A multi-population competitive evolutionary algorithm based on genotype preference for multimodal multi-objective optimization

Many existing multimodal multi-objective evolutionary algorithms (MMOEAs) exhibit poor performance in addressing multimodal multi-objective optimization problems (MMOPs), mainly due to limited genetic diversity in environmental selection. In this paper, we propose a multi-population competitive evolutionary algorithm based on genotype preference (MPCEA-GP) to solve MMOPs. Firstly, we propose a population selection strategy based on genotype preference to maintain the genetic diversity of the population. This strategy utilizes the spectral radius to assess the overall convergence quality of the population, rather than evaluating each individual separately, and favors selecting the population with the minimum spectral radius, thereby preserving the genotypes of both optimal and suboptimal individuals. Secondly, to address the challenge of diminished genetic diversity during the evolutionary process, we incorporate historical survival population with substantial genetic diversity into the competition between parent and offspring, and preferentially select individuals with significant genotype differences to recombine into a new population. By merging two selected populations, a joint population with sufficient genetic diversity is constructed. Finally, a genotype-phenotype-based fitness criterion is devised to evaluate the fitness of individuals. This criterion not only compares genotypes using the Pareto dominance principle but also concurrently considers both genotype and phenotype diversity, aiding the population in more precisely identifying individuals with both good convergence and diversity. Empirical results show that MPCEA-GP outperforms state-of-the-art MMOEAs for 40 chosen benchmark functions and two complex real-world applications.