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Evolutionary Algorithm for Generalized Nash Equilibrium Problems

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Optimization, Simulation, and Control

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 76))

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Abstract

This paper considers a method for finding multiple, hopefully all, solutions of the generalized Nash equilibrium problem (GNEP). Based on a merit function of the quasi-variational inequality (QVI) problem to GNEP, we reformulated GNEP as an unconstrained global optimization problem. To deal with the latter problem, we employ the evolutionary algorithm with adaptive fitness functions which help to search multiple global solutions. Numerical experiments for some test problems show the practical effectiveness of the method.

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References

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Acknowledgements

This research was supported in part by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, National University of Mongolia, Ulaanbaatar, Mongolia

    Mend-Amar Majig & Rentsen Enkhbat

  2. Graduate School of Informatics, Kyoto University, Kyoto, Japan

    Masao Fukushima

Authors
  1. Mend-Amar Majig
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  2. Rentsen Enkhbat
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  3. Masao Fukushima
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Corresponding author

Correspondence to Mend-Amar Majig .

Editor information

Editors and Affiliations

  1. , Institute of Mathematics, National University of Mongolia, University Street 1, Ulaanbaatar, 210646, Erdenet, Mongolia

    Altannar Chinchuluun

  2. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  3. The School of Economic Studies, Dept.of Mathematics & Computer Science, National University of Mongolia, Ulaanbaatar, 210646, Mongolia

    Rentsen Enkhbat

  4. , Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom

    E. N. Pistikopoulos

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Majig, MA., Enkhbat, R., Fukushima, M. (2013). Evolutionary Algorithm for Generalized Nash Equilibrium Problems. In: Chinchuluun, A., Pardalos, P., Enkhbat, R., Pistikopoulos, E. (eds) Optimization, Simulation, and Control. Springer Optimization and Its Applications, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5131-0_7

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