Decomposition-Based Multi-Objective Evolutionary Algorithm with Model-Based Ideal Point Estimation

Abstract

The ideal point is critical in the multi-objective optimization problem (MOP), which consists of the best value of each objective. It is widely used for normalizing the objective space and guiding the evolution of the population. Since the ideal point cannot know prior, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) takes the best objective values of the population as the estimated ideal point. However, the population-based ideal point estimation may cause the estimated ideal point to be appropriate for (1) no objective or (2) only some objectives. In our analysis, the unreliable estimation deteriorates the performance of MOEA/D. These two scenarios often occur when the MOP with mixed bias (i.e., position-related bias and distance-related bias). To overcome this, we propose to incorporate the model-based ideal point estimation in MOEA/D. The new algorithm (called MOEA/D-MIPE) employs the radial basis function model and a remedy scheme to estimate the ideal point. In experimental studies, we compare MOEA/D-MIPE with seven state-of-the-art algorithms on various MOPs. The results show that MOEA/D-MIPE has excellent potential.