Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has achieved great success in the field of evolutionary multi-objective optimization. It decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems. Each sub-problem is optimized by using information from its neighboring sub-problems. Therefore, the neighborhood size of each sub-problem plays an important role in MOEA/D. Different neighborhood sizes are tested in this paper. Experimental results demonstrate that larger neighborhood size helps achieve better convergence and diversity with more CPU time and vice versa. MOEA/D uses constant neighborhood size during the whole process, and it is difficult to balance the convergence, diversity and running time. Therefore, this paper propose an algorithm based on MOEA/D. The algorithm adjusts the neighborhood size dynamically in different generations and different sub-problems to reduce the running time while the convergence and diversity of this algorithm are similar or better than other state-of-the-art algorithms. Compared to the original MOEA/D, experimental results show that adjusting the neighborhood size dynamically is a good way to reduce the running time significantly while maintaining the convergence and diversity. Furthermore, the algorithm proposed in this paper is compared with five state-of-the-art algorithms based on MOEA/D. The experimental results show that the proposed algorithm outperforms the others in efficiency while performs similarly in convergence and diversity.INDEX TERMS MOEA/D, dynamic neighborhood size, diversity and convergence, running time.

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) is effective to solve most multi-objective optimization problems (MOPs) in the past 20 years. However, the algorithm MOEA/D with constant weight vectors has bad performance in solving several MOPs with discontinuous Pareto front (PF). This paper analyses the limitations of the constant weight vectors in MOEA/D and explains the necessity of adjusting the weight vectors in the processing. This paper proposes a weight vector adjustment method for MOEA/D (MOEA/D-WVA). It deletes the weight vectors which have bad search direction, and adds some new weight vectors in the processing. Experimental studies are conducted on several MOPs with discontinuous PF to compare the MOEA/D-WVA with other state-of-the-art multi-objective optimization algorithms in solving those MOPs with complex PF. The results show MOEA/D-WVA performs better than other algorithms on those MOPs with discontinuous PF. INDEX TERMS MOEA/D; discontinuous PF; search direction; weight vector; adjustment.

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