Multiobjectivization of Single-Objective Optimization in Evolutionary Computation: A Survey.

Abstract

Multiobjectivization has emerged as a new promising paradigm to solve single-objective optimization problems (SOPs) in evolutionary computation, where an SOP is transformed into a multiobjective optimization problem (MOP) and solved by an evolutionary algorithm to find the optimal solutions of the original SOP. The transformation of an SOP into an MOP can be done by adding helper-objective(s) into the original objective, decomposing the original objective into multiple subobjectives, or aggregating subobjectives of the original objective into multiple scalar objectives. Multiobjectivization bridges the gap between SOPs and MOPs by transforming an SOP into the counterpart MOP, through which multiobjective optimization methods manage to attain superior solutions of the original SOP. Particularly, using multiobjectivization to solve SOPs can reduce the number of local optima, create new search paths from local optima to global optima, attain more incomparability solutions, and/or improve solution diversity. Since the term "multiobjectivization" was coined by Knowles et al. in 2001, this subject has accumulated plenty of works in the last two decades, yet there is a lack of systematic and comprehensive survey of these efforts. This article presents a comprehensive multifacet survey of the state-of-the-art multiobjectivization methods. Particularly, a new taxonomy of the methods is provided in this article and the advantages, limitations, challenges, theoretical analyses, benchmarks, applications, as well as future directions of the multiobjectivization methods are discussed.