Tree-Structured Decomposition and Adaptation in MOEA/D

Abstract

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) converts a multiobjective optimization problem (MOP) into a set of simple subproblems, and deals with them simultaneously to approximate the Pareto optimal set (PS) of the original MOP. Normally in MOEA/D, a set of weight vectors are predefined and kept unchanged during the search process. In the last few years, it has been demonstrated in some cases that a set of predefined subproblems may fail to achieve a good approximation to the Pareto optimal set. The major reason is that it is usually unable to define a proper set of subproblems, which take full consideration of the characteristics of the MOP beforehand. Therefore, it is imperative to develop a way to adaptively redefine the subproblems during the search process. This paper proposes a tree-structured decomposition and adaptation (TDA) strategy to achieve this goal. The basic idea is to use a tree structure to decompose the search domain into a set of subdomains that are related with some subproblems, and adaptively maintain these subdomains by analyzing the search behaviors of MOEA/D in these subdomains. The TDA strategy has been applied to a variety of test instances. Experimental results show the advantages of TDA on improving MOEA/D in dealing with MOPs with different characteristics.