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Multi\(^3\): Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization

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Evolutionary Multi-Criterion Optimization (EMO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12654))

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Abstract

In this work we examine the inner mechanisms of the recently developed sophisticated local search procedure SOMOGSA. This method solves multimodal single-objective continuous optimization problems by first expanding the problem with an additional objective (e.g., a sphere function) to the bi-objective space, and subsequently exploiting local structures and ridges of the resulting landscapes. Our study particularly focusses on the sensitivity of this multiobjectivization approach w.r.t. (i) the parametrization of the artificial second objective, as well as (ii) the position of the initial starting points in the search space.

As SOMOGSA is a modular framework for encapsulating local search, we integrate Gradient and Nelder-Mead local search (as optimizers in the respective module) and compare the performance of the resulting hybrid local search to their original single-objective counterparts. We show that the SOMOGSA framework can significantly boost local search by multiobjectivization. Combined with more sophisticated local search and metaheuristics this may help in solving highly multimodal optimization problems in future.

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Notes

  1. 1.

    For two points \(a,b \in \mathbb {R}^m\) we state that a dominates b, if \(a_i \le b_i\) for all \(i \in \{1,\ldots , m\}\) and \(a_j<b_j\) for at least one \(j \in \{1,\ldots , m\}\). As a reminder, within this work, we only consider bi-objective problems, i.e., \(m = 2\).

  2. 2.

    LHS implementation of the pyDOE package: https://pythonhosted.org/pyDOE/.

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Acknowledgement

The authors acknowledge support by the European Research Center for Information Systems (ERCIS).

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Authors and Affiliations

  1. Statistics and Optimization Group, University of Münster, Münster, Germany

    Pelin Aspar, Pascal Kerschke, Vera Steinhoff, Heike Trautmann & Christian Grimme

  2. LIACS, University of Leiden, Leiden, The Netherlands

    Pelin Aspar

Authors
  1. Pelin Aspar
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  2. Pascal Kerschke
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  3. Vera Steinhoff
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  4. Heike Trautmann
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  5. Christian Grimme
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Corresponding authors

Correspondence to Pelin Aspar , Pascal Kerschke , Vera Steinhoff , Heike Trautmann or Christian Grimme .

Editor information

Editors and Affiliations

  1. Southern University of Science and Technology, Shenzhen, China

    Hisao Ishibuchi

  2. City University of Hong Kong, Kowloon Tong, China

    Qingfu Zhang

  3. Southern University of Science and Technology, Shenzhen, China

    Ran Cheng

  4. University of Exeter, Exeter, UK

    Ke Li

  5. Xi'an Jiaotong University, Xi'an, China

    Hui Li

  6. Xidian University, Xi'an, China

    Handing Wang

  7. East China Normal University, Shanghai, China

    Aimin Zhou

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Aspar, P., Kerschke, P., Steinhoff, V., Trautmann, H., Grimme, C. (2021). Multi\(^3\): Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization. In: Ishibuchi, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2021. Lecture Notes in Computer Science(), vol 12654. Springer, Cham. https://doi.org/10.1007/978-3-030-72062-9_25

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  • DOI: https://doi.org/10.1007/978-3-030-72062-9_25

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  • Online ISBN: 978-3-030-72062-9

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