MOEA/D-ARA+SBX: A new multi-objective evolutionary algorithm based on decomposition with artificial raindrop algorithm and simulated binary crossover

In the field of optimization computation, there has been a growing interest in applying intelligent algorithms to solve multi-objective optimization problems (MOPs). This paper focuses mainly on the multi-objective evolutionary algorithm based on decomposition, MOEA/D for short, which offers a practical general algorithmic framework of evolutionary multi-objective optimization, and has been achieved great success for a wide range of MOPs. Like most other algorithms, however, MOEA/D has its limitations, which are reflected in three aspects: the problem of balancing diversity and convergence, non-uniform distribution of the Pareto front (PF), and weak convergence of the algorithm. To alleviate these limitations, a new combination of the artificial raindrop algorithm (ARA) and a simulated binary crossover (SBX) operator is first integrated into the framework of MOEA/D to balance the convergence and diversity. Thus, our proposed approach is called MOEA/D with ARA and SBX (MOEA/D-ARA+SBX). On the other hand, the raindrop pool in ARA is further extended to an external elitist archive, which retains only non-dominated solutions and discards all others. In addition, the k-nearest neighbors approach is introduced to prune away redundant non-dominated solutions. In such a way, a Pareto approximate subset with good distribution to the true PF may be achieved. Based on the relevant mathematical theory and some assumptions, it is proven that MOEA/D-ARA+SBX can converge to the true PF with probability one. For performance evaluation and comparison purposes, the proposed approach was applied to 44 multi-objective test problems with all types of Pareto set shape, and compared with 16 other versions of MOEA/D. The experimental results indicate its advantages over other approaches.