An Experimental Study of Transfer Functions and Binarization Strategies in Binary Arithmetic Optimization Algorithms for the Set Covering Problem

Metaheuristics have proven to be effective in solving large-scale combinatorial problems by combining global exploration with local exploitation, all within a reasonably short time. The balance between these phases is crucial to avoid slow or premature convergence. We propose binary variants of the Arithmetic Optimization Algorithm for the set cover problem, integrating a two-step binarization scheme based on transfer functions with binarization rules and a greedy repair operator to ensure feasibility. We evaluate the proposed solution using forty-five instances from OR-Beasley and compare it with representative approaches, including genetic algorithms, path-relinking strategies, and Lagrangian-based heuristics. The quality of the solution is evaluated using relative percentage deviation and stability with the coefficient of variation. The results show competitive deviations and consistently low variation, confirming that our approach is a robust alternative with a solid balance between exploration and exploitation.