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• A two-stage evolution strategy is proposed for solving multi-objective problem. • The convergence and diversity should be balanced in multi-objective optimization. • A local searching method can improve the diversity of solutions in the space. • Experimental results have been presented by using statistical method. The balance of convergence and diversity plays a significant role to the performance of multi-objective evolutionary algorithms (MOEAs). The MOEA/D is a very popular multi-objective optimization algorithm and has been used to solve various real world problems. Like many other algorithms, the MOEA/D also has insufficient ability of convergence and diversity when tackling certain complex multi-objective optimization problems (MOPs). In this paper, a novel algorithm named MOEA/D-TS is proposed for effectively solving MOPs. The new algorithm adopts two stages evolution strategies, the first stage is focused on pushing the solutions into the area of the Pareto front and speeding up its convergence ability, after that, the second stage conducts in the operating solution's diversity and makes the solutions distributed uniformly. The performance of MOEA/D-TS is validated in the ZDT, DTLZ and IMOP problems. Compared with others popular and variants algorithms, the experimental results demonstrate that the proposed algorithm has advantage over other algorithms with regard to the convergence and diversity in most of the tested problems. [ABSTRACT FROM AUTHOR]