Hybrid evolutionary algorithm for solving general variational inequality problems

  • Authors:

  • Mend-Amar Majig;Abdel-Rahman Hedar;Masao Fukushima

  • Affiliations:

  • Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2007

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Abstract

This paper considers the problem of finding as many as possible, hopefully all, solutions of the general (i.e., not necessarily monotone) variational inequality problem (VIP). Based on global optimization reformulation of VIP, we propose a hybrid evolutionary algorithm that incorporates local search in promising regions. In order to prevent searching process from returning to the already detected global or local solutions, we employ the tunneling and hump-tunneling function techniques. The proposed algorithm is tested on a set of test problems in the MCPLIB library and numerical results indicate that it works well in practice.