Binary Chaotic White Shark Optimizer for the Unicost Set Covering Problem

Pablo Zúñiga-Valenzuela, Broderick Crawford (), Felipe Cisternas-Caneo, Eduardo Rodriguez-Tello, Ricardo Soto, José Barrera-Garcia and Fernando Lepe-Silva
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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
Fernando Lepe-Silva: Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile

Mathematics, 2025, vol. 13, issue 13, 1-39

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.

Keywords: White Shark Optimizer; chaotic maps; metaheuristics; combinatorial optimization; binarization techniques; exploration–exploitation balance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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