Improved differential evolution algorithm for solving multi-person noncooperative game

Abstract

In this paper, the nonzero sum multi-person noncooperative game is considered, and this game can be viewed as a global optimization problem. For solving this problem, an improved differential evolution algorithm is proposed. Our algorithm combines multi-strategy differential operators and crossover operators with a random walk. First, the population is initialized by a set of good points. Second, the single mutation mode is replaced by a multi-mode. Meanwhile, a random walk mechanism is introduced in the crossover process of the differential evolution algorithm. The convergence of the improved algorithm is then proved by using an infinite product method. Finally, the proposed algorithm is illustrated via some numerical examples, and the experimental results show that the proposed new algorithm can solve the multi-person game.