6 results
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2. A new multi-section based technique for constrained optimization problems with interval-valued objective function.
- Author
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Karmakar, Samiran and Bhunia, Asoke Kumar
- Subjects
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MATHEMATICAL optimization , *MATHEMATICAL bounds , *DECISION making , *PROBLEM solving , *ALGORITHMS , *NUMERICAL calculations - Abstract
Abstract: In this paper, an efficient optimization technique is proposed for constrained optimization problems with interval valued objective function. At first, the significance of interval-valued objective function and the meaning of the interval-valued solution of the proposed problem have been explained with graphical interpretation. Generally, this type of problems has infinitely many compromise solutions. The aim of this approach is to obtain one of such solutions with higher accuracy and lower computational cost. The proposed technique is mainly based on the splitting criterion of the accepted/prescribed search region, calculation of the interval inclusion functions and the selection of subregion depending on the modified interval order relations in the context of the decision makers’ point of view. Novel interval oriented constraint satisfaction rules are used for non-interval equality and inequality constraints. Clearly, the proposed technique is nothing but an imitation of well known interval analysis based branch and bound (B &B) optimization approach. The modified multi-section division criterion with some new interval oriented constraint satisfaction rules for non-interval-valued equality and inequality constraints and some novel interval order relations in the context of the decision makers’ point of view have been applied to increase the efficiency of the proposed algorithm. Finally, the technique is applied for solving some test problems and the results are compared with the same obtained from the existing methods. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
3. 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
- Subjects
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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
- Full Text
- View/download PDF
4. An adaptive nonmonotone trust-region method with curvilinear search for minimax problem
- Author
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Wang, Fu-Sheng and Wang, Chuan-Long
- Subjects
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ALGORITHMS , *MATHEMATICAL optimization , *NEWTON-Raphson method , *PROBLEM solving , *LINE integrals , *MONOTONIC functions , *CHEBYSHEV approximation - Abstract
Abstract: In this paper we propose an adaptive nonmonotone algorithm for minimax problem. Unlike traditional nonmonotone method, the nonmonotone technique applied to our method is based on the nonmonotone technique proposed by Zhang and Hager [H.C. Zhang, W.W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim. 14(4)(2004) 1043–1056] instead of that presented by Grippo et al. [L. Grippo, F. Lampariello, S. Lucidi, A nonmonotone line search technique for Newton’s method, SIAM J. Numer. Anal. 23(4)(1986) 707–716]. Meanwhile, by using adaptive technique, it can adaptively perform the nonmonotone trust-region step or nonmonotone curvilinear search step when the solution of subproblems is unacceptable. Global and superlinear convergences of the method are obtained under suitable conditions. Preliminary numerical results are reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
5. An effective immune based two-phase approach for the optimal reliability–redundancy allocation problem
- Author
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Hsieh, Y.-C. and You, P.-S.
- Subjects
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RELIABILITY in engineering , *REDUNDANCY in engineering , *ALGORITHMS , *MATHEMATICAL optimization , *NUMERICAL analysis , *PROBLEM solving , *NONLINEAR theories - Abstract
Abstract: Highly reliable systems can reduce loss of money and time in practice. System reliability can be enhanced by: (i) increasing component reliabilities and/or (ii) providing redundancy at the component level. A trade-off between these two options is necessary for nonlinear-constrained reliability optimization. The problem of maximizing system reliability through component reliability choices and component redundancy is called as reliability–redundancy allocation problem, and it is a difficult but realistic nonlinear mixed-integer optimization problem. In this paper, under nonlinear constraints of weight, cost, and volume, we propose a new immune based two-phase approach to solve the reliability–redundancy allocation problem. In the first phase, an immune based algorithm (IA) is developed to solve the allocation problem, and in the second phase we present a new procedure to improve the solutions by IA. Numerical results of four benchmark problems are reported and compared. As shown, the solutions by the new proposed approach are all superior to those best solutions by typical approaches in the literature. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
6. Nonmonotone algorithm for minimax optimization problems
- Author
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Wang, Fusheng and Wang, Yanping
- Subjects
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MATHEMATICAL optimization , *NONMONOTONIC logic , *FINANCE , *MANAGEMENT , *ENGINEERING , *ALGORITHMS , *CHEBYSHEV approximation , *PROBLEM solving , *STOCHASTIC convergence , *NUMERICAL analysis - Abstract
Abstract: Many real life problems can be stated as a minimax optimization problem, such as the problems in economics, finance, management, engineering and other fields. In this paper, we present an algorithm with nonmonotone strategy and second-order correction technique for minimax optimization problems. Using this scheme, the new algorithm can overcome the difficulties of the Maratos effect occurred in the nonsmooth optimization, and the global and superlinear convergence of the algorithm can be achieved accordingly. Numerical experiments indicate some advantages of this scheme. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
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