Simultaneous use of two normalization methods in decomposition-based multi-objective evolutionary algorithms

Linjun He, Ke Shang, Hisao Ishibuchi

Abstract: In real-world applications, the order of magnitude in each objective varies, whereas most of fitness evaluation methods in many-objective solvers are scaling dependent. Objective space normalization has a large effect on the performance of each algorithm (i.e., on the practical applicability of each algorithm to real-world problems). In order to put equal emphasis on each objective, a normalization mechanism is always encouraged to be employed in the framework of the algorithm. Decomposition-based algorithms have become more and more popular in many-objective optimization. MOEA/D is a representative decomposition-based algorithm. Recently, some negative effects of normalization have been reported, which may deteriorate the practical applicability of MOEA/D to real-world problems. In this paper, to remedy the performance deterioration introduced by normalization in MOEA/D, we propose an idea of using two types of normalization methods in MOEA/D simultaneously (denoted as MOEA/D-2N). The proposed idea is compared with the standard MOEA/D and MOEA/D with normalization (denoted as MOEA/D-N) via two widely-used test suites (as well as their variants) and a real-world optimization problem. Experimental results show that MOEA/D-2N can effectively evolve a more diverse set of solutions and achieve robust and comparable performance compared with the standard MOEA/D and MOEA/D-N.