Multi-Objective Evolutionary Algorithm Based on Decomposition With Orthogonal Experimental Design

Multi-objective evolutionary optimisation algorithms (MOEAs) have become a widely adopted way of solving the multi-objective optimisation problems (MOPs). The decomposition-based MOEAs demonstrate a promising performance for solving regular MOPs. However, when handling the irregular MOPs, the decomposition-based MOEAs cannot offer a convincing performance because no intersection between weight vector and the Pareto Front (PF) may lead to the same optimal solution assigned to the different weight vectors. To solve this problem, this paper proposes an MOEA based on decomposition with the orthogonal experimental design (MOEA/D-OED) that involves the selection operation, Orthogonal Experimental Design (OED) operation, and adjustment operation. The selection operation is to judge the unpromising weight vectors based on the history data of relative reduction values and convergence degree. The OED method based on the relative reduction function could make an explicit guidance for removing the worthless weight vectors. The adjustment operation brings in an estimation indicator of both diversity and convergence for adding new weight vectors into the interesting regions. To verify the versatility of the proposed MOEA/D-OED, 26 test problems with various PFs are evaluated in this paper. Empirical results have demonstrated that the proposed MOEA/D-OED outperforms eight representative MOEAs on MOPs with various types of PFs, showing promising versatility. The proposed algorithm shows highly competitive performance on all the various MOPs.