# Game Theory-Inspired Evolutionary Algorithm for Global Optimization
## 1 Introduction  
Several approaches have been proposed to model the specific intelligent behavior, such as the ant colony algorithm [1] based on the behavior of ants searching for food; the firefly algorithm, inspired by the flashing behavior of fireflies [2]; the fish swarm algorithm, inspired by the collective movement of the fish and their various social behaviors [3, 4]; artificial bee colony [5], and its variants [6]; cuckoo search [7]; and artificial immune system [8], etc. Some other kinds of algorithms, like neural computation [9] or brainstorming algorithms [10], are enlightened from the advanced activities of human brain, which focus on the intelligence of cell behaviors. Obviously, those studies are concentrated on the simulated biologic behavior rule or biological mechanism. Game theory, which is a theory for the science of logical decision-making in humans and computers, is applied to an extensive range of behavioral relations [11]. A game typically involves several players, strategies or actions, orders, and payoffs, which are similar to the individuals, genetic operators (selection, crossover and mutation), and fitness involved in evolutionary algorithms. Players usually select a strategy based on the expected payoffs. Otherwise, they apply learning methods, such as reinforcement learning [12], belief learning [13], imitation [14], directional learning [15, 16], and rule learning [17], to guarantee gains. A player makes a decision based on his/her perception of the actions of other players. Evolution through natural selection is typically attributed to improvement and progress, and game-theoretic arguments are more appropriate than optimization algorithms in studying frequency-dependent selection [18]. Replicator and adaptivedynamics describe short- and long-term evolution in the phenotype space and have been applied in a variety of fields ranging from animal behavior and ecology to speciation, macroevolution, and human language. Evolutionary game theory is an essential component of a mathematical and computational approach to biology. In addition to focus on agent-based automated negotiation research, there are studies [19; 20] on searching the strategies through co-evolutionary learning using EAs and game-theoretic analysis. Additionally, recent research [21] suggests that predictive adaptive responses can lead to differential development among initially-similar individuals and increase evolutionary fitness, which is an adaptive change in long-term behavior or development because it is triggered by environmental exposure. The use of a learning strategy can help an entity win against the top entries from the Othello League without explicitly applying human knowledge [22]. Aimed at obtaining an optimization approach embodied the mechanism of behavior game fully, a game evolutionary model used to calculate the payoffs expectation was established [23]. Game mechanisms can be used to devolve a new intelligent algorithm. Thus, this work investigates a game theory-inspired evolutionary algorithm for global optimization (GameEA), which is an optimization approach based on behavioral expectation. The contributions of this study are summarized as follows. * A novel game evolutionary algorithm (GameEA) is introduced which is a framework to simulate human game behavior. GameEA includes imitation and belief learning strategies and a payoff expectation mechanism. Learning strategies are used to improve competitiveness of the players, while the payoff expectation formulation is employed to estimate and master the information of the players. * We compared GameEA with the standard genetic algorithm (StGA) [24], island-model genetic algorithms (IMGA) [25], finding multimodal solutions using restricted tournament selection (RTS) [26], dual-population genetic algorithm (DPGA) [27], and GameEA outperforms the compared four algorithms in terms of stability and accuracy. The remainder of this paper is organized as follows: Section 2 presents some related works.