Recently, evolutionary multi-objective optimization (EMO) algorithms have been used in various application fields. Whereas many new EMO algorithms are proposed every year, well-known EMO algorithms such as NSGA-II, MOEA/D, SMS-EMOA and NSGA-III have been still frequently used in application papers as shown by their number of citations. Since most EMO algorithms have been designed for and evaluated by artificial test problems such as DTLZ and WFG, they do not always work well on real-world problems. Main difficulties of real-world problems are as follows: (i) their Pareto front shapes are irregular, (ii) some objectives have much larger values than others, (iii) some decision variables have much larger values than others, (iv) some objectives are highly correlated, and (v) solution evaluation is expensive. In this paper, we focus on the first four difficulties (except for expensive solution evaluation). Our goal is to clearly explain problematic search behaviors of NSGA-II, MOEA/D, SMS-EMOA and NSGA-III caused by these difficulties using simple distance minimization problems. We formulate various distance minimization problems with the above-mentioned four difficulties by changing the location of each target point on the map as well as the size and shape of the map. We also suggest simple remedies for performance improvement of each algorithm for real-world applications without changing the algorithm itself.

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Visual Explanations of Some Problematic Search Behaviors of Frequently-Used EMO Algorithms

  • Hisao Ishibuchi,
  • Lie Meng Pang

摘要

Recently, evolutionary multi-objective optimization (EMO) algorithms have been used in various application fields. Whereas many new EMO algorithms are proposed every year, well-known EMO algorithms such as NSGA-II, MOEA/D, SMS-EMOA and NSGA-III have been still frequently used in application papers as shown by their number of citations. Since most EMO algorithms have been designed for and evaluated by artificial test problems such as DTLZ and WFG, they do not always work well on real-world problems. Main difficulties of real-world problems are as follows: (i) their Pareto front shapes are irregular, (ii) some objectives have much larger values than others, (iii) some decision variables have much larger values than others, (iv) some objectives are highly correlated, and (v) solution evaluation is expensive. In this paper, we focus on the first four difficulties (except for expensive solution evaluation). Our goal is to clearly explain problematic search behaviors of NSGA-II, MOEA/D, SMS-EMOA and NSGA-III caused by these difficulties using simple distance minimization problems. We formulate various distance minimization problems with the above-mentioned four difficulties by changing the location of each target point on the map as well as the size and shape of the map. We also suggest simple remedies for performance improvement of each algorithm for real-world applications without changing the algorithm itself.