1,919
Views
4
CrossRef citations to date
0
Altmetric
Research Article

An Enhanced GWO Algorithm with Improved Explorative Search Capability for Global Optimization and Data Clustering

ORCID Icon, & ORCID Icon
Article: 2166232 | Received 29 Aug 2022, Accepted 04 Jan 2023, Published online: 31 Jan 2023

References

  • Abualigah, L., M. Abd Elaziz, P. Sumari, Z. Woo Geem, and A. H. Gandomi. 2022. Reptile Search Algorithm (RSA): A Nature-Inspired Meta-Heuristic Optimizer. Expert Systems with Applications 191:116158. doi:10.1016/j.eswa.2021.116158.
  • Abualigah, L., and M. Alkhrabsheh. 2022. Amended Hybrid Multi-Verse Optimizer with Genetic Algorithm for Solving Task Scheduling Problem in Cloud Computing. The Journal of Supercomputing 78 (1):740–383. doi:10.1007/s11227-021-03915-0.
  • Abualigah, L., and A. Diabat. 2020. A Comprehensive Survey of the Grasshopper Optimization Algorithm: Results, Variants, and Applications. Neural Computing & Applications 32 (19):15533–56. doi:10.1007/s00521-020-04789-8.
  • Abualigah, L., A. Diabat, S. Mirjalili, M. Abd Elaziz, and A. H. Gandomi. 2021. The Arithmetic Optimization Algorithm. Computer Methods in Applied Mechanics and Engineering 376:113609. doi:10.1016/j.cma.2020.113609.
  • Ahmadi, R., G. Ekbatanifard, and P. Bayat. 2021. A Modified Grey Wolf Optimizer Based Data Clustering Algorithm. Applied Artificial Intelligence 35 (1):63–79. doi:10.1080/08839514.2020.1842109.
  • Akbari, E., A. Rahimnejad, and S. Andrew Gadsden. 2021. A Greedy Non-Hierarchical Grey Wolf Optimizer for Real-World Optimization. Electronics letters 57 (13):499–501. doi:10.1049/ell2.12176.
  • Alba, E., and B. Dorronsoro. 2005. The Exploration/Exploitation Tradeoff in Dynamic Cellular Genetic Algorithms. IEEE Transactions on Evolutionary Computation 9 (2):126–42. doi:10.1109/TEVC.2005.843751.
  • Alotaibi, Y. 2022. A New Meta-Heuristics Data Clustering Algorithm Based on Tabu Search and Adaptive Search Memory. Symmetry 14 (3):623. doi:10.3390/sym14030623.
  • Al-Sultan, K. S. 1995. A Tabu Search Approach to the Clustering Problem. Pattern recognition 28 (9):1443–51. doi:10.1016/0031-3203(95)00022-R.
  • Al-Tashi, Q., S. Jadid Abdul Kadir, H. Md Rais, S. Mirjalili, and H. Alhussian. 2019. Binary Optimization Using Hybrid Grey Wolf Optimization for Feature Selection. IEEE Access 7:39496–508. doi:10.1109/ACCESS.2019.2906757.
  • Al-Tashi, Q., H. Rais, and S. Jadid. 2018. “Feature Selection Method Based on Grey Wolf Optimization for Coronary Artery Disease Classification.” In International Conference of Reliable Information and Communication Technology, Hotel Bangi-Putrajaya, Kuala Lumpur, Mal, 257–66.
  • Aydilek, I. B. 2018. A Hybrid Firefly and Particle Swarm Optimization Algorithm for Computationally Expensive Numerical Problems. Applied Soft Computing 66:232–49. doi:10.1016/j.asoc.2018.02.025.
  • Azizi, M., S. Arash Mousavi Ghasemi, R. Goli Ejlali, and S. Talatahari. 2020. Optimum Design of Fuzzy Controller Using Hybrid Ant Lion Optimizer and Jaya Algorithm. Artificial Intelligence Review 53 (3):1553–84. doi:10.1007/s10462-019-09713-8.
  • Bansal, J. C., S. Kumar Joshi, and A. K. Nagar. 2018. Fitness Varying Gravitational Constant in GSA. Applied Intelligence 48 (10):3446–61. doi:10.1007/s10489-018-1148-8.
  • Bansal, J. C., and S. Singh. 2021. A Better Exploration Strategy in Grey Wolf Optimizer. Journal of Ambient Intelligence and Humanized Computing 12 (1):1099–118. doi:10.1007/s12652-020-02153-1.
  • Biswas, A., K. K. Mishra, S. Tiwari, and A. K. Misra. 2013. Physics-Inspired Optimization Algorithms: A Survey. Journal of Optimization 2013:1–16. doi:10.1155/2013/438152.
  • Bratton, D., and J. Kennedy. 2007. “Defining a Standard for Particle Swarm Optimization.” In 2007 IEEE Swarm Intelligence Symposium, Honolulu, Hawaii, 120–27.
  • Cao, C., D. Chicco, and M. M. Hoffman. 2020. The MCC-F1 Curve: A Performance Evaluation Technique for Binary Classification. ArXivPreprint ArXiv:2006 11278ArXivPreprint ArXiv:2006 11278 ArXivPreprint ArXiv:2006 11278:ArXivPreprint ArXiv:2006 11278. https://arxiv.org/abs/2006.1127
  • Chen, H., X. Yueting, M. Wang, and X. Zhao. 2019. A Balanced Whale Optimization Algorithm for Constrained Engineering Design Problems. Applied Mathematical Modelling 71:45–59. doi:10.1016/j.apm.2019.02.004.
  • Chicco, D., and G. Jurman. 2020. The Advantages of the Matthews Correlation Coefficient (MCC) over F1 Score and Accuracy in Binary Classification Evaluation. BMC Genomics 21 (1):1–13. doi:10.1186/s12864-019-6413-7.
  • Das, S., A. Abraham, and A. Konar. 2008. Automatic Kernel Clustering with a Multi-Elitist Particle Swarm Optimization Algorithm. Pattern recognition letters 29 (5):688–99. doi:10.1016/j.patrec.2007.12.002.
  • Dorigo, M. 2007. Ant Colony Optimization. Scholarpedia 2 (3):1461. doi:10.4249/scholarpedia.1461.
  • Draa, A., S. Bouzoubia, and I. Boukhalfa. 2015. A Sinusoidal Differential Evolution Algorithm for Numerical Optimisation. Applied Soft Computing 27:99–126. doi:10.1016/j.asoc.2014.11.003.
  • Dua, D., and C. Graff. 2017. “{UCI} Machine Learning Repository.” http://archive.ics.uci.edu/ml.
  • Elkorany, A. S., M. Marey, K. M. Almustafa, and Z. F. Elsharkawy. 2022. Breast Cancer Diagnosis Using Support Vector Machines Optimized by Whale Optimization and Dragonfly Algorithms. IEEE Access 10. doi:10.1109/ACCESS.2022.3186021.
  • Fan, Q., H. Huang, Y. Li, Z. Han, Y. Hu, and D. Huang. 2021. Beetle Antenna Strategy Based Grey Wolf Optimization. Expert Systems with Applications 165:113882. doi:10.1016/j.eswa.2020.113882.
  • Faris, H., I. Aljarah, M. Azmi Al-Betar, and S. Mirjalili. 2018. Grey Wolf Optimizer: A Review of Recent Variants and Applications. Neural Computing & Applications 30 (2):413–35. doi:10.1007/s00521-017-3272-5.
  • Gao, Z.M., and J. Zhao. 2019. An Improved Grey Wolf Optimization Algorithm with Variable Weights. Computational intelligence and neuroscience 2019:1–13. doi:10.1155/2019/2981282.
  • Ghany, K. K. A., A. Mohamed AbdelAziz, T. Hassan a Soliman, and A. Abu El-Magd Sewisy. 2022. A Hybrid Modified Step Whale Optimization Algorithm with Tabu Search for Data Clustering. Journal of King Saud University-Computer and Information Sciences 34(3): 832–839.
  • Gupta, S., and K. Deep. 2019. Hybrid Grey Wolf Optimizer with Mutation Operator. In Soft Computing for Problem Solving edited byBansal, Jagdish Chand, Das, Kedar Nath, Nagar, Atulya, Deep, Kusum, Ojha, Akshay Kumar, 961–68. Singapore: Springer.
  • Hatamlou, A. 2013. Black Hole: A New Heuristic Optimization Approach for Data Clustering. Information Sciences 222:175–84. doi:10.1016/j.ins.2012.08.023.
  • Heidari, A. A., S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja, and H. Chen. 2019. Harris Hawks Optimization: Algorithm and Applications. Future Generation Computer Systems 97:849–72. doi:10.1016/j.future.2019.02.028.
  • Holland, J. H. 1992. Genetic Algorithms. Scientific American 267 (1):66–73. doi:10.1038/scientificamerican0792-66.
  • Hooda, H., and O. Prakash Verma. 2022. Fuzzy Clustering Using Gravitational Search Algorithm for Brain Image Segmentation. Multimedia Tools and Applications 81 (20):1–20. doi:10.1007/s11042-022-12336-x.
  • Hou, Y., H. Gao, Z. Wang, and D. Chuansheng. 2022. Improved Grey Wolf Optimization Algorithm and Application. Sensors 22 (10):3810. doi:10.3390/s22103810.
  • Hung, C.C., and H. Purnawan. 2008. “A Hybrid Rough K-Means Algorithm and Particle Swarm Optimization for Image Classification.” In Mexican International Conference on Artificial Intelligence, Berlin Heidelberg, 585–93.
  • Ikotun, A. M., A. E. Ezugwu, L. Abualigah, B. Abuhaija, and J. Heming. 2022. K-Means Clustering Algorithms: A Comprehensive Review, Variants Analysis, and Advances in the Era of Big Data. Information Sciences 622:178–210. doi:10.1016/j.ins.2022.11.139.
  • Jamil, M., and X.S. Yang. 2013. A Literature Survey of Benchmark Functions for Global Optimization Problems. ArXiv Preprint ArXiv:1308 4008 4(2):150–194.
  • Jayabarathi, T., T. Raghunathan, B. R. Adarsh, and P. Nagaratnam Suganthan. 2016. Economic Dispatch Using Hybrid Grey Wolf Optimizer. Energy 111:630–41. doi:10.1016/j.energy.2016.05.105.
  • Jayakumar, N., S. Subramanian, S. Ganesan, and E. B. Elanchezhian. 2016. Grey Wolf Optimization for Combined Heat and Power Dispatch with Cogeneration Systems. International Journal of Electrical Power & Energy Systems 74:252–64. doi:10.1016/j.ijepes.2015.07.031.
  • Kamboj, V. K. 2016. A Novel Hybrid PSO–GWO Approach for Unit Commitment Problem. Neural Computing & Applications 27 (6):1643–55. doi:10.1007/s00521-015-1962-4.
  • Kamboj, V. K., S. K. Bath, and J. S. Dhillon. 2016. Solution of Non-Convex Economic Load Dispatch Problem Using Grey Wolf Optimizer. Neural Computing & Applications 27 (5):1301–16. doi:10.1007/s00521-015-1934-8.
  • Kapoor, S., I. Zeya, C. Singhal, and S. Jagannath Nanda. 2017. A Grey Wolf Optimizer Based Automatic Clustering Algorithm for Satellite Image Segmentation. Procedia computer science 115:415–22. doi:10.1016/j.procs.2017.09.100.
  • Karaboga, D. 2010. Artificial Bee Colony Algorithm. Scholarpedia 5 (3):6915. doi:10.4249/scholarpedia.6915.
  • Kar, M. K., S. Kumar, A. K. Kumar Singh, S. Panigrahi, M. Cherukuri, and P. Sharma. 2022. Design and Analysis of FOPID-Based Damping Controllers Using a Modified Grey Wolf Optimization Algorithm. International Transactions on Electrical Energy Systems 2022 2022:1–31. others. doi:10.1155/2022/5339630.
  • Katarya, R., and O. Prakash Verma. 2018. Recommender System with Grey Wolf Optimizer and FCM. Neural Computing & Applications 30 (5):1679–87. doi:10.1007/s00521-016-2817-3.
  • Kaveh, A., and K. Biabani Hamedani. 2022. Improved Arithmetic Optimization Algorithm and Its Application to Discrete Structural Optimization. Structures 35:748–64. doi:10.1016/j.istruc.2021.11.012.
  • Kennedy, J., and R. Eberhart. 1995. “Particle Swarm Optimization.” In Proceedings of ICNN’95-International Conference on Neural Networks, Perth, WA, Australia, 4:1942–48.
  • Khairuzzaman, A. K. M., and S. Chaudhury. 2017. Multilevel Thresholding Using Grey Wolf Optimizer for Image Segmentation. Expert Systems with Applications 86:64–76. doi:10.1016/j.eswa.2017.04.029.
  • Kiani, F., and A. Seyyedabbasi. 2022. Metaheuristic Algorithms in IoT: Optimized Edge Node Localization. In Engineering Applications of Modern Metaheuristics, 19–39. Cham: Springer.
  • Kiani, F., A. Seyyedabbasi, S. Nematzadeh, F. Candan, T. Çevik, F. Aysin Anka, G. Randazzo, S. Lanza, and A. Muzirafuti. 2022. Adaptive Metaheuristic-Based Methods for Autonomous Robot Path Planning: Sustainable Agricultural Applications. Applied Sciences 12 (3):943. doi:10.3390/app12030943.
  • Kirkpatrick, S., C. Daniel Gelatt, and M. P. Vecchi. 1983. Optimization by Simulated Annealing. Science 220 (4598):671–80. doi:10.1126/science.220.4598.671.
  • Kumar, V., J. Kumar Chhabra, and D. Kumar. 2017. Grey Wolf Algorithm-Based Clustering Technique. Journal of Intelligent Systems 26 (1):153–68. doi:10.1515/jisys-2014-0137.
  • Lamos-Sweeney, J. D. 2012. Deep Learning Using Genetic Algorithms. Rochester Institute of Technology.
  • Lee, J., and D. Perkins. 2021. A Simulated Annealing Algorithm with a Dual Perturbation Method for Clustering. Pattern recognition 112:107713. doi:10.1016/j.patcog.2020.107713.
  • Lin, L., and M. Gen. 2009. Auto-Tuning Strategy for Evolutionary Algorithms: Balancing between Exploration and Exploitation. Soft Computing 13 (2):157–68. doi:10.1007/s00500-008-0303-2.
  • Liu, Y., W. Xindong, and Y. Shen. 2011. Automatic Clustering Using Genetic Algorithms. Applied Mathematics and Computation 218 (4):1267–79. doi:10.1016/j.amc.2011.06.007.
  • Long, W., J. Jiao, X. Liang, and M. Tang. 2018. An Exploration-Enhanced Grey Wolf Optimizer to Solve High-Dimensional Numerical Optimization. Engineering Applications of Artificial Intelligence 68:63–80. doi:10.1016/j.engappai.2017.10.024.
  • Maulik, U., and S. Bandyopadhyay. 2000. Genetic Algorithm-Based Clustering Technique. Pattern recognition 33 (9):1455–65. doi:10.1016/S0031-3203(99)00137-5.
  • Merwe, D. W. V. D., and A. P. Engelbrecht. 2003. “Data Clustering Using Particle Swarm Optimization.” 2003 Congress on Evolutionary Computation, CEC 2003 - Proceedings 1: 215–20. 10.1109/CEC.2003.1299577.
  • Merwe, D. W. D., and A. Petrus Engelbrecht. 2003. Data Clustering Using Particle Swarm Optimization. The 2003 Congress on Evolutionary Computation 2003 (1):215–20. ( CEC’03).
  • Mirjalili, S. 2015a. The Ant Lion Optimizer. Advances in Engineering Software 83:80–98. doi:10.1016/j.advengsoft.2015.01.010.
  • Mirjalili, S. 2015b. How Effective is the Grey Wolf Optimizer in Training Multi-Layer Perceptrons. Applied Intelligence 43 (1):150–61. doi:10.1007/s10489-014-0645-7.
  • Mirjalili, S. 2015c. Moth-Flame Optimization Algorithm: A Novel Nature-Inspired Heuristic Paradigm. Knowledge-Based Systems 89:228–49. doi:10.1016/j.knosys.2015.07.006.
  • Mirjalili, S. 2016a. Dragonfly Algorithm: A New Meta-Heuristic Optimization Technique for Solving Single-Objective, Discrete, and Multi-Objective Problems. Neural Computing & Applications 27 (4):1053–73. doi:10.1007/s00521-015-1920-1.
  • Mirjalili, S. 2016b. SCA: A Sine Cosine Algorithm for Solving Optimization Problems. Knowledge-Based Systems 96:120–33. doi:10.1016/j.knosys.2015.12.022.
  • Mirjalili, S., and A. Lewis. 2016. The Whale Optimization Algorithm. Advances in Engineering Software 95:51–67. doi:10.1016/j.advengsoft.2016.01.008.
  • Mirjalili, S. Z., S. Mirjalili, S. Saremi, H. Faris, and I. Aljarah. 2018. Grasshopper Optimization Algorithm for Multi-Objective Optimization Problems. Applied Intelligence 48 (4):805–20. doi:10.1007/s10489-017-1019-8.
  • Mirjalili, S., S. Mohammad Mirjalili, and A. Hatamlou. 2016. Multi-Verse Optimizer: A Nature-Inspired Algorithm for Global Optimization. Neural Computing & Applications 27 (2):495–513. doi:10.1007/s00521-015-1870-7.
  • Mirjalili, S., S. Mohammad Mirjalili, and A. Lewis. 2014a. Grey Wolf Optimizer. Advances in Engineering Software 69:46–61. doi:10.1016/j.advengsoft.2013.12.007.
  • Mirjalili, S., S. Mohammad Mirjalili, and A. Lewis. 2014b. Grey Wolf Optimizer. Advances in Engineering Software 69 (March):46–61. doi:10.1016/j.advengsoft.2013.12.007.
  • Mirjalili, S., S. Zaiton Mohd Hashim, and H. Moradian Sardroudi. 2012. Training Feedforward Neural Networks Using Hybrid Particle Swarm Optimization and Gravitational Search Algorithm. Applied Mathematics and Computation 218 (22):11125–37. doi:10.1016/j.amc.2012.04.069.
  • Mittal, N., U. Singh, and B. Singh Sohi. 2016. Modified Grey Wolf Optimizer for Global Engineering Optimization. Applied Computational Intelligence and Soft Computing 2016:1–16. doi:10.1155/2016/7950348.
  • Nadimi-Shahraki, M. H., S. Taghian, and S. Mirjalili. 2021. An Improved Grey Wolf Optimizer for Solving Engineering Problems. Expert Systems with Applications 166:113917. March. doi: https://doi.org/10.1016/j.eswa.2020.113917.
  • Obadina, O. O., M. A. Thaha, Z. Mohamed, and M. Hasan Shaheed. 2022. Grey-Box Modelling and Fuzzy Logic Control of a Leader–Follower Robot Manipulator System: A Hybrid Grey Wolf–Whale Optimisation Approach. ISA transactions 129:572–93. doi:10.1016/j.isatra.2022.02.023.
  • Olorunda, O., and A. P. Engelbrecht. 2008. “Measuring Exploration/Exploitation in Particle Swarms Using Swarm Diversity.” In 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence), Hong Kong, China, 1128–34.
  • Panigrahi, S., and H. Sekhar Behera. 2019. Nonlinear Time Series Forecasting Using a Novel Self-Adaptive TLBO-MFLANN Model. International Journal of Computational Intelligence Studies 8 (1–2):4–26. doi:10.1504/IJCISTUDIES.2019.098013.
  • Parpinelli, R. S., and H. S. Lopes. 2011. New Inspirations in Swarm Intelligence: A Survey. International Journal of Bio-Inspired Computation 3 (1):1–16. doi:10.1504/IJBIC.2011.038700.
  • Pradhan, M., P. Kumar Roy, and T. Pal. 2016. Grey Wolf Optimization Applied to Economic Load Dispatch Problems. International Journal of Electrical Power & Energy Systems 83:325–34. doi:10.1016/j.ijepes.2016.04.034.
  • Qiang, T., X. Chen, and X. Liu. 2019. Multi-Strategy Ensemble Grey Wolf Optimizer and Its Application to Feature Selection. Applied Soft Computing 76:16–30. doi:10.1016/j.asoc.2018.11.047.
  • Qin, A. K., V. Ling Huang, and P. N. Suganthan. 2008. Differential Evolution Algorithm with Strategy Adaptation for Global Numerical Optimization. IEEE Transactions on Evolutionary Computation 13 (2):398–417. doi:10.1109/TEVC.2008.927706.
  • Rana, S., S. Jasola, and R. Kumar. 2010. A Hybrid Sequential Approach for Data Clustering Using K-Means and Particle Swarm Optimization Algorithm. International Journal of Engineering, Science and Technology 2 (6). doi:10.4314/ijest.v2i6.63708.
  • Rao, R. 2016. Jaya: A Simple and New Optimization Algorithm for Solving Constrained and Unconstrained Optimization Problems. International Journal of Industrial Engineering Computations 7 (1):19–34. doi:10.5267/j.ijiec.2015.8.004.
  • Rao, R. V., V. J. Savsani, and D. P. Vakharia. 2011. Teaching–learning-Based Optimization: A Novel Method for Constrained Mechanical Design Optimization Problems. Computer-Aided Design 43 (3):303–15. doi:10.1016/j.cad.2010.12.015.
  • Rashedi, E., H. Nezamabadi-Pour, and S. Saryazdi. 2009. GSA: A Gravitational Search Algorithm. Information Sciences 179 (13):2232–48. doi:10.1016/j.ins.2009.03.004.
  • Rutenbar, R. A. 1989. Simulated Annealing Algorithms: An Overview. IEEE Circuits and Devices Magazine 5 (1):19–26. doi:10.1109/101.17235.
  • Saida, I. B., K. Nadjet, and B. Omar. 2014. A New Algorithm for Data Clustering Based on Cuckoo Search Optimization. In Genetic and Evolutionary Computing edited byPan, Jeng-Shyang, Krömer, Pavel, Snásel, Václav,55–64. Prague, Czech Republic: Springer.
  • Selim, S. Z., and K. 1. Alsultan. 1991. A Simulated Annealing Algorithm for the Clustering Problem. Pattern recognition 24 (10):1003–08. doi:10.1016/0031-3203(91)90097-O.
  • Seyyedabbasi, A., and F. Kiani. 2021. I-GWO and Ex-GWO: Improved Algorithms of the Grey Wolf Optimizer to Solve Global Optimization Problems. Engineering with Computers 37 (1):509–32. doi:10.1007/s00366-019-00837-7.
  • Seyyedabbasi, A., and F. Kiani. 2022. Sand Cat Swarm Optimization: A Nature-Inspired Algorithm to Solve Global Optimization Problems. Engineering with Computers 1–25. doi:10.1007/s00366-022-01604-x.
  • Shial, G., S. Sahoo, and S. Panigrahi. 2022a. “Community Detection and Disease Identification Using Meta-Heuristic Based Clustering Methods.” In 2022 IEEE India Council International Subsections Conference (INDISCON) , 1–6.
  • Shial, G., S. Sahoo, and S. Panigrahi. 2022b. “Identification and Analysis of Breast Cancer Disease Using Swarm and Evolutionary Algorithm.” In 2022 IEEE Region 10 Symposium (TENSYMP), IIT Bombay, Mumbai, 1–6.
  • Singh, S., and J. Chand Bansal. 2022. Mutation-Driven Grey Wolf Optimizer with Modified Search Mechanism. Expert Systems with Applications 194:116450. doi:10.1016/j.eswa.2021.116450.
  • Song, X., L. Tang, S. Zhao, X. Zhang, L. Lei, J. Huang, and W. Cai. 2015. Grey Wolf Optimizer for Parameter Estimation in Surface Waves. Soil Dynamics and Earthquake Engineering 75:147–57. doi:10.1016/j.soildyn.2015.04.004.
  • Song, J., J. Wang, and L. Haiyan. 2018. A Novel Combined Model Based on Advanced Optimization Algorithm for Short-Term Wind Speed Forecasting. Applied Energy 215:643–58. doi:10.1016/j.apenergy.2018.02.070.
  • Sulaiman, M. H., Z. Mustaffa, M. Rusllim Mohamed, and O. Aliman. 2015. Using the Gray Wolf Optimizer for Solving Optimal Reactive Power Dispatch Problem. Applied Soft Computing 32:286–92. doi:10.1016/j.asoc.2015.03.041.
  • Teng, Z.J., L. Jin-Ling, and L.W. Guo. 2019. An Improved Hybrid Grey Wolf Optimization Algorithm. Soft Computing 23 (15):6617–31. doi:10.1007/s00500-018-3310-y.
  • Thiele, L., K. Miettinen, P. J. Korhonen, and J. Molina. 2009. A Preference-Based Evolutionary Algorithm for Multi-Objective Optimization. Evolutionary Computation 17 (3):411–36. doi:10.1162/evco.2009.17.3.411.
  • Venkateswaran, C., M. Ramachandran, S. Chinnasamy, C. Sivaji, and M. Amudha. 2022. An Extensive Study on Gravitational Search Algorithm. Materials and Its Characterization 1 (1):9–16. doi:10.46632/mc/1/1/2.
  • Wang, H., Q. Geng, and Z. Qiao. 2014. “Parameter Tuning of Particle Swarm Optimization by Using Taguchi Method and Its Application to Motor Design.” In 2014 4th IEEE International Conference on Information Science and Technology, Shenzhen, China, 722–26.
  • Xiaobing, Y., X. WangYing, and L. ChenLiang. 2021. Opposition-Based Learning Grey Wolf Optimizer for Global Optimization. Knowledge-Based Systems 226:107139. doi:10.1016/j.knosys.2021.107139.
  • Xiao, J., Y. Yan, J. Zhang, and Y. Tang. 2010. A Quantum-Inspired Genetic Algorithm for k-Means Clustering. Expert Systems with Applications 37 (7):4966–73. doi:10.1016/j.eswa.2009.12.017.
  • Yang, X.S. 2013. Bat Algorithm: Literature Review and Applications. ArXiv Preprint ArXiv:1308 3900 5(3):141–149.
  • Yang, X.S., and S. Deb. 2010. Engineering Optimisation by Cuckoo Search. ArXiv Preprint ArXiv:1005 2908 1(4):330–343.
  • Yang, X.S., and A. Hossein Gandomi. 2012. Bat Algorithm: A Novel Approach for Global Engineering Optimization. Engineering Computations 29 (5):464–83. doi:10.1108/02644401211235834.
  • Zeebaree, D. Q., H. Haron, A. Mohsin Abdulazeez, and S. R. M. Zeebaree. 2017. Combination of K-Means Clustering with Genetic Algorithm: A Review. International Journal of Applied Engineering Research 12 (24):14238–45.
  • Zhang, X., Q. Kang, J. Cheng, and X. Wang. 2018. A Novel Hybrid Algorithm Based on Biogeography-Based Optimization and Grey Wolf Optimizer. Applied Soft Computing 67:197–214. doi:10.1016/j.asoc.2018.02.049.
  • Zhang, X., Q. Lin, W. Mao, S. Liu, Z. Dou, and G. Liu. 2021. Hybrid Particle Swarm and Grey Wolf Optimizer and Its Application to Clustering Optimization. Applied Soft Computing 101:107061. doi:10.1016/j.asoc.2020.107061.
  • Zhang, S., and Y. Zhou. 2015. Grey Wolf Optimizer Based on Powell Local Optimization Method for Clustering Analysis. Discrete Dynamics in Nature and Society 2015:1–17. doi:10.1155/2015/481360.
  • Zhao, J., and Z. Ming Gao. 2020. “An Improved Grey Wolf Optimization Algorithm with Multiple Tunnels for Updating.” In Journal of Physics: Conference Series. Vol. 1678. Hindawi. 10.1088/1742-6596/1678/1/012096.
  • Zhou, X., F. Miao, and M. Hongjiang. 2018. Genetic Algorithm with an Improved Initial Population Technique for Automatic Clustering of Low-Dimensional Data. Information 9 (4):101. doi:10.3390/info9040101.