Journal of Global Optimization

, Volume 38, Issue 4, pp 637–651 | Cite as

Hybrid evolutionary algorithm for solving general variational inequality problems

  • Mend-Amar Majig
  • Abdel-Rahman Hedar
  • Masao FukushimaEmail author
Original Paper


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.


Variational inequality Global optimization Evolutionary algorithm Local search Tunneling function 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Mend-Amar Majig
    • 1
  • Abdel-Rahman Hedar
    • 1
  • Masao Fukushima
    • 1
    Email author
  1. 1.Department of Applied Mathematics and Physics, Graduate School of InformaticsKyoto UniversityKyotoJapan

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