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Attraction Basins in Metaheuristics: A Systematic Mapping Study

Author

Listed:
  • Mihael Baketarić

    (Faculty of Electrical Engineering and Computer Science, University of Maribor, 2000 Maribor, Slovenia)

  • Marjan Mernik

    (Faculty of Electrical Engineering and Computer Science, University of Maribor, 2000 Maribor, Slovenia)

  • Tomaž Kosar

    (Faculty of Electrical Engineering and Computer Science, University of Maribor, 2000 Maribor, Slovenia)

Abstract

Context : In this study, we report on a Systematic Mapping Study (SMS) for attraction basins in the domain of metaheuristics. Objective : To identify research trends, potential issues, and proposed solutions on attraction basins in the field of metaheuristics. Research goals were inspired by the previous paper, published in 2021, where attraction basins were used to measure exploration and exploitation. Method : We conducted the SMS in the following steps: Defining research questions, conducting the search in the ISI Web of Science and Scopus databases, full-text screening, iterative forward and backward snowballing (with ongoing full-text screening), classifying, and data extraction. Results : Attraction basins within discrete domains are understood far better than those within continuous domains. Attraction basins on dynamic problems have hardly been investigated. Multi-objective problems are investigated poorly in both domains, although slightly more often within a continuous domain. There is a lack of parallel and scalable algorithms to compute attraction basins and a general framework that would unite all different definitions/implementations used for attraction basins. Conclusions : Findings regarding attraction basins in the field of metaheuristics reveal that the concept alone is poorly exploited, as well as identify open issues where researchers may improve their research.

Suggested Citation

  • Mihael Baketarić & Marjan Mernik & Tomaž Kosar, 2021. "Attraction Basins in Metaheuristics: A Systematic Mapping Study," Mathematics, MDPI, vol. 9(23), pages 1-25, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3036-:d:688770
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    References listed on IDEAS

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    1. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
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    4. Page, Frank H., Jr. & Wooders, Myrna H., 2005. "Strategic Basins of Attraction, the Farsighted Core, and Network Formation Games," Economic Research Papers 269618, University of Warwick - Department of Economics.
    5. Eugenio Vicario, 2021. "Imitation and Local Interactions: Long Run Equilibrium Selection," Games, MDPI, vol. 12(2), pages 1-19, April.
    6. Madalina M. Drugan, 2019. "Estimating the number of basins of attraction of multi-objective combinatorial problems," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1367-1407, May.
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