Abstract
Krill Herd (KH) is a novel swarm-based intelligent optimization method developed through the idealization of the krill swarm. In the basic KH method, all the movement parameters used are originated from real nature-driven data found in the literature. The parameter setting based on such data is not necessarily the best selection. In this work, a systematic method is presented for the selection of the best parameter setting for the KH algorithm through an extensive study of arrays of high-dimensional benchmark problems. An important finding is that the best performance of KH can be obtained by setting effective coefficient of the krill individual (C best ), food coefficient(C food ), maximum diffusion speed (D max ), crossover probability (C r ) and mutation probability (M u ) parameters to 4.00, 4.25, 0.014, 0.225, and 0.025, respectively. This finding would eliminate the concerns regarding the optimal tuning of the KH algorithm for its most future applications.
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References
Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997), doi:10.1023/A:1008202821328
Gandomi, A.H., Yang, X.-S., Talatahari, S., Deb, S.: Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization. Comput. Math. Appl. 63(1), 191–200 (2012), doi:10.1016/j.camwa.2011.11.010
Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Global Optim. 39(3), 459–471 (2007), doi:10.1007/s10898-007-9149-x
Li, X., Yin, M.: Self-adaptive constrained artificial bee colony for constrained numerical optimization. Neural Comput. Appl. 24(3-4), 723–734 (2012), doi:10.1007/s00521-012-1285-7
Fister, I., Fister Jr., I., Zumer, J.B.: Memetic artificial bee colony algorithm for large-scale global optimization. In: IEEE Congress on Evolutionary Computation (CEC 2012), Brisbane, Australia, June 10-15, pp. 1–8. IEEE (2012), doi:10.1109/CEC.2012.6252938
Gandomi, A.H., Alavi, A.H.: Multi-stage genetic programming: A new strategy to nonlinear system modeling. Inf. Sci. 181(23), 5227–5239 (2011), doi:10.1016/j.ins.2011.07.026
Gandomi, A.H., Yang, X.-S., Alavi, A.H.: Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng. Comput. 29(1), 17–35 (2013), doi:10.1007/s00366-011-0241-y
Yang, X.S., Deb, S.: Cuckoo search via Lévy flights. In: Proceeding of World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), Coimbatore, India, pp. 210–214. IEEE Publications, USA (2009)
Gandomi, A.H., Talatahari, S., Yang, X.-S., Deb, S.: Design optimization of truss structures using cuckoo search algorithm. Struct. Des. Tall Spec. 22(17), 1330–1349 (2013), doi:10.1002/tal.1033
Li, X., Wang, J., Yin, M.: Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Comput. Appl. 24(6), 1233–1247 (2013), doi:10.1007/s00521-013-1354-6
Fister Jr, I., Yang, X.-S., Fister, D., Fister, I.: Cuckoo Search: A Brief Literature Review. In: Yang, X.-S. (ed.) Cuckoo Search and Firefly Algorithm. SCI, vol. 516, pp. 49–62. Springer, Heidelberg (2014)
Fister Jr, I., Fister, D., Fister, I.: A comprehensive review of cuckoo search: variants and hybrids. Int. J. Math. Model. Numer. Optim. 4(4), 387–409 (2013)
Simon, D.: Biogeography-based optimization. IEEE Trans. Evolut. Comput. 12(6), 702–713 (2008), doi:10.1109/TEVC.2008.919004
Li, X., Wang, J., Zhou, J., Yin, M.: A perturb biogeography based optimization with mutation for global numerical optimization. Appl. Math. Comput. 218(2), 598–609 (2011), doi:10.1016/j.amc.2011.05.110
Li, X., Yin, M.: Multi-operator based biogeography based optimization with mutation for global numerical optimization. Comput. Math. Appl. 64(9), 2833–2844 (2012), doi:10.1016/j.camwa.2012.04.015
Saremi, S., Mirjalili, S., Lewis, A.: Biogeography-based optimisation with chaos. Neural Comput. Appl. (2014), doi:10.1007/s00521-014-1597-x
Li, X., Zhang, J., Yin, M.: Animal migration optimization: an optimization algorithm inspired by animal migration behavior. Neural Comput. Appl. (2013), doi:10.1007/s00521-013-1433-8
Mirjalili, S., Mirjalili, S.M., Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014), doi:10.1016/j.advengsoft.2013.12.007
Geem, Z.W., Kim, J.H., Loganathan, G.V.: A new heuristic optimization algorithm: harmony search. Simulation 76(2), 60–68 (2001), doi:10.1177/003754970107600201
Wang, G., Guo, L., Duan, H., Wang, H., Liu, L., Shao, M.: Hybridizing harmony search with biogeography based optimization for global numerical optimization. J. Comput. Theor. Nanos. 10(10), 2318–2328 (2013), doi:10.1166/jctn.2013.3207
Kennedy, J., Eberhart, R.: Particle swarm optimization. Paper presented at the Proceeding of the IEEE International Conference on Neural Networks, Perth, Australia, November 27-December 1 (1995)
Talatahari, S., Kheirollahi, M., Farahmandpour, C., Gandomi, A.H.: A multi-stage particle swarm for optimum design of truss structures. Neural Comput. Appl. 23(5), 1297–1309 (2013), doi:10.1007/s00521-012-1072-5
Mirjalili, S., Lewis, A.: S-shaped versus V-shaped transfer functions for binary particle swarm optimization. Swarm Evol. Comput. 9, 1–14 (2013), doi:10.1016/j.swevo.2012.09.002
Mirjalili, S., Wang, G.-G., Coelho, L.S.: Binary optimization using hybrid particle swarm optimization and gravitational search algorithm. Neural Comput. Appl. (2014), doi:10.1007/s00521-014-1629-6
Gandomi, A.H.: Interior Search Algorithm (ISA): A Novel Approach for Global Optimization. ISA Trans. (2014), doi:10.1016/j.isatra.2014.03.018
Yang, X.S.: Firefly algorithm, stochastic test functions and design optimisation. Int J of Bio-Inspired Computation 2(2), 78–84 (2010)
Fister, I., Fister Jr., I., Yang, X.-S., Brest, J.: A comprehensive review of firefly algorithms. Swarm Evol. Comput. 13, 34–46 (2013), doi:10.1016/j.swevo.2013.06.001
Wang, G.-G., Guo, L., Duan, H., Wang, H.: A new improved firefly algorithm for global numerical optimization. J. Comput. Theor. Nanos. 11(2), 477–485 (2014), doi:10.1166/jctn.2014.3383
Kaveh, A., Talatahari, S.: A novel heuristic optimization method: charged system search. Acta Mech. 213(3-4), 267–289 (2010), doi:10.1007/s00707-009-0270-4
Gandomi, A.H., Yang, X.-S., Alavi, A.H., Talatahari, S.: Bat algorithm for constrained optimization tasks. Neural Comput. Appl. 22(6), 1239–1255 (2013), doi:10.1007/s00521-012-1028-9
Yang, X.S., Gandomi, A.H.: Bat algorithm: a novel approach for global engineering optimization. Eng. Computation 29(5), 464–483 (2012), doi:10.1108/02644401211235834
Fister Jr., I., Fong, S., Brest, J., Fister, I.: A Novel Hybrid Self-Adaptive Bat Algorithm. Sci. World J. 2014, 1–12 (2014), doi:10.1155/2014/709738
Mirjalili, S., Mirjalili, S.M., Yang, X.-S.: Binary bat algorithm. Neural Comput. Appl. (2013), doi:10.1007/s00521-013-1525-5
Zhang, Y., Huang, D., Ji, M., Xie, F.: Image segmentation using PSO and PCM with Mahalanobis distance. Expert Syst. Appl. 38(7), 9036–9040 (2011), doi:10.1016/j.eswa.2011.01.041
Chen, C.-H., Yang, S.-Y.: Neural fuzzy inference systems with knowledge-based cultural differential evolution for nonlinear system control. Inf. Sci. (2014), doi:10.1016/j.ins.2014.02.071
Mukherjee, R., Patra, G.R., Kundu, R., Das, S.: Cluster-based differential evolution with Crowding Archive for niching in dynamic environments. Inf. Sci. (2014), doi:10.1016/j.ins.2013.11.025
Li, X., Yin, M.: Multiobjective binary biogeography based optimization for feature selection using gene expression data. IEEE Trans. Nanobiosci. 12(4), 343–353 (2013), doi:10.1109/TNB.2013.2294716
Fister, I., Mernik, M., Filipič, B.: A hybrid self-adaptive evolutionary algorithm for marker optimization in the clothing industry. Appl. Soft Compt. 10(2), 409–422 (2010), doi:10.1016/j.asoc.2009.08.001
Li, X., Yin, M.: Parameter estimation for chaotic systems by hybrid differential evolution algorithm and artificial bee colony algorithm. Nonlinear Dynam. (2014), doi:10.1007/s11071-014-1273-9
Li, X., Yin, M.: Application of Differential Evolution Algorithm on Self-Potential Data. PLoS ONE 7(12), e51199 (2012), doi:10.1371/journal.pone.0051199
Mirjalili, S., Mohd Hashim, S.Z., Moradian Sardroudi, H.: Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl. Math. Comput. 218(22), 11125–11137 (2012), doi:10.1016/j.amc.2012.04.069
Mirjalili, S., Mirjalili, S.M., Lewis, A.: Let a biogeography-based optimizer train your Multi-Layer Perceptron. Inf. Sci. 269, 188–209 (2014), doi:10.1016/j.ins.2014.01.038
Li, X., Yin, M.: An opposition-based differential evolution algorithm for permutation flow shop scheduling based on diversity measure. Adv. Eng. Softw. 55, 10–31 (2013), doi:10.1016/j.advengsoft.2012.09.003
Yang, X.S., Gandomi, A.H., Talatahari, S., Alavi, A.H.: Metaheuristics in Water, Geotechnical and Transport Engineering. Elsevier, Waltham (2013)
Gandomi, A.H., Yang, X.S., Talatahari, S., Alavi, A.H.: Metaheuristic Applications in Structures and Infrastructures. Elsevier, Waltham (2013)
Gandomi, A.H., Alavi, A.H.: Krill herd: A new bio-inspired optimization algorithm. Commun. Nonlinear Sci. Numer. Simulat. 17(12), 4831–4845 (2012), doi:10.1016/j.cnsns.2012.05.010
Wang, G.-G., Guo, L., Gandomi, A.H., Hao, G.-S., Wang, H.: Chaotic krill herd algorithm. Inf. Sci. 274, 17–34 (2014), doi:10.1016/j.ins.2014.02.123
Wang, G.-G., Gandomi, A.H., Alavi, A.H.: A chaotic particle-swarm krill herd algorithm for global numerical optimization. Kybernetes 42(6), 962–978 (2013), doi:10.1108/K-11-2012-0108
Saremi, S., Mirjalili, S.M., Mirjalili, S.: Chaotic Krill Herd Optimization Algorithm. Procedia Technology 12, 180–185 (2014), doi:10.1016/j.protcy.2013.12.473
Wang, G.-G., Gandomi, A.H., Alavi, A.H.: Stud krill herd algorithm. Neurocomputing 128, 363–370 (2014), doi:10.1016/j.neucom.2013.08.031
Wang, G., Guo, L., Gandomi, A.H., Cao, L., Alavi, A.H., Duan, H., Li, J.: Lévy-flight krill herd algorithm. Math. Probl. Eng. 2013, 1–14 (2013), doi:10.1155/2013/682073
Guo, L., Wang, G.-G., Gandomi, A.H., Alavi, A.H., Duan, H.: A new improved krill herd algorithm for global numerical optimization. Neurocomputing 138, 392–402 (2014), doi:10.1016/j.neucom.2014.01.023
Wang, G.-G., Gandomi, A.H., Alavi, A.H.: An effective krill herd algorithm with migration operator in biogeography-based optimization. Appl. Math. Model. 38(9-10), 2454–2462 (2014), doi:10.1016/j.apm.2013.10.052
Wang, G., Guo, L., Wang, H., Duan, H., Liu, L., Li, J.: Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput. Appl. 24(3-4), 853–871 (2014), doi:10.1007/s00521-012-1304-8
Wang, G.-G., Gandomi, A.H., Alavi, A.H., Hao, G.-S.: Hybrid krill herd algorithm with differential evolution for global numerical optimization. Neural Comput. Appl. 25(2), 297–308 (2014), doi:10.1007/s00521-013-1485-9
Li, J., Tang, Y., Hua, C., Guan, X.: An improved krill herd algorithm: Krill herd with linear decreasing step. Appl. Math. Comput. 234, 356–367 (2014), doi:10.1016/j.amc.2014.01.146
Wang, G.-G., Guo, L., Gandomi, A.H., Alavi, A.H., Duan, H.: Simulated annealing-based krill herd algorithm for global optimization. Abstr. Appl. Anal. 2013, 1–11 (2013), doi:10.1155/2013/213853
Wang, G.-G., Gandomi, A.H., Yang, X.-S., Alavi, A.H.: A new hybrid method based on krill herd and cuckoo search for global optimization tasks. Int. J. of Bio-Inspired Computation (2013)
Gandomi, A.H., Talatahari, S., Tadbiri, F., Alavi, A.H.: Krill herd algorithm for optimum design of truss structures. Int. J. of Bio-Inspired Computation 5(5), 281–288 (2013), doi:10.1504/IJBIC.2013.057191
Gandomi, A.H., Alavi, A.H.: An introduction of krill herd algorithm for engineering optimization. J. Civil Eng. Manag. (2013)
Gandomi, A.H., Alavi, A.H., Talatahari, S.: Structural Optimization using Krill Herd Algorithm. In: Swarm Intelligence and Bio-Inspired Computation: Theory and Applications, pp. 335–349. Elsevier (2013)
Yao, X., Liu, Y., Lin, G.: Evolutionary programming made faster. IEEE Trans. Evolut. Comput. 3(2), 82–102 (1999)
Yang, X.-S., Cui, Z., Xiao, R., Gandomi, A.H., Karamanoglu, M.: Swarm Intelligence and Bio-Inspired Computation. Elsevier, Waltham (2013)
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Wang, GG., Gandomi, A.H., Alavi, A.H. (2015). Study of Lagrangian and Evolutionary Parameters in Krill Herd Algorithm. In: Fister, I., Fister Jr., I. (eds) Adaptation and Hybridization in Computational Intelligence. Adaptation, Learning, and Optimization, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-14400-9_5
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