A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions

There are many challengeable multiobjective optimization problems in different areas, whose optimization objectives are usually diversionary. Decomposition methods and evolution mechanisms enable multiobjective evolutionary algorithms based on decomposition (MOEA/D) to tackle these complex optimization problems efficiently. Therefore, MOEA/D has found wide applications in various fields and been attracting increasingly significant attention from both academia and industry since it was first proposed by Zhang and Li in 2007. Many efforts that are dedicated to improving and extending MOEA/D have been summarized shortly by some papers in their introductions, and there exists only one article that reviewed MOEA/D comprehensively in 2017. However, a number of MOEA/D variants with novel methods solving versatile problems in different fields have been emerging since then. This article is motivated by a more systematic survey of MOEA/D from its original ideas to edge-cutting works, including its basic framework and a comprehensive overview of the improvements on key components (decomposition method, weight vector generation method, and evolutionary operator) and the extensions to both many-objective and constrained multiobjective optimizations. The findings of this survey are categorized in seven aspects with corresponding references. In addition, different from introducing briefly the future research directions of MOEA/D in conclusion of the survey in 2017, we present a more detailed outlook that explores not only the novel challenges but also the future research directions, including three aspects in theory and application researches, its challenges in many-objective optimization, and some issues applying MOEA/D to the cutting-edge areas. It is expected that our work will help researchers to start their MOEA/D-based investigations.