Effects of using two neighborhood structures on the performance of cellular evolutionary algorithms for many-objective optimization

Cellular evolutionary algorithms usually use a single neighborhood structure for local selection. When a new solution is to be generated by crossover and/or mutation for a cell, a pair of parent solutions is selected from its neighbors. The current solution at the cell is replaced with the newly generated offspring if the offspring has the higher fitness value than the current one. That is, the ldquoreplace-if-betterrdquo policy is used for the replacement of the current solution. Local selection, crossover, mutation and replacement are iterated at every cell in cellular algorithms. A recently proposed multiobjective evolutionary algorithm called MOEA/D by Zhang and Li (2007) can be viewed as a cellular algorithm where each cell has its own scalarizing fitness function with a different weight vector. We can introduce a spatial structure to MOEA/D by the Euclidean distance between weight vectors. Its main difference from standard cellular algorithms is that a newly generated offspring for a cell is compared with not only the current solution of the cell but also its neighbors for local replacement in MOEA/D. In this paper, we examine the effect of local replacement on the search ability of a cellular version of MOEA/D. Whereas the same neighborhood structure was used for local selection and local replacement in the original MOEA/D, we examine the use of different neighborhood structures for local selection and local replacement. It is shown through computational experiments on multiobjective 0/1 knapsack problems with two, four and six objectives that local replacement plays an important role in MOEA/D especially for many-objective optimization problems.