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Chaotic cuckoo search


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

    Book  MATH  Google Scholar 

  2. 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 

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

    MATH  Google Scholar 

  4. 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 

  5. 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

    MathSciNet  Article  MATH  Google Scholar 

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

  7. 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 

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

  9. 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

  10. 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

  11. 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

  12. 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 

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

    Google Scholar 

  14. 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 

  15. 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 

  16. 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 

  17. 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

  18. 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 

  19. 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

  20. 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

  21. 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

    MathSciNet  Article  Google Scholar 

  22. 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 

  23. 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 

  24. 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

  25. 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

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

  27. 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

    MathSciNet  Article  MATH  Google Scholar 

  28. 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 

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

  30. 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

    MathSciNet  Article  MATH  Google Scholar 

  31. 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

    MathSciNet  Article  MATH  Google Scholar 

  32. 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 

  33. 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

  34. 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

  35. 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

  36. 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

  37. 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

  38. 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

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

  40. 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

  41. 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

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

    Google Scholar 

  43. 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

  44. 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

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

  46. 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 

  47. 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 

  48. 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 

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

    Google Scholar 

  50. 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

    MathSciNet  Article  Google Scholar 

  51. 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 

  52. 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 

  53. 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 

  54. 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 

  55. 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

  56. 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

  57. 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 

  58. 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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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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Corresponding author

Correspondence to Gai-Ge Wang.

Additional information

S. Deb is pioneer of cuckoo search algorithm.

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

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Wang, GG., Deb, S., Gandomi, A.H. et al. Chaotic cuckoo search. Soft Comput 20, 3349–3362 (2016).

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  • Global optimization
  • Cuckoo search
  • Chaotic maps
  • Multimodal function