Moboa: a proposal for multiple objective bean optimization algorithm

Abstract The primary objective of multi-objective evolutionary algorithms (MOEAs) is to find a set of evenly distributed nondominated solutions that approximate the Pareto front (PF) of a multi-objective optimization problem (MOP) or a many-objective optimization problem (MaOP). This implies that the approximated solution set obtained by MOEAs should be as close to PF as possible while remaining diverse, adhering to criteria of convergence and diversity. However, existing MOEAs exhibit an imbalance between achieving convergence and maintaining diversity in the objective space. As far as the diversity criterion is concerned, it is still a challenge to achieve an evenly distributed approximation set with different sizes for a problem with a complicated PF shape. Furthermore, Pareto dominance has its own weaknesses as the selection criterion in evolutionary multiobjective optimization. Algorithms based on Pareto criterion (PC) can suffer from problems such as slow convergence to the optimal front and inferior performance on problems with many objectives. To effectively address these challenges, we propose a multi-objective bean optimization algorithm (MOBOA). Given that the selection of parent species, representing global optimal solutions, directly influences the convergence and diversity of the algorithm, MOBOA incorporates a preference order equilibrium parent species selection strategy (POEPSS). By extending the Pareto criterion with the preference order optimization criterion, the algorithm effectively enhances parent species selection pressure across multiple objectives. To balance convergence and diversity, MOBOA proposes a multi-population global search strategy explicitly maintaining an external archive during the search process. Leveraging the inherent multi-population advantages of bean optimization algorithm (BOA), the algorithm facilitates information sharing among the main population, auxiliary populations, and historical archive solution sets. Additionally, a diversity enhancement strategy is employed in the environmental selection stage, introducing the environmental selection strategy of the SPEA2 algorithm to generate a set of evenly distributed nondominated solutions. Experimental results on a series of widely used MOPs and MaOPs demonstrate that the proposed algorithm exhibits higher effectiveness and competitiveness compared to state-of-the-art algorithms.