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Biased Random-Key Genetic Algorithm with Local Search Applied to the Maximum Diversity Problem

Author

Listed:
  • Geiza Silva

    (Centre of Mathematics, Computing and Cognition, Universidade Federal do ABC, Santo André 09210-580, Brazil
    Department of Statistics, CASTLab, Universidade Federal Pernambuco, Recife 50670-901, Brazil)

  • André Leite

    (Department of Statistics, CASTLab, Universidade Federal Pernambuco, Recife 50670-901, Brazil)

  • Raydonal Ospina

    (Department of Statistics, CASTLab, Universidade Federal Pernambuco, Recife 50670-901, Brazil
    Department of Statistics, Federal University of Bahia, Salvador 40170-110, Brazil)

  • Víctor Leiva

    (School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

  • Jorge Figueroa-Zúñiga

    (Department of Statistics, Universidad de Concepción, Concepción 4070386, Chile)

  • Cecilia Castro

    (Centre of Mathematics, Universidade do Minho, 4710-057 Braga, Portugal)

Abstract

The maximum diversity problem (MDP) aims to select a subset with a predetermined number of elements from a given set, maximizing the diversity among them. This NP-hard problem requires efficient algorithms that can generate high-quality solutions within reasonable computational time. In this study, we propose a novel approach that combines the biased random-key genetic algorithm (BRKGA) with local search to tackle the MDP. Our computational study utilizes a comprehensive set of MDPLib instances, and demonstrates the superior average performance of our proposed algorithm compared to existing literature results. The MDP has a wide range of practical applications, including biology, ecology, and management. We provide future research directions for improving the algorithm’s performance and exploring its applicability in real-world scenarios.

Suggested Citation

  • Geiza Silva & André Leite & Raydonal Ospina & Víctor Leiva & Jorge Figueroa-Zúñiga & Cecilia Castro, 2023. "Biased Random-Key Genetic Algorithm with Local Search Applied to the Maximum Diversity Problem," Mathematics, MDPI, vol. 11(14), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3072-:d:1192177
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    References listed on IDEAS

    as
    1. Duarte, Abraham & Marti, Rafael, 2007. "Tabu search and GRASP for the maximum diversity problem," European Journal of Operational Research, Elsevier, vol. 178(1), pages 71-84, April.
    2. Thiago Noronha & Mauricio Resende & Celso Ribeiro, 2011. "A biased random-key genetic algorithm for routing and wavelength assignment," Journal of Global Optimization, Springer, vol. 50(3), pages 503-518, July.
    3. R Aringhieri & R Cordone, 2011. "Comparing local search metaheuristics for the maximum diversity problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 266-280, February.
    4. James C. Bean, 1994. "Genetic Algorithms and Random Keys for Sequencing and Optimization," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 154-160, May.
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