Variable Reconstruction for Evolutionary Expensive Large-Scale Multiobjective Optimization and Its Application on Aerodynamic Design

Expensive multiobjective optimization problems (EMOPs) are complex optimization problems exacted from real-world applications, where each objective function evaluation (FE) involves expensive computations or physical experiments. Many surrogate-assisted evolutionary algorithms (SAEAs) have been designed to solve EMOPs. Nevertheless, EMOPs with large-scale decision variables remain challenging for existing SAEAs, leading to difficulties in maintaining convergence and diversity. To address this deficiency, we proposed a variable reconstruction-based SAEA (VREA) to balance convergence enhancement and diversity maintenance. Generally, a cluster-based variable reconstruction strategy reconstructs the original large-scale decision variables into low-dimensional weight variables. Thus, the population can be rapidly pushed towards the Pareto set (PS) by optimizing low-dimensional weight variables with the assistance of surrogate models. Population diversity is improved due to the cluster-based variable reconstruction strategy. An adaptive search step size strategy is proposed to balance exploration and exploitation further. Experimental comparisons with four state-of-the-art SAEAs are conducted on benchmark EMOPs with up to 1000 decision variables and an aerodynamic design task. Experimental results demonstrate that VREA obtains well-converged and diverse solutions with limited real FEs.