Periodical Weight Vector Update Using an Unbounded External Archive for Decomposition-Based Evolutionary Multi-Objective Optimization

Abstract

Decomposition-based evolutionary multiobjective optimization (EMO) algorithms are very popular. The basic idea of decomposition-based EMO algorithms is to decompose a multi/many-objective optimization problem into several single-objective subproblems using a set of weight vectors and a scalarizing function. The weight vector specification plays an important role in decomposition-based EMO algorithms for obtaining a set of well-distributed solutions. In this paper, we propose a new method to update weight vectors for decomposition-based EMO algorithms. The proposed method uses an unbounded external archive to store all the nondominated solutions among examined solutions during the execution of an EMO algorithm, and periodically select a set of uniformly distributed solutions from the archive. Then, the selected solutions are projected to the weight vector space and used as a set of weight vectors for decomposition-based algorithms. The usefulness of the proposed weight vector update method is demonstrated by integrating it into a most frequently used decomposition-based EMO algorithm, i.e., MOEA/D. Experimental results show that the proposed weight vector update method works well on MOEA/D. Our experimental results also show that MOEA/D with the proposed weight vector update method outperforms other weight vector adaptation-based algorithms on many-objective test problems.