increasing scarcity of water resources, the growing importance of the optimization operation of the multireservoir system in water resources development, utilization, and management is increasingly evident. Some of the existing optimization methods are inadequate in applicability and effectiveness. Therefore, we need further research in how to enhance the applicability and effectiveness of the algorithm. On the basis of the research of the multireservoir system’s operating parameters in the Urumqi River basin, we establish a multiobjective optimization problem (MOP model of water resources development, which meets the requirements of water resources development. In the mathematical model, the domestic water consumption is the biggest, the production of industry and agricultural is the largest, the gross output value of industry and agricultural is the highest, and the investment of the water development is the minimum. We use the weighted variable-step shuffled frog leaping algorithm (SFLA to resolve it, which satisfies the constraints. Through establishing the test function and performance metrics, we deduce the evolutionary algorithms, which suit for solving MOP of the scheduling, and realize the multiobjective optimization of the multireservoir system. After that, using the fuzzy theory, we convert the competitive multiobjective function into single objective problem of maximum satisfaction, which is the only solution. A feasible solution is provided to resolve the multiobjective scheduling optimization of multireservoir system in the Urumqi River basin. It is the significance of the layout of production, the regional protection of ecological environment, and the sufficient and rational use of natural resources, in Urumqi and the surrounding areas.

  3. Optimization of Capacitated Vehicle Routing Problem by Nested Particle Swarm Optimization

    Karuppusamy Kanthavel

    2011-01-01

    Full Text Available Problem statement: Vehicle routing problem determines the optimum route for each vehicle as a sequence of visiting cities. The problem has been defined as NP-hard and exact solution is relatively difficult to achieve for real time large scale models. Though several attempts to solve the problem were made in the literature, new approaches may be tried to solve the problem to further reduce computational efforts. Approach: In this context this study focuses on maximum utilization of loading capacity and determines the optimum set of vehicle routes for Capacitated Vehicle Routing Problem (CVRP by a Nested Particle Swarm Optimization (NPSO technique. The algorithm is implemented as Master PSO and slave PSO for the identification of candidate list and route sequence in nested form to optimize the model. Results: Benchmarking data set of capacitated vehicle routing is considered for the evaluations. The total distance of set vehicle route obtained by the new approach is compared with the best known solution and other existing techniques. Conclusions/Recommendations: The NPSO produces significant results and computational performance than the existing PSO algorithms. This newly proposed NPSO algorithm develops the vehicle schedule without any local optimization technique.

  4. Strange Behaviors of Interior-point Methods for Solving Semidefinite Programming Problems in Polynomial Optimization

    Nakata, M.; Muramatsu, M.; Waki, H.

    2008-01-01

    We observe that in a simple one-dimensional polynomial optimization problem (POP), the `optimal' values of semidefinite programming (SDP) relaxation problems reported by the standard SDP solvers converge to the optimal value of the POP, while the true optimal values of SDP relaxation problems are st

  5. An Efficient Optimization Method for Solving Unsupervised Data Classification Problems

    Parvaneh Shabanzadeh

    2015-01-01

    Full Text Available Unsupervised data classification (or clustering analysis is one of the most useful tools and a descriptive task in data mining that seeks to classify homogeneous groups of objects based on similarity and is used in many medical disciplines and various applications. In general, there is no single algorithm that is suitable for all types of data, conditions, and applications. Each algorithm has its own advantages, limitations, and deficiencies. Hence, research for novel and effective approaches for unsupervised data classification is still active. In this paper a heuristic algorithm, Biogeography-Based Optimization (BBO algorithm, was adapted for data clustering problems by modifying the main operators of BBO algorithm, which is inspired from the natural biogeography distribution of different species. Similar to other population-based algorithms, BBO algorithm starts with an initial population of candidate solutions to an optimization problem and an objective function that is calculated for them. To evaluate the performance of the proposed algorithm assessment was carried on six medical and real life datasets and was compared with eight well known and recent unsupervised data classification algorithms. Numerical results demonstrate that the proposed evolutionary optimization algorithm is efficient for unsupervised data classification.

  6. A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems

    Yong WANG; Zixing CAI

    2009-01-01

    In the real-world applications, most optimization problems are subject to different types of constraints. These problems are known as constrained optimization problems (COPs). Solving COPs is a very important area in the optimization field. In this paper, a hybrid multi-swarm particle swarm optimization (HMPSO) is proposed to deal with COPs. This method adopts a parallel search operator in which the current swarm is partitioned into several subswarms and particle swarm optimization (PSO) is severed as the search engine for each sub-swarm. Moreover, in order to explore more promising regions of the search space, differential evolution (DE) is incorporated to improve the personal best of each particle. First, the method is tested on 13 benchmark test functions and compared with three stateof-the-art approaches. The simulation results indicate that the proposed HMPSO is highly competitive in solving the 13 benchmark test functions. Afterward, the effectiveness of some mechanisms proposed in this paper and the effect of the parameter setting were validated by various experiments. Finally, HMPSO is further applied to solve 24 benchmark test functions collected in the 2006 IEEE Congress on Evolutionary Computation (CEC2006) and the experimental results indicate that HMPSO is able to deal with 22 test functions.

  7. Adjoint optimization of natural convection problems: differentially heated cavity

    Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.

    2016-06-01

    Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7 ) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here

  8. An optimization spiking neural p system for approximately solving combinatorial optimization problems.

    Zhang, Gexiang; Rong, Haina; Neri, Ferrante; Pérez-Jiménez, Mario J

    2014-08-01

    Membrane systems (also called P systems) refer to the computing models abstracted from the structure and the functioning of the living cell as well as from the cooperation of cells in tissues, organs, and other populations of cells. Spiking neural P systems (SNPS) are a class of distributed and parallel computing models that incorporate the idea of spiking neurons into P systems. To attain the solution of optimization problems, P systems are used to properly organize evolutionary operators of heuristic approaches, which are named as membrane-inspired evolutionary algorithms (MIEAs). This paper proposes a novel way to design a P system for directly obtaining the approximate solutions of combinatorial optimization problems without the aid of evolutionary operators like in the case of MIEAs. To this aim, an extended spiking neural P system (ESNPS) has been proposed by introducing the probabilistic selection of evolution rules and multi-neurons output and a family of ESNPS, called optimization spiking neural P system (OSNPS), are further designed through introducing a guider to adaptively adjust rule probabilities to approximately solve combinatorial optimization problems. Extensive experiments on knapsack problems have been reported to experimentally prove the viability and effectiveness of the proposed neural system.

  9. Analyze the optimal solutions of optimization problems by means of fractional gradient based system using VIM

    Firat Evirgen

    2016-04-01

    Full Text Available In this paper, a class of Nonlinear Programming problem is modeled with gradient based system of fractional order differential equations in Caputo's sense. To see the overlap between the equilibrium point of the fractional order dynamic system and theoptimal solution of the NLP problem in a longer timespan the Multistage Variational İteration Method isapplied. The comparisons among the multistage variational iteration method, the variationaliteration method and the fourth order Runge-Kutta method in fractional and integer order showthat fractional order model and techniques can be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programming problems.

  10. New attitude penalty functions for spacecraft optimal control problems

    Schaub, H.; Junkins, J.L. [Texas A and M Univ., College Station, TX (United States). Dept. of Aerospace Engineering; Robinett, R.D. [Sandia National Labs., Albuquerque, NM (United States)

    1996-03-01

    A solution of a spacecraft optimal control problem, whose cost function relies on an attitude description, usually depends on the choice of attitude coordinates used. A problem could be solved using 3-2-1 Euler angles or using classical Rodriguez parameters and yield two different ``optimal`` solutions, unless the performance index in invariant with respect to the attitude coordinate choice. Another problem arising with many attitude coordinates is that they have no sense of when a body has tumbled beyond 180{degrees} from the reference attitude. In many such cases it would be easier (i.e. cost less) to let the body complete the revolution than to force it to reverse the rotation and return to the desired attitude. This paper develops a universal attitude penalty function g() whose value is independent of the attitude coordinates chosen to represent it. Furthermore, this function will achieve its maximum value only when a principal rotation of {plus_minus}180{degrees} from the target state is performed. This will implicitly permit the g() function to sense the shortest rotational distance back to the reference state. An attitude penalty function which depends on the Modified Rodriguez Parameters (MRP) will also be presented. These recently discovered MRPs are a non-singular three-parameter set which can describe any three-attitude. This MRP penalty function is simpler than the attitude coordinate independent g() function, but retains the useful property of avoiding lengthy principal rotations of more than {plus_minus}180{degrees}.

  11. On the robust optimization to the uncertain vaccination strategy problem

    Chaerani, D., E-mail: d.chaerani@unpad.ac.id; Anggriani, N., E-mail: d.chaerani@unpad.ac.id; Firdaniza, E-mail: d.chaerani@unpad.ac.id [Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Padjadjaran Indonesia, Jalan Raya Bandung Sumedang KM 21 Jatinangor Sumedang 45363 (Indonesia)

    2014-02-21

    In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.

  12. Active Set Algorithm for Large-Scale Continuous Knapsack Problems with Application to Topology Optimization Problems

    Tavakoli, Ruhollah

    2010-01-01

    The structure of many real-world optimization problems includes minimization of a nonlinear (or quadratic) functional subject to bound and singly linear constraints (in the form of either equality or bilateral inequality) which are commonly called as continuous knapsack problems. Since there are efficient methods to solve large-scale bound constrained nonlinear programs, it is desirable to adapt these methods to solve knapsack problems, while preserving their efficiency and convergence theories. The goal of this paper is to introduce a general framework to extend a box-constrained optimization solver to solve knapsack problems. This framework includes two main ingredients which are O(n) methods; in terms of the computational cost and required memory; for the projection onto the knapsack constrains and the null-space manipulation of the related linear constraint. The main focus of this work is on the extension of Hager-Zhang active set algorithm (SIAM J. Optim. 2006, pp. 526--557). The main reasons for this ch...

  13. Optimal tests for the two-sample spherical location problem

    Ley, Christophe; Verdebout, Thomas

    2012-01-01

    We tackle the classical two-sample spherical location problem for directional data by having recourse to the Le Cam methodology, habitually used in classical "linear" multivariate analysis. More precisely we construct locally and asymptotically optimal (in the maximin sense) parametric tests, which we then turn into semi-parametric ones in two distinct ways. First, by using a studentization argument; this leads to so-called pseudo-FvML tests. Second, by resorting to the invariance principle; this leads to efficient rank-based tests. Within each construction, the semi-parametric tests inherit optimality under a given distribution (the FvML in the first case, any rotationally symmetric one in the second) from their parametric counterparts and also improve on the latter by being valid under the whole class of rotationally symmetric distributions. Asymptotic relative efficiencies are calculated and the finite-sample behavior of the proposed tests is investigated by means of a Monte Carlo simulation.

  14. Approximability of optimization problems through adiabatic quantum computation

    Cruz-Santos, William

    2014-01-01

    The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l

  15. Scenario tree generation and multi-asset financial optimization problems

    Geyer, Alois; Hanke, Michael; Weissensteiner, Alex

    2013-01-01

    We compare two popular scenario tree generation methods in the context of financial optimization: moment matching and scenario reduction. Using a simple problem with a known analytic solution, moment matching-when ensuring absence of arbitrage-replicates this solution precisely. On the other hand......, even if the scenario trees generated by scenario reduction are arbitrage-free, the solutions are biased and highly variable. These results hold for correlated and uncorrelated asset returns, as well as for normal and non-normal returns. © 2013 Elsevier B.V. All rights reserved....

  16. Model reduction for optimization of structural-acoustic coupling problems

    Creixell Mediante, Ester; Jensen, Jakob Søndergaard; Brunskog, Jonas;

    2016-01-01

    , which becomes highly time consuming since many iterations may be required. The use of model reduction techniques to speed up the computations is studied in this work. The Component Mode Synthesis (CMS) method and the Multi-Model Reduction (MMR) method are adapted for problems with structure......Fully coupled structural-acoustic models of complex systems, such as those used in the hearing aid field, may have several hundreds of thousands of nodes. When there is a strong structure-acoustic interaction, performing optimization on one part requires the complete model to be taken into account...

  17. THE INVERSE PROBLEM OF OPTIMAL REGULATORS AND ITS AP PLICATION

    2000-01-01

    This paper presents a new solution to the inverse problem of linear optimal regulators to minimize a cost function and meet the requirements of relative stability in the presence of a constant but unknown disturbance. A state feedback matrix is developed using Lyapunov's second method. Moreover, the relationships between the state feedback matrix and the cost function are obtained, and a formula to solve the weighting matrices is suggest ed. The developed method is applied successfully to design the horizontal loops in the inertial navigation system.

  18. Can linear superiorization be useful for linear optimization problems?

    Censor, Yair

    2017-04-01

    Linear superiorization (LinSup) considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are: (i) does LinSup provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? (ii) How does LinSup fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: ‘yes’ and ‘very well’, respectively.

  19. Topology optimization of coated structures and material interface problems

    Clausen, Anders; Aage, Niels; Sigmund, Ole

    2015-01-01

    This paper presents a novel method for including coated structures and prescribed material interface properties into the minimum compliance topology optimization problem. Several elements of the method are applicable to a broader range of interface problems. The approach extends the standard SIMP...... method by including the normalized norm of the spatial gradient of the design field into the material interpolation function, enforcing coating material at interfaces by attributing particular properties. The length scales of the base structure and the coating are separated by introducing a two......-step filtering/projection approach. The modeled coating thickness is derived analytically, and the coating is shown to be accurately controlled and applied in a highly uniform manner over the structure. An alternative interpretation of the model is to perform single-material design for additive manufacturing...

  20. Approximation Algorithms for Optimal Decision Trees and Adaptive TSP Problems

    Gupta, Anupam; Nagarajan, Viswanath; Ravi, R

    2010-01-01

    We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any particular disease, what is a good adaptive strategy to perform these tests to minimize the expected cost to identify the disease? We settle the approximability of this problem by giving a tight $O(\\log m)$-approximation algorithm. We also consider a more substantial generalization, the Adaptive TSP problem. Given an underlying metric space, a random subset $S$ of cities is drawn from a known distribution, but $S$ is initially unknown to us--we get information about whether any city is in $S$ only when we visit the city in question. What is a good adaptive way of visiting all the cities in the random subset $S$ while minimizing the expected distance traveled? For this problem, we give the first poly-logarithmic approximation, and show that this algorithm is best possible unless w...

  1. Enhanced ant colony optimization for inventory routing problem

    Wong, Lily; Moin, Noor Hasnah

    2015-10-01

    The inventory routing problem (IRP) integrates and coordinates two important components of supply chain management which are transportation and inventory management. We consider a one-to-many IRP network for a finite planning horizon. The demand for each product is deterministic and time varying as well as a fleet of capacitated homogeneous vehicles, housed at a depot/warehouse, delivers the products from the warehouse to meet the demand specified by the customers in each period. The inventory holding cost is product specific and is incurred at the customer sites. The objective is to determine the amount of inventory and to construct a delivery routing that minimizes both the total transportation and inventory holding cost while ensuring each customer's demand is met over the planning horizon. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (best integer) for each instance considered. We propose an enhanced ant colony optimization (ACO) to solve the problem and the built route is improved by using local search. The computational experiments demonstrating the effectiveness of our approach is presented.

  2. Global Optimal Solution to Discrete Value Selection Problem with Inequality Constraints

    Ruan, Ning

    2012-01-01

    This paper presents a canonical dual method for solving a quadratic discrete value selection problem subjected to inequality constraints. The problem is first transformed into a problem with quadratic objective and 0-1 integer variables. The dual problem of the 0-1 programming problem is thus constructed by using the canonical duality theory. Under appropriate conditions, this dual problem is a maximization problem of a concave function over a convex continuous space. Numerical simulation studies, including some large scale problems, are carried out so as to demonstrate the effectiveness and efficiency of the method proposed.

  3. Modified Monkey Optimization Algorithm for Solving Optimal Reactive Power Dispatch Problem

    Kanagasabai Lenin

    2015-04-01

    Full Text Available In this paper, a novel approach Modified Monkey optimization (MMO algorithm for solving optimal reactive power dispatch problem has been presented. MMO is a population based stochastic meta-heuristic algorithm and it is inspired by intelligent foraging behaviour of monkeys. This paper improves both local leader and global leader phases.  The proposed (MMO algorithm has been tested in standard IEEE 30 bus test system and simulation results show the worthy performance of the proposed algorithm in reducing the real power loss.

  4. A New Optimization Framework To Solve The Optimal Feeder Reconfiguration And Capacitor Placement Problems

    Mohammad-Reza Askari

    2015-07-01

    Full Text Available Abstract This paper introduces a new stochastic optimization framework based bat algorithm BA to solve the optimal distribution feeder reconfiguration DFR as well as the shunt capacitor placement and sizing in the distribution systems. The objective functions to be investigated are minimization of the active power losses and minimization of the total network costs an. In order to consider the uncertainties of the active and reactive loads in the problem point estimate method PEM with 2m scheme is employed as the stochastic tool. The feasibility and good performance of the proposed method are examined on the IEEE 69-bus test system.

  5. Solving the Traveling Salesman's Problem Using the African Buffalo Optimization

    Odili, Julius Beneoluchi; Mohmad Kahar, Mohd Nizam

    2016-01-01

    This paper proposes the African Buffalo Optimization (ABO) which is a new metaheuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills, and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman's Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation, and good memory of its previous personal exploits as well as tapping from the herd's collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive. PMID:26880872

  6. Solving the Traveling Salesman's Problem Using the African Buffalo Optimization.

    Odili, Julius Beneoluchi; Mohmad Kahar, Mohd Nizam

    2016-01-01

    This paper proposes the African Buffalo Optimization (ABO) which is a new metaheuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills, and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman's Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation, and good memory of its previous personal exploits as well as tapping from the herd's collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive.

  7. Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints

    Kmet', Tibor; Kmet'ová, Mária

    2009-09-01

    A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.

  8. SECOND-ORDER OPTIMALITY CONDITIONS FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY 3-DIMENSIONAL NEVIER-STOKES EQUATIONS

    2006-01-01

    This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.

  9. PARETO OPTIMAL SOLUTIONS FOR MULTI-OBJECTIVE GENERALIZED ASSIGNMENT PROBLEM

    S. Prakash

    2012-01-01

    Full Text Available

    ENGLISH ABSTRACT: The Multi-Objective Generalized Assignment Problem (MGAP with two objectives, where one objective is linear and the other one is non-linear, has been considered, with the constraints that a job is assigned to only one worker – though he may be assigned more than one job, depending upon the time available to him. An algorithm is proposed to find the set of Pareto optimal solutions of the problem, determining assignments of jobs to workers with two objectives without setting priorities for them. The two objectives are to minimise the total cost of the assignment and to reduce the time taken to complete all the jobs.

    AFRIKAANSE OPSOMMING: ‘n Multi-doelwit veralgemeende toekenningsprobleem (“multi-objective generalised assignment problem – MGAP” met twee doelwitte, waar die een lineêr en die ander nielineêr is nie, word bestudeer, met die randvoorwaarde dat ‘n taak slegs toegedeel word aan een werker – alhoewel meer as een taak aan hom toegedeel kan word sou die tyd beskikbaar wees. ‘n Algoritme word voorgestel om die stel Pareto-optimale oplossings te vind wat die taaktoedelings aan werkers onderhewig aan die twee doelwitte doen sonder dat prioriteite toegeken word. Die twee doelwitte is om die totale koste van die opdrag te minimiseer en om die tyd te verminder om al die take te voltooi.

  10. An optimal iterative solver for the Stokes problem

    Wathen, A. [Univ. of Bristol (United Kingdom); Silvester, D.

    1994-12-31

    Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal solver for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.

  11. Solving Nonlinear Optimization Problems of Real Functions in Complex Variables by Complex-Valued Iterative Methods.

    Zhang, Songchuan; Xia, Youshen

    2016-12-28

    Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an ℓ₁-norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.

  12. Applying Soft Arc Consistency to Distributed Constraint Optimization Problems

    Matsui, Toshihiro; Silaghi, Marius C.; Hirayama, Katsutoshi; Yokoo, Makot; Matsuo, Hiroshi

    The Distributed Constraint Optimization Problem (DCOP) is a fundamental framework of multi-agent systems. With DCOPs a multi-agent system is represented as a set of variables and a set of constraints/cost functions. Distributed task scheduling and distributed resource allocation can be formalized as DCOPs. In this paper, we propose an efficient method that applies directed soft arc consistency to a DCOP. In particular, we focus on DCOP solvers that employ pseudo-trees. A pseudo-tree is a graph structure for a constraint network that represents a partial ordering of variables. Some pseudo-tree-based search algorithms perform optimistic searches using explicit/implicit backtracking in parallel. However, for cost functions taking a wide range of cost values, such exact algorithms require many search iterations. Therefore additional improvements are necessary to reduce the number of search iterations. A previous study used a dynamic programming-based preprocessing technique that estimates the lower bound values of costs. However, there are opportunities for further improvements of efficiency. In addition, modifications of the search algorithm are necessary to use the estimated lower bounds. The proposed method applies soft arc consistency (soft AC) enforcement to DCOP. In the proposed method, directed soft AC is performed based on a pseudo-tree in a bottom up manner. Using the directed soft AC, the global lower bound value of cost functions is passed up to the root node of the pseudo-tree. It also totally reduces values of binary cost functions. As a result, the original problem is converted to an equivalent problem. The equivalent problem is efficiently solved using common search algorithms. Therefore, no major modifications are necessary in search algorithms. The performance of the proposed method is evaluated by experimentation. The results show that it is more efficient than previous methods.

  13. 3D Topology optimization of Stokes flow problems

    Gersborg-Hansen, Allan; Dammann, Bernd

    , the optimizer suggests a design that stretches the hot-cold interface, which is encouraging since "stretching and folding" is known to be key ingredients in efficient mixing. The modelling is performed using a finite element based solver, with analytically derived sensitivities that drives a gradient based...... for the fluid behavior in a micro fluidic device. Such a device has finite size and a large degree of freedom for the design of geometry. Physically Stokes flow is an exotic inertia free flow. This, however, complicates mixing by passive devices. Passive devices, that is, devices without moving parts, are often...... of practical interest since they are easily manufacturable and maintenance free. In order to tackle such a challenging problem a robust method is needed which we approach by this contribution. The finite size of a micro fluidic device calls for 3D modelling of the equations, in particular when the design...

  14. Optimal Rapid Restart of Heuristic Methods of NP Hard Problems

    侯越先; 王芳

    2004-01-01

    Many heuristic search methods exhibit a remarkable variability in the time required to solve some particular problem instances. Their cost distributions are often heavy-tailed. It has been demonstrated that, in most cases, rapid restart (RR) method can prominently suppress the heavy-tailed nature of the instances and improve computation efficiency. However, it is usually time-consuming to check whether an algorithm on a specific instance is heavy-tailed or not. Moreover, if the heavy-tailed distribution is confirmed and the RR method is relevant, an optimal RR threshold should be chosen to facilitate the RR mechanism. In this paper, an approximate approach is proposed to quickly check whether an algorithm on a specific instance is heavy-tailed or not.The method is realized by means of calculating the maximal Lyapunov exponent of its generic running trace.Then a statistical formula to estimate the optimal RR threshold is educed. The method is based on common nonparametric estimation, e. g. , Kernel estimation. Two heuristic methods are selected to verify our method. The experimental results are consistent with the theoretical consideration perfectly.

  15. Modified Lagrangian and Least Root Approaches for General Nonlinear Optimization Problems

    W. Oettli; X.Q. Yang

    2002-01-01

    In this paper we study nonlinear Lagrangian methods for optimization problems with side constraints.Nonlinear Lagrangian dual problems are introduced and their relations with the original problem are established.Moreover, a least root approach is investigated for these optimization problems.

  16. Optimal Control Approaches to the Aggregate Production Planning Problem

    Yasser A. Davizón

    2015-12-01

    Full Text Available In the area of production planning and control, the aggregate production planning (APP problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.

  17. AN ADAPTIVE MEMBRANE ALGORITHM FOR SOLVING COMBINATORIAL OPTIMIZATION PROBLEMS

    Juanjuan HE; Jianhua XIAO; Zehui SHAO

    2014-01-01

    Membrane algorithms (MAs), which inherit from P systems, constitute a new parallel and distribute framework for approximate computation. In the paper, a membrane algorithm is proposed with the improvement that the involved parameters can be adaptively chosen. In the algorithm, some membranes can evolve dynamically during the computing process to specify the values of the requested parameters. The new algorithm is tested on a well-known combinatorial optimization problem, the travelling salesman problem. The em-pirical evidence suggests that the proposed approach is efficient and reliable when dealing with 11 benchmark instances, particularly obtaining the best of the known solutions in eight instances. Compared with the genetic algorithm, simulated annealing algorithm, neural net-work and a fine-tuned non-adaptive membrane algorithm, our algorithm performs better than them. In practice, to design the airline network that minimize the total routing cost on the CAB data with twenty-five US cities, we can quickly obtain high quality solutions using our algorithm.

  18. SEQUENTIAL SYSTEMS OF LINEAR EQUATIONS ALGORITHM FOR NONLINEAR OPTIMIZATION PROBLEMS - INEQUALITY CONSTRAINED PROBLEMS

    Zi-you Gao; Tian-de Guo; Guo-ping He; Fang Wu

    2002-01-01

    In this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations having a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQPtype algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.

  19. Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem

    2006-01-01

    Capacitated vehicle routing problem (CVRP) is an NP-hard problem. For large-scale problems, it is quite difficult to achieve an optimal solution with traditional optimization methods due to the high computational complexity. A new hybrid approximation algorithm is developed in this work to solve the problem. In the hybrid algorithm, discrete particle swarm optimization (DPSO) combines global search and local search to search for the optimal results and simulated annealing (SA) uses certain probability to avoid being trapped in a local optimum. The computational study showed that the proposed algorithm is a feasible and effective approach for capacitated vehicle routing problem, especially for large scale problems.

  20. Crisscross Optimization Algorithm and Monte Carlo Simulation for Solving Optimal Distributed Generation Allocation Problem

    Xiangang Peng

    2015-12-01

    Full Text Available Distributed generation (DG systems are integral parts in future distribution networks. In this paper, a novel approach integrating crisscross optimization algorithm and Monte Carlo simulation (CSO-MCS is implemented to solve the optimal DG allocation (ODGA problem. The feature of applying CSO to address the ODGA problem lies in three interacting operators, namely horizontal crossover, vertical crossover and competitive operator. The horizontal crossover can search new solutions in a hypercube space with a larger probability while in the periphery of each hypercube with a decreasing probability. The vertical crossover can effectively facilitate those stagnant dimensions of a population to escape from premature convergence. The competitive operator allows the crisscross search to always maintain in a historical best position to quicken the converge rate. It is the combination of the double search strategies and competitive mechanism that enables CSO significant advantage in convergence speed and accuracy. Moreover, to deal with system uncertainties such as the output power of wind turbine and photovoltaic generators, an MCS-based method is adopted to solve the probabilistic power flow. The effectiveness of the CSO-MCS method is validated on the typical 33-bus and 69-bus test system, and results substantiate the suitability of CSO-MCS for multi-objective ODGA problem.

  1. Multiswarm comprehensive learning particle swarm optimization for solving multiobjective optimization problems

    Yu, Xiang; Zhang, Xueqing

    2017-01-01

    Comprehensive learning particle swarm optimization (CLPSO) is a powerful state-of-the-art single-objective metaheuristic. Extending from CLPSO, this paper proposes multiswarm CLPSO (MSCLPSO) for multiobjective optimization. MSCLPSO involves multiple swarms, with each swarm associated with a separate original objective. Each particle’s personal best position is determined just according to the corresponding single objective. Elitists are stored externally. MSCLPSO differs from existing multiobjective particle swarm optimizers in three aspects. First, each swarm focuses on optimizing the associated objective using CLPSO, without learning from the elitists or any other swarm. Second, mutation is applied to the elitists and the mutation strategy appropriately exploits the personal best positions and elitists. Third, a modified differential evolution (DE) strategy is applied to some extreme and least crowded elitists. The DE strategy updates an elitist based on the differences of the elitists. The personal best positions carry useful information about the Pareto set, and the mutation and DE strategies help MSCLPSO discover the true Pareto front. Experiments conducted on various benchmark problems demonstrate that MSCLPSO can find nondominated solutions distributed reasonably over the true Pareto front in a single run. PMID:28192508

  2. Multiswarm comprehensive learning particle swarm optimization for solving multiobjective optimization problems.

    Yu, Xiang; Zhang, Xueqing

    2017-01-01

    Comprehensive learning particle swarm optimization (CLPSO) is a powerful state-of-the-art single-objective metaheuristic. Extending from CLPSO, this paper proposes multiswarm CLPSO (MSCLPSO) for multiobjective optimization. MSCLPSO involves multiple swarms, with each swarm associated with a separate original objective. Each particle's personal best position is determined just according to the corresponding single objective. Elitists are stored externally. MSCLPSO differs from existing multiobjective particle swarm optimizers in three aspects. First, each swarm focuses on optimizing the associated objective using CLPSO, without learning from the elitists or any other swarm. Second, mutation is applied to the elitists and the mutation strategy appropriately exploits the personal best positions and elitists. Third, a modified differential evolution (DE) strategy is applied to some extreme and least crowded elitists. The DE strategy updates an elitist based on the differences of the elitists. The personal best positions carry useful information about the Pareto set, and the mutation and DE strategies help MSCLPSO discover the true Pareto front. Experiments conducted on various benchmark problems demonstrate that MSCLPSO can find nondominated solutions distributed reasonably over the true Pareto front in a single run.

  3. Improved Glowworm Swarm Optimization Algorithm for Multilevel Color Image Thresholding Problem

    Lifang He; Songwei Huang

    2016-01-01

    The thresholding process finds the proper threshold values by optimizing a criterion, which can be considered as a constrained optimization problem. The computation time of traditional thresholding techniques will increase dramatically for multilevel thresholding. To greatly overcome this problem, swarm intelligence algorithm is widely used to search optimal thresholds. In this paper, an improved glowworm swarm optimization (IGSO) algorithm has been presented to find the optimal multilevel th...

  4. A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems

    Pongsakorn Sunthrayuth

    2012-01-01

    Full Text Available We introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, zero set of the sum of a maximal monotone operators and inverse-strongly monotone mappings, and the set of common fixed points of an infinite family of nonexpansive mappings with infinite real number. Furthermore, we prove under some mild conditions that the proposed iterative algorithm converges strongly to a common element of the above four sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. The results presented in the paper improve and extend the recent ones announced by many others.

  5. Pseudospectral Collocation Methods for the Direct Transcription of Optimal Control Problems

    2003-04-01

    solving optimal control problems for trajectory optimization, spacecraft attitude control, jet thruster control, missile guidance and many other... optimal control problems using a pseudospectral direct transcription method. These problems are stated here so that they may be referred to elsewhere...e.g., [7]. 2.3 Prototypical Examples Throughout this thesis two example problems are used to demonstrate various prop- erties associated with solving

  6. Particle Swarm Optimization-Proximal Point Algorithm for Nonlinear Complementarity Problems

    Chai Jun-Feng; Wang Shu-Yan

    2013-01-01

    A new algorithm is presented for solving the nonlinear complementarity problem by combining the particle swarm and proximal point algorithm, which is called the particle swarm optimization-proximal point algorithm. The algorithm mainly transforms nonlinear complementarity problems into unconstrained optimization problems of smooth functions using the maximum entropy function and then optimizes the problem using the proximal point algorithm as the outer algorithm and particle swarm algorithm a...

  7. Efficient Output Solution for Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

    Sie Long Kek

    2015-01-01

    Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.

  8. Optimal Control Problem of Feeding Adaptations of Daphnia and Neural Network Simulation

    Kmet', Tibor; Kmet'ov, Mria

    2010-09-01

    A neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints and open final time. The optimal control problem is transcribed into nonlinear programming problem, which is implemented with adaptive critic neural network [9] and recurrent neural network for solving nonlinear proprojection equations [10]. The proposed simulation methods is illustrated by the optimal control problem of feeding adaptation of filter feeders of Daphnia. Results show that adaptive critic based systematic approach and neural network solving of nonlinear equations hold promise for obtaining the optimal control with control and state constraints and open final time.

  9. Forward-backward Stochastic Differential Equations and Backward Linear Quadratic Stochastic Optimal Control Problem

    ZHANG DE-TAO

    2009-01-01

    In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations.

  10. 26 CFR 49.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 16 2010-04-01 2010-04-01 true Introduction. 49.0-1 Section 49.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) MISCELLANEOUS EXCISE TAXES FACILITIES AND SERVICES EXCISE TAXES Introduction § 49.0-1 Introduction. The regulations in this part 49...

  11. 26 CFR 44.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 16 2010-04-01 2010-04-01 true Introduction. 44.0-1 Section 44.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) MISCELLANEOUS EXCISE TAXES TAXES ON WAGERING; EFFECTIVE JANUARY 1, 1955 Introduction § 44.0-1 Introduction. (a) In general....

  12. 26 CFR 46.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 16 2010-04-01 2010-04-01 true Introduction. 46.0-1 Section 46.0-1 Internal... TAX ON POLICIES ISSUED BY FOREIGN INSURERS AND OBLIGATIONS NOT IN REGISTERED FORM Introduction § 46.0-1 Introduction. The regulations in this part 46 relate to the taxes on policies issued by...

  13. 26 CFR 48.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 16 2010-04-01 2010-04-01 true Introduction. 48.0-1 Section 48.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) MISCELLANEOUS EXCISE TAXES MANUFACTURERS AND RETAILERS EXCISE TAXES Introduction § 48.0-1 Introduction. The regulations in this part 48...

  14. 26 CFR 20.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 14 2010-04-01 2010-04-01 false Introduction. 20.0-1 Section 20.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES ESTATE TAX; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general....

  15. 26 CFR 52.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 17 2010-04-01 2010-04-01 false Introduction. 52.0-1 Section 52.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) MISCELLANEOUS EXCISE TAXES (CONTINUED) ENVIRONMENTAL TAXES § 52.0-1 Introduction. The regulations in this part 52 are...

  16. 26 CFR 25.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 14 2010-04-01 2010-04-01 false Introduction. 25.0-1 Section 25.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) ESTATE AND GIFT TAXES GIFT TAX; GIFTS MADE AFTER DECEMBER 31, 1954 Gift Tax § 25.0-1 Introduction. (a) In general. (1) The...

  17. 26 CFR 41.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 16 2010-04-01 2010-04-01 true Introduction. 41.0-1 Section 41.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) MISCELLANEOUS EXCISE TAXES EXCISE TAX ON USE OF CERTAIN HIGHWAY MOTOR VEHICLES Introduction § 41.0-1 Introduction. The regulations...

  18. 26 CFR 43.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 16 2010-04-01 2010-04-01 true Introduction. 43.0-1 Section 43.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) MISCELLANEOUS EXCISE TAXES EXCISE TAX ON TRANSPORTATION BY WATER § 43.0-1 Introduction. The regulations in this part 43 are...

  19. 26 CFR 31.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 15 2010-04-01 2010-04-01 false Introduction. 31.0-1 Section 31.0-1 Internal... OF INCOME TAX AT SOURCE EMPLOYMENT TAXES AND COLLECTION OF INCOME TAX AT SOURCE Introduction § 31.0-1 Introduction. (a) In general. The regulations in this part relate to the employment taxes imposed by subtitle...

  20. 26 CFR 40.0-1 - Introduction.

    2010-04-01

    ... 26 Internal Revenue 16 2010-04-01 2010-04-01 true Introduction. 40.0-1 Section 40.0-1 Internal Revenue INTERNAL REVENUE SERVICE, DEPARTMENT OF THE TREASURY (CONTINUED) MISCELLANEOUS EXCISE TAXES EXCISE TAX PROCEDURAL REGULATIONS § 40.0-1 Introduction. (a) In general. The regulations in this part 40...

  1. 28 CFR 0.1 - Organizational units.

    2010-07-01

    ... 28 Judicial Administration 1 2010-07-01 2010-07-01 false Organizational units. 0.1 Section 0.1 Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE Organizational Structure of the Department of Justice § 0.1 Organizational units. The Department of Justice shall...

  2. Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

    Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)

    2015-04-15

    The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.

  3. Methods of centers and methods of feasible directions for the solution of optimal control problems.

    Polak, E.; Mukai, H.; Pironneau, O.

    1971-01-01

    Demonstration of the applicability of methods of centers and of methods of feasible directions to optimal control problems. Presented experimental results show that extensions of Frank-Wolfe (1956), Zoutendijk (1960), and Pironneau-Polak (1971) algorithms for nonlinear programming problems can be quite efficient in solving optimal control problems.

  4. Existence of the Optimal Control for Stochastic Boundary Control Problems Governed by Semilinear Parabolic Equations

    Weifeng Wang

    2014-01-01

    Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.

  5. Examining the Solution for Solving Optimization Problems using Swarm Intelligence and Its Applications

    V. Selvi

    2012-06-01

    Full Text Available - SI is a computational and collective behavioral metaphor that is used for solving problems. The problems can be solved by SI by taking ants, termites, bees and wasps as an example. The application of SI algorithm are ACO, PSO and ABC which have been already applied to solve real world optimization problems in engineering. ACO is a member of SI in which ACO is inspired by the behaviour of ant colonies and it constitutes some metaheuristic optimization. ACO’s aim is to search for an optimal path with the help of graph. In PSO, a solution of continuous optimization problems can be solved , because PSO is population based stochastic optimization techniques for the solution of continuous optimization problem. In ABC the solution for the problem is found with help of foraging behaviour of honey bees. It is also swarm based meta heuristic algorithm. This paper presents the experimental verification of ACO and EACO.

  6. A MATLAB GUI for a Legendre Pseudospectral algorithm for optimal control problems

    Hall, Andrew O.

    1999-01-01

    Approved for public release; distribution is unlimited This implementation of a Legendre-Gauss-Lobatto Pseudospectral (LGLP) algorithm takes advantage of the MATLAB Graphical User Interface (GUI) and the Optimization Toolbox to allow an efficient implementation of a direct solution technique. Direct solutions techniques solve optimal control problems without solving for the optimality conditions. Using the LGLP method, an optimal control problem is discretized into a Nonlinear Program (NLP...

  7. A maximum principle for smooth optimal impulsive control problems with multipoint state constraints

    Dykhta, V. A.; Samsonyuk, O. N.

    2009-06-01

    A nonlinear optimal impulsive control problem with trajectories of bounded variation subject to intermediate state constraints at a finite number on nonfixed instants of time is considered. Features of this problem are discussed from the viewpoint of the extension of the classical optimal control problem with the corresponding state constraints. A necessary optimality condition is formulated in the form of a smooth maximum principle; thorough comments are given, a short proof is presented, and examples are discussed.

  8. An Evolutionary Algorithm to Optimization of Discrete Problem Based on Pheromone

    2001-01-01

    The pheromone based positive feedback approach of ant algorithmis int r oduced in evolutionary computation of discrete problem, so as to accomplish the optimization of each allele. It ensures stable converge of the algorithm into global optimum. The optimal cutting problem is studied as an example to analyze the performance of the algorithm. The experimental results show the novel performa nce of the algorithm in the optimization of discrete problem.

  9. A numerical method for solving optimal control problems using state parametrization

    Mehne, H.; Borzabadi, A.

    2006-06-01

    A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.

  10. Optimization and Robustness in Planning and Scheduling Problems. Application to Container Terminals

    Rodríguez Molins, Mario

    2015-01-01

    Despite the continuous evolution in computers and information technology, real-world combinatorial optimization problems are NP-problems, in particular in the domain of planning and scheduling. Thus, although exact techniques from the Operations Research (OR) field, such as Linear Programming, could be applied to solve optimization problems, they are difficult to apply in real-world scenarios since they usually require too much computational time, i.e: an optimized solution is ...

  11. On optimal solutions of the constrained ℓ 0 regularization and its penalty problem

    Zhang, Na; Li, Qia

    2017-02-01

    The constrained {{\\ell}0} regularization plays an important role in sparse reconstruction. A widely used approach for solving this problem is the penalty method, of which the least square penalty problem is a special case. However, the connections between global minimizers of the constrained {{\\ell}0} problem and its penalty problem have never been studied in a systematic way. This work provides a comprehensive investigation on optimal solutions of these two problems and their connections. We give detailed descriptions of optimal solutions of the two problems, including existence, stability with respect to the parameter, cardinality and strictness. In particular, we find that the optimal solution set of the penalty problem is piecewise constant with respect to the penalty parameter. Then we analyze in-depth the relationship between optimal solutions of the two problems. It is shown that, in the noisy case the least square penalty problem probably has no common optimal solutions with the constrained {{\\ell}0} problem for any penalty parameter. Under a mild condition on the penalty function, we establish that the penalty problem has the same optimal solution set as the constrained {{\\ell}0} problem when the penalty parameter is sufficiently large. Based on the conditions, we further propose exact penalty problems for the constrained {{\\ell}0} problem. Finally, we present a numerical example to illustrate our main theoretical results.

  12. A comparative study of three simulation optimization algorithms for solving high dimensional multi-objective optimization problems in water resources

    Schütze, Niels; Wöhling, Thomas; de Play, Michael

    2010-05-01

    Some real-world optimization problems in water resources have a high-dimensional space of decision variables and more than one objective function. In this work, we compare three general-purpose, multi-objective simulation optimization algorithms, namely NSGA-II, AMALGAM, and CMA-ES-MO when solving three real case Multi-objective Optimization Problems (MOPs): (i) a high-dimensional soil hydraulic parameter estimation problem; (ii) a multipurpose multi-reservoir operation problem; and (iii) a scheduling problem in deficit irrigation. We analyze the behaviour of the three algorithms on these test problems considering their formulations ranging from 40 up to 120 decision variables and 2 to 4 objectives. The computational effort required by each algorithm in order to reach the true Pareto front is also analyzed.

  13. Optimal Control Problem Governed by Semilinear Parabolic Equation and its Algorithm

    Chun-fa Li; Xue Yang; En-min Feng

    2008-01-01

    In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.

  14. Couplings in Multi-criterion Aerodynamic Optimization Problems Using Adjoint Methods and Game Strategies

    Tang Zhili; Dong Jun

    2009-01-01

    complete and complete decisions of the leader and followers respectively. Several design examples illustrate the efficiency of the coupling algorithms for multi-criterion aerodynamic design optimization problems.

  15. Comparison of Optimal Design Methods in Inverse Problems

    2011-05-11

    optimal design methods were implemented using constrained optimization algorithms, either MATLAB’s fmincon or SolvOpt, developed by A. Kuntsevich and...A. Kuntsevich and F. Kappel. SolvOpt, Retrieved December 2009, from http://www.kfunigraz.ac.at/imawww/ kuntsevich /solvopt/. [18] G. Pacini, and R.N

  16. A Particle Swarm Optimization with Adaptive Multi-Swarm Strategy for Capacitated Vehicle Routing Problem

    Kui-Ting CHEN

    2015-12-01

    Full Text Available Capacitated vehicle routing problem with pickups and deliveries (CVRPPD is one of the most challenging combinatorial optimization problems which include goods delivery/pickup optimization, vehicle number optimization, routing path optimization and transportation cost minimization. The conventional particle swarm optimization (PSO is difficult to find an optimal solution of the CVRPPD due to its simple search strategy. A PSO with adaptive multi-swarm strategy (AMSPSO is proposed to solve the CVRPPD in this paper. The proposed AMSPSO employs multiple PSO algorithms and an adaptive algorithm with punishment mechanism to search the optimal solution, which can deal with large-scale optimization problems. The simulation results prove that the proposed AMSPSO can solve the CVRPPD with the least number of vehicles and less transportation cost, simultaneously.

  17. 次线性Emden—Fowler方程两点边值问题的C[0,1]正解的唯一性%The uniqueness of the C[ 0,1 ] positive solution of the two-point boundary value problem of the sublinear Emden-Fowler equations

    刘炳; 闫宝强

    2012-01-01

    Two-point boundary value problem of the sublinear Emden-Fowler equations has been addressed in many literatures, but the uniqueness of the C[0,1 ] positive solution has not been investigated. We employ monotone iterative method to address such problem and derive the uniqueness of the C[ 0,1 ] positive solution of the boundary value problem of such equations.%次线性Emden-Fowler方程两点边值问题在很多文献中用到,但对于该类问题的C[0,1]正解的唯一性还没有研究。本文利用单调迭代方法,对这一问题进行了研究,得出了该类方程两点边值问题的C[0,1]正解是存在且唯一的。

  18. Optimization of constrained multiple-objective reliability problems using evolutionary algorithms

    Salazar, Daniel [Instituto de Sistemas Inteligentes y Aplicaciones Numericas en Ingenieria (IUSIANI), Division de Computacion Evolutiva y Aplicaciones (CEANI), Universidad de Las Palmas de Gran Canaria, Islas Canarias (Spain) and Facultad de Ingenieria, Universidad Central Venezuela, Caracas (Venezuela)]. E-mail: danielsalazaraponte@gmail.com; Rocco, Claudio M. [Facultad de Ingenieria, Universidad Central Venezuela, Caracas (Venezuela)]. E-mail: crocco@reacciun.ve; Galvan, Blas J. [Instituto de Sistemas Inteligentes y Aplicaciones Numericas en Ingenieria (IUSIANI), Division de Computacion Evolutiva y Aplicaciones (CEANI), Universidad de Las Palmas de Gran Canaria, Islas Canarias (Spain)]. E-mail: bgalvan@step.es

    2006-09-15

    This paper illustrates the use of multi-objective optimization to solve three types of reliability optimization problems: to find the optimal number of redundant components, find the reliability of components, and determine both their redundancy and reliability. In general, these problems have been formulated as single objective mixed-integer non-linear programming problems with one or several constraints and solved by using mathematical programming techniques or special heuristics. In this work, these problems are reformulated as multiple-objective problems (MOP) and then solved by using a second-generation Multiple-Objective Evolutionary Algorithm (MOEA) that allows handling constraints. The MOEA used in this paper (NSGA-II) demonstrates the ability to identify a set of optimal solutions (Pareto front), which provides the Decision Maker with a complete picture of the optimal solution space. Finally, the advantages of both MOP and MOEA approaches are illustrated by solving four redundancy problems taken from the literature.

  19. Diagnostic criteria for idiopathic inflammatory myopathies. Problems of their optimization

    O. A. Antelava

    2014-01-01

    Full Text Available The paper deals with the problems of optimizing the diagnostic criteria for idiopathic inflammatory myopathies (IIM, a group of heterogeneous rare autoimmune diseases characterized by inflammatory lesion in the skeletal muscles. The representatives of this group are traditionally considered to be polymyositis (PM, dermatomyositis (DM, and inclusion-body myositis. The authors detail the history of classification criteria for IIM from those proposed by T.A. Medsger et al. (1970 relying on its clinical picture, laboratory data and instrumental findings, as well as the criteria (including the first introduced exclusion ones elaborated by A. Bohan and J.B. Peter in 1975, which remain fundamental in both clinical practice and researches. The basis for the clinical and serological criteria proposed by Y. Troyanov et al. (2005 for IIM is the identification of myositis-overlap syndromes. The classificational (subtype identification and therapeutic value of the criteria based on clinical and serological characteristics was supported by the Hungarian investigators A. Vancsa et al. (2010 who investigated the relationship between the clinical and therapeutic characteristics of IIM and positivity for myositis-specific and myositis-associated antibodies. The criteria developed by M.C. Dalakas (1991, 2003 are based on the specific immunopathological features of a histological pattern, which allow the differentiation of DM, PM, and inclusion-body myositis from other myopathic syndromes. The 2004 European Neuromuscular Center (ENMC criteria first identify necrotizing autoimmune myopathy and nonspecific myositis as individual subtypes. The serological classification of IIM, which is based onthe assessment of autoantibodies that play an important role in the pathogenesis of the disease, is of indubitable interest. There is an obvious need for the correct and timely diagnosis of both IIM as a whole and its subtypes in particular, which is complicated by

  20. Quantum Field Theory in (0 + 1) Dimensions

    Boozer, A. D.

    2007-01-01

    We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…

  1. An Optimization Problem for Predicting the Maximal Effect of Degradation of Mechanical Structures

    Achtziger, W.; Bendsøe, Martin P.; Taylor, J. E.

    2000-01-01

    -product, this gives insight in terms of a mechanical interpretation of the optimization problem. We derive an equivalent convex problem formulation and a convex dual problem, and for dyadic matrices A(i) a quadratic programming problem formulation is developed. A nontrivial numerical example is included, based...

  2. FIRST-ORDER METHODS FOR SOLVING THE OPTIMAL STATIC H∞-SYNTHESIS PROBLEM

    EI-Sayed M.E. Mostafa

    2007-01-01

    In this paper, we consider the static output feedback (SOF) H∞-synthesis problem posed as a nonlinear semi-definite programming (NSDP) problem. Two numerical algorithms are developed to tackle the NSDP problem by solving the corresponding KarushKuhn-Tucker first-order necessary optimality conditions iteratively. Numerical results for various benchmark problems illustrating the performance of the proposed methods are given.

  3. Probabilistic Analysis of Combinatorial Optimization Problems on Hypergraph Matchings

    2012-02-01

    PfBng; (16) where Bn is the event that there are no empty boxes, for which it holds (see, e.g., Feller , 1968): PfBng D nX iD0 .1/i n i ! 1 i n...Combinatorics, Academic Press, New York. Feller , W. (1968) An Introduction to Probability Theory and Its Applications, volume I, John Wiley & Sons, New York, 3rd

  4. An Improved Immune Genetic Algorithm for Solving the Optimization Problems of Computer Communication Networks

    SUN Li-juan; LI Chao

    2003-01-01

    Obtaining the average delay and selecting a route in a communication network are multi-constrained nonlinear optimization problems. In this paper, based on the immune genetic algorithm, a new fuzzy self-adaptive mutation operator and a new upside-down code operator are proposed. This improved IGA is further successfully applied to solve optimal problems of computer communication nets.

  5. Optimal Stopping Problems Driven by Lévy Processes and Pasting Principles

    Surya, B.A.

    2007-01-01

    Solving optimal stopping problems driven by Lévy processes has been a challenging task and has found many applications in modern theory of mathematical finance. For example situations in which optimal stopping typically arise include the problem of finding the arbitrage-free price of the American p

  6. Improving the efficiency of solving discrete optimization problems: The case of VRP

    Belov, A.; Slastnikov, S.

    2016-02-01

    Paper is devoted constructing efficient metaheuristics algorithms for discrete optimization problems. Particularly, we consider vehicle routing problem applying original ant colony optimization method to solve it. Besides, some parts of algorithm are separated for parallel computing. Some experimental results are performed to compare the efficiency of these methods.

  7. A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations

    2008-01-01

    In this paper,we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations.A spectral approximation scheme for the parabolic optimal control problem is presented.We obtain a posteriori error estimates of the approximated solutions for both the state and the control.

  8. Optimization in First Semester Calculus: A Look at a Classic Problem

    LaRue, Renee; Infante, Nicole Engelke

    2015-01-01

    Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional…

  9. Applying Analytical Derivative and Sparse Matrix Techniques to Large-Scale Process Optimization Problems

    2000-01-01

    The performance of analytical derivative and sparse matrix techniques applied to a traditional densesequential quadratic programming(SQP) is studied, and the strategy utilizing those techniques is also presented. Computational results on two typicalchemical optimization problems demonstrate significant enhancement in efficiency, which shows this strategy ispromising and suitable for large-scale process optimization problems.

  10. Topology optimization of unsteady flow problems using the lattice Boltzmann method

    Nørgaard, Sebastian Arlund; Sigmund, Ole; Lazarov, Boyan Stefanov

    2016-01-01

    This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems....... The optimization problem is solved with a gradient based method, and the design sensitivities are computed by solving the discrete adjoint problem. For moderate Reynolds number flows, it is demonstrated that topology optimization can successfully account for unsteady effects such as vortex shedding and time......-varying boundary conditions. Such effects are relevant in several engineering applications, i.e. fluid pumps and control valves....

  11. Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance

    Bonnard, B; Glaser, S J; Lapert, M; Sugny, D; Zhang, Y

    2012-01-01

    The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.

  12. Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle–Pock algorithm

    Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan

    2012-01-01

    The primal–dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1–26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems...... for the purpose of designing iterative image reconstruction algorithms for CT. The primal–dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application...... modeling breast CT with low-intensity x-ray illumination is presented....

  13. An interpretation of the Gini coefficient in a Stiglitz two-type optimal tax problem

    Rasmussen, Bo Sandemann

    2015-01-01

    In a two-type Stiglitz (1982) model of optimal non-linear taxation it is shown that when the utility function relating to consumption is logaritmic the shadow price of the incentive constraint relating to the optimal tax problem exactly equals the Gini coefficient of the second-best optimal income...

  14. An Interpretation of the Gini Coefficient in a Stiglitz Two-Type Optimal Tax Problem

    Rasmussen, Bo Sandemann

    2014-01-01

    In a two-type Stiglitz (1982) model of optimal non-linear taxation it is shown that when the utility function relating to consumption is logaritmic the shadow price of the incentive constraint relating to the optimal tax problem exactly equals the Gini coefficient of the second-best optimal income...

  15. Newton-type method for the variational discretization of topology optimization problems

    Evgrafov, Anton

    2013-01-01

    We present a locally quadratically convergent optimization algorithm for solving topology optimization problems. The distinguishing feature of the algorithm is to treat the design as a smooth function of the state and not vice versa as in the traditional nested approach to topology optimization, ...

  16. EXISTENCE OF 0-1 UNIVERSAL MINIMAL TOTAL DOMINATING FUNCTIONS

    FANG Qizhi

    2004-01-01

    In this paper, we study the existence of 0-1 universal minimal total dominating functions in a graph. We establish a formulation of linear inequalities to characterize universal minimal total dominating functions and show that for a kind of graphs whose adjacent matrices are balanced, the existence of universal minimal total dominating functions coincides with that of 0-1 ones. It is also proved that for general graphs, the problem of testing the existence of 0-1 universal minimal total dominating functions is NP-hard.

  17. SEQUENTIAL CONVEX PROGRAMMING METHODS FOR SOLVING LARGE TOPOLOGY OPTIMIZATION PROBLEMS: IMPLEMENTATION AND COMPUTATIONAL RESULTS

    Qin Ni; Ch. Zillober; K. Schittkowski

    2005-01-01

    In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming (SCP). A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.

  18. A recurrent neural network for solving a class of generalized convex optimization problems.

    Hosseini, Alireza; Wang, Jun; Hosseini, S Mohammad

    2013-08-01

    In this paper, we propose a penalty-based recurrent neural network for solving a class of constrained optimization problems with generalized convex objective functions. The model has a simple structure described by using a differential inclusion. It is also applicable for any nonsmooth optimization problem with affine equality and convex inequality constraints, provided that the objective function is regular and pseudoconvex on feasible region of the problem. It is proven herein that the state vector of the proposed neural network globally converges to and stays thereafter in the feasible region in finite time, and converges to the optimal solution set of the problem.

  19. Mixed Nonlinear Complementarity Problems via Nonlinear Optimization: Numerical Results on Multi-Rigid-Body Contact Problems with Friction

    Andreani, Roberto; Friedlander, Ana; Mello, Margarida P.; Santos, Sandra A.

    2005-06-01

    In this work we show that the mixed nonlinear complementarity problem may be formulated as an equivalent nonlinear bound-constrained optimization problem that preserves the smoothness of the original data. One may thus take advantage of existing codes for bound-constrained optimization. This approach is implemented and tested by means of an extensive set of numerical experiments, showing promising results. The mixed nonlinear complementarity problems considered in the tests arise from the discretization of a motion planning problem concerning a set of rigid 3D bodies in contact in the presence of friction. We solve the complementarity problem associated with a single time frame, thus calculating the contact forces and accelerations of the bodies involved.

  20. Topology optimization problems with design-dependent sets of constraints

    Schou, Marie-Louise Højlund

    Topology optimization is a design tool which is used in numerous fields. It can be used whenever the design is driven by weight and strength considerations. The basic concept of topology optimization is the interpretation of partial differential equation coefficients as effective material...... that a general nonlinear interior-point algorithm applied to the MPEC formulations outperforms a general nonlinear active-set sequential quadratic programming method. Inspired by this, we implement an interior-point algorithm such that we have full control of all aspects of the code. Solving the stress...

  1. Solving the optimal attention allocation problem in manual control

    Kleinman, D. L.

    1976-01-01

    Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.

  2. Improved Glowworm Swarm Optimization Algorithm for Multilevel Color Image Thresholding Problem

    Lifang He

    2016-01-01

    Full Text Available The thresholding process finds the proper threshold values by optimizing a criterion, which can be considered as a constrained optimization problem. The computation time of traditional thresholding techniques will increase dramatically for multilevel thresholding. To greatly overcome this problem, swarm intelligence algorithm is widely used to search optimal thresholds. In this paper, an improved glowworm swarm optimization (IGSO algorithm has been presented to find the optimal multilevel thresholds of color image based on the between-class variance and minimum cross entropy (MCE. The proposed methods are examined on standard set of color test images by using various numbers of threshold values. The results are then compared with those of basic glowworm swarm optimization, adaptive particle swarm optimization (APSO, and self-adaptive differential evolution (SaDE. The simulation results show that the proposed method can find the optimal thresholds accurately and efficiently and is an effective multilevel thresholding method for color image segmentation.

  3. A Hybrid Intelligent Algorithm for Optimal Birandom Portfolio Selection Problems

    Qi Li

    2014-01-01

    Full Text Available Birandom portfolio selection problems have been well developed and widely applied in recent years. To solve these problems better, this paper designs a new hybrid intelligent algorithm which combines the improved LGMS-FOA algorithm with birandom simulation. Since all the existing algorithms solving these problems are based on genetic algorithm and birandom simulation, some comparisons between the new hybrid intelligent algorithm and the existing algorithms are given in terms of numerical experiments, which demonstrate that the new hybrid intelligent algorithm is more effective and precise when the numbers of the objective function computations are the same.

  4. Real-Time Mass Passenger Transport Network Optimization Problems

    2005-01-01

    The aim of Real-Time Mass Transport Vehicle Routing Problem (MTVRP) is to find a solution to route n vehicles in real time to pick up and deliver m passengers. This problem is described in the context of flexible large-scale mass transportation options that use new technologies for communication among passengers and vehicles. The solution of such a problem is relevant to future transportation options involving large scale real-time routing of shared-ride fleet transit vehicles. However, the g...

  5. Why Scientists Chase Big Problems: Individual Strategy and Social Optimality

    Bergstrom, Carl T; Song, Yangbo

    2016-01-01

    Scientists pursue collective knowledge, but they also seek personal recognition from their peers. When scientists decide whether or not to work on a big new problem, they weigh the potential rewards of a major discovery against the costs of setting aside other projects. These self-interested choices can potentially spread researchers across problems in an efficient manner, but efficiency is not guaranteed. We use simple economic models to understand such decisions and their collective consequences. Academic science differs from industrial R&D in that academics often share partial solutions to gain reputation. This convention of Open Science is thought to accelerate collective discovery, but we find that it need not do so. The ability to share partial results influences which scientists work on a particular problem; consequently, Open Science can slow down the solution of a problem if it deters entry by important actors.

  6. Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications

    2015-06-24

    CONTRACT NUMBER 5b. GRANT NUMBER FA9550-12-1-0153 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Mittelmann, Hans D 5d. PROJECT NUMBER 5e. TASK NUMBER 5f...problems. The size 16 three-dimensional quadratic assignment problem Q3AP from wireless communications was solved using a sophisticated approach...placement of the sensors. However, available MINLP solvers are not sufficiently effective, even in the convex case, and a hybrid Benders

  7. Isogeometric Shape Optimization for Quasi-static and Transient Problems

    Wang, Z.P.

    2016-01-01

    The recently developed isogeometric analysis (IGA) was aimed, from the start, at integrating computer aided design (CAD) and analysis. This synthesis of geometry and analysis has naturally led to renewed interest in developing structural shape optimization. The advantages of using isogeometric analy

  8. On some fundamental properties of structural topology optimization problems

    Stolpe, Mathias

    2009-01-01

    --1. We show, by examples which can be solved by hand calculations, that the optimal solutions in general are not unique and possibly do not have an active volume constraint. These observations have immediate consequences on the theoretical convergence properties of penalization approaches. Furthermore...

  9. Topology optimization for transient wave propagation problems in one dimension

    Dahl, Jonas; Jensen, Jakob Søndergaard; Sigmund, Ole

    2008-01-01

    Structures exhibiting band gap properties, i.e., having frequency ranges for which the structure attenuates propagating waves, have applications in damping of acoustic and elastic wave propagation and in optical communication. A topology optimization method for synthesis of such structures, emplo...

  10. Some Results on Optimal Dividend Problem in Two Risk Models

    Shuaiqi Zhang

    2010-12-01

    Full Text Available The compound Poisson risk model and the compound Poisson risk model perturbed by diffusion are considered in the presence of a dividend barrier with solvency constraints. Moreover, it extends the known result due to [1]. Ref. [1] finds the optimal dividend policy is of a barrier type for a jump-diffusion model with exponentially distributed jumps. In this paper, it turns out that there can be two different solutions depending on the model’s parameters. Furthermore, an interesting result is given: the proportional transaction cost has no effect on the dividend barrier. The objective of the corporation is to maximize the cumulative expected discounted dividends payout with solvency constraints before the time of ruin. It is well known that under some reasonable assumptions, optimal dividend strategy is a barrier strategy, i.e., there is a level b_{1}(b_{2} so that whenever surplus goes above the level b_{1}(b_{2}, the excess is paid out as dividends. However, the optimal level b_{1}(b_{2} may be unacceptably low from a solvency point of view. Therefore, some constraints should imposed on an insurance company such as to pay out dividends unless the surplus has reached a level b^{1}_{c}>b_{1}(b^2_{c}>b_{2} . We show that in this case a barrier strategy at b^{1}_{c}(b^2_{c} is optimal.

  11. Stochastic Approaches to Interactive Multi-Criteria Optimization Problems

    1986-01-01

    A stochastic approach to the development of interactive algorithms for multicriteria optimization is discussed in this paper. These algorithms are based on the idea of a random search and the use of a decision-maker who can compare any two decisions. The questions of both theoretical analysis (proof of convergence, investigation of stability) and practical implementation of these algorithms are discussed.

  12. Application of Fuzzy Optimization to the Orienteering Problem

    Madhushi Verma

    2015-01-01

    Full Text Available This paper deals with the orienteering problem (OP which is a combination of two well-known problems (i.e., travelling salesman problem and the knapsack problem. OP is an NP-hard problem and is useful in appropriately modeling several challenging applications. As the parameters involved in these applications cannot be measured precisely, depicting them using crisp numbers is unrealistic. Further, the decision maker may be satisfied with graded satisfaction levels of solutions, which cannot be formulated using a crisp program. To deal with the above-stated two issues, we formulate the fuzzy orienteering problem (FOP and provide a method to solve it. Here we state the two necessary conditions of OP of maximizing the total collected score and minimizing the time taken to traverse a path (within the specified time bound as fuzzy goals and the remaining necessary conditions as crisp constraints. Using the max-min formulation of the fuzzy sets obtained from the fuzzy goals, we calculate the fuzzy decision sets (Z and Z∗ that contain the feasible paths and the desirable paths, respectively, along with the degrees to which they are acceptable. To efficiently solve large instances of FOP, we also present a parallel algorithm on CREW PRAM model.

  13. An optimization method for the problems of thermal cloaking of material bodies

    Alekseev, G. V.; Levin, V. A.

    2016-11-01

    Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.

  14. Multi-agent Optimization Design for Multi-resource Job Shop Scheduling Problems

    Xue, Fan; Fan, Wei

    As a practical generalization of the job shop scheduling problem, multi-resource job shop scheduling problem (MRJSSP) is discussed in this paper. In this problem, operations may be processed by a type of resources and jobs have individual deadlines. How to design and optimize this problem with DSAFO, a novel multi-agent algorithm, is introduced in detail by a case study, including problem analysis, agent role specification, and parameter selection. Experimental results show the effectiveness and efficiency of designing and optimizing MRJSSPs with multi-agent.

  15. Gradient vs. approximation design optimization techniques in low-dimensional convex problems

    Fedorik, Filip

    2013-10-01

    Design Optimization methods' application in structural designing represents a suitable manner for efficient designs of practical problems. The optimization techniques' implementation into multi-physical softwares permits designers to utilize them in a wide range of engineering problems. These methods are usually based on modified mathematical programming techniques and/or their combinations to improve universality and robustness for various human and technical problems. The presented paper deals with the analysis of optimization methods and tools within the frame of one to three-dimensional strictly convex optimization problems, which represent a component of the Design Optimization module in the Ansys program. The First Order method, based on combination of steepest descent and conjugate gradient method, and Supbproblem Approximation method, which uses approximation of dependent variables' functions, accompanying with facilitation of Random, Sweep, Factorial and Gradient Tools, are analyzed, where in different characteristics of the methods are observed.

  16. A note on fixed point optimality criteria for the location problem with arbitrary norms: Reply

    Juel, Henrik; Love, Robert F.

    1983-01-01

    The single-facility location problem in continuous space is considered, with distances given by arbitrary norms. When distances are Euclidean, for many practical problems the optimal location of the new facility coincides with one of the existing facilities. This property carries over to problems...

  17. Optimal anisotropic three-phase conducting composites: Plane problem

    Cherkaev, Andrej

    2010-01-01

    The paper establishes tight lower bound for effective conductivity tensor $K_*$ of two-dimensional three-phase conducting anisotropic composites and defines optimal microstructures. It is assumed that three materials are mixed with fixed volume fractions and that the conductivity of one of the materials is infinite. The bound expands the Hashin-Shtrikman and Translation bounds to multiphase structures, it is derived using the technique of {\\em localized polyconvexity} that is a combination of Translation method and additional inequalities on the fields in the materials; similar technique was used by Nesi (1995) and Cherkaev (2009) for isotropic multiphase composites. This paper expands the bounds to the anisotropic composites. The lower bound of conductivity (G-closure) is a piece-wise analytic function of eigenvalues of $K_*$, that depends only on conductivities of components and their volume fractions. Also, we find optimal microstructures that realize the bounds, developing the technique suggested earlier ...

  18. Optimization and Reliability Problems in Structural Design of Wind Turbines

    Sørensen, John Dalsgaard

    2007-01-01

    reliability index equal to 3. An example with fatigue failure indicates that the reliability level is almost the same for single wind turbines and for wind turbines in wind farms if the wake effects are modeled equivalently in the design equation and the limit state equation.......Reliability-based cost-benefit optimization formulations for wind turbines are presented. Some of the improtant aspects for stochastic modeling of loads, strengths and models uncertainties for wind turbines are described. Single wind turbines and wind turbines in wind farms with wake effects...... are discussed. Limit state equations are presented for fatigue limit states and for ultimate limit states with extreme wind load, and illustrated by bending failure. Illustrative examples are presented, and as a part of the results optimal reliability levels are obtained which corresponds to an annual...

  19. Optimization of the drayage problem using exact methods

    Reinhardt, Line Blander; Pisinger, David; Spoorendonk, Simon;

    2016-01-01

    . The influence of the side constraints on the overall cost is analysed. By exploring the fact that the number of possible routes in the considered case is quite limited, we show that the model can be solved within a minute by use of column enumeration. Alternative constraints and problem formulations......Major liner shipping companies offer pre- and end-haulage as part of a door-to-door service, but unfortunately pre- and end-haulage is frequently one of the major bottlenecks in efficient liner shipping due to the lack of coordination between customers.In this paper, we apply techniques from...... vehicle routing problems to schedule pre- and end-haulage of containers, and perform tests on data from a major liner shipping company. The paper considers several versions of the scheduling problem such as having multiple empty container depots, and having to balance the empty container depot levels...

  20. A HIGH PERFORMANCE OPTIMIZATION TECHNIQUE FOR POLE BALANCING PROBLEM

    Bahadır KARASULU

    2008-02-01

    Full Text Available High performance computing techniques can be used effectively for solution of the complex scientific problems. Pole balancing problem is a basic benchmark tool of robotic field, which is an important field of Artificial Intelligence research areas. In this study, a solution is developed for pole balancing problem using Artificial Neural Network (ANN and high performance computation technique. Algorithm, that basis of the Reinforcement Learning method which is used to find the force of pole's balance, is transfered to parallel environment. In Implementation, C is preferred as programming language and Message Passing Interface (MPI is used for parallel computation technique. Self–Organizing Map (SOM ANN model's neurons (artificial neural nodes and their weights are distributed to six processors of a server computer which equipped with each quad core processor (total 24 processors. In this way, performance values are obtained for different number of artificial neural nodes. Success of method based on results is discussed.

  1. Generalized Hill Climbing Algorithms For Discrete Optimization Problems

    2011-07-21

    a general framework for a variety of iterative local search strategies for discrete optimization. Tabu search (TS) uses the concept of memory by...Sons, New York, NY. Jacobson, S.H., A.W. Johnson, K.A. Sullivan, and M.A. Fleischer [1996], " Metaheuristics for a Flexible Assembly System Design/Loading...Equations with Linear Algebra (Second Edition), Academic Press, New York, NY. Romeo, F. and A. Sangiovanni-Vincentelli [1991], "A Theoretical Framework

  2. Compiling Planning into Quantum Optimization Problems: A Comparative Study

    2015-06-07

    become available: quantum annealing. Quantum annealing is one of the most accessible quantum algorithms for a computer sci- ence audience not versed...in quantum computing because of its close ties to classical optimization algorithms such as simulated annealing. While large-scale universal quantum ...devices designed to run only this type of quantum algorithm . Other types of quan- tum algorithms are known that take on quite a different form, and are

  3. IPDO-2007 - Inverse Problems, Design and Optimization Symposium

    2007-12-01

    TRANSDUCER 107 INVERSE APPROACHES TO DRYING OF SLICED FOODS 509 108 INVERSE APPROACHES IN IMPROVEMENT OF AIR POLUTION PLUME DISPERSION MODELS FOR... Air Force Office of Scientific Research Optimization & Discrete Mathematics / NL Suite 325, Room 3112 875 Randolph Street Arlington, VA 22203-1768 11...G.S., Orlande, H.R.B., Tanaka, M. and Colaco, M.J.), Miami Beach, FL, April 16-18, 2007. 5. Inverse Approaches in Improvement of Air Pollution Plume

  4. Topology Optimization for Wave Propagation Problems with Experimental Validation

    Christiansen, Rasmus Ellebæk

    from acoustics, however problems for TE or TM polarized electromagnetic waves and shear waves in solids in two dimensions may be treated using the proposed methods with minor modifications. A brief introduction to wave problems and to density-based topology optimizationis included, as is a brief...... designed using the proposed method is provided. A novel approach for designing meta material slabs with selectively tuned negative refractive behavior is outlined. Numerical examples demonstrating the behavior of a slab under different conditions is provided. Results from an experimental studydemonstrating...

  5. Optimization of the imported air express cargo distribution problem

    Hwang, T.L.

    2013-03-01

    Full Text Available This study examines the delivering network of imported air express cargo as an integrated multi-depot vehicle routing problem. Integrated multi-depot vehicle routing problem attempts to decide which service centers should be used and how much freight should be unloaded in each service center. The role of an exchange point which is allowing the delivery vans and shuttles to exchange imported and exported goods is also addressed. Test results demonstrate the feasibility of the four models so these are highly promising for use in a diverse array of applications, such as in home delivery and reverse logistics.

  6. On Quadratic Scalarization of One Class of Vector Optimization Problems in Banach Spaces

    V. M. Bogomaz

    2012-01-01

    Full Text Available We study vector optimization problems in partially ordered Banach Spaces. We sup­pose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the ”clas­sical” scalarization of vector optimization problems in the form of weighted sum and also we propose other type of scalarization for vector optimization problem, the socalled adaptive scalarization, which inherits some ideas of Pascoletti-Serafini approach. As a result, we show that the scalar nonlinear optimization problems can byturn approxi­mated by the quadratic minimization problems. The advantage of such regularization is especially interesting from a numerical point of view because it gives a possibility to apply rather simple computational methods for the approximation of the whole set of efficient solutions.

  7. A Collection of Challenging Optimization Problems in Science, Engineering and Economics

    Mehta, Dhagash

    2015-01-01

    Function optimization and finding simultaneous solutions of a system of nonlinear equations (SNE) are two closely related and important optimization problems. However, unlike in the case of function optimization in which one is required to find the global minimum and sometimes local minima, a database of challenging SNEs where one is required to find stationary points (extrama and saddle points) is not readily available. In this article, we initiate building such a database of important SNE (which also includes related function optimization problems), arising from Science, Engineering and Economics. After providing a short review of the most commonly used mathematical and computational approaches to find solutions of such systems, we provide a preliminary list of challenging problems by writing the Mathematical formulation down, briefly explaning the origin and importance of the problem and giving a short account on the currently known results, for each of the problems. We anticipate that this database will n...

  8. Optimal control problems with switching points. Ph.D. Thesis, 1990 Final Report

    Seywald, Hans

    1991-01-01

    An overview is presented of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

  9. The Human Group Optimizer (HGO): Mimicking the collective intelligence of human groups as an optimization tool for combinatorial problems

    De Vincenzo, Ilario; Carbone, Giuseppe

    2016-01-01

    A large number of optimization algorithms have been developed by researchers to solve a variety of complex problems in operations management area. We present a novel optimization algorithm belonging to the class of swarm intelligence optimization methods. The algorithm mimics the decision making process of human groups and exploits the dynamics of this process as an optimization tool for combinatorial problems. In order to achieve this aim, a continuous-time Markov process is proposed to describe the behavior of a population of socially interacting agents, modelling how humans in a group modify their opinions driven by self-interest and consensus seeking. As in the case of a collection of spins, the dynamics of such a system is characterized by a phase transition from low to high values of the overall consenus (magnetization). We recognize this phase transition as being associated with the emergence of a collective superior intelligence of the population. While this state being active, a cooling schedule is a...

  10. A Uniaxial Optimal Perfectly Matched Layer Method for Time-harmonic Scattering Problems

    YANG XIAO-YING; MA FU-MING; ZHANG DE-YUE; DU XIN-WEI

    2010-01-01

    We develop a uniaxial optimal perfectly matched layer (opt PML) method for solving the time-harmonic scattering problems by choosing a particular absorbing function with unbounded integral in a rectangular domain. With this choice, the solution of the optimal PML problem not only converges exponentially to the solution of the original scatting problem, but also is insensitive to the thickness of the PML layer for sufficiently small parameter e0. Numerical experiments are included to illustrate the competitive behavior of the proposed optimal method.

  11. Fish School Search Algorithm for Solving Optimal Reactive Power Dispatch Problem

    K. Lenin

    2013-01-01

    Full Text Available This paper presents an algorithm for solving the multi-objective reactive power dispatch problem in a power system. Modal analysis of the system is used for static voltage stability assessment. Loss minimization and maximization of voltage stability margin are taken as the objectives. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. This paper presents fish school search a novel method of swarm intelligence for solving above problem. Fish school search Algorithm, which was inspired by the natural schooling behaviours of fish, a powerful stochastic optimization technique has been utilised to solve the reactive power optimization problem.

  12. Optimization of multi-objective integrated process planning and scheduling problem using a priority based optimization algorithm

    Ausaf, Muhammad Farhan; Gao, Liang; Li, Xinyu

    2015-12-01

    For increasing the overall performance of modern manufacturing systems, effective integration of process planning and scheduling functions has been an important area of consideration among researchers. Owing to the complexity of handling process planning and scheduling simultaneously, most of the research work has been limited to solving the integrated process planning and scheduling (IPPS) problem for a single objective function. As there are many conflicting objectives when dealing with process planning and scheduling, real world problems cannot be fully captured considering only a single objective for optimization. Therefore considering multi-objective IPPS (MOIPPS) problem is inevitable. Unfortunately, only a handful of research papers are available on solving MOIPPS problem. In this paper, an optimization algorithm for solving MOIPPS problem is presented. The proposed algorithm uses a set of dispatching rules coupled with priority assignment to optimize the IPPS problem for various objectives like makespan, total machine load, total tardiness, etc. A fixed sized external archive coupled with a crowding distance mechanism is used to store and maintain the non-dominated solutions. To compare the results with other algorithms, a C-matric based method has been used. Instances from four recent papers have been solved to demonstrate the effectiveness of the proposed algorithm. The experimental results show that the proposed method is an efficient approach for solving the MOIPPS problem.

  13. Optimization problems of the third edge-connectivity of graphs

    WANG; Yingqian

    2006-01-01

    The third edge-connectivity λ3(G) of a graph G is defined as the minimum cardinality over all sets of edges, if any, whose deletion disconnects G and each component of the resulting graph has at least 3 vertices. An upper bound has been established for λ3(G) whenever λ3(G) is well-defined. This paper first introduces two combinatorial optimization concepts, that is, maximality and superiority, of λ3(G), and then proves the Ore type sufficient conditions for G to be maximally and super third edge-connected. These concepts and results are useful in network reliability analysis.

  14. SOLVING TRUST REGION PROBLEM IN LARGE SCALE OPTIMIZATION

    Bing-sheng He

    2000-01-01

    This paper presents a new method for solving the basic problem in the “model trust region” approach to large scale minimization: Compute a vector x such that 1/2xTHx + cTx = min, subject to the constraint ‖x‖2≤a. The method is a combination of the CG method and a projection and contraction (PC) method. The first (CG) method with x0 = 0 as the start point either directly offers a solution of the problem, or--as soon as the norm of the iterate greater than a, --it gives a suitable starting point and a favourable choice of a crucial scaling parameter in the second (PC) method. Some numerical examples are given, which indicate that the method is applicable.

  15. Ant colony optimization for the real-time train routing selection problem

    SAMA, Marcella; Pellegrini, Paola; D'Ariano, Andrea; Rodriguez, Joaquin; Pacciarelli, Dario

    2016-01-01

    This paper deals with the real-time problem of scheduling and routing trains in a railway network. In the related literature, this problem is usually solved starting from a subset of routing alternatives and computing the near-optimal solution of the simplified routing problem. We study how to select the best subset of routing alternatives for each train among all possible alternatives. The real-time train routing selection problem is formulated as an integer linear programming formulation an...

  16. Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation

    Yong, Jiongmin

    2012-01-01

    A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value function of the problem. Well-posedness and some properties of such an equation is studied, and time-consistent equilibrium strategies are constructed. As special cases, the linear-quadratic problem and a generalized Merton's portfolio problem are investigated.

  17. Multicriteria analysis of real-life engineering optimization problems: statement and solution

    Statnikov, R.B.; Bordetsky, A.; Statnikov, A.

    2005-01-01

    The article of record as published may be located at http://dx.doi.org/10.1016/j.na.2005.01.028 The majority of engineering problems are essentially multicriteria. These criteria are usually contradictory. That is why specialists experience significant difficulties in correctly stating engineering optimization problems, so designers often end up solving ill-posed problems. In general, it is impossible to reduce multicriteria problems to single-criterion ones. For the correct st...

  18. A STACKELBERG DIFFERENTIAL GAMES SOLUTION TO A PROBLEM OF OPTIMAL INTERTEMPORAL INVESTMENT AND TAX RATE DESIGN

    ZHANG Rong; LIU Xing

    2004-01-01

    Using the Stackelberg differential games(SDG) theory, we quantitatively study a problem of optimal intertemporal investment and tax rate design. Under some appropriate assumptions, the open-loop Stackelberg equilibrium solutions are obtained. Equilibrium solutions show that: 1. The optimal strategies derived from differential game and unilateral optimal control approaches are different; 2. It is not always the best strategy for the government to use a constant tax rate over the whole time period; 3. The admissible size of tax rate adjustment may have great effect on the government's optimal strategy; 4.SDG approach has no significant effect on the firm's optimal investment strategy.

  19. Ant colony optimization techniques for the hamiltonian p-median problem

    M. Zohrehbandian

    2010-12-01

    Full Text Available Location-Routing problems involve locating a number of facilitiesamong candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. A special case of these problems is Hamiltonian p-Median problem (HpMP. This research applies the metaheuristic method of ant colony optimization (ACO to solve the HpMP. Modifications are made to the ACO algorithm used to solve the traditional vehicle routing problem (VRP in order to allow the search of the optimal solution of the HpMP. Regarding this metaheuristic algorithm a computational experiment is reported as well.

  20. The solution of singular optimal control problems using direct collocation and nonlinear programming

    Downey, James R.; Conway, Bruce A.

    1992-08-01

    This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.

  1. On Compliance and Buckling Objective Functions in Topology Optimization of Snap-Through Problems

    Lindgaard, Esben; Dahl, Jonas

    2013-01-01

    This paper deals with topology optimization of static geometrically nonlinear structures experiencing snap-through behaviour. Different compliance and buckling criterion functions are studied and applied for topology optimization of a point loaded curved beam problem with the aim of maximizing...... the snap-through buckling load. The response of the optimized structures obtained using the considered objective functions are evaluated and compared. Due to the intrinsic nonlinear nature of the problem, the load level at which the objective function is evaluated has a tremendous effect on the resulting...... optimized design. A well-known issue in buckling topology optimization is artificial buckling modes in low density regions. The typical remedy applied for linear buckling does not have a natural extension to nonlinear problems, and we propose an alternative approach. Some possible negative implications...

  2. An optimal control problem for ovine brucellosis with culling.

    Nannyonga, B; Mwanga, G G; Luboobi, L S

    2015-01-01

    A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnseba et al. [A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2-11. Available at http://www.math.u-bordeaux1.fr/∼pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost.

  3. GLOBAL OPTIMIZATION OF PUMP CONFIGURATION PROBLEM USING EXTENDED CROWDING GENETIC ALGORITHM

    Zhang Guijun; Wu Tihua; Ye Rong

    2004-01-01

    An extended crowding genetic algorithm (ECGA) is introduced for solving optimal pump configuration problem,which was presented by T.Westerlund in 1994.This problem has been found to be non-convex,and the objective function contained several local optima and global optimality could not be ensured by all the traditional MINLP optimization method.The concepts of species conserving and composite encoding are introduced to crowding genetic algorithm (CGA) for maintain the diversity of population more effectively and coping with the continuous and/or discrete variables in MINLP problem.The solution of three-levels pump configuration got from DICOPT++ software (OA algorithm) is also given.By comparing with the solutions obtained from DICOPT++,ECP method,and MIN-MIN method,the ECGA algorithm proved to be very effective in finding the global optimal solution of multi-levels pump configuration via using the problem-specific information.

  4. Methods of solving of the optimal stabilization problem for stationary smooth control systems. Part I

    G. Kondrat'ev

    1999-10-01

    Full Text Available In this article some ideas of Hamilton mechanics and differential-algebraic Geometry are used to exact definition of the potential function (Bellman-Lyapunov function in the optimal stabilization problem of smooth finite-dimensional systems.

  5. Optimal Stopping Problems with Power Function of Lévy Processes

    Surya, B.A.

    2006-01-01

    This talk is based on the joint paper with A.E. Kyprianou: "Kyprianou, A. E., and Surya, B. A. On the Novikov-Shiryaev optimal stopping problems in continuous time. Elect. Comm. in Probab., 10 (2005), 146-154.

  6. On the Limit Matrix Obtained in the Homogenization of an Optimal Control Problem

    S Kesavan; M Rajesh

    2002-05-01

    A new formulation for the limit matrix occurring in the cost functional of an optimal control problem on homogenization is obtained. It is used to obtain an upper bound for this matrix (in the sense of positive definite matrices).

  7. A GLOBALLY AND SUPERLINEARLY CONVERGENT TRUST REGION METHOD FOR LC1 OPTIMIZATION PROBLEMS

    ZhangLiping; LaiYanlian

    2001-01-01

    Abstract. A new trust region algorithm for solving convex LC1 optimization problem is present-ed. It is proved that the algorithm is globally convergent and the rate of convergence is superlin-ear under some reasonable assumptions.

  8. An adaptive ant colony system algorithm for continuous-space optimization problems

    李艳君; 吴铁军

    2003-01-01

    Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates.Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved.

  9. An adaptive ant colony system algorithm for continuous-space optimization problems

    李艳君; 吴铁军

    2003-01-01

    Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates. Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved.

  10. An Efficient Approach to a Class of Non-smooth Optimization Problems

    李兴斯

    1994-01-01

    This paper presents an entropy-based smoothing technique for solving a class of non-smooth optimization problems that are in some way related to the maximum function.Basic ideas concerning this approach are that we replace the non-smooth maximum function by a smooth one,called aggregate function,which is derived by employing the maximum entropy principle and its useful properties are proved.Wilh this smoothing technique,both unconstrained and constrained mimma.x problems are transformed into unconstrained optimization problems of smooth functions such that this class of non-smooth optimization problems can be solved by some existing unconstrained optimization softwares for smooth functions The present approach can be very easily implemented on computers with very fast and -.Inhie convergence.

  11. Optimization of the Forcing Term for the Solution of Two-Point Boundary Value Problems

    Gianni Arioli

    2013-01-01

    by standard methods of constrained optimization, for example, with Lagrange multipliers. We provide an application of this algorithm to the planar restricted three body problem in order to study the planning of low-thrust transfer orbits.

  12. Methods of solving of the optimal stabilization problem for stationary smooth control systems. Part II Ending

    G. Kondrat'ev

    1999-12-01

    Full Text Available In this article some ideas of Hamilton mechanics and differential-algebraic Geometry are used to exact definition of the potential function (Bellman-Lyapunov function in the optimal stabilization problem of smooth finite-dimensional systems.

  13. Approximation methods of mixed l 1/H2 optimization problems for MIMO discrete-time systems

    李昇平

    2004-01-01

    The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is eonsidered. This problem is formulated as minimizing the l1-norm of a dosed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Becatse the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.

  14. Application of particle swarm optimization algorithm in the heating system planning problem.

    Ma, Rong-Jiang; Yu, Nan-Yang; Hu, Jun-Yi

    2013-01-01

    Based on the life cycle cost (LCC) approach, this paper presents an integral mathematical model and particle swarm optimization (PSO) algorithm for the heating system planning (HSP) problem. The proposed mathematical model minimizes the cost of heating system as the objective for a given life cycle time. For the particularity of HSP problem, the general particle swarm optimization algorithm was improved. An actual case study was calculated to check its feasibility in practical use. The results show that the improved particle swarm optimization (IPSO) algorithm can more preferably solve the HSP problem than PSO algorithm. Moreover, the results also present the potential to provide useful information when making decisions in the practical planning process. Therefore, it is believed that if this approach is applied correctly and in combination with other elements, it can become a powerful and effective optimization tool for HSP problem.

  15. Approximating stationary points of stochastic optimization problems in Banach space

    Balaji, Ramamurthy; Xu, Huifu

    2008-11-01

    In this paper, we present a uniform strong law of large numbers for random set-valued mappings in separable Banach space and apply it to analyze the sample average approximation of Clarke stationary points of a nonsmooth one stage stochastic minimization problem in separable Banach space. Moreover, under Hausdorff continuity, we show that with probability approaching one exponentially fast with the increase of sample size, the sample average of a convex compact set-valued mapping converges to its expected value uniformly. The result is used to establish exponential convergence of stationary sequence under some metric regularity conditions.

  16. Hybrid constraint programming and metaheuristic methods for large scale optimization problems

    2011-01-01

    This work presents hybrid Constraint Programming (CP) and metaheuristic methods for the solution of Large Scale Optimization Problems; it aims at integrating concepts and mechanisms from the metaheuristic methods to a CP-based tree search environment in order to exploit the advantages of both approaches. The modeling and solution of large scale combinatorial optimization problem is a topic which has arisen the interest of many researcherers in the Operations Research field; combinatori...

  17. Phase Transitions in Combinatorial Optimization Problems Basics, Algorithms and Statistical Mechanics

    Hartmann, Alexander K

    2005-01-01

    A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics. The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary

  18. The First Survey for Abilities of Wavelets in Solving Optimal Control Problems by Embedding Methods

    A. Fakharzadeh

    2007-06-01

    Full Text Available By a brief review on the applications of wavelets in solving optimal control problems, a multiresolution analysis for two dimensional Sobolev spaces and the square spline wavelets are considered. Regarding the density and approximation properties of these wavelets, for the first time, they are employed for solving optimal control problems by embedding method. Existence and the determination way for the solution are also discussed. Finally, the abilities of the new approach are explained by a numerical example and some comparisons

  19. Robust Optimization for Time-Cost Tradeoff Problem in Construction Projects

    Ming Li; Guangdong Wu

    2014-01-01

    Construction projects are generally subject to uncertainty, which influences the realization of time-cost tradeoff in project management. This paper addresses a time-cost tradeoff problem under uncertainty, in which activities in projects can be executed in different construction modes corresponding to specified time and cost with interval uncertainty. Based on multiobjective robust optimization method, a robust optimization model for time-cost tradeoff problem is developed. In order to illus...

  20. New algorithms for some NP-optimization problems by DNA computing

    2002-01-01

    There are lots of DNA computation models now. The model developed by Martyn Amos' group is special in its error-resistant property, but unfortunately, its computational power is limited and cannot solve optimization problems efficiently. In this paper, some new methods have been introduced to enlarge the computational power of this model. And based on these new methods, several DNA algorithms have been designed to solve some NP-optimization problems such as minimal vertex cover, maximal clique and MAX-3SAT.

  1. A Closer Look At Differential Evolution For The Optimal Well Placement Problem

    Carosio, Grazieli L. C.; Humphries, Thomas D.; Haynes, Ronald D.; Farquharson, Colin G.

    2015-01-01

    Energy demand has increased considerably with the growth of world population, increasing the interest in the hydrocarbon reservoir management problem. Companies are concerned with maximizing oil recovery while minimizing capital investment and operational costs. A first step in solving this problem is to consider optimal well placement. In this work, we investigate the Differential Evolution (DE) optimization method, using distinct configurations with respect to population size, mutation fact...

  2. On unified modeling, theory, and method for solving multi-scale global optimization problems

    Gao, David Yang

    2016-10-01

    A unified model is proposed for general optimization problems in multi-scale complex systems. Based on this model and necessary assumptions in physics, the canonical duality theory is presented in a precise way to include traditional duality theories and popular methods as special applications. Two conjectures on NP-hardness are proposed, which should play important roles for correctly understanding and efficiently solving challenging real-world problems. Applications are illustrated for both nonconvex continuous optimization and mixed integer nonlinear programming.

  3. Deterministic Annealing Optimization for Witsenhausen's and Related Decentralized Stochastic Control Problems

    Mehmetoglu, Mustafa; Akyol, Emrah; Rose, Kenneth

    2016-01-01

    This note studies the global optimization of controller mappings in discrete-time stochastic control problems including Witsenhausen's celebrated 1968 counter-example. We propose a generally applicable non-convex numerical optimization method based on the concept of deterministic annealing-which is derived from information-theoretic principles and was successfully employed in several problems including vector quantization, classification, and regression. We present comparative numerical resul...

  4. Lotsize optimization leading to a $p$-median problem with cardinalities

    Gaul, Constantin; Rambau, Joerg

    2008-01-01

    We consider the problem of approximating the branch and size dependent demand of a fashion discounter with many branches by a distributing process being based on the branch delivery restricted to integral multiples of lots from a small set of available lot-types. We propose a formalized model which arises from a practical cooperation with an industry partner. Besides an integer linear programming formulation and a primal heuristic for this problem we also consider a more abstract version which we relate to several other classical optimization problems like the p-median problem, the facility location problem or the matching problem.

  5. Ncpol2sdpa -- Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables

    Wittek, Peter

    2013-01-01

    A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only problems of commuting variables have efficient generators. We develop an implementation for problems of noncommuting problems that creates the relaxation to be solved by SDPA -- a high-performance solver that runs in a distributed environment. We further exploit the inherent sparsity of optimization problems in quantum physics to reduce the complexity of resulting relaxation. Constrained problems with a relaxation of order two may contain up to a hundred variables. The implementation is available in C++ and Python. The tool helps solve problems such as finding the ground state energy or testing quantum correlations.

  6. On the acceleration of the double smoothing technique for unconstrained convex optimization problems

    Bot, Radu Ioan

    2012-01-01

    In this article we investigate the possibilities of accelerating the double smoothing technique when solving unconstrained nondifferentiable convex optimization problems. This approach relies on the regularization in two steps of the Fenchel dual problem associated to the problem to be solved into an optimization problem having a differentiable strongly convex objective function with Lipschitz continuous gradient. The doubly regularized dual problem is then solved via a fast gradient method. The aim of this paper is to show how do the properties of the functions in the objective of the primal problem influence the implementation of the double smoothing approach and its rate of convergence. The theoretical results are applied to linear inverse problems by making use of different regularization functionals.

  7. Scalable Effective Approaches for Quadratic Assignment Problems Based on Conic Optimization and Applications

    2012-02-09

    several optimization models and algorithm design for problems from computer vision and learning , research on sparse solutions in quadratic optimization...following papers: [9] L. Mukherjee, V. Singh, J. Peng and C. Hinrichs. Learning kernels for variants of normalized cuts: Convex relaxations and...are very small gaps compared to state-of-the-art knowledge in comunications . Table 1. Bounds for adjacency matrix

  8. A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet

    Boualem Djehiche

    2014-01-01

    a two-mode optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy.

  9. Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay

    Frederico, G. S. F.; Torres, D. F. M.

    2012-01-01

    We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of variations and optimal control with delays.

  10. UDU factored Lyapunov recursions solve optimal reduced-order LQG problems

    Willigenburg, van L.G.; Koning, de W.L.

    2004-01-01

    A new algorithm is presented to solve both the finite-horizon time-varying and infinite-horizon time-invariant discrete-time optimal reduced-order LQG problem. In both cases the first order necessary optimality conditions can be represented by two non-linearly coupled discrete-time Lyapunov equation

  11. Algorithmic and technical improvements: Optimal solutions to the (Generalized) Multi-Weber Problem

    K.E. Rosing (Kenneth); B. Harris (Britton)

    1992-01-01

    textabstractRosing has recently demonstrated a new method for obtaining optimal solutions to the (Generalized) Multi-Weber Problem and proved the optimality of the results. The method develops all convex hulls and then covers the destinations with disjoint convex hulls. This paper seeks to improve i

  12. CCBlade Documentation: Release 0.1.0

    Ning, S. A. [National Renewable Energy Lab. (NREL), Golden, CO (United States)

    2013-09-01

    CCBlade predicts aerodynamic loading of wind turbine blades using blade element momentum (BEM) theory. CC stands for continuity and convergence. CCBlade was developed primarily for use in gradient-based optimization applications where C1 and robust convergence are essential.

  13. A One-Layer Recurrent Neural Network for Pseudoconvex Optimization Problems With Equality and Inequality Constraints.

    Qin, Sitian; Yang, Xiudong; Xue, Xiaoping; Song, Jiahui

    2016-05-24

    Pseudoconvex optimization problem, as an important nonconvex optimization problem, plays an important role in scientific and engineering applications. In this paper, a recurrent one-layer neural network is proposed for solving the pseudoconvex optimization problem with equality and inequality constraints. It is proved that from any initial state, the state of the proposed neural network reaches the feasible region in finite time and stays there thereafter. It is also proved that the state of the proposed neural network is convergent to an optimal solution of the related problem. Compared with the related existing recurrent neural networks for the pseudoconvex optimization problems, the proposed neural network in this paper does not need the penalty parameters and has a better convergence. Meanwhile, the proposed neural network is used to solve three nonsmooth optimization problems, and we make some detailed comparisons with the known related conclusions. In the end, some numerical examples are provided to illustrate the effectiveness of the performance of the proposed neural network.

  14. New Meta-Heuristic for Combinatorial Optimization Problems:Intersection Based Scaling

    Peng Zou; Zhi Zhou; Ying-Yu Wan; Guo-Liang Chen; Jun Gu

    2004-01-01

    Combinatorial optimization problems are found in many application fields such as computer science, engineering and economy. In this paper, a new efficient meta-heuristic, Intersection-Based Scaling (IBS for abbreviation),is proposed and it can be applied to the combinatorial optimization problems. The main idea of IBS is to scale the size of the instance based on the intersection of some local optima, and to simplify the search space by extracting the intersection from the instance, which makes the search more efficient. The combination of IBS with some local search heuristics of different combinatorial optimization problems such as Traveling Salesman Problem (TSP) and Graph Partitioning Problem (GPP) is studied, and comparisons are made with some of the best heuristic algorithms and meta-heuristic algorithms. It is found that it has significantly improved the performance of existing local search heuristics and significantly outperforms the known best algorithms.

  15. Evaluation of Genetic Algorithm Concepts using Model Problems. Part 1; Single-Objective Optimization

    Holst, Terry L.; Pulliam, Thomas H.

    2003-01-01

    A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.

  16. Deterministic Time-inconsistent Optimal Control Problems - an Essentially Cooperative Approach

    Jiong-min YONG

    2012-01-01

    A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations.To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control,a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced.Under certain conditions,it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem,which is the value function of a time-consistent optimal control problem.Moreover,it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.

  17. Hybrid Method for a Class of Stochastic Bi-criteria Optimization Problems

    Wan Zhong

    2010-01-01

    Full Text Available We study a class of stochastic bi-criteria optimization problems with one quadratic and one linear objective functions and some linear inequality constraints. A hybrid method of chance-constrained programming (CCP combined with variance expectation (VE is proposed to find the optimal solution of the original problem. By introducing the expectation level, the bi-criteria problem is converted into a single-objective problem. By introducing the confidence level and the preference level of decision maker, we obtain a relaxed robust deterministic formulation of the stochastic problem. Then, an interactive algorithm is developed to solve the obtained deterministic model with three parameters, reflecting the preferences of decision maker. Numerical experiments show that the proposed method is superior to the existing methods. The optimal solution obtained by our method has less violation of the constraints and reflects the satisfaction degree of decision-maker.

  18. Optimization of location routing inventory problem with transshipment

    Ghani, Nor Edayu Abd; Shariff, S. Sarifah Radiah; Zahari, Siti Meriam

    2015-05-01

    Location Routing Inventory Problem (LRIP) is a collaboration of the three components in the supply chain. It is confined by location-allocation, vehicle routing and inventory management. The aim of the study is to minimize the total system cost in the supply chain. Transshipment is introduced in order to allow the products to be shipped to a customer who experiences a shortage, either directly from the supplier or from another customer. In the study, LRIP is introduced with the transshipment (LRIPT) and customers act as the transshipment points. We select the transshipment point by using the p-center and we present the results in two divisions of cases. Based on the analysis, the results indicated that LRIPT performed well compared to LRIP.

  19. Evaluation of Genetic Algorithm Concepts Using Model Problems. Part 2; Multi-Objective Optimization

    Holst, Terry L.; Pulliam, Thomas H.

    2003-01-01

    A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.

  20. Portfolio optimization problem with nonidentical variances of asset returns using statistical mechanical informatics

    Shinzato, Takashi

    2016-12-01

    The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We defined two characteristic quantities of an optimal portfolio, namely, minimal investment risk and investment concentration, in order to solve the portfolio optimization problem and analytically determined their asymptotical behaviors using replica analysis. Numerical experiments were also performed, and a comparison between the results of our simulation and those obtained via replica analysis validated our proposed method.

  1. Solving Two-Level Optimization Problems with Applications to Robust Design and Energy Markets

    2011-01-01

    ˆ if for all    ,ˆ ,  ),(),,(max)ˆ,( xxgxxgxxg  for all x ( Bazaraa et al., 1993). 11 Definition 2.2: Objective...complementary 25 problems by taking the Karush-Kuhn-Tucker (KKT) ( Bazaraa et al., 1993) conditions to each player‟s optimization problem and combining...based optimization algorithms ( Bazaraa et al., 1993) are used as opposed to population- based optimization ones (such as Genetic Algorithms or Simulated

  2. Ant Colony Optimization with Memory and Its Application to Traveling Salesman Problem

    Wang, Rong-Long; Zhao, Li-Qing; Zhou, Xiao-Fan

    Ant Colony Optimization (ACO) is one of the most recent techniques for solving combinatorial optimization problems, and has been unexpectedly successful. Therefore, many improvements have been proposed to improve the performance of the ACO algorithm. In this paper an ant colony optimization with memory is proposed, which is applied to the classical traveling salesman problem (TSP). In the proposed algorithm, each ant searches the solution not only according to the pheromone and heuristic information but also based on the memory which is from the solution of the last iteration. A large number of simulation runs are performed, and simulation results illustrate that the proposed algorithm performs better than the compared algorithms.

  3. Industrial Application of Topology Optimization for Combined Conductive and Convective Heat Transfer Problems

    Zhou, Mingdong; Alexandersen, Joe; Sigmund, Ole

    2016-01-01

    This paper presents an industrial application of topology optimization for combined conductive and convective heat transfer problems. The solution is based on a synergy of computer aided design and engineering software tools from Dassault Systemes. The considered physical problem of steady......-state heat transfer under convection is simulated using SIMULIA-Abaqus. A corresponding topology optimization feature is provided by SIMULIA-Tosca. By following a standard workflow of design optimization, the proposed solution is able to accommodate practical design scenarios and results in efficient...

  4. Optimal randomized EREW PRAM algorithms for finding spanning forests and for other basic graph connectivity problems

    Halperin, S.; Zwick, U. [Tel Aviv Univ. (Israel)

    1996-12-31

    We present the first randomized O(log n) time and O(m + n) work EREW PRAM algorithm for finding a spanning forest of an undirected graph G = (V, E) with n vertices and m edges. Our algorithm is optimal with respect to time, work and space. As a consequence we get optimal randomized EREW PRAM algorithms for other basic connectivity problems such as finding a bipartite partition, finding bridges and biconnected components, and finding Euler tours in Eulerean graphs. For other problems such as finding an ear decomposition, finding an open ear decomposition, finding a strong orientation, and finding an st-numbering we get optimal randomized CREW PRAM algorithms.

  5. Linearization of a Matrix Riccati Equation Associated to an Optimal Control Problem

    Foued Zitouni

    2014-01-01

    Full Text Available The matrix Riccati equation that must be solved to obtain the solution to stochastic optimal control problems known as LQG homing is linearized for a class of processes. The results generalize a theorem proved by Whittle and the one-dimensional case already considered by the authors. A particular two-dimensional problem is solved explicitly.

  6. The Orienteering Problem under Uncertainty Stochastic Programming and Robust Optimization compared

    Evers, L.; Glorie, K.; Ster, S. van der; Barros, A.I.; Monsuur, H.

    2012-01-01

    The Orienteering Problem (OP) is a generalization of the well-known traveling salesman problem and has many interesting applications in logistics, tourism and defense. To reflect real-life situations, we focus on an uncertain variant of the OP. Two main approaches that deal with optimization under u

  7. Using whole number models with Boolean variables for solving optimization problems in the oil industry

    Smorodinskiy, B.I.

    1984-01-01

    A theoretical justification is given for a method for solving one of the common problems in whole number linear programming with Boolean variables. It is shown that a number of optimization problems in the oil industry can be reduced to this model.

  8. Optimization-based decision support systems for planning problems in processing industries

    Claassen, G.D.H.

    2014-01-01

    Summary Optimization-based decision support systems for planning problems in processing industries Nowadays, efficient planning of material flows within and between supply chains is of vital importance and has become one of the most challenging problems for decision support in practice. The tremendo

  9. Analysis of Ant Colony Optimization and Population-Based Evolutionary Algorithms on Dynamic Problems

    Lissovoi, Andrei

    This thesis presents new running time analyses of nature-inspired algorithms on various dynamic problems. It aims to identify and analyse the features of algorithms and problem classes which allow efficient optimization to occur in the presence of dynamic behaviour. We consider the following...

  10. Industrial Application of Topology Optimization for Combined Conductive and Convective Heat Transfer Problems

    Zhou, Mingdong; Alexandersen, Joe; Sigmund, Ole;

    2016-01-01

    This paper presents an industrial application of topology optimization for combined conductive and convective heat transfer problems. The solution is based on a synergy of computer aided design and engineering software tools from Dassault Systemes. The considered physical problem of steady...

  11. A non-penalty recurrent neural network for solving a class of constrained optimization problems.

    Hosseini, Alireza

    2016-01-01

    In this paper, we explain a methodology to analyze convergence of some differential inclusion-based neural networks for solving nonsmooth optimization problems. For a general differential inclusion, we show that if its right hand-side set valued map satisfies some conditions, then solution trajectory of the differential inclusion converges to optimal solution set of its corresponding in optimization problem. Based on the obtained methodology, we introduce a new recurrent neural network for solving nonsmooth optimization problems. Objective function does not need to be convex on R(n) nor does the new neural network model require any penalty parameter. We compare our new method with some penalty-based and non-penalty based models. Moreover for differentiable cases, we implement circuit diagram of the new neural network.

  12. A LEVEL SET BASED SHAPE OPTIMIZATION METHOD FOR AN ELLIPTIC OBSTACLE PROBLEM

    Burger, Martin

    2011-04-01

    In this paper, we construct a level set method for an elliptic obstacle problem, which can be reformulated as a shape optimization problem. We provide a detailed shape sensitivity analysis for this reformulation and a stability result for the shape Hessian at the optimal shape. Using the shape sensitivities, we construct a geometric gradient flow, which can be realized in the context of level set methods. We prove the convergence of the gradient flow to an optimal shape and provide a complete analysis of the level set method in terms of viscosity solutions. To our knowledge this is the first complete analysis of a level set method for a nonlocal shape optimization problem. Finally, we discuss the implementation of the methods and illustrate its behavior through several computational experiments. © 2011 World Scientific Publishing Company.

  13. Topology optimization of bounded acoustic problems using the hybrid finite element-wave based method

    Goo, Seongyeol; Wang, Semyung; Kook, Junghwan

    2017-01-01

    This paper presents an alternative topology optimization method for bounded acoustic problems that uses the hybrid finite element-wave based method (FE-WBM). The conventional method for the topology optimization of bounded acoustic problems is based on the finite element method (FEM), which...... is limited to low frequency applications due to considerable computational efforts. To this end, we propose a gradient-based topology optimization method that uses the hybrid FE-WBM whereby the entire domain of a problem is partitioned into design and non-design domains. In this respect, the FEM is used...... as a design domain of topology optimization, and the WBM is used as a non-design domain to increase computational efficiency. The adjoint variable method based on the hybrid FE-WBM is also proposed as a means of computing design sensitivities. Numerical examples are presented to demonstrate the effectiveness...

  14. A Continuous Feedback Optimal Control based on Second-Variations for Problems with Control Constraints

    Olympio, Joris T

    2011-01-01

    The paper describes a continuous second-variation algorithm to solve optimal control problems where the control is defined on a closed set. A second order expansion of a Lagrangian provides linear updates of the control to construct a locally feedback optimal control of the problem. Since the process involves a backward and a forward stage, which require storing trajectories, a method has been devised to accurately store continuous solutions of ordinary differential equations. Thanks to the continuous approach, the method adapts implicitly the numerical time mesh. The novel method is demonstrated on bang-bang optimal control problems, showing the suitability of the method to identify automatically optimal switching points in the control.

  15. An Adaptive Finite Element Method Based on Optimal Error Estimates for Linear Elliptic Problems

    汤雁

    2004-01-01

    The subject of the work is to propose a series of papers about adaptive finite element methods based on optimal error control estimate. This paper is the third part in a series of papers on adaptive finite element methods based on optimal error estimates for linear elliptic problems on the concave corner domains. In the preceding two papers (part 1:Adaptive finite element method based on optimal error estimate for linear elliptic problems on concave corner domain; part 2:Adaptive finite element method based on optimal error estimate for linear elliptic problems on nonconvex polygonal domains), we presented adaptive finite element methods based on the energy norm and the maximum norm. In this paper, an important result is presented and analyzed. The algorithm for error control in the energy norm and maximum norm in part 1 and part 2 in this series of papers is based on this result.

  16. SOME OPTIMALITY AND DUALITY RESULTS FOR AN EFFICIENT SOLUTION OF MULTIOBJECTIVE NONLINEAR FRACTIONAL PROGRAMMING PROBLEM

    Paras Bhatnagar

    2012-10-01

    Full Text Available Kaul and Kaur [7] obtained necessary optimality conditions for a non-linear programming problem by taking the objective and constraint functions to be semilocally convex and their right differentials at a point to be lower semi-continuous. Suneja and Gupta [12] established the necessary optimality conditions without assuming the semilocal convexity of the objective and constraint functions but their right differentials at the optimal point to be convex. Suneja and Gupta [13] established necessary optimality conditions for an efficient solution of a multiobjective non-linear programming problem by taking the right differentials of the objective functions and constraintfunctions at the efficient point to be convex. In this paper we obtain some results for a properly efficient solution of a multiobjective non-linear fractional programming problem involving semilocally convex and related functions by assuming generalized Slater type constraint qualification.

  17. Solving the pre-marshalling problem to optimality with A* and IDA*

    Tierney, Kevin; Pacino, Dario; Voß, Stefan

    2016-01-01

    We present a novel solution approach to the container pre-marshalling problem using the A* and IDA* algorithms combined with several novel branching and symmetry breaking rules that significantly increases the number of pre-marshalling instances that can be solved to optimality. A* and IDA......* are graph search algorithms that use heuristics combined with a complete graph search to find optimal solutions to problems. The container pre-marshalling problem is a key problem for container terminals seeking to reduce delays of inter-modal container transports. The goal of the container pre......-marshalling problem is to find the minimal sequence of container movements to shuffle containers in a set of stacks such that the resulting stacks are arranged according to the time each container must leave the stacks. We evaluate our approach on three well-known datasets of pre-marshalling problem instances...

  18. New numerical methods for open-loop and feedback solutions to dynamic optimization problems

    Ghosh, Pradipto

    The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development

  19. L^1 -optimality conditions for the circular restricted three-body problem

    Chen, Zheng

    2016-06-01

    In this paper, the L^1 -minimization for the translational motion of a spacecraft in the circular restricted three-body problem (CRTBP) is considered. Necessary conditions are derived by using the Pontryagin Maximum Principle (PMP), revealing the existence of bang-bang and singular controls. Singular extremals are analyzed, recalling the existence of the Fuller phenomenon according to the theories developed in (Marchal in J Optim Theory Appl 11(5):441-486, 1973; Zelikin and Borisov in Theory of Chattering Control with Applications to Astronautics, Robotics, Economics, and Engineering. Birkhäuser, Basal 1994; in J Math Sci 114(3):1227-1344, 2003). The sufficient optimality conditions for the L^1 -minimization problem with fixed endpoints have been developed in (Chen et al. in SIAM J Control Optim 54(3):1245-1265, 2016). In the current paper, we establish second-order conditions for optimal control problems with more general final conditions defined by a smooth submanifold target. In addition, the numerical implementation to check these optimality conditions is given. Finally, approximating the Earth-Moon-Spacecraft system by the CRTBP, an L^1 -minimization trajectory for the translational motion of a spacecraft is computed by combining a shooting method with a continuation method in (Caillau et al. in Celest Mech Dyn Astron 114:137-150, 2012; Caillau and Daoud in SIAM J Control Optim 50(6):3178-3202, 2012). The local optimality of the computed trajectory is asserted thanks to the second-order optimality conditions developed.

  20. A Hybrid Improved Genetic Algorithm and Its Application in Dynamic Optimization Problems of Chemical Processes

    SUN Fan; DU Wenli; QI Rongbin; QIAN Feng; ZHONG Weimin

    2013-01-01

    The solutions of dynamic optimization problems are usually very difficult due to their highly nonlinear and multidimensional nature.Genetic algorithm(GA)has been proved to be a feasible method when the gradient is difficult to calculate.Its advantage is that the control profiles at all time stages are optimized simultaneously,but its convergence is very slow in the later period of evolution and it is easily trapped in the local optimum.In this study,a hybrid improved genetic algorithm(HIGA)for solving dynamic optimization problems is proposed to overcome these defects.Simplex method(SM)is used to perform the local search in the neighborhood of the optimal solution.By using SM,the ideal searching direction of global optimal solution could be found as soon as possible and the convergence speed of the algorithm is improved.The hybrid algorithm presents some improvements,such as protecting the best individual,accepting immigrations,as well as employing adaptive crossover and Gaussian mutation operators.The efficiency of the proposed algorithm is demonstrated by solving several dynamic optimization problems.At last,HIGA is applied to the optimal production of secreted protein in a fed batch reactor and the optimal feed-rate found by HIGA is effective and relatively stable.

  1. A new SQP algorithm and numerical experiments for nonlinear inequality constrained optimization problem

    Mahdi Sohrabi-Haghighat

    2014-06-01

    Full Text Available In this paper, a new algorithm based on SQP method is presented to solve the nonlinear inequality constrained optimization problem. As compared with the other existing SQP methods, per single iteration, the basic feasible descent direction is computed by solving at most two equality constrained quadratic programming. Furthermore, there is no need for any auxiliary problem to obtain the coefficients and update the parameters. Under some suitable conditions, the global and superlinear convergence are shown. Keywords: Global convergence, Inequality constrained optimization, Nonlinear programming problem, SQP method, Superlinear convergence rate.

  2. From weierstrass to ky fan theorems and existence results on Optimization and Equilibrium Problems

    Wilfredo Sosa

    2013-08-01

    Full Text Available In this work, we study coerciveness notions and their implications to existence conditions. We start with the presentation of classical ideas of coerciveness in the framework of Optimization Theory, and, then, using a classical technical result, introduced by Ky Fan in 1961, we extend these ideas first to Optimization Problems and then to Equilibrium Problems. We point out the importance of related conditions to the introduced coerciveness notion in order to obtain existence results for Equilibrium Problems, without using monotonicity or generalized monotonicity assumptions.

  3. Algorithm for Solving the Optimization Problem for the Temperature Distribution on a Plate

    Ayriyan, A; Grigorian, H; Kolkovska, N; Lebedev, A

    2015-01-01

    The work describes the maximization problem regarding heating of an area on the surface of a thin plate within a given temperature range. The solution of the problem is applied to ion injectors. The given temperature range corresponds to a required pressure of a saturated gas comprising evaporated atoms of the plate material. In order to find the solution, a one-parameter optimization problem was formulated and implemented leading to optimization of the plate's specific geometry. It was shown that a heated area can be increased up to 23.5% in comparison with the regular rectangle form of a given plate configuration.

  4. Applications of intelligent optimization in biology and medicine current trends and open problems

    Grosan, Crina; Tolba, Mohamed

    2016-01-01

    This volume provides updated, in-depth material on the application of intelligent optimization in biology and medicine. The aim of the book is to present solutions to the challenges and problems facing biology and medicine applications. This Volume comprises of 13 chapters, including an overview chapter, providing an up-to-date and state-of-the research on the application of intelligent optimization for bioinformatics applications, DNA based Steganography, a modified Particle Swarm Optimization Algorithm for Solving Capacitated Maximal Covering Location Problem in Healthcare Systems, Optimization Methods for Medical Image Super Resolution Reconstruction and breast cancer classification. Moreover, some chapters that describe several bio-inspired approaches in MEDLINE Text Mining, DNA-Binding Proteins and Classes, Optimized Tumor Breast Cancer Classification using Combining Random Subspace and Static Classifiers Selection Paradigms, and Dental Image Registration. The book will be a useful compendium for a broad...

  5. Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality

    Mariela Olguín

    2015-01-01

    Full Text Available The objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy g. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positive h (the parameter of the finite element method approximation. Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameter h goes to zero.

  6. A Hybrid Method for Modeling and Solving Supply Chain Optimization Problems with Soft and Logical Constraints

    Paweł Sitek

    2016-01-01

    Full Text Available This paper presents a hybrid method for modeling and solving supply chain optimization problems with soft, hard, and logical constraints. Ability to implement soft and logical constraints is a very important functionality for supply chain optimization models. Such constraints are particularly useful for modeling problems resulting from commercial agreements, contracts, competition, technology, safety, and environmental conditions. Two programming and solving environments, mathematical programming (MP and constraint logic programming (CLP, were combined in the hybrid method. This integration, hybridization, and the adequate multidimensional transformation of the problem (as a presolving method helped to substantially reduce the search space of combinatorial models for supply chain optimization problems. The operation research MP and declarative CLP, where constraints are modeled in different ways and different solving procedures are implemented, were linked together to use the strengths of both. This approach is particularly important for the decision and combinatorial optimization models with the objective function and constraints, there are many decision variables, and these are summed (common in manufacturing, supply chain management, project management, and logistic problems. The ECLiPSe system with Eplex library was proposed to implement a hybrid method. Additionally, the proposed hybrid transformed model is compared with the MILP-Mixed Integer Linear Programming model on the same data instances. For illustrative models, its use allowed finding optimal solutions eight to one hundred times faster and reducing the size of the combinatorial problem to a significant extent.

  7. Variational principles and optimal solutions of the inverse problems of creep bending of plates

    Bormotin, K. S.; Oleinikov, A. I.

    2012-09-01

    It is shown that inverse problems of steady-state creep bending of plates in both the geometrically linear and nonlinear formulations can be represented in a variational formulation. Steady-state values of the obtained functionals corresponding to the solutions of the problems of inelastic deformation and elastic unloading are determined by applying a finite element procedure to the functionals. Optimal laws of creep deformation are formulated using the criterion of minimizing damage in the functionals of the inverse problems. The formulated problems are reduced to the problems solved by the finite element method using MSC.Marc software.

  8. A Parallel Biological Optimization Algorithm to Solve the Unbalanced Assignment Problem Based on DNA Molecular Computing.

    Wang, Zhaocai; Pu, Jun; Cao, Liling; Tan, Jian

    2015-10-23

    The unbalanced assignment problem (UAP) is to optimally resolve the problem of assigning n jobs to m individuals (m parallel DNA algorithm for solving the unbalanced assignment problem using DNA molecular operations. We reasonably design flexible-length DNA strands representing different jobs and individuals, take appropriate steps, and get the solutions of the UAP in the proper length range and O(mn) time. We extend the application of DNA molecular operations and simultaneity to simplify the complexity of the computation.

  9. A Transformation Approach to Optimal Control Problems with Bounded State Variables

    Hanafy, Lawrence Hanafy

    1971-01-01

    A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.

  10. Almost Optimal Interior Penalty Discontinuous Approximations of Symmetric Elliptic Problems on Non-Matching Grids

    Lazarov, R D; Pasciak, J E; Schoberl, J; Vassilevski, P S

    2001-08-08

    We consider an interior penalty discontinuous approximation for symmetric elliptic problems of second order on non-matching grids in this paper. The main result is an almost optimal error estimate for the interior penalty approximation of the original problem based on the partition of the domain into a finite number of subdomains. Further, an error analysis for the finite element approximation of the penalty formulation is given. Finally, numerical experiments on a series of model second order problems are presented.

  11. Numerical solution of the problem of optimizing the process of oil displacement by steam

    Temirbekov, N. M.; Baigereyev, D. R.

    2016-06-01

    The paper is devoted to the problem of optimizing the process of steam stimulation on the oil reservoir by controlling the steam pressure on the injection well to achieve preassigned temperature distribution along the reservoir at a given time of development. The relevance of the study of this problem is related to the need to improve methods of heavy oil development, the proportion of which exceeds the reserves of light oils, and it tends to grow. As a mathematical model of oil displacement by steam, three-phase non-isothermal flow equations is considered. The problem of optimal control is formulated, an algorithm for the numerical solution is proposed. As a reference regime, temperature distribution corresponding to the constant pressure of injected steam is accepted. The solution of the optimization problem shows that choosing the steam pressure on the injection well, one can improve the efficiency of steam-stimulation and reduce the pressure of the injected steam.

  12. Applying Ant Colony Optimization to the Problem of Cell Planning in Mobile Telephone System Radio Network

    Osmar Viera Carcache

    2017-03-01

    Full Text Available This paper presents a computational proposal for the solution of the Cell Planning Problem. The importance of this problem in the area of Telecommunications imposes it as a reference in the search for new methods of optimization. Due to the complexity of the problem, this work uses a discrete relaxation and proposes a mathematical model for the application of the Meta-heuristic Ant Colony Optimization (ACO. For the analysis of the results, 5 instances of the problem of different sizes were selected and the Ants System (AS algorithm was applied. The results show that the proposal efficiently explores the search space, finding the optimal solution for each instance with a relatively low computational cost. These results are compared with 3 evolutionary alternatives of international reference that have been applied to the same study instances, showing a significant improvement by our proposal.

  13. A multi-objective improved teaching-learning based optimization algorithm for unconstrained and constrained optimization problems

    R. Venkata Rao

    2014-01-01

    Full Text Available The present work proposes a multi-objective improved teaching-learning based optimization (MO-ITLBO algorithm for unconstrained and constrained multi-objective function optimization. The MO-ITLBO algorithm is the improved version of basic teaching-learning based optimization (TLBO algorithm adapted for multi-objective problems. The basic TLBO algorithm is improved to enhance its exploration and exploitation capacities by introducing the concept of number of teachers, adaptive teaching factor, tutorial training and self-motivated learning. The MO-ITLBO algorithm uses a grid-based approach to adaptively assess the non-dominated solutions (i.e. Pareto front maintained in an external archive. The performance of the MO-ITLBO algorithm is assessed by implementing it on unconstrained and constrained test problems proposed for the Congress on Evolutionary Computation 2009 (CEC 2009 competition. The performance assessment is done by using the inverted generational distance (IGD measure. The IGD measures obtained by using the MO-ITLBO algorithm are compared with the IGD measures of the other state-of-the-art algorithms available in the literature. Finally, Lexicographic ordering is used to assess the overall performance of competitive algorithms. Results have shown that the proposed MO-ITLBO algorithm has obtained the 1st rank in the optimization of unconstrained test functions and the 3rd rank in the optimization of constrained test functions.

  14. A novel hybrid optimization algorithm for diferential-algebraic control problems

    F. S. Lobato

    2007-09-01

    Full Text Available Dynamic optimization problems can be numerically solved by direct, indirect and Hamilton-Jacobi-Bellman methods. In this paper, the differential-algebraic approach is incorporated into a hybrid method, extending the concepts of structural and differential indexes, consistent initialization analysis, index reduction and dynamic degrees of freedom to the optimal control problem. The resultant differential-algebraic optimal control problem is solved in the following steps: transformation of the original problem into a standard nonlinear programming problem that provides control and state variables, switching time estimates and costate variables profiles with the DIRCOL code; definition of the switching function and the automatically generated sequence of index-1 differential-algebraic boundary value problems from Pontryagin’s minimum principle by using the developed Otima code; and finally, application of the COLDAE code with the results of the direct method as an initial guess. The proposed hybrid method is illustrated with a pressure-constrained batch reactor optimization problem associated with the slack variable method.

  15. A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming

    Tapia, R. A.; Vanrooy, D. L.

    1976-01-01

    A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

  16. Particle swarm optimization with random keys applied to the nuclear reactor reload problem

    Meneses, Anderson Alvarenga de Moura [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE). Programa de Engenharia Nuclear; Fundacao Educacional de Macae (FUNEMAC), RJ (Brazil). Faculdade Professor Miguel Angelo da Silva Santos; Machado, Marcelo Dornellas; Medeiros, Jose Antonio Carlos Canedo; Schirru, Roberto [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE). Programa de Engenharia Nuclear]. E-mails: ameneses@con.ufrj.br; marcelo@lmp.ufrj.br; canedo@lmp.ufrj.br; schirru@lmp.ufrj.br

    2007-07-01

    In 1995, Kennedy and Eberhart presented the Particle Swarm Optimization (PSO), an Artificial Intelligence metaheuristic technique to optimize non-linear continuous functions. The concept of Swarm Intelligence is based on the socials aspects of intelligence, it means, the ability of individuals to learn with their own experience in a group as well as to take advantage of the performance of other individuals. Some PSO models for discrete search spaces have been developed for combinatorial optimization, although none of them presented satisfactory results to optimize a combinatorial problem as the nuclear reactor fuel reloading problem (NRFRP). In this sense, we developed the Particle Swarm Optimization with Random Keys (PSORK) in previous research to solve Combinatorial Problems. Experiences demonstrated that PSORK performed comparable to or better than other techniques. Thus, PSORK metaheuristic is being applied in optimization studies of the NRFRP for Angra 1 Nuclear Power Plant. Results will be compared with Genetic Algorithms and the manual method provided by a specialist. In this experience, the problem is being modeled for an eight-core symmetry and three-dimensional geometry, aiming at the minimization of the Nuclear Enthalpy Power Peaking Factor as well as the maximization of the cycle length. (author)

  17. A genetic algorithm for the pareto optimal solution set of multi-objective shortest path problem

    HU Shi-cheng; XU Xiao-fei; ZHAN De-chen

    2005-01-01

    Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the multi-objective shortest path problem (MSPP) has a set of pareto optimal solutions and cannot be solved in polynomial time. The present algorithms focused mainly on how to obtain a precisely pareto optimal solution for MSPP resulting in a long time to obtain multiple pareto optimal solutions with them. In order to obtain a set of satisfied solutions for MSPP in reasonable time to meet the demand of a decision maker, a genetic algorithm MSPP-GA is presented to solve the MSPP with typically competing objectives, cost and time, in this paper. The encoding of the solution and the operators such as crossover, mutation and selection are developed.The algorithm introduced pareto domination tournament and sharing based selection operator, which can not only directly search the pareto optimal frontier but also maintain the diversity of populations in the process of evolutionary computation. Experimental results show that MSPP-GA can obtain most efficient solutions distributed all along the pareto frontier in less time than an exact algorithm. The algorithm proposed in this paper provides a new and effective method of how to obtain the set of pareto optimal solutions for other multiple objective optimization problems in a short time.

  18. Direct SQP-methods for solving optimal control problems with delays

    Goellmann, L.; Bueskens, C.; Maurer, H.

    1994-12-31

    The maximum principle for optimal control problems with delays leads to a boundary value problem (BVP) which is retarded in the state and advanced in the costate function. Based on shooting techniques, solution methods for this type of BVP have been proposed. In recent years, direct optimization methods have been favored for solving control problems without delays. Direct methods approximate the control and the state over a fixed mesh and solve the resulting NLP-problem with SQP-methods. These methods dispense with the costate function and have shown to be robust and efficient. In this paper, we propose a direct SQP-method for retarded control problems. In contrast to conventional direct methods, only the control variable is approximated by e.g. spline-functions. The state is computed via a high order Runge-Kutta type algorithm and does not enter explicitly the NLP-problem through an equation. This approach reduces the number of optimization variables considerably and is implementable even on a PC. Our method is illustrated by the numerical solution of retarded control problems with constraints. In particular, we consider the control of a continuous stirred tank reactor which has been solved by dynamic programming. This example illustrates the robustness and efficiency of the proposed method. Open questions concerning sufficient conditions and convergence of discretized NLP-problems are discussed.

  19. A priority-based heuristic algorithm (PBHA for optimizing integrated process planning and scheduling problem

    Muhammad Farhan Ausaf

    2015-12-01

    Full Text Available Process planning and scheduling are two important components of a manufacturing setup. It is important to integrate them to achieve better global optimality and improved system performance. To find optimal solutions for integrated process planning and scheduling (IPPS problem, numerous algorithm-based approaches exist. Most of these approaches try to use existing meta-heuristic algorithms for solving the IPPS problem. Although these approaches have been shown to be effective in optimizing the IPPS problem, there is still room for improvement in terms of quality of solution and algorithm efficiency, especially for more complicated problems. Dispatching rules have been successfully utilized for solving complicated scheduling problems, but haven’t been considered extensively for the IPPS problem. This approach incorporates dispatching rules with the concept of prioritizing jobs, in an algorithm called priority-based heuristic algorithm (PBHA. PBHA tries to establish job and machine priority for selecting operations. Priority assignment and a set of dispatching rules are simultaneously used to generate both the process plans and schedules for all jobs and machines. The algorithm was tested for a series of benchmark problems. The proposed algorithm was able to achieve superior results for most complex problems presented in recent literature while utilizing lesser computational resources.

  20. 0/1背包问题的c++实现

    贺晓伟

    2011-01-01

    the 0 / 1 knapsack problem of computer science is a classic problem.In practical problems,we often need to solve the optimization problem,the study of how to limited conditions,find the optimal value of optimization function.Greedy algorithm to solve such%0/1背包问题是计算机科学中的一个经典问题。实际问题中我们经常需要解决最优化问题,即研究如何在限制条件下,求出优化函数的最优值。贪婪算法是解决此类问题的一种直观的求解方法。因为所求问题的最优解可以通过一系列局部最优的选择完成,或者反过来说,一个问题的最优解包含了其子问题的最优解。因此此类具有最优子结构性质的问题可以用贪婪算法。其主要思想为:求解过程中,采用逐步构造最优解的方法,在每个阶段,都做出一个看上去最优的决策(按照一定标准即贪婪准则)。决策一旦作出,就不可再更改。