Relation between Neighborhood Size and MOEA/D Performance on Many-Objective Problems

MOEA/D is a simple but powerful scalarizing function-based EMO algorithm. Its high search ability has been demonstrated for a wide variety of multiobjective problems. MOEA/D can be viewed as a cellular algorithm. Each cell has a different weight vector and a single solution. A certain number of the nearest cells are defined for each cell as its neighbors based on the Euclidean distance between weight vectors. A new solution is generated for each cell from current solutions in its neighboring cells. The generated solution is compared with the current solutions in the neighboring cells for solution replacement. In this paper, we examine the relation between the neighborhood size and the performance of MOEA/D. In order to examine the effect of local mating and local replacement separately, we use a variant of MOEA/D with two different neighborhoods: One is for local mating and the other is for local replacement. The performance of MOEA/D with various combinations of two neighborhoods is examined using the hypervolume in the objective space and a diversity measure in the decision space for many-objective problems. Experimental results show that MOEA/D with a large replacement neighborhood has high search ability in the objective space. However, it is also shown that small replacement and mating neighborhoods are beneficial for diversity maintenance in the decision space. It is also shown that the appropriate specification of two neighborhoods strongly depends on the problem.