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A Partition-Based Random Search Method for Multimodal Optimization

Author

Listed:
  • Ziwei Lin

    (Politecnico di Milano, Department of Mechanical Engineering, 20133 Milan, Italy)

  • Andrea Matta

    (Politecnico di Milano, Department of Mechanical Engineering, 20133 Milan, Italy)

  • Sichang Du

    (Department of Industrial Engineering and Management, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China)

  • Evren Sahin

    (Laboratoire Genie Industriel, CentraleSupelec, Paris Saclay University, 3 Rue Joliot-Curie, 91192 Gif-sur-Yvette, France)

Abstract

Practical optimization problems are often too complex to be formulated exactly. Knowing multiple good alternatives can help decision-makers easily switch solutions when needed, such as when faced with unforeseen constraints. A multimodal optimization task aims to find multiple global optima as well as high-quality local optima of an optimization problem. Evolutionary algorithms with niching techniques are commonly used for such problems, where a rough estimate of the optima number is required to determine the population size. In this paper, a partition-based random search method is proposed, in which the entire feasible domain is partitioned into smaller and smaller subregions iteratively. Promising regions are partitioned faster than unpromising regions, thus, promising areas will be exploited earlier than unpromising areas. All promising areas are exploited in parallel, which allows multiple good solutions to be found in a single run. The proposed method does not require prior knowledge about the optima number and it is not sensitive to the distance parameter. By cooperating with local search to refine the obtained solutions, the proposed method demonstrates good performance in many benchmark functions with multiple global optima. In addition, in problems with numerous local optima, high-quality local optima are captured earlier than low-quality local optima.

Suggested Citation

  • Ziwei Lin & Andrea Matta & Sichang Du & Evren Sahin, 2022. "A Partition-Based Random Search Method for Multimodal Optimization," Mathematics, MDPI, vol. 11(1), pages 1-30, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:17-:d:1009604
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    References listed on IDEAS

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