An aggregated pairwise comparison-based evolutionary algorithm for multi-objective and many-objective optimization

Abstract

As the number of objectives increases, the ability of Pareto optimality in providing enough comparability among alternative solutions would be deteriorated seriously. In order to address this issue, this paper proposes a simple yet efficient fitness evaluation approach based on the piecewise aggregated pairwise comparisons (PAPC)11The aggregation of pairwise comparisons refers to that, for a solution x, its fitness value is the aggregation of the comparison results of x and other solutions in the population (Li et al., 2015). with the assistance of the two-stage selection strategy. The advantages of the proposed PAPC are threefold: (1) all the optimal solutions of the PAPC fitness being less than 0 are non-dominated solutions, (2) for the dominated solutions, PAPC is a metric of the distance to the non-dominated solution front, and (3) for the non-dominated solutions, PAPC rewards the diversity and penalizes the clustering behavior. Accordingly, PAPC can increase the comparability among candidate solutions with an explicit consideration of the convergence and diversity. Then, we develop a two-stage selection strategy and a niching strategy to assist PAPC to maintain diversity of solutions. We conduct experiments on a suite of test problems with up to 10 objectives, where the algorithm is also extended to handle constrained problems. The experimental results validate the effectiveness of the proposed algorithm on both multi-objective optimization problems and many-objective optimization problems.