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Mathematics
Volume 13
Issue 19
10.3390/math13193129
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

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

by
Broderick Crawford
1,*,
Ricardo Soto
1,
Hugo Caballero
1,
Gino Astorga
2,
Felipe Cisternas-Caneo
1,
Fabián Solís-Piñones
1 and
Giovanni Giachetti
3
1
Escuela de Ingeniería Informática, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2241, Valparaíso 2362807, Chile
2
Escuela de Negocios Internacionales, Universidad de Valparaíso, Alcalde Prieto Nieto 452, Viña del Mar 2572048, Chile
3
Facultad de Ingeniería, Universidad Andres Bello, Antonio Varas 880, Providencia, Santiago 7591538, Chile
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(19), 3129; https://doi.org/10.3390/math13193129
Submission received: 2 August 2025 / Revised: 22 September 2025 / Accepted: 27 September 2025 / Published: 30 September 2025
(This article belongs to the Special Issue Mathematical Optimization and Metaheuristics: Applications and Integration with Artificial Intelligence)
Versions Notes

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 arithmetic optimization algorithm; binary metaheuristics; binarization techniques; set covering problem; combinatorial optimization; exploration–exploitation balance

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MDPI and ACS Style

Crawford, B.; Soto, R.; Caballero, H.; Astorga, G.; Cisternas-Caneo, F.; Solís-Piñones, F.; Giachetti, G. An Experimental Study of Transfer Functions and Binarization Strategies in Binary Arithmetic Optimization Algorithms for the Set Covering Problem. Mathematics 2025, 13, 3129. https://doi.org/10.3390/math13193129

AMA Style

Crawford B, Soto R, Caballero H, Astorga G, Cisternas-Caneo F, Solís-Piñones F, Giachetti G. An Experimental Study of Transfer Functions and Binarization Strategies in Binary Arithmetic Optimization Algorithms for the Set Covering Problem. Mathematics. 2025; 13(19):3129. https://doi.org/10.3390/math13193129

Chicago/Turabian Style

Crawford, Broderick, Ricardo Soto, Hugo Caballero, Gino Astorga, Felipe Cisternas-Caneo, Fabián Solís-Piñones, and Giovanni Giachetti. 2025. "An Experimental Study of Transfer Functions and Binarization Strategies in Binary Arithmetic Optimization Algorithms for the Set Covering Problem" Mathematics 13, no. 19: 3129. https://doi.org/10.3390/math13193129

APA Style

Crawford, B., Soto, R., Caballero, H., Astorga, G., Cisternas-Caneo, F., Solís-Piñones, F., & Giachetti, G. (2025). An Experimental Study of Transfer Functions and Binarization Strategies in Binary Arithmetic Optimization Algorithms for the Set Covering Problem. Mathematics, 13(19), 3129. https://doi.org/10.3390/math13193129

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