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On the Convergence of Decomposition Algorithms in Many-Objective Problems

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Evolutionary Multi-Criterion Optimization (EMO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11411))

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Abstract

Decomposition methods have been considered for dealing with many-objective problems, since the Pareto-dominance selection was found to become ineffective as the number of objectives grow beyond four. As decomposition methods change the multiobjective problem into a set of single-objective problems, the difficulties found by evolutionary algorithms in many-objective optimization were expected to become alleviated. This paper studies the convergence properties of two decomposition schemes, respectively based on Euclidean norm and on Tchebyschev norm, in many-objective optimization. Numerical experiments show that the solution sequences obtained from Tchebyschev norm decomposition becomes stuck at a finite distance from the Pareto-set, while the sequences obtained from Euclidean norm decomposition may be adjusted such that an asymptotic convergence is achieved. Explanations for those different convergence behaviors are obtained from recently developed analytical tools.

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Authors and Affiliations

  1. Department of Mathematics, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil

    Ricardo H. C. Takahashi

Authors
  1. Ricardo H. C. Takahashi
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Correspondence to Ricardo H. C. Takahashi .

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Editors and Affiliations

  1. Michigan State University, East Lansing, MI, USA

    Kalyanmoy Deb

  2. Michigan State University, East Lansing, MI, USA

    Erik Goodman

  3. CINVESTAV-IPN, Mexico, Mexico

    Carlos A. Coello Coello

  4. University of Wuppertal, Wuppertal, Germany

    Kathrin Klamroth

  5. University of Jyvaskyla, Jyväskylä, Finland

    Kaisa Miettinen

  6. Otto von Guericke University Magdeburg, Magdeburg, Germany

    Sanaz Mostaghim

  7. Cornell University, Ithaca, NY, USA

    Patrick Reed

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Takahashi, R.H.C. (2019). On the Convergence of Decomposition Algorithms in Many-Objective Problems. In: Deb, K., et al. Evolutionary Multi-Criterion Optimization. EMO 2019. Lecture Notes in Computer Science(), vol 11411. Springer, Cham. https://doi.org/10.1007/978-3-030-12598-1_4

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  • DOI: https://doi.org/10.1007/978-3-030-12598-1_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12597-4

  • Online ISBN: 978-3-030-12598-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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