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Pareto Optimal Set Approximation by Models: A Linear Case

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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

The optimum of a multiobjective optimization problem (MOP) usually consists of a set of tradeoff solutions, called Pareto optimal set, that balances different objectives. In the community of evolutionary computation, an internal or external population with a limited size is usually used to approximate the Pareto optimal set. Since the Pareto optimal set forms a manifold in both the decision and objective spaces under mild conditions, it is possible to use a model as well as a population of solutions to approximate the Pareto optimal set. Following this idea, the paper proposes to use a set of linear models to approximate the Pareto optimal set in the decision space. The basic idea is to partition the manifold into different segments and use a linear model to approximate each segment in a local area. To implement the algorithm, the models are incorporated in the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework. The proposed algorithm is applied to a test suite, and the comparison study demonstrates that models can help to improve the performance of algorithms that only use solutions to approximate the Pareto optimal set.

This work is supported by the National Natural Science Foundation of China under Grant Nos. 61673180, 61731009, and 61703382, and the Fundamental Research Funds for the Central Universities.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Technology, East China Normal University, Shanghai, China

    Aimin Zhou, Haoying Zhao & Guixu Zhang

  2. Beijing Electro-Mechanical Engineering Institute, Beijing, China

    Hu Zhang

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  1. Aimin Zhou
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  2. Haoying Zhao
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  3. Hu Zhang
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  4. Guixu Zhang
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Corresponding author

Correspondence to Aimin Zhou .

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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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Zhou, A., Zhao, H., Zhang, H., Zhang, G. (2019). Pareto Optimal Set Approximation by Models: A Linear Case. 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_36

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  • DOI: https://doi.org/10.1007/978-3-030-12598-1_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12597-4

  • Online ISBN: 978-3-030-12598-1

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