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Chaotic cuckoo search

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Abstract

This study proposes a novel chaotic cuckoo search (CCS) optimization method by incorporating chaotic theory into cuckoo search (CS) algorithm. In CCS, chaos characteristics are combined with the CS with the intention of further enhancing its performance. Further, the elitism scheme is incorporated into CCS to preserve the best cuckoos. In CCS method, 12 chaotic maps are applied to tune the step size of the cuckoos used in the original CS method. Twenty-seven benchmark functions and an engineering case are utilized to investigate the efficiency of CCS. The results clearly demonstrate that the performance of CCS together with a suitable chaotic map is comparable as well as superior to that of the CS and other metaheuristic algorithms.

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References

  • Beyer H (2001) The theory of evolution strategies. Springer, New York

    Book  MATH  Google Scholar 

  • Cai X, Fan S, Tan Y (2012) Light responsive curve selection for photosynthesis operator of APOA. Int J Bio-Inspir Comput 4(6):373–379

    Article  Google Scholar 

  • Dorigo M, Stutzle T (2004) Ant colony optimization. MIT Press, Cambridge

    MATH  Google Scholar 

  • Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern B Cybern 26(1):29–41. doi:10.1109/3477.484436

    Article  Google Scholar 

  • Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845. doi:10.1016/j.cnsns.2012.05.010

    Article  MathSciNet  MATH  Google Scholar 

  • Gandomi AH, Yang X-S (2014) Chaotic bat algorithm. J Comput Sci 5(2):224–232. doi:10.1016/j.jocs.2013.10.002

  • Gandomi AH, Yang X-S, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23–24):2325–2336. doi:10.1016/j.compstruc.2011.08.002

    Article  Google Scholar 

  • Gandomi AH, Yang XS, Talatahari S, Alavi AH (2013a) Metaheuristic applications in structures and infrastructures. Elsevier, Waltham

  • Gandomi AH, Yang X-S, Alavi AH, Talatahari S (2013b) Bat algorithm for constrained optimization tasks. Neural Comput Appl 22(6):1239–1255. doi:10.1007/s00521-012-1028-9

  • Gandomi AH, Yang XS, Talatahari S, Alavi AH (2013c) Firefly algorithm with chaos. Commun Nonlinear Sci Numer Simulat 18(1):89–98. doi:10.1016/j.cnsns.2012.06.009

  • Gandomi AH, Yun GJ, Yang X-S, Talatahari S (2013d) Chaos-enhanced accelerated particle swarm optimization. Commun Nonlinear Sci Numer Simulat 18(2):327–340. doi:10.1016/j.cnsns.2012.07.017

  • Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68. doi:10.1177/003754970107600201

    Article  Google Scholar 

  • Goldberg DE (1998) Genetic algorithms in search. Optimization and machine learning. Addison-Wesley, New York

    Google Scholar 

  • Guo L, Wang G-G, Gandomi AH, Alavi AH, Duan H (2014) A new improved krill herd algorithm for global numerical optimization. Neurocomputing 138:392–402. doi:10.1016/j.neucom.2014.01.023

    Article  Google Scholar 

  • Jia D, Zheng G, Khurram Khan M (2011) An effective memetic differential evolution algorithm based on chaotic local search. Inf Sci 181(15):3175–3187. doi:10.1016/j.ins.2011.03.018

    Article  Google Scholar 

  • Kaveh A, Sheikholeslami R, Talatahari S, Keshvari-Ilkhichi M (2014) Chaotic swarming of particles: a new method for size optimization of truss structures. Adv Eng Softw 67:136–147. doi:10.1016/j.advengsoft.2013.09.006

    Article  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Paper presented at the proceeding of the IEEE international conference on neural networks, Perth, 27 November 1995–1 December 1995

  • Li X, Yin M (2012) Application of differential evolution algorithm on self-potential data. PLoS One 7(12):e51199. doi:10.1371/journal.pone.0051199

    Article  Google Scholar 

  • Li X, Yin M (2013a) Multiobjective binary biogeography based optimization for feature selection using gene expression data. IEEE Trans Nanobiosci 12(4):343–353. doi:10.1109/TNB.2013.2294716

  • Li X, Yin M (2013b) An opposition-based differential evolution algorithm for permutation flow shop scheduling based on diversity measure. Adv Eng Softw 55:10–31. doi:10.1016/j.advengsoft.2012.09.003

  • Li X, Yin M (2015) Modified cuckoo search algorithm with self adaptive parameter method. Inf Sci 298:80–97. doi:10.1016/j.ins.2014.11.042

    Article  MathSciNet  Google Scholar 

  • 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. doi:10.1007/s00521-013-1433-8

    Article  Google Scholar 

  • Mirjalili S, Lewis A (2013) S-shaped versus V-shaped transfer functions for binary particle swarm optimization. Swarm Evol Comput 9:1–14. doi:10.1016/j.swevo.2012.09.002

    Article  Google Scholar 

  • Mirjalili S, Mirjalili SM, Yang X-S (2013) Binary bat algorithm. Neural Comput Appl 25(3–4):663–681. doi:10.1007/s00521-013-1525-5

  • Mirjalili S, Mirjalili SM, Lewis A (2014a) Let a biogeography-based optimizer train your multi-layer perceptron. Inf Sci 269:188–209. doi:10.1016/j.ins.2014.01.038

  • Mirjalili S, Mirjalili SM, Lewis A (2014b) Grey wolf optimizer. Adv Eng Softw 69:46–61. doi:10.1016/j.advengsoft.2013.12.007

  • Nouhi B, Talatahari S, Kheiri H, Cattani C (2013) Chaotic charged system search with a feasible-based method for constraint optimization problems. Math Probl Eng 2013:1–8. doi:10.1155/2013/391765

    Article  MathSciNet  MATH  Google Scholar 

  • Shumeet B (1994) Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning. Carnegie Mellon University, Pittsburgh, PA

    Google Scholar 

  • Simon D (2008) Biogeography-based optimization. IEEE Trans Evolut Comput 12(6):702–713. doi:10.1109/TEVC.2008.919004

  • Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359. doi:10.1023/A:1008202821328

    Article  MathSciNet  MATH  Google Scholar 

  • Talatahari S, Farahmand Azar B, Sheikholeslami R, Gandomi AH (2012) Imperialist competitive algorithm combined with chaos for global optimization. Commun Nonlinear Sci Numer Simulat 17(3):1312–1319. doi:10.1016/j.cnsns.2011.08.021

    Article  MathSciNet  MATH  Google Scholar 

  • Talatahari S, Kheirollahi M, Farahmandpour C, Gandomi AH (2013) A multi-stage particle swarm for optimum design of truss structures. Neural Comput Appl 23(5):1297–1309. doi:10.1007/s00521-012-1072-5

    Article  Google Scholar 

  • Wang G, Guo L, Duan H, Wang H, Liu L, Shao M (2013a) Hybridizing harmony search with biogeography based optimization for global numerical optimization. J Comput Theor Nanos 10(10):2318–2328. doi:10.1166/jctn.2013.3207

  • Wang G-G, Gandomi AH, Alavi AH (2013b) A chaotic particle-swarm krill herd algorithm for global numerical optimization. Kybernetes 42(6):962–978. doi:10.1108/K-11-2012-0108

  • Wang G, Guo L, Wang H, Duan H, Liu L, Li J (2014a) Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput Appl 24(3–4):853–871. doi:10.1007/s00521-012-1304-8

  • Wang G-G, Gandomi AH, Zhao X, Chu HE (2014b) Hybridizing harmony search algorithm with cuckoo search for global numerical optimization. Soft Comput. doi:10.1007/s00500-014-1502-7

  • Wang G-G, Guo L, Duan H, Wang H (2014c) A new improved firefly algorithm for global numerical optimization. J Comput Theor Nanos 11(2):477–485. doi:10.1166/jctn.2014.3383

  • Wang G-G, Guo L, Gandomi AH, Hao G-S, Wang H (2014d) Chaotic krill herd algorithm. Inf Sci 274:17–34. doi:10.1016/j.ins.2014.02.123

  • Wang G-G, Gandomi AH, Alavi AH (2014e) Stud krill herd algorithm. Neurocomputing 128:363–370. doi:10.1016/j.neucom.2013.08.031

  • Wang G-G, Gandomi AH, Alavi AH, Hao G-S (2014f) Hybrid krill herd algorithm with differential evolution for global numerical optimization. Neural Comput Appl 25(2):297–308. doi:10.1007/s00521-013-1485-9

  • Wang G-G, Gandomi AH, Alavi AH (2014g) An effective krill herd algorithm with migration operator in biogeography-based optimization. Appl Math Model 38(9–10):2454–2462. doi:10.1016/j.apm.2013.10.052

  • Wang G-G, Deb S, Cui Z (2015) Monarch butterfly optimization. Neural Comput Appl. doi:10.1007/s00521-015-1923-y

    Google Scholar 

  • Xie L, Zeng J, Formato RA (2012) Selection strategies for gravitational constant \(G\) in artificial physics optimisation based on analysis of convergence properties. Int J Bio-Inspir Comput 4(6):380–391

  • Yang XS (2010a) A new metaheuristic bat-inspired algorithm. In: González JR, Pelta DA, Cruz C, Terrazas G, Krasnogor N (eds) Nature inspired cooperative strategies for optimization (NICSO 2010), vol 284. Studies in computational intelligence. Springer, Heidelberg, pp 65–74. doi:10.1007/978-3-642-12538-6_6

  • Yang XS (2010b) Nature-inspired metaheuristic algorithms, 2nd edn. Luniver Press, Frome

  • Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1(4):330–343. doi:10.1504/IJMMNO.2010.03543

    MATH  Google Scholar 

  • Yang XS, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483. doi:10.1108/02644401211235834

    Article  Google Scholar 

  • Yang X-S, Hosseini SSS, Gandomi AH (2012) Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect. Appl Soft Compt 12(3):1180–1186. doi:10.1016/j.asoc.2011.09.017

    Article  Google Scholar 

  • Yang XS, Gandomi AH, Talatahari S, Alavi AH (2013) Metaheuristics in water. Geotechnical and transport engineering. Elsevier, Waltham

    Google Scholar 

  • Yang X-S, Karamanoglu M, He X (2014) Flower pollination algorithm: a novel approach for multiobjective optimization. Eng Optim 46(9):1222–1237. doi:10.1080/0305215X.2013.832237

    Article  MathSciNet  Google Scholar 

  • Zhang Z, Feng Z (2012) Two-stage updating pheromone for invariant ant colony optimization algorithm. Expert Syst Appl 39(1):706–712. doi:10.1016/j.eswa.2011.07.062

    Article  Google Scholar 

  • Zhang Y, Huang D, Ji M, Xie F (2011) Image segmentation using PSO and PCM with Mahalanobis distance. Expert Syst Appl 38(7):9036–9040. doi:10.1016/j.eswa.2011.01.041

    Article  Google Scholar 

  • Zhang Z, Zhang N, Feng Z (2014) Multi-satellite control resource scheduling based on ant colony optimization. Expert Syst Appl 41(6):2816–2823. doi:10.1016/j.eswa.2013.10.014

    Article  Google Scholar 

  • Zou D, Gao L, Li S, Wu J (2011) An effective global harmony search algorithm for reliability problems. Expert Syst Appl 38(4):4642–4648. doi:10.1016/j.eswa.2010.09.120

    Article  Google Scholar 

  • Zhao X, Lin W, Zhang Q (2014a) Enhanced particle swarm optimization based on principal component analysis and line search. Appl Math Comput 229:440–456. doi:10.1016/j.amc.2013.12.068

  • Zhao X, Liu Z, Yang X (2014b) A multi-swarm cooperative multistage perturbation guiding particle swarm optimizer. Appl Soft Compt 22:77–93. doi:10.1016/j.asoc.2014.04.042

  • Zou D, Gao L, Wu J, Li S, Li Y (2010) A novel global harmony search algorithm for reliability problems. Comput Ind Eng 58(2):307–316. doi:10.1016/j.cie.2009.11.003

    Article  Google Scholar 

  • Zou D, Gao L, Li S, Wu J (2011) Solving 0–1 knapsack problem by a novel global harmony search algorithm. Appl Soft Compt 11(2):1556–1564. doi:10.1016/j.asoc.2010.07.019

    Article  Google Scholar 

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Acknowledgments

This work was supported by Research Fund for the Doctoral Program of Jiangsu Normal University (No. 9213614102) and National Natural Science Foundation of China (No. 61305149).

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Correspondence to Gai-Ge Wang.

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Communicated by S. Deb, T. Hanne and S. Fong.

S. Deb is pioneer of cuckoo search algorithm.

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Wang, GG., Deb, S., Gandomi, A.H. et al. Chaotic cuckoo search. Soft Comput 20, 3349–3362 (2016). https://doi.org/10.1007/s00500-015-1726-1

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