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Binary Chaotic White Shark Optimizer for the Unicost Set Covering Problem

Author

Listed:
  • Pablo Zúñiga-Valenzuela

    (Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile)

  • Broderick Crawford

    (Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile)

  • Felipe Cisternas-Caneo

    (Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile)

  • Eduardo Rodriguez-Tello

    (Cinvestav Unidad Tamaulipas, Km. 5.5 Carretera Victoria-Soto La Marina, Victoria 87130, Tamaulipas, Mexico)

  • Ricardo Soto

    (Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile)

  • José Barrera-Garcia

    (Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile
    Escuela de Negocios y Economía, Pontificia Universidad Católica de Valparaíso, Amunátegui 1838, Viña del Mar 2580129, Chile)

  • Fernando Lepe-Silva

    (Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile)

Abstract

The Unicost Set Covering Problem (USCP), an NP-hard combinatorial optimization challenge, demands efficient methods to minimize the number of sets covering a universe. This study introduces a binary White Shark Optimizer (WSO) enhanced with V3 transfer functions, elitist binarization, and chaotic maps. To evaluate algorithm performance, we employ the Relative Percentage Deviation (RPD), which measures the percentage difference between the obtained solutions and optimal values. Our approach achieves outstanding results on six benchmark instances: WSO-ELIT_CIRCLE delivers an RPD of 0.7% for structured instances, while WSO-ELIT_SINU attains an RPD of 0.96% in cyclic instances, showing empirical improvements over standard methods. Experimental results demonstrate that circle chaotic maps excel in structured problems, while sinusoidal maps perform optimally in cyclic instances, with observed improvements up to 7.31% over baseline approaches. Diversity and convergence analyses show structured instances favor exploitation-driven strategies, whereas cyclic instances benefit from adaptive exploration. This work establishes WSO as a robust metaheuristic for USCP, with applications in resource allocation and network design.

Suggested Citation

  • Pablo Zúñiga-Valenzuela & Broderick Crawford & Felipe Cisternas-Caneo & Eduardo Rodriguez-Tello & Ricardo Soto & José Barrera-Garcia & Fernando Lepe-Silva, 2025. "Binary Chaotic White Shark Optimizer for the Unicost Set Covering Problem," Mathematics, MDPI, vol. 13(13), pages 1-39, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2175-:d:1694042
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    References listed on IDEAS

    as
    1. Zhu, Pengxing & Hu, Jianjun & Zhu, Zhennan & Xiao, Feng & Li, Jiajia & Peng, Hang, 2025. "An efficient energy management method for plug-in hybrid electric vehicles based on multi-source and multi-feature velocity prediction and improved extreme learning machine," Applied Energy, Elsevier, vol. 380(C).
    2. Qingyuan Xu & Jinjin Li, 2020. "The Relationship between the Unicost Set Covering Problem and the Attribute Reduction Problem in Rough Set Theory," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, June.
    3. Naji-Azimi, Zahra & Toth, Paolo & Galli, Laura, 2010. "An electromagnetism metaheuristic for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 205(2), pages 290-300, September.
    4. Fernando Lepe-Silva & Broderick Crawford & Felipe Cisternas-Caneo & José Barrera-Garcia & Ricardo Soto, 2024. "A Binary Chaotic White Shark Optimizer," Mathematics, MDPI, vol. 12(20), pages 1-35, October.
    5. Broderick Crawford & Ricardo Soto & Gino Astorga & José García & Carlos Castro & Fernando Paredes, 2017. "Putting Continuous Metaheuristics to Work in Binary Search Spaces," Complexity, Hindawi, vol. 2017, pages 1-19, May.
    6. Felipe Cisternas-Caneo & Broderick Crawford & Ricardo Soto & Giovanni Giachetti & Álex Paz & Alvaro Peña Fritz, 2024. "Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics," Mathematics, MDPI, vol. 12(2), pages 1-39, January.
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