Volume 2, Issue 1, ICCK Transactions on Swarm and Evolutionary Learning
Volume 2, Issue 1, 2026
Submit Manuscript Edit a Special Issue
Article QR Code
Article QR Code
Scan the QR code for reading
Popular articles
ICCK Transactions on Swarm and Evolutionary Learning, Volume 2, Issue 1, 2026: 19-40

Free to Read | Research Article | 02 February 2026
Battle Royale Optimizer with Ring Neighborhood Topology
1 Department of Medicine, Louisiana State University Health Sciences Center, Shreveport, LA 71103, United States
2 Faculty of Electrical Engineering and Informatics, University of Pardubice, Pardubice, Czech Republic
3 Software Engineering Department, Istanbul Topkapi University, Istanbul, Turkey
4 Faculty of Electrical & Computer Engineering, University of Tabriz, Tabriz, Iran
5 Depto. de Ingeniería Industrial, Tecnológico Nacional de México/Instituto Tecnológico de Jiquilpan, Jiquilpan, Michoacán, México
6 Depto. de Ingeniería Electro-Fotónica, Universidad de Guadalajara, CUCEI, Guadalajara, Jalisco, México
* Corresponding Author: Jorge Ramos-Frutos, [email protected]
ARK: ark:/57805/tsel.2025.751954
Received: 26 November 2025, Accepted: 16 January 2026, Published: 02 February 2026  
Abstract
Recently, battle royale optimizer (BRO), a game-based metaheuristic search algorithm, has been proposed for continuous optimization, inspired by a genre of digital games known as "battle royale." In BRO, each individual chooses the nearest opponent as a competitor. For this purpose, the Euclidean distance between individuals is calculated. This interaction corresponds to an increase in computational complexity by a factor of n. To improve the computational complexity of BRO, a modified methodology is proposed using a ring topology, namely, BRO-RT. In the modified version, a set of individuals is arranged in a ring such that each has a neighborhood comprising several individuals to its left and right. Instead of a pairwise comparison with all individuals in the population, the best individual among the left and right neighborhoods is selected as the competitor. We compared the proposed scheme with the original BRO and six popular optimization algorithms. All algorithms are tested in several benchmark functions and engineering optimization problems. Experimental results show that the BRO-RT demonstrates competitive performance compared to nine state-of-the-art methods across most benchmark functions. Additionally, the compression spring design problem was utilized to assess the proposed method's ability to solve real-world engineering problems. These results demonstrate that BRO-RT yields promising results when applied to real-world engineering problems. Finally, while BRO is ranked first and BRO-RT second, they achieved competitive results; BRO-RT has the advantages of lower computational complexity and faster run times than the original BRO algorithm.

Graphical Abstract
Battle Royale Optimizer with Ring Neighborhood Topology

Keywords
Battle royale optimization
ring topology
optimization

Data Availability Statement
Data will be made available on request.

Funding
This work was supported without any funding.

Conflicts of Interest
The authors declare no conflicts of interest.

AI Use Statement
The authors declare that no generative AI was used in the preparation of this manuscript.

Ethical Approval and Consent to Participate
Not applicable.

References
  1. Lazar, A. (2002). Heuristic knowledge discovery for archaeological data using genetic algorithms and rough sets. In Heuristic and optimization for knowledge discovery (pp. 263-278). IGI Global.
    [CrossRef]   [Google Scholar]
  2. Bianchi, L., Dorigo, M., Gambardella, L. M., & Gutjahr, W. J. (2009). A survey on metaheuristics for stochastic combinatorial optimization. Natural Computing, 8(2), 239-287.
    [CrossRef]   [Google Scholar]
  3. Rahkar Farshi, T. (2021). Battle royale optimization algorithm. Neural Computing and Applications, 33(4), 1139--1157.
    [CrossRef]   [Google Scholar]
  4. Yang, X. S. (2020). Nature-inspired optimization algorithms. Academic Press.
    [Google Scholar]
  5. Schwefel, H. P. (1984). Evolution Strategies: A Family of Non-Linear Optimization Techniques Based on Imitating some Principles of Organic Evolution. Annals of Operations Research, 1.
    [CrossRef]   [Google Scholar]
  6. Glover, F., & McMillan, C. (1986). The general employee scheduling problem. An integration of MS and AI. Computers & operations research, 13(5), 563--573.
    [CrossRef]   [Google Scholar]
  7. Kirkpatrick, S., Gelatt Jr, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. science, 220(4598), 671-680.
    [CrossRef]   [Google Scholar]
  8. Simon, D. (2008). Biogeography-based optimization. IEEE transactions on evolutionary computation, 12(6), 702-713.
    [CrossRef]   [Google Scholar]
  9. Askarzadeh, A. (2014). Bird mating optimizer: an optimization algorithm inspired by bird mating strategies. Communications in Nonlinear Science and Numerical Simulation, 19(4), 1213--1228.
    [CrossRef]   [Google Scholar]
  10. Eberhart, R., & Kennedy, J. (1995). A new optimizer using particle swarm theory. In MHS'95. Proceedings of the sixth international symposium on micro machine and human science (pp. 39--43). IEEE.
    [CrossRef]   [Google Scholar]
  11. Talbi, E. G., Roux, O., Fonlupt, C., & Robillard, D. (1999, April). Parallel ant colonies for combinatorial optimization problems. In International Parallel Processing Symposium (pp. 239-247). Berlin, Heidelberg: Springer Berlin Heidelberg.
    [CrossRef]   [Google Scholar]
  12. Bitam, S., Batouche, M., & Talbi, E. G. (2010, April). A survey on bee colony algorithms. In 2010 IEEE international symposium on parallel & distributed processing, workshops and phd forum (ipdpsw) (pp. 1-8). IEEE.
    [CrossRef]   [Google Scholar]
  13. Ma, M., Luo, Q., Zhou, Y., Chen, X., & Li, L. (2015). An improved animal migration optimization algorithm for clustering analysis. Discrete Dynamics in Nature and Society, 2015(1), 194792.
    [CrossRef]   [Google Scholar]
  14. Mousavirad, S. J., & Ebrahimpour-Komleh, H. (2017). Human mental search: a new population-based metaheuristic optimization algorithm. Applied Intelligence, 47(3), 850-887.
    [CrossRef]   [Google Scholar]
  15. Fausto, F., Cuevas, E., Valdivia, A., & González, A. (2017). A global optimization algorithm inspired in the behavior of selfish herds. Biosystems, 160, 39-55.
    [CrossRef]   [Google Scholar]
  16. Tu, S., Rehman, O. U., Rehman, S. U., Ullah, S., Waqas, M., & Zhu, R. (2020). A novel quantum inspired particle swarm optimization algorithm for electromagnetic applications. IEEE Access, 8, 21909-21916.
    [CrossRef]   [Google Scholar]
  17. Tabrizian, Z., Afshari, E., Amiri, G. G., Ali Beigy, M. H., & Nejad, S. M. P. (2013). A New Damage Detection Method: Big Bang‐Big Crunch (BB‐BC) Algorithm. Shock and Vibration, 20(4), 633-648.
    [CrossRef]   [Google Scholar]
  18. Zha, J., Zeng, G. Q., & Lu, Y. Z. (2010, December). Hysteretic optimization for protein folding on the lattice. In 2010 International Conference on Computational Intelligence and Software Engineering (pp. 1-4). IEEE.
    [CrossRef]   [Google Scholar]
  19. Doğan, B., & Ölmez, T. (2015). A new metaheuristic for numerical function optimization: Vortex Search algorithm. Information sciences, 293, 125-145.
    [CrossRef]   [Google Scholar]
  20. Boussaïd, I., Lepagnot, J., & Siarry, P. (2013). A survey on optimization metaheuristics. Information sciences, 237, 82-117.
    [CrossRef]   [Google Scholar]
  21. Wolpert, D. H., & Macready, W. G. (2002). No free lunch theorems for optimization. IEEE transactions on evolutionary computation, 1(1), 67-82.
    [CrossRef]   [Google Scholar]
  22. Camacho Villalón, C. L., Stützle, T., & Dorigo, M. (2020, October). Grey wolf, firefly and bat algorithms: Three widespread algorithms that do not contain any novelty. In International conference on swarm intelligence (pp. 121-133). Cham: Springer International Publishing.
    [CrossRef]   [Google Scholar]
  23. Aranha, C., Camacho Villalón, C. L., Campelo, F., Dorigo, M., Ruiz, R., Sevaux, M., ... & Stützle, T. (2022). Metaphor-based metaheuristics, a call for action: the elephant in the room. Swarm Intelligence, 16(1), 1-6.
    [CrossRef]   [Google Scholar]
  24. Deng, W., Shang, S., Cai, X., Zhao, H., Song, Y., & Xu, J. (2021). An improved differential evolution algorithm and its application in optimization problem. Soft Computing-A Fusion of Foundations, Methodologies & Applications, 25(7).
    [CrossRef]   [Google Scholar]
  25. Seyyedabbasi, A., & Kiani, F. (2021). I-GWO and Ex-GWO: improved algorithms of the Grey Wolf Optimizer to solve global optimization problems. Engineering with Computers, 37(1), 509-532.
    [CrossRef]   [Google Scholar]
  26. Ghosh, A., Das, S., & Das, A. K. (2020). A simple two-phase differential evolution for improved global numerical optimization. Soft Computing-A Fusion of Foundations, Methodologies & Applications, 24(8).
    [CrossRef]   [Google Scholar]
  27. Li, Y., Xiang, R., Jiao, L., & Liu, R. (2012). An improved cooperative quantum-behaved particle swarm optimization. Soft Computing, 16(6), 1061-1069.
    [CrossRef]   [Google Scholar]
  28. Akan, S., & Akan, T. (2022). Battle royale optimizer with a new movement strategy. In Handbook of nature-inspired optimization algorithms: the state of the art: volume I: solving single objective bound-constrained real-parameter numerical optimization problems (pp. 265-279). Cham: Springer International Publishing.
    [CrossRef]   [Google Scholar]
  29. Akan, T., Agahian, S., & Dehkharghani, R. (2022). Binbro: Binary battle royale optimizer algorithm. Expert systems with applications, 195, 116599.
    [CrossRef]   [Google Scholar]
  30. Agahian, S., & Akan, T. (2022). Battle royale optimizer for training multi-layer perceptron. Evolving Systems, 13(4), 563-575.
    [CrossRef]   [Google Scholar]
  31. Wu, H., Zhang, X., Song, L., Su, C., & Gu, L. (2022). A hybrid improved bro algorithm and its application in inverse kinematics of 7r 6dof robot. Advances in Mechanical Engineering, 14(3), 16878132221085125.
    [CrossRef]   [Google Scholar]
  32. Halim, Z., Sargana, H. M., & Waqas, M. (2021). Clustering of graphs using pseudo-guided random walk. Journal of Computational Science, 51, 101281.
    [CrossRef]   [Google Scholar]
  33. Paz, A., & Moran, S. (1981). Non deterministic polynomial optimization problems and their approximations. Theoretical Computer Science, 15(3), 251-277.
    [CrossRef]   [Google Scholar]
  34. Box, M. J. (1965). A new method of constrained optimization and a comparison with other methods. The Computer Journal, 8(1), 42-52.
    [CrossRef]   [Google Scholar]
  35. Krus, P., & Ölvander, J. (2013). Performance index and meta-optimization of a direct search optimization method. Engineering optimization, 45(10), 1167--1185.
    [CrossRef]   [Google Scholar]
  36. Tripathi, D. P., & Jena, U. R. (2017, August). DSSO-directional shrinking search optimization. In IOP Conference Series: Materials Science and Engineering (Vol. 225, No. 1, p. 012280). IOP Publishing.
    [CrossRef]   [Google Scholar]
  37. Zhang, W., Li, G., Zhang, W., Liang, J., & Yen, G. G. (2019). A cluster based PSO with leader updating mechanism and ring-topology for multimodal multi-objective optimization. Swarm and Evolutionary Computation, 50, 100569.
    [CrossRef]   [Google Scholar]
  38. Li, X. (2009). Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Transactions on Evolutionary Computation, 14(1), 150--169.
    [CrossRef]   [Google Scholar]
  39. Wang, Y. X., & Xiang, Q. L. (2008, June). Particle swarms with dynamic ring topology. In 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence) (pp. 419-423). IEEE.
    [CrossRef]   [Google Scholar]
  40. Kennedy, J., & Eberhart, R. (1995, November). Particle swarm optimization. In Proceedings of ICNN'95-international conference on neural networks (Vol. 4, pp. 1942-1948). IEEE.
    [CrossRef]   [Google Scholar]
  41. Houssein, E. H., Oliva, D., Samee, N. A., Mahmoud, N. F., & Emam, M. M. (2023). Liver cancer algorithm: A novel bio-inspired optimizer. Computers in Biology and Medicine, 165, 107389.
    [CrossRef]   [Google Scholar]
  42. Xue, J., & Shen, B. (2023). Dung beetle optimizer: A new meta-heuristic algorithm for global optimization. The Journal of Supercomputing, 79(7), 7305--7336.
    [CrossRef]   [Google Scholar]
  43. Suganthan, P. N., Hansen, N., Liang, J. J., Deb, K., Chen, Y.-P., Auger, A., & Tiwari, S. (2005). Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. KanGAL report, 2005005(2005), 2005.
    [Google Scholar]
  44. Tang, K., Li, X., Suganthan, P. N., Yang, Z., & Weise, T. (2007). Benchmark functions for the CEC’2010 special session and competition on large-scale global optimization. Nature inspired computation and applications laboratory, USTC, China, 24, 1-18.
    [Google Scholar]
  45. Premkumar, M., Jangir, P., Kumar, B. S., Sowmya, R., Alhelou, H. H., Abualigah, L., ... & Mirjalili, S. (2021). A new arithmetic optimization algorithm for solving real-world multiobjective CEC-2021 constrained optimization problems: diversity analysis and validations. IEEE Access, 9, 84263-84295.
    [CrossRef]   [Google Scholar]
  46. Holland, J. H. (1992). Genetic algorithms. Scientific american, 267(1), 66-73.
    [Google Scholar]
  47. Storn, R., & Price, K. (1997). Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization, 11(4), 341-359.
    [CrossRef]   [Google Scholar]
  48. Rashedi, E., Nezamabadi-Pour, H., & Saryazdi, S. (2009). GSA: a gravitational search algorithm. Information sciences, 179(13), 2232-2248.
    [CrossRef]   [Google Scholar]
  49. Yang, X. S. (2009, October). Firefly algorithms for multimodal optimization. In International symposium on stochastic algorithms (pp. 169-178). Berlin, Heidelberg: Springer Berlin Heidelberg.
    [CrossRef]   [Google Scholar]

Cite This Article
APA Style
Akan, T., Zálabský, T., Shirini, K., Ramos-Frutos, J., Oliva, D., & Bhuiyan, M. A. (2026). Battle Royale Optimizer with Ring Neighborhood Topology. ICCK Transactions on Swarm and Evolutionary Learning, 2(1), 19–40. https://doi.org/10.62762/TSEL.2025.751954
Export Citation
RIS Format
Compatible with EndNote, Zotero, Mendeley, and other reference managers
RIS format data for reference managers
TY  - JOUR
AU  - Akan, Taymaz
AU  - Zálabský, Tomáš
AU  - Shirini, Kimia
AU  - Ramos-Frutos, Jorge
AU  - Oliva, Diego
AU  - Bhuiyan, Mohammad A.
PY  - 2026
DA  - 2026/02/02
TI  - Battle Royale Optimizer with Ring Neighborhood Topology
JO  - ICCK Transactions on Swarm and Evolutionary Learning
T2  - ICCK Transactions on Swarm and Evolutionary Learning
JF  - ICCK Transactions on Swarm and Evolutionary Learning
VL  - 2
IS  - 1
SP  - 19
EP  - 40
DO  - 10.62762/TSEL.2025.751954
UR  - https://www.icck.org/article/abs/TSEL.2025.751954
KW  - Battle royale optimization
KW  - ring topology
KW  - optimization
AB  - Recently, battle royale optimizer (BRO), a game-based metaheuristic search algorithm, has been proposed for continuous optimization, inspired by a genre of digital games known as "battle royale." In BRO, each individual chooses the nearest opponent as a competitor. For this purpose, the Euclidean distance between individuals is calculated. This interaction corresponds to an increase in computational complexity by a factor of n. To improve the computational complexity of BRO, a modified methodology is proposed using a ring topology, namely, BRO-RT. In the modified version, a set of individuals is arranged in a ring such that each has a neighborhood comprising several individuals to its left and right. Instead of a pairwise comparison with all individuals in the population, the best individual among the left and right neighborhoods is selected as the competitor. We compared the proposed scheme with the original BRO and six popular optimization algorithms. All algorithms are tested in several benchmark functions and engineering optimization problems. Experimental results show that the BRO-RT demonstrates competitive performance compared to nine state-of-the-art methods across most benchmark functions. Additionally, the compression spring design problem was utilized to assess the proposed method's ability to solve real-world engineering problems. These results demonstrate that BRO-RT yields promising results when applied to real-world engineering problems. Finally, while BRO is ranked first and BRO-RT second, they achieved competitive results; BRO-RT has the advantages of lower computational complexity and faster run times than the original BRO algorithm.
SN  - 3069-2962
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 
BibTeX Format
Compatible with LaTeX, BibTeX, and other reference managers
BibTeX format data for LaTeX and reference managers
@article{Akan2026Battle,
  author = {Taymaz Akan and Tomáš Zálabský and Kimia Shirini and Jorge Ramos-Frutos and Diego Oliva and Mohammad A. Bhuiyan},
  title = {Battle Royale Optimizer with Ring Neighborhood Topology},
  journal = {ICCK Transactions on Swarm and Evolutionary Learning},
  year = {2026},
  volume = {2},
  number = {1},
  pages = {19-40},
  doi = {10.62762/TSEL.2025.751954},
  url = {https://www.icck.org/article/abs/TSEL.2025.751954},
  abstract = {Recently, battle royale optimizer (BRO), a game-based metaheuristic search algorithm, has been proposed for continuous optimization, inspired by a genre of digital games known as "battle royale." In BRO, each individual chooses the nearest opponent as a competitor. For this purpose, the Euclidean distance between individuals is calculated. This interaction corresponds to an increase in computational complexity by a factor of n. To improve the computational complexity of BRO, a modified methodology is proposed using a ring topology, namely, BRO-RT. In the modified version, a set of individuals is arranged in a ring such that each has a neighborhood comprising several individuals to its left and right. Instead of a pairwise comparison with all individuals in the population, the best individual among the left and right neighborhoods is selected as the competitor. We compared the proposed scheme with the original BRO and six popular optimization algorithms. All algorithms are tested in several benchmark functions and engineering optimization problems. Experimental results show that the BRO-RT demonstrates competitive performance compared to nine state-of-the-art methods across most benchmark functions. Additionally, the compression spring design problem was utilized to assess the proposed method's ability to solve real-world engineering problems. These results demonstrate that BRO-RT yields promising results when applied to real-world engineering problems. Finally, while BRO is ranked first and BRO-RT second, they achieved competitive results; BRO-RT has the advantages of lower computational complexity and faster run times than the original BRO algorithm.},
  keywords = {Battle royale optimization, ring topology, optimization},
  issn = {3069-2962},
  publisher = {Institute of Central Computation and Knowledge}
}

Article Metrics
Citations:

Crossref

0

Scopus

0

Web of Science

0
Article Access Statistics:
Views: 30
PDF Downloads: 11

Publisher's Note
ICCK stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and Permissions
Institute of Central Computation and Knowledge (ICCK) or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ICCK Transactions on Swarm and Evolutionary Learning

ICCK Transactions on Swarm and Evolutionary Learning

ISSN: 3069-2962 (Online)

Email: [email protected]

Portico

Portico

All published articles are preserved here permanently:
https://www.portico.org/publishers/icck/