TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

CiteScore 2025: 2.7 (Q1)

Powered by:Powered by

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Implementation of heuristic combinatorial algorithms based on binomial coefficients for network design

, * , , , ,

* Corresponding author · click or hover a name for details

pp. 479–487Vol. 29Issue 2-AFebruary 2026DOI: 10.47974/JDMSC-2483 Crossmark XML
Received:
15 Apr 2025
Published Online:
31 Dec 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2483
Pages:
479–487

Abstract

It is very important for complicated communication networks to be well designed so that they can use their resources well, handle errors, and grow as needed.  This study shows a new way to solve network design problems using heuristic combinatorial methods based on binomial coefficients.  The suggested method is based on carefully choosing which nodes to connect in order to minimise connection costs and increase network stability. Binomial coefficients (n k)  are used carefully to create groups of possible node pairs. This makes it easier to explore different design options in an organised way. The combinatorial framework sorts and ranks possible network designs based on performance measures like degree centrality, path redundancy, and minimal spanning constraints. The algorithm uses heuristics like greedy estimate, repeated revision, and probability sampling to find its way through the very large solution space. One important new idea is to use Pascal’s Triangle and the symmetry in (n k) = (n n–k) to cut down on the amount of work that needs to be done on the computer. This study presents a method that can be used on a large scale and is based on math.

Keywords

Heuristic algorithmsCombinatorial optimizationBinomial coefficientsNetwork designFault tolerance

Subject Classifications

03E05

References

[1] H. Dai, Y. Li, and X. Zhou, “An OSGI-MPH algorithm for solving combinatorial optimization problem,” in Proceedings of the 4th International Conference on Advanced Electronic Materials, Computers and Software Engineering (AEMCSE), Changsha, China, pp. 398–401 (2021).
[2] C. Gong, Y. Nan, L. M. Pang, H. Ishibuchi, and Q. Zhang, “Initial populations with a few heuristic solutions significantly improve evolutionary multi-objective combinatorial optimization,” in Proceedings of the IEEE Symposium Series on Computational Intelligence (SSCI), Mexico City, Mexico, pp. 1398–1405 (2023).
[3] L. Tang, W. Ying, M. Huang, and Y. Zou, “Research on ship crew scheduling algorithm based on improved grey wolf optimization,” in Proceedings of the IEEE 4th International Conference on Information Technology, Big Data and Artificial Intelligence (ICIBA), Chongqing, China, pp. 400–403 (2024).
[4] Y. Shao, Y. Liu, L. Zhang, H. Wang, and K. Li, “Multi-objective neural evolutionary algorithm for combinatorial optimization problems,” IEEE Transactions on Neural Networks and Learning Systems, vol. 34, no. 4, pp. 2133–2143 (Apr. 2023).
[5] D. Zeghida, N. Bounour, and D. Meslati, “The Ant-Step algorithms: Reloading the ant system heuristic and the overlooked basic variants,” in Proceedings of the IEEE 2nd International Conference on Electronics, Control, Optimization and Computer Science (ICECOCS), Kenitra, Morocco (2020).
[6] H. Ishibuchi, N. Akedo, and Y. Nojima, “Behavior of multiobjective evolutionary algorithms on many-objective knapsack problems,” IEEE Transactions on Evolutionary Computation, vol. 19, no. 2, pp. 264–283 (2014).
[7] J. Lu and Y. Sun, “Application of heuristic function optimization strategy of A algorithm in path planning of mobile robot,”* in Proceedings of the 5th International Conference on Computer Engineering and Applications (ICCEA), Hangzhou, China, pp. 77–80 (2024).
[8] Y. He, T. C. Hou, and Z. W. Zeng, “UAV path planning based on improved A and dynamic window approach,”* Mechanics Science and Technology for Aerospace Engineering, pp. 1–9 (2023).
[9] C. V. Nalawade, Y. Bhosale, S. Agale, and P. Fate, “Smart Shade: A cutting-edge automated livestock care and environmental control system,” International Journal of Electrical, Electronics and Computer Systems, vol. 13, no. 2, pp. 14–21 (2025).
[10] H. Lee and R. Johnson, “IoT-enabled smart cities: Challenges and opportunities in data management and analysis,” International Journal of Advanced Electrical and Computer Engineering, vol. 13, no. 1, pp. 25–31 (2025).
[11] A. Konovalenko, L. M. Hvattum, and S. Urrutia, “Two paradigms for combining optimization and satisfiability: Maximum satisfiability and optimum satisfiability problems,” Journal of Information and Optimization Sciences, pp. 1–29 (2025), doi: 10.47974/JIOS-1392.
[12] S. Dhingra and D. Kumar, “Hyperspectral image classification using meta-heuristics and artificial neural network,” Journal of Information and Optimization Sciences, vol. 43, no. 8, pp. 2167–2179 (2022), doi: 10.1080/02522667.2022.2133222.

Views: 94Downloads: 80Citations: 0