Document Type : Review Paper

Authors

1 Department of Industrial Management, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Industrial Management, Science and Research Branch, Islamic Azad University, Tehran, Iran

3 Department of Industrial Management, South Tehran Branch, Islamic Azad University, Tehran, Iran.

Abstract

Over the past decade, solving complex optimization problems with metaheuristic algorithms has attracted many experts and researchers.There are exact methods and approximate methods to solve optimization problems. Nature has always been a model for humans to draw the best mechanisms and the best engineering out of it and use it to solve their problems. The concept of optimization is evident in several natural processes, such as the evolution of species, the behavior of social groups, the immune system, and the search strategies of various animal populations. For this purpose, the use of nature-inspired optimization algorithms is increasingly being developed to solve various scientific and engineering problems due to their simplicity and flexibility. Anything in a particular situation can solve a significant problem for human society. This paper presents a comprehensive overview of the metaheuristic algorithms and classifications in this field and offers a novel classification based on the features of these algorithms.

Keywords

Main Subjects

  • Glover, F. W., & Kochenberger, G. A. (2006). Handbook of metaheuristics. Springer Science & Business Media.
  • Rajpurohit, J., Sharma, T. K., Abraham, A., & Vaishali, A. (2017). Glossary of metaheuristic algorithms. International journal comput information system industrial managment applications9, 181-205.
  • Odili, J. B., Kahar, M. N. M., & Anwar, S. (2015). African buffalo optimization: a swarm-intelligence technique. Procedia computer science, 76, 443-448.
  • Subramanian, C., Sekar, A. S. S., & Subramanian, K. (2013). A new engineering optimization method: African wild dog algorithm. International journal of soft computing8(3), 163-170.
  • Shayeghi, H., & Dadashpour, J. (2012). Anarchic society optimization based PID control of an automatic voltage regulator (AVR) system. Electrical and electronic engineering2(4), 199-207.
  • Li, X., Zhang, J., & Yin, M. (2014). Animal migration optimization: an optimization algorithm inspired by animal migration behavior. Neural computing and applications24, 1867-1877.
  • Colorni, A., Dorigo, M., & Maniezzo, V. (1991). Distributed optimization by ant colonies. Proceedings of the first European conference on artificial life(Vol. 142, pp. 134-142).
  • Mirjalili, S. (2015). The ant lion optimizer. Advances in engineering software83, 80-98.
  • Uymaz, S. A., Tezel, G., & Yel, E. (2015). Artificial algae algorithm (AAA) for nonlinear global optimization. Applied soft computing31, 153-171.
  • Karaboga, D., & Basturk, B. (2007). A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of global optimization, 39, 459-471.
  • Alatas, B. (2011). ACROA: artificial chemical reaction optimization algorithm for global optimization. Expert systems with applications38(10), 13170-13180.
  • Civicioglu, P. (2013). Artificial cooperative search algorithm for numerical optimization problems. Information sciences229, 58-76.
  • Adham, M. T., & Bentley, P. J. (2014). An artificial ecosystem algorithm applied to static and dynamic travelling salesman problems. 2014 IEEE international conference on evolvable systems(pp. 149-156). IEEE.
  • Li, X. L. (2002). An optimizing method based on autonomous animats: fish-swarm algorithm. Systems engineering-theory & practice22(11), 32-38.
  • Li, J., Cui, Z., & Shi, Z. (2012). An improved artificial plant optimization algorithm for coverage problem in WSN. Sensor letters10(8), 1874-1878.
  • Chen, T. (2009). A simulative bionic intelligent optimization algorithm: artificial searching swarm algorithm and its performance analysis. 2009 international joint conference on computational sciences and optimization(Vol. 2, pp. 864-866). IEEE. https://doi.org/10.1109/CSO.2009.183
  • Yan, G. W., & Hao, Z. J. (2013). A novel optimization algorithm based on atmosphere clouds model. International journal of computational intelligence and applications12(01), 135-151.
  • Civicioglu, P. (2013). Backtracking search optimization algorithm for numerical optimization problems. Applied mathematics and computation219(15), 8121-8144.
  • Muller, S. D., Marchetto, J., Airaghi, S., & Kournoutsakos, P. (2002). Optimization based on bacterial chemotaxis. IEEE transactions on evolutionary computation6(1), 16-29.
  • Niu, B., & Wang, H. (2012). Bacterial colony optimization. Discrete dynamics in nature and society2012. https://doi.org/10.1155/2012/698057
  • Das, S., Chowdhury, A., & Abraham, A. (2009). A bacterial evolutionary algorithm for automatic data clustering. 2009 IEEE congress on evolutionary computation(pp. 2403-2410). IEEE.
  • Passino, K. M. (2002). Biomimicry of bacterial foraging for distributed optimization and control. IEEE control systems magazine22(3), 52-67.
  • Chu, Y., Mi, H., Liao, H., Ji, Z., & Wu, Q. H. (2008). A fast bacterial swarming algorithm for high-dimensional function optimization. 2008 IEEE congress on evolutionary computation (IEEE world congress on computational intelligence)(pp. 3135-3140). IEEE.
  • Yang, X. S. (2010). A new metaheuristic bat-inspired algorithm. Nature inspired cooperative strategies for optimization (NICSO 2010), 65-74. https://doi.org/10.1007/978-3-642-12538-6_6
  • Erol, O. K., & Eksin, I. (2006). A new optimization method: big bang–big crunch. Advances in engineering software37(2), 106-111.
  • Simon, D. (2008). Biogeography-based optimization. IEEE transactions on evolutionary computation12(6), 702-713.
  • Askarzadeh, A. (2014). Bird mating optimizer: an optimization algorithm inspired by bird mating strategies. Communications in nonlinear science and numerical simulation19(4), 1213-1228.
  • Meng, X. B., Gao, X. Z., Lu, L., Liu, Y., & Zhang, H. (2016). A new bio-inspired optimisation algorithm: bird swarm algorithm. Journal of experimental & theoretical artificial intelligence28(4), 673-687.
  • Hatamlou, A. (2013). Black hole: a new heuristic optimization approach for data clustering. Information sciences222, 175-184.
  • Taherdangkoo, M., Shirzadi, M. H., Yazdi, M., & Bagheri, M. H. (2013). A robust clustering method based on blind, naked mole-rats (BNMR) algorithm. Swarm and evolutionary computation10, 1-11.
  • Shi, Y. (2015). An optimization algorithm based on brainstorming process. Emerging research on swarm intelligence and algorithm optimization(pp. 1-35). IGI Global.
  • Findik, O. (2015). Bull optimization algorithm based on genetic operators for continuous optimization problems. Turkish journal of electrical engineering & computer sciences23, 2225-2239.
  • Comellas, F., & Martinez-Navarro, J. (2009). Bumblebees: a multiagent combinatorial optimization algorithm inspired by social insect behaviour. Proceedings of the first acm/sigevo summit on genetic and evolutionary computation(pp. 811-814). Association for Computing Machinery. https://doi.org/10.1145/1543834.1543949
  • Ibrahim, M. K., & Ali, R. S. (2016). Novel optimization algorithm inspired by camel traveling behavior. Iraqi journal for electrical and electronic engineering12(2), 167-177.
  • Chu, S. C., Tsai, P. W., & Pan, J. S. (2006). Cat swarm optimization. PRICAI 2006: trends in artificial intelligence: 9th Pacific Rim international conference on artificial intelligence Guilin, China, August 7-11, 2006 proceedings 9(pp. 854-858). Springer Berlin Heidelberg.
  • Formato, R. A. (2007). Central force optimization. Progress in electromagnetics research77(1), 425-491.
  • Kaveh, A., & Talatahari, S. (2010). A novel heuristic optimization method: charged system search. Acta mechanica213(3-4), 267-289. https://doi.org/10.1007/s00707-009-0270-4
  • Meng, X., Liu, Y., Gao, X., & Zhang, H. (2014). A new bio-inspired algorithm: chicken swarm optimization. Advances in swarm intelligence: 5th international conference, ICSI 2014, Hefei, China, October 17-20, 2014, Proceedings, Part I 5(pp. 86-94). Springer international publishing. https://doi.org/10.1007/978-3-319-11857-4_10
  • De Castro, L. N., & Von Zuben, F. J. (2000). The clonal selection algorithm with engineering applications. Proceedings of GECCO(Vol. 2000, pp. 36-39). https://www.researchgate.net/publication/2468677
  • Obagbuwa, I. C., & Adewumi, A. O. (2014). An improved cockroach swarm optimization. The scientific world journal2014. https://doi.org/10.1155/2014/375358
  • Kaveh, A., & Mahdavi, V. R. (2014). Colliding bodies optimization: a novel meta-heuristic method. Computers & structures139, 18-27.
  • Milani, A., & Santucci, V. (2012). Community of scientist optimization: an autonomy oriented approach to distributed optimization. AI communications25(2), 157-172.
  • Iordache, S. (2010). Consultant-guided search: a new metaheuristic for combinatorial optimization problems. Proceedings of the 12th annual conference on genetic and evolutionary computation(pp. 225-232). Association for Computing Machinery.
  • Salcedo-Sanz, S., Del Ser, J., Landa-Torres, I., Gil-López, S., & Portilla-Figueras, J. A. (2014). The coral reefs optimization algorithm: a novel metaheuristic for efficiently solving optimization problems. The scientific world journal2014. https://doi.org/10.1155/2014/739768
  • Hansen, N., Müller, S. D., & Koumoutsakos, P. (2003). Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evolutionary computation11(1), 1-18.
  • Feng, X., Ma, M., & Yu, H. (2016). Crystal energy optimization algorithm. Computational intelligence32(2), 284-322.
  • Yang, X. S., & Deb, S. (2009). Cuckoo search via Lévy flights. 2009 world congress on nature & biologically inspired computing (NaBIC)(pp. 210-214). IEEE.
  • Reynolds, R. G. (1994). An introduction to cultural algorithms. Proceedings of the 3rd annual conference on evolutionary programming (pp. 131-139). World Scientific Publishing. https://doi.org/10.1142/9789814534116
  • Eesa, A. S., Brifcani, A. M. A., & Orman, Z. (2013). Cuttlefish algorithm-a novel bio-inspired optimization algorithm. International journal of scientific & engineering research4(9), 1978-1986.
  • Kadioglu, S., & Sellmann, M. (2009). Dialectic search. International conference on principles and practice of constraint programming- CP 2009. CP 2009. Lecture Notes in computer science (vol 5732). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04244-7_39
  • Storn, R., & Price, K. (1997). Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization11(4), 341-359.
  • Civicioglu, P. (2012). Transforming geocentric Cartesian coordinates to geodetic coordinates by using differential search algorithm. Computers & geosciences46, 229-247.
  • Kaveh, A., & Farhoudi, N. (2013). A new optimization method: dolphin echolocation. Advances in engineering software59, 53-70.
  • Shiqin, Y., Jianjun, J., & Guangxing, Y. (2009). A dolphin partner optimization. 2009 WRI global congress on intelligent systems(Vol. 1, pp. 124-128). IEEE. https://doi.org/10.1155%2F2014%2F739768
  • Mirjalili, S. (2016). Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural computing and applications27, 1053-1073.
  • Yang, X. S., & Deb, S. (2010). Eagle strategy using Lévy walk and firefly algorithms for stochastic optimization. In Nature inspired cooperative strategies for optimization (NICSO 2010) (pp. 101-111). Springer Berlin, Heidelberg.
  • Parpinelli, R. S., & Lopes, H. S. (2011). An eco-inspired evolutionary algorithm applied to numerical optimization. 2011 third world congress on nature and biologically inspired computing(pp. 466-471). IEEE. https://doi.org/10.1109/NaBIC.2011.6089631

 

 

  • Sur, C., Sharma, S., & Shukla, A. (2013). Egyptian vulture optimization algorithm–a new nature inspired meta-heuristics for knapsack problem. The 9th international conference on computing and informationtechnology (IC2IT2013) 9th-10th May 2013 King Mongkut's University of technology North Bangkok(pp. 227-237). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-37371-8_26
  • Cuevas, E., Oliva, D., Zaldivar, D., Pérez-Cisneros, M., & Sossa, H. (2012). Circle detection using electro-magnetism optimization. Information sciences182(1), 40-55.
  • Wang, G. G., Deb, S., & Coelho, L. D. S. (2015). Elephant herding optimization. 2015 3rd international symposium on computational and business intelligence (ISCBI)(pp. 1-5). IEEE. https://doi.org/10.1109/ISCBI.2015.8
  • Deb, S., Fong, S., & Tian, Z. (2015). Elephant search algorithm for optimization problems. 2015 tenth international conference on digital information management (ICDIM)(pp. 249-255). IEEE. https://doi.org/10.1109/ICDIM.2015.7381893
  • Auger, A. (2005). Convergence results for the (1, λ)-SA-ES using the theory of ϕ-irreducible Markov chains. Theoretical computer science334(1-3), 35-69.
  • Fogel, D. B., & Fogel, L. J. (2005). An introduction to evolutionary programming. Artificial evolution: European conference, AE 95 Brest, France, September 4–6, 1995 selected papers(pp. 21-33). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-61108-8_28
  • Ghorbani, N., & Babaei, E. (2014). Exchange market algorithm. Applied soft computing19, 177-187. https://doi.org/10.1016/j.asoc.2014.02.006
  • Razmjooy, N., Khalilpour, M., & Ramezani, M. (2016). A new meta-heuristic optimization algorithm inspired by FIFA world cup competitions: theory and its application in PID designing for AVR system. Journal of control, automation and electrical systems27, 419-440.
  • Yang, X. S. (2009). Firefly algorithms for multimodal optimization. Stochastic algorithms: foundations and applications: 5th international symposium, SAGA 2009, Sapporo, Japan, October 26-28, 2009. Proceedings 5(pp. 169-178). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-04944-6_14
  • Tan, Y., & Zhu, Y. (2010). Fireworks algorithm for optimization. Advances in swarm intelligence: first international conference, ICSI 2010, Beijing, China, June 12-15, 2010, Proceedings, Part I 1(pp. 355-364). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-13495-1_44
  • Bastos Filho, C. J., de Lima Neto, F. B., Lins, A. J., Nascimento, A. I., & Lima, M. P. (2008). A novel search algorithm based on fish school behavior. 2008 IEEE international conference on systems, man and cybernetics(pp. 2646-2651). IEEE. https://doi.org/10.1109/ICSMC.2008.4811695
  • Yang, X. S. (2012). Flower pollination algorithm for global optimization. Unconventional computation and natural computation: 11th international conference, UCNC 2012, Orléan, France, September 3-7, 2012. Proceedings 11(pp. 240-249). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-32894-7_27
  • Xavier, A. E., & Xavier, V. L. (2016). Flying elephants: a general method for solving non-differentiable problems. Journal of heuristics22, 649-664.
  • Ghaemi, M., & Feizi-Derakhshi, M. R. (2014). Forest optimization algorithm. Expert systems with applications41(15), 6676-6687.
  • Pan, W. T. (2012). A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowledge-based systems26, 69-74.
  • Shah-Hosseini, H. (2011). Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimisation. International journal of computational science and engineering6(1-2), 132-140.
  • Abdechiri, M., Meybodi, M. R., & Bahrami, H. (2013). Gases Brownian motion optimization: an algorithm for optimization (GBMO). Applied soft computing13(5), 2932-2946.
  • Ferreira, C. (2002). Gene expression programming in problem solving. Soft computing and industry: recent applications, 635-653. https://doi.org/10.1007/978-1-4471-0123-9_54
  • Beiranvand, H., Rokrok, E., & Beiranvand, K. (2015). General relativity search algorithm for optimization in real numbers space. International journal of mechatronics, electrical and computer technology (IJMEC), 5(15), 2157-2168.
  • Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Addison Welssey Publishing Company. https://dl.acm.org/doi/10.5555/534133
  • Krishnanand, K. N., & Ghose, D. (2009). Glowworm swarm optimization for simultaneous capture of multiple local optima of multimodal functions. Swarm intelligence3, 87-124.
  • Osaba, E., Diaz, F., & Onieva, E. (2014). Golden ball: a novel meta-heuristic to solve combinatorial optimization problems based on soccer concepts. Applied intelligence41, 145-166.
  • Su, S., Wang, J., Fan, W., & Yin, X. (2007). Good lattice swarm algorithm for constrained engineering design optimization. 2007 international conference on wireless communications, networking and mobile computing(pp. 6421-6424). IEEE. https://doi.org/10.1109/WICOM.2007.1575
  • Saremi, S., Mirjalili, S., & Lewis, A. (2017). Grasshopper optimisation algorithm: theory and application. Advances in engineering software, 105, 30-47.
  • Webster, B., & Bernhard, P. J. (2003). A local search optimization algorithm based on natural principles of gravitation. Proceedings of the international conference on information and knowledge engineering (pp. 1-18). Florida Tech. https://repository.lib.fit.edu/handle/11141/117
  • Dueck, G. (1993). New optimization heuristics: the great deluge algorithm and the record-to-record travel. Journal of computational physics104(1), 86-92.
  • Mozaffari, A., Fathi, A., & Behzadipour, S. (2012). The great salmon run: a novel bio-inspired algorithm for artificial system design and optimisation. International journal of bio-inspired computation4(5), 286-301.
  • Melvix, J. L. (2014). Greedy politics optimization: metaheuristic inspired by political strategies adopted during state assembly elections. 2014 IEEE international advance computing conference (IACC)(pp. 1157-1162). IEEE. https://doi.org/10.1109/IAdCC.2014.6779490
  • Ahrari, A., & Atai, A. A. (2010). Grenade explosion method—a novel tool for optimization of multimodal functions. Applied soft computing10(4), 1132-1140.
  • Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software69, 46-61.
  • Eita, M. A., & Fahmy, M. M. (2009). Group counseling optimization: a novel approach. Research and development in intelligent systems xxvi: incorporating applications and innovations in intelligent systems XVII(pp. 195-208). London: Springer London. https://doi.org/10.1007/978-1-84882-983-1_14
  • He, S., Wu, Q. H., & Saunders, J. R. (2009). Group search optimizer: an optimization algorithm inspired by animal searching behavior. IEEE transactions on evolutionary computation13(5), 973-990.
  • Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A new heuristic optimization algorithm: harmony search. Simulation76(2), 60-68.
  • Hatamlou, A. (2014). Heart: a novel optimization algorithm for cluster analysis. Progress in artificial intelligence2(2-3), 167-173.
  • Chen, H., Zhu, Y., Hu, K., & He, X. (2010). Hierarchical swarm model: a new approach to optimization. Discrete dynamics in nature and society2010, 1-30. http://dx.doi.org/10.1155/2010/379649
  • Abbass, H. A. (2001). MBO: marriage in honey bee’s optimization-a haplometrosis polygynous swarming approach. Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546)(Vol. 1, pp. 207-214). IEEE. https://doi.org/10.1109/CEC.2001.934391
  • El-Dosuky, M., El-Bassiouny, A., Hamza, T., & Rashad, M. (2012). New hoopoe heuristic optimization. https://doi.org/10.48550/arXiv.1211.6410
  • Zhang, L. M., Dahlmann, C., & Zhang, Y. (2009). Human-inspired algorithms for continuous function optimization. 2009 IEEE international conference on intelligent computing and intelligent systems(Vol. 1, pp. 318-321). IEEE. https://doi.org/10.1109/ICICISYS.2009.5357838
  • Oftadeh, R., & Mahjoob, M. J. (2009). A new meta-heuristic optimization algorithm: hunting search. 2009 fifth international conference on soft computing, computing with words and perceptions in system analysis, decision and control(pp. 1-5). IEEE. https://doi.org/10.1109/ICSCCW.2009.5379451
  • Atashpaz-Gargari, E., & Lucas, C. (2007). Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. 2007 IEEE congress on evolutionary computation(pp. 4661-4667). IEEE. https://doi.org/10.1109/CEC.2007.4425083
  • Shah-Hosseini, H. (2009). The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm. International journal of bio-inspired computation1(1-2), 71-79.
  • Gandomi, A. H. (2014). Interior search algorithm (ISA): a novel approach for global optimization. ISA transactions53(4), 1168-1183.
  • Tang, D., Dong, S., Jiang, Y., Li, H., & Huang, Y. (2015). ITGO: invasive tumor growth optimization algorithm. Applied soft computing, 36, 670-698.
  • Mehrabian, A. R., & Lucas, C. (2006). A novel numerical optimization algorithm inspired from weed colonization. Ecological informatics1(4), 355-366.
  • Javidy, B., Hatamlou, A., & Mirjalili, S. (2015). Ions motion algorithm for solving optimization problems. Applied soft computing32, 72-79.
  • Chen, C. C., Tsai, Y. C., Liu, I. I., Lai, C. C., Yeh, Y. T., Kuo, S. Y., & Chou, Y. H. (2015). A novel metaheuristic: jaguar algorithm with learning behavior. 2015 IEEE international conference on systems, man, and cybernetics(pp. 1595-1600). IEEE. https://doi.org/10.1109/SMC.2015.282
  • Hernández, H., & Blum, C. (2012). Distributed graph coloring: an approach based on the calling behavior of Japanese tree frogs. Swarm intelligence6, 117-150.
  • De Melo, V. V. (2014). Kaizen programming. Proceedings of the 2014 annual conference on genetic and evolutionary computation(pp. 895-902). Association for Computing Machinery. https://doi.org/10.1145/2576768.2598264
  • Hajiaghaei-Keshteli, M., & Aminnayeri, M. (2014). Solving the integrated scheduling of production and rail transportation problem by keshtel algorithm. Applied soft computing25, 184-203.
  • Gandomi, A. H., & Alavi, A. H. (2012). Krill herd: a new bio-inspired optimization algorithm. Communications in nonlinear science and numerical simulation17(12), 4831-4845.
  • Husseinzadeh Kashan, A. (2009). League championship algorithm: a new algorithm for numerical function optimization. 2009 international conference of soft computing and pattern recognition(pp. 43-48). IEEE. https://doi.org/10.1109/SoCPaR.2009.21
  • Shareef, H., Ibrahim, A. A., & Mutlag, A. H. (2015). Lightning search algorithm. Applied soft computing36, 315-333.
  • Yazdani, M., & Jolai, F. (2016). Lion optimization algorithm (LOA): a nature-inspired metaheuristic algorithm. Journal of computational design and engineering3(1), 24-36.
  • Chen, S. (2009). Locust swarms-a new multi-optima search technique. 2009 IEEE congress on evolutionary computation(pp. 1745-1752). IEEE. https://doi.org/10.1109/CEC.2009.4983152
  • Mo, H., & Xu, L. (2013). Magnetotactic bacteria optimization algorithm for multimodal optimization. 2013 IEEE symposium on swarm intelligence (SIS)(pp. 240-247). IEEE. https://doi.org/10.1109/SIS.2013.6615185
  • Duman, E., Uysal, M., & Alkaya, A. F. (2011). Migrating bird's optimization: a new meta-heuristic approach and its application to the quadratic assignment problem. Applications of evolutionary computation: evoapplications 2011: EvoCOMPLEX, EvoGAMES, EvoIASP, EvoINTELLIGENCE, EvoNUM, and EvoSTOC, Torino, Italy, April 27-29, 2011, proceedings, part I(pp. 254-263). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-20525-5_26
  • Sadollah, A., Bahreininejad, A., Eskandar, H., & Hamdi, M. (2012). Mine blast algorithm for optimization of truss structures with discrete variables. Computers & structures102, 49-63.
  • Wang, G. G., Zhao, X., & Deb, S. (2015). A novel monarch butterfly optimization with greedy strategy and self-adaptive. 2015 second international conference on soft computing and machine intelligence (ISCMI)(pp. 45-50). IEEE. https://doi.org/10.1109/ISCMI.2015.19
  • Mucherino, A., & Seref, O. (2007). Monkey search: a novel metaheuristic search for global optimization. AIP conference proceedings(Vol. 953, No. 1, pp. 162-173). American Institute of Physics. https://doi.org/10.1063/1.2817338
  • Mirjalili, S. (2015). Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowledge-based systems89, 228-249.
  • Mirjalili, S., Mirjalili, S. M., & Hatamlou, A. (2016). Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural computing and applications27, 495-513.
  • Husseinzadeh Kashan, A. (2015). A new metaheuristic for optimization: optics inspired optimization (OIO). Computers & operations research55, 99-125.
  • Premaratne, U., Samarabandu, J., & Sidhu, T. (2009). A new biologically inspired optimization algorithm. 2009 international conference on industrial and information systems (ICIIS)(pp. 279-284). IEEE. https://doi.org/10.1109/ICIINFS.2009.5429852
  • Borji, A. (2007). A new global optimization algorithm inspired by parliamentary political competitions. MICAI 2007: advances in artificial intelligence: 6th Mexican international conference on artificial intelligence, Aguascalientes, Mexico, November 4-10, 2007. Proceedings 6(pp. 61-71). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-76631-5_7
  • Eberhart, R., & Kennedy, J. (1995). A new optimizer using particle swarm theory. MHS'95. Proceedings of the sixth international symposium on micro machine and human science(pp. 39-43). IEEE. https://doi.org/10.1109/MHS.1995.494215
  • Hooke, R., & Jeeves, T. A. (1961). Direct search solution of numerical and statistical Problems. Journal of the ACM (JACM)8(2), 212-229.
  • Gheraibia, Y., & Moussaoui, A. (2013). Penguins search optimization algorithm (PeSOA). Recent trends in applied artificial intelligence: 26th international conference on industrial, engineering and other applications of applied intelligent systems, IEA/AIE 2013, Amsterdam, the Netherlands, June 17-21, 2013. Proceedings 26(pp. 222-231). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-38577-3_23
  • Murase, H., & Wadano, A. (1998). Photosynthetic algorithm for machine learning and TSP. IFAC proceedings volumes31(12), 19-24.
  • Cai, W., Yang, W., & Chen, X. (2008). A global optimization algorithm based on plant growth theory: plant growth optimization. 2008 international conference on intelligent computation technology and automation (ICICTA)(Vol. 1, pp. 1194-1199). IEEE. https://doi.org/10.1109/ICICTA.2008.416
  • Salhi, A., & Fraga, E. S. (2011). Nature-inspired optimisation approaches and the new plant propagation algorithm. Proceeding of the international conference on numerical analysis and optimization (icemath2011). Yogyakarta, Indonesia. https://www.researchgate.net/publication
  • Ribeiro, C. C., Hansen, P., Taillard, É. D., & Voss, S. (2002). POPMUSIC—Partial optimization metaheuristic under special intensification conditions. Essays and surveys in metaheuristics, 15, 613-629.
  • Jung, S. H. (2003). Queen-bee evolution for genetic algorithms, Electronics letters, 39, 575-576.
  • Brabazon, A., Cui, W., & O’Neill, M. (2016). The raven roosting optimisation algorithm. Soft computing, 20, 525-545.
  • Kaveh, A., & Khayatazad, M. (2012). A new meta-heuristic method: ray optimization. Computers & structures, 112, 283-294.
  • Sharma, A. (2010). A new optimizing algorithm using reincarnation concept. 2010 11th international symposium on computational intelligence and informatics (CINTI)(pp. 281-288). IEEE. https://doi.org/10.1109/CINTI.2010.5672231
  • Rabanal, P., Rodríguez, I., & Rubio, F. (2007). Using river formation dynamics to design heuristic algorithms. Unconventional computation: 6th international conference, UC 2007, Kingston, Canada, August 13-17, 2007. Proceedings 6(pp. 163-177). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-73554-0
  • Havens, T. C., Spain, C. J., Salmon, N. G., & Keller, J. M. (2008). Roach infestation optimization. 2008 IEEE swarm intelligence symposium(pp. 1-7). IEEE. https://doi.org/10.1007/3-540-61108-8_28
  • He, X., Zhang, S., & Wang, J. (2015). A novel algorithm inspired by plant root growth with self-similarity propagation. 1st international conference on industrial networks and intelligent systems (INISCom) (pp. 157-162). https://doi.org/10.1109/SIS.2008.4668317
  • Labbi, Y., Attous, D. B., Gabbar, H. A., Mahdad, B., & Zidan, A. (2016). A new rooted tree optimization algorithm for economic dispatch with valve-point effect. International journal of electrical power & energy systems79, 298-311. https://doi.org/10.1109/SIS.2008.4668317
  • Merrikh-Bayat, F. (2015). The runner-root algorithm: a metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature. Applied soft computing33, 292-303.
  • Karci, A., & Alatas, B. (2006). Thinking capability of saplings growing up algorithm. Intelligent data engineering and automated learning–IDEAL 2006: 7th international conference, Burgos, Spain, September 20-23, 2006. Proceedings 7(pp. 386-393). Springer Berlin Heidelberg. https://doi.org/10.1007/11875581_47
  • Glover, F. (1977). Heuristics for integer programming using surrogate constraints. Decision sciences8(1), 156-166.
  • Felipe, D., Goldbarg, E. F. G., & Goldbarg, M. C. (2014). Scientific algorithms for the car renter salesman problem. 2014 IEEE congress on evolutionary computation (CEC)(pp. 873-879). IEEE. https://doi.org/10.1109/CEC.2014.6900556
  • Wang, P., Zhu, Z., & Huang, S. (2013). Seven-spot ladybird optimization: a novel and efficient metaheuristic algorithm for numerical optimization. The scientific world journal2013. https://doi.org/10.1155/2013/378515
  • Abedinia, O., Amjady, N., & Ghasemi, A. (2016). A new metaheuristic algorithm based on shark smell optimization. Complexity21(5), 97-116.
  • Kim, H., & Ahn, B. (2001). A new evolutionary algorithm based on sheep flocks heredity model. 2001 IEEE pacific rim conference on communications, computers and signal processing (IEEE Cat. No. 01CH37233)(Vol. 2, pp. 514-517). IEEE. https://doi.org/10.1109/PACRIM.2001.953683
  • Eusuff, M. M., & Lansey, K. E. (2003). Optimization of water distribution network design using the shuffled frog leaping algorithm. Journal of water resources planning and management129(3), 210-225.
  • Pedroso, J. P. (2007). Simple metaheuristics using the simplex algorithm for non-linear programming. Engineering stochastic local search algorithms. Designing, implementing and analyzing effective heuristics: international workshop, SLS 2007, Brussels, Belgium, September 6-8, 2007. Proceedings(pp. 217-221). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-74446-7_21
  • Kirkpatrick, S., Gelatt Jr, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science220(4598), 671-680.
  • Du, H., Wu, X., & Zhuang, J. (2006). Small-world optimization algorithm for function optimization. Advances in natural computation: second international conference, ICNC 2006, Xi’an, China, September 24-28, 2006. Proceedings, Part II 2(pp. 264-273). Springer Berlin Heidelberg. https://doi.org/10.1007/11881223_33
  • Purnomo, H. D., & Wee, H. M. (2013). Soccer game optimization: an innovative integration of evolutionary algorithm and swarm intelligence algorithm. Meta-Heuristics optimization algorithms in engineering, business, economics, and finance(pp. 386-420). IGI Global.
  • Xie, X. F., Zhang, W. J., & Yang, Z. L. (2002). Social cognitive optimization for nonlinear programming problems. International conference on machine learning and cybernetics(Vol. 2, pp. 779-783). IEEE.
  • Xu, Y., Cui, Z., & Zeng, J. (2010). Social emotional optimization algorithm for nonlinear constrained optimization problems. Swarm, evolutionary, and memetic computing: first international conference on swarm, evolutionary, and memetic computing, SEMCCO 2010, Chennai, India, December 16-18, 2010. Proceedings 1(pp. 583-590). Springer Berlin Heidelberg.
  • Cuevas, E., Cienfuegos, M., Zaldívar, D., & Pérez-Cisneros, M. (2013). A swarm optimization algorithm inspired in the behavior of the social-spider. Expert systems with applications40(16), 6374-6384.
  • Ray, T., & Liew, K. M. (2003). Society and civilization: an optimization algorithm based on the simulation of social behavior. IEEE transactions on evolutionary computation7(4), 386-396.
  • Raouf, O. A., & Hezam, I. M. (2017). Sperm motility algorithm: a novel metaheuristic approach for global optimisation. International journal of operational research28(2), 143-163.
  • Ebrahimi, A., & Khamehchi, E. (2016). Sperm whale algorithm: an effective metaheuristic algorithm for production optimization problems. Journal of natural gas science and engineering29, 211-222.
  • Bansal, J. C., Sharma, H., Jadon, S. S., & Clerc, M. (2014). Spider monkey optimization algorithm for numerical optimization. Memetic computing, 6, 31-47.
  • Tamura, K., & Yasuda, K. (2011). Spiral dynamics inspired optimization. Journal of advanced computational intelligence and intelligent informatics, 15, 1116-1122.
  • Bishop, J. M. (1989). Stochastic searching networks. 1989 first IEE international conference on artificial neural networks, (Conf. Publ. No. 313)(pp. 329-331). IET.
  • Salimi, H. (2015). Stochastic fractal search: a powerful metaheuristic algorithm. Knowledge-based systems75, 1-18.
  • Merrikh-Bayat, F. (2014). A numerical optimization algorithm inspired by the strawberry plant. https://doi.org/10.48550/arXiv.1407.7399
  • Neshat, M., Sepidnam, G., & Sargolzaei, M. (2013). Swallow swarm optimization algorithm: a new method to optimization. Neural computing and applications, 23, 429-454.
  • Cheng, M. Y., & Prayogo, D. (2014). Symbiotic organisms search: a new metaheuristic optimization algorithm. Computers & structures, 139, 98-112.
  • Glover, F. (1986). Future paths for integer programming and links to artificial intelligence. Computers & operations research13(5), 533-549.
  • Rao, R. V., Savsani, V. J., & Vakharia, D. P. (2011). Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Computer-aided design43(3), 303-315.
  • Hedayatzadeh, R., Salmassi, F. A., Keshtgari, M., Akbari, R., & Ziarati, K. (2010). Termite colony optimization: a novel approach for optimizing continuous problems. 2010 18th Iranian conference on electrical engineering(pp. 553-558). IEEE. DOI:1109/IRANIANCEE.2010.5507009
  • Cortés, P., García, J. M., Muñuzuri, J., & Onieva, L. (2008). Viral systems: a new bio-inspired optimisation approach. Computers & operations research35(9), 2840-2860.
  • Li, M. D., Zhao, H., Weng, X. W., & Han, T. (2016). A novel nature-inspired algorithm for optimization: virus colony search. Advances in engineering software92, 65-88.
  • Juarez, J. R. C., Wang, H. J., Lai, Y. C., & Liang, Y. C. (2009). Virus optimization algorithm (VOA): a novel metaheuristic for solving continuous optimization problems. 2009 Asia pacific industrial engineering and management systems conference (APIEMS 2009)(pp. 2166-2174).
  • Doğan, B., & Ölmez, T. (2015). A new metaheuristic for numerical function optimization: vortex Search algorithm. Information sciences293, 125-145.
  • Pinto, P., Runkler, T. A., & Sousa, J. M. (2005). Wasp swarm optimization of logistic systems. Adaptive and natural computing algorithms: proceedings of the international conference in coimbra, portugal, 2005(pp. 264-267). Springer Vienna.
  • Eskandar, H., Sadollah, A., Bahreininejad, A., & Hamdi, M. (2012). Water cycle algorithm–a novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & structures110, 151-166.
  • Kaveh, A., & Bakhshpoori, T. (2016). Water evaporation optimization: a novel physically inspired optimization algorithm. Computers & structures167, 69-85.
  • Zheng, Y. J. (2015). Water wave optimization: a new nature-inspired metaheuristic. Computers & operations research55, 1-11.
  • Tran, T. H., & Ng, K. M. (2011). A water-flow algorithm for flexible flow shop scheduling with intermediate buffers. Journal of scheduling14, 483-500.
  • Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in engineering software95, 51-67.
  • Bayraktar, Z., Komurcu, M., & Werner, D. H. (2010). Wind driven optimization (WDO): a novel nature-inspired optimization algorithm and its application to electromagnetics. 2010 IEEE antennas and propagation society international symposium(pp. 1-4). IEEE.
  • Tang, R., Fong, S., Yang, X. S., & Deb, S. (2012). Wolf search algorithm with ephemeral memory. Seventh international conference on digital information management (ICDIM 2012)(pp. 165-172). IEEE.
  • Arnaout, J. P. (2014). Worm optimization: a novel optimization algorithm inspired by C. Elegans. Proceedings of the 2014 international conference on industrial engineering and operations management, Indonesia(pp. 2499-2505). Bali, Indonesia.
  • Nguyen, H. T., & Bhanu, B. (2012). Zombie survival optimization: a swarm intelligence algorithm inspired by zombie foraging. Proceedings of the 21st international conference on pattern recognition (ICPR2012)(pp. 987-990). IEEE.
  • Birattari, M., Paquete, L., Stützle, T., & Varrentrapp, K. (2001). Classification of metaheuristics and design of experiments for the analysis of components (AIDA-01-05). http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/77018
  • Dhiman, G., & Kumar, V. (2017). Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Advances in engineering software114, 48-70.
  • Memari, A., Ahmad, R., & Rahim, A. R. A. (2017). Metaheuristic algorithms: guidelines for implementation. Journal of soft computing and decision support systems, 4(6), 1-6.
  • Hajiaghaei-Keshteli, M., & Aminnayeri, M. (2014). Solving the integrated scheduling of production and rail transportation problem by keshtel algorithm. Applied soft computing25, 184-203.
  • Hajiaghaei-Keshteli, M., & Aminnayeri, M. (2013). Keshtel algorithm (KA); a new optimization algorithm inspired by keshtels’ feeding. Proceeding in IEEE conference on industrial engineering and management systems(pp. 2249-2253). IEEE.
  • Fathollahi-Fard, A. M., Hajiaghaei-Keshteli, M., & Tavakkoli-Moghaddam, R. (2020). Red deer algorithm (RDA): a new nature-inspired meta-heuristic. Soft computing24, 14637-14665.
  • Cheraghalipour, A., Hajiaghaei-Keshteli, M., & Paydar, M. M. (2018). Tree growth algorithm (TGA): a novel approach for solving optimization problems. Engineering applications of artificial intelligence72, 393-414.
  • Fathollahi-Fard, A. M., Hajiaghaei-Keshteli, M., & Tavakkoli-Moghaddam, R. (2018). The social engineering optimizer (SEO). Engineering applications of artificial intelligence72, 267-293.
  • Husseinzadeh Kashan, A., Tavakkoli-Moghaddam, R., & Gen, M. (2019). Find-fix-finish-exploit-analyze (F3EA) meta-heuristic algorithm: an effective algorithm with new evolutionary operators for global optimization. Computers & industrial engineering128, 192-218.
  • Prasad, N., Rajpal, B., R Mangalore, K. K., Shastri, R., & Pradeep, N. (2021). Frontal and non-frontal face detection using deep neural networks (DNN). International journal of research in industrial engineering10(1), 9-21.
  • Rajabi Moshtaghi, H., Toloie Eshlaghy, A., & Motadel, M. R. (2021). A comprehensive review on meta-heuristic algorithms and their classification with novel approach. Journal of applied research on industrial engineering8(1), 63-89.
  • Ghobadi, A., Tavakkoli Moghadam, R., Fallah, M., & Kazemipoor, H. (2021). Multi-depot electric vehicle routing problem with fuzzy time windows and pickup/delivery constraints. Journal of applied research on industrial engineering8(1), 1-18.
  • Holland, J. H. (1960). Iterative circuit computers. Papers presented at the May 3-5, 1960, western joint IRE-AIEE-ACM computer conference(pp. 259-265). Association for Computing Machinery. https://dl.acm.org/doi/abs/10.1145/1460361.1460397
  • Fogel, L. J., Owens, A. J., & Walsh, M. J. (1966). Artificial intelligence through simulated evolution. New York: Wiley. https://scirp.org/reference/referencespapers.aspx?referenceid=1652105
  • Koza J. R. (1989). Hierarchical genetic algorithms operating on populations of computer programs. Proceedings of the 11th international joint conference on artificial intelligence (pp. 768-774). San Mateo, CA, USA.
  • Dorigo, M. (1992). Optimization, learning and natural algorithms (Ph. D. Thesis, Politecnico di Milano). https://www.semanticscholar.org/paper/Optimization%2C-Learning-and-Natural-Algorithms-Dorigo/2b735a5cd94b0b5868e071255bd187a901cb975a
  • Storn, R., & Price, K. (1996). Minimizing the real functions of the ICEC'96 contest by differential evolution. Proceedings of IEEE international conference on evolutionary computation(pp. 842-844). IEEE.
  • Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization technical report-tr06. Erciyes university, engineering faculty, computer engineering department. (Vol. 200, pp. 1-10). https://abc.erciyes.edu.tr/pub/tr06_2005.pdf
  • Pham, D. T., Ghanbarzadeh, A., Koc, E., Otri, S., Rahim, S., & Zaidi, M. (2005). The bees algorithm - a novel tool for complex optimisation problems. DOI: 1016/B978-008045157-2/50081-X