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An adaptive genetic algorithm for solving bilevel linear programming problem

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Abstract

Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the genetic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes may be infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.

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Authors and Affiliations

  1. School of Management, China University of Geosciences, Wuhan, 430074, P. R. China

    Wang Guang-min  (王先甲)

  2. Institute of Systems Engineering, Wuhan University, Wuhan, 430072, P. R. China

    Wang Xian-jia  (万仲平)

  3. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China

    Wan Zhong-ping  (贾世会)

  4. School of Science, Wuhan University of Science and Technology, Wuhan, 430081, P. R. China

    Jia Shi-hui  (丁协平)

Authors
  1. Wang Guang-min  (王先甲)
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  2. Wang Xian-jia  (万仲平)
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  3. Wan Zhong-ping  (贾世会)
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  4. Jia Shi-hui  (丁协平)
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Corresponding author

Correspondence to Wang Xian-jia  (万仲平).

Additional information

Communicated by ZHANG Shi-sheng

Project supported by the National Natural Science Foundation of China (Nos. 60574071 and 70771080)

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Wang, Gm., Wang, Xj., Wan, Zp. et al. An adaptive genetic algorithm for solving bilevel linear programming problem. Appl. Math. Mech.-Engl. Ed. 28, 1605–1612 (2007). https://doi.org/10.1007/s10483-007-1207-1

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  • DOI: https://doi.org/10.1007/s10483-007-1207-1

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Chinese Library Classification

2000 Mathematics Subject Classification

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