A Relation-and-Regression-assisted Evolutionary Algorithm for Expensive Constrained Multi-objective Optimization

Expensive constrained multi-objective optimization problems involve computationally expensive objectives and constraints, which impose stiff challenges on traditional evolutionary algorithms to optimize within limited function evaluations. To address this, some surrogate-assisted constrained multi-objective evolutionary algorithms have been proposed, where surrogate models are constructed to replace expensive function evaluations. However, most existing surrogate models are either regression or classification models, which are liable to poor reliability in approximating complicated constraints. In this paper, a relation-and-regression-assisted constrained multi-objective evolutionary algorithm, named RCMOEA, is proposed. In RCMOEA, each regression model is constructed to approximate each objective function, and each relation model is built to learn the relation of constraint values between any two solutions. Based on the constructed surrogate models, a relation-and-regression-based constrained Pareto dominance, denoted as RCPD, is proposed to compare solution pairs. By adopting RCPD as the dominance criterion, the RCPD-based selection strategy is proposed for selecting offspring solutions. Also, the distance-based infill sampling strategy is proposed to preserve the diversity of solutions. Experimental results demonstrate the superiority of RCMOEA over the compared algorithms.