Mathematics and Computational Sciences

Efficient cluster center optimization: A novel hybrid metaheuristic

Document Type : Original Article

Authors

Saeideh Barkhordari Firozabadi 1
Seyed Abolfazl Shahzadeh Fazeli 1
Jamal Zarepour Ahmadabadi 2
Seyed Mehdi S Karbassi 3

1 Deparetment of Computer Science, Yazd University, Yazd, Iran

2 Department of Computer Science, Yazd University, Yazd, Iran

3 Department of Mathematical Science, Yazd University, Yazd, Iran

https://doi.org/10.30511/mcs.2025.2041731.1235
Abstract
Metaheuristics have proved highly effective in addressing optimization challenges. Various algorithms address the clustering problem to find optimal centers for the clusters. One of the disadvantages of some of these algorithms is stagnation in local optima, especially for big data. If this problem is not properly solved, the clustering process will suffer. This research introduces a new hybrid method by merging the capabilities of two metaheuristic algorithms: Harris hawks optimization algorithm (HHO) and slime mould algorithm (SMA). These metaheuristic methods are employed to determine the best location for the cluster centers. Optimization aims to reduce intra-cluster distance. In other words, the data points of each cluster should be close to its cluster center and also to avoid local optima. The effectiveness of these techniques is assessed and contrasted with the SMA and HHO algorithms on Iris, Vowel and Wine data sets. Compared to mentioned algorithms, our proposed method exhibits significantly improved convergence speed. The results also proved this method can properly find the optimal centers for clustering which finally improves the performance of the proposed method.

Keywords

Clustering
Metaheuristic
Slime mould algorithm
Harris hawks optimization algorithm

Subjects

[1] Abdollahzadeh, B., Gharehchopogh, F. S., Khodadadi, N., Mirjalili, S. (2022). Mountain gazelle optimizer: A new nature-inspired metaheuristic algorithm for global optimization problems. Advancein Engineering Software, 174, 103282.
[2] Barkhordari Firozabadi, S., Shahzadeh Fazeli, S. A., Zarepour Ahmadabadi, J., Karbassi, S. M., (2023). Improving the performance of the FCM algorithm in clustering using the DBSCAN algorithm. Iranian Journal of Numerical Analysis and Optimization, 13(4): 763-774, https://doi: 10.22067/ijnao.2023.82361.1260.
[3] Bezdek, J. C., Ehrlich, R., Full, W. (1984). FCM: The fuzzy c-means clustering algorithm. Computersmand geosciences, 10(2-3), 191-203.
[4] Digalakis, J. G., Margaritis, K. G. (2001). On benchmarking functions for genetic algorithms. International journal of computer mathematics, 77(4), 481-506.
[5] Ester, M., Kriegel, H. P., Sander, J., Xu, X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. Inkdd, (34), 226-231.
[6] Faris, H., Mirjalili, S., Aljarah, I., Mafarja, M., Heidari, A. A. (2020). Salp swarm algorithm: theory,mliterature review and application in extreme learning machines. Nature-inspired optimizers: theories, literature reviews and applications, 185-199.
[7] Gandomi, A. H., Yang, X. S., Alavi, A. H. (2013). Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Engineering with computers, 29, 17-35.
[8] Heidari, A. A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., Chen, H. (2019). Harris hawks optimization: Algorithm and applications. Future generation computer systems, 97, 849-872.
[9] Ikotun, A. M., Ezugwu, A. E., Abualigah, L., Abuhaija, B., Heming, J. (2023). K-means clustering algorithms: A comprehensive review, variants analysis, and advances in the era of big data. Information Sciences, 622, 178-210.
[10] Ishak Boushaki, S., Kamel, N., Bendjeghaba, O. (2018). High-dimensional text datasets clustering algorithm based on cuckoo search and latent semantic indexing. Journal of Information and Knowledge Management, 17(3), 1850033.
[11] Jain, M., Saihjpal, V., Singh, N., Singh, S. B. (2022). An overview of variants and advancements of PSO algorithm. Applied Sciences, 12(17), 8392.
[12] Katoch, S., Chauhan, S. S., Kumar, V. (2021). A review on genetic algorithm: past, present, and future. Multimedia tools and applications, 80, 8091-8126.
[13] Kaur, S., Awasthi, L. K., Sangal, A. L., Dhiman, G. (2020). Tunicate Swarm Algorithm: A new bioinspired based metaheuristic paradigm for global optimization. Engineering Applications of Artificial Intelligence, 90, 103541.
[14] Kaveh, A., Talatahari, S., Khodadadi, N. (2020). Stochastic paint optimizer: theory and application in civil engineering. Engineering with Computers, 1-32.
[15] Kennedy, J., Eberhart, R. (1995). Particle swarm optimization. In Proceedings of ICNN’95-international conference on neural networks IEEE, 4, 1942-1948.
[16] Khalilpourazari, S., Khalilpourazary, S. (2019). An efficient hybrid algorithm based on Water Cycle and Moth-Flame Optimization algorithms for solving numerical and constrained engineering optimization problems. Soft Computing, 23, 1699-722.
[17] Khanduja, N., Bhushan, B. (2020). Recent advances and application of metaheuristic algorithms: A survey (2014-2020). Metaheuristic and Evolutionary Computation: Algorithms and Applications, 207-228.
[18] Li, M. D., Zhao, H., Weng, X. W., Han, T. (2016). A novel nature-inspired algorithm for optimization: Virus colony search, Adv. Eng. Softw. 92, 65-88. https://doi.org/10.1016/j.advengsoft.2015.11.004.
[19] MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, (14), 281-297.
[20] Mirjalili, S., Hashim, S. Z. M. (2010). A new hybrid PSOGSA algorithm for function optimization. 2010 international conference on computer and information application IEEE.
[21] Mirjalili, S., Mirjalili, S. M., Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software, 69, 46-61.
[22] Mohammadi-Balani, A., Nayeri, M. D., Azar, A., Taghizadeh-Yazdi, M. (2021). Golden eagle optimizer: A nature-inspired metaheuristic algorithm. Computers and Industrial Engineering, 152, 107050.
[23] Mosavi, E., Shahzadeh Fazeli, S. A., Abbasi, E., Kaveh-Yazdy, F., (2025). Using Hybrid Mountain Gazelle Optimization and Particle Swarm Optimization Algorithms to Improve Clustering. Cluster Comput., https://doi.org/10.1007/s10586-024-05029-7.
[24] Mosavi, E., Shahzadeh Fazeli, S. A., Abbasi, E., Kaveh-Yazdy, F., (2025). Unite and Conquer Approach for Data Clustering Based on Particle Swarm Optimization and Moth Flame Optimization. Iranian Journal of Numerical Analysis and Optimization, https://doi:10.22067/ijnao.2025.89754.1508.
[25] Oyewole, G. J., Thopil, G. A. (2023). Data clustering: application and trends. Artificial Intelligence Review 56(7), 6439-6475.
[26] Price, K. V. (2013). Differential evolution. Handbook of optimization: From classical to modern approach, Berlin, Heidelberg: Springer Berlin Heidelberg, 187-214.
[27] Purushothaman, R., Rajagopalan, S. P., Dhandapani, G. (2020). Hybridizing Gray Wolf Optimization (GWO) with Grasshopper Optimization Algorithm (GOA) for text feature selection and clustering. Applied Soft Computing, 96, 106651.
[28] Rajwar, K., Deep, K., Das, S. (2023). An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges. Artificial Intelligence Review, 56(11), 13187-13257.
[29] Rodriguez, M. Z., Comin, C. H., Casanova, D., Bruno, O. M., Amancio, D. R., Costa, L. D. F., Rodrigues, F. A. (2019). Clustering algorithms: A comparative approach. PloS one, 14(1), p.e0210236.
[30] Saremi, v, Mirjalili, S., Lewis, A. (2017). Grasshopper optimisation algorithm: theory and application, Advances in engineering software, 105, 30-47.
[31] Sarkar, S., Roy, A., Purkayastha, B. S. (2014). A comparative analysis of particle swarm optimization and K-means algorithm for text clustering using Nepali Wordnet. Int. J. Nat. Lang. Comput.(IJNLC), 3(3).
[32] Shimin, Li., Chen, H., Wang, M., Heidari, A. A., Mirjalili, S. (2020). Slime mould algorithm: A new method for stochastic optimization. Future Generation Computer Systems, 111, 300-323.
[33] Singh, T., Saxena, N., Khurana, M., Singh, D., Abdalla, V., Alshazly, H. (2021). Data clustering using moth-flame optimization algorithm. Sensors, 21(12), 4086.
[34] Talbi, E. G. (2002). A Taxonomy of Hybrid Metaheuristi. Journal of Heuristics, 8, 541-546.
[35] Talbi, E. G. (2009). Metaheuristics: from design to implementation. John Wiley ans Sons.
[36] Yang, X. S. (2010). Firefly algorithm, stochastic test functions and design optimisation. International journal of bio-inspired computation, 2(2), 78-84.
[37] Yao, X., Liu, Y., Lin, G. (1999). Evolutionary programming made faster. IEEE Trans Evol Comput, 3, 82–102.
Mathematics and Computational Sciences
Volume 6, Issue 1
Winter 2025
Pages 116-146

  • Receive Date 24 September 2024
  • Revise Date 28 January 2025
  • Accept Date 31 January 2025

Home

Submit Manuscript

Reviewers

Contact Us