High-dimensional expensive multi-objective optimization via additive structure

Expensive multi-objective problems (MOPs) are extremely challenging due to the high evaluation cost to find satisfying solutions with adequate precision, especially in high-dimensional cases. However, most of the current EGO-based algorithms for expensive MOPs are limited to low decision dimensions because of the exponential difficulty in high dimensional circumstances. This paper presents High-Dimensional Expensive Multi-objective Optimization with Additive structure (ADD-HDEMO) to solve high-dimensional expensive MOPs via additive structural kernel and identifies two key challenges in this endeavor. First, we integrate multiple sub-objectives in high-dimensional expensive MOPs into a single objective with the decision space unchanged. Then, we infer the dependence correlation between the decision and objective space of the augmented EMOP via an additive GP kernel structure where Gibbs sampling is used to learn the latent additive structure. Furthermore, we parallel the proposed algorithm by introducing a multi-point sampling mechanism when recommending infill points. The effectiveness of the proposed method is evaluated on ZDT and DTLZ benchmarks compared with three other EGO-based multi-objective optimization approaches, ParEGO, SMS-EGO and MOEA/D-EGO. Our analyses demonstrate that ADD-HDEMO is effective in solving high-dimensional expensive MOPs.