Metaheuristics Algorithms: Overview, Applications, and Modifications
Keywords:
Metaheuristic Algorithms, Optimization Techniques, Swarm Intelligence, Evolutionary Computation, Global Optimization, Genetic Algorithm, Particle Swarm OptimizationSynopsis
Metaheuristic algorithms have emerged as essential tools for solving complex optimization problems across disciplines such as engineering, logistics, finance, and healthcare. Their ability to efficiently explore large, nonlinear, and uncertain search spaces makes them highly effective where traditional methods often fail.
This book, Metaheuristics Algorithms: Overview, Applications, and Modifications, offers a structured overview of key algorithmic families—including evolutionary, swarm-based, physics-inspired, and human-based approaches—supported by theoretical foundations, classifications, and real-world applications. Emphasis is placed on recent advancements, hybridizations, and performance-enhancing modifications.
Designed for students, researchers, and practitioners, the content balances academic rigor with practical relevance, aiming to guide both implementation and innovation in metaheuristic optimization.
I am grateful to my colleagues and reviewers for their valuable input, and to Reta N. Mussa for the attractive design of the book cover. My appreciation also extends to Deep Science Publishing for enabling its open-access dissemination. I hope this work contributes meaningfully to advancing research in computational intelligence and intelligent optimization.
References
Abdel-Basset, M., Abdel-Fatah, L., & Sangaiah, A. K. (2018). Metaheuristic Algorithms: A Comprehensive Review. In Computational Intelligence for Multimedia Big Data on the Cloud with Engineering Applications (pp. 185–231). Elsevier. https://doi.org/10.1016/B978-0-12-813314-9.00010-4
Acan, A., Altincay, H., Tekol, Y., & Unveren, A. (n.d.). A genetic algorithm with multiple crossover operators for optimal frequency assignment problem. The 2003 Congress on Evolutionary Computation, 2003. CEC ’03., 256–263. https://doi.org/10.1109/CEC.2003.1299583
Acan, A., & Unveren, A. (2007). A shared-memory ACO+GA hybrid for combinatorial optimization. 2007 IEEE Congress on Evolutionary Computation, 2078–2085. https://doi.org/10.1109/CEC.2007.4424729
Acan, A., & Ünveren, A. (2015). A great deluge and tabu search hybrid with two-stage memory support for quadratic assignment problem. Applied Soft Computing, 36, 185–203. https://doi.org/10.1016/j.asoc.2015.06.061
Acan, A., & Ünveren, A. (2020). Multiobjective great deluge algorithm with two-stage archive support. Engineering Applications of Artificial Intelligence, 87, 103239. https://doi.org/10.1016/j.engappai.2019.103239
Agarwal, P., & Mehta, S. (2014). Nature-Inspired Algorithms: State-of-Art, Problems and Prospects. In International Journal of Computer Applications (Vol. 100, Issue 14).
Agrawal, P., Abutarboush, H. F., Ganesh, T., & Mohamed, A. W. (2021). Metaheuristic Algorithms on Feature Selection: A Survey of One Decade of Research (2009-2019). IEEE Access, 9, 26766–26791. https://doi.org/10.1109/ACCESS.2021.3056407
Almufti, S., Marqas, R., & Asaad, R. (2019). Comparative study between elephant herding optimization (EHO) and U-turning ant colony optimization (U-TACO) in solving symmetric traveling salesman problem (STSP). Journal Of Advanced Computer Science & Technology, 8(2), 32.
Asaad, R. R., & Abdulnabi, N. L. (2018). Using Local Searches Algorithms with Ant Colony Optimization for the Solution of TSP Problems. Academic Journal of Nawroz University, 7(3), 1–6. https://doi.org/10.25007/ajnu.v7n3a193
Almufti, S. (2017). Using Swarm Intelligence for solving NPHard Problems. Academic Journal of Nawroz University, 6(3), 46–50. https://doi.org/10.25007/ajnu.v6n3a78
Almufti, S., Asaad, R., & Salim, B. (2018). Review on elephant herding optimization algorithm performance in solving optimization problems. International Journal of Engineering & Technology, 7, 6109-6114.
Almufti, S. (2021). The novel Social Spider Optimization Algorithm: Overview, Modifications, and Applications. ICONTECH INTERNATIONAL JOURNAL, 5(2), 32–51. https://doi.org/10.46291/icontechvol5iss2pp32-51
Almufti, S. (2022). Vibrating Particles System Algorithm: Overview, Modifications and Applications. ICONTECH INTERNATIONAL JOURNAL, 6(3), 1–11. https://doi.org/10.46291/icontechvol6iss3pp1-11
Almufti, S. M. (2015). U-Turning Ant Colony Algorithm powered by Great Deluge Algorithm for the solution of TSP Problem.
Almufti, S. M. (2022a). Lion algorithm: Overview, modifications and applications E I N F O. International Research Journal of Science, 2(2), 176–186. https://doi.org/10.5281/zenodo.6973555
Almufti, S. M. (2022b). Vibrating Particles System Algorithm performance in solving Constrained Optimization Problem. Academic Journal of Nawroz University, 11(3), 231–242. https://doi.org/10.25007/ajnu.v11n3a1499
Almufti, S. M., Ahmad, H. B., Marqas, R. B., & Asaad, R. R. (2021). Grey wolf optimizer: Overview, modifications and applications. International Research Journal of Science, Technology, Education,and Management, 1(1),1-1.
Almufti, S. M., Alkurdi, A. A. H., & Khoursheed, E. A. (2022). Artificial Bee Colony Algorithm Performances in Solving Constraint-Based Optimization Problem. 21, 2022.
Almufti, S. M., Asaad, R. R., & Salim, B. W. (2018). Review on Elephant Herding Optimization Algorithm Performance in Solving Optimization Problems. Article in International Journal of Engineering and Technology, 7(4), 6109–6114. https://doi.org/10.14419/ijet.v7i4.23127
Almufti, S. M., Saeed, V. A., & Marqas, R. B. (2019). Taxonomy of Bio-Inspired Optimization Algorithms.
Almufti, S. M., & Shaban, A. (2018). U-Turning Ant Colony Algorithm for Solving Symmetric Traveling Salesman Problem. Academic Journal of Nawroz University, 7(4), 45. https://doi.org/10.25007/ajnu.v7n4a270
Bäck, T., & Schwefel, H.-P. (1993). An Overview of Evolutionary Algorithms for Parameter Optimization.Evolutionary Computation, 1(1), 1–23. https://doi.org/10.1162/evco.1993.1.1.1
Ihsan, R. R., Almufti, S. M., Ormani, B. M., Asaad, R. R., & Marqas, R. B. (2021). A survey on Cat Swarm Optimization algorithm. Asian J. Res. Comput. Sci, 10, 22-32.
Bartz-Beielstein, T., Branke, J., Mehnen, J., & Mersmann, O. (2014). Evolutionary Algorithms. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 4(3), 178–195. https://doi.org/10.1002/widm.1124
Bhuvaneswari, M., Hariraman, S., Anantharaj, B., Balaji, N., & Professor, A. (2014). Nature Inspired Algorithms: A Review. In International Journal of Emerging Technology in Computer Science & Electronics (IJETCSE) (Vol. 12).
Dehghani, M., Trojovská, E., & Trojovský, P. (2022). A new human-based metaheuristic algorithm for solving optimization problems on the base of simulation of driving training process. Scientific Reports, 12(1), 9924. https://doi.org/10.1038/s41598-022-14225-7
Dhiman, G., & Kumar, V. (2017). Spotted hyena optimizer: A novel bio-inspired based metaheuristic technique for engineering applications. Advances in Engineering Software, 114, 48–70. https://doi.org/10.1016/j.advengsoft.2017.05.014
Dubey, H. M., Panigrahi, B. K., & Pandit, M. (2014). Bio-inspired optimisation for economic load dispatch: A review. International Journal of Bio-Inspired Computation, 6(1), 7–21. https://doi.org/10.1504/IJBIC.2014.059967
Ridwan B. Marqas, Saman M. Almufti, Pawan Shivan Othman, & Chyavan Mohammed Abdulrahman. (2020). Evaluation of EHO, U-TACO and TS Metaheuristics algorithms in Solving TSP. JOURNAL OF XI’AN UNIVERSITY OF ARCHITECTURE & TECHNOLOGY, XII(IV). https://doi.org/10.37896/jxat12.04/1062
Fister, I., Yang, X.-S., Fister, I., Brest, J., & Fister, D. (2013). A Brief Review of Nature-Inspired Algorithms for Optimization. http://arxiv.org/abs/1307.4186
Gogna, A., & Tayal, A. (2013). Metaheuristics: review and application. Journal of Experimental & Theoretical Artificial Intelligence, 25(4), 503–526. https://doi.org/10.1080/0952813X.2013.782347
Kennedy, J., & Eberhart, R. (n.d.). Particle swarm optimization. Proceedings of ICNN’95 - International Conference on Neural Networks, 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
Ferinia, R., Kumar, D.L.S., Kumar, B.S. et al. Factors determining customers desire to analyse supply chain management in intelligent IoT. J Comb Optim 45, 72 (2023). https://doi.org/10.1007/s10878-023- 01007-8
Klau, G. W., Lesh, N., Marks, J., & Mitzenmacher, M. (2010). Human-guided search. Journal of Heuristics, 16(3), 289–310. https://doi.org/10.1007/s10732-009-9107-5
Luis, J., & Sequera, C. (n.d.). 7 Tune Up of a Genetic Algorithm to Group Documentary Collections. www.intechopen.com
Almufti, S. (2019). Historical survey on metaheuristics algorithms. International Journal of Scientific World, 7(1), 1. https://doi.org/10.14419/ijsw.v7i1.29497
Almufti, S. M. (2022). Hybridizing Ant Colony Optimization Algorithm for Optimizing Edge-Detector Techniques. Academic Journal of Nawroz University, 11(2), 135–145. https://doi.org/10.25007/ajnu.v11n2a1320
Almufti, S., Yahya Zebari, A., & Khalid Omer, H. (2019). A comparative study of particle swarm optimization and genetic algorithm. Journal of Advanced Computer Science & Technology, 8(2), 40. https://doi.org/10.14419/jacst.v8i2.29401
Shaban, A. A., Dela Fuente, J. A., Salih, M. S., & Ali, R. I. (2023). Review of swarm intelligence for solving symmetric traveling salesman problem. Qubahan Academic Journal, 3(2), 10–27.
modifications, and applications from 1992 to 2022. Polaris Global Journal of Scholarly Research and Trends, 1(1), 10–17. https://doi.org/10.58429/pgjsrt.v1n1a85
Almufti, S.M. (2015). U-Turning Ant Colony Algorithm powered by Great Deluge Algorithm for the solution of TSP Problem. Famagusta, Cyprus: EMU. Retrieved from http://i-rep.emu.edu.tr:8080/jspui/handle/11129/1734
Almufti, S.M. (2019). Historical survey on metaheuristics algorithms. International Journal of Scientific World.
Almufti, S.M. (2022b). Hybridizing Ant Colony Optimization Algorithm for Optimizing Edge-Detector Techniques. Academic Journal of Nawroz University, 11(2), 135-145.
Almufti, S.M., Marqas, R.B., Othman, P.S., & Sallow, A.B. (2021). Single-based and Population-based Metaheuristics for Solving NP-hard Problems. Iraqi J Sci, 62(5), 1-11.
Asaad, R.R., & Abdulnabi, N.L. (2018). Using local searches algorithms with Ant colony optimization for the solution of TSP problems. Academic Journal of Nawroz University, 1-6.
Blum, C. (2005). Ant colony optimization: Introduction and recent trends. Physics of Life Reviews, 353–373.
Dorigo, M. & Gambardella, L.M. (1997). Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, 1(1), 53-66.
Dorigo, M. (1992). Optimization, Learning and Natural Algorithms. Politecnico di Milano, Italy.
Stutzle, T., Lopez-Ibznez, M., & Dorigo, M. (2011). A Concise Overview of Applications of Ant Colony Optimization. In Wiley Encyclopedia of Operations Research and Management Science.
Almufti, S. M. (2015). U-Turning Ant Colony Algorithm powered by Great Deluge Algorithm for the solution of TSP Problem. Retrieved from Hdl.handle.net
Almufti, S. M. (2017a). Historical survey on metaheuristics algorithms. International Journal of Scientific World, 7(1), 1-12. doi:https://doi.org/10.14419/IJSW.V7I1.29497
Almufti, S. M. (2017b). Using Swarm Intelligence for solving NP-Hard Problems. Academic Journal of Nawroz University, 6(3), 46-50. doi:https://doi.org/10.25007/ajnu.v6n3a78
Bauer, H., de, I. H., & Silvestre, I. (2003). Lion (Panthera leo) social behaviour in the West and Central African savannah belt. Mammalian Biology, 68(4), 239-243. doi:https://doi.org/10.1078/1616-5047-00090
BR, R. (2014). Lion algorithm for standard and large scale bilinear system identification: a global optimization based on lion’s social behavior. IEEE congress on evolutionary computation (CEC), 2116–2123.
Chander, S., Vijaya, P., & Dhyani, P. (2018). Multi kernel and dynamic fractional lion optimization algorithm for data clustering. Alexandria Engineering Journal, 57(1), 267-276. doi:https://doi.org/10.1016/j.aej.2016.12.013
Chintalapalli, R. M., & Ananthula, V. R. (2018). M-LionWhale: multi-objective optimisation model for secure routing in mobile ad-hoc network. IET Communications, 12(12), 1406-1415. doi:10.1049/iet-com.2017.1279
G, J., & brunda, S. S. (2018). An Improved K-Lion Optimization Algorithm With Feature Selection Methods for Text Document Cluster. International Journal of Computer Sciences and Engineering, 6(7), 245-251.
KC, L., JC, H., & JT, W. (2018). Feature selection with modified lion’s algorithms and support vector machine for high-dimensional data. Appl Soft Comput 68.
Marqas, R. B., Almufti, S. M., Ahmed, H. B., & Asaad, R. R. (2021). Grey wolf optimizer: Overview, modifications and applications. International Research Journal of Science, Technology, Education, and Management, 1(1), 44-56. doi: https://doi.org/10.5281/zenodo.5195644
MB, W., & N, G. (2018). Route discovery for vehicular Ad hoc networks using modified lion algorithm. Alexandria Eng J 57.
Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey Wolf Optimizer. Advances in Engineering Software.
Rajakumar, B. (2012). The Lion's Algorithm: A New Nature-Inspired Search Algorithm. Procedia Technology, 6, 126-135. doi:https://doi.org/10.1016/j.protcy.2012.10.016
Rajakumar, B. R. (2020). Lion Algorithm and Its Applications. In M. Khosravy, N. Gupta, N. Patel, & T. Senjyu, Frontier Applications of Nature Inspired Computation (pp. 100-119). Springer Nature Singapore. doi:https://doi.org/10.1007/978-981-15-2133-1_5
Ranjan, N. M., & Prasadb, R. S. (n.d.). lion fuzzy neural network-based evolutionary model for text classification using context and sense based features. Applied Soft Computing. doi:https://doi.org/10.1016/j.asoc.2018.07.016
RK, A., & UD, K. (2017). AFL-TOHIP: Adaptive fractional lion optimization to topology-hiding multi-path routing in mobile Ad hoc network. 727–732.
Salim, B. W., Almufti, S. M., & Asaad, R. R. (2019). Review on elephant herding optimization algorithm performance in solving optimization problems. International Journal of Engineering & Technology, 7(4), 6109-6114. doi:10.14419/ijet.v7i4.23127
Satish, C., P., V., & Praveen, D. (2017). Multi-objective-based adaptive dynamic directive operative fractional lion algorithm for data clustering. International Conference on Infocom Technologies and Unmanned Systems (Trends and Future Directions). doi:10.1109/ICTUS.2017.8286066
Y, L., Y, H., & M, Z. (2018). Short-term load forecasting for electric vehicle chargingstation based on niche immunity lion algorithm and convolutional neural network. Energies.
Yazdani, M., & Jolai, F. (2016). Lion Optimization Algorithm (LOA): A nature-inspired. Journal of Computational Design and Engineering, 3(1). doi:https://doi.org/10.1016/j.jcde.2015.06.003
Almufti, S. (2022). Lion algorithm: Overview, modifications and applications. International Research Journal of Science, 2(2), 176–186. https://doi.org/10.5281/zenodo.6973555
Acan, A., Altincay, H., Tekol, Y., & Unveren, A. (n.d.). A genetic algorithm with multiple crossover operators for optimal frequency assignment problem. The 2003 Congress on Evolutionary Computation, 2003. CEC ’03., 256–263. https://doi.org/10.1109/CEC.2003.1299583
Almufti, S. (2021). The novel Social Spider Optimization Algorithm: Overview, Modifications, and Applications. ICONTECH INTERNATIONAL JOURNAL, 5(2), 32–51. https://doi.org/10.46291/icontechvol5iss2pp32-51
Almufti, S. M. (n.d.). U-Turning Ant Colony Algorithm powered by Great Deluge Algorithm for the solution of TSP Problem.
Almufti, S. M., Marqas, R. B., Othman, P. S., & Sallow, A. B. (2021). Single-based and population-based metaheuristics for solving np-hard problems. Iraqi Journal of Science, 62(5), 1710–1720. https://doi.org/10.24996/ijs.2021.62.5.34
Dokeroglu, T., Sevinc, E., Kucukyilmaz, T., & Cosar, A. (2019). A survey on new generation metaheuristic algorithms. Computers & Industrial Engineering, 137, 106040. https://doi.org/10.1016/j.cie.2019.106040
Evaluation of EHO, U-TACO and TS Metaheuristics algorithms in Solving TSP. (2020). JOURNAL OF XI’AN UNIVERSITY OF ARCHITECTURE & TECHNOLOGY, XII(IV). https://doi.org/10.37896/jxat12.04/1062
Fister, I., Yang, X.-S., Fister, D., & Fister, I. (2014). Cuckoo Search: A Brief Literature Review (pp. 49–62). https://doi.org/10.1007/978-3-319-02141-6_3
Gogna, A., & Tayal, A. (2013). Metaheuristics: review and application. Journal of Experimental & Theoretical Artificial Intelligence, 25(4), 503–526. https://doi.org/10.1080/0952813X.2013.782347
Hedar, A.-R., & Fukushima, M. (2006). Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization. Journal of Global Optimization, 35(4), 521–549. https://doi.org/10.1007/s10898-005-3693-z
Hwang, S.-F., & He, R.-S. (2006). A hybrid real-parameter genetic algorithm for function optimization. Advanced Engineering Informatics, 20(1), 7–21. https://doi.org/10.1016/j.aei.2005.09.001
Jati, G. K., Manurung, H. M., & Suyanto. (2012). Discrete cuckoo search for traveling salesman problem. 2012 7th International Conference on Computing and Convergence Technology (ICCCT), 993–997.
Joshi, A. S., Kulkarni, O., Kakandikar, G. M., & Nandedkar, V. M. (2017). Cuckoo Search Optimization- A Review. Materials Today: Proceedings, 4(8), 7262–7269. https://doi.org/10.1016/j.matpr.2017.07.055
Kaveh, A., & Bakhshpoori, T. (2019). Metaheuristics: Outlines, MATLAB Codes and Examples. In Metaheuristics: Outlines, MATLAB Codes and Examples. Springer International Publishing. https://doi.org/10.1007/978-3-030-04067-3
Kennedy, J., & Eberhart, R. (n.d.). Particle swarm optimization. Proceedings of ICNN’95 - International Conference on Neural Networks, 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
Liu, J. (2005). Novel orthogonal simulated annealing with fractional factorial analysis to solve global optimization problems. Engineering Optimization, 37(5), 499–519. https://doi.org/10.1080/03052150500066646
M. Almufti, S. (2019). Historical survey on metaheuristics algorithms. International Journal of Scientific World, 7(1), 1. https://doi.org/10.14419/ijsw.v7i1.29497
M. Almufti, S., Ahmad Shaban, A., Ismael Ali, R., & A. Dela Fuente, J. (2023). Overview of Metaheuristic Algorithms. Polaris Global Journal of Scholarly Research and Trends, 2(2), 10–32. https://doi.org/10.58429/pgjsrt.v2n2a144
M. Almufti, S., Boya Marqas, R., & Ashqi Saeed, V. (2019). Taxonomy of bio-inspired optimization algorithms. Journal of Advanced Computer Science & Technology, 8(2), 23. https://doi.org/10.14419/jacst.v8i2.29402
M. Almufti, S., Yahya Zebari, A., & Khalid Omer, H. (2019). A comparative study of particle swarm optimization and genetic algorithm. Journal of Advanced Computer Science & Technology, 8(2), 40. https://doi.org/10.14419/jacst.v8i2.29401
Mareli, M., & Twala, B. (2018). An adaptive Cuckoo search algorithm for optimisation. Applied Computing and Informatics, 14(2), 107–115. https://doi.org/10.1016/j.aci.2017.09.001
Nguyen, T. T., Vo, D. N., & Dinh, B. H. (2016). Cuckoo search algorithm for combined heat and power economic dispatch. International Journal of Electrical Power & Energy Systems, 81, 204–214. https://doi.org/10.1016/j.ijepes.2016.02.026
Sharma, A., Sharma, A., Chowdary, V., Srivastava, A., & Joshi, P. (2021). Cuckoo Search Algorithm: A Review of Recent Variants and Engineering Applications (pp. 177–194). https://doi.org/10.1007/978-981-15-7571-6_8
Shi, Y., & Eberhart, R. (n.d.). A modified particle swarm optimizer. 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360), 69–73. https://doi.org/10.1109/ICEC.1998.699146
Soneji, H., & Sanghvi, R. C. (2012). Towards the improvement of Cuckoo search algorithm. 2012 World Congress on Information and Communication Technologies, 878–883. https://doi.org/10.1109/WICT.2012.6409199
Xin-She Yang, & Suash Deb. (2010). Engineering optimisation by cuckoo search. Int. J. Mathematical Modelling and Numerical Optimisation, 1(4), 330–343.
Yang, X.-S., & Suash Deb. (2009). Cuckoo Search via Levy flights. 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC), 210–214. https://doi.org/10.1109/NABIC.2009.5393690
Yang, X.-She. (2010). Nature-inspired metaheuristic algorithms. Luniver Press.
Zou, F., Wang, L., Hei, X., & Chen, D. (2015). Teaching–learning-based optimization with learning experience of other learners and its application. Applied Soft Computing, 37, 725–736. https://doi.org/10.1016/j.asoc.2015.08.047
Almufti, S. M., Marqas, R. B., Asaad, R. R., & Shaban, A. A. (2025). Cuckoo search algorithm: overview, modifications, and applications. International Journal of Scientific World.
Ab Rashid MFF (2017) A hybrid Ant-Wolf Algorithm to optimize assembly sequence planning problem. Assembly Autom 37(2):238–248
Al-Aboody NA, Al-Raweshidy HS (2016) Grey wolf optimization-based energy-efficient routing protocol for heterogeneous wireless sensor networks. In: 2016 4th international symposium on computational and business intelligence (ISCBI). IEEE, pp 101–107
Almufti S., (2018), U-Turning Ant Colony Algorithm powered by Great Deluge Algorithm for the solution of TSP Problem, Hdl.handle.net, 2018. [Online].
Almufti, S. (2017a). Using Swarm Intelligence for solving NPHard Problems. Academic Journal Of Nawroz University, 6(3), 46-50. doi: 10.25007/ajnu.v6n3a78
Almufti, S. (2019a). Historical survey on metaheuristics algorithms. International Journal Of Scientific World, 7(1), 1. doi: 10.14419/ijsw.v7i1.29497
Almufti, S. (2021b). The novel Social Spider Optimization Algorithm: Overview, Modifications, and Applications. ICONTECH INTERNATIONAL JOURNAL, 5(2), 32-51. doi: 10.46291/icontechvol5iss2pp32-51
Almufti, S., Marqas, R., Othman, P., & Sallow, A. (2021a). Single-based and Population-Based Metaheuristics Algorithms Performances in Solving NP-hard Problems. Iraqi Journal Of Science. doi: 10.24996/10.24996/ijs.2021.62.5.34 Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Amirsadri, S., Mousavirad, S., & Ebrahimpour-Komleh, H. (2017). A Levy flight-based grey wolf optimizer combined with back-propagation algorithm for neural network training. Neural Computing And Applications, 30(12), 3707-3720. doi: 10.1007/s00521-017-2952-5
Asaad, R., & Abdulnabi, N. (2018). Using Local Searches Algorithms with Ant Colony Optimization for the Solution of TSP Problems. Academic Journal Of Nawroz University, 7(3), 1-6. doi: 10.25007/ajnu.v7n3a193
Balamurugan, R., Natarajan, A., & Premalatha, K. (2015). Stellar-Mass Black Hole Optimization for Biclustering Microarray Gene Expression Data. Applied Artificial Intelligence, 29(4), 353-381. doi: 10.1080/08839514.2015.1016391
Bianchi L, Dorigo M, Gambardella LM, Gutjahr WJ (2009) A survey on metaheuristics for stochastic combinatorial optimization. Nat Comput 8(2):239–287.
Dao TK (2016) Enhanced diversity herds grey wolf optimizer for optimal area coverage in wireless sensor networks. In: Genetic and evolutionary computing: proceedings of the tenth international conference on genetic and evolutionary computing, November 7–9, 2016 Fuzhou City, Fujian Province, China, vol 536. Springer, p 174
Das KR, Das D, Das J (2015) Optimal tuning of pid controller using gwo algorithm for speed control in dc motor. In: 2015 international conference on soft computing techniques and implementations (ICSCTI). IEEE, pp 108–112.
Eary E, Yamany W, Hassanien AE, Snasel V (2015) Multiobjective gray-wolf optimization for attribute reduction. Procedia Comput Sci 65:623–632
Emary E, Zawbaa HM, Hassanien AE (2016) Binary grey wolf optimization approaches for feature selection. Neurocomputing 172:371–381
Faris, H., Aljarah, I., Al-Betar, M., & Mirjalili, S. (2017). Grey wolf optimizer: a review of recent variants and applications. Neural Computing And Applications, 30(2), 413-435. doi: 10.1007/s00521-017-3272-5
Fouad MM, Hafez AI, Hassanien AE, Snasel V (2015) Grey wolves optimizer-based localization approach in WSNs. In: 2015 11th international computer engineering conference (ICENCO). IEEE, pp 256–260.
Gao ZM, Zhao J (2019) An improved grey wolf optimization algorithm with variable weights. Comput Intell Neurosci. https:// doi.org/10.1155/2019/2981282.
Glover F.,(1986), Future paths for integer programming and links to artificial intelligence, Computers & Operations Research, vol. 13, no. 5, pp. 533-549. Available: 10.1016/0305-0548(86)90048-1. https://doi.org/10.1016/0305-0548(86)90048-1.
Harifi, S., Mohammadzadeh, J., Khalilian, M., & Ebrahimnejad, S. (2020). Giza Pyramids Construction: an ancient-inspired metaheuristic algorithm for optimization. Evolutionary Intelligence. doi: 10.1007/s12065-020-00451-3
Ihsan, R., Almufti, S., Ormani, B., Asaad, R., & Marqas, R. (2021). A Survey on Cat Swarm Optimization Algorithm. Asian Journal Of Research In Computer Science, 22-32. doi: 10.9734/ajrcos/2021/v10i230237.
Jayabarathi T, Raghunathan T, Adarsh BR, Suganthan PN (2016) Economic dispatch using hybrid grey wolf optimizer. Energy 111:630–641
Joshi H, Arora S (2017) Enhanced grey wolf optimisation algorithm for constrained optimisation problems. Int J Swarm Intell 3(2–3):126–151
Kohli M, Arora S (2018) Chaotic grey wolf optimization algorithm for constrained optimization problems. J Comput Design Eng 5(4):458–472
Korayem L, Khorsid M, Kassem SS (2015) Using grey wolf algorithm to solve the capacitated vehicle routing problem. In: IOP conference series: materials science and engineering, vol 83. IOP Publishing, p 012014
Korayem L, Khorsid M, Kassem SS (2015) Using Grey Wolf algorithm to solve the capacitated vehicle routing problem. In: IOP conference series: materials science and engineering, vol 83, no 1. IOP Publishing, p 012014.
Kumar V, Chhabra JK, Kumar D (2017) Grey wolf algorithmbased clustering technique. J Intell Syst 26(1):153–168
Li L, Sun L, Kang W, Guo J, Han C, Li S (2016) Fuzzy multilevel image thresholding based on modified discrete grey wolf optimizer and local information aggregation. IEEE Access 4:6438–6450
Li SX, Wang JS (2015) Dynamic modeling of steam condenser and design of pi controller based on grey wolf optimizer. Math Probl Eng 2015:9
Liu H, Hua G, Yin H, Xu Y (2018) An intelligent grey wolf optimizer algorithm for distributed compressed sensing. Comput Intell Neurosci. https://doi.org/10.1155/2018/1723191
Long W, Jiao J, Liang X, Tang M (2018) An exploration-enhanced grey wolf optimizer to solve high-dimensional numerical optimization. Eng Appl Artif Intell 68:63–80
Long W, Wu T, Cai S, Liang X, Jiao J, Xu M (2019) A novel grey wolf optimizer algorithm with refraction learning. IEEE Access 7:57805–57819
Lu C, Gao L, Li X, Xiao S (2017) A hybrid multi-objective grey wolf optimizer for dynamic scheduling in a real-world welding industry. Eng Appl Artif Intell 57:61–79
Lu C, Xiao S, Li X, Gao L (2016) An effective multi-objective discrete grey wolf optimizer for a real-world scheduling problem in welding production. Adv Eng Softw 99:161–176
Luo Q, Zhang S, Li Z, Zhou Y (2015) A novel complex-valued encoding grey wolf optimization algorithm. Algorithms 9(1):4
Marashdih, A.W., Zaaba, Z.F., Almufti, S.M. (2018). The Problems and Challenges of Infeasible Paths in Static Analysis.Int. J. Eng.Technol.2018,7, 412–417.
Marqas, R., Almufti, S., & Asaad, R. (2019). Comparative study between elephant herding optimization (EHO) and U-turning ant colony optimization (U-TACO) in solving symmetric traveling salesman problem (STSP). Journal Of Advanced Computer Science & Technology, 8(2), 32. doi: 10.14419/jacst.v8i2.29403.
Marqas, R., Almufti, S., Othman, P., & Abdulrahman, C. (2020). Evaluation of EHO, U-TACO and TS Metaheuristics algorithms in Solving TSP. JOURNAL OF XI'an UNIVERSITY OF ARCHITECTURE & TECHNOLOGY, XII(IV). doi: 10.37896/jxat12.04/1062.
Medjahed SA, Ait ST, Benyettou A, Ouali M (2016) Gray wolf optimizer for hyperspectral band selection. Appl Soft Comput 40:178–186
Mirjalili S (2015) How effective is the Grey wolf optimizer in training multi-layer perceptrons. Appl Intell 43(1):150–161
Mirjalili S (2015b) How effective is the grey wolf optimizer in training multi-layer perceptrons. Appl Intell 43(1):150–161
Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513
Mittal N, Singh U, Sohi BS (2016) Modified grey wolf optimizer for global engineering optimization. Appl Comput Intell Soft Comput 2016:8
Mohamed AAA, El-Gaafary AAM, Mohamed YS, Hemeida AM (2015) Design static var compensator controller using artificial neural network optimized by modify grey wolf optimization. In: 2015 international joint conference on neural networks (IJCNN). IEEE, pp 1–7
Mosavi MR, Khishe M, Ghamgosar A (2016) Classification of sonar data set using neural network trained by gray wolf optimization. Neural Netw World 26(4):393
Negi G., Kumar A., Pant S. and Ram M., (2020), GWO: a review and applications, International Journal of System Assurance Engineering and Management, vol. 12, no. 1, pp. 1-8,. Available: 10.1007/s13198-020-00995-8 [Accessed 2 August 2021].
Panda, M., & Das, B. (2019). Grey Wolf Optimizer and Its Applications: A Survey. Lecture Notes In Electrical Engineering, 179-194. doi: 10.1007/978-981-13-7091-5_17
Parsian A, Ramezani M, Ghadimi N (2017) A hybrid neural network-Gray Wolf optimization algorithm for melanoma detection. Biomed Res 28(8)
Saeed, V., Marqas, R., & Almufti, S. (2019). Taxonomy of bio-inspired optimization algorithms. Journal Of Advanced Computer Science & Technology, 8(2), 23. doi: 10.14419/jacst.v8i2.29402.
Salim B., Almufti, S., R. Asaad, (2018). Review on Elephant Herding Optimization Algorithm Performance in Solving Optimization Problems. International Journal of Engineering & Technology 7 : 6109-6114
Sanchez D, Melin P, Castillo O (2017) A Grey Wolf optimizer for modular granular neural networks for human recognition. Comput Intell Neurosci
Shaban, A., & Almufti, S. (2018). U-Turning Ant Colony Algorithm for Solving Symmetric Traveling Salesman Problem. Academic Journal Of Nawroz University, 7(4), 45-49. doi: 10.25007/ajnu.v6n4a270
Singh N, Singh SB (2017a) Hybrid algorithm of particle swarm optimization and grey wolf optimizer for improving convergence performance. J Appl Math. https://doi.org/10.1155/2018/ 1723191
Singh N, Singh SB (2017b) A novel hybrid GWO-SCA approach for optimization problems. Eng Sci Technol Int J 20(6):1586–1601
Song HM, Sulaiman MH, Mohamed MR (2014) An application of grey wolf optimizer for solving combined economic emission dispatch problems. Int Rev Model Simul (IREMOS) 7(5):838–844
Song X, Tang L, Zhao S, Zhang X, Li L, Huang J, Cai W (2015) Grey Wolf optimizer for parameter estimation in surface waves. Soil Dyn Earthq Eng 75:147–157.
Tawhid MA, Ali AF (2017) A Hybrid grey wolf optimizer and genetic algorithm for minimizing potential energy function. Memetic Comput 9(4):347–359
Tsai PW, Dao TK, et al (2016) Robot path planning optimization based on multiobjective grey wolf optimizer. In: International conference on genetic and evolutionary computing. Springer, pp 166–173
Vosooghifard M, Ebrahimpour H (2015) Applying grey wolf optimizer-based decision tree classifer for cancer classification on gene expression data. In: 2015 5th international conference on computer and knowledge engineering (ICCKE). IEEE, pp 147–151
Wen L, Dongquan Z, Songjin XU (2015) Improved Grey Wolf Optimization algorithm for constrained optimization problem. J Comput Appl 35(9):2590–2595
Wong LI, Sulaiman MH, Mohamed MR, Hong MS (2014) Grey wolf optimizer for solving economic dispatch problems. In: 2014 IEEE international conference on power and energy (PECon). IEEE, pp 150–154
Yadav S, Verma SK, Nagar SK (2016) Optimized pid controller for magnetic levitation system. IFAC-ChaptersOnLine 49(1):778–782
Yahya Zebari, A., Almufti, S., & Khalid Omer, H. (2019). A comparative study of particle swarm optimization and genetic algorithm. Journal Of Advanced Computer Science & Technology, 8(2), 40. doi: 10.14419/jacst.v8i2.29401
Yahya Zebari, A., M. Almufti, S., & Mohammed Abdulrahman, C. (2020). Bat algorithm (BA): review, applications and modifications. International Journal Of Scientific World, 8(1), 1. doi: 10.14419/ijsw.v8i1.30120
Yamany W, Emary E, Hassanien AE (2016) New rough set attribute reduction algorithm based on grey wolf optimization. In: The 1st international conference on advanced intelligent system and informatics (AISI2015), November 28–30, 2015, Beni Suef, Egypt. Springer, pp 241–251
Yang H, Liu J (2015) A hybrid clustering algorithm based on grey wolf optimizer and k-means algorithm. J Jiangxi Univ Sci Technol 5:015
Yassien E, Masadeh R, Alzaqebah A, Shaheen (2017) A Grey Wolf optimization applied to the 0/1 knapsack problem. Int J Comput Appl (0975–8887) 169(5)
Zhang S, Zhou Y (2015) Grey wolf optimizer based on Powell local optimization method for clustering analysis. Discret Dyn Nat Soc 2015:17
Almufti, S. M., Marqas, H. B., & Asaad, R. B. (2021c). Grey wolf optimizer: Overview, modifications and applications. International Research Journal of Science, 1(1), 44–56. https://doi.org/10.5281/zenodo.5195644
A. Kaveh, V. M. (2015). Colliding Bodies Optimization. springer.
Abualigah, L. (2019). Feature Selection and Enhanced Krill Herd Algorithm for Text Document Clustering. Studies in Computational Intelligence. doi:10.1007/978-3-030-10674-4_2
Almufti, S. M. (2015). U-Turning Ant Colony Algorithm powered by Great Deluge Algorithm for the solution of TSP Problem. Retrieved from Hdl.handle.net
Almufti, S. M. (2019). Historical survey on metaheuristics algorithms. International Journal of Scientific World, 7(1), 1-12. doi:10.14419/ijsw.v7i1.29497
Almufti, S. M., Marqas, R. B., Othman, P. S., & Sallow, A. B. (2021). Single-based and Population-based Metaheuristics for Solving NP-hard Problems. Iraqi J Sci, 62(5), 1-11.
Celik, Y., & Kutucu, H. (2018). Solving the Tension/Compression Spring Design Problem by an Improved Firefly Algorithm. Retrieved from http://ceur-ws.org/Vol-2255/chapter2.pdf
Celik, Y., & Kutucu, H. (2018). Solving the Tension/Compression Spring Design Problem by an Improved Firefly Algorithm.
Deb, S., Fong, S., & Tian, Z. (2015). Elephant Search Algorithm for optimization problems. Tenth International Conference on Digital Information Management (ICDIM).
GENC, H. M., EKS˙IN, I., & EROL, O. K. (2013). Big bang-big crunch optimization algorithm with local directional moves. Turkish Journal of Electrical Engineering & Computer Sciences, 21, 1359 – 1375. doi:10.3906/elk-1106-46
Gnetchejo, P. J. (2019). Enhanced Vibrating Particles System Algorithm for Parameters Estimation of Photovoltaic System. Journal of Power and Energy Engineering, 7, 1-26.
Ihsan, R. R., Almufti, S. M., Ormani, B. M., Asaad, R. R., & Marqas, R. B. (2021). A Survey on Cat Swarm Optimization Algorithm. Asian Journal of Research in Computer Science, 10(2), 22-32.
Kaveh, A., & Bakhshpoor, T. (2019). Metaheuristics: Outlines, MATLAB Codes and Examples. Springer.
Kaveh, A., & Farhoudi, N. (2013). A new optimization method: Dolphin echolocation. Advances in Engineering Software, 59, 53–70.
Kaveh, A., & Ghazaan, M. I. (2017). A new meta-heuristic algorithm: Vibrating particles system. Scientia Iranica, 24(2), 551-566.
Kaveh, A., & Ghazaan, M. I. (2017). Vibrating particles system algorithm for truss optimization with multiple natural frequency constraints. Acta Mech. doi:10.1007/s00707-016-1725-z
Kaveha, A., & Sabeti, S. (2019). Optimal design of monopile offshore wind turbine structures using CBO, ECBO, and VPS algorithms. Scientia Iranica, 26(3), 1232-1248.
Lobato, F. S., & Jr., V. S. (2014). Fish swarm optimization algorithm applied to engineering system design. Latin American Journal of Solids and Structures, 11(1). doi: https://doi.org/10.1590/S1679-78252014000100009
Marqas, R. B., Almufti, S. M., Ahmed, H. B., & Asaad, R. R. (2021). Grey wolf optimizer: Overview, modifications and applications. International Research Journal of Science, Technology, Education, and Management, 1(1), 44-56.
Ou, L., Zeng, G., Chang, Y.-C., & Lin, C.-T. (2020). Multi-Objective Vibration-Based Particle-Swarm-Optimized Fuzzy Controller With Application to Boundary-Following of Mobile-Robot Simulation Environment. 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC).
Parmar, A., Kumar, Y., Singh, P. K., & Singh, V. (2019). Vibrating Particle System Algorithm for Hard Clustering problem. SCIENCE & TECHNOLOGY, 27(2), 815 - 827.
Rao, R. V. (2016). Teaching Learning Based Optimization Algorithm. Springer.
Sheta, A., Faris, H., Braik, M., & Mirjalili, S. (2020). Nature-inspired metaheuristics search algorithms for solving the economic load dispatch problem of power system: a comparison study. In Applied nature-inspired computing: algorithms and case studies (pp. 199-230). Springer, Singapore.
Tabrizian, Z., Amiri, G. G., & Beigy, M. H. (2014). Charged System Search Algorithm Utilized for Structural Damage Detection. Shock and Vibration. doi:10.1155/2014/194753
Uymaz, S. A., & Tezel, G. (2014). Cuckoo Search (CS) Optimization Algorithm for Solving Constrained Optimization Problems. International Conference on Computer Science, Engineering and Technology.
Zebari, A. Y., Omer, H. K., & Almufti, S. M. (2019). A comparative study of particle swarm optimization and genetic algorithm. Journal of Advanced Computer Science & Technology, 8(2), 40-45. doi:10.14419/jacst.v8i2.29401
Almufti, S. (2022a). Vibrating Particles System Algorithm: Overview, modifications and applications. ICONTECH International Journal, 6(3), 1–11. https://doi.org/10.46291/icontechvol6iss3pp1-11
Almufti, S. M. (2022b). Vibrating Particles System Algorithm performance in solving constrained op-timization problem. Academic Journal of Nawroz University, 11(3), 231–242. https://doi.org/10.25007/ajnu.v11n3a1499
