Enhancing Metaheuristic Algorithm Performance Through Structured Population and Evolutionary Game Theory

Héctor Escobar-Cuevas, Erik Cuevas, Alberto Luque-Chang (), Oscar Barba-Toscano and Marco Pérez-Cisneros
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Héctor Escobar-Cuevas: Department of Electro-Photonic Engineering, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara 44430, Jalisco, Mexico
Erik Cuevas: Department of Electro-Photonic Engineering, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara 44430, Jalisco, Mexico
Alberto Luque-Chang: Department of Electro-Photonic Engineering, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara 44430, Jalisco, Mexico
Oscar Barba-Toscano: Department of Electro-Photonic Engineering, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara 44430, Jalisco, Mexico
Marco Pérez-Cisneros: Department of Electro-Photonic Engineering, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara 44430, Jalisco, Mexico

Mathematics, 2024, vol. 12, issue 23, 1-44

Abstract: Diversity is crucial for metaheuristic algorithms. It prevents early convergence, balances exploration and exploitation, and helps to avoid local optima. Traditional metaheuristic algorithms tend to rely on a single strategy for generating new solutions, often resulting in a lack of diversity. In contrast, employing multiple strategies encourages a variety of search behaviors and a diverse pool of potential solutions, thereby improving the exploration of the search space. Evolutionary Game Theory (EGT) modifies agents’ strategies through competition, promoting successful strategies and eliminating weaker ones. Structured populations, as opposed to unstructured ones, preserve diverse strategies through localized competition, meaning that an individual’s strategy is influenced by only a subset or group of the population and not all elements. This paper presents a novel metaheuristic method based on EGT applied to structured populations. Initially, individuals are positioned near optimal regions using the Metropolis–Hastings algorithm. Subsequently, each individual is endowed with a unique search strategy. Considering a certain number of clusters, the complete population is segmented. Within these clusters, the method enhances search efficiency and solution quality by adapting all strategies through an intra-cluster competition. To assess the effectiveness of the proposed method, it has been compared against several well-known metaheuristic algorithms across a suite of 30 test functions. The results indicated that the new methodology outperformed the established techniques, delivering higher-quality solutions and faster convergence rates.

Keywords: metaheuristic; game theory; optimization; competition; Metropolis–Hastings (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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