Abstract
Monarch butterfly optimization algorithm (MBO) has recently been proposed as a robust metaheuristic optimization algorithm for solving numerical global optimization problems. To enhance the performance of MBO algorithm, harmony search (HS) is introduced as a mutation operator during the adjusting operator of MBO. A novel hybrid metaheuristic optimization method, the so-called HMBO, is introduced to find the best solution for the global optimization problems. HMBO combines HS exploration with MBO exploitation, and therefore, it produces potential candidate solutions. The implementation process for enhancing MBO method is also presented. To evaluate the effectiveness of this improvement, fourteen standard benchmark functions are used. The mean and the best performance of these benchmark functions in 20, 50, and 100 dimensions demonstrated that HMBO often performs better than the original MBO and other population-based optimization algorithms such as ACO, BBO, DE, ES, GAPBIL, PSO and SGA. Moreover, the t-test result proved that the performance differences between the enhanced HMBO and the original MBO as well as the other optimization methods are statistically significant.
Similar content being viewed by others
References
Yang XS (2010) Nature-inspired metaheuristic algorithms. Luniver press, Frome
Michalewicz Z, Fogel DB (2013) How to solve it: modern heuristics. Springer, Berlin
Van Laarhoven PJ, Aarts EH (1987) Simulated annealing. Simulated annealing theory and applications. Springer, Netherlands, pp 7–15
Wang G, Guo L, Wang H, Duan H, Liu L, Li J (2014) Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput Appl 24(3–4):853–871
Gandomi AH, Yang XS, Talatahari S, Alavi AH (2013) Metaheuristic applications in structures and infrastructures. Newnes, Oxford
Yang XS, Deb S, Hanne T, He X (2015) Attraction and diffusion in nature-inspired optimization algorithms. Neural Comput Appl 24:1–8
Ouaarab A, Ahiod B, Yang XS (2014) Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput Appl 24(7–8):1659–1669
Yang XS, Gandomi AH, Talatahari S, Alavi AH (2012) Metaheuristics in water, geotechnical and transport engineering. Newnes, Oxford
Horst R, Tuy H (2013) Global optimization: deterministic approaches. Springer, Berlin
Ding S, Zhang Y, Chen J, Jia W (2013) Research on using genetic algorithms to optimize Elman neural networks. Neural Comput Appl 23(2):293–297
Mitchell M (1998) An introduction to genetic algorithms. MIT press, Cambridge
Zhao M, Ren J, Ji L, Fu C, Li J, Zhou M (2012) Parameter selection of support vector machines and genetic algorithm based on change area search. Neural Comput Appl 21(1):1–8
Khatib W, Fleming PJ (1998) The stud GA: a mini revolution? In: International conference on parallel problem solving from nature. Springer, Berlin, pp 683–691
Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Beyer HG, Schwefel HP (2002) Evolution strategies—a comprehensive introduction. Neural Comput 1(1):3–52
Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection, vol 1. MIT press, Cambridge
Glover F (1989) Tabu search—part I. ORSA J Comput 1(3):190–206
Glover F (1990) Tabu search-part II. ORSA J Comput 2(1):4–32
Glover F, Laguna M (2013) Tabu search. In: Du DZ, Pardalos PM (eds) Handbook of combinatorial optimization. Springer, Berlin, pp 3261–3362
Li X, Yin M (2014) Self-adaptive constrained artificial bee colony for constrained numerical optimization. Neural Comput Appl 24(3–4):723–734
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471
Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science. New York, NY, pp 39–43
Mirjalili S, Wang GG, Coelho LdS (2014) Binary optimization using hybrid particle swarm optimization and gravitational search algorithm. Neural Comput Appl 25(6):1423–1435
Yang XS (2009) Firefly algorithms for multimodal optimization. In: International symposium on stochastic algorithms. Springer, Berlin, pp 169–178
Fister I, Yang XS, Brest J (2013) A comprehensive review of firefly algorithms. Swarm Evol Comput 13:34–46
Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713
Wang GG, Gandomi AH, Alavi AH (2014) An effective krill herd algorithm with migration operator in biogeography-based optimization. Appl Math Model 38(9):2454–2462
Xiong P, Wang Z, Malkowski S, Wang Q, Saremi S, Mirjalili S, Lewis A (2014) Biogeography-based optimisation with chaos. Neural Comput Appl 25(5):1077–1097
Colorni A, Dorigo M, Maniezzo V (1991) Distributed optimization by ant colonies. In: Proceedings of the first European conference on artificial life. Paris, France, pp 134–142
Dorigo M, Blum C (2005) Ant colony optimization theory: a survey. Theor Comput Sci 344(2):243–278
Socha K, Blum C (2007) An ant colony optimization algorithm for continuous optimization: application to feed-forward neural network training. Neural Comput Appl 16(3):235–247
Yang XS, Deb S (2009) Cuckoo search via Levy flights. In: Nature and biologically inspired computing, 2009. NaBIC 2009. World Congress on 2009. IEEE, pp 210–214
Li X, Zhang J, Yin M (2014) Animal migration optimization: an optimization algorithm inspired by animal migration behavior. Neural Comput Appl 24(7–8):1867–1877
Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65–74
Gandomi AH, Yang XS, Alavi AH, Talatahari S (2013) Bat algorithm for constrained optimization tasks. Neural Comput Appl 22(6):1239–1255
Meng X, Liu Y, Gao X, Zhang H (2014) A new bio-inspired algorithm: chicken swarm optimization. In: International conference in swarm intelligence. Springer, Berlin, pp 86–94
Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci 17(12):L4831–4845
Li J, Tang Y, Hua C, Guan X (2014) An improved krill herd algorithm: krill herd with linear decreasing step. Appl Math Comput 234:356–367
Geem ZW, Kim JH, Loganathan G (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68
Wang GG, Deb S, Cui Z (2015) Monarch butterfly optimization. Neural Comput Appl 28:1–20
Ghetas M, Yong CH, Sumari P (2015) Harmony-based monarch butterfly optimization algorithm. In: Proceedings of the 2015 IEEE international conference control system, computing and engineering (ICCSCE). IEEE, pp 156–161
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge
Wang G, Guo L (2013) A novel hybrid bat algorithm with harmony search for global numerical optimization. J Appl Math 2013:1–21
Wang GG, Gandomi AH, Zhao X, Chu HCE (2016) Hybridizing harmony search algorithm with cuckoo search for global numerical optimization. Soft Comput 20(1):273–285
Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579
Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102
Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Beyer HG (2013) The theory of evolution strategies. Springer, New York, pp 1–373
Yang S, Yao X (2005) Experimental study on population-based incremental learning algorithms for dynamic optimization problems. Soft Comput 9(11):815–834
Ghetas M, Yong CH (2017) Resource management framework for multi-tier service using case-based reasoning and optimization algorithm. Arab J Sci Eng 43:1–15
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Ghetas, M., Chan, H.Y. Integrating mutation scheme into monarch butterfly algorithm for global numerical optimization. Neural Comput & Applic 32, 2165–2181 (2020). https://doi.org/10.1007/s00521-018-3676-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-018-3676-x