Genetic algorithm based on simplex method for solving linear-quadratic bilevel programming problem

Authors:
Guangmin Wang;Zhongping Wan;Xianjia Wang;Yibing Lv
Affiliations:
School of Economics and Management, China University of Geosciences, Wuhan 430074, PR China;School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China;Institute of System Engineering, Wuhan University, Wuhan 430072, PR China;School of Information and Mathematics, Yangtze University, Jingzhou, 434102, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

The bilevel programming problems are useful tools for solving the hierarchy decision problems. In this paper, a genetic algorithm based on the simplex method is constructed to solve the linear-quadratic bilevel programming problem (LQBP). By use of Kuhn-Tucker conditions of the lower level programming, the LQBP is transformed into a single level programming which can be simplified to a linear programming by the chromosome according to the rule. Thus, in our proposed genetic algorithm, only the linear programming is solved by the simplex method to obtain the feasibility and fitness value of the chromosome. Finally, the feasibility of the proposed approach is demonstrated by the example.