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Mathematics
Volume 14
Issue 11
10.3390/math14111807
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Simple Distance-Ranked Metaheuristic with Reference-Guided Exploration for Improved Optimization Performance

by
Erik Cuevas
1,
Carlos Guzmán-Rosales
1,*,
Mario Vásquez
1,
Óscar A. González-Sánchez
1,
Héctor Escobar-Cuevas
1,
Nahum Aguirre
1,
Oscar Barba-Toscano
1,
Marco Perez
1 and
Dmitrii Kaplun
2,3
1
Department of Electro-Photonic Engineering, Centro Universitario de Ciencias Exactas e Ingenierías, University of Guadalajara, Av. Revolución 1500, Guadalajara 44430, Mexico
2
Higher School of Artificial Intelligence Technologies, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya, 29, 195251 Saint Petersburg, Russia
3
Intelligent Devices Institute, Saint Petersburg Electrotechnical University “LETI”, Prof. Popova, 5, 197022 Saint Petersburg, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(11), 1807; https://doi.org/10.3390/math14111807 (registering DOI)
Submission received: 9 April 2026 / Revised: 19 May 2026 / Accepted: 20 May 2026 / Published: 23 May 2026
Versions Notes

Abstract

In most metaheuristic approaches, particles are handled based on their fitness values without considering the distribution of solutions within the search space. Although this approach is simple, it causes particles to prematurely converge into a limited region of the search space due to the loss of diversity within the population. To address this limitation, this study proposes a metaheuristic approach in which particles are assigned to different search behaviors based on their Euclidean distance to the best solution. At each iteration, the population is divided into three groups: an exploitation set composed of the closest particles, an exploration set composed of the farthest particles, and a reference set composed of intermediate-distance particles. Two dedicated operators manage these groups: exploitation particles perform fine-grained refinement around the current best, whereas exploration particles search for new regions guided by randomly selected reference particles. In addition, an elitist acceptance mechanism ensures that only improved positions are retained, thereby promoting monotonic progress. This distance-based framework provides a distributed population of particles, where each particle is driven by its relevance to the optimal solution in the search space. This ensures a good diversity of solutions and prevents premature convergence and redundant search efforts. Experimental results on benchmark functions show that the method outperforms several State-of-the-Art metaheuristic algorithms in both solution quality and convergence behavior.
Keywords: metaheuristics; spatial distribution; distance-based grouping; exploration–exploitation balance; premature convergence avoidance metaheuristics; spatial distribution; distance-based grouping; exploration–exploitation balance; premature convergence avoidance

Share and Cite

MDPI and ACS Style

Cuevas, E.; Guzmán-Rosales, C.; Vásquez, M.; González-Sánchez, Ó.A.; Escobar-Cuevas, H.; Aguirre, N.; Barba-Toscano, O.; Perez, M.; Kaplun, D. Simple Distance-Ranked Metaheuristic with Reference-Guided Exploration for Improved Optimization Performance. Mathematics 2026, 14, 1807. https://doi.org/10.3390/math14111807

AMA Style

Cuevas E, Guzmán-Rosales C, Vásquez M, González-Sánchez ÓA, Escobar-Cuevas H, Aguirre N, Barba-Toscano O, Perez M, Kaplun D. Simple Distance-Ranked Metaheuristic with Reference-Guided Exploration for Improved Optimization Performance. Mathematics. 2026; 14(11):1807. https://doi.org/10.3390/math14111807

Chicago/Turabian Style

Cuevas, Erik, Carlos Guzmán-Rosales, Mario Vásquez, Óscar A. González-Sánchez, Héctor Escobar-Cuevas, Nahum Aguirre, Oscar Barba-Toscano, Marco Perez, and Dmitrii Kaplun. 2026. "Simple Distance-Ranked Metaheuristic with Reference-Guided Exploration for Improved Optimization Performance" Mathematics 14, no. 11: 1807. https://doi.org/10.3390/math14111807

APA Style

Cuevas, E., Guzmán-Rosales, C., Vásquez, M., González-Sánchez, Ó. A., Escobar-Cuevas, H., Aguirre, N., Barba-Toscano, O., Perez, M., & Kaplun, D. (2026). Simple Distance-Ranked Metaheuristic with Reference-Guided Exploration for Improved Optimization Performance. Mathematics, 14(11), 1807. https://doi.org/10.3390/math14111807

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