Regression and relation-assisted evolutionary algorithm for high-dimensional expensive multi-objective optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have gained a lot of attention to handle expensive multi-objective optimization problems (EMOPs). However, when it comes to high-dimensional EMOPs (HEMOPs), the performance of existing SAEAs degrades dramatically because of the dimensionality sensitivity issue, in which effective surrogate models are difficult to build. To this end, we propose a regression- and relation-assisted evolutionary algorithm (${\text{R}}^2\text{AEA}$) to deal with HEMOPs, which involves a regression-assisted weight optimization (RWO) stage and a relation-assisted multi-objective optimization (RMO) stage. To be specific, the RWO is facilitated by the problem transformation strategy and regression models. It reformulates the high-dimensional problem into a relative low-dimensional one and intends to converge to the Pareto-optimal front (PF) efficiently. Thereafter, the RMO concentrates on maintaining the population diversity with a new infill sampling criterion, which considers the optimization performance as well as the uncertainty estimated by the predicted entropy. To validate its effectiveness, we compare ${\text{R}}^2\text{AEA}$ with five state-of-the-art algorithms on various benchmark test suites with dimensions varying from 50 to 200, and six real-world HEMOPs. Experimental results show the superiority of ${\text{R}}^2\text{AEA}$ in terms of convergence speed and diversity maintenance with limited computational resources.