Solving Bi-level Programming with Multiple Linear Objectives at Lower Level Using Particle Swarm Optimization
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Authors
Fatehem Matroud
- Islamic Azad University, Abadan branch, Department of mathematic, Abadan, Iran.
Habibeh Sadeghi
- Department of Mathematics, Shahid Chamran University of Ahwaz, Ahwaz, Iran.
Abstract
Bi-level programming is a tool for modeling decentralized decisions that consists of the objective of the leader at its first level and that of the follower at the second level. This paper deals with general bi-level optimization problems with multiple objectives at the lower level of decision making. We present Particle swarm optimization (PSO) algorithm for solving this problem. Also, two numerical examples are given to illustrate efficiency of the proposed algorithm.
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ISRP Style
Fatehem Matroud, Habibeh Sadeghi, Solving Bi-level Programming with Multiple Linear Objectives at Lower Level Using Particle Swarm Optimization, Journal of Mathematics and Computer Science, 7 (2013), no. 3, 221-229
AMA Style
Matroud Fatehem, Sadeghi Habibeh, Solving Bi-level Programming with Multiple Linear Objectives at Lower Level Using Particle Swarm Optimization. J Math Comput SCI-JM. (2013); 7(3):221-229
Chicago/Turabian Style
Matroud, Fatehem, Sadeghi, Habibeh. "Solving Bi-level Programming with Multiple Linear Objectives at Lower Level Using Particle Swarm Optimization." Journal of Mathematics and Computer Science, 7, no. 3 (2013): 221-229
Keywords
- Bi-level optimization
- Multi objective optimization
- Particle Swarm Optimization.
MSC
References
-
[1]
M. A. Abo-Sinna, I. A. Baky , Interactive balance space approach for solving multi- level multiobjective Programming problems, Information Sciences, 177 (2007), 3397-3410
-
[2]
G. Anandalingam, T. Fries, Hierarchical Optimization: an introduction, Annals of Operations Research, 34 (1992), 1-11
-
[3]
Z. Ankhili, A. Mansouri, An exact penalty on bilevel programs with linear vector optimization lower level, European Journal of Operational Research , 197 (2009), 36-41
-
[4]
J. Bard, Practical Bilevel Optimization, Algorithms and Applications, Kluwer Academic Publishers, Dordrecht, London (1998)
-
[5]
H. Bonnel, J. Morgan, Semi vectorial bilevel optimization problem: penalty approach , Journal of Optimization Theory and Applications, 131(3) (2006), 365-382
-
[6]
HI. Calvete, C. Gale, on linear bilevel problems with multiple objective at the lower level , Journal of Omega , 39 (2011), 33-40
-
[7]
HI. Calvete, C. Gale, P. M. Mateo, A new approach for solving linear bilevel problems using genetic algorithms , European Journal of operational Research , 188 (2008), 14-28
-
[8]
M. H. Farahi, E. Ansari , A new approach to solve Multi-objective linear bilevel programming problems, Journal of mathematics and computer Science, 1 (2010), 238 - 438
-
[9]
J. Fliege, L. N. Vicente, Multicriteria Approach to Bilevel Optimization, Journals of Optimization theory and application, 131 (2006), 209-225
-
[10]
D. Kalyanmoy, A. Sinha , Solving Bilevel Multiobjective Optimization Problems Using Evolutionary Algorithms KanGAL Report Number, , (2008)
-
[11]
R. Khalesi, H. Maleki, A new method for solving fuzzy MCDM problems, Journal of mathematics and computer Science, 1 (2010), 238-438
-
[12]
X. Li, P. Tian, X. Min, A Hierarchical Particle Swarm Optimization for Solving Bilevel Programming Problems, Lecture Notes in Computer Science , 4029 (2006), 1169-1178
-
[13]
I. Nishizaki, M. Sakawa, Stackelberg solutions to multiobjective two level linear programming problems, Journal of Optimization Theory and Applications, 103 (1999), 161-182
-
[14]
M. Rostami, M. Kianpour, E. bashardoust, A numerical algorithm for solving nonlinear fuzzy differential equations, Journal of mathematics and computer Science, 177 (2007), 3397-3410
-
[15]
Y. Shi, R. C. Eberhart, A Modied Particle Swarm Optimizer, In IEEE International Conference of Evolutionary Computation, (1998)
-
[16]
X. Shi, H. Xia, Interactive bilevel multiobjective decision making, Journal of the Operational Research Society, 48 (1997), 943-949
-
[17]
X. Shi, H. Xia, Model and interactive algorithm of bilevel multiobjective decision making with multiple interconnected decision makers, Journal of MultiCriteria Decision Analysis, 10 (2001), 27-34
-
[18]
Y. Zheng, Z. Wan, G. Wang, A fuzzy interactive method for a class of bilevel multi- objective programming problem, Expert Systems with Applications, 38 (2011), 10384-10388