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
Institute of Scientific and Technical Information of China (English)
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.
Emergence of robust solutions to 0-1 optimization problems in multi-agent systems
DEFF Research Database (Denmark)
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...... in a given time interval by one and only one robot and the total working costs have to be minimized (or total profits maximized). A specifically constructed dynamical system approach (coupled selection equations) is used which is based on pattern formation principles and results in fault resistant and robust...
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this article, we propose sharpening the gain of the chaotic annealing neural network to solve 0- 1 constrained optimization problem. During the chaotic annealing, the gain of the neurons gradually increases and finally arrives at a large value. This strategy can accelerate the convergence of the network to the binary state and keep the satisfaction of the constrains. The simulations, which take the knapsack problems as examples,demonstrate that the approach is efficient both in approximating the global solution and the number of iterations.
Chaotic Neural Network Technique for "0-1" Programming Problems
Institute of Scientific and Technical Information of China (English)
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.
Institute of Scientific and Technical Information of China (English)
薛峰; 陈刚; 高尚
2011-01-01
The classical particle swarm optimization is a powerful method to find the minimum of a numerical function,on a continuous definition domain. The particle swarm optimization algorithm combine the ideal of the genetic algorithm is recommended to solve 0-1 integer programming problem. All the 6 hybrid particle swarm optimization algorithms are proved effective. Especially the hybrid particle swarm optimization algorithm with across strategy A and mutation strategy C is a simple and effective better algorithm than others. It can easily be modified for any combinatorial problem for which we have no good specialized algorithm.%经典的粒子群是一个有效的寻找连续函数极值的方法,结合遗传算法的思想提出的混合粒子群算法来解决0-1整数规划问题,经过比较测试,6种混合粒子群算法的效果都比较好,特别交叉策略A和变异策略C的混合粒子群算法是最好的且简单有效的算法.对于目前还没有好的解法的组合优化问题,很容易地修改此算法就可解决.
Simulated Annealing for the 0/1 Multidimensional Knapsack Problem
Institute of Scientific and Technical Information of China (English)
Fubin Qian; Rui Ding
2007-01-01
In this paper a simulated annealing (SA) algorithm is presented for the 0/1 multidimensional knapsack problem. Problem-specific knowledge is incorporated in the algorithm description and evaluation of parameters in order to look into the performance of finite-time implementations of SA. Computational results show that SA performs much better than a genetic algorithm in terms of solution time, whilst having a modest loss of solution quality.
Linearization of multi-objective multi-quadratic 0-1 programming problems
Directory of Open Access Journals (Sweden)
Shifali Bhargava
2014-03-01
Full Text Available A linearization technique is developed for multi-objective multi-quadratic 0-1 programming problems with linear and quadratic constraints to reduce it to multi-objective linear mixed 0-1 programming problems. The method proposed in this paper needs only O (kn additional continuous variables where k is the number of quadratic constraints and n is the number of initial 0-1 variables. Keywords: Knapsack Constraint, Linearization, Multi-Objective, Multi-Quadratic, Optimal Solution.
An Improved Hybrid Encoding Cuckoo Search Algorithm for 0-1 Knapsack Problems
Yanhong Feng; Ke Jia; Yichao He
2014-01-01
Cuckoo search (CS) is a new robust swarm intelligence method that is based on the brood parasitism of some cuckoo species. In this paper, an improved hybrid encoding cuckoo search algorithm (ICS) with greedy strategy is put forward for solving 0-1 knapsack problems. First of all, for solving binary optimization problem with ICS, based on the idea of individual hybrid encoding, the cuckoo search over a continuous space is transformed into the synchronous evolution search over discrete space....
A Thermodynamical Selection-Based Discrete Differential Evolution for the 0-1 Knapsack Problem
Directory of Open Access Journals (Sweden)
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.
A Novel Harmony Search Algorithm Based on Teaching-Learning Strategies for 0-1 Knapsack Problems
Shouheng Tuo; Longquan Yong; Fang’an Deng
2014-01-01
To enhance the performance of harmony search (HS) algorithm on solving the discrete optimization problems, this paper proposes a novel harmony search algorithm based on teaching-learning (HSTL) strategies to solve 0-1 knapsack problems. In the HSTL algorithm, firstly, a method is presented to adjust dimension dynamically for selected harmony vector in optimization procedure. In addition, four strategies (harmony memory consideration, teaching-learning strategy, local pitch adjusting, and rand...
An improved hybrid encoding cuckoo search algorithm for 0-1 knapsack problems.
Feng, Yanhong; Jia, Ke; He, Yichao
2014-01-01
Cuckoo search (CS) is a new robust swarm intelligence method that is based on the brood parasitism of some cuckoo species. In this paper, an improved hybrid encoding cuckoo search algorithm (ICS) with greedy strategy is put forward for solving 0-1 knapsack problems. First of all, for solving binary optimization problem with ICS, based on the idea of individual hybrid encoding, the cuckoo search over a continuous space is transformed into the synchronous evolution search over discrete space. Subsequently, the concept of confidence interval (CI) is introduced; hence, the new position updating is designed and genetic mutation with a small probability is introduced. The former enables the population to move towards the global best solution rapidly in every generation, and the latter can effectively prevent the ICS from trapping into the local optimum. Furthermore, the greedy transform method is used to repair the infeasible solution and optimize the feasible solution. Experiments with a large number of KP instances show the effectiveness of the proposed algorithm and its ability to achieve good quality solutions. PMID:24527026
A Novel Discrete Global-Best Harmony Search Algorithm for Solving 0-1 Knapsack Problems
Directory of Open Access Journals (Sweden)
Wan-li Xiang
2014-01-01
is applied to decide whether or not a new randomly generated harmony is included into the HM. The proposed DGHS is evaluated on twenty knapsack problems with different scales and compared with other three metaheuristics from the literature. The experimental results indicate that DGHS is efficient, effective, and robust for solving difficult 0-1 knapsack problems.
Optimal obstacle control problem
Institute of Scientific and Technical Information of China (English)
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.
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.
Yanhong Feng; Gai-Ge Wang; Qingjiang Feng; Xiang-Jun Zhao
2014-01-01
An effective hybrid cuckoo search algorithm (CS) with improved shuffled frog-leaping algorithm (ISFLA) is put forward for solving 0-1 knapsack problem. First of all, with the framework of SFLA, an improved frog-leap operator is designed with the effect of the global optimal information on the frog leaping and information exchange between frog individuals combined with genetic mutation with a small probability. Subsequently, in order to improve the ...
Solving the 0/1 Knapsack Problem by a Biomolecular DNA Computer
Directory of Open Access Journals (Sweden)
Hassan Taghipour
2013-01-01
Full Text Available Solving some mathematical problems such as NP-complete problems by conventional silicon-based computers is problematic and takes so long time. DNA computing is an alternative method of computing which uses DNA molecules for computing purposes. DNA computers have massive degrees of parallel processing capability. The massive parallel processing characteristic of DNA computers is of particular interest in solving NP-complete and hard combinatorial problems. NP-complete problems such as knapsack problem and other hard combinatorial problems can be easily solved by DNA computers in a very short period of time comparing to conventional silicon-based computers. Sticker-based DNA computing is one of the methods of DNA computing. In this paper, the sticker based DNA computing was used for solving the 0/1 knapsack problem. At first, a biomolecular solution space was constructed by using appropriate DNA memory complexes. Then, by the application of a sticker-based parallel algorithm using biological operations, knapsack problem was resolved in polynomial time.
Design optimization of a 0.1-ton/day active magnetic regenerative hydrogen liquefier
Zhang, L.; Sherif, S. A.; DeGregoria, A. J.; Zimm, C. B.; Veziroglu, T. N.
2000-04-01
A design optimization procedure of a 0.1-ton/day active magnetic regenerative (AMR) hydrogen liquefier model is described. The liquefier is proposed for the industrial liquid hydrogen market with overall efficiency being the primary measure of performance. This performance is described here in terms of particle size, bed length, and inter-stage temperature. Efficiency comparable to larger gas cycle plants is predicted. The magnetic liquefier may be modified to operate as a two-stage magnetic refrigerator between 77 and 20 K with high efficiency. The paper describes an optimization method as applied to the design of a two-stage AMR hydrogen liquefier and presents the associated results. A five-parameter optimization process is performed since there are five changeable parameters; the low- and high-stage particle sizes, the low- and high-stage bed lengths, and the inter-stage temperature. Model results are presented and compared with experimental results of an actual liquefier.
a Genetic Algorithm Based on Sexual Selection for the Multidimensional 0/1 Knapsack Problems
Varnamkhasti, Mohammad Jalali; Lee, Lai Soon
In this study, a new technique is presented for choosing mate chromosomes during sexual selection in a genetic algorithm. The population is divided into groups of males and females. During the sexual selection, the female chromosome is selected by the tournament selection while the male chromosome is selected based on the hamming distance from the selected female chromosome, fitness value or active genes. Computational experiments are conducted on the proposed technique and the results are compared with some selection mechanisms commonly used for solving multidimensional 0/1 knapsack problems published in the literature.
Directory of Open Access Journals (Sweden)
Yanhong Feng
2014-01-01
Full Text Available An effective hybrid cuckoo search algorithm (CS with improved shuffled frog-leaping algorithm (ISFLA is put forward for solving 0-1 knapsack problem. First of all, with the framework of SFLA, an improved frog-leap operator is designed with the effect of the global optimal information on the frog leaping and information exchange between frog individuals combined with genetic mutation with a small probability. Subsequently, in order to improve the convergence speed and enhance the exploitation ability, a novel CS model is proposed with considering the specific advantages of Lévy flights and frog-leap operator. Furthermore, the greedy transform method is used to repair the infeasible solution and optimize the feasible solution. Finally, numerical simulations are carried out on six different types of 0-1 knapsack instances, and the comparative results have shown the effectiveness of the proposed algorithm and its ability to achieve good quality solutions, which outperforms the binary cuckoo search, the binary differential evolution, and the genetic algorithm.
Feng, Yanhong; Wang, Gai-Ge; Feng, Qingjiang; Zhao, Xiang-Jun
2014-01-01
An effective hybrid cuckoo search algorithm (CS) with improved shuffled frog-leaping algorithm (ISFLA) is put forward for solving 0-1 knapsack problem. First of all, with the framework of SFLA, an improved frog-leap operator is designed with the effect of the global optimal information on the frog leaping and information exchange between frog individuals combined with genetic mutation with a small probability. Subsequently, in order to improve the convergence speed and enhance the exploitation ability, a novel CS model is proposed with considering the specific advantages of Lévy flights and frog-leap operator. Furthermore, the greedy transform method is used to repair the infeasible solution and optimize the feasible solution. Finally, numerical simulations are carried out on six different types of 0-1 knapsack instances, and the comparative results have shown the effectiveness of the proposed algorithm and its ability to achieve good quality solutions, which outperforms the binary cuckoo search, the binary differential evolution, and the genetic algorithm. PMID:25404940
Bee Colony Algorithm for the Multi-objective 0-1 Programming Problem%多目标0-1规划问题的蜂群算法
Institute of Scientific and Technical Information of China (English)
韩燕燕; 马良; 赵小强
2012-01-01
In order to solve the multi-objective 0-1 programming problem with linear constrains, we present a new intelligent optimization algorithm--bee colony algorithm. The algorithm is coded and implemented on microcomputer through aseries of numerical tests. Comparisons with genetic algorithm, ant colony optimization algorithm and cellular ant colony algorithm show that the bee colony algorithm can get more pareto solutions to the multi-objective 0-1 programming problem. And the effectiveness of the Bee Colony Algorithm is validated.%针对多目标0-1规划问题,本文给出一种新型的智能优化算法——蜂群算法进行求解,并通过实例验证,与遗传算法、蚁群算法和元胞蚁群算法作了相应比较.就多目标0-1规划问题而言,蜂群算法能得到更多的Pareto解,说明了蜂群算法在解决该类问题上的有效性.
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
Institute of Scientific and Technical Information of China (English)
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.
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
求解0-1背包问题的一种新混合算法%New hybrid algorithm to solve 0-1 knapsack problem
Institute of Scientific and Technical Information of China (English)
孙怀影; 耿寅融; 单谦
2012-01-01
When using dynamic programming algorithm to solve 0-1 knapsack problem, its time complexity and space complexity both are O(nC). Its space complexity is not acceptable in case of large scale problem. From the recursive equations for computing optimal value of 0-1 knapsack problem, Memory Efficient Dynamic Programming(MEDP) is proposed. In order to conquer the drawback of MEDP, a new hybrid algorithm is put forward, which combines divided-and-conquered strategy with it and whose time complexity is O(nC). The hybrid algorithm eliminates the backtracking step, while it can find the goods put into the knapsack under the space complexity O( [n/d] + C), where d is the word length of computer. Experimental result demonstrates that the algorithm works identically with the theory.%用动态规划算法求解0-1背包问题的时空复杂度为O(nC).这个空间复杂度在求解大规模问题上是不可接受的.从计算0-1背包问题最优值的递归方程出发,给出高效利用内存的动态规划算法.为了克服内存高效的动态规划算法带来的缺点,设计新混合算法求解0-1背包问题.该新混合算法的时间复杂度为O(nC)；它消除了回溯阶段,并且为求得放入背包的物品所使用的空间复杂度仅为O([n/d]+C),其中d为计算机字长.实验结果表明,混合算法的工作效率与理论分析相同.
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…
Decomposition Approaches for Optimization Problems
Kinable, Joris
2014-01-01
This dissertation encompasses the development of decomposition approaches for a variety of both real-world and fundamental optimization problems. Many optimization problems comprise of multiple interconnected subproblems, often rendering them too large or too complicated to solve as a single integral problem. Decomposition approaches are required to deal with these problems efficiently. By decomposing a problem into multiple subproblems, efficient dedicated procedures can be employed to solve...
Topology optimization for acoustic problems
DEFF Research Database (Denmark)
Dühring, Maria Bayard
2006-01-01
In this paper a method to control acoustic properties in a room with topology optimization is presented. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized by distribution of material in a design domain along the ceiling in 2D and 3D. Nice 0-1 designs...
求解0-1背包问题的改进混合遗传算法%Improved Hybrid Genetic Algorithm for Solving 0-1 Knapsack Problem
Institute of Scientific and Technical Information of China (English)
刘寒冰; 张亚娟
2015-01-01
针对一种混合遗传算法所采用的贪心变换法的不足，给出了一种改进的贪心修正法；并基于稳态复制的策略，对遗传算法的选择操作进行改进，给出了随机选择操作。在此基础上，提出了一种改进的混合遗传算法，并将新算法用于解决大规模的0-1背包问题，通过实例将新算法与 HGA 算法进行实验对比分析，并研究了变异概率对新算法性能的影响。实验结果表明新算法收敛速度快，寻优能力强。%An improved greedy correction method is advanced for overcome the flaw of greedy transform method adopted by hybrid genetic algorithm (HGA). And based on steady state reproduction strategy, the choice method of random selection is advanced. These new methods are combined with genetic algorithm to propose a high-efficient hybrid genetic algorithm (IHGA), and new algorithm was used to solve large-scale 0-1 knapsack problem. By many simulation experiments, IHGA algorithm is compared with HGA algorithm, and how the mutation probability affect the performance of the new algorithm has been studied. The experimental results show that the new algorithm has higher convergent speed and better optimization capability.
About an optimal visiting problem
Bagagiolo, Fabio; Benetton, Michela
2010-01-01
In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous "Traveling Salesman Problem" and brings all its computational diculties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equat...
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
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.
Institute of Scientific and Technical Information of China (English)
孙娟; 盛红波; 孙小玲
2007-01-01
In this paper,a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems was studied.The method was based on the Lagrangian relaxation and the surrogate constraint technique for finding feasible solutions.The Lagrangian relaxations were solved with the maximum-flow algorithm and the Lagrangian bounds Was determined with the outer approximation method.Computational results show the efficiency of the proposed method for multi-dimensional quadratic 0-1 knapsack problems.
Topology optimization of flow problems
DEFF Research Database (Denmark)
Gersborg, Allan Roulund
2007-01-01
of the computed topology design using standard, credible analysis tools with a body-fitted mesh. Also, the thesis encompasses work on how to utilize the finite volume method (FVM) in the topology optimization context. This is motivated by the momentous position the FVM has in the fluid dynamics community......This thesis investigates how to apply topology optimization using the material distribution technique to steady-state viscous incompressible flow problems. The target design applications are fluid devices that are optimized with respect to minimizing the energy loss, characteristic properties...... of the velocity field or mixing properties. To reduce the computational complexity of the topology optimization problems the primary focus is put on the Stokes equation in 2D and in 3D. However, the thesis also contains examples with the 2D Navier-Stokes equation as well as an example with convection dominated...
About an Optimal Visiting Problem
Energy Technology Data Exchange (ETDEWEB)
Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it; Benetton, Michela [Unversita di Trento, Dipartimento di Matematica (Italy)
2012-02-15
In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous 'Traveling Salesman Problem' and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equation. We introduce some 'external' variables, one per target, which keep in memory whether the corresponding target is already visited or not, and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton-Jacobi equation turns out to be discontinuous.
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1994-01-01
The paper studies the problem of determining the number and dimensions of sizes of apparel so as to maximize profits. It develops a simple one-variable bisection search algorithm that gives the optimal solution. An example is solved interactively using a Macintosh LC and Math CAD, a mathematical...
The Duality on Vector Optimization Problems
Institute of Scientific and Technical Information of China (English)
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.
Optimization in HIV screening problems
Directory of Open Access Journals (Sweden)
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.
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
Institute of Scientific and Technical Information of China (English)
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.
Stability Analysis for Stochastic Optimization Problems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
On Alternative Optimal Solutions to Linear Fractional Optimization Problems
Institute of Scientific and Technical Information of China (English)
ShengjiaXue
2004-01-01
The structure of the optimal solution set is derived for linear fractional optimization problems with the representation theorem of polyhedral sets．And the computational procedure in determining all optimal solutions is also given．
Some Undecidable Problems on Approximability of NP Optimization Problems
Institute of Scientific and Technical Information of China (English)
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 of Uncertainty Features for Transportation Problems
Eggenberg, Niklaus; Salani, Matteo; Bierlaire, Michel
2008-01-01
In this work we present the concept of Uncertainty Feature Optimization (UFO), an optimization framework to handle problems due to noisy data. We show that UFO is an extension of standard methods as robust optimization and stochastic optimization and we show that the method can be used when no information of the data uncertainty sets is available. We present a proof of concept for the multiple knapsack problem and we show applications to some routing problems: vehicle routing with stochastic ...
CASE STUDY IN OPTIMAL TELEVISION ADVERTS SELECTION AS KNAPSACK PROBLEM
Directory of Open Access Journals (Sweden)
E. Ivokhin
2014-06-01
Full Text Available In this research paper, we shall consider the application of classical 0-1 knapsack problem with a single constraint to selection of television advertisements at critical periods such as prime time news, news adjacencies, break in news and peak times using the WINQSB software. In the end of this paper we shall formulate the task of investigation of the post optimality solution of optimal Television Adverts Selection with respect to time allocated for every group adverts.
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.
Artificial Ant Species on Solving Optimization Problems
Pintea, Camelia-M.
2013-01-01
During the last years several ant-based techniques were involved to solve hard and complex optimization problems. The current paper is a short study about the influence of artificial ant species in solving optimization problems. There are studied the artificial Pharaoh Ants, Lasius Niger and also artificial ants with no special specificity used commonly in Ant Colony Optimization.
Ant colony optimization in continuous problem
Institute of Scientific and Technical Information of China (English)
YU Ling; LIU Kang; LI Kaishi
2007-01-01
Based on the analysis of the basic ant colony optimization and optimum problem in a continuous space,an ant colony optimization (ACO) for continuous problem is constructed and discussed. The algorithm is efficient and beneficial to the study of the ant colony optimization in a continuous space.
On Optimizing the Satisfiability (SAT) Problem
Institute of Scientific and Technical Information of China (English)
GU Jun; GU Qianping; DU Dingzhu
1999-01-01
The satisfiability(SAT) problem is abasic problem in computing theory. Presently, an active area of researchon SAT problem is to design efficient optimization algorithms forfinding a solution for a satisfiable CNF formula. A newformulation, the Universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real spacehas been developed. Many optimization techniques,such as the steepest descent method, Newton's method, and thecoordinate descent method, can be used to solve the Universal SAT problem. In this paper, we prove that, when the initial solution issufficiently close to the optimal solution, the steepest descent methodhas a linear convergence ratio β<1, Newton's method has aconvergence ratio of order two, and the convergence ratio of thecoordinate descent method is approximately (1-β/m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the Universal SAT problem is alsopresented in this paper.
Multiple optimal solutions to a sort of nonlinear optimization problem
Institute of Scientific and Technical Information of China (English)
Xue Shengjia
2007-01-01
The optimization problem is considered in which the objective function is pseudolinear(both pseudoconvex and pseudoconcave) and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions ( ifthe uniqueness condition is not satisfied ) are provided. Finally, an illustrative example is also given.
Global optimization in inverse problem of scatterometry
Afraites, Lekbir; Hazart, Jérôme; Schiavone, Patrick
2009-01-01
International audience In the current work, we consider the inverse problem in scatterometry which consists in determining the feature shape from an experimental ellipsometric signature. The reformulation of the given nonlinear identification problem was considered as a parametric optimization problem using the Least Square criterion. In this work, a design procedure for global robust optimization is developed using Kriging and global optimization approaches. Robustness is determined by Kr...
Ant Colony Optimization and Hypergraph Covering Problems
Pat, Ankit
2011-01-01
Ant Colony Optimization (ACO) is a very popular metaheuristic for solving computationally hard combinatorial optimization problems. Runtime analysis of ACO with respect to various pseudo-boolean functions and different graph based combinatorial optimization problems has been taken up in recent years. In this paper, we investigate the runtime behavior of an MMAS*(Max-Min Ant System) ACO algorithm on some well known hypergraph covering problems that are NP-Hard. In particular, we have addressed the Minimum Edge Cover problem, the Minimum Vertex Cover problem and the Maximum Weak- Independent Set problem. The influence of pheromone values and heuristic information on the running time is analysed. The results indicate that the heuristic information has greater impact towards improving the expected optimization time as compared to pheromone values. For certain instances of hypergraphs, we show that the MMAS* algorithm gives a constant order expected optimization time when the dominance of heuristic information is ...
Constrained Graph Optimization: Interdiction and Preservation Problems
Energy Technology Data Exchange (ETDEWEB)
Schild, Aaron V [Los Alamos National Laboratory
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
Topology optimization of wave-propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures.......Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures....
A Mathematical Optimization Problem in Bioinformatics
Heyer, Laurie J.
2008-01-01
This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…
Metaheuristic optimization of acoustic inverse problems.
A.V. van Leijen; L. Rothkrantz; F. Groen
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
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…
Particle swarm optimization for complex nonlinear optimization problems
Alexandridis, Alex; Famelis, Ioannis Th.; Tsitouras, Charalambos
2016-06-01
This work presents the application of a technique belonging to evolutionary computation, namely particle swarm optimization (PSO), to complex nonlinear optimization problems. To be more specific, a PSO optimizer is setup and applied to the derivation of Runge-Kutta pairs for the numerical solution of initial value problems. The effect of critical PSO operational parameters on the performance of the proposed scheme is thoroughly investigated.
Fast Solvers of Fredholm Optimal Control Problems
Institute of Scientific and Technical Information of China (English)
Mario; Borzì
2010-01-01
The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.
Optimization problems on the Sierpinski gasket
Directory of Open Access Journals (Sweden)
Marek Galewski
2016-04-01
Full Text Available We investigate the existence of an optimal process for such an optimal control problem in which the dynamics is given by the Dirichlet problem driven by weak Laplacian on the Sierpinski gasket. To accomplish this task using a direct variational approach with no global growth conditions on the nonlinear term, we consider the existence of solutions, their uniqueness and their dependence on a functional parameter for mentioned Dirichlet problem. This allows us to prove that the optimal control problem admits at least one solution.
Topology Optimization for Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
2011-01-01
.This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...
Binary Cockroach Swarm Optimization for Combinatorial Optimization Problem
Directory of Open Access Journals (Sweden)
Ibidun Christiana Obagbuwa
2016-09-01
Full Text Available The Cockroach Swarm Optimization (CSO algorithm is inspired by cockroach social behavior. It is a simple and efficient meta-heuristic algorithm and has been applied to solve global optimization problems successfully. The original CSO algorithm and its variants operate mainly in continuous search space and cannot solve binary-coded optimization problems directly. Many optimization problems have their decision variables in binary. Binary Cockroach Swarm Optimization (BCSO is proposed in this paper to tackle such problems and was evaluated on the popular Traveling Salesman Problem (TSP, which is considered to be an NP-hard Combinatorial Optimization Problem (COP. A transfer function was employed to map a continuous search space CSO to binary search space. The performance of the proposed algorithm was tested firstly on benchmark functions through simulation studies and compared with the performance of existing binary particle swarm optimization and continuous space versions of CSO. The proposed BCSO was adapted to TSP and applied to a set of benchmark instances of symmetric TSP from the TSP library. The results of the proposed Binary Cockroach Swarm Optimization (BCSO algorithm on TSP were compared to other meta-heuristic algorithms.
Ant Colony Optimization for Capacity Problems
Directory of Open Access Journals (Sweden)
Tad Gonsalves
2015-01-01
Full Text Available This paper deals with the optimization of the capac ity of a terminal railway station using the Ant Colony Optimization algorithm. The capacity of the terminal station is defined as the number of trains that depart from the station in un it interval of time. The railway capacity optimization problem is framed as a typical symmetr ical Travelling Salesman Problem (TSP, with the TSP nodes representing the train arrival / departure events and the TSP total cost representing the total time-interval of the schedul e. The application problem is then optimized using the ACO algorithm. The simulation experiments validate the formulation of the railway capacity problem as a TSP and the ACO algorithm pro duces optimal solutions superior to those produced by the domain experts.
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...
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...
OPTIMAL CONTROL PROBLEM FOR PARABOLIC VARIATIONAL INEQUALITIES
Institute of Scientific and Technical Information of China (English)
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.
Generalized Benders’ Decomposition for topology optimization problems
DEFF Research Database (Denmark)
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...
Topology optimization for transient heat transfer problems
DEFF Research Database (Denmark)
Zeidan, Said; Sigmund, Ole; Lazarov, Boyan Stefanov
The focus of this work is on passive control of transient heat transfer problems using the topology optimization (TopOpt) method [1]. The goal is to find distributions of a limited amount of phase change material (PCM), within a given design domain, which optimizes the heat energy storage [2]. Our...
An improved group search optimizer for mechanical design optimization problems
Institute of Scientific and Technical Information of China (English)
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.
Finite Volumes Discretization of Topology Optimization Problems
DEFF Research Database (Denmark)
Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter
Utilizing control in the coecients of partial dierential equations (PDEs) for the purpose of optimal design, or topology optimization, is a well established technique in both academia and industry. Advantages of using control in the coecients for optimal design purposes include the exibility...... 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...... the optimization procedure. As topology optimization is gaining maturity, the method is applied to increasingly more complex coupled multi-physical problems. As a result it becomes vital to utilize robust and mature PDE solvers within a topology optimization framework. Finite volume methods (FVMs) represent...
Topology Optimization for Transient Wave Propagation Problems
DEFF Research Database (Denmark)
Matzen, René
The study of elastic and optical waves together with intensive material research has revolutionized everyday as well as cutting edge technology in very tangible ways within the last century. Therefore it is important to continue the investigative work towards improving existing as well as innovate...... optimization is still in its infancy. A generic optimization problem is formulated with an objective function that can be field, velocity, and acceleration dependent, as well as it can accommodate the dependency of filtered signals essential in signal shape optimization [P3]. The analytical design gradients......] optimizes structures that accommodate non-dispersive slow light, with important applications for optical buffering devices....
Particle Swarm Optimization for Structural Design Problems
Saruhan, Hamit
2010-01-01
The aim of this paper is to employ the Particle Swarm Optimization (PSO) technique to a mechanical engineering design problem which is minimizing the volume of a cantilevered beam subject to bending strength constraints. Mechanical engineering design problems are complex activities which are computing capability are more and more required. The most of these problems are solved by conventional mathematical programming techniques that require gradient information. These techniques have several ...
Topology optimization of Channel flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.
2005-01-01
This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low to moderate Reynolds numbers. This makes the flow problem non-linear and hence a non-trivial extension of the work of [Borrvall&Petersson 2002...... 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......]. 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...
Better relaxations of classical discrete optimization problems.
Energy Technology Data Exchange (ETDEWEB)
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.
Solving constrained optimization problems with hybrid particle swarm optimization
Zahara, Erwie; Hu, Chia-Hsin
2008-11-01
Constrained optimization problems (COPs) are very important in that they frequently appear in the real world. A COP, in which both the function and constraints may be nonlinear, consists of the optimization of a function subject to constraints. Constraint handling is one of the major concerns when solving COPs with particle swarm optimization (PSO) combined with the Nelder-Mead simplex search method (NM-PSO). This article proposes embedded constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, as a special operator in NM-PSO for dealing with constraints. Experiments using 13 benchmark problems are explained and the NM-PSO results are compared with the best known solutions reported in the literature. Comparison with three different meta-heuristics demonstrates that NM-PSO with the embedded constraint operator is extremely effective and efficient at locating optimal solutions.
Topology optimization of fluid mechanics problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan
While topology optimization for solid continuum structures have been studied for about 20 years and for the special case of trusses for many more years, topology optimization of fluid mechanics problems is more recent. Borrvall and Petersson [1] is the seminal reference for topology optimization......D Navier-Stokes equation as well as an example with convection dominated transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the present work gives a proof-of-concept for the application of the method within fluid mechanics problems and it remains...... processing tool. Prior to design manufacturing this allows the engineer to quantify the performance of the computed topology design using standard, credible analysis tools with a body-fitted mesh. [1] Borrvall and Petersson (2003) "Topology optimization of fluids in Stokes flow", Int. J. Num. Meth. Fluids...
Statistical Physics of Hard Optimization Problems
Zdeborová, Lenka
2008-01-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the NP-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system ...
A simple convex optimization problem with many applications
DEFF Research Database (Denmark)
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...
The inverse problem of the optimal regulator.
Yokoyama, R.; Kinnen, E.
1972-01-01
The inverse problem of the optimal regulator is considered for a general class of multi-input systems with integral-type performance indices. A new phase variable canonical form is shown to be convenient for this analysis. The advantage of the canonical form is to separate the state variables into subvectors of directly controlled, indirectly controlled, and uncontrollable components. Necessary and sufficient conditions for optimized performance indices are given. With the nonlinearities of the system restricted to functions of the directly controlled state variables, additional results are developed about the nonnegative property of optimized loss functions.
基于蜂群遗传算法的0-1背包问题%The O-1 Knapsack Problem Based on the Bee-Swarm Genetic Algorithm
Institute of Scientific and Technical Information of China (English)
吴迪; 姜永增; 宋广军
2011-01-01
针对0-1背包问题,本文提出了基于蜂群遗传算法的优化求解方案.该算法包括两个种群,一个主要用于全局搜索,另一个主要用于局部搜索;每个个体采用二进制编码;采用最优个体交叉策略;对当前解的处理措施是将还未装入背包且性价比最好的物品装进背包,直至不能装为止;不符合约束条件的解采用诱变因子指导变异处理;遗传算子包括单点交叉算子、简单变异算子、主动进化算子和抑制算子.本算法充分发挥了遗传算法的群体搜索和全局收敛的特性,快速地并行搜索,有效地克服了经典遗传算法容易陷入局部最优问题.数值实验表明,该算法在求解0-1背包问题中取得了较好的效果,同样可以应用于其它的组合优化问题.%This paper presents a bee-swarm genetic algorithm for the 0-1 knapsack problem.There are two populations, one for global search, and the other for local search.Each individual adopts the binary code.Only the best one can crossover.The strategy of managing the feasible solution is to enclose the goods which is out of the knapsack and cost-effective, until no goods can be put into.The solution which does not accord with the constraint condition mutates under the instruction of mutagens.The genetic operators include order crossover operator, two-block-exchange mutation operator and restraint operator.The method sufficiently takes the advantage of the genetic algorithm such as group search and global convergence in order to have a quick parallel search, which efficiently overcomes the problem of local optimization.The experimental results show that the bee swarm genetic algorithm is efficient in solving the 0-1 Knapsack problem, and is also suitable for other combinatorial optimization problems.
Singularity Theory for Nonlinear Optimization Problems
Casti, J.L.
1987-01-01
Techniques from the theory of singularities of smooth mappings are employed to study the reduction of nonlinear optimization problems to simpler forms. It is shown how singularity theory ideas can be used to: (1) reduce the decision-space dimensionality; (2) transform the constraint space to simpler form for primal algorithms; (3) provide sensitivity analysis.
Optimization problems arising in robust stability theory
Energy Technology Data Exchange (ETDEWEB)
Polyak, B.
1994-12-31
Robustness is one of the main topics in modern control theory. We consider one aspect of the theme - robust stability analysis under parametric uncertainty. It deals with stability problems for linear time-invariant differential or difference equations with uncertainties in their coefficients. Various optimization problems concerning {open_quotes}the largest{close_quotes} admissible uncertainty naturally arise. Examples: (1) Find the largest cube inscribed in stability domain; (2) Find the box with the largest volume preserving stability; (3) Describe a boundary of a two-dimensional image of a box under linear or nonlinear transformation; (4) Find a sum or a project of sets on a complex plane, e.g., find a product of n discs. These problems require new duality results and new necessary conditions of optimality.
Enhanced Bee Colony Algorithm for Complex Optimization Problems
S.Suriya; R. Deepalakshmi; S.Suresh kannan; Dr.S.P.SHANTHARAJAH
2012-01-01
Optimization problems are considered to be one kind of NP hard problems. Usually heuristic approaches are found to provide solutions for NP hard problems. There are a plenty of heuristic algorithmsavailable to solve optimization problems namely: Ant Colony Optimization, Particle Swarm Optimization, Bee Colony Optimization, etc. The basic Bee Colony algorithm, a population based search algorithm, is analyzed to be a novel tool for complex optimization problems. The algorithm mimics the food fo...
Using combinatorial problem decomposition for optimizing plutonium inventory management
International Nuclear Information System (INIS)
Plutonium Inventory Management Optimization can be modeled as a very large 0-1 linear program. To solve it, problem decomposition is necessary, since other classic techniques are not efficient for such a size. The first decomposition consists in favoring constraints that are the most difficult to reach and variables that have the highest influence on the cost: fortunately, both correspond to stock output decisions. The second decomposition consists in mixing continuous linear program solving and integer linear program solving. Besides, the first decisions to be taken are systematically favored, for they are based on data considered to be sure, when data supporting later decisions in known with less accuracy and confidence. (author)
Statistical physics of hard optimization problems
Zdeborová, Lenka
2009-06-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.
Evolutionary strategies for solving optimization problems
Ebeling, Werner; Reimann, Axel; Molgedey, Lutz
We will give a survey of applications of thermodynamically and biologically oriented evolutionary strategies for optimization problems. Primarily, we investigate the solution of discrete optimization problems, most of combinatorial type, using a certain class of coupled differential equations. The problem is to find the minimum on a large set of real numbers (the potential) Ui, defined on the integer set i = 1 ...s, where s is an extremely large nu mber. The stationary states of the system correspond to relative optima on the discrete set. First, several elementary evolutionary strategies are described by simple deterministic equations, leading to a high-dimensional system of coupled differential equations. The known equations for thermodynamic search processes and for simple models of biological evolution are unified by defining a two-parameter family of equations which embed both cases. The unified equations model mixed Boltzmann/Darwin- strategies including basic elements of thermodynamical and biological evolution as well. In a next step a master equation model in the occupation number space is defined. We investigate the transition probabilities and the convergence properties using tools from the theory of stochastic processes. Several examples are analyzed. In particular we study the optimization of theoretical model sequences with simple valuation rules. In order to demonstrate that the strategies developed here may also be used to investigate realistic problems we present an example application to RNA folding (search for a minimum free energy configuration).
Optimization of Pr0.9Ca0.1MnO3 thin ﬁlms with varying in-situ oxygen annealing treatments
Directory of Open Access Journals (Sweden)
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.
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 ...
The optimization (ALARA) problem: A direct formulation
International Nuclear Information System (INIS)
An alternative method to that set out by the International Commission on Radiological Protection (ICRP) for implementing the optimization (ALARA) principle of radiation protection is proposed. The method follows directly from the basic dose limitation system and naturally integrates the three components of the system. An essential feature of the method is that 'all exposures' is taken to mean 'each and every one' rather than the 'sum of individual doses', as in the usual method using the collective dose concept. The method draws on established techniques from optimization theory and those aspects of micro-economic theory which form the basis of cost-benefit analysis. The method takes separate account of both the direct costs to the community of the effects of radiation exposures and each individual's 'risk-benefit' attitudes to radiation exposures. The conundrum concerning the 'value of a life' turns out to be operationally and quantitatively irrelevant. Various constraints including the dose limits, economic and social constraints and natural physical constraints are included in the method which leads directly to a standard form problem in mathematical programming. A practical advantage of the method is that it is conceptually consistent with the operational methods used and judgements made regularly by health physicists and radiation safety officers. While the proposed method allows an optimization problem to be readily specified, it does require some familiarity with optimization solution techniques in larger applications. (author). 15 refs, 2 figs
Optimization problems for switched systems with impulsive control
Institute of Scientific and Technical Information of China (English)
Junhao HU; Huayou WANG; Xinzhi LIU; Bin LIU
2005-01-01
By using Impulsive Maximum Principal and three stage optimization method,this paper discusses optimization problems for linear impulsive switched systems with hybrid controls,which includes continuous control and impulsive control.The linear quadratic optimization problems without constraints such as optimal hybrid control,optimal stability and optimal switching instants are addressed in detail.These results are applicable to optimal control problems in economics,mechanics,and management.
Optimal control problem for the extended Fisher–Kolmogorov equation
Indian Academy of Sciences (India)
Ning Duan
2016-02-01
In this paper, the optimal control problem for the extended Fisher–Kolmogorov equation is studied. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved and the optimality system is established.
A novel metaheuristic for continuous optimization problems: Virus optimization algorithm
Liang, Yun-Chia; Rodolfo Cuevas Juarez, Josue
2016-01-01
A novel metaheuristic for continuous optimization problems, named the virus optimization algorithm (VOA), is introduced and investigated. VOA is an iteratively population-based method that imitates the behaviour of viruses attacking a living cell. The number of viruses grows at each replication and is controlled by an immune system (a so-called 'antivirus') to prevent the explosive growth of the virus population. The viruses are divided into two classes (strong and common) to balance the exploitation and exploration effects. The performance of the VOA is validated through a set of eight benchmark functions, which are also subject to rotation and shifting effects to test its robustness. Extensive comparisons were conducted with over 40 well-known metaheuristic algorithms and their variations, such as artificial bee colony, artificial immune system, differential evolution, evolutionary programming, evolutionary strategy, genetic algorithm, harmony search, invasive weed optimization, memetic algorithm, particle swarm optimization and simulated annealing. The results showed that the VOA is a viable solution for continuous optimization.
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...
Statistical Physics of Hard Optimization Problems
Zdeborová, Lenka
2008-01-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the NP-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this thesis is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied co...
Optimal Planning and Problem-Solving
Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg
2008-01-01
CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.
Properties of solutions of optimization problems for set functions
Directory of Open Access Journals (Sweden)
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.
Linux software for large topology optimization problems
DEFF Research Database (Denmark)
evolving product, which allows a parallel solution of the PDE, it lacks the important feature that the matrix-generation part of the computations is localized to each processor. This is well-known to be critical for obtaining a useful speedup on a Linux cluster and it motivates the search for a COMSOL......-like package for large topology optimization problems. One candidate for such software is developed for Linux by Sandia Nat’l Lab in the USA being the Sundance system. Sundance also uses a symbolic representation of the PDE and a scalable numerical solution is achieved by employing the underlying Trilinos...
Ant Colony Optimization for Container Loading Problem
Directory of Open Access Journals (Sweden)
H. V. Seow
2012-01-01
Full Text Available Problem statement: The Container Loading Problem (CLP considers packing a subset of given rectangular boxes into a rectangular container of fixed dimensions in the most optimum way. This was very important in the logistics industries and warehousing problems, since the cost can be reduced by increasing the space utilization ratio. Approach: This problem was solved in a two-phased Ant Colony Optimization (ACO where a tower building approach was used as the inner heuristic. In the first phase, ACO with its probabilistic decision rule was used to construct a sequence of boxes. The boxes were then arranged into a container with the tower building heuristic in the second phase. The pheromone feedback of ACO using pheromone updating rule helped to improve the solutions. Results: Computational experiments were conducted on benchmark data set and the results obtained from the proposed algorithm are shown to be comparable with other methods from the literatures. Conclusion: ACO has the capability to solve the CLP.
Particle Swarm Optimization for Structural Design Problems
Directory of Open Access Journals (Sweden)
Hamit SARUHAN
2010-02-01
Full Text Available The aim of this paper is to employ the Particle Swarm Optimization (PSO technique to a mechanical engineering design problem which is minimizing the volume of a cantilevered beam subject to bending strength constraints. Mechanical engineering design problems are complex activities which are computing capability are more and more required. The most of these problems are solved by conventional mathematical programming techniques that require gradient information. These techniques have several drawbacks from which the main one is becoming trapped in local optima. As an alternative to gradient-based techniques, the PSO does not require the evaluation of gradients of the objective function. The PSO algorithm employs the generation of guided random positions when they search for the global optimum point. The PSO which is a nature inspired heuristics search technique imitates the social behavior of bird flocking. The results obtained by the PSO are compared with Mathematical Programming (MP. It is demonstrated that the PSO performed and obtained better convergence reliability on the global optimum point than the MP. Using the MP, the volume of 2961000 mm3 was obtained while the beam volume of 2945345 mm3 was obtained by the PSO.
Chemical Reaction Optimization for Max Flow Problem
Directory of Open Access Journals (Sweden)
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.
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.
Enhanced Bee Colony Algorithm for Complex Optimization Problems
Directory of Open Access Journals (Sweden)
S.Suriya
2012-01-01
Full Text Available Optimization problems are considered to be one kind of NP hard problems. Usually heuristic approaches are found to provide solutions for NP hard problems. There are a plenty of heuristic algorithmsavailable to solve optimization problems namely: Ant Colony Optimization, Particle Swarm Optimization, Bee Colony Optimization, etc. The basic Bee Colony algorithm, a population based search algorithm, is analyzed to be a novel tool for complex optimization problems. The algorithm mimics the food foraging behavior of swarmsof honey bees. This paper deals with a modified fitness function of Bee Colony algorithm. The effect of problem dimensionality on the performance of the algorithms will be investigated. This enhanced Bee Colony Optimization will be evaluated based on the well-known benchmark problems. The testing functions like Rastrigin, Rosenbrock, Ackley, Griewank and Sphere are used to evaluavate the performance of the enhanced Bee Colony algorithm. The simulation will be developed on MATLAB.
Artificial Bee Colony Optimization for Multiobjective Quadratic Assignment Problem
Eleyan, Haytham Mohammed
2015-01-01
ABSTRACT: Excellent ability of swarm intelligence can be used to solve multi-objective combinatorial optimization problems. Bee colony algorithms are new swarm intelligence techniques inspired from the smart behaviors of real honeybees in their foraging behavior. Artificial bee colony optimization algorithm has recently been applied for difficult real-valued and combinational optimization problems. Multiobjective quadratic assignment problem (mQAP) is a well-known and hard combinational optim...
Matheuristics for robust optimization: application to real-world problems
Toklu, Nihat Engin; Gambardella, Luca Maria; Montemanni, Roberto
2014-01-01
In the field of optimization, the perspective that the problem data are subject to uncertainty is gaining more and more interest. The uncertainty in an optimization problem represents the measurement errors during the phase of collecting data, or unforeseen changes in the environment while implementing the optimal solution in practice. When the uncertainty is ignored, an optimal solution according to the mathematical model can turn out to be far from optimal, or even infeasible in realit...
SolveDB: Integrating Optimization Problem Solvers Into SQL Databases
DEFF Research Database (Denmark)
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...
A STABILITY THEOREM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS
Institute of Scientific and Technical Information of China (English)
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.
Group search optimizer for the mobile location management problem.
Wang, Dan; Xiong, Congcong; Huang, Wei
2014-01-01
We propose a diversity-guided group search optimizer-based approach for solving the location management problem in mobile computing. The location management problem, which is to find the optimal network configurations of management under the mobile computing environment, is considered here as an optimization problem. The proposed diversity-guided group search optimizer algorithm is realized with the aid of diversity operator, which helps alleviate the premature convergence problem of group search optimizer algorithm, a successful optimization algorithm inspired by the animal behavior. To address the location management problem, diversity-guided group search optimizer algorithm is exploited to optimize network configurations of management by minimizing the sum of location update cost and location paging cost. Experimental results illustrate the effectiveness of the proposed approach. PMID:25180199
Hierarchical control based on Hopfield network for nonseparable optimization problems
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The nonseparable optimization control problem is considered, where the overall objective function is not of an additive form with respect to subsystems. Since there exists the problem that computation is very slow when using iterative algorithms in multiobjective optimization, Hopfield optimization hierarchical network based on IPM is presented to overcome such slow computation difficulty. Asymptotic stability of this Hopfield network is proved and its equilibrium point is the optimal point of the original problem. The simulation shows that the net is effective to deal with the optimization control problem for large-scale nonseparable steady state systems.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Energy Technology Data Exchange (ETDEWEB)
Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
Immune Algorithm for Solving the Optimization Problems of Computer Communication Networks
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The basic problem in optimizing communication networks is to assign a proper circuit for each origindestination pair in networks so as to minimize the average network delay, and the network optimal route selection model is a multi-constrained 0-1 nonlinear programming problem. In this paper, a new stochastic optimization algorithm, Immune Algorithm, is applied to solve the optimization problem in communication networks. And the backbone network vBNS is chosen to illustrate the technique of evaluating delay in a virtual network. At last, IA is compared with the optimization method in communication networks based on Genetic Algorithm, and the result shows that IA is better than GA in global optimum finding.
Optimization, Randomized Approximability, and Boolean Constraint Satisfaction Problems
Yamakami, Tomoyuki
2011-01-01
We give a unified treatment to optimization problems that can be expressed in the form of nonnegative-real-weighted Boolean constraint satisfaction problems. Creignou, Khanna, Sudan, Trevisan, and Williamson studied the complexity of approximating their optimal solutions whose optimality is measured by the sums of outcomes of constraints. To explore a wider range of optimization constraint satisfaction problems, following an early work of Marchetti-Spaccamela and Romano, we study the case where the optimality is measured by products of constraints' outcomes. We completely classify those problems into three categories: PO problems, NPO-hard problems, and intermediate problems that lie between the former two categories. To prove this trichotomy theorem, we analyze characteristics of nonnegative-real-weighted constraints using a variant of the notion of T-constructibility developed earlier for complex-weighted counting constraint satisfaction problems.
Enhanced ant colony optimization for multiscale problems
Hu, Nan; Fish, Jacob
2016-03-01
The present manuscript addresses the issue of computational complexity of optimizing nonlinear composite materials and structures at multiple scales. Several solutions are detailed to meet the enormous computational challenge of optimizing nonlinear structures at multiple scales including: (i) enhanced sampling procedure that provides superior performance of the well-known ant colony optimization algorithm, (ii) a mapping-based meshing of a representative volume element that unlike unstructured meshing permits sensitivity analysis on coarse meshes, and (iii) a multilevel optimization procedure that takes advantage of possible weak coupling of certain scales. We demonstrate the proposed optimization procedure on elastic and inelastic laminated plates involving three scales.
On Optimal Solutions of Decision Problems with Imperfect Recall
Ambrus-Lakatos, Lorand
1999-01-01
In this paper, I study decision theory in the presence of imperfect recall. I use an extension of the standard strategy concept for the analysis of extensive form games in order to examine the range of imperfect recall problems for which there exists an optimal solution. Optimality is assessed in terms of perfect recall problems associated to their corresponding imperfect recall problems.
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.
Usage of the particle swarm optimization in problems of mechanics
Directory of Open Access Journals (Sweden)
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.
CAI, Dapeng
2008-01-01
We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to the finite horizon problems is optimal for the infinite horizon problems under the overtaking criterion.
Solving Multiobjective Optimization Problems Using Artificial Bee Colony Algorithm
Beiwei Zhang; Hanning Chen; Yunlong Zhu; Wenping Zou
2011-01-01
Multiobjective optimization has been a difficult problem and focus for research in fields of science and engineering. This paper presents a novel algorithm based on artificial bee colony (ABC) to deal with multi-objective optimization problems. ABC is one of the most recently introduced algorithms based on the intelligent foraging behavior of a honey bee swarm. It uses less control parameters, and it can be efficiently used for solving multimodal and multidimensional optimization problems. Ou...
An ant colony optimization algorithm for job shop scheduling problem
Edson Flórez; Wilfredo Gómez; MSc. Lola Bautista
2013-01-01
The nature has inspired several metaheuristics, outstanding among these is Ant Colony Optimization (ACO), which have proved to be very effective and efficient in problems of high complexity (NP-hard) in combinatorial optimization. This paper describes the implementation of an ACO model algorithm known as Elitist Ant System (EAS), applied to a combinatorial optimization problem called Job Shop Scheduling Problem (JSSP). We propose a method that seeks to reduce delays designating th...
LDRD Final Report: Global Optimization for Engineering Science Problems
Energy Technology Data Exchange (ETDEWEB)
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.
Handling Optimization under Uncertainty Problem Using Robust Counterpart Methodology
Directory of Open Access Journals (Sweden)
Diah Chaerani
2013-01-01
Full Text Available In this paper we discuss the robust counterpart (RC methodology to handle the optimization under uncertainty problem as proposed by Ben-Tal and Nemirovskii. This optimization methodology incorporates the uncertain data in U a so-called uncertainty set and replaces the uncertain problem by its so-called robust counterpart. We apply the RC approach to uncertain Conic Optimization (CO problems, with special attention to robust linear optimization (RLO problem and include a discussion on parametric uncertainty for that case. Some new supported examples are presented to give a clear description of the used of RC methodology theorem.
An Effective Hybrid Optimization Algorithm for Capacitated Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
无
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.
Identification and optimization problems in plasma physics
International Nuclear Information System (INIS)
Parameter identification of the current in a tokamak plasma is studied. Plasma equilibrium in a vacuum container with a diaphragm is analyzed. A variable metric method with reduced optimization with nonlinear equality constraints; and a quasi-Newton reduced optimization method with constraints giving priority to restoration are presented
An optimal design problem in wave propagation
DEFF Research Database (Denmark)
Bellido, J.C.; Donoso, Alberto
2007-01-01
of finding the best distributions of the two initial materials in a rod in order to minimize the vibration energy in the structure under periodic loading of driving frequency Omega. We comment on relaxation and optimality conditions, and perform numerical simulations of the optimal configurations. We prove...... also the existence of classical solutions in certain cases....
ISOGEOMETRIC SHAPE OPTIMIZATION FOR ELECTROMAGNETIC SCATTERING PROBLEMS
DEFF Research Database (Denmark)
Nguyen, D. M.; Evgrafov, Anton; Gravesen, Jens
2012-01-01
We consider the benchmark problem of magnetic energy density enhancement in a small spatial region by varying the shape of two symmetric conducting scatterers. We view this problem as a prototype for a wide variety of geometric design problems in electromagnetic applications. Our approach...
Institute of Scientific and Technical Information of China (English)
Xu Zhang; En-min Feng
2004-01-01
This paper studies the two-dimensional layout optimization problem.An optimization model with performance constraints is presented.The layout problem is partitioned intofinite subproblems in terms of graph theory,in such a way of that each subproblem overcomes its on-o inature optimal variable.A minimax problem is constructed that is locally equivalent to each subproblem.By using this minimax problem,we present the optimality function for every subproblem and prove that the first order necessary optimality condition is satisfied at a point if and only if this point is a zero of optimality function.
Advances in bio-inspired computing for combinatorial optimization problems
Pintea, Camelia-Mihaela
2013-01-01
Advances in Bio-inspired Combinatorial Optimization Problems' illustrates several recent bio-inspired efficient algorithms for solving NP-hard problems.Theoretical bio-inspired concepts and models, in particular for agents, ants and virtual robots are described. Large-scale optimization problems, for example: the Generalized Traveling Salesman Problem and the Railway Traveling Salesman Problem, are solved and their results are discussed.Some of the main concepts and models described in this book are: inner rule to guide ant search - a recent model in ant optimization, heterogeneous sensitive a
Fuzzy Optimal Solution to Fuzzy Transportation Problem: A New Approach
Directory of Open Access Journals (Sweden)
S. Mohanaselvi
2012-03-01
Full Text Available In this paper we propose a new algorithm for the initial fuzzy feasible solution to a fully fuzzy transportation problem. Then by using fuzzy version of modified distribution method, we obtain the fuzzy optimal solution for the fully fuzzy transportation problem without converting to a classical transportation problem. A numerical example is provided to illustrate the proposed algorithm. It can be seen that the proposed algorithm gives a better fuzzy optimal solution to the given fuzzy transportation problem.
Implementation of Travelling Salesman Problem Using ant Colony Optimization
Directory of Open Access Journals (Sweden)
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.
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.
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.
Topology Optimization in wave-propagation and flow problems
DEFF Research Database (Denmark)
Sigmund, Ole; Jensen, Jakob Søndergaard; Gersborg-Hansen, A.;
2004-01-01
We discuss recent extensions of the topology optimization method to wave-propagation and flow problems. More specifically, we optimize material distribution in scalar wave propagation problems modelled by Helmholtz equation. Moreover, we investigate the influence of the inertia term on the optima...
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
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.
Optimal Control Problems for Nonlinear Variational Evolution Inequalities
Directory of Open Access Journals (Sweden)
Eun-Young Ju
2013-01-01
Full Text Available We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.
Sufficient conditions for Lagrange, Mayer, and Bolza optimization problems
Directory of Open Access Journals (Sweden)
Boltyanski V.
2001-01-01
Full Text Available The Maximum Principle [2,13] is a well known necessary condition for optimality. This condition, generally, is not sufficient. In [3], the author proved that if there exists regular synthesis of trajectories, the Maximum Principle also is a sufficient condition for time-optimality. In this article, we generalize this result for Lagrange, Mayer, and Bolza optimization problems.
The structure of optimal parameters for image restoration problems
de los Reyes, J. C.; Sch?nlieb, C. B.; Valkonen, T.
2015-01-01
We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general type of regulariser is considered, which encompasses total variation (TV), total generalized variation (TGV) and infimal-convolution total variation (ICTV). We prove that under certain conditions on the given data optimal parameters derived by bilevel optim...
Optimal Sum-Rate of the Vector Gaussian CEO Problem
Ekrem, Ersen
2012-01-01
We study the vector Gaussian CEO problem, and obtain the optimal sum-rate that attains any given distortion. We show that the evaluation of the Berger-Tung inner bound with jointly Gaussian auxiliary random variables is optimal. We prove this optimality result by using channel enhancement in conjunction with a recent outer bound for the rate-distortion region of the vector Gaussian CEO problem.
OPTIMAL CONTROL PROBLEM OF SOME DIFFERENTIAL INCLUSION AND APPROXIMATION
Directory of Open Access Journals (Sweden)
DEBINSKA-NAGORSKA A.
2002-01-01
Full Text Available In this paper we present the optimal control problem governed by a variational inclusion with the monotone operator and a quadratic costfunctional. We apply standart Galerkin method to the approximation of the problem. After giving some results on the existance of optimal control we shall prove the existance of weak condensation points of a set of solution of approximate problems. Each of these points is a solution of the initial optimization problem. Finally we shall give a simple example using the obtaned results.
Directory of Open Access Journals (Sweden)
K. Lenin
2013-03-01
Full Text Available Reactive Power Optimization is a complex combinatorial optimization problem involving non-linear function having multiple local minima, non-linear and discontinuous constrains. This paper presents Attractive and repulsive Particle Swarm Optimization (ARPSO and Random Virus Algorithm (RVA in trying to overcome the Problem of premature convergence. RVA and ARPSO is applied to Reactive Power Optimization problem and is evaluated on standard IEEE 30Bus System. The results show that RVA prevents premature convergence to high degree but still keeps a rapid convergence. It gives best solution when compared to Attractive and repulsive Particle Swarm Optimization (ARPSO and Particle Swarm Optimization (PSO.
Treating the Future Equally: Solving Undiscounted Infinite Horizon Optimization Problems
Cai, Dapeng; Nitta, Gyoshin
2007-01-01
Infinite horizon optimization problems accompany two perplexities. First, the infinite series of utility sequences may diverge. Second, boundary conditions at the infinite terminal time may not be rigorously expressed. In this paper, we show that under two fairly general conditions, the limit of the solution to the undiscounted finite horizon problem is optimal among feasible paths for the undiscounted infinite horizon problem, in the sense of the overtaking criterion. Applied to a simple Ram...
Fuzzy Optimal Solution to Fuzzy Transportation Problem: A New Approach
S. Mohanaselvi; K. Ganesan
2012-01-01
In this paper we propose a new algorithm for the initial fuzzy feasible solution to a fully fuzzy transportation problem. Then by using fuzzy version of modified distribution method, we obtain the fuzzy optimal solution for the fully fuzzy transportation problem without converting to a classical transportation problem. A numerical example is provided to illustrate the proposed algorithm. It can be seen that the proposed algorithm gives a better fuzzy optimal solution to the given fuzzy transp...
Remarks on a benchmark nonlinear constrained optimization problem
Institute of Scientific and Technical Information of China (English)
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.
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.
Topology optimization of fluid-structure-interaction problems in poroelasticity
DEFF Research Database (Denmark)
Andreasen, Casper Schousboe; Sigmund, Ole
2013-01-01
This paper presents a method for applying topology optimization to fluid-structure interaction problems in saturated poroelastic media. The method relies on a multiple-scale method applied to periodic media. The resulting model couples the Stokes flow in the pores of the structure with the deform...... by topology optimization in order to optimize the performance of a shock absorber and test the pressure loading capabilities and optimization of an internally pressurized lid. © 2013 Published by Elsevier B.V....
Optimal control problems related to the navigation channel engineering
Institute of Scientific and Technical Information of China (English)
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.
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.
Optimal Solutions for the Temporal Precedence Problem
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Makris, Christos; Sioutas, Spyros;
2002-01-01
In this paper we refer to the Temporal Precedence Problem on Pure Pointer Machines . This problem asks for the design of a data structure, maintaining a set of stored elements and supporting the following two operations: insert and precedes . The operation insert (a) introduces a new element...... 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......,b) operation in O (log log d ) time, where d is the temporal distance between the elements a and b ....
Topology optimization problems with design-dependent sets of constraints
DEFF Research Database (Denmark)
Schou, Marie-Louise Højlund
Topology optimization is a design tool which is used in numerous fields. It can be used whenever the design is driven by weight and strength considerations. The basic concept of topology optimization is the interpretation of partial differential equation coefficients as effective material...... properties and designing through changing these coefficients. For example, consider a continuous structure. Then the basic concept is to represent this structure by small pieces of material that are coinciding with the elements of a finite element model of the structure. This thesis treats stress constrained...... structural topology optimization problems. For such problems a stress constraint for an element should only be present in the optimization problem when the structural design variable corresponding to this element has a value greater than zero. We model the stress constrained topology optimization problem...
The Uniqueness of Optimal Solution for Linear Programming Problem
Institute of Scientific and Technical Information of China (English)
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.
3D Topology optimization of Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Dammann, Bernd
The present talk is concerned with the application of topology optimization to creeping flow problems in 3D. This research is driven by the fact that topology optimization has proven very successful as a tool in academic and industrial design problems. Success stories are reported from such diverse...... fields as solid mechanics and optics and is due to the method's flexibility in the (rough) parametrization of the design, see [1] and the reference therein for an overview. Borrvall and Petersson [2] is the seminal reference for topology optimization in fluid flow problems. They considered design...... of energy efficient devices for 2D Stokes flow. Creeping flow problems are described by the Stokes equations which model very viscous fluids at macro scales or ordinary fluids at very small scales. The latter gives the motivation for topology optimization problems based on the Stokes equations being a model...
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.
Constraint Optimization for Highly Constrained Logistic Problems
DEFF Research Database (Denmark)
Mochnacs, Maria Kinga; Tanaka, Meang Akira; Nyborg, Anders;
This report investigates whether propagators combined with branch and bound algorithm are suitable for solving the storage area stowage problem within reasonable time. The approach has not been attempted before and experiments show that the implementation was not capable of solving the storage area...
Optimal Wafer Cutting in Shuttle Layout Problems
DEFF Research Database (Denmark)
Nisted, Lasse; Pisinger, David; Altman, Avri
2011-01-01
. The shuttle layout problem is frequently solved in two phases: first, a floorplan of the shuttle is generated. Then, a cutting plan is found which minimizes the overall number of wafers needed to satisfy the demand of each die type. Since some die types require special production technologies, only compatible...
Path Optimization Algorithm For Network Problems Using Job Sequencing Technique
Directory of Open Access Journals (Sweden)
Punit Kumar Singh
2012-06-01
Full Text Available The job sequencing technique is used to determine an optimal sequence. It performs a series of jobs by a number of specific orders so that it calculates the optimal cost. In this paper, we propose a novel approach to find an optimal path from source to destination by taking advantage of job sequencing technique. Wehave used n jobs m machine sequencing technique and this is divided into n jobs 2 machine problems. Using Johnson’s sequencing rule, we solved the problem and obtained the (n-1 sub sequences of the route. Using the proposed algorithm, we calculated the optimal sequence, which leads to the shortest path of the network.
TWO OPTIMAL CONTROL PROBLEMS IN CANCER CHEMOTHERAPY WITH DRUG RESISTANCE
Directory of Open Access Journals (Sweden)
Werner Krabs
2012-01-01
Full Text Available We investigate two well-known basic optimal control problems forchemotherapeutic cancer treatment modified by introducing a timedependent “resistance factor”. This factor should be responsible for the effect of the drug resistance of tumor cells on the dynamical growth for the tumor. Both optimal control problems have common pointwise but different integral constraints on the control. We show that in both models the usually practised bang-bang control is optimal if the resistance is sufficiently strong. Further, we discuss different optimal strategies in both models for general resistance.
Mathematical programming methods for large-scale topology optimization problems
DEFF Research Database (Denmark)
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...
Optimality conditions for the numerical solution of optimization problems with PDE constraints :
Energy Technology Data Exchange (ETDEWEB)
Aguilo Valentin, Miguel Alejandro; Ridzal, Denis
2014-03-01
A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.
H-Optimal Control in Coefficients for Dirichlet Parabolic Problems
Directory of Open Access Journals (Sweden)
I. G. Balanenko
2010-01-01
Full Text Available In the paper the Dirichlet optimal control problem associated with a linear parabolic equation the coefficients of which we take as controls in L1(Ω has been studied. Since equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, it is shown that the optimal control problem in the coefficients can be stated in different settings depending on the choice of the class of admissible solutions. Using the direct method in the Calculus of Variations, the solvability of the above optimal control problems in the so-called class of inadmissible solutions has been discussed.
Topology optimization for acoustic-structure interaction problems
DEFF Research Database (Denmark)
Yoon, Gil Ho; Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
to subdomain interfaces evolving during the optimization process. In this paper, we propose to use a mixed finite element formulation with displacements and pressure as primary variables (u/p formulation) which eliminates the need for explicit boundary representation. In order to describe the Helmholtz......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......-dimensional acoustic-structure interaction problems are optimized to show the validity of the proposed method....
A Numerical Embedding Method for Solving the Nonlinear Optimization Problem
Institute of Scientific and Technical Information of China (English)
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.
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.
Integrating packing and distribution problems and optimization through mathematical programming
Fabio Miguel; Mariano Frutos; Fernando Tohmé; Máximo Méndez
2016-01-01
This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP) problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Proble...
Gradient Gene Algorithm: a Fast Optimization Method to MST Problem
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The extension of Minimum Spanning Tree(MST) problem is an NP hardproblem which does not exit a polynomial time algorithm. In this paper, a fast optimizat ion method on MST problem--the Gradient Gene Algorithm is introduced. Compar ed with other evolutionary algorithms on MST problem, it is more advanced: firstly, very simple and easy to realize; then, efficient and accurate; finally general on other combination optimization problems.
The Tactical Berth Allocation Problem: integrated optimization in container terminals
Vacca, Ilaria; Salani, Matteo; Bierlaire, Michel
2010-01-01
In the context of container terminal operations, the simultaneous optimization of decision problems that are usually solved hierarchically by terminal's planners represents nowadays a promising research trend. In this talk we introduce the Tactical Berth Allocation Problem (TBAP), that deals with the integration of the berth allocation problem (BAP) and the quay crane assignment problem (QCAP). The objective is to schedule incoming ships over a time horizon, assigning them a berthing position...
Topology optimization of 3D Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan
Topology optimization has been applied to a multitude of physical systems and is now a mature technology used in industrial practice, see [1] for an overview. Borrvall and Petersson [2] introduced topology optimization of Stokes flow problems which initiated works on extending topology optimization...... 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...... 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...
Ant Colony Algorithm for the Weighted Item Layout Optimization Problem
Xu, Yi-Chun; Liu, Yong; Xiao, Ren-Bin; Amos, Martyn
2010-01-01
This paper discusses the problem of placing weighted items in a circular container in two-dimensional space. This problem is of great practical significance in various mechanical engineering domains, such as the design of communication satellites. Two constructive heuristics are proposed, one for packing circular items and the other for packing rectangular items. These work by first optimizing object placement order, and then optimizing object positioning. Based on these heuristics, an ant colony optimization (ACO) algorithm is described to search first for optimal positioning order, and then for the optimal layout. We describe the results of numerical experiments, in which we test two versions of our ACO algorithm alongside local search methods previously described in the literature. Our results show that the constructive heuristic-based ACO performs better than existing methods on larger problem instances.
Ant Colony Optimization and the Minimum Cut Problem
DEFF Research Database (Denmark)
Kötzing, Timo; Lehre, Per Kristian; Neumann, Frank;
2010-01-01
Ant Colony Optimization (ACO) is a powerful metaheuristic for solving combinatorial optimization problems. With this paper we contribute to the theoretical understanding of this kind of algorithm by investigating the classical minimum cut problem. An ACO algorithm similar to the one that was proved...... successful for the minimum spanning tree problem is studied. Using rigorous runtime analyses we show how the ACO algorithm behaves similarly to Karger and Stein's algorithm for the minimum cut problem as long as the use of pheromone values is limited. Hence optimal solutions are obtained in expected...... polynomial time. On the other hand, we show that high use of pheromones has a negative effect, and the ACO algorithm may get trapped in local optima resulting in an exponential runtime to obtain an optimal solution. This result indicates that ACO algorithms may be inappropriate for finding minimum cuts....
Topology optimization of vibration and wave propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2007-01-01
The method of topology optimization is a versatile method to determine optimal material layouts in mechanical structures. The method relies on, in principle, unlimited design freedom that can be used to design materials, structures and devices with significantly improved performance and sometimes...... novel functionality. This paper addresses basic issues in simulation and topology design of vibration and wave propagation problems. Steady-state and transient wave propagation problems are addressed and application examples for both cases are presented....
A Cooperative Coevolutionary Cuckoo Search Algorithm for Optimization Problem
Hongqing Zheng; Yongquan Zhou
2013-01-01
Taking inspiration from an organizational evolutionary algorithm for numerical optimization, this paper designs a kind of dynamic population and combining evolutionary operators to form a novel algorithm, a cooperative coevolutionary cuckoo search algorithm (CCCS), for solving both unconstrained, constrained optimization and engineering problems. A population of this algorithm consists of organizations, and an organization consists of dynamic individuals. In experiments, fifteen unconstrained...
Issues related to topology optimization of snap-through problems
DEFF Research Database (Denmark)
Lindgaard, Esben; Dahl, Jonas
2012-01-01
This work focuses on issues related to topology optimization of static geometrically nonlinear structures experiencing snap-through behaviour. Different compliance and buckling criterion functions are studied and applied to topology optimization of a point loaded curved beam problem with the aim ...
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 .
CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
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.
borealis - A generalized global update algorithm for Boolean optimization problems
Zhu, Zheng; Katzgraber, Helmut G
2016-01-01
Optimization problems with Boolean variables that fall into the nondeterministic polynomial (NP) class are of fundamental importance in computer science, mathematics, physics and industrial applications. Most notably, solving constraint-satisfaction problems, which are related to spin-glass-like Hamiltonians in physics, remains a difficult numerical task. As such, there has been great interest in designing efficient heuristics to solve these computationally difficult problems. Inspired by parallel tempering Monte Carlo in conjunction with the rejection-free isoenergetic cluster algorithm developed for Ising spin glasses, we present a generalized global update optimization heuristic that can be applied to different NP-complete problems with Boolean variables. The global cluster updates allow for a wide-spread sampling of phase space, thus considerably speeding up optimization. By carefully tuning the pseudo-temperature (needed to randomize the configurations) of the problem, we show that the method can efficie...
Exact solution for an optimal impermeable parachute problem
Lupu, Mircea; Scheiber, Ernest
2002-10-01
In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.
A problem of optimal control with free initial state
Directory of Open Access Journals (Sweden)
Louadj Kahina
2012-04-01
Full Text Available We are studying an optimal control problem with free initial condition. The initial state of the optimized system is not known exactly, information on initial state is exhausted by inclusions x0 ∈ X0. Accessible controls for optimization of continuous dynamic system are discrete controls defined on quantized axes. The method presented is based on the concepts and operations of the adaptive method [9] of linear programming. The results are illustrated by a fourth order problem, efficiency estimates of proposed methods are given.
Continuity for vector optimization problems with equilibrium constraints
Institute of Scientific and Technical Information of China (English)
WU Yunan
2004-01-01
The concept of vector optimization problems with equilibrium constraints (VOPEC) is introduced. By using the continuity results of the approximate solution set to the equilibrium problem, we obtain the same results of the marginal map and the approximate value in VOPEC (ε) for vector-valued mapping.
Reverse convex problems: an approach based on optimality conditions
Directory of Open Access Journals (Sweden)
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.
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.
Strong Duality and Optimality Conditions for Generalized Equilibrium Problems
Directory of Open Access Journals (Sweden)
D. H. Fang
2013-01-01
Full Text Available We consider a generalized equilibrium problem involving DC functions. By using the properties of the epigraph of the conjugate functions, some sufficient and/or necessary conditions for the weak and strong duality results and optimality conditions for generalized equilibrium problems are provided.
OPTIMAL THICKNESS OF A CYLINDRICAL SHELL - AN OPTIMAL CONTROL PROBLEM IN LINEAR ELASTICITY THEORY
Directory of Open Access Journals (Sweden)
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.
Global Optimization for Bus Line Timetable Setting Problem
Directory of Open Access Journals (Sweden)
Qun Chen
2014-01-01
Full Text Available This paper defines bus timetables setting problem during each time period divided in terms of passenger flow intensity; it is supposed that passengers evenly arrive and bus runs are set evenly; the problem is to determine bus runs assignment in each time period to minimize the total waiting time of passengers on platforms if the number of the total runs is known. For such a multistage decision problem, this paper designed a dynamic programming algorithm to solve it. Global optimization procedures using dynamic programming are developed. A numerical example about bus runs assignment optimization of a single line is given to demonstrate the efficiency of the proposed methodology, showing that optimizing buses’ departure time using dynamic programming can save computational time and find the global optimal solution.
Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer
Rosenberg, Gili; Haghnegahdar, Poya; Goddard, Phil; Carr, Peter; Wu, Kesheng; de Prado, Marcos Lopez
2016-09-01
We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multi-period portfolio optimization problem we solve is significantly harder than the continuous variable problem. We present insight into how results may be improved using suitable software enhancements, and why current quantum annealing technology limits the size of problem that can be successfully solved today. The formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques.
A New Fenchel Dual Problem in Vector Optimization
Indian Academy of Sciences (India)
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.
Large scale optimization algorithms : applications to solution of inverse problems
Repetti, Audrey
2015-01-01
An efficient approach for solving an inverse problem is to define the recovered signal/image as a minimizer of a penalized criterion which is often split in a sum of simpler functions composed with linear operators. In the situations of practical interest, these functions may be neither convex nor smooth. In addition, large scale optimization problems often have to be faced. This thesis is devoted to the design of new methods to solve such difficult minimization problems, while paying attenti...
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.
Reactive Robustness and Integrated Approaches for Railway Optimization Problems
DEFF Research Database (Denmark)
Haahr, Jørgen Thorlund
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...... in individual chapters, some of which are papers that have been submitted to international scientific journals in operations research. The problems have been formulated as optimization problems and solution methods have been proposed to solve them using optimization theory and various solution techniques....... In collaboration with industry and academic partners real-life and realistic data has been used to benchmark and test the solution methods. A central actor and theme of the thesis is the rolling stock running on the railway networks. A public timetable is given, and in order to service the departures...
Optimal Component Lumping: problem formulation and solution techniques
DEFF Research Database (Denmark)
Lin, Bao; Leibovici, Claude F.; Jørgensen, Sten Bay
2008-01-01
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...... such applications in process modeling, simulation and design. A pseudo-component approach that lumps a large number of components in a system into a much smaller number of hypothetical groups reduces the dimensionality at the cost of losing information. Moreover, empirical and heuristic approaches are commonly used...... to determine the lumping scheme. Given an objective function defined with a linear weighting rule, an optimal lumping problem is formulated as a mixed integer nonlinear programming (MINLP) problem both in discrete and in continuous settings. A reformulation of the original problem is also presented, which...
An Ant Colony Optimization Algorithm For Job Shop Scheduling Problem
Directory of Open Access Journals (Sweden)
Edson Florez
2013-07-01
Full Text Available The nature has inspired several metaheuristics, outstanding among these is Ant Colony Optimization(ACO, which have proved to be very effective and efficient in problems of high complexity (NP-hard incombinatorial optimization. This paper describes the implementation of an ACO model algorithm known asElitist Ant System (EAS, applied to a combinatorial optimization problem called Job Shop SchedulingProblem (JSSP. We propose a method that seeks to reduce delays designating the operation immediatelyavailable, but considering the operations that lacklittle to be available and have a greater amount ofpheromone. The performance of the algorithm was evaluated for problems of JSSP reference, comparingthe quality of the solutions obtained regarding thebest known solution of the most effective methods.Thesolutions were of good quality and obtained with aremarkable efficiency by having to make a very lownumber of objective function evaluations.
CAI, Dapeng
2008-01-01
We aim to generalize the results of Cai and Nitta (2007) by allowing both the utility and production function to depend on time. We also consider an additional intertemporal optimality criterion. We clarify the conditions under which the limit of the solutions for the finite horizon problems is optimal among all attainable paths for the infinite horizon problems under the overtaking criterion, as well as the conditions under which such a limit is the unique optimum under the sum-of-utilities criterion. The results are applied to a parametric example of the one-sector growth model to examine the impacts of discounting on optimal paths.
Finding the optimal values of some of the variables in SAT or MAX-SAT problems
Energy Technology Data Exchange (ETDEWEB)
Hammer, P.
1994-12-31
The properties of weak and strong persistency are introduced for SAT and MAX-SAT problems. These properties allow the detection of partial 0-1 assignments which can be extended to (optimal) solutions of these problems. A polytope is associated with any SAT or MAX-SAT problem, and it is shown that it has half-integral vertices. Furthermore, it is shown that the integer components of any of the vertices of this polytope have a weak persistency property, generalizing on the 1975 result of Nemhauser and Trotter. When applied to a MAX-2-SAT problem, along with a network flow calculation based on the roof-duality approach introduced by Hammer, Hansen, and Simeone in 1984, this technique yields a 3/4-approximation of the MAX-2-SAT problem.
Integrating packing and distribution problems and optimization through mathematical programming
Directory of Open Access Journals (Sweden)
Fabio Miguel
2016-06-01
Full Text Available This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW, which is a variant of the Travelling Salesman Problem (again a NP-Hard problem with extra constraints. Here we model those two problems in a single framework and use an evolutionary meta-heuristics to solve them jointly. Furthermore, we use data from a real world company as a test-bed for the method introduced here.
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...
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.
Global optimization over linear constraint non-convex programming problem
Institute of Scientific and Technical Information of China (English)
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.
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.
Integrated network design and scheduling problems : optimization algorithms and applications.
Energy Technology Data Exchange (ETDEWEB)
Nurre, Sarah G.; Carlson, Jeffrey J.
2014-01-01
We consider the class of integrated network design and scheduling problems. These problems focus on selecting and scheduling operations that will change the characteristics of a network, while being speci cally concerned with the performance of the network over time. Motivating applications of INDS problems include infrastructure restoration after extreme events and building humanitarian distribution supply chains. While similar models have been proposed, no one has performed an extensive review of INDS problems from their complexity, network and scheduling characteristics, information, and solution methods. We examine INDS problems under a parallel identical machine scheduling environment where the performance of the network is evaluated by solving classic network optimization problems. We classify that all considered INDS problems as NP-Hard and propose a novel heuristic dispatching rule algorithm that selects and schedules sets of arcs based on their interactions in the network. We present computational analysis based on realistic data sets representing the infrastructures of coastal New Hanover County, North Carolina, lower Manhattan, New York, and a realistic arti cial community CLARC County. These tests demonstrate the importance of a dispatching rule to arrive at near-optimal solutions during real-time decision making activities. We extend INDS problems to incorporate release dates which represent the earliest an operation can be performed and exible release dates through the introduction of specialized machine(s) that can perform work to move the release date earlier in time. An online optimization setting is explored where the release date of a component is not known.
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.
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 ...
Optimal reinsurance/investment problems for general insurance models
Liu, Yuping; 10.1214/08-AAP582
2009-01-01
In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random measure, representing the randomness from the financial market and the insurance claims, respectively. The random safety loading and stochastic interest rates are allowed in the model so that the reserve process is non-Markovian in general. The insurance company can manage the reserves through both portfolios of the investment and a reinsurance policy to optimize a certain utility function, defined in a generic way. The main feature of the problem lies in the intrinsic constraint on the part of reinsurance policy, which is only proportional to the claim-size instead of the current level of reserve, and hence it is quite different from the optimal investment/consumption problem with constraints in finance. Necessary and sufficient conditions for both well posedness and solvability...
Adaptive double chain quantum genetic algorithm for constrained optimization problems
Institute of Scientific and Technical Information of China (English)
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.
State-Constrained Optimal Control Problems of Impulsive Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Forcadel, Nicolas, E-mail: forcadel@ceremade.dauphine.fr [Universite Paris-Dauphine, Ceremade (France); Rao Zhiping, E-mail: Zhiping.Rao@ensta-paristech.fr; Zidani, Hasnaa, E-mail: Hasnaa.Zidani@ensta-paristech.fr [ENSTA ParisTech and INRIA-Saclay, Equipe COMMANDS (France)
2013-08-01
The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption.
On a Nonsmooth Vector Optimization Problem with Generalized Cone Invexity
Directory of Open Access Journals (Sweden)
Hehua Jiao
2012-01-01
Full Text Available By using Clarke’s generalized gradients we consider a nonsmooth vector optimization problem with cone constraints and introduce some generalized cone-invex functions called K-α-generalized invex, K-α-nonsmooth invex, and other related functions. Several sufficient optimality conditions and Mond-Weir type weak and converse duality results are obtained for this problem under the assumptions of the generalized cone invexity. The results presented in this paper generalize and extend the previously known results in this area.
Optimal control problems for impulsive systems with integral boundary conditions
Directory of Open Access Journals (Sweden)
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.
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.
An optimized finite-difference scheme for wave propagation problems
Zingg, D. W.; Lomax, H.; Jurgens, H.
1993-01-01
Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.
Heuristic Optimization for the Discrete Virtual Power Plant Dispatch Problem
DEFF Research Database (Denmark)
Petersen, Mette Kirschmeyer; Hansen, Lars Henrik; Bendtsen, Jan Dimon;
2014-01-01
We consider a Virtual Power Plant, which is given the task of dispatching a fluctuating power supply to a portfolio of flexible consumers. The flexible consumers are modeled as discrete batch processes, and the associated optimization problem is denoted the Discrete Virtual Power Plant Dispatch...... Problem. First NP-completeness of the Discrete Virtual Power Plant Dispatch Problem is proved formally. We then proceed to develop tailored versions of the meta-heuristic algorithms Hill Climber and Greedy Randomized Adaptive Search Procedure (GRASP). The algorithms are tuned and tested on portfolios...... of varying sizes. We find that all the tailored algorithms perform satisfactorily in the sense that they are able to find sub-optimal, but usable, solutions to very large problems (on the order of 10 5 units) at computation times on the scale of just 10 seconds, which is far beyond the capabilities...
Global Sufficient Optimality Conditions for a Special Cubic Minimization Problem
Directory of Open Access Journals (Sweden)
Xiaomei Zhang
2012-01-01
Full Text Available We present some sufficient global optimality conditions for a special cubic minimization problem with box constraints or binary constraints by extending the global subdifferential approach proposed by V. Jeyakumar et al. (2006. The present conditions generalize the results developed in the work of V. Jeyakumar et al. where a quadratic minimization problem with box constraints or binary constraints was considered. In addition, a special diagonal matrix is constructed, which is used to provide a convenient method for justifying the proposed sufficient conditions. Then, the reformulation of the sufficient conditions follows. It is worth noting that this reformulation is also applicable to the quadratic minimization problem with box or binary constraints considered in the works of V. Jeyakumar et al. (2006 and Y. Wang et al. (2010. Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.
Infinite horizon optimal control problems with multiple thermostatic hybrid dynamics
Bagagiolo, Fabio; Danieli, Katia
2010-01-01
We study an optimal control problem for a hybrid system exhibiting several internal switching variables whose discrete evolutions are governed by some delayed thermostatic laws. By the dynamic programming technique we prove that the value function is the unique viscosity solution of a system of several Hamilton-Jacobi equations, suitably coupled. The method involves a contraction principle and some suitably adapted results for exit-time problems with discontinuous exit cost.
Decomposition of large-scale stochastic optimal control problems
Barty, Kengy; Carpentier, Pierre; Girardeau, Pierre
2009-01-01
In this paper, we present an Uzawa-based heuristic that is adapted to some type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale independent subsystems, though linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We out...
Optimizing Human Diet Problem Based on Price and Taste Using
Hossein EGHBALI; Mohammad Ali EGHBALI; Ali VAHIDIAN KAMYAD
2012-01-01
Low price and good taste of foods are regarded as two major factors for optimal human nutrition. Due to price fluctuations and taste diversity, these two factors cannot be certainly and determinately evaluated. This problem must be viewed from another perspective because of the uncertainty about the amount of nutrients per unit of foods and also diversity of people’s daily needs to receive them.This paper discusses human diet problem in fuzzy environment. The approach deals with multi-objecti...
MNP：A Class of NP Optimization Problems
Institute of Scientific and Technical Information of China (English)
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.
A Multi-Objective Genetic Algorithm for Optimal Portfolio Problems
Institute of Scientific and Technical Information of China (English)
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.
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
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.
Directory of Open Access Journals (Sweden)
Sahay Rishi R.
2013-01-01
Full Text Available A second order Mond-Weir type dual is presented for a non-differentiable multiobjective optimization problem with square root terms in the objective as well as in the constraints. Optimality and duality results are presented. Classes of generalized higher order η - bonvex and related functions are introduced to study the optimality and duality results. A fractional case is presented at the end.
Bonnans, J Frédéric; Dupuis, Xavier
2012-01-01
This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions.
A Case Study to Test Mozaik for Different Optimization Problems
Energy Technology Data Exchange (ETDEWEB)
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.
Lower bounding problems for stress constrained discrete structural topology optimization problems
DEFF Research Database (Denmark)
Stolpe, Mathias; Stainko, Roman; Kocvara, Michal
2007-01-01
as a non-convex mixed 0–1 program. For this problem, several convex and mildly non-convex continuous relaxations are presented. Reformulations of these relaxations, obtained by using duality results from semi-definite and second order cone programming, are also presented. The reformulated problems...... are suitable for implementation in a nonlinear branch and bound framework for solving the considered class of problems to global optimality....
On some fundamental properties of structural topology optimization problems
DEFF Research Database (Denmark)
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...
On two formulations of an optimal insulation problem
DEFF Research Database (Denmark)
Munoz, Eduardo; Allaire, Gregoire; Bendsøe, Martin P.
2007-01-01
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...
Features for Exploiting Black-Box Optimization Problem Structure
DEFF Research Database (Denmark)
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...
Topology optimization of 3D Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Sigmund, Ole; Bendsøe, Martin P.
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...
Reduced-Complexity Semidefinite Relaxations of Optimal Power Flow Problems
DEFF Research Database (Denmark)
Andersen, Martin Skovgaard; Hansson, Anders; Vandenberghe, Lieven
2014-01-01
We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by dropping some equality constraints in the conversion, we obtain semidefinite relaxations that are computationally cheaper, but potentially weake...
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.
On the One-Dimensional Optimal Switching Problem
Bayraktar, Erhan; Egami, Masahiko
2007-01-01
We explicitly solve the optimal switching problem for one-dimensional diffusions by directly employing the dynamic programming principle and the excessive characterization of the value function. The shape of the value function and the smooth fit principle then can be proved using the properties of concave functions.
THE TANGENT CONES ON CONSTRAINT QUALIFICATIONS IN OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
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.
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
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.
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
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.
Proposal of Evolutionary Simplex Method for Global Optimization Problem
Shimizu, Yoshiaki
To make an agile decision in a rational manner, role of optimization engineering has been notified increasingly under diversified customer demand. With this point of view, in this paper, we have proposed a new evolutionary method serving as an optimization technique in the paradigm of optimization engineering. The developed method has prospects to solve globally various complicated problem appearing in real world applications. It is evolved from the conventional method known as Nelder and Mead’s Simplex method by virtue of idea borrowed from recent meta-heuristic method such as PSO. Mentioning an algorithm to handle linear inequality constraints effectively, we have validated effectiveness of the proposed method through comparison with other methods using several benchmark problems.
Numerical methods for optimal control problems with state constraints
Pytlak, Radosław
1999-01-01
While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.
Optimizing investment fund allocation using vehicle routing problem framework
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita
2014-07-01
The objective of investment is to maximize total returns or minimize total risks. To determine the optimum order of investment, vehicle routing problem method is used. The method which is widely used in the field of resource distribution shares almost similar characteristics with the problem of investment fund allocation. In this paper we describe and elucidate the concept of using vehicle routing problem framework in optimizing the allocation of investment fund. To better illustrate these similarities, sectorial data from FTSE Bursa Malaysia is used. Results show that different values of utility for risk-averse investors generate the same investment routes.
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.
An ant colony optimization method for generalized TSP problem
Institute of Scientific and Technical Information of China (English)
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.
Global Optimization Approach to Non-convex Problems
Institute of Scientific and Technical Information of China (English)
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.
Problem statement for optimal design of steel structures
Directory of Open Access Journals (Sweden)
Ginzburg Aleksandr Vital'evich
2014-07-01
Full Text Available The presented article considers the following complex of tasks. The main stages of the life cycle of a building construction with the indication of process entrance and process exit are described. Requirements imposed on steel constructions are considered. The optimum range of application for steel designs is specified, as well as merits and demerits of a design material. The nomenclature of metal designs is listed - the block diagram is constructed. Possible optimality criteria of steel designs, offered by various authors for various types of constructions are considered. It is established that most often the criterion of a minimum of design mass is accepted as criterion of optimality; more rarely - a minimum of the given expenses, a minimum of a design cost in business. In the present article special attention is paid to a type of objective function of optimization problem. It is also established that depending on the accepted optimality criterion, the use of different types of functions is possible. This complexity of objective function depends on completeness of optimality criterion application. In the work the authors consider the following objective functions: the mass of the main element of a design; objective function by criterion of factory cost; objective function by criterion of cost in business. According to these examples it can be seen that objective functions by the criteria of labor expenses for production of designs are generally non-linear, which complicates solving the optimization problem. Another important factor influencing the problem of optimal design solution for steel designs, which is analyzed, is account for operating restrictions. In the article 8 groups of restrictions are analyzed. Attempts to completely account for the parameters of objective function optimized by particular optimality criteria, taking into account all the operating restrictions, considerably complicates the problem of designing. For solving this
LGMS-FOA: An Improved Fruit Fly Optimization Algorithm for Solving Optimization Problems
Directory of Open Access Journals (Sweden)
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.
A Cooperative Coevolutionary Cuckoo Search Algorithm for Optimization Problem
Directory of Open Access Journals (Sweden)
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.
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.
Optimal Parallel Algorithm for the Knapsack Problem Without Memory Conflicts
Institute of Scientific and Technical Information of China (English)
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.
Multicast Routing Problem Using Tree-Based Cuckoo Optimization Algorithm
Directory of Open Access Journals (Sweden)
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.
Cashier Problem: a Greedy Algorithm and an optimal Solution
Directory of Open Access Journals (Sweden)
Nicolae GIURGITEANU
2006-01-01
Full Text Available We will remind briefly the cashier problem. A cashier has leeway a range of different fractional coins and has to pay a certain amount using the most reduced number of coins. If we mark the pay-desk monetary with P {p ,..., pn } 1 = , each pi having as denomination di and with A the final sum, the cashier must determine a coins subset { } m S q ,..., q 1 = of P, so that i m i id q A Σ==1. In order to solve this problem, there are several solutions consisting in greedy algorithms. Although there is an optimal solution, in the present article we will highlight a greedy algorithm and an optimal solution for this problem. The solution known at the time being use a lot of memory and, in addition, is difficult to justify, occurring the risk of misunderstanding by the reader. Our solution is simpler and uses little memory
Belief propagation : an asymptotically optimal algorithm for the random assignment problem
Salez, Justin; Shah, Devavrat
2009-01-01
The random assignment problem asks for the minimum-cost perfect matching in the complete $n\\times n$ bipartite graph $\\Knn$ with i.i.d. edge weights, say uniform on $[0,1]$. In a remarkable work by Aldous (2001), the optimal cost was shown to converge to $\\zeta(2)$ as $n\\to\\infty$, as conjectured by M\\'ezard and Parisi (1987) through the so-called cavity method. The latter also suggested a non-rigorous decentralized strategy for finding the optimum, which turned out to be an instance of the B...
Discrete particle swarm optimization algorithm for solving optimal sensor deployment problem
Directory of Open Access Journals (Sweden)
Rapaić Milan R.
2008-01-01
Full Text Available This paper addresses the Optimal Sensor Deployment Problem (OSDP. The goal is to maximize the probability of target detection, with simultaneous cost minimization. The problem is solved by the Discrete PSO (DPSO algorithm, a novel modification of the PSO algorithm, originally presented in the current paper. DPSO is general-purpose optimizer well suited for conducting search within a discrete search space. Its applicability is not limited to OSDP, it can be used to solve any combinatorial and integer programming problem. The effectiveness of the DPSO in solving OSDP was demonstrated on several examples.
Particle Swarm Optimization Applied to the Economic Dispatch Problem
Directory of Open Access Journals (Sweden)
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
Multiresolution strategies for the numerical solution of optimal control problems
Jain, Sachin
There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a
Optimizing Human Diet Problem Based on Price and Taste Using
Directory of Open Access Journals (Sweden)
Hossein EGHBALI
2012-07-01
Full Text Available Low price and good taste of foods are regarded as two major factors for optimal human nutrition. Due to price fluctuations and taste diversity, these two factors cannot be certainly and determinately evaluated. This problem must be viewed from another perspective because of the uncertainty about the amount of nutrients per unit of foods and also diversity of people’s daily needs to receive them.This paper discusses human diet problem in fuzzy environment. The approach deals with multi-objective fuzzy linear programming problem using a fuzzy programming technique for its solution. By prescribing a diet merely based on crisp data, some ofthe realities are neglected. For the same reason, we dealt with human diet problem through fuzzy approach. Results indicated uncertainty about factors of nutrition diet -including taste and price, amount of nutrients and their intake- would affect diet quality, making the proposed diet more realistic.
RECIPES FOR BUILDING THE DUAL OF CONIC OPTIMIZATION PROBLEM
Directory of Open Access Journals (Sweden)
Diah Chaerani
2010-08-01
Full Text Available Building the dual of the primal problem of Conic Optimization (CO isa very important step to make the ¯nding optimal solution. In many cases a givenproblem does not have the simple structure of CO problem (i.e., minimizing a linearfunction over an intersection between a±ne space and convex cones but there areseveral conic constraints and sometimes also equality constraints. In this paper wedeal with the question how to form the dual problem in such cases. We discuss theanswer by considering several conic constraints with or without equality constraints.The recipes for building the dual of such cases is formed in standard matrix forms,such that it can be used easily on the numerical experiment. Special attention isgiven to dual development of special classes of CO problems, i.e., conic quadraticand semide¯nite problems. In this paper, we also brie°y present some preliminariestheory on CO as an introduction to the main topic
Rigorous location of phase transitions in hard optimization problems.
Achlioptas, Dimitris; Naor, Assaf; Peres, Yuval
2005-06-01
It is widely believed that for many optimization problems, no algorithm is substantially more efficient than exhaustive search. This means that finding optimal solutions for many practical problems is completely beyond any current or projected computational capacity. To understand the origin of this extreme 'hardness', computer scientists, mathematicians and physicists have been investigating for two decades a connection between computational complexity and phase transitions in random instances of constraint satisfaction problems. Here we present a mathematically rigorous method for locating such phase transitions. Our method works by analysing the distribution of distances between pairs of solutions as constraints are added. By identifying critical behaviour in the evolution of this distribution, we can pinpoint the threshold location for a number of problems, including the two most-studied ones: random k-SAT and random graph colouring. Our results prove that the heuristic predictions of statistical physics in this context are essentially correct. Moreover, we establish that random instances of constraint satisfaction problems have solutions well beyond the reach of any analysed algorithm. PMID:15944693
A matrix product state method for solving combinatorial optimization problems
Pelton, S. S.; Chamon, C.; Mucciolo, E. R.
2015-03-01
We present a method based on a matrix product state representation to solve combinatorial optimization problems. All constraints are met by mapping Boolean gates into projection operators and applying operators sequentially. The method provides exact solutions with high success probability, even in the case of frustrated systems. The computational cost of the method is controlled by the maximum relative entropy of the system. Results of numerical simulations for several types of problems will be shown and discussed. NSF Grants CCF-1116590 and CCF-1117241.
A NOTE ON IRREVERSIBLE INVESTMENT, HEDGING AND OPTIMAL CONSUMPTION PROBLEMS
VICKY HENDERSON; DAVID HOBSON
2006-01-01
A canonical problem in real option pricing, as described in the classic text of Dixit and Pindyck [2], is to determine the optimal time to invest at a fixed cost, to receive in return a stochastic cashflow. In this paper we are interested in this problem in an incomplete market where the cashflow is not spanned by the traded assets. We follow the formulation in Miao and Wang [21]; our contribution is to show that significant progress can be made in solving the Hamilton-Jacobi-Bellman equation...
Novel electromagnetism-like mechanism method for multiobjective optimization problems
Institute of Scientific and Technical Information of China (English)
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.
MODIFIED GENETIC ALGORITHM APPLIED TO SOLVE PRODUCT FAMILY OPTIMIZATION PROBLEM
Institute of Scientific and Technical Information of China (English)
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.
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...
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.
Non-concave and behavioural optimal portfolio choice problems
Meireles Rodrigues, Andrea Sofia; Rodrigues, Andrea
2014-01-01
Our aim is to examine the problem of optimal asset allocation for investors exhibiting a behaviour in the face of uncertainty which is not consistent with the usual axioms of Expected Utility Theory. This thesis is divided into two main parts. In the first one, comprising Chapter II, we consider an arbitrage-free discrete-time financial model and an investor whose risk preferences are represented by a possibly nonconcave utility function (defined on the non-negative half-line only...
Optimizing Distribution Problems using WinQSB Software
Directory of Open Access Journals (Sweden)
Daniel Mihai Amariei
2015-07-01
Full Text Available In the present paper we are presenting a problem of distribution using the Network Modeling Module of the WinQSB software, were we have 5 athletes which we must assign the optimal sample, function of the obtained time, so as to obtain the maximum output of the athletes. Also we analyzed the case of an accident of 2 athletes, the coupling of 3 athletes with 5 various athletic events causing the maximum coupling, done using the Hungarian algorithm.
Higher order variational time discretization of optimal control problems
Campos, C M; Ober-Blöbaum, S
2012-01-01
We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction preserve important structural properties of the system, like the evolution of the momentum maps or the energy behavior. Here, we employ higher order quadrature rules based on polynomial collocation. The resulting variational time discretization decreases the overall computational effort.
Artificial Fish School Algorithm Applied in a Combinatorial Optimization Problem
Yun Cai
2010-01-01
An improved artificial fish swarm algorithm (AFSA) for solving a combinatorial optimization problem—a berth allocation problem (BAP), which was formulated. Its objective is to minimize the turnaround time of vessels at container terminals so as to improve operation efficiency customer satisfaction. An adaptive artificial fish swarm algorithm was proposed to solve it. Firstly, the basic principle and the algorithm design of the AFSA were introduced. Then, for a test case, computational experim...
Guaranteed Discrete Energy Optimization on Large Protein Design Problems.
Simoncini, David; Allouche, David; de Givry, Simon; Delmas, Céline; Barbe, Sophie; Schiex, Thomas
2015-12-01
In Computational Protein Design (CPD), assuming a rigid backbone and amino-acid rotamer library, the problem of finding a sequence with an optimal conformation is NP-hard. In this paper, using Dunbrack's rotamer library and Talaris2014 decomposable energy function, we use an exact deterministic method combining branch and bound, arc consistency, and tree-decomposition to provenly identify the global minimum energy sequence-conformation on full-redesign problems, defining search spaces of size up to 10(234). This is achieved on a single core of a standard computing server, requiring a maximum of 66GB RAM. A variant of the algorithm is able to exhaustively enumerate all sequence-conformations within an energy threshold of the optimum. These proven optimal solutions are then used to evaluate the frequencies and amplitudes, in energy and sequence, at which an existing CPD-dedicated simulated annealing implementation may miss the optimum on these full redesign problems. The probability of finding an optimum drops close to 0 very quickly. In the worst case, despite 1,000 repeats, the annealing algorithm remained more than 1 Rosetta unit away from the optimum, leading to design sequences that could differ from the optimal sequence by more than 30% of their amino acids. PMID:26610100
Parallel particle swarm optimization algorithm in nuclear problems
International Nuclear Information System (INIS)
Particle Swarm Optimization (PSO) is a population-based metaheuristic (PBM), in which solution candidates evolve through simulation of a simplified social adaptation model. Putting together robustness, efficiency and simplicity, PSO has gained great popularity. Many successful applications of PSO are reported, in which PSO demonstrated to have advantages over other well-established PBM. However, computational costs are still a great constraint for PSO, as well as for all other PBMs, especially in optimization problems with time consuming objective functions. To overcome such difficulty, parallel computation has been used. The default advantage of parallel PSO (PPSO) is the reduction of computational time. Master-slave approaches, exploring this characteristic are the most investigated. However, much more should be expected. It is known that PSO may be improved by more elaborated neighborhood topologies. Hence, in this work, we develop several different PPSO algorithms exploring the advantages of enhanced neighborhood topologies implemented by communication strategies in multiprocessor architectures. The proposed PPSOs have been applied to two complex and time consuming nuclear engineering problems: reactor core design and fuel reload optimization. After exhaustive experiments, it has been concluded that: PPSO still improves solutions after many thousands of iterations, making prohibitive the efficient use of serial (non-parallel) PSO in such kind of realworld problems; and PPSO with more elaborated communication strategies demonstrated to be more efficient and robust than the master-slave model. Advantages and peculiarities of each model are carefully discussed in this work. (author)
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
Directory of Open Access Journals (Sweden)
Yan Sun
2015-09-01
Full Text Available Purpose: The purpose of study is to solve the multi-modal transportation routing planning problem that aims to select an optimal route to move a consignment of goods from its origin to its destination through the multi-modal transportation network. And the optimization is from two viewpoints including cost and time. Design/methodology/approach: In this study, a bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. Minimizing the total transportation cost and the total transportation time are set as the optimization objectives of the model. In order to balance the benefit between the two objectives, Pareto optimality is utilized to solve the model by gaining its Pareto frontier. The Pareto frontier of the model can provide the multi-modal transportation operator (MTO and customers with better decision support and it is gained by the normalized normal constraint method. Then, an experimental case study is designed to verify the feasibility of the model and Pareto optimality by using the mathematical programming software Lingo. Finally, the sensitivity analysis of the demand and supply in the multi-modal transportation organization is performed based on the designed case. Findings: The calculation results indicate that the proposed model and Pareto optimality have good performance in dealing with the bi-objective optimization. The sensitivity analysis also shows the influence of the variation of the demand and supply on the multi-modal transportation organization clearly. Therefore, this method can be further promoted to the practice. Originality/value: A bi-objective mixed integer linear programming model is proposed to optimize the multi-modal transportation routing planning problem. The Pareto frontier based sensitivity analysis of the demand and supply in the multi-modal transportation organization is performed based on the designed case.
Ant Colony Optimization for Capacitated Vehicle Routing Problem
Directory of Open Access Journals (Sweden)
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.
APPLYING PARTICLE SWARM OPTIMIZATION TO JOB-SHOP SCHEDULING PROBLEM
Institute of Scientific and Technical Information of China (English)
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.
Use of genetic algorithms for solving problems of optimal cutting
Directory of Open Access Journals (Sweden)
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.
Multiobjective Optimization Problem of Multireservoir System in Semiarid Areas
Directory of Open Access Journals (Sweden)
Z. J. Chen
2013-01-01
Full Text Available With the increasing scarcity of water resources, the growing importance of the optimization operation of the multireservoir system in water resources development, utilization, and management is increasingly evident. Some of the existing optimization methods are inadequate in applicability and effectiveness. Therefore, we need further research in how to enhance the applicability and effectiveness of the algorithm. On the basis of the research of the multireservoir system’s operating parameters in the Urumqi River basin, we establish a multiobjective optimization problem (MOP model of water resources development, which meets the requirements of water resources development. In the mathematical model, the domestic water consumption is the biggest, the production of industry and agricultural is the largest, the gross output value of industry and agricultural is the highest, and the investment of the water development is the minimum. We use the weighted variable-step shuffled frog leaping algorithm (SFLA to resolve it, which satisfies the constraints. Through establishing the test function and performance metrics, we deduce the evolutionary algorithms, which suit for solving MOP of the scheduling, and realize the multiobjective optimization of the multireservoir system. After that, using the fuzzy theory, we convert the competitive multiobjective function into single objective problem of maximum satisfaction, which is the only solution. A feasible solution is provided to resolve the multiobjective scheduling optimization of multireservoir system in the Urumqi River basin. It is the significance of the layout of production, the regional protection of ecological environment, and the sufficient and rational use of natural resources, in Urumqi and the surrounding areas.
Optimization of Capacitated Vehicle Routing Problem by Nested Particle Swarm Optimization
Directory of Open Access Journals (Sweden)
Karuppusamy Kanthavel
2011-01-01
Full Text Available Problem statement: Vehicle routing problem determines the optimum route for each vehicle as a sequence of visiting cities. The problem has been defined as NP-hard and exact solution is relatively difficult to achieve for real time large scale models. Though several attempts to solve the problem were made in the literature, new approaches may be tried to solve the problem to further reduce computational efforts. Approach: In this context this study focuses on maximum utilization of loading capacity and determines the optimum set of vehicle routes for Capacitated Vehicle Routing Problem (CVRP by a Nested Particle Swarm Optimization (NPSO technique. The algorithm is implemented as Master PSO and slave PSO for the identification of candidate list and route sequence in nested form to optimize the model. Results: Benchmarking data set of capacitated vehicle routing is considered for the evaluations. The total distance of set vehicle route obtained by the new approach is compared with the best known solution and other existing techniques. Conclusions/Recommendations: The NPSO produces significant results and computational performance than the existing PSO algorithms. This newly proposed NPSO algorithm develops the vehicle schedule without any local optimization technique.
A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems
Institute of Scientific and Technical Information of China (English)
Yong WANG; Zixing CAI
2009-01-01
In the real-world applications, most optimization problems are subject to different types of constraints. These problems are known as constrained optimization problems (COPs). Solving COPs is a very important area in the optimization field. In this paper, a hybrid multi-swarm particle swarm optimization (HMPSO) is proposed to deal with COPs. This method adopts a parallel search operator in which the current swarm is partitioned into several subswarms and particle swarm optimization (PSO) is severed as the search engine for each sub-swarm. Moreover, in order to explore more promising regions of the search space, differential evolution (DE) is incorporated to improve the personal best of each particle. First, the method is tested on 13 benchmark test functions and compared with three stateof-the-art approaches. The simulation results indicate that the proposed HMPSO is highly competitive in solving the 13 benchmark test functions. Afterward, the effectiveness of some mechanisms proposed in this paper and the effect of the parameter setting were validated by various experiments. Finally, HMPSO is further applied to solve 24 benchmark test functions collected in the 2006 IEEE Congress on Evolutionary Computation (CEC2006) and the experimental results indicate that HMPSO is able to deal with 22 test functions.
Adjoint optimization of natural convection problems: differentially heated cavity
Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.
2016-06-01
Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7 ) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here
Directory of Open Access Journals (Sweden)
Qilin Wang
2011-01-01
Full Text Available Some new properties are obtained for generalized second-order contingent (adjacent epiderivatives of set-valued maps. By employing the generalized second-order adjacent epiderivatives, necessary and sufficient conditions of Benson proper efficient solutions are given for set-valued optimization problems. The results obtained improve the corresponding results in the literature.
Directory of Open Access Journals (Sweden)
Vivek Patel
2012-08-01
Full Text Available Nature inspired population based algorithms is a research field which simulates different natural phenomena to solve a wide range of problems. Researchers have proposed several algorithms considering different natural phenomena. Teaching-Learning-based optimization (TLBO is one of the recently proposed population based algorithm which simulates the teaching-learning process of the class room. This algorithm does not require any algorithm-specific control parameters. In this paper, elitism concept is introduced in the TLBO algorithm and its effect on the performance of the algorithm is investigated. The effects of common controlling parameters such as the population size and the number of generations on the performance of the algorithm are also investigated. The proposed algorithm is tested on 35 constrained benchmark functions with different characteristics and the performance of the algorithm is compared with that of other well known optimization algorithms. The proposed algorithm can be applied to various optimization problems of the industrial environment.
Directory of Open Access Journals (Sweden)
Firat Evirgen
2016-04-01
Full Text Available In this paper, a class of Nonlinear Programming problem is modeled with gradient based system of fractional order differential equations in Caputo's sense. To see the overlap between the equilibrium point of the fractional order dynamic system and theoptimal solution of the NLP problem in a longer timespan the Multistage Variational İteration Method isapplied. The comparisons among the multistage variational iteration method, the variationaliteration method and the fourth order Runge-Kutta method in fractional and integer order showthat fractional order model and techniques can be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programming problems.
Study on ant colony optimization for fuel loading pattern problem
International Nuclear Information System (INIS)
Modified ant colony optimization (ACO) was applied to the in-core fuel loading pattern (LP) optimization problem to minimize the power peaking factor (PPF) in the modeled 1/4 symmetry PWR core. Loading order was found to be important in ACO. Three different loading orders with and without the adjacent effect between fuel assemblies (FAs) were compared, and it was found that the loading order from the central core is preferable because many selections of FAs to be inserted are available in the core center region. LPs were determined from pheromone trail and heuristic information, which is a priori knowledge based on the feature of the problem. Three types of heuristic information were compared to obtain the desirable performance of searching LPs with low PPF. Moreover, mutation operation, such as the genetic algorithm (GA), was introduced into the ACO algorithm to avoid searching similar LPs because heuristic information used in ACO tends to localize the searching space in the LP problem. The performance of ACO with some improvement was compared with those of simulated annealing and GA. In conclusion, good performance can be achieved by setting proper heuristic information and mutation operation parameter in ACO. (author)
On the robust optimization to the uncertain vaccination strategy problem
International Nuclear Information System (INIS)
In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented
On the influence of problem definition in sensor placement optimization
Pettit, Chris L.; Vecherin, Sergey N.; Wilson, D. Keith
2009-05-01
The combinatorial nature of sensor placement optimization has motivated the use of heuristic algorithms to avoid the high computational costs of finding global optima by focusing instead on satisfactory local optima. Transition of an optimization strategy from research to practice should involve a detailed inquiry into the dependence of its results on the representation of realistic scenarios. A sampling method was used to examine how the specification of a sensor placement problem for optimization affects the statistical properties of various ensembles of optimum networks produced by a heuristic algorithm. Features sampled in each ensemble were the resolution of the grid used for computing network coverage, the range of each sensor, and the dimensions of obstacles to line-of-sight sensing. The candidate placement grid also was sampled to examine the consequences of being unable to place sensors at a subset of a regularly spaced grid. The objective function was the number of sensors required to exceed a probability of detection threshold throughout the coverage area. The relative importance of variability in each parameter was found to depend on the widths and baseline values of the assumed variability ranges. Important length scale ratios were identified for ensuring the feasibility and integrity of the optimization process.
On the robust optimization to the uncertain vaccination strategy problem
Energy Technology Data Exchange (ETDEWEB)
Chaerani, D., E-mail: d.chaerani@unpad.ac.id; Anggriani, N., E-mail: d.chaerani@unpad.ac.id; Firdaniza, E-mail: d.chaerani@unpad.ac.id [Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Padjadjaran Indonesia, Jalan Raya Bandung Sumedang KM 21 Jatinangor Sumedang 45363 (Indonesia)
2014-02-21
In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.
Artificial Fish School Algorithm Applied in a Combinatorial Optimization Problem
Directory of Open Access Journals (Sweden)
Yun Cai
2010-11-01
Full Text Available An improved artificial fish swarm algorithm (AFSA for solving a combinatorial optimization problem—a berth allocation problem (BAP, which was formulated. Its objective is to minimize the turnaround time of vessels at container terminals so as to improve operation efficiency customer satisfaction. An adaptive artificial fish swarm algorithm was proposed to solve it. Firstly, the basic principle and the algorithm design of the AFSA were introduced. Then, for a test case, computational experiments explored the effect of algorithm parameters on the convergence of the algorithm. Experimental results verified the validity and feasibility of the proposed algorithm with rational parameters, and show that the algorithm has better convergence performance than genetic algorithm (GA and ant colony optimization (ACO.
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...
Rao, R. V.; Savsani, V. J.; Balic, J.
2012-12-01
An efficient optimization algorithm called teaching-learning-based optimization (TLBO) is proposed in this article to solve continuous unconstrained and constrained optimization problems. The proposed method is based on the effect of the influence of a teacher on the output of learners in a class. The basic philosophy of the method is explained in detail. The algorithm is tested on 25 different unconstrained benchmark functions and 35 constrained benchmark functions with different characteristics. For the constrained benchmark functions, TLBO is tested with different constraint handling techniques such as superiority of feasible solutions, self-adaptive penalty, ɛ-constraint, stochastic ranking and ensemble of constraints. The performance of the TLBO algorithm is compared with that of other optimization algorithms and the results show the better performance of the proposed algorithm.
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
Wolf Search Algorithm for Solving Optimal Reactive Power Dispatch Problem
Kanagasabai Lenin; B.Ravindhranath Reddy; M.Surya Kalavathi
2015-01-01
This paper presents a new bio-inspired heuristic optimization algorithm called the Wolf Search Algorithm (WSA) for solving the multi-objective reactive power dispatch problem. Wolf Search algorithm is a new bio – inspired heuristic algorithm which based on wolf preying behaviour. The way wolves search for food and survive by avoiding their enemies has been imitated to formulate the algorithm for solving the reactive power dispatches. And the speciality of wolf is possessing both individual...
Combining Multiple Strategies for Multiarmed Bandit Problems and Asymptotic Optimality
Directory of Open Access Journals (Sweden)
Hyeong Soo Chang
2015-01-01
Full Text Available This brief paper provides a simple algorithm that selects a strategy at each time in a given set of multiple strategies for stochastic multiarmed bandit problems, thereby playing the arm by the chosen strategy at each time. The algorithm follows the idea of the probabilistic ϵt-switching in the ϵt-greedy strategy and is asymptotically optimal in the sense that the selected strategy converges to the best in the set under some conditions on the strategies in the set and the sequence of {ϵt}.
Topology optimization of coated structures and material interface problems
DEFF Research Database (Denmark)
Clausen, Anders; Aage, Niels; Sigmund, Ole
2015-01-01
This paper presents a novel method for including coated structures and prescribed material interface properties into the minimum compliance topology optimization problem. Several elements of the method are applicable to a broader range of interface problems. The approach extends the standard SIMP...... 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...
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...
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.
A DE-Based Scatter Search for Global Optimization Problems
Directory of Open Access Journals (Sweden)
Kun Li
2015-01-01
Full Text Available This paper proposes a hybrid scatter search (SS algorithm for continuous global optimization problems by incorporating the evolution mechanism of differential evolution (DE into the reference set updated procedure of SS to act as the new solution generation method. This hybrid algorithm is called a DE-based SS (SSDE algorithm. Since different kinds of mutation operators of DE have been proposed in the literature and they have shown different search abilities for different kinds of problems, four traditional mutation operators are adopted in the hybrid SSDE algorithm. To adaptively select the mutation operator that is most appropriate to the current problem, an adaptive mechanism for the candidate mutation operators is developed. In addition, to enhance the exploration ability of SSDE, a reinitialization method is adopted to create a new population and subsequently construct a new reference set whenever the search process of SSDE is trapped in local optimum. Computational experiments on benchmark problems show that the proposed SSDE is competitive or superior to some state-of-the-art algorithms in the literature.
Analysis of optimal and near-optimal continuous-thrust transfer problems in general circular orbit
Kéchichian, Jean A.
2009-09-01
A pair of practical problems in optimal continuous-thrust transfer in general circular orbit is analyzed within the context of analytic averaging for rapid computations leading to near-optimal solutions. The first problem addresses the minimum-time transfer between inclined circular orbits by proposing an analytic solution based on a split-sequence strategy in which the equatorial inclination and node controls are done separately by optimally selecting the intermediate orbit size at the sequence switch point that results in the minimum-time transfer. The consideration of the equatorial inclination and node state variables besides the orbital velocity variable is needed to further account for the important J2 perturbation that precesses the orbit plane during the transfer, unlike the thrust-only case in which it is sufficient to consider the relative inclination and velocity variables thus reducing the dimensionality of the system equations. Further extensions of the split-sequence strategy with analytic J2 effect are thus possible for equal computational ease. The second problem addresses the maximization of the equatorial inclination in fixed time by adopting a particular thrust-averaging scheme that controls only the inclination and velocity variables, leaving the node at the mercy of the J2 precession, providing robust fast-converging codes that lead to efficient near-optimal solutions. Example transfers for both sets of problems are solved showing near-optimal features as far as transfer time is concerned, by directly comparing the solutions to "exact" purely numerical counterparts that rely on precision integration of the raw unaveraged system dynamics with continuously varying thrust vector orientation in three-dimensional space.
Applying dynamic programming to a gas-lift optimization problem
Energy Technology Data Exchange (ETDEWEB)
Camponogara, Eduardo; Nakashima, Paulo H.R. [Santa Catarina Univ., Florianopolis (Brazil). Dept. de Automacao e Sistemas]. E-mails: camponog@das.ufsc.br; phrn@das.ufsc.br
2003-07-01
The ever-increasing demand for nonrenewable resources and the pressure from stockholders are two forces pressing the oil industry for higher efficiency. The opportunities for advances abound in all sectors of the industry, in particular production processes in gas-lift oil wells, which are often favored to draw oil from high-depth reservoirs. Of concern in this paper is the task of distributing the limited supply of gas to the wells so as to induce an optimal oil production. Narrowing this task to the steady-state response of the wells gives rise to the gas-lift optimization problem, whose variables decide which wells should be active as well as the gas-injection and whose objective is profit maximization. The paper elaborates on a few properties of the problem and delivers a dynamic programming algorithm to find approximate solutions. The effectiveness of the algorithm was demonstrated by contrasting its solutions against upper bounds obtained with continuous relaxation. As closure, the paper outlines a few directions for future research. (author)
Directory of Open Access Journals (Sweden)
Mohammad-Reza Askari
2015-07-01
Full Text Available Abstract This paper introduces a new stochastic optimization framework based bat algorithm BA to solve the optimal distribution feeder reconfiguration DFR as well as the shunt capacitor placement and sizing in the distribution systems. The objective functions to be investigated are minimization of the active power losses and minimization of the total network costs an. In order to consider the uncertainties of the active and reactive loads in the problem point estimate method PEM with 2m scheme is employed as the stochastic tool. The feasibility and good performance of the proposed method are examined on the IEEE 69-bus test system.
Modified Monkey Optimization Algorithm for Solving Optimal Reactive Power Dispatch Problem
Directory of Open Access Journals (Sweden)
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.
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
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
An optimal iterative solver for the Stokes problem
Energy Technology Data Exchange (ETDEWEB)
Wathen, A. [Univ. of Bristol (United Kingdom); Silvester, D.
1994-12-31
Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal solver for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.
A program package for solving nonlinear optimization problems
International Nuclear Information System (INIS)
For the solution of nonlinear optimization problems, sixteen programs have been prepared and tested on FACOM M200 computer. A set of auxiliary programs has also been equipped to facilitate the use of this program package, with the main stress on the reduction of the effort that is required for the preparation of the main program. An attempt has been made to unify the input/output format as far as possible throughout the auxiliary programs. The programs have been classified broadly into two categories according to whether it can treat the problems with constraints or not. Moreover, from the viewpoint of the characteristics of the solution techniques, the programs that can be used only for the problems without constraints have been sub-divided into the following three classes; the first class involves only the objective function values themselves, the second involves the values of the objective function and their first partial derivatives, and the last involves the second partial derivatives as well. In order to make this program package available to various users, the explanation on the calculational procedure, the meaning of the arguments in the calling sequence of each program and the instructions about input data requirements of each auxiliary program have been presented together with the sample input/output listings. (author)
Directory of Open Access Journals (Sweden)
Hifza Afaq
2011-05-01
Full Text Available The multi objective optimization problems can be found in various fields such as finance, automobile design, aircraft design, path optimization etc. This paper reviews some of the existing literature on multi objective optimization problems and some of the existing Swarm Intelligence (SI based techniques to solve these problems. The objective of this paper is to provide a starting point to the multi objective optimization problems to the reader.
OPTIMAL HARVESTING CONTROL PROBLEM FOR LINEAR AGE-DEPENDENT POPULATION DYNAMICS
Institute of Scientific and Technical Information of China (English)
LuoZhixue; WangMiansen
2003-01-01
An optimal harvesting problem for linear age-dependent population dynamics is investigated.By Mazur''s Theorem,the existence of solutions of the optimal control problem(OH) is demonstrated.The first order necessary conditions of optimality for problem (OH) is obtained by the conception of normal cone.Finally,under suitable assumptions,the uniqueness of solutions of the optimal control problem (OH) is given.The results extend some knowncriteria.
Human opinion dynamics: An inspiration to solve complex optimization problems
Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P.; Kapur, Pawan
2013-10-01
Human interactions give rise to the formation of different kinds of opinions in a society. The study of formations and dynamics of opinions has been one of the most important areas in social physics. The opinion dynamics and associated social structure leads to decision making or so called opinion consensus. Opinion formation is a process of collective intelligence evolving from the integrative tendencies of social influence with the disintegrative effects of individualisation, and therefore could be exploited for developing search strategies. Here, we demonstrate that human opinion dynamics can be utilised to solve complex mathematical optimization problems. The results have been compared with a standard algorithm inspired from bird flocking behaviour and the comparison proves the efficacy of the proposed approach in general. Our investigation may open new avenues towards understanding the collective decision making.
An Optimized and Scalable Eigensolver for Sequences of Eigenvalue Problems
Berljafa, Mario; Di Napoli, Edoardo
2014-01-01
In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution of one problem fosters the initialization of the next. In addition, some eigenproblem sequences show a connection between the solutions of adjacent eigenproblems. Whenever is possible to unravel the existence of such a connection, the eigenproblem sequence is said to be a correlated. When facing with a sequence of correlated eigenproblems the current strategy amounts to solving each eigenproblem in isolation. We propose a novel approach which exploits such correlation through the use of an eigensolver based on subspace iteration and accelerated with Chebyshev polynomials (ChFSI). The resulting eigensolver, is optimized by minimizing the number of matvec multiplications and parallelized using the Elemental library framework. Numerical results shows that ChFSI achieves excell...
Wolf Search Algorithm for Solving Optimal Reactive Power Dispatch Problem
Directory of Open Access Journals (Sweden)
Kanagasabai Lenin
2015-03-01
Full Text Available This paper presents a new bio-inspired heuristic optimization algorithm called the Wolf Search Algorithm (WSA for solving the multi-objective reactive power dispatch problem. Wolf Search algorithm is a new bio – inspired heuristic algorithm which based on wolf preying behaviour. The way wolves search for food and survive by avoiding their enemies has been imitated to formulate the algorithm for solving the reactive power dispatches. And the speciality of wolf is possessing both individual local searching ability and autonomous flocking movement and this special property has been utilized to formulate the search algorithm .The proposed (WSA algorithm has been tested on standard IEEE 30 bus test system and simulation results shows clearly about the good performance of the proposed algorithm .
AN EFFECTIVE SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM FOR NONLINEAR OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
贺国平; 高自友; 郑永果
2002-01-01
In this paper, a new globally convergent algorithm for nonlinear optimization problems with equality and inequality constraints is presented. The new algorithm is of SQP type which determines a search direction by solving a quadratic programming subproblem per iteration. Some revisions on the quadratic programming subproblem have been made in such a way that the associated constraint region is nonempty for each point x generated by the algorithm, i.e. , the subproblems always have optimal solutions. The new algorithm has two important properties. The computation of revision parameter for guaranteeing the consistency of quadratic subproblem and the computation of the second order correction step for superlinear convergence use the same inverse of a matrix per iteration, so the computation amount of the new algorithm will not be increased much more than other SQP type algorithms; Another is that the new algorithm can give automatically a feasible point as a starting point for the quadratic subproblems per iteration, this will obivously simplify the computation procedure of the subproblems. Some numerical results are reported.
Optimal Rapid Restart of Heuristic Methods of NP Hard Problems
Institute of Scientific and Technical Information of China (English)
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.
AN ADAPTIVE MEMBRANE ALGORITHM FOR SOLVING COMBINATORIAL OPTIMIZATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
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.
Modified Lagrangian and Least Root Approaches for General Nonlinear Optimization Problems
Institute of Scientific and Technical Information of China (English)
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.
Institute of Scientific and Technical Information of China (English)
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.
Directory of Open Access Journals (Sweden)
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.
A modified teaching–learning based optimization for multi-objective optimal power flow problem
International Nuclear Information System (INIS)
Highlights: • A new modified teaching–learning based algorithm is proposed. • A self-adaptive wavelet mutation strategy is used to enhance the performance. • To avoid reaching a large repository size, a fuzzy clustering technique is used. • An efficiently smart population selection is utilized. • Simulations show the superiority of this algorithm compared with other ones. - Abstract: In this paper, a modified teaching–learning based optimization algorithm is analyzed to solve the multi-objective optimal power flow problem considering the total fuel cost and total emission of the units. The modified phase of the optimization algorithm utilizes a self-adapting wavelet mutation strategy. Moreover, a fuzzy clustering technique is proposed to avoid extremely large repository size besides a smart population selection for the next iteration. These techniques make the algorithm searching a larger space to find the optimal solutions while speed of the convergence remains good. The IEEE 30-Bus and 57-Bus systems are used to illustrate performance of the proposed algorithm and results are compared with those in literatures. It is verified that the proposed approach has better performance over other techniques
Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Capacitated vehicle routing problem (CVRP) is an NP-hard problem. For large-scale problems, it is quite difficult to achieve an optimal solution with traditional optimization methods due to the high computational complexity. A new hybrid approximation algorithm is developed in this work to solve the problem. In the hybrid algorithm, discrete particle swarm optimization (DPSO) combines global search and local search to search for the optimal results and simulated annealing (SA) uses certain probability to avoid being trapped in a local optimum. The computational study showed that the proposed algorithm is a feasible and effective approach for capacitated vehicle routing problem, especially for large scale problems.
Directory of Open Access Journals (Sweden)
R. Venkata Rao
2013-01-01
Full Text Available Teaching-Learning-based optimization (TLBO is a recently proposed population based algorithm, which simulates the teaching-learning process of the class room. This algorithm requires only the common control parameters and does not require any algorithm-specific control parameters. In this paper, the effect of elitism on the performance of the TLBO algorithm is investigated while solving unconstrained benchmark problems. The effects of common control parameters such as the population size and the number of generations on the performance of the algorithm are also investigated. The proposed algorithm is tested on 76 unconstrained benchmark functions with different characteristics and the performance of the algorithm is compared with that of other well known optimization algorithms. A statistical test is also performed to investigate the results obtained using different algorithms. The results have proved the effectiveness of the proposed elitist TLBO algorithm.
Using Bee Colony Optimization to Solve the Task Scheduling Problem in Homogenous Systems
Vahid Arabnejad; Ali Moeini; Nasrollah Moghadam
2011-01-01
Bee colony optimization (BCO) is one of the most recent algorithms in swarm intelligence that can be used in optimization problems this algorithm is based on the intelligent behavior of honey bees in foraging process. In this paper bee colony optimization is applied to solve the task scheduling problem which tasks have dependency with each other. Scheduling of tasks that represents by directed acyclic graph is a NP-complete problem. The main purpose of this problem is obtaining the minimum sc...
Directory of Open Access Journals (Sweden)
Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
The Fighter Problem: Optimal Allocation of a Discrete Commodity
Bartroff, Jay
2011-01-01
The Fighter problem with discrete ammunition is studied. An aircraft (fighter) equipped with $n$ anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which follows a homogeneous Poisson process with known intensity. If $j$ of the $n$ missiles are spent at an encounter they destroy an enemy plane with probability $a(j)$, where $a(0) = 0 $ and $\\{a(j)\\}$ is a known, strictly increasing concave sequence, e.g., $a(j) = 1-q^j, \\; \\, 0 < q < 1$. If the enemy is not destroyed, the enemy shoots the fighter down with known probability $1-u$, where $0 \\le u \\le 1$. The goal of the fighter is to shoot down as many enemy airplanes as possible during a given time period $[0, T]$. Let $K (n, t)$ be the smallest optimal number of missiles to be used at a present encounter, when the fighter has flying time $t$ remaining and $n$ missiles remaining. Three seemingly obvious properties of $K(n, t)$ have been conjectured: [A] The closer to the destination, the more of the $n$ missiles one should use, ...
Institute of Scientific and Technical Information of China (English)
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.
Institute of Scientific and Technical Information of China (English)
陆娟; 肖敏; 卢丽丽
2011-01-01
通过单因素试验(培养基用水、碳源、氮源、培养温度和培养基初始pH值)和正交试验对地农芽孢杆菌(Bacillus licheniformis)8-37-0-1发酵产生Levan果聚糖的培养基组成及培养条件进行优化,采用苯酚-硫酸法测定多糖含量.结果表明:以蔗糖100g/L、牛肉膏1.0g/L、酵母粉0.6g/L、K2HPO4 3.0g/L、KH2PO4 3.0g/L、NaCl 1.0g/L、MgSO4·7H2O 0.2g/L、FeSO4·7H2O 0.001g/L,自来水配制,培养基初始pH5.0,30℃培养8-37-0-1菌株24h,Levan果聚糖产量达到最高值41.7g/L,约是未优化时的5.0倍.
Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control
Energy Technology Data Exchange (ETDEWEB)
Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)
2015-04-15
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.
Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems
Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III
2012-01-01
In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.
Directory of Open Access Journals (Sweden)
Weifeng Wang
2014-01-01
Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.
2010-04-01
... 26 Internal Revenue 16 2010-04-01 2010-04-01 true Introduction. 44.0-1 Section 44.0-1 Internal... ON WAGERING; EFFECTIVE JANUARY 1, 1955 Introduction § 44.0-1 Introduction. (a) In general. The... provisions of subtitle F of the Code (Procedure and Administration) which have special application to...
2010-04-01
... 26 Internal Revenue 14 2010-04-01 2010-04-01 false Introduction. 20.0-1 Section 20.0-1 Internal...; ESTATES OF DECEDENTS DYING AFTER AUGUST 16, 1954 Introduction § 20.0-1 Introduction. (a) In general. (1... administration provisions. Subtitle F of the Internal Revenue Code contains some sections which are applicable...
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...
Directory of Open Access Journals (Sweden)
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.
Chaudhuri, Arindam
2013-01-01
We present a dynamic algorithm for solving the Longest Common Subsequence Problem using Ant Colony Optimization Technique. The Ant Colony Optimization Technique has been applied to solve many problems in Optimization Theory, Machine Learning and Telecommunication Networks etc. In particular, application of this theory in NP-Hard Problems has a remarkable significance. Given two strings, the traditional technique for finding Longest Common Subsequence is based on Dynamic Programming which cons...
An Evolutionary Algorithm to Optimization of Discrete Problem Based on Pheromone
Institute of Scientific and Technical Information of China (English)
无
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.
Optimization and Robustness in Planning and Scheduling Problems. Application to Container Terminals
RODRÍGUEZ MOLINS, MARIO
2015-01-01
Despite the continuous evolution in computers and information technology, real-world combinatorial optimization problems are NP-problems, in particular in the domain of planning and scheduling. Thus, although exact techniques from the Operations Research (OR) field, such as Linear Programming, could be applied to solve optimization problems, they are difficult to apply in real-world scenarios since they usually require too much computational time, i.e: an optimized solution is ...
Model Guided Sampling Optimization for Low-dimensional Problems
Bajer, L. (Lukáš); Holeňa, M. (Martin)
2015-01-01
Optimization of very expensive black-box functions requires utilization of maximum information gathered by the process of optimization. Model Guided Sampling Optimization (MGSO) forms a more robust alternative to Jones’ Gaussian-process-based EGO algorithm. Instead of EGO’s maximizing expected improvement, the MGSO uses sampling the probability of improvement which is shown to be helpful against trapping in local minima. Further, the MGSO can reach close-to-optimum solutions faster than stand...
Institute of Scientific and Technical Information of China (English)
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.
Optimal Control Problem Governed by Semilinear Parabolic Equation and its Algorithm
Institute of Scientific and Technical Information of China (English)
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.
Pareto optimality and robustness in bi-blending problems
Herrera, J.F.; Casado, L.G.; Hendrix, E.M.T.; García, I.
2014-01-01
The mixture design problem for two products concerns finding simultaneously two recipes of a blending problem with linear, quadratic and semi-continuity constraints. A solution of the blending problem minimizes a linear cost objective and an integer valued objective that keeps track of the number of
Optimization of casting process based on the theory of inventive problem solving
Liu Feng; Yang Yi; Li Xionglong
2011-01-01
Optimization of casting process involves the adjustment of parameters as well as the improvement of process schemes and measures. This paper proposes a new method based on the Theory of Inventive Problem Solving (TRIZ) for casting process optimization, and realizes the idea of applying TRIZ to optimize the casting process of a magnesium alloy intake manifold. By this method, the casting process is optimized so as to remove the shrinkage pores. The successful optimization of casting process de...
Diagnostic criteria for idiopathic inflammatory myopathies. Problems of their optimization
Directory of Open Access Journals (Sweden)
O. A. Antelava
2014-01-01
Full Text Available The paper deals with the problems of optimizing the diagnostic criteria for idiopathic inflammatory myopathies (IIM, a group of heterogeneous rare autoimmune diseases characterized by inflammatory lesion in the skeletal muscles. The representatives of this group are traditionally considered to be polymyositis (PM, dermatomyositis (DM, and inclusion-body myositis. The authors detail the history of classification criteria for IIM from those proposed by T.A. Medsger et al. (1970 relying on its clinical picture, laboratory data and instrumental findings, as well as the criteria (including the first introduced exclusion ones elaborated by A. Bohan and J.B. Peter in 1975, which remain fundamental in both clinical practice and researches. The basis for the clinical and serological criteria proposed by Y. Troyanov et al. (2005 for IIM is the identification of myositis-overlap syndromes. The classificational (subtype identification and therapeutic value of the criteria based on clinical and serological characteristics was supported by the Hungarian investigators A. Vancsa et al. (2010 who investigated the relationship between the clinical and therapeutic characteristics of IIM and positivity for myositis-specific and myositis-associated antibodies. The criteria developed by M.C. Dalakas (1991, 2003 are based on the specific immunopathological features of a histological pattern, which allow the differentiation of DM, PM, and inclusion-body myositis from other myopathic syndromes. The 2004 European Neuromuscular Center (ENMC criteria first identify necrotizing autoimmune myopathy and nonspecific myositis as individual subtypes. The serological classification of IIM, which is based onthe assessment of autoantibodies that play an important role in the pathogenesis of the disease, is of indubitable interest. There is an obvious need for the correct and timely diagnosis of both IIM as a whole and its subtypes in particular, which is complicated by
Implicit optimality criterion for convex SIP problem with box constrained index set
Kostyukova, O. I.; Tchemisova, T. V.
2012-01-01
We consider a convex problem of Semi-Infinite Programming (SIP) with multidimensional index set. In study of this problem we apply the approach suggested in [20] for convex SIP problems with one-dimensional index sets and based on the notions of immobile indices and their immobility orders. For the problem under consideration we formulate optimality conditions that are explicit and have the form of criterion. We compare this criterion with other known optimality conditions for ...
Sandal, Leif Kristoffer; Berge, Gerhard
2001-01-01
Dynamic optimization problems covers a great class of problems in management science and technology. The classical problem formulations being the variational approach as in classical mechanics, like Hamilton's principle and the optimal control theory in economics as the Pontryagin's maximum principle. In this account we start with a general problem formulation as an alternative to an approach based on solving differential equations. We focus on creating an analytical environment aimed at deri...
Magnússon, Sindri; Chathuranga Weeraddana, Pradeep; Fischione, Carlo
2014-01-01
The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial, though their global optimality is not guaranteed. Existing semi-definite programming relaxation based approaches are restricted to OPF problems where zero duality holds. In this paper, an efficient novel method to address the general nonconvex OPF problem is...
FIRST-ORDER METHODS FOR SOLVING THE OPTIMAL STATIC H∞-SYNTHESIS PROBLEM
Institute of Scientific and Technical Information of China (English)
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.
Institute of Scientific and Technical Information of China (English)
帅斌; 赵佳虹
2011-01-01
An improved multi-objective 0-1 mixed-integer linear programming model for the location routing problem in hazardous waste logistics was proposed, in which the optimization objectives are to minimize total costs and risks, and the constraints include waste types and treatment technologies, capacity and operation costs of treatment centers. A TOPSIS ( technique for order preference by similarity to an ideal solution) algorithm was designed to solve this multi-objective model. The feasibility and advantage of the proposed model was demonstrated through a representative example taken from literature. Comparing with an exiting model, the proposed model reduced the risk by 7. 69％ at the expense of a little rise in cost by 0. 70％ .%为了解决危险废物回收、加工和处理中心选址问题,确定加工技术类别、安排危险废物和废物残余车辆运输路径,将回收环节纳入危险废物物流系统,考虑废物类型与加工技术的多样性、中心运营费用、废物与加工技术的相容性以及中心能力富余量约束,以费用和风险最小化为优化目标,建立了危险废物物流系统的改进多目标0-1混合整数线性规划模型.采用TOPSIS(technique for order preference by similarity to an ideal solution)方法求解模型.结果表明,与现有模型相比,本文模型的多目标优化方案以增加0.70%的费用为代价,将风险降低7.69%.
Vocational Education Network Optimization Program Implementation Problems and Solutions
Šīna, Inga
2015-01-01
The aim of the paper is to analyze two-year results of the optimization programs of vocational school network and vocational education balancing solutions in the European Social Fund project " Improvement of national qualification system, vocational education contents and co-operation among the bodies involved in vocational education." The topic is of particular importance as the prestige of vocational education is low, the school network optimization yielded no results and vocational trainin...
Institute of Scientific and Technical Information of China (English)
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。
Institute of Scientific and Technical Information of China (English)
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.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The performance of analytical derivative and sparse matrix techniques applied to a traditional densesequential quadratic programming(SQP) is studied, and the strategy utilizing those techniques is also presented. Computational results on two typicalchemical optimization problems demonstrate significant enhancement in efficiency, which shows this strategy ispromising and suitable for large-scale process optimization problems.
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.
Institute of Scientific and Technical Information of China (English)
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.
Directory of Open Access Journals (Sweden)
Jingtao Shi
2013-01-01
Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
Jingtao Shi; Zhiyong Yu
2013-01-01
This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
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
Institute of Scientific and Technical Information of China (English)
钟卫涛; 邵之江; 张余岳; 钱积新
2000-01-01
The performance of analytical derivative and sparse matrix techniques applied to a traditional dense sequential quadratic programming (SQP) is studied, and the strategy utilizing those techniques is also presented.Computational results on two typical chemical optimization problems demonstrate significant enhancement in efficiency, which shows this strategy is promising and suitable for large-scale process optimization problems.
Directory of Open Access Journals (Sweden)
Qu Chiwen
2016-01-01
Full Text Available The standard cuckoo search algorithm is of low accuracy and easy to fall into local optimal value in the later evolution. In this paper, an improved cuckoo algorithm is proposed. Dynamic change of parameter of probability is introduced to improve the convergence speed. Complex method is quoted to improve the capabilities of local search algorithm. A non-fixed multi-segment mapping penalty function is adopted to realize constraint processing algorithms. The results of the optimization problem constrained by standard test functions and two engineering design show that this algorithm is effective for solving constrained optimization problems and suitable for engineering design and other constrained optimization problems.
DEFF Research Database (Denmark)
Sidky, Emil Y.; Jørgensen, Jakob Heide; Pan, Xiaochuan
2012-01-01
The primal–dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1–26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems...... for the purpose of designing iterative image reconstruction algorithms for CT. The primal–dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application...... modeling breast CT with low-intensity x-ray illumination is presented....
Topology optimization of unsteady flow problems using the lattice Boltzmann method
DEFF Research Database (Denmark)
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....
A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems
Ali, Hegagi M.; Pereira, Fernando Lobo; Gama, Sílvio M. A.
2016-09-01
In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo sense. We use a new approach to prove necessary conditions of optimality in the form of Pontryagin maximum principle for fractional nonlinear optimal control problems. Moreover, a new method based on a generalization of the Mittag-Leffler function is used to solving this class of fractional optimal control problems. A simple example is provided to illustrate the effectiveness of our main result.
Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance
Bonnard, B; Glaser, S J; Lapert, M; Sugny, D; Zhang, Y
2012-01-01
The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.
稻垣, 陽介; イナガキ, ヨウスケ; Yousuke, Inagaki
2007-01-01
The efficiency of Monte Carlo simulated annealing algorithm based on the generalized statistics of Tsallis (GSA) is compared with conventional simulated annealing (CSA) based on Boltzmann-Gibbs statistics. Application to the discrete-time optimal growth problem demonstrates that the replacement of CSA by GSA has the potential to speed up optimizations with no loss of accuracy in finding optimal policy function.
An interpretation of the Gini coefficient in a Stiglitz two-type optimal tax problem
DEFF Research Database (Denmark)
Rasmussen, Bo Sandemann
2015-01-01
In a two-type Stiglitz (1982) model of optimal non-linear taxation it is shown that when the utility function relating to consumption is logaritmic the shadow price of the incentive constraint relating to the optimal tax problem exactly equals the Gini coefficient of the second-best optimal income...
An Interpretation of the Gini Coefficient in a Stiglitz Two-Type Optimal Tax Problem
DEFF Research Database (Denmark)
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...
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…
Ghoniem, Ahmed
2007-01-01
This dissertation addresses the development of enhanced formulations for minimax and mixed-integer programming models for certain industrial and logistical systems, along with the design and implementation of efficient algorithmic strategies. We first examine the general class of minimax mixed-integer 0-1 problems of the type that frequently arise in decomposition approaches and in a variety of location and scheduling problems. We conduct an extensive polyhedral analysis of this problem in o...
Muhammad Farhan Ausaf; Liang Gao; Xinyu Li; Ghiath Al Aqel
2015-01-01
Process planning and scheduling are two important components of a manufacturing setup. It is important to integrate them to achieve better global optimality and improved system performance. To find optimal solutions for integrated process planning and scheduling (IPPS) problem, numerous algorithm-based approaches exist. Most of these approaches try to use existing meta-heuristic algorithms for solving the IPPS problem. Although these approaches have been shown to be effective in optimizing th...
Institute of Scientific and Technical Information of China (English)
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.
Second-order cone programming formulations for a class of problems in structural optimization
Makrodimopoulos, A.; A. Bhaskar; Keane, A.J.
2010-01-01
This paper provides efficient and easy to implement formulations for two problems in structural optimization as second-order cone programming (SOCP) problems based on the minimum compliance method and derived using the principle of complementary energy. In truss optimization both single and multiple loads (where we optimize the worst-case compliance) are considered. By using a heuristic which is based on the SOCP duality we can consider a simple ground structure and...
Optimization of travel salesman problem using the ant colony system and Greedy search
International Nuclear Information System (INIS)
In this paper we present some results obtained during the development of optimization systems that can be used to design refueling and patterns of control rods in a BWR. These systems use ant colonies and Greedy search. The first phase of this project is to be familiar with these optimization techniques applied to the problem of travel salesman problem (TSP). The utility of TSP study is that, like the refueling design and pattern design of control rods are problems of combinative optimization. Even, the similarity with the problem of the refueling design is remarkable. It is presented some results for the TSP with the 32 state capitals of Mexico country. (Author)
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.
A Hybrid Intelligent Algorithm for Optimal Birandom Portfolio Selection Problems
Directory of Open Access Journals (Sweden)
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.
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.
Directory of Open Access Journals (Sweden)
R. Berdysheva
1998-03-01
Full Text Available Lower bounds of stability, pseudostability and quasistability radii of lexicographic set in vector combinatorial problem on systems of subsets of finite set with partial criteria of more general kinds have been found.
On some fundamental properties of structural topology optimization problems
DEFF Research Database (Denmark)
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...
Topology optimization of mass distribution problems in Stokes flow
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Berggren, Martin; Dammann, Bernd
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...
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
Some Results on Optimal Dividend Problem in Two Risk Models
Directory of Open Access Journals (Sweden)
Shuaiqi Zhang
2010-12-01
Full Text Available The compound Poisson risk model and the compound Poisson risk model perturbed by diffusion are considered in the presence of a dividend barrier with solvency constraints. Moreover, it extends the known result due to [1]. Ref. [1] finds the optimal dividend policy is of a barrier type for a jump-diffusion model with exponentially distributed jumps. In this paper, it turns out that there can be two different solutions depending on the model’s parameters. Furthermore, an interesting result is given: the proportional transaction cost has no effect on the dividend barrier. The objective of the corporation is to maximize the cumulative expected discounted dividends payout with solvency constraints before the time of ruin. It is well known that under some reasonable assumptions, optimal dividend strategy is a barrier strategy, i.e., there is a level b_{1}(b_{2} so that whenever surplus goes above the level b_{1}(b_{2}, the excess is paid out as dividends. However, the optimal level b_{1}(b_{2} may be unacceptably low from a solvency point of view. Therefore, some constraints should imposed on an insurance company such as to pay out dividends unless the surplus has reached a level b^{1}_{c}>b_{1}(b^2_{c}>b_{2} . We show that in this case a barrier strategy at b^{1}_{c}(b^2_{c} is optimal.
Why Scientists Chase Big Problems: Individual Strategy and Social Optimality
Bergstrom, Carl T.; Foster, Jacob G.; Song, Yangbo
2016-01-01
Scientists pursue collective knowledge, but they also seek personal recognition from their peers. When scientists decide whether or not to work on a big new problem, they weigh the potential rewards of a major discovery against the costs of setting aside other projects. These self-interested choices can potentially spread researchers across problems in an efficient manner, but efficiency is not guaranteed. We use simple economic models to understand such decisions and their collective consequ...
Grammatical evolution hyper-heuristic for combinatorial optimization problems
Sabar, Nasar; Ayob, Masri; Kendall, Graham; Qu, Rong
2013-01-01
Designing generic problem solvers that perform well across a diverse set of problems is a challenging task. In this work, we propose a hyper-heuristic framework to automatically generate an effective and generic solution method by utilizing grammatical evolution. In the proposed framework, grammatical evolution is used as an online solver builder, which takes several heuristic components (e.g., different acceptance criteria and different neighborhood structures) as inputs and evolves template...
Value-At-Risk Optimal Policies for Revenue Management Problems
Koenig, M; Meissner, J
2010-01-01
Consider a single-leg dynamic revenue management problem with fare classes controlled by capacity in a risk-averse setting. The revenue management strategy aims at limiting the down-side risk, and in particular, value-at-risk. A value-at-risk optimised policy offers an advantage when considering applications which do not allow for a large number of reiterations. They allow for specifying a confidence level regarding undesired scenarios. We state the underlying problem as a Markov decision pro...
EXISTENCE OF 0-1 UNIVERSAL MINIMAL TOTAL DOMINATING FUNCTIONS
Institute of Scientific and Technical Information of China (English)
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.
Kamil, Anton A.; Adli Mustafa; Khlipah Ibrahim
2009-01-01
Problem statement: The most important character within optimization problem is the uncertainty of the future returns. Approach: To handle such problems, we utilized probabilistic methods alongside with optimization techniques. We developed single stage and two stage stochastic programming with recourse. The models were developed for risk adverse investors and the objective of the stochastic programming models is to minimize the maximum downside semi deviation. We used the so-called Here-and-N...
On relaxation of state-constrained optimal control problem in coefficients for biharmonic equation
Directory of Open Access Journals (Sweden)
P. I. Kogut
2015-01-01
Full Text Available We study a Dirichlet optimal control problem for biharmonic equation withcontrol and state constraints. The coecient of the biharmonic operator, the weightu, we take as a control in L1(Ω. We discuss the relaxation approach and show thatsome optimal solutions to the original problem can be attained in the limit byoptimal solutions of some extremal problem for variational inequality with a specialpenalized cost functional.
Optimal solution of investment problems via linear parabolic equations generated by Kalman filter
Nikolai Dokuchaev
2008-01-01
We consider optimal investment problems for a diffusion market model with non-observable random drifts that evolve as an Ito's process. Admissible strategies do not use direct observations of the market parameters, but rather use historical stock prices. For a non-linear problem with a general performance criterion, the optimal portfolio strategy is expressed via the solution of a scalar minimization problem and a linear parabolic equation with coefficients generated by the Kalman filter.
Chebyshev Finite Difference Method for Solving Constrained Quadratic Optimal Control Problems
M Maleki; M. Dadkhah Tirani
2011-01-01
. In this paper the Chebyshev finite difference method is employed for finding the approximate solution of time varying constrained optimal control problems. This approach consists of reducing the optimal control problem to a nonlinear mathematical programming problem. To this end, the collocation points (Chebyshev Gauss-Lobatto nodes) are introduced then the state and control variables are approximated using special Chebyshev series with unknown parameters. The performan...
Zhang, Gexiang; Cheng, Jixiang; Gheorghe, Marian; Research Group on Natural Computing (Universidad de Sevilla) (Coordinador)
2010-01-01
This paper proposes an approximate optimization algorithm combining P systems with ant colony optimization, called ACOPS, to solve traveling salesman prob- lems, which are well-known and extensively studied NP-complete combinatorial optimization problems. ACOPS uses the pheromone model and pheromone update rules defined by ant colony optimization algorithms, and the hierarchical membrane structure and transformation/communication rules of P systems. First, the parameter setting of...
An Optimal Stopping Problem in Dynamic Fuzzy Systems with Fuzzy Rewards
Yoshida, Yuji
1995-01-01
This paper deals with an optimal stopping problem in dynamic fuzzy systems with fuzzy rewards, and shows that the optimal discounted fuzzy reward is characterized by a unique solution of a fuzzy relational equation. We define a fuzzy expectation with a density given by fuzzy goals and we estimate discounted fuzzy rewads by the fuzzy expectation. This paper characterizes the optimal fuzzy expected value and gives an optimal stopping time.
Directory of Open Access Journals (Sweden)
Pintu Das
2015-09-01
Full Text Available Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. The paper aims to give computational algorithm to solve a multi-objective non-linear programming problem (MONLPP using neutrosophic optimization method. The proposed method is for solving MONLPP with single valued neutrosophic data. We made a comparative study of optimal solution between intuitionistic fuzzy and neutrosophic optimization technique. The developed algorithm has been illustrated by a numerical example. Finally, optimal riser design problem is presented as an application of such technique.
Optimization approaches for treating nuclear power plant problems
International Nuclear Information System (INIS)
Electricity generation is the process of generating electric energy from other forms of energy. There are many technologies that can be and are used to generate electricity. One of these technologies is the nuclear power. A nuclear power plant (NPP) is a thermal power station in which the heat source is one or more nuclear reactors. As in a conventional thermal power station the heat is used to generate steam which drives a steam turbine connected to a generator which produces electricity. As of February 2nd, 2012, there were 439 nuclear power plants in operation through the world. NPP are usually considered to be base load stations, which are best suited to constant power output. The thesis consists of five chapters: Chapter I presents a survey on some important concepts of the NPP problems. Chapter II introduces the economic future of nuclear power. It presents nuclear energy scenarios beyond 2015, market potential for electricity generation to 2030 and economics of new plant construction. Chapter III presents a reliability centered problem of power plant preventive maintenance scheduling. NPP preventive maintenance scheduling problem with fuzzy parameters in the constraints is solved. A case study is provided to demonstrate the efficiency of proposed model. A comparison study between the deterministic case and fuzzy case for the problem of concern is carried out. Chapter IV introduces a fuzzy approach to the generation expansion planning problem (GEP) in a multiobjective environment. The GEP problem as an integer programming model with fuzzy parameters in the constraints is formulated. A parametric study is carried out for the GEP problem. A case study is provided to demonstrate the efficiency of our proposed model. A comparison study between our approach and the deterministic one is made. Chapter V is concerned with the conclusions arrived in carrying out this thesis and gives some suggestions for further research.
Solving function optimization problems with the immune principle
Institute of Scientific and Technical Information of China (English)
左兴权; 李士勇
2004-01-01
Adaptive immune evolutionary algorithm is proposed based on the principle of adaptive immune response. Two new algorithm parameters of expansion radius and mutation radius are defined to construct a small neighborhood and a large neighborhood, then expansion and mutation operations are designed to search the local and global regions of solution space simultaneously by using the two neighborhoods, thus, two-level neighborhood search mechanism is realized. The degree of the diversity in the population is described with the average Euclideandistance among all individuals, and it is used to adjust algorithm parameters adaptively to accelerate convergence and avoid getting stuck at local optima. The algorithm is proved to be convergent and its optimization principle is analyzed. The experiment results of multi-modal function optimization show that the algorithm is effective.
Optimal anisotropic three-phase conducting composites: Plane problem
Cherkaev, Andrej
2010-01-01
The paper establishes tight lower bound for effective conductivity tensor $K_*$ of two-dimensional three-phase conducting anisotropic composites and defines optimal microstructures. It is assumed that three materials are mixed with fixed volume fractions and that the conductivity of one of the materials is infinite. The bound expands the Hashin-Shtrikman and Translation bounds to multiphase structures, it is derived using the technique of {\\em localized polyconvexity} that is a combination of Translation method and additional inequalities on the fields in the materials; similar technique was used by Nesi (1995) and Cherkaev (2009) for isotropic multiphase composites. This paper expands the bounds to the anisotropic composites. The lower bound of conductivity (G-closure) is a piece-wise analytic function of eigenvalues of $K_*$, that depends only on conductivities of components and their volume fractions. Also, we find optimal microstructures that realize the bounds, developing the technique suggested earlier ...
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.
Andreica, Mugurel Ionut
2010-01-01
In this paper we present novel algorithmic solutions for several resource processing and data transfer multicriteria optimization problems. The results of most of the presented techniques are strategies which solve the considered problems (almost) optimally. Thus, the developed algorithms construct intelligent strategies which can be implemented by agents in specific situations. All the described solutions make use of the properties of the considered problems and, thus, they are not applicable to a very general class of problems. However, by considering the specific details of each problem, we were able to obtain very efficient results.
Optimization of the drayage problem using exact methods
DEFF Research Database (Denmark)
Reinhardt, Line Blander; Pisinger, David; Spoorendonk, Simon;
2016-01-01
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......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....... 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...
A HIGH PERFORMANCE OPTIMIZATION TECHNIQUE FOR POLE BALANCING PROBLEM
Directory of Open Access Journals (Sweden)
Bahadır KARASULU
2008-02-01
Full Text Available High performance computing techniques can be used effectively for solution of the complex scientific problems. Pole balancing problem is a basic benchmark tool of robotic field, which is an important field of Artificial Intelligence research areas. In this study, a solution is developed for pole balancing problem using Artificial Neural Network (ANN and high performance computation technique. Algorithm, that basis of the Reinforcement Learning method which is used to find the force of pole's balance, is transfered to parallel environment. In Implementation, C is preferred as programming language and Message Passing Interface (MPI is used for parallel computation technique. Self–Organizing Map (SOM ANN model's neurons (artificial neural nodes and their weights are distributed to six processors of a server computer which equipped with each quad core processor (total 24 processors. In this way, performance values are obtained for different number of artificial neural nodes. Success of method based on results is discussed.
Optimization of the imported air express cargo distribution problem
Directory of Open Access Journals (Sweden)
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.
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...
On Compliance and Buckling Objective Functions in Topology Optimization of Snap-Through Problems
DEFF Research Database (Denmark)
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...... 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...... of the analysis method and optimization formulation. We apply a nonlinear path tracing algorithm capable of detecting different types of stability points and an optimization formulation that handles possible mode switching. This is an extension into the topology optimization realm of a method developed, and used...
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...
Optimal capital structure: Problems with the Harvard and Damodaran Approaches
Fernadez, Pablo
2002-01-01
In this paper we will present an analysis of the optimal capital structure using two examples: one proposed by the Harvard Business School and the other proposed by Damodaran. First, we highlight certain inconsistencies in the debt and equity costs assumed by the Harvard Business School note from a number of viewpoints. We calculate the incremental cost of debt implied in Harvard's note and we find also inconsistencies: surprisingly, the last two debt increments have a cost of 14.75% and 18.5...
Optimization problems of the third edge-connectivity of graphs
Institute of Scientific and Technical Information of China (English)
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.
Generalized monotonically convergent algorithms for solving quantum optimal control problems
Ohtsuki, Yukiyoshi; Turinici, Gabriel; Rabitz, Herschel
2004-03-01
A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to "trapping" and that relaxation processes may remove such unfavorable behavior.
Optimization and Reliability Problems in Structural Design of Wind Turbines
DEFF Research Database (Denmark)
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...
Fish School Search Algorithm for Solving Optimal Reactive Power Dispatch Problem
Directory of Open Access Journals (Sweden)
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.
A Uniaxial Optimal Perfectly Matched Layer Method for Time-harmonic Scattering Problems
Institute of Scientific and Technical Information of China (English)
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.
Selvi, V; Dr. R. Umarani
2012-01-01
- SI is a computational and collective behavioral metaphor that is used for solving problems. The problems can be solved by SI by taking ants, termites, bees and wasps as an example. The application of SI algorithm are ACO, PSO and ABC which have been already applied to solve real world optimization problems in engineering. ACO is a member of SI in which ACO is inspired by the behaviour of ant colonies and it constitutes some metaheuristic optimization. ACO’s aim is to search for an optimal p...
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.
SOLVING TRUST REGION PROBLEM IN LARGE SCALE OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Bing-sheng He
2000-01-01
This paper presents a new method for solving the basic problem in the “model trust region” approach to large scale minimization: Compute a vector x such that 1/2xTHx + cTx = min, subject to the constraint ‖x‖2≤a. The method is a combination of the CG method and a projection and contraction (PC) method. The first (CG) method with x0 = 0 as the start point either directly offers a solution of the problem, or--as soon as the norm of the iterate greater than a, --it gives a suitable starting point and a favourable choice of a crucial scaling parameter in the second (PC) method. Some numerical examples are given, which indicate that the method is applicable.
Optimal calculational schemes for solving multigroup photon transport problem
International Nuclear Information System (INIS)
A scheme of complex algorithm for solving multigroup equation of radiation transport is suggested. The algorithm is based on using the method of successive collisions, the method of forward scattering and the spherical harmonics method, and is realized in the FORAP program (FORTRAN, BESM-6 computer). As an example the results of calculating reactor photon transport in water are presented. The considered algorithm being modified may be used for solving neutron transport problems
Solving inverse problems in imaging using robust and regularized optimization
Gonzalez Gonzalez, Adriana
2016-01-01
Digital images play an important role in human life since they allow observing, analyzing, studying and characterizing the world surrounding us. Their use is ubiquitous in many applications such as medicine, biology, astronomy and industrial manufacture. Nonetheless, the desired digital images are often not available and need to be recovered from corrupted, incomplete and/or indirect observations. Determining the unknown image from the available observations is called an inverse problem. In t...
Stochastic optimization models for a single-sink transportation problem
Maggioni, Francesca; Kaut, Michal; Bertazzi, Luca
2008-01-01
In this paper we study a single-sink transportation problem in which the production capacity of the suppliers and the demand of the single customer are stochastic. Shipments are performed by capacitated vehicles, which have to be booked in advance, before the realization of the production capacity and the demand. Once the production capacity and the demand are revealed, there is an option to cancel some of the booked vehicles against a cancellation fee. If the quantity shipped from the suppli...
Optimization Problem of a Sea vehicle Entry into Water
Directory of Open Access Journals (Sweden)
S. K. Gurtu
1994-07-01
Full Text Available For a vehicle diving into the sea, the variation of velocity with horizontal distance covered was studied, the conditions being that the vehicle requires minimum time and that the horizontal distance is fixed. The variation of the vehicle's trajectory angle and time versus depth was also investigated. The variational problem makes use of the isoperimetric condition. The second-order differential equation was solved by the Runge-Kutta-Nystrom. method and the isoperimetric condition by Simpson's rule.
The berth allocation problem: Optimizing vessel arrival time
Mihalis M Golias; Georgios K Saharidis; Maria Boile; Sotirios Theofanis; Ierapetritou, Marianthi G.
2009-01-01
The berth scheduling problem deals with the assignment of vessels to berths in a marine terminal, with the objective to maximize the ocean carriers’ satisfaction (minimize delays) and/or minimize the terminal operator's costs. In the existing literature, two main assumptions are made regarding the status of a vessel: (a) either all vessels to be served are already in the port before the planning period starts, or (b) they are scheduled to arrive after the planning period starts. The latter ca...
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.
Institute of Scientific and Technical Information of China (English)
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.
Kim, Yong Yook
2004-01-01
The objective of this work was to employ artificial neural networks (NN) to solve inverse problems in different engineering fields, overcoming various obstacles in applying NN to different problems and benefiting from the experience of solving different types of inverse problems. The inverse problems investigated are: 1) damage detection in structures, 2) detection of an anomaly in a light-diffusive medium, such as human tissue using optical imaging, 3) structural optimization of fiber optic ...
A new evolutionary algorithm with LQV learning for combinatorial problems optimization
International Nuclear Information System (INIS)
Genetic algorithms are biologically motivated adaptive systems which have been used, with good results, for combinatorial problems optimization. In this work, a new learning mode, to be used by the population-based incremental learning algorithm, has the aim to build a new evolutionary algorithm to be used in optimization of numerical problems and combinatorial problems. This new learning mode uses a variable learning rate during the optimization process, constituting a process known as proportional reward. The development of this new algorithm aims its application in the optimization of reload problem of PWR nuclear reactors, in order to increase the useful life of the nuclear fuel. For the test, two classes of problems are used: numerical problems and combinatorial problems. Due to the fact that the reload problem is a combinatorial problem, the major interest relies on the last class. The results achieved with the tests indicate the applicability of the new learning mode, showing its potential as a developing tool in the solution of reload problem. (author)
Newton-type method for the variational discretization of topology optimization problems
DEFF Research Database (Denmark)
Evgrafov, Anton
2013-01-01
We present a locally quadratically convergent optimization algorithm for solving topology optimization problems. The distinguishing feature of the algorithm is to treat the design as a smooth function of the state and not vice versa as in the traditional nested approach to topology optimization......, which we achieve by inverting a part of perturbed optimality conditions for the problem. In this way, the computational bottleneck is conveniently shifted from evaluating the merit function to a direction finding subproblem. The latter involves solving certain linearized PDEs, and the computational...... effort is similar to that of finding a gradient of the merit function in the traditional nested approach. We illustrate the performance of the algorithm on benchmark topology optimized problems in fluid mechanics....
DEFF Research Database (Denmark)
Vesterstrøm, Jacob Svaneborg; Thomsen, Rene
2004-01-01
Several extensions to evolutionary algorithms (EAs) and particle swarm optimization (PSO) have been suggested during the last decades offering improved performance on selected benchmark problems. Recently, another search heuristic termed differential evolution (DE) has shown superior performance...
Directory of Open Access Journals (Sweden)
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.
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.
GLOBAL OPTIMIZATION OF PUMP CONFIGURATION PROBLEM USING EXTENDED CROWDING GENETIC ALGORITHM
Institute of Scientific and Technical Information of China (English)
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.
Directory of Open Access Journals (Sweden)
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.
Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer
Miele, A.; Basapur, V. K.
1984-01-01
The maneuver considered in the present investigation involves the coplanar transfer of a spacecraft from a high earth orbit (HEO) to a low earth orbit (LEO). HEO can be a geosynchronous earth orbit (GEO). The basic concept utilized involves the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. The considered type of flight is also called synergetic space flight. With respect to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The Bolza problem of optimal control is stated, and the first-order optimality conditions for this problem are given. The one-arc approach, the two-arc approach, and the three-subarc approach are discussed. Attention is given to the Chebyshev problem of optimal control, details concerning aeroassisted orbital transfer (AOT), AOT optimization problems, and numerical experiments.
An adaptive ant colony system algorithm for continuous-space optimization problems
Institute of Scientific and Technical Information of China (English)
李艳君; 吴铁军
2003-01-01
Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates. Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved.
An adaptive ant colony system algorithm for continuous-space optimization problems
Institute of Scientific and Technical Information of China (English)
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.
Approximation methods of mixed l 1/H2 optimization problems for MIMO discrete-time systems
Institute of Scientific and Technical Information of China (English)
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.
On the Limit Matrix Obtained in the Homogenization of an Optimal Control Problem
Indian Academy of Sciences (India)
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).
Implementation of genetic algorithm technique for solving ROP detector layout optimization problem
International Nuclear Information System (INIS)
The regional overpower protection (ROP) systems protect CANDU® reactors against overpower in the fuel that could reduce the safety margin-to-dryout. The overpower could originate from localized power peaking within the core or a general increase in the core power level. The design of the detector layout for the ROP systems is a challenging discrete optimization problem. In recent years, two algorithms have been developed to find a quasi-optimal solution to this detector layout optimization problem. Both of these algorithms utilize the simulated annealing (SA) algorithm as their optimization engine. In the present paper, an alternative optimization algorithm, namely the genetic algorithm (GA), has been implemented as the optimization engine. The implementation is done within the ADORE algorithm. Based on this preliminary studies performed on four different sizes of ROP system, it has been demonstrated that the GA technique is able to produce good results. (author)
Manapova, Aigul
2016-08-01
We consider optimal control problems for second order elliptic equations with non-self-adjoint operators-convection-diffusion problems. Control processes are described by semi-linear convection-diffusion equation with discontinuous data and solutions (states) subject to the boundary interface conditions of imperfect type (i.e., problems with a jump of the coefficients and the solution on the interface; the jump of the solution is proportional to the normal component of the flux). Controls are involved in the coefficients of diffusion and convective transfer. We prove differentiability and Lipshitz continuity of the cost functional, depending on a state of the system and a control. The calculation of the gradients uses the numerical solutions of direct problems for the state and adjoint problems.
Liang, J J; Song, H; B. Y. Qu; Liu, Z. F.
2014-01-01
In path planning problems, the most important task is to find a suitable collision-free path which satisfies some certain criteria (the shortest path length, security, feasibility, smoothness, and so on), so defining a suitable curve to describe path is essential. Three different commonly used curves are compared and discussed based on their performance on solving a set of path planning problems. Dynamic multiswarm particle swarm optimizer is employed to optimize the necessary parameters for ...
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
Hybrid constraint programming and metaheuristic methods for large scale optimization problems
Parisini, Fabio
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...
On the smooth-fit property for one-dimensional optimal switching problem
Pham, Huyen
2004-01-01
This paper studies the problem of optimal switching for one-dimensional diffusion, which may be regarded as sequential optimal stopping problem with changes of regimes. The resulting dynamic programming principle leads to a system of variational inequa-lities, and the state space is divided into continuation regions and switching regions. By means of viscosity solutions approach, we prove the smoot-fit $C^1$ property of the value functions.
Km. Shweta; Alka Singh
2013-01-01
Ant Colony optimization has proved suitable to solve a wide range of combinatorial optimization(or NP-hard) problems as the Travelling Salesman Problem (TSP). The first step of ACO algorithm is to setthe parameters that drive the algorithm. The parameter has an important impact on the performance of theant colony algorithm. The basic parameters that are used in ACO algorithms are; the relative importance (orweight) of pheromone, the relative importance of heuristics value, initial pheromone v...
UFO: Uncertainty Feature Optimization, an Implicit Paradigm for Problems with Noisy Data
Eggenberg, Niklaus; Salani, Matteo; Bierlaire, Michel
2008-01-01
Optimization problems due to noisy data solved using stochastic programming or robust optimization approaches require the explicit characterization of an uncertainty set U that models the nature of the noise. Such approaches depend on the modeling of the uncertainty set and suffer from an erroneous estimation of the noise. In this paper, we introduce a framework that considers the uncertain data implicitly. We define the concept of Uncertainty Features (UF), which are problem-specific struct...
New algorithms for some NP-optimization problems by DNA computing
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
There are lots of DNA computation models now. The model developed by Martyn Amos' group is special in its error-resistant property, but unfortunately, its computational power is limited and cannot solve optimization problems efficiently. In this paper, some new methods have been introduced to enlarge the computational power of this model. And based on these new methods, several DNA algorithms have been designed to solve some NP-optimization problems such as minimal vertex cover, maximal clique and MAX-3SAT.
Ant Colony Optimization ACO For The Traveling Salesman Problem TSP Using Partitioning
Alok Bajpai; Raghav Yadav
2015-01-01
Abstract An ant colony optimization is a technique which was introduced in 1990s and which can be applied to a variety of discrete combinatorial optimization problem and to continuous optimization. The ACO algorithm is simulated with the foraging behavior of the real ants to find the incremental solution constructions and to realize a pheromone laying-and-following mechanism. This pheromone is the indirect communication among the ants. In this paper we introduces the partitioning technique ba...
MPI parallel programming of mixed integer optimization problems using CPLEX with COIN-OR
Aldasoro Marcellan, Unai; Garín Martín, María Araceli; Merino Maestre, María; Pérez Sainz de Rozas, Gloria
2012-01-01
The aim of this technical report is to present some detailed explanations in order to help to understand and use the Message Passing Interface (MPI) parallel programming for solving several mixed integer optimization problems. We have developed a C++ experimental code that uses the IBM ILOG CPLEX optimizer within the COmputational INfrastructure for Operations Research (COIN-OR) and MPI parallel computing for solving the optimization models under UNIX-like systems. The computational experienc...
Predatory Search Strategy Based on Swarm Intelligence for Continuous Optimization Problems
Wang, J. W.; H. F. Wang; Ip, W. H.; Furuta, K; Kanno, T.; Zhang, W. J.
2013-01-01
We propose an approach to solve continuous variable optimization problems. The approach is based on the integration of predatory search strategy (PSS) and swarm intelligence technique. The integration is further based on two newly defined concepts proposed for the PSS, namely, “restriction” and “neighborhood,” and takes the particle swarm optimization (PSO) algorithm as the local optimizer. The PSS is for the switch of exploitation and exploration (in particular by the adjustment of neighborh...
A Simulation-Based Optimization Approach for Integrated Port Resource Allocation Problem
Ilati, Gholamreza; Sheikholeslami, Abdorreza; Hassannayebi, Erfan
2014-01-01
Todays, due to the rapid increase in shipping volumes, the container terminals are faced with the challenge to cope with these increasing demands. To handle this challenge, it is crucial to use flexible and efficient optimization approach in order to decrease operating cost. In this paper, a simulation-based optimization approach is proposed to construct a near-optimal berth allocation plan integrated with a plan for tug assignment and for resolution of the quay crane re-allocation problem. ...
A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet
Directory of Open Access Journals (Sweden)
Boualem Djehiche
2014-01-01
a two-mode optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy.
A Multi-Model Reduction Technique for Optimization of Coupled Structural-Acoustic Problems
DEFF Research Database (Denmark)
Creixell Mediante, Ester; Jensen, Jakob Søndergaard; Brunskog, Jonas;
2016-01-01
Finite Element models of structural-acoustic coupled systems can become very large for complex structures with multiple connected parts. Optimization of the performance of the structure based on harmonic analysis of the system requires solving the coupled problem iteratively and for several frequ....... Several methods are compared in terms of accuracy and size of the reduced systems for optimization of simple models....
A new solving procedure by m-M calculus for problems of constrained optimization
Directory of Open Access Journals (Sweden)
Prešić Slaviša
2007-01-01
Full Text Available In this paper we state two procedures for constrained optimization based on the concepts of m-M Calculus. The first procedure is called basic and the second is called quick solving procedure. The quick solving procedure is very effective. It can also be applied to problems of unconstrained optimization. .
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.
Using Bee Colony Optimization to Solve the Task Scheduling Problem in Homogenous Systems
Directory of Open Access Journals (Sweden)
Vahid Arabnejad
2011-09-01
Full Text Available Bee colony optimization (BCO is one of the most recent algorithms in swarm intelligence that can be used in optimization problems this algorithm is based on the intelligent behavior of honey bees in foraging process. In this paper bee colony optimization is applied to solve the task scheduling problem which tasks have dependency with each other. Scheduling of tasks that represents by directed acyclic graph is a NP-complete problem. The main purpose of this problem is obtaining the minimum schedule length that is called make-span. To realize the performance of BCO in this problem, the obtained results are presented and compared with the most successful methods such as Ant colony system, Tabu search and simulate annealing. The comparison shows that BCO produces the solutions in a different way and it is still among the bests.
Hybrid Method for a Class of Stochastic Bi-criteria Optimization Problems
Directory of Open Access Journals (Sweden)
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.
Deterministic Time-inconsistent Optimal Control Problems - an Essentially Cooperative Approach
Institute of Scientific and Technical Information of China (English)
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.
New Meta-Heuristic for Combinatorial Optimization Problems:Intersection Based Scaling
Institute of Scientific and Technical Information of China (English)
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.
Conceptual design optimization of rectilinear building frames: A knapsack problem approach
Sharafi, Pezhman; Teh, Lip H.; Hadi, Muhammad N. S.
2015-10-01
This article presents an automated technique for preliminary layout (conceptual design) optimization of rectilinear, orthogonal building frames in which the shape of the building plan, the number of bays and the size of unsupported spans are variables. It adopts the knapsack problem as the applied combinatorial optimization problem, and describes how the conceptual design optimization problem can be generally modelled as the unbounded multi-constraint multiple knapsack problem. It discusses some special cases, which can be modelled more efficiently as the single knapsack problem, the multiple-choice knapsack problem or the multiple knapsack problem. A knapsack contains sub-rectangles that define the floor plan and the location of columns. Particular conditions or preferences for the conceptual design can be incorporated as constraints on the knapsacks and/or sub-rectangles. A bi-objective knapsack problem is defined with the aim of obtaining a conceptual design having minimum cost and maximum plan regularity (minimum structural eccentricity). A multi-objective ant colony algorithm is formulated to solve the combinatorial optimization problem. A numerical example is included to demonstrate the application of the present method and the robustness of the algorithm.
Spin analysis of 0+1→0+1 and its application to π+d→π+d data
International Nuclear Information System (INIS)
The polarization structure of the reaction 0+1→0+1 is discussed in the optimal transversity frame. First, the relationship between the observables and the bilinear products of amplitudes (''bicoms'') is given when only Lorentz invariance is imposed. Then parity conservation and time-reversal invariance are also imposed, resulting in modified relationships. The measurements of spin correlations between initial- and final-state spins needed to determine the amplitudes completely are enumerated. The results are applied to the existing π-d data, and the consequences of any possible dibaryon resonances are examined
Spin analysis of 0+1-->0+1 and its application to π+d-->π+d data
Arash, Firooz; Moravcsik, Michael J.; Goldstein, Gary R.
1985-11-01
The polarization structure of the reaction 0+1-->0+1 is discussed in the optimal transversity frame. First, the relationship between the observables and the bilinear products of amplitudes (``bicoms'') is given when only Lorentz invariance is imposed. Then parity conservation and time-reversal invariance are also imposed, resulting in modified relationships. The measurements of spin correlations between initial- and final-state spins needed to determine the amplitudes completely are enumerated. The results are applied to the existing π-d data, and the consequences of any possible dibaryon resonances are examined.
DEFF Research Database (Denmark)
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...
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
Optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian
Yang, Ray
2011-01-01
We discuss the optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian. This work is related to, but addresses a different problem from, recent work of Caffarelli, Roquejoffre, and Sire. A variant of the boundary Harnack inequality is also proved, where it is no longer required that the function be 0 along the boundary.
Topology optimization of heat conduction problems using the finite volume method
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole
2006-01-01
This note addresses the use of the finite volume method (FVM) for topology optimization of a heat conduction problem. Issues pertaining to the proper choice of cost functions, sensitivity analysis and example test problems are used to illustrate the effect of applying the FVM as an analysis tool...
Linearization of a Matrix Riccati Equation Associated to an Optimal Control Problem
Directory of Open Access Journals (Sweden)
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.
On solving discrete optimization problems with one random element under general regret functions
Ghosh, D.; Mandal, P.K.; Das, S.
2005-01-01
In this paper we consider the class of stochastic discrete optimization problems in which the feasibility of a solution does not depend on the particular values the random elements in the problem take. Given a regret function, we introduce the concept of the risk associated with a solution, and defi
Biswas, Md. Haider Ali; de Pinho, Maria do Rosario
2013-01-01
Here we derive a nonsmooth maximum principle for optimal control problems with both state and mixed constraints. Crucial to our development is a convexity assumption on the "velocity set". The approach consists of applying known penalization techniques for state constraints together with recent results for mixed constrained problems.
Analysis of Ant Colony Optimization and Population-Based Evolutionary Algorithms on Dynamic Problems
DEFF Research Database (Denmark)
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...
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.
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.
An Adaptive Finite Element Method Based on Optimal Error Estimates for Linear Elliptic Problems
Institute of Scientific and Technical Information of China (English)
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.
Directory of Open Access Journals (Sweden)
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.
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.
Institute of Scientific and Technical Information of China (English)
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.
Directory of Open Access Journals (Sweden)
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.
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...
CCBlade Documentation: Release 0.1.0
Energy Technology Data Exchange (ETDEWEB)
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.
Directory of Open Access Journals (Sweden)
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.
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.
Chebyshev Finite Difference Method for Solving Constrained Quadratic Optimal Control Problems
Directory of Open Access Journals (Sweden)
M. Maleki*
2011-06-01
Full Text Available . In this paper the Chebyshev finite difference method is employed for finding the approximate solution of time varying constrained optimal control problems. This approach consists of reducing the optimal control problem to a nonlinear mathematical programming problem. To this end, the collocation points (Chebyshev Gauss-Lobatto nodes are introduced then the state and control variables are approximated using special Chebyshev series with unknown parameters. The performance index is parameterized and the system dynamics and constraints are then replaced with a set of algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the technique.
A new ant colony optimization model for complex graph-based problems
González-Pardo, Antonio
2014-01-01
Tesis doctoral inédita leída en la Universidad Autónoma de Madrid. Escuela Politécnica Superior, Departamento de Ingeniería Informática. Fecha de lectura: julio de 2014 Nowadays, there is a huge number of problems that due to their complexity have employed heuristic-based algorithms to search for near-to-optimal (or even optimal) solutions. These problems are usually NP-complete, so classical algorithms are not the best candidates to address these problems because they need a larg...
Optimal control of a convective boundary condition in a thermistor problem
Energy Technology Data Exchange (ETDEWEB)
Hrynkiv, Volodymyr [Worcester Polytechnic Institute; Lenhart, Suzanne M [ORNL; Protopopescu, Vladimir A [ORNL
2008-01-01
We consider the optimal control of a two-dimensional steady-state thermistor. The problem is described by a system of two nonlinear elliptic partial differential equations with appropriate boundary conditions which model the coupling of the thermistor to its surroundings. Based on physical considerations, an objective functional to be minimized is introduced and the convective boundary coefficient is taken as the control. Existence and uniqueness of the optimal control are proven. To characterize this optimal control, the optimality system consisting of the state and adjoint equations is derived.
Measuring process solutions in a reprocessing plant to 0. 1%
Energy Technology Data Exchange (ETDEWEB)
Crawford, J.M.; Ehinger, M.H.; Ellis, J.H.
1980-03-01
Measurement of SNM in reprocessing plant solutions involves two major problems; measurement of bulk solution quantities and analysis of highly radioactive samples. It has been shown at the BNFP that bulk measurements can be made routinely under operating conditions to less than 0.1% total uncertainty. Two specific advances in measurement technology have been largely responsible for this improved performance. The quartz bourdon tube electromanometer replaces the fluid manometer for differential pressure measurements. The vibrating tube densimeter provides accurate measurement of density in lab samples. These instruments, coupled with a rigorous measurement and quality control procedures, are the means to achieve better than 0.1% performance.
Mittal, Shashi; Schulz, Andreas S.
2012-01-01
In this paper, we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination of more than one function. Examples of such problems include those in which the objective function is a product or ratio of two linear functions, parallel machine scheduling problems with the makespan objective, robust versions of weighted multiobjective optimization problems, and assortment optimization problems with logit ...
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.
A Novel Hybrid Crossover based Artificial Bee Colony Algorithm for Optimization Problem
Kumar, Sandeep; Sharma, Vivek Kumar; Kumari, Rajani
2014-01-01
Artificial bee colony (ABC) algorithm has proved its importance in solving a number of problems including engineering optimization problems. ABC algorithm is one of the most popular and youngest member of the family of population based nature inspired meta-heuristic swarm intelligence method. ABC has been proved its superiority over some other Nature Inspired Algorithms (NIA) when applied for both benchmark functions and real world problems. The performance of search process of ABC depends on...
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.
Energy Technology Data Exchange (ETDEWEB)
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.
SHAPE STABILITY OF OPTIMAL CONTROL PROBLEMS IN COEFFICIENTS FOR COUPLED SYSTEM OF HAMMERSTEIN TYPE
Directory of Open Access Journals (Sweden)
P. I. Kogut
2014-01-01
Full Text Available In this paper we consider an optimal control problem (OCP for the coupledsystem of a nonlinear monotone Dirichlet problem with matrix-valued L∞(Ω;RN×N-controls in coecients and a nonlinear equation of Hammerstein type, where solution nonlinearly depends on L∞ -control. Since problems of this type have no solutions in general, we make a special assumption on the coecients of the state equations and introduce the class of so-called solenoidal admissible controls. Using the direct method in calculus of variations, we prove the existence of an optimal control. We also study the stability of the optimal control problem with respect to the domain perturbation. In particular, we derive the sucient conditions of the Mosco-stability for the given class of OCPs.
Directory of Open Access Journals (Sweden)
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.
Pintu Das; Tapan Kumar Roy
2015-01-01
Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. The paper aims to give computational algorithm to solve a multi-objective non-linear programming problem (MONLPP) using neutrosophic optimization method. The proposed method is for solving MONLPP with single valued neutrosophic data. We mad...
A novel hybrid optimization algorithm for diferential-algebraic control problems
Directory of Open Access Journals (Sweden)
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.
Application of multi-stage Monte Carlo method for solving machining optimization problems
Directory of Open Access Journals (Sweden)
Miloš Madić
2014-08-01
Full Text Available Enhancing the overall machining performance implies optimization of machining processes, i.e. determination of optimal machining parameters combination. Optimization of machining processes is an active field of research where different optimization methods are being used to determine an optimal combination of different machining parameters. In this paper, multi-stage Monte Carlo (MC method was employed to determine optimal combinations of machining parameters for six machining processes, i.e. drilling, turning, turn-milling, abrasive waterjet machining, electrochemical discharge machining and electrochemical micromachining. Optimization solutions obtained by using multi-stage MC method were compared with the optimization solutions of past researchers obtained by using meta-heuristic optimization methods, e.g. genetic algorithm, simulated annealing algorithm, artificial bee colony algorithm and teaching learning based optimization algorithm. The obtained results prove the applicability and suitability of the multi-stage MC method for solving machining optimization problems with up to four independent variables. Specific features, merits and drawbacks of the MC method were also discussed.
A genetic algorithm for the pareto optimal solution set of multi-objective shortest path problem
Institute of Scientific and Technical Information of China (English)
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.
The Sizing and Optimization Language, (SOL): Computer language for design problems
Lucas, Stephen H.; Scotti, Stephen J.
1988-01-01
The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
Zongyuan Huang
2010-01-01
Full Text Available This paper is concerned with a kind of corporate international optimal portfolio and consumption choice problems, in which the investor can invest her or his wealth either in a domestic bond (bank account or in an oversea real project with production. The bank pays a lower interest rate for deposit and takes a higher rate for any loan. First, we show that Bellman's dynamic programming principle still holds in our setting; second, in terms of the foregoing principle, we obtain the investor's optimal portfolio proportion for a general maximizing expected utility problem and give the corresponding economic analysis; third, for the special but nontrivial Constant Relative Risk Aversion (CRRA case, we get the investors optimal investment and consumption solution; last but not least, we give some numerical simulation results to illustrate the influence of volatility parameters on the optimal investment strategy.
Institute of Scientific and Technical Information of China (English)
Danping Yang; Yanzhen Chang; Wenbin Liu
2008-01-01
In this paper,we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type,which includes some parameter estimation application.The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.We derive a priori error estimates and superconvergence analysis for both the control and the state approximations.We also give the optimal L2-norm error estimates and the almost optimal L8-norm estimates about the state and co-state.The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.
Cost-Optimal Operation of Energy Storage Units: Benefits of a Problem-Specific Approach
Siemer, Lars; Kleinhans, David
2015-01-01
The integration of large shares of electricity produced by non-dispatchable Renewable Energy Sources (RES) leads to an increasingly volatile energy generation side, with temporary local overproduction. The application of energy storage units has the potential to use this excess electricity from RES efficiently and to prevent curtailment. The objective of this work is to calculate cost-optimal charging strategies for energy storage units used as buffers. For this purpose, a new mathematical optimization method is presented that is applicable to general storage-related problems. Due to a tremendous gain in efficiency of this method compared with standard solvers and proven optimality, calculations of complex problems as well as a high-resolution sensitivity analysis of multiple system combinations are feasible within a very short time. As an example technology, Power-to-Heat converters used in combination with thermal storage units are investigated in detail and optimal system configurations, including storage ...
Directory of Open Access Journals (Sweden)
Souad Mekni
2014-11-01
Full Text Available In this paper, a modified invasive weed optimization (IWO algorithm is presented for optimization of multiobjective flexible job shop scheduling problems (FJSSPs with the criteria to minimize the maximum completion time (makespan, the total workload of machines and the workload of the critical machine. IWO is a bio-inspired metaheuristic that mimics the ecological behaviour of weeds in colonizing and finding suitable place for growth and reproduction. IWO is developed to solve continuous optimization problems that’s why the heuristic rule the Smallest Position Value (SPV is used to convert the continuous position values to the discrete job sequences. The computational experiments show that the proposed algorithm is highly competitive to the state-of-the-art methods in the literature since it is able to find the optimal and best-known solutions on the instances studied.
Directory of Open Access Journals (Sweden)
R. Karthick
2012-09-01
Full Text Available The optimization technique is used for the identification of some best values from the various populations. The Evolutionary algorithm is used as a basic concept of the Evolutionary Programming Strategy. To solve many of the numeric and combinatorial problems the evolutionary programming is applied. The optimization problem is obtained using the crossover and mutation. The mutation operation is performed to identify the best fitness values and solution so as to obtain the result. This paper focuses on Optimization technique which is based on the solution selection process. This process helps to enhance the performance of the optimization technique. This paper mainly helps to identify the best fitness values from the various other populations.
Bot, Radu Ioan
2012-01-01
The aim of this paper is to develop an efficient algorithm for solving a class of unconstrained nondifferentiable convex optimization problems in finite dimensional spaces. To this end we formulate first its Fenchel dual problem and regularize it in two steps into a differentiable strongly convex one with Lipschitz continuous gradient. The doubly regularized dual problem is then solved via a fast gradient method with the aim of accelerating the resulting convergence scheme. The theoretical results are finally applied to an l1 regularization problem arising in image processing.
Institute of Scientific and Technical Information of China (English)
ZHANG Xinhua
2006-01-01
Aim to the manufacturing supply chain optimization problem with time windows, presents an improved orthogonal genetic algorithm to solve it. At first, we decompose this problem into two sub-problems (distribution and routing) plus an interface mechanism to allow the two algorithms to collaborate in a master-slave fashion, with the distribution algorithm driving the routing algorithm. At second, we describe the proposed improved orthogonal genetic algorithm for solving giving problem detailedly. Finally, the examples suggest that this proposed approach is feasible, correct and valid.
Ibrahim, Ireen Munira; Liong, Choong-Yeun; Bakar, Sakhinah Abu; Ahmad, Norazura; Najmuddin, Ahmad Farid
2015-12-01
The Emergency Department (ED) is a very complex system with limited resources to support increase in demand. ED services are considered as good quality if they can meet the patient's expectation. Long waiting times and length of stay is always the main problem faced by the management. The management of ED should give greater emphasis on their capacity of resources in order to increase the quality of services, which conforms to patient satisfaction. This paper is a review of work in progress of a study being conducted in a government hospital in Selangor, Malaysia. This paper proposed a simulation optimization model framework which is used to study ED operations and problems as well as to find an optimal solution to the problems. The integration of simulation and optimization is hoped can assist management in decision making process regarding their resource capacity planning in order to improve current and future ED operations.
Global Optimization for Sum of Linear Ratios Problem Using New Pruning Technique
Directory of Open Access Journals (Sweden)
2009-02-01
Full Text Available A global optimization algorithm is proposed for solving sum of general linear ratios problem (P using new pruning technique. Firstly, an equivalent problem (P1 of the (P is derived by exploiting the characteristics of linear constraints. Then, by utilizing linearization method the relaxation linear programming (RLP of the (P1 can be constructed and the proposed algorithm is convergent to the global minimum of the (P through the successive refinement of the linear relaxation of feasible region and solutions of a series of (RLP. Then, a new pruning technique is proposed, this technique offers a possibility to cut away a large part of the current investigated feasible region by the optimization algorithm, which can be utilized as an accelerating device for global optimization of problem (P. Finally, the numerical experiments are given to illustrate the feasibility of the proposed algorithm.
Direct Method for Resolution of Optimal Control Problem with Free Initial Condition
Directory of Open Access Journals (Sweden)
Louadj Kahina
2012-01-01
Full Text Available The theory of control analyzes the proprieties of commanded systems. Problems of optimal control (OC have been intensively investigated in the world literature for over forty years. During this period, series of fundamental results have been obtained, among which should be noted the maximum principle (Pontryagin et al., 1962 and dynamic programming (Bellman, 1963. For many of the problems of the optimal control theory (OCT, adequate solutions are found (Bryson and Yu-chi, 1969, Lee and Markus, 1967, Gabasov and Kirillova, 1977, 1978, 1980. Results of the theory were taken up in various fields of science, engineering, and economics. The present paper aims at extending the constructive methods of Balashevich et al., (2000 that were developed for the problems of optimal control with the bounded initial state is not fixed are considered.
A Hybrid TCNN Optimization Approach for the Capacity Vehicle Routing Problem
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A novel approximation algorithm was proposed for the problem of finding the minimum total cost of all routes in Capacity Vehicle Routing Problem (CVRP). CVRP can be partitioned into three parts: the selection of vehicles among the available vehicles, the initial routing of the selected fleet and the routing optimization. Fuzzy Cmeans (FCM) can group the customers with close Euclidean distance into the same vehicle according to the principle of similar feature partition. Transiently chaotic neural network (TCNN) combines local search and global search, possessing high search efficiency. It will solve the routes to near optimality. A simple tabu search (TS)procedure can improve the routes to more optimality. The computations on benchmark problems and comparisons with other results in literatures show that the proposed algorithm is a viable and effective approach for CVRP.
Qu Chiwen; He Wei
2016-01-01
The standard cuckoo search algorithm is of low accuracy and easy to fall into local optimal value in the later evolution. In this paper, an improved cuckoo algorithm is proposed. Dynamic change of parameter of probability is introduced to improve the convergence speed. Complex method is quoted to improve the capabilities of local search algorithm. A non-fixed multi-segment mapping penalty function is adopted to realize constraint processing algorithms. The results of the optimization problem ...
Rolling optimization algorithm based on collision window for single machine scheduling problem
Institute of Scientific and Technical Information of China (English)
Wang Changjun; Xi Yugeng
2005-01-01
Focusing on the single machine scheduling problem which minimizes the total completion time in the presence of dynamic job arrivals, a rolling optimization scheduling algorithm is proposed based on the analysis of the character and structure of scheduling. An optimal scheduling strategy in collision window is presented. Performance evaluation of this algorithm is given. Simulation indicates that the proposed algorithm is better than other common heuristic algorithms on both the total performance and stability.
Discrete particle swarm optimization for the minimum labelling Steiner tree problem
Consoli, S.; Moreno-Pérez, JA; Darby-Dowman, K; Mladenović, N
2009-01-01
Particle Swarm Optimization is a population-based method inspired by the social behaviour of individuals inside swarms in nature. Solutions of the problem are modelled as members of the swarm which fly in the solution space. The improvement of the swarm is obtained from the continuous movement of the particles that constitute the swarm submitted to the effect of inertia and the attraction of the members who lead the swarm. This work focuses on a recent Discrete Particle Swarm Optimization for...
Faggian, Silvia
2007-01-01
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author, or by Faggian and Gozzi. Necessary and sufficient optimality conditions for open loop controls are established. Moreover the co-state variable is shown t...
Maximum Principle for Boundary Control Problems Arising in Optimal Investment with Vintage Capital
Silvia Faggian
2008-01-01
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author et al. [26, 27, 28, 29, 30]. Necessary and sufficient optimality conditions for open loop controls are established. Moreover the co-state variable is show...
Institute of Scientific and Technical Information of China (English)
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。
Ayvaz, M. Tamer
2016-07-01
In this study, a new simulation-optimization approach is proposed for solving the areal groundwater pollution source identification problems which is an ill-posed inverse problem. In the simulation part of the proposed approach, groundwater flow and pollution transport processes are simulated by modeling the given aquifer system on MODFLOW and MT3DMS models. The developed simulation model is then integrated to a newly proposed hybrid optimization model where a binary genetic algorithm and a generalized reduced gradient method are mutually used. This is a novel approach and it is employed for the first time in the areal pollution source identification problems. The objective of the proposed hybrid optimization approach is to simultaneously identify the spatial distributions and input concentrations of the unknown areal groundwater pollution sources by using the limited number of pollution concentration time series at the monitoring well locations. The applicability of the proposed simulation-optimization approach is evaluated on a hypothetical aquifer model for different pollution source distributions. Furthermore, model performance is evaluated for measurement error conditions, different genetic algorithm parameter combinations, different numbers and locations of the monitoring wells, and different heterogeneous hydraulic conductivity fields. Identified results indicated that the proposed simulation-optimization approach may be an effective way to solve the areal groundwater pollution source identification problems.
Directory of Open Access Journals (Sweden)
Anton A. Kamil
2009-01-01
Full Text Available Problem statement: The most important character within optimization problem is the uncertainty of the future returns. Approach: To handle such problems, we utilized probabilistic methods alongside with optimization techniques. We developed single stage and two stage stochastic programming with recourse. The models were developed for risk adverse investors and the objective of the stochastic programming models is to minimize the maximum downside semi deviation. We used the so-called Here-and-Now approach where the decision-maker makes decision now before observing the actual outcome for the stochastic parameter. Results: We compared the optimal portfolios between the single stage and two stage models with the incorporation of the deviation measure. The models were applied to the optimal selection of stocks listed in Bursa Malaysia and the return of the optimal portfolio was compared between the two stochastic models. Conclusion: The results showed that the two stage model outperforms the single stage model in the optimal and in-sample analysis.
An adaptive metamodel-based global optimization algorithm for black-box type problems
Jie, Haoxiang; Wu, Yizhong; Ding, Jianwan
2015-11-01
In this article, an adaptive metamodel-based global optimization (AMGO) algorithm is presented to solve unconstrained black-box problems. In the AMGO algorithm, a type of hybrid model composed of kriging and augmented radial basis function (RBF) is used as the surrogate model. The weight factors of hybrid model are adaptively selected in the optimization process. To balance the local and global search, a sub-optimization problem is constructed during each iteration to determine the new iterative points. As numerical experiments, six standard two-dimensional test functions are selected to show the distributions of iterative points. The AMGO algorithm is also tested on seven well-known benchmark optimization problems and contrasted with three representative metamodel-based optimization methods: efficient global optimization (EGO), GutmannRBF and hybrid and adaptive metamodel (HAM). The test results demonstrate the efficiency and robustness of the proposed method. The AMGO algorithm is finally applied to the structural design of the import and export chamber of a cycloid gear pump, achieving satisfactory results.
CLASSIFICATION OF RESTRAINTS IN THE OPTIMIZATION PROBLEM OF A COLD-FORMED PROFILE
Directory of Open Access Journals (Sweden)
Agnieszka Łukowicz
2015-11-01
Full Text Available This work describes the restraints in the optimization problem. This is an important and complicated issue because it requires taking into account a vast range of information related to the design and production. In order to describe the relations of a specific optimization problem, it is essential to adopt appropriate criteria and to collect information on all kinds of restraints, i.e. boundary conditions. The following paper verifies the various restraints and defines three subsets: design assumptions, technological limitations and standard conditions. The provided classification was made with reference to the analysis of the construction applicability of the newly patented cold-formed profile.
Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function
Pearson, John W.
2012-11-21
Optimal control problems with partial differential equations as constraints play an important role in many applications. The inclusion of bound constraints for the state variable poses a significant challenge for optimization methods. Our focus here is on the incorporation of the constraints via the Moreau-Yosida regularization technique. This method has been studied recently and has proven to be advantageous compared with other approaches. In this paper, we develop robust preconditioners for the efficient solution of the Newton steps associated with the fast solution of the Moreau-Yosida regularized problem. Numerical results illustrate the efficiency of our approach. © 2012 John Wiley & Sons, Ltd.
Directory of Open Access Journals (Sweden)
Tao Zhang
2012-01-01
Full Text Available An elite quantum behaved particle swarm optimization (EQPSO algorithm is proposed, in which an elite strategy is exerted for the global best particle to prevent premature convergence of the swarm. The EQPSO algorithm is employed for solving bilevel multiobjective programming problem (BLMPP in this study, which has never been reported in other literatures. Finally, we use eight different test problems to measure and evaluate the proposed algorithm, including low dimension and high dimension BLMPPs, as well as attempt to solve the BLMPPs whose theoretical Pareto optimal front is not known. The experimental results show that the proposed algorithm is a feasible and efficient method for solving BLMPPs.