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

  • Hecheng Li
  • Yuping Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4247)

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.

Keywords

Crossover Operator Benchmark Problem Hybrid Genetic Algorithm Bilevel Programming Bilevel Programming Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hecheng Li
    • 1
  • Yuping Wang
    • 2
  1. 1.Department of Mathematics ScienceXidian UniversityXi’anChina
  2. 2.School of Computer Science and TechnologyXidian UniversityXi’anChina

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