Multi-objective decomposition evolutionary algorithm with objective modification-based dominance and external archive

Abstract

In practice, the multi-objective optimization problem (MOP) is typically challenging in two aspects. On the one hand, its Pareto front has imbalanced search difficulties; on the other hand, its search space contains many dominance resistant solutions (DRSs). Decomposing a complicated MOP into several simple MOPs for collaborative optimization (M2M) has been acknowledged to be efficient in coping with the imbalanced search difficulty. Nevertheless, the convergence efficiency of the M2M-based multi-objective evolutionary algorithm (MOEA) is rarely investigated, especially on the MOP with DRSs. This paper reveals two convergence challenges faced by M2M-based MOEAs. Subsequently, a variant called MOEA/D-OMDEA is proposed to achieve better convergence efficiency without sacrificing advantages in diversity preservation. MOEA/D-OMDEA integrates a new relaxed dominance criterion, namely the OM-dominance criterion, into its environmental selection to alleviate the negative influence of inferior solutions (e.g., DRSs) as well as to better balance convergence and diversity. MOEA/D-OMDEA is compared with ten state-of-the-art MOEAs on two sets of MOP benchmarks with different characteristics and a real-world problem. Experimental results indicate that MOEA/D-OMDEA can significantly outperform the other ten competitors on these problems. In addition, this paper provides a thorough analysis of the effectiveness of each new algorithmic component and the sensitivity of each newly-introduced parameter.