A Novel Multi-objective Evolutionary Algorithm Based on a Further Decomposition Strategy

Abstract

In multi-objective evolutionary algorithms (MOEAs) based on the constrained decomposition approach, the closest sub objective space to the sub-problem is treated as a feasible region for this sub-problem, where the solutions are regarded to be better than that outside it. This approach is expected to maintain the population's diversity. However, due to the inconsistency of the weight vectors and the current population, it leads to the disequilibrium of sub-problems that a lot of individuals may be located around one sub-problem, which obviously hampers the population's diversity. Thus, this paper suggests a novel MOEA based on a further decomposition strategy (MOEA/FD). The parents and offspring populations all with the size N are combined to a union population with 2N solutions and then they are associated to the preset N weight vectors using the constrained decomposition approach. Then, the number of sub-problems with no associated solution can be computed, and the sub-problem associated with the largest number of solutions is iteratively found to further decompose it into two sub-problems, which is achieved by using a clustering method. At last, N decomposed sub-problems can be found with no less than one solution in their feasible regions. At last, in each feasible region, a simple convergence indicator is used to select a well converged solution for next evolution. When compared to six competitive MOEAs, MOEA/FD presents some advantages on tackling seventeen well-known test problems.