An Expensive Multi-objective Optimization Algorithm Based on Regional Density Ratio

Training surrogate models with high quality often requires a sufficient quantity of labelled data with a balanced distribution. However, obtaining enough labelled solutions for expensive optimization problems is challenging, let alone achieving a uniformly distributed training dataset. In this paper, we propose an expensive multi-objective evolutionary algorithm based on regional density ratio (MOEA-RDR) for solving computationally expensive problems. In MOEA-RDR, a new evaluation metric, integrating the uncertainty measures of Gaussian process models with the underlying assumptions of semi-supervised techniques, is introduced to select unlabelled solutions to participate in the training of surrogate models. A number of experiments are conducted on WFG test problems, and the experimental results show that our proposed method is more efficient than four state-of-the-art algorithms for solving computationally expensive multi-objective problems.