A Distribution Control of Weight Vector Set for Multi-objective Evolutionary Algorithms

For solving multi-objective optimization problems with evolutionary algorithms, the decomposing the Pareto front by using a set of weight vectors is a promising approach. Although an appropriate distribution of weight vectors depends on the Pareto front shape, the uniformly distributed weight vector set is generally employed since the shape is unknown before the search. This work proposes a simple way to control the weight vector distribution appropriate for several Pareto front shapes. The proposed approach changes the distribution of the weight vector set based on the intermediate objective vector in the objective space. A user-defined parameter determines the intermediate objective vector in the static method, and the objective values of the obtained solutions dynamically determine the intermediate objective vector in the dynamic method. In this work, we focus on MOEA/D as a representative decomposition-based multi-objective evolutionary algorithm and apply the proposed static and dynamic methods for it. The experimental results on WFG test problems with different Pareto front shapes show that the proposed static and dynamic methods improve the uniformity of the obtained solutions for several Pareto front shapes and the dynamic method can find an appropriate intermediate objective vector for each Pareto front shape.