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Pareto-based evolutionary multiobjective approaches and the generalized Nash equilibrium problem

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Abstract

Pareto-based evolutionary multiobjective approaches are methods that use the Pareto dominance concept to guide the search of evolutionary algorithms towards the Pareto frontier of a problem. To address the challenge of providing an entire set of optimal solutions they use specially designed mechanisms for preserving search diversity and maintaining the non-dominated solutions set. The limitation of the Pareto dominance relation in high-dimensional spaces has rendered these methods inefficient for many-objective optimization. In this paper we aim to exploit existing Pareto-based methods to compute the generalized Nash equilibrium for multi-player games by replacing the Pareto dominance relation with an equilibrium generative relation. The generalized Nash equilibrium extends the Nash equilibrium concept by considering constraints over players’ strategies. Numerical experiments indicate that the selected methods can be employed for equilibria computation even for games with up to twenty players.

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Acknowledgements

This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS - UEFISCDI, Project Number PN-II-RU-TE-2014-4-2560.

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Correspondence to Noémi Gaskó.

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Appendix

Appendix

Modifications made to the PLATEMO code are listed in what follows. Apart from function NDSort, function NashAscends is used to determine the relation between strategies x and y, while function game returns the domination count for each individual in the population.

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Lung, R.I., Gaskó, N. & Suciu, M.A. Pareto-based evolutionary multiobjective approaches and the generalized Nash equilibrium problem. J Heuristics (2020). https://doi.org/10.1007/s10732-020-09438-w

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Keywords

  • Generalized Nash equilibrium problem
  • Multi-objective optimization
  • Evolutionary algorithms