Abstract
Large-scale multi-objective optimization problems (MOPs) that involve a large number of decision variables, have emerged from many real-world applications. While evolutionary algorithms (EAs) have been widely acknowledged as a mainstream method for MOPs, most research progress and successful applications of EAs have been restricted to MOPs with small-scale decision variables. More recently, it has been reported that traditional multi-objective EAs (MOEAs) suffer severe deterioration with the increase of decision variables. As a result, and motivated by the emergence of real-world large-scale MOPs, investigation of MOEAs in this aspect has attracted much more attention in the past decade. This paper reviews the progress of evolutionary computation for large-scale multi-objective optimization from two angles. From the key difficulties of the large-scale MOPs, the scalability analysis is discussed by focusing on the performance of existing MOEAs and the challenges induced by the increase of the number of decision variables. From the perspective of methodology, the large-scale MOEAs are categorized into three classes and introduced respectively: divide and conquer based, dimensionality reduction based and enhanced search-based approaches. Several future research directions are also discussed.
Highlights
Many real-world optimization problems involve multiple objectives, which are called multi-objective optimization problems (MOPs)[1]
Scalability of multi-objective EAs (MOEAs), which characterizes the changing trend of algorithm performance with the problem size, is a long-standing concern in the evolutionary computation community[12], and is critical to whether MOEAs can be applied to broader real-world problems
This paper focuses on the scalability of MOEAs with respect to the number of decision variables and presents an extensive review of recent progresses on evolutionary computation for large-scale multi-objective optimization in the last decade
Summary
Many real-world optimization problems involve multiple objectives, which are called multi-objective optimization problems (MOPs)[1]. Research on designing MOEAs with high scalability originates from practical needs To this end, basic ideas include simplifying large-scale MOPs via divide-and-conquer methodology[29] and dimensionality reduction[30] and improving the search ability of MOEAs by rebalancing the exploration and exploitation[28]. Basic ideas include simplifying large-scale MOPs via divide-and-conquer methodology[29] and dimensionality reduction[30] and improving the search ability of MOEAs by rebalancing the exploration and exploitation[28] From these three aspects, this paper summarizes the advances in scalable algorithm designs. The main focus is on how characteristics of MOPs and scalability challenges are integrated into the design of highly scalable MOEAs. To summarize, this paper focuses on the scalability of MOEAs with respect to the number of decision variables and presents an extensive review of recent progresses on evolutionary computation for large-scale multi-objective optimization in the last decade.
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