32 results
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2. A fuzzy MCDM method for solving marine transshipment container port selection problems
- Author
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Chou, Chien-Chang
- Subjects
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FUZZY algorithms , *ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Abstract: “Transshipment” is a very popular and important issue in the present international trade container transportation market. In order to reduce the international trade container transportation operation cost, it is very important for shipping companies to choose the best transshipment container port. The aim of this paper is to present a new Fuzzy Multiple Criteria Decision Making Method (FMCDM) for solving the transshipment container port selection problem under fuzzy environment. In this paper we present first the canonical representation of multiplication operation on three fuzzy numbers, and then this canonical representation is applied to the selection of transshipment container port. Based on the canonical representation, the decision maker of shipping company can determine quickly the ranking order of all candidate transshipment container ports and select easily the best one. [Copyright &y& Elsevier]
- Published
- 2007
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3. A similar particle swarm optimization algorithm for job-shop scheduling to minimize makespan
- Author
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Lian, Zhigang, Jiao, Bin, and Gu, Xingsheng
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PRODUCTION scheduling , *ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Abstract: The job-shop scheduling problem (JSSP) is a branch of production scheduling, and it is well known that this problem is NP-hard. Many different approaches have been applied to JSSP and a rich harvest has been obtained. However, some JSSP, even with moderate size, cannot be solved to guarantee optimality. The standard particle optimization algorithm generally is used to solve continuous optimization problems, and is used rarely to solve discrete problems such as JSSP. This paper presents a similar PSO algorithm to solve JSSP. At the same time, some new valid algorithm operators are proposed in this paper, and through simulation we find out the effectiveness of them. Three representative (Taillard) instances were made by computational experiments, through comparing the SPSO algorithm with standard GA, and we obtained that the SPSOA is more clearly efficacious than standard GA for JSSP to minimize makespan. [Copyright &y& Elsevier]
- Published
- 2006
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4. A new filled function method for unconstrained global optimization
- Author
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Yang, Yongjian and Shang, Youlin
- Subjects
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MATHEMATICS , *ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, a new definition of the filled function is given, it is different from the primary definition which was given by Ge in paper [R.P. Ge, A filled function method for finding a global minimzer of a function of several variables, Math. Program. 46 (1990) 191–204]. Based on the definition, a new filled function is proposed, and it has better properties. An algorithm for unconstrained global optimization is developed from the new filled function. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]
- Published
- 2006
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5. Solving 0-1 knapsack problems based on amoeboid organism algorithm.
- Author
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Zhang, Xiaoge, Huang, Shiyan, Hu, Yong, Zhang, Yajuan, Mahadevan, Sankaran, and Deng, Yong
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KNAPSACK problems , *PROBLEM solving , *ALGORITHMS , *DISCRETE systems , *MATHEMATICAL optimization , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: The 0-1 knapsack problem is an open issue in discrete optimization problems, which plays an important role in real applications. In this paper, a new bio-inspired model is proposed to solve this problem. The proposed method has three main steps. First, the 0-1 knapsack problem is converted into a directed graph by the network converting algorithm. Then, for the purpose of using the amoeboid organism model, the longest path problem is transformed into the shortest path problem. Finally, the shortest path problem can be well handled by the amoeboid organism algorithm. Numerical examples are given to illustrate the efficiency of the proposed model. [Copyright &y& Elsevier]
- Published
- 2013
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6. Application of generalized diagonal dominance in wireless sensor network optimization problems
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Cvetković, Lj. and Kostić, V.
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WIRELESS sensor networks , *MATHEMATICAL optimization , *ALGORITHMS , *GAME theory , *MATRICES (Mathematics) , *MATHEMATICAL analysis - Abstract
Abstract: The recent application of the diagonal dominance in the development of the optimization algorithms in the wireless sensor networks design, has been done by Yuan and Yu (2006) , extended in Yu et al. (2006) , and surveyed in Machado and Tekinay . In this paper, we will use the concept of generalized diagonal dominance, to improve the obtained results regarding the power control game, in three directions. We also discuss the applicability of such improvements. [Copyright &y& Elsevier]
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- 2012
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7. A new global optimization approach for convex multiplicative programming
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Gao, Yuelin, Wu, Guorong, and Ma, Weimin
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GLOBAL analysis (Mathematics) , *MATHEMATICAL optimization , *CONVEX programming , *ALGORITHMS , *APPROXIMATION theory , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, by solving the relaxed quasiconcave programming problem in outcome space, a new global optimization algorithm for convex multiplicative programming is presented. Two kinds of techniques are employed to establish the algorithm. The first one is outer approximation technique which is applied to shrink relaxation area of quasiconcave programming problem and to compute appropriate feasible points and to raise the capacity of bounding. And the other one is branch and bound technique which is used to guarantee global optimization. Some numerical results are presented to demonstrate the effectiveness and feasibility of the proposed algorithm. [Copyright &y& Elsevier]
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- 2010
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8. A primal-dual interior-point algorithm for second-order cone optimization with full Nesterov–Todd step
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Wang, G.Q. and Bai, Y.Q.
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INTERIOR-point methods , *ALGORITHMS , *MATHEMATICAL optimization , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis - Abstract
Abstract: In this paper we propose a primal-dual path-following interior-point algorithm for second-order cone optimization. The algorithm is based on a new technique for finding the search directions and the strategy of the central path. At each iteration, we use only full Nesterov–Todd step. Moreover, we derive the currently best known iteration bound for the algorithm with small-update method, namely, , where N denotes the number of second-order cones in the problem formulation and the desired accuracy. [Copyright &y& Elsevier]
- Published
- 2009
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9. Convergence analysis of Tikhonov-type regularization algorithms for multiobjective optimization problems
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Chen, Zhe, Xiang, Changhe, Zhao, Kequan, and Liu, Xuewen
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STOCHASTIC convergence , *ALGORITHMS , *MATHEMATICAL optimization , *PARETO optimum , *ASYMPTOTES , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we introduce a vector-valued Tikhonov-type regularization algorithm for an extended-valued multiobjective optimization problem. Under some mild conditions, we prove that any sequence generated by this algorithm converges to a weak Pareto optimal solution of the multiobjective optimization problem. Our results improve and generalize some known results. [Copyright &y& Elsevier]
- Published
- 2009
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10. Capacity maximization for reversible data hiding based on dynamic programming approach
- Author
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Chung, Kuo-Liang, Huang, Yong-Huai, Yang, Wei-Ning, Hsu, Yu-Chiao, and Chen, Chyou-Hwa
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DYNAMIC programming , *ALGORITHMS , *EMBEDDINGS (Mathematics) , *MATHEMATICAL analysis , *MATHEMATICAL optimization - Abstract
Abstract: Recently, an efficient reversible lossless data hiding algorithm by Ni et al. was presented. Their fast algorithm can recover the original image without any distortion and its PSNR lower bound is higher than that of all existing reversible data hiding algorithms. Instead of selecting the peak-valley pairs in a greedy way, this paper presents a dynamic programming-based reversible data hiding algorithm to determine the most suitable peak-valley pairs such that the embedding capacity object can be maximized. Based on some artificial map images, experimental results demonstrate that our proposed algorithm has 9% embedding capacity improvement ratio and has the similar image quality performance when compared to Ni et al.’s algorithm although it has some execution-time degradation. For natural images, the embedding capacity of Ni et al.’s algorithm is very close to the maximal embedding capacity obtained by our proposed algorithm. Furthermore, the comparison between our proposed dynamic programming-based algorithm and the reversible data hiding algorithm by Chang et al. is investigated. [Copyright &y& Elsevier]
- Published
- 2009
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11. An affine scaling optimal path method with interior backtracking curvilinear technique for linear constrained optimization
- Author
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Wang, Yunjuan and Zhu, Detong
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MATHEMATICAL optimization , *PATHS & cycles in graph theory , *ALGORITHMS , *STOCHASTIC convergence , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
Abstract: This paper presents an affine scaling optimal path approach in association with nonmonotonic interior backtracking line search technique for nonlinear optimization subject to linear constraints. We shall employ the eigensystem decomposition and affine scaling mapping to form affine scaling optimal curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature. Theoretical analysis is given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]
- Published
- 2009
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12. A new image thresholding method based on Gaussian mixture model
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Huang, Zhi-Kai and Chau, Kwok-Wing
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GAUSSIAN processes , *ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, an efficient approach to search for the global threshold of image using Gaussian mixture model is proposed. Firstly, a gray-level histogram of an image is represented as a function of the frequencies of gray-level. Then to fit the Gaussian mixtures to the histogram of image, the expectation maximization (EM) algorithm is developed to estimate the number of Gaussian mixture of such histograms and their corresponding parameterization. Finally, the optimal threshold which is the average of these Gaussian mixture means is chosen. And the experimental results show that the new algorithm performs better. [Copyright &y& Elsevier]
- Published
- 2008
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13. Knowledge-based cooperative particle swarm optimization
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Jie, Jing, Zeng, Jianchao, Han, Chongzhao, and Wang, Qinghua
- Subjects
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MATHEMATICAL optimization , *MATHEMATICAL analysis , *ALGORITHMS , *SIMULATION methods & models - Abstract
Abstract: Particle swarm optimization is a novel swarm-intelligence-based algorithm and a valid optimization technique. However, the algorithm suffers from the premature convergence problem when facing to complex optimization problem. In order to keep the balance between the global exploration and the local exploitation validly, the paper develops a knowledge-based cooperative particle swarm optimization (KCPSO). KCPSO mainly simulates the self-cognitive and self-learning process of evolutionary agents in special environment, and introduces a knowledge billboard to record varieties of search information. Moreover, KCPSO takes advantage of multi-swarm to maintain the swarm diversity and tries to guide their evolution by the shared information. Under the guide of the shared information, KCPSO manipulates each sub-swarm to go on with local exploitation in different local area, in which every particle follows a social learning behavior mode; at the same time, KCPSO carries out the global exploration through the escaping behavior and the cooperative behavior of the particles in different sub-swarms. KCPSO can maintain appropriate swarm diversity and alleviate the premature convergence validly. The proposed model was applied to some well-known benchmarks. The relative experimental results show KCPSO is a robust global optimization method for the complex multimodal functions. [Copyright &y& Elsevier]
- Published
- 2008
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14. An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position
- Author
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Xi, Maolong, Sun, Jun, and Xu, Wenbo
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ALGORITHMS , *SIMULATION methods & models , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Abstract: Quantum-behaved particle swarm optimization (QPSO) algorithm is a global convergence guaranteed algorithms, which outperforms original PSO in search ability but has fewer parameters to control. In this paper, we propose an improved quantum-behaved particle swarm optimization with weighted mean best position according to fitness values of the particles. It is shown that the improved QPSO has faster local convergence speed, resulting in better balance between the global and local searching of the algorithm, and thus generating good performance. The proposed improved QPSO, called weighted QPSO (WQPSO) algorithm, is tested on several benchmark functions and compared with QPSO and standard PSO. The experiment results show the superiority of WQPSO. [Copyright &y& Elsevier]
- Published
- 2008
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15. A novel ecological particle swarm optimization algorithm and its population dynamics analysis
- Author
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Kang, Qi, Wang, Lei, and Wu, Qi-di
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MATHEMATICAL optimization , *POPULATION dynamics , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: This paper presents a novel particle swarm optimization algorithm from the angle of ecological population evolution, called the ecological particle swarm optimization, or EPSO. Initially, ecological population competition model (EPCM) is presented. From the basis of the EPCM, the EPSO algorithm and its general framework are proposed; in which particle swarm system with ecological hierarchy and competition model is defined and two collocating strategies of inertia weight factor are considered. The convergence performance and population dynamics including population aggregation and population diversity of the proposed approach are discussed separately through empirical simulations with well-known benchmarks from the standard literature. [Copyright &y& Elsevier]
- Published
- 2008
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16. An evolutionary algorithm for dynamic multi-objective optimization
- Author
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Wang, Yuping and Dang, Chuangyin
- Subjects
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ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICAL analysis , *MUTATIONS (Algebra) - Abstract
Abstract: In this paper, the dynamic multi-objective optimization problem (DMOP) is first approximated by a series of static multi-objective optimization problems (SMOPs) by dividing the time period into several equal subperiods. In each subperiod, the dynamic multi-objective optimization problem is seen as a static multi-objective optimization problem by taking the time parameter fixed. Then, to decrease the amount of computation and efficiently solve the static problems, each static multi-objective optimization problem is transformed into a two-objective optimization problem based on two re-defined objectives. Finally, a new crossover operator and mutation operator adapting to the environment changing are designed. Based on these techniques, a new evolutionary algorithm is proposed. The simulation results indicate that the proposed algorithm can effectively track the varying Pareto fronts with time. [Copyright &y& Elsevier]
- Published
- 2008
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17. Solving unconstrained optimization problem with a filter-based nonmonotone pattern search algorithm
- Author
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Wu, Ting
- Subjects
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ALGORITHMS , *FOUNDATIONS of arithmetic , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Abstract: This paper proposes a new frame-based pattern search algorithm for unconstrained optimization. The implementation of filter leads the sequence of function values at iterates nonmonotonically decreasing and thus motivates us to consider nonmonotone technique. Furthermore, the use of these two techniques can improve the efficiency of general pattern search algorithms. The numerical results show that the new algorithm is practical and efficient. [Copyright &y& Elsevier]
- Published
- 2008
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18. Application of particle swarm optimization for distribution feeder reconfiguration considering distributed generators
- Author
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Olamaei, J., Niknam, T., and Gharehpetian, G.
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ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICAL analysis , *MATHEMATICAL models - Abstract
Abstract: In many countries the power systems are going to move toward creating a competitive structure for selling and buying electrical energy. These changes and the numerous advantages of the distributed generation units (DGs) in term of their technology enhancement and economical considerations have created more incentives to use these kinds of generators than before. Therefore, it is necessary to study the impact of DGs on the power systems, especially on the distribution networks. The distribution feeder reconfiguration (DFR) is one of the most important control schemes in the distribution networks, which can be affected by DGs. This paper presents a new approach to DFR at the distribution networks considering DGs. The main objective of the DFR is to minimize the deviation of the bus voltage, the number of switching operations and the total cost of the active power generated by DGs and distribution companies. Since the DFR is a nonlinear optimization problem, we apply the particle swarm optimization (PSO) approach to solve it. The feasibility of the proposed approach is demonstrated and compared with other evolutionary methods such as genetic algorithm (GA), Tabu search (TS) and differential evolution (DE) over a realistic distribution test system. [Copyright &y& Elsevier]
- Published
- 2008
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19. A robust solution approach for nonconvex quadratic programs with additional multiplicative constraints
- Author
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Shen, Peiping, Duan, Yunpeng, and Ma, Yuan
- Subjects
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QUADRATIC programming , *MATHEMATICAL optimization , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, a robust algorithm is proposed for globally solving a nonconvex quadratic programming problem (P1) with several additional multiplicative constraints. To our knowledge, little progress has been made so far for globally solving problem (P1). The proposed algorithm is based on a robust solution approach that provides an essential -optimal solution. This solution is also stable under small perturbations of the constraints, and it turns out that such a robust optimal solution is adequately guaranteed to be feasible and to be close to the actual optimal solution. Convergence of the algorithm is shown and three solved sample problems are given to illustrate the robust stability and feasibility of the present algorithm. [Copyright &y& Elsevier]
- Published
- 2008
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20. Adaptive differential evolution algorithm for multiobjective optimization problems
- Author
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Qian, Weiyi and li, Ajun
- Subjects
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ALGORITHMS , *MATHEMATICAL optimization , *DIFFERENTIAL equations , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, a new adaptive differential evolution algorithm (ADEA) is proposed for multiobjective optimization problems. In ADEA, the variable parameter F based on the number of the current Pareto-front and the diversity of the current solutions is given for adjusting search size in every generation to find Pareto solutions in mutation operator, and the select operator combines the advantages of DE with the mechanisms of Pareto-based ranking and crowding distance sorting. ADEA is implemented on five classical multiobjective problems, the results illustrate that ADEA efficiently achieves two goals of multiobjective optimization problems: find the solutions converge to the true Pareto-front and uniform spread along the front. [Copyright &y& Elsevier]
- Published
- 2008
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21. Global convergence of slanting filter methods for nonlinear programming
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Karas, Elizabeth W., Oening, Ana P., and Ribeiro, Ademir A.
- Subjects
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NONLINEAR programming , *ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates. Independently of how these iterates are computed, we prove that all accumulation points of the sequence generated by the algorithm are feasible. Computing the new iterates by the inexact restoration method, we prove stationarity of all accumulation points of the sequence. [Copyright &y& Elsevier]
- Published
- 2008
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22. A co-evolving framework for robust particle swarm optimization
- Author
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Luo, Qiang and Yi, Dongyun
- Subjects
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ALGORITHMS , *MATHEMATICAL optimization , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: Particle swarm optimization (PSO) as an efficient and powerful problem-solving strategy has been widely used, but appropriate adjustment of its parameters usually requires a lot of time and labor. So a co-evolving framework is proposed to improve the robustness of the PSO. In this paper, within this framework the fuzzy rules for the manipulation of the inertia weights are co-evolved with the particles. And the simulation results on a suite of test functions show that the use of this co-evolving framework improves the performance of the PSO, especially the robustness against the dimensional variation of the test functions. [Copyright &y& Elsevier]
- Published
- 2008
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23. Development of a hybrid dynamic programming approach for solving discrete nonlinear knapsack problems
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Ghassemi-Tari, Farhad and Jahangiri, Eshagh
- Subjects
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MATHEMATICAL optimization , *DYNAMIC programming , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: A multiple-choice knapsack problem can be formulated as a discrete nonlinear knapsack problem (DNKP). A powerful method for solving DNKP is the dynamic programming solution approach. The use of this powerful approach however is limited since the growth of the number of decision variables and state variables requires an extensive computer memory storage and computational time. In this paper we developed a hybrid algorithm for improving the computational efficiency of the dynamic programming when it is applied for solving the DNKP. In the hybrid algorithm, three routines of the imbedded state, surrogate constraints, and bounding scheme are incorporated for increasing the efficiency of this solution approach. We then conducted an experimental study for comparing the computational efficiency of the hybrid algorithm with the imbedded state dynamic programming approach. [Copyright &y& Elsevier]
- Published
- 2007
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24. Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms
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Tavazoei, Mohammad Saleh and Haeri, Mohammad
- Subjects
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ALGORITHMS , *MATHEMATICAL optimization , *NONLINEAR theories , *MATHEMATICAL analysis - Abstract
Abstract: The aim of this paper is to propose and compare different one-dimensional maps as chaotic search patterns in the constraint nonlinear optimization problems. For this purpose, about 10 one-dimensional maps are introduced that can be used as search pattern in chaos optimization algorithms. We apply these maps in specific optimization algorithm (weighted gradient direction based chaos optimization algorithm) and compare them based on numerical simulation results. [Copyright &y& Elsevier]
- Published
- 2007
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25. The dragon war
- Author
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Mertz, Joachim
- Subjects
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MATHEMATICAL optimization , *ALGORITHMS , *FUNCTIONAL equations , *MATHEMATICAL analysis - Abstract
Abstract: This article presents an approach to solve the travelling salesman problem using linear optimisation with a suitable set of constraints. Such approaches are well known as Cutting Plane methods but previously applied algorithms still suffer from the NP-completeness of the problem causing an exponential number of computational steps in the worst case. The method presented in this paper both tolerates non-integer results for a dedicated class of solutions (symmetric solutions) and avoids other ones (asymmetric solutions). It is thus able to deal with the inherent complexity of the travelling salesman problem.Therefore the overall complexity of the optimisation algorithm remains polynomial in the worst case. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
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26. On the convergence of partitioning group correction algorithms
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Li, J.X. and Zhang, H.W.
- Subjects
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ALGORITHMS , *STOCHASTIC convergence , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Abstract: This paper studies a successive partitioning group correction algorithm and its some modified algorithms for solving large scale sparse unconstrained optimization problems. The methods depend on a symmetric consistent partition of the columns of the Hessian matrix. A q-superlinear convergence result and an r-convergence rate estimate show that the methods have good local convergence properties. The numerical results show that the methods, especially the modified algorithms, may be competitive with some current used algorithms. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
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27. An effective co-evolutionary differential evolution for constrained optimization
- Author
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Huang, Fu-zhuo, Wang, Ling, and He, Qie
- Subjects
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MATHEMATICAL optimization , *MATHEMATICAL analysis , *ALGORITHMS , *DIFFERENTIAL equations - Abstract
Abstract: Many practical problems can be formulated as constrained optimization problems. Due to the simple concept and easy implementation, the penalty function method has been one of the most common techniques to handle constraints. However, the performance of this technique greatly relies on the setting of penalty factors, which are usually determined by manual trial and error, and the suitable penalty factors are often problem-dependent and difficult to set. In this paper, a differential evolution approach based on a co-evolution mechanism, named CDE, is proposed to solve the constrained problems. First, a special penalty function is designed to handle the constraints. Second, a co-evolution model is presented and differential evolution (DE) is employed to perform evolutionary search in spaces of both solutions and penalty factors. Thus, the solutions and penalty factors evolve interactively and self-adaptively, and both the satisfactory solutions and suitable penalty factors can be obtained simultaneously. Simulation results based on several benchmark functions and three well-known constrained design problems as well as comparisons with some existed methods demonstrate the effectiveness, efficiency and robustness of the proposed method. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
28. A new global optimization algorithm for signomial geometric programming via Lagrangian relaxation
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Qu, Shao-Jian, Zhang, Ke-Cun, and Ji, Ying
- Subjects
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ALGORITHMS , *LAGRANGE equations , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, a global optimization algorithm, which relies on the exponential variable transformation of the signomial geometric programming (SGP) and the Lagrangian duality of the transformed programming, is proposed for solving the signomial geometric programming (SGP). The difficulty in utilizing Lagrangian duality within a global optimization context is that the restricted Lagrangian function for a given estimate of the Lagrangian multipliers is often nonconvex. Minimizing a linear underestimation of the restricted Lagrangian overcomes this difficulty and facilitates the use of Lagrangian duality within a global optimization framework. In the new algorithm the lower bounds are obtained by minimizing the linear relaxation of restricted Lagrangian function for a given estimate of the Lagrange multipliers. A branch-and-bound algorithm is presented that relies on these Lagrangian relaxations to provide lower bounds and on the interval Newton method to facilitate convergence in the neighborhood of the global solution. Computational results show that the algorithm is efficient. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
29. A probabilistic cooperative–competitive hierarchical model for global optimization
- Author
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Leung, K.S., King, I., and Wong, Y.B.
- Subjects
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MATHEMATICAL optimization , *COMBINATORIAL optimization , *MATHEMATICAL analysis , *ALGORITHMS - Abstract
Abstract: Stochastic searching methods have been applied widely to areas such as continuous and combinatorial optimization problems in a number of disciplines. Many existing methods solve these problems by navigating on the surface of the possibly rugged landscape. This kind of navigation is not very effective because the property of the landscape at different resolutions can be very different. Time spent at the beginning of the search on the detailed part of the landscape is often useless. Appropriate searching strategies should be adopted at different resolutions. In this paper, we propose a new probabilistic searching model for global optimization. The main contributions of the model are (1) to provide a basis for resolution control and smoothing of search space and (2) to introduce continuous memory into stochastic search. The basis of resolution control is achieved by dividing the search space into a finite number of n-dimensional partitions structurally. The number of partitions governs the resolution of the search space. The more the partitions, the finer is the search space and the more detailed and rugged is the landscape. The benefits are twofold. First, the rugged landscape problem can be smoothed, because the ruggedness is a matter of the number of partitions. Hence, the difficulty in search due to the ruggedness of the landscape can be controlled. Second, it provides a basis to implement algorithms that may change the ‘view’ of the landscape during the search process because we can dynamically divide the search space accordingly. Another important feature that we use is continuous memory. Throughout the search process, searching experience is continuously accumulated in order to shape the global picture of the search space guiding the future searching direction. We present results on the algorithm performance in handling numerical function optimization. The empirical results show that our new model is comparable to, and in many cases performs better than, that of the other advanced methods in terms of solution quality and computation required. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
30. An efficient algorithm for the smallest enclosing ball problem in high dimensions
- Author
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Pan, Shaohua and Li, Xingsi
- Subjects
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ALGORITHMS , *MATHEMATICAL optimization , *DIMENSIONS , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: Consider the problem of computing the smallest enclosing ball of a set of m balls in . This problem arises in many applications such as location analysis, military operations, and pattern recognition, etc. In this paper, we reformulate this problem as an unconstrained convex optimization problem involving the maximum function max{0, t}, and then develop a simple algorithm particularly suitable for problems in high dimensions. This algorithm could efficiently handle problems of dimension n up to 10,000 under a moderately large m, as well as problems of dimension m up to 10,000 under a moderately large n. Numerical results are given to show the efficiency of algorithm. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
31. Parameters identification problem of the nonlinear dynamical system in microbial continuous cultures
- Author
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Gao, Caixia, Feng, Enmin, Wang, Zongtao, and Xiu, Zhilong
- Subjects
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MATHEMATICAL optimization , *ALGORITHMS , *MATHEMATICAL analysis , *DYNAMICS - Abstract
Abstract: In this paper, the nonlinear dynamic system of continuous glycerol fermentations to 1,3-propanediol by klebsiella pneumoniae is investigated. Considering big errors between the experimental results and computational values in the previous works, we establish the parameter identification model for the system. The properties of the solutions for the nonlinear dynamic system are discussed and the identifiability of the parameters is proved. Finally the feasible optimization algorithm is constructed to find the optimal parameters for the system. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
32. A class of filled functions for box constrained continuous global optimization
- Author
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Zhu, Wenxing
- Subjects
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ALGORITHMS , *ALGEBRA , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
Abstract: In this paper we show that the unconstrained continuous global minimization problem cannot be solved by any algorithm, so we consider the box constrained continuous global minimization problem. We present a definition of filled function for the problem. Moreover, a new class of filled functions are constructed, which contains only one parameter. A randomized algorithm is designed to solve the box constrained continuous global minimization problem based on the filled function. Numerical experiments are presented to show the practicability of the algorithm. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
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