Game-theoretic Evolutionary Algorithm Based on Behavioral Expectation and its Performance Analysis

Game theory has been widely recognized as an important tool in many fields, which provides general mathematical techniques for analyzing situations in which two or more individuals make decisions that will influence one another's welfare. This paper presents a game-theoretic evolutionary algorithm based on behavioral expectation, which is a type of optimization approach based on game theory. A formulation to estimate the payoffs expectation is given, which is a mechanism of trying to master the player's information so as to facilitate the player becoming the rational decision maker. GameEA has one population (players set), and generates new offspring only by the imitation operator and the belief learning operator. The imitation operator is used to learn strategies and actions from other players to improve its competitiveness and applies it into the future game, namely that one player updates its chromosome by strategically copying some segments of gene sequences from the competitor. Belief learning refers to models in which a player adjusts its own strategies, behavior or chromosome by analyzing current history information with respect to an improvement of solution quality. The experimental results on various classes of problems using real-valued representation show that GameEA outperforms not only the standard genetic algorithm (GA) but also other GAs having additional mechanisms of accuracy enhancement. Finally, we compare the convergence of GameEA with different numbers of players to determine whether this parameter has a significant effect on convergence. The statistical results show that at the 0.05 significance level, the number of players has a crucial impact on GameEA's performance. The results suggest that 50 or 100 players will provide good results with unimodal functions, while 200 players will provide good results for multimodal functions.