Efficient optimization of many objectives by approximation-guided evolution

Markus Wagner, Karl Bringmann, Tobias Friedrich, Frank Neumann

Research output: Contribution to journalArticleResearchpeer-review

27 Citations (Scopus)

Abstract

Multi-objective optimization problems arise frequently in applications, but can often only be solved approximately by heuristic approaches. Evolutionary algorithms have been widely used to tackle multi-objective problems. These algorithms use different measures to ensure diversity in the objective space but are not guided by a formal notion of approximation. We present a framework for evolutionary multi-objective optimization that allows to work with a formal notion of approximation. This approximation-guided evolutionary algorithm (AGE) has a worst-case runtime linear in the number of objectives and works with an archive that is an approximation of the non-dominated objective vectors seen during the run of the algorithm. Our experimental results show that AGE finds competitive or better solutions not only regarding the achieved approximation, but also regarding the total hypervolume. For all considered test problems, even for many (i.e., more than ten) dimensions, AGE discovers a good approximation of the Pareto front. This is not the case for established algorithms such as NSGA-II, SPEA2, and SMS-EMOA. In this paper we compare AGE with two additional algorithms that use very fast hypervolume-approximations to guide their search. This significantly speeds up the runtime of the hypervolume-based algorithms, which now allows a comparison of the underlying selection schemes.

Original languageEnglish
Pages (from-to)465-479
Number of pages15
JournalEuropean Journal of Operational Research
Volume243
Issue number2
DOIs
Publication statusPublished - 1 Jun 2015
Externally publishedYes

Keywords

  • Approximation
  • Comparative study
  • Multi-objective optimization

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