Estimating Feasible Region Shapes in Decomposition-based Surrogate-Assisted Multiobjective Evolutionary Algorithms

Abstract

In real-world optimization, function evaluations are often computationally and/or financially expensive. To solve such expensive multiobjective optimization problems (EMOPs), many decomposition-based surrogate-assisted multiobjective evolutionary algorithms (SAMOEAs) have been developed. Typically, decomposition-based SAMOEAs divide an EMOP into multiple subproblems using a set of weight vectors. However, the performance of decomposition-based SAMOEAs strongly depends on the shape of the feasible region (FR shape). To address this issue, this paper proposes a framework that estimates the FR shape in advance and adaptively adjusts the weight vectors accordingly. Experimental results show that the performance dependence of three popular decomposition-based SAMOEAs, i.e., MCEA/D, LDS-AF, and SFA/DE, is effectively mitigated by integrating the proposed framework.