Efficient Tournament Selection Using Data Envelopment Analysis in Multiobjective Genetic Algorithms with Pareto Front Modeling and Reference Pairing

In the real world, multiobjective optimization problems require the efficient acquisition of diverse solutions. Various multiobjective evolutionary algorithms (MOEAs) have been developed to address these problems. Typically, MOEAs use the same scoring criteria for both survival and mating selection, despite their different roles. Survival selection should ensure convergence and diversity, whereas mating selection should focus on selecting individuals with higher convergence for crossover. In this article, an efficient selection algorithm is proposed that integrates data envelopment analysis (DEA), Pareto front modeling, and a reference crossover mechanism. In survival selection, algorithms are used to ensure high convergence and diversity. In a previous study, DEA was employed to select individuals with higher convergence in mating selection. This approach balances convergence and diversity. In addition, Pareto front modeling addresses the convexity assumption issue in DEA. In this study, by selecting constraint solutions obtained through DEA as crossover targets, the algorithm makes crossover with superior solutions possible, enhancing optimization speed and diversity. The algorithm is particularly effective for benchmark functions that benefit from neighborhood crossover. In comparisons using the hypervolume metric on the WFG and DTLZ benchmark functions, the proposed algorithm outperformed NSGA-II, NSGA-III, AGE-MOEA-II, DEA-GA, MOEA/D, and other previous algorithms. The results of a Wilcoxon rank-sum test also showed that the proposed algorithm is statistically superior.