Binary Chaotic White Shark Optimizer for the Unicost Set Covering Problem

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.