Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

A GENETIC ALGORITHM BASED ON OPTIMALITY CONDITIONS FOR NONLINEAR BILEVEL PROGRAMMING PROBLEMS

  • Li, Hecheng (School of Computer Science and Technology, Xidian University) ;
  • Wang, Yuping (School of Computer Science and Technology, Xidian University)
  • Received : 2009.08.13
  • Accepted : 2009.09.25
  • Published : 2010.05.30
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Abstract

For a class of nonlinear bilevel programming problems in which the follower's problem is linear, the paper develops a genetic algorithm based on the optimality conditions of linear programming. At first, we denote an individual by selecting a base of the follower's linear programming, and use the optimality conditions given in the simplex method to denote the follower's solution functions. Then, the follower's problem and variables are replaced by these optimality conditions and the solution functions, which makes the original bilevel programming become a single-level one only including the leader's variables. At last, the single-level problem is solved by using some classical optimization techniques, and its objective value is regarded as the fitness of the individual. The numerical results illustrate that the proposed algorithm is efficient and stable.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

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