A survey of decomposition approaches in multiobjective evolutionary algorithms

Since the multiobjective evolutionary algorithm based on decomposition (MOEA/D) was proposed by Zhang and Li in 2007, this interesting framework has attracted a considerable attention from researchers. In MOEA/D, a multiobjective optimization problem is decomposed into a series of aggregated subproblems, which are optimized simultaneously in a collaborative way by using the information from their neighboring subproblems. The decomposition approach has significant impact on MOEA/D as it directs the evolutionary search. Many improved MOEA/D variants proposed various kinds of decomposition approaches and have shown promising performance for different kinds of problems. In this paper, we give a survey of decomposition approaches, which are classified into five categories, i.e., the tradition decomposition, the modified Tchebycheff decomposition, the modified penalty-based boundary intersection decomposition, the constrained decomposition, and other special cases of decomposition. Moreover, discussions are further given in this paper to analyze the performance of different decomposition approaches. One clarifies the difference between Tchebycheff decomposition and Pareto-based domination. The other one compares the performance of various decomposition approaches on different benchmark problems. Experiments results have demonstrated that the Tchebycheff decomposition and its varieties are robust on solving most problems while some specific decomposition approaches are very effective for some problems with special features.