Nash equilibrium sorting genetic algorithm for simultaneous competitive maximal covering location with multiple players

In this article, a new genetic algorithm (GA), called the Nash equilibrium sorting genetic algorithm (NESGA,) is introduced to identify Nash equilibria for the competitive maximal covering location problem with two and three competitors, which is a combinatorial game theory problem where it is computationally intractable to enumerate all decision options of the competitors. Although GAs are widely used in combinatorial optimization, their applications to non-cooperative, simultaneous games have been limited owing to challenges in guiding the evolutionary search to Nash equilibria, which are not necessarily on the Pareto front of the search space and cannot be found by current multi-objective GAs. A novel fitness assignment strategy is proposed to help the NESGA to converge to multiple Nash equilibria. Computational experiments show that the NESGA can discover multiple Nash equilibria in a single run and outperform other game-theoretic GAs.