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A Hybrid Genetic Algorithm for Solving a Class of Nonlinear Bilevel Programming Problems

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Simulated Evolution and Learning (SEAL 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4247))

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Abstract

In this paper, a special nonlinear bilevel programming problem (BLPP), in which the follower’s problem is a convex quadratic programming in y, is transformed into an equivalent single-level programming problem by using Karush-Kuhn-Tucker(K-K-T) condition. To solve the equivalent problem effectively, firstly, a genetic algorithm is incorporated with Lemke algorithm. For x fixed, the optimal solution y of the follower’s problem can be obtained by Lemke algorithm, then (x,y) is a feasible or approximately feasible solution of the transformed problem and considered as a point in the population; secondly, based on the best individuals in the population, a special crossover operator is designed to generate high quality individuals; finally, a new hybrid genetic algorithm is proposed for solving this class of bilevel programming problems. The simulation on 20 benchmark problems demonstrates the effectiveness of the proposed algorithm.

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Author information

Authors and Affiliations

  1. Department of Mathematics Science, Xidian University, Xi’an, 710071, China

    Hecheng Li

  2. School of Computer Science and Technology, Xidian University, Xi’an, 710071, China

    Yuping Wang

Authors
  1. Hecheng Li
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  2. Yuping Wang
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Editor information

Editors and Affiliations

  1. Department of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung County Taiwan, ROC

    Tzai-Der Wang

  2. School of Computer Science and information Technology, RMIT University, VIC 3001, Melbourne, Australia

    Xiaodong Li

  3. AI-ECON Research Center, Department of Economics, National Chengchi University, 11623, Taipei, Taiwan

    Shu-Heng Chen

  4. Department of Computer Science and Technology, University of Sci. & Tech. of China, 230026, Hefei, Anhui, P.R. China

    Xufa Wang

  5. School of Information Technology and Electrical Engineering, University of New South Wales, Australian Defence Force Academy, Canberra, Australia

    Hussein Abbass

  6. The Univertity of Tokyo, Japan

    Hitoshi Iba

  7. Department of Computer, University of Science and Technology of China, 230027, Hefei, China

    Guo-Liang Chen

  8. University of Birmingham, Birmingham, UK

    Xin Yao

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© 2006 Springer-Verlag Berlin Heidelberg

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Li, H., Wang, Y. (2006). A Hybrid Genetic Algorithm for Solving a Class of Nonlinear Bilevel Programming Problems. In: Wang, TD., et al. Simulated Evolution and Learning. SEAL 2006. Lecture Notes in Computer Science, vol 4247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11903697_52

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  • DOI: https://doi.org/10.1007/11903697_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-47331-2

  • Online ISBN: 978-3-540-47332-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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