The Combination of MOEA/D and WOF for Solving High-Dimensional Expensive Multiobjective Optimization Problems

The research on expensive multiobjective optimization has attracted particular attention in the area of multiobjective evolutionary computation. Many existing multiobjective evolutionary algorithms (MOEAs) are only suited for small-scale expensive multiobjective optimization problems (MOPs) with less than ten decision variables. The main reason lies in the fact that some optimization techniques used in expensive MOEAs, such as Gaussian Process (GP), are not applicable for exploring high-dimensional search space. The naive way to overcome this difficulty is to convert a high-dimensional expensive MOP into a low-dimensional MOP, which can be solved by existing expensive MOEAs efficiently. In this paper, we investigate the combination of MOEA/D with a weighted optimization framework (WOF) and GP, denoted by MOEA/D-WOFGP, for solving high-dimensional expensive MOPs, where the WOF converts a high-dimensional MOP into a low-dimensional search space of weight variables, and the GP-based learning method is used to predict high-quality solutions within a limited number of function evaluations. Some experiments are conducted to compare the performance of MOEA/D-WOFGP with other expensive MOEAs assisted by variable grouping. Our experimental results show that MOEA/D-WOFGP is advantageous when dealing with high-dimensional expensive MOPs.