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

Broderick Crawford (), Ricardo Soto, Hugo Caballero, Gino Astorga, Felipe Cisternas-Caneo, Fabián Solís-Piñones and Giovanni Giachetti
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Broderick Crawford: Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile
Ricardo Soto: Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile
Hugo Caballero: Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile
Gino Astorga: Escuela de Negocios Internacionales, Universidad de Valparaíso, Alcalde Prieto Nieto 452, Viña del Mar 2572048, Chile
Felipe Cisternas-Caneo: Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile
Fabián Solís-Piñones: Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile
Giovanni Giachetti: Facultad de Ingeniería, Universidad Andres Bello, Antonio Varas 880, Providencia, Santiago 7591538, Chile

Mathematics, 2025, vol. 13, issue 19, 1-27

Abstract: 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.

Keywords: arithmetic optimization algorithm; binary metaheuristics; binarization techniques; set covering problem; combinatorial optimization; exploration–exploitation balance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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