Abstract
Multi-objective optimization is a blooming research area since many real-world problems comprise multiple objectives. Multi-objective evolutionary algorithms (MOEAs) have been widely used to solve the multi-objective optimization problems. In particular, the decomposition based MOEA (MOEA/D) has achieved considerable successes in tackling multi-objective optimization problems. The covariance matrix adaptation evolution strategy (CMAES) is known for its effectiveness in solving complex numerical optimization problems. This study integrates CMAES into MOEA/D as the MOEA/D-CMAES for the merits of MOEA/D framework in multi-objective optimization and CMAES in complex numerical optimization. In MOEA/D-CMAES, each subproblem is handled with one CMAES. To avoid the drastic increase in the number of offspring generated and their fitness evaluations, MOEA/D-CMAES generates only one offspring in each subproblem. The multivariate normal distribution in each CMAES is updated by the collaboration of the offspring generated in the present subproblem and those of other subproblems. Experimental results show that MOEA/D-CMAES outperforms MOEA/D using differential evolution in terms of hypervolume and convergence speed, which validate the effectiveness and efficiency of MOEA/D-CMAES in multi-objective optimization.