A modification to MOEA/D-DE for multiobjective optimization problems with complicated Pareto sets

This paper presents an algorithm, named the uniform design multiobjective differential algorithm based on decomposition (UMODE/D), for optimizing multiobjective problems. The algorithm is a modification to the new version of MOEA/D based on differential evolution (DE), i.e., MOEA/D-DE proposed by Li and Zhang (2009) [20]. Its distinguishing features include: (1) The uniform design method is applied to generate the aggregation coefficient vectors so that the decomposed scalar optimization subproblems are uniformly distributed, and therefore the algorithm could explore uniformly the region of interest from the initial iteration; (2) The simplified quadratic approximation with three best points is employed to improve the local search ability and the accuracy of the minimum scalar aggregation function value. UMODE/D is compared with the original MOEA/D-DE and NSGA-II by solving a wide set of problems with complicated Pareto set shapes in this paper. Experimental results indicate that UMODE/D significantly outperforms MOEA/D-DE and NSGA-II on these test problems. Two sets of experiments are carried out to illustrate the efficiency of the uniform design method and the simplified quadratic approximation separately. In addition, UMODE/D is tested on CEC 2009 problems and combinatorial knapsack problems. Experimental results show that the proposed algorithm performs better than the further improved MOEA/D for almost all the CEC 2009 problems, and the results obtained are very competitive when comparing UMODE/D with some other algorithms on these multiobjective knapsack problems.