Soft Computing

, Volume 23, Issue 21, pp 11297–11312 | Cite as

Dimension-by-dimension enhanced cuckoo search algorithm for global optimization

  • Liang Chen
  • Houqing LuEmail author
  • Hongwei Li
  • Guojun Wang
  • Li Chen
Methodologies and Application


Cuckoo search (CS) algorithm is an efficient meta-heuristic algorithm that has been successfully applied in many fields. However, the algorithm uses the whole updating and evaluating strategy on solutions. For solving multi-dimensional optimization problems, solutions with partial dimension evolution may be discarded due to mutual interference among dimensions. Therefore, this strategy may deteriorate the quality solution and convergence rate of algorithm. To overcome this defect and enhance the algorithm performance, a dimension-by-dimension enhanced CS algorithm is proposed. In the global explorative random walk, the improved algorithm uses the dimension-by-dimension updating and evaluating strategy on solutions. This strategy combines the updated values of each dimension with the values of other dimensions into a new solution. In addition, a greedy strategy is adopted to accept new solution and the search center is set as the current optimal solution. The proposed algorithm was tested on fourteen well-known benchmark functions. The numerical results show that the improved algorithm can effectively enhance the quality solution and convergence rate for the global optimization problems.


Cuckoo search (CS) Dimension-by-dimension enhanced Meta-heuristic Lévy flights 



This work is supported by the National Natural Science Foundation of China (No. 51705531) and the Jiangsu Province Science Foundation for Youths (No. BK20150724).

Compliance with ethical standards

Conflict of interest

Liang Chen declares that he has no conflict of interest. Houqing Lu declares that he has no conflict of interest. Hongwei Li declares that he has no conflict of interest. Guojun wang declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


  1. Bhandari AK, Singh VK, Kumar A, Singh GK (2014) Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur’s entropy. Expert Syst Appl 41:3538–3560. CrossRefGoogle Scholar
  2. Brown CT, Liebovitch LS, Glendon R (2007) Lévy flights in Dobe Ju/’hoansi foraging patterns. Hum Ecol 35:129–138CrossRefGoogle Scholar
  3. Chakraborty S, Chatterjee S, Dey N, Ashour AS, Ashour AS, Shi FQ, Mali K (2017) Modified cuckoo search algorithm in microscopic image segmentation of hippocampus. Microsc Res Tech 80:1051–1072. CrossRefGoogle Scholar
  4. Civicioglu P, Besdok E (2013) A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms. Artif Intell Rev 39:315–346. CrossRefGoogle Scholar
  5. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B Cybern A Publ IEEE Syst Man Cybern Soc 26:29CrossRefGoogle Scholar
  6. Fateen SEK, Bonilla-Petriciolet A (2014) Gradient-based cuckoo search for global optimization. Math Probl Eng 2014:1–12MathSciNetCrossRefGoogle Scholar
  7. Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35. CrossRefGoogle Scholar
  8. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman, San FranciscozbMATHGoogle Scholar
  9. Holland JH (1992) Adaptation in natural and artificial systems. MIT Press, MassachusettsCrossRefGoogle Scholar
  10. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization (Vol. 200). Technical report-tr06, Erciyes university, engineering faculty, computer engineering departmentGoogle Scholar
  11. Karaboga D, Akay B (2009) A comparative study of Artificial Bee Colony algorithm. Appl Math Comput 214:108–132MathSciNetzbMATHGoogle Scholar
  12. Katarya R, Verma OP (2017) An effective collaborative movie recommender system with cuckoo search. Egypt Inform J 18:105–112. CrossRefGoogle Scholar
  13. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks, 1995. Proceedings, vol 1944, pp 1942–1948Google Scholar
  14. Layeb A, Boussalia SR (2012) A novel quantum inspired cuckoo search algorithm for bin packing problem international. J Inf Technol Comput Sci 4:58–67Google Scholar
  15. Li M, Cao D (2013) Hybrid optimization algorithm of Cuckoo search and DE computer. Eng Appl 49:57–60. CrossRefGoogle Scholar
  16. Li X, Wang J, Yin M (2013) Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Comput Appl 24:1233–1247CrossRefGoogle Scholar
  17. Liang JJ, Runarsson TP, Mezura-Montes E, Clerc M, Suganthan PN, Coello CC, Deb K (2005) Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization. J Appl Mech 41(8):8–31Google Scholar
  18. Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10:281–295. CrossRefGoogle Scholar
  19. Meng X, Liu Y, Gao X, Zhang H (2014) A new bio-inspired algorithm: chicken swarm optimization. In: International conference in swarm intelligence. Springer, Cham, pp 86–94Google Scholar
  20. Moravej Z, Akhlaghi A (2013) A novel approach based on cuckoo search for DG allocation in distribution network. Int J Electr Power Energy Syst 44:672–679. CrossRefGoogle Scholar
  21. Pandey AC, Rajpoot DS, Saraswat M (2017) Twitter sentiment analysis using hybrid cuckoo search method. Inf Process Manag 53:764–779. CrossRefGoogle Scholar
  22. Reynolds AM, Frye MA (2007) Free-flight odor tracking in drosophila is consistent with an optimal intermittent scale-free search. Plos ONE 2:e354CrossRefGoogle Scholar
  23. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359MathSciNetCrossRefGoogle Scholar
  24. Suresh S, Lal S, Reddy CS, Kiran MS (2017) A novel adaptive cuckoo search algorithm for contrast enhancement of satellite images. IEEE J Sel Top Appl Earth Observ Remote Sens 10:3665–3676. CrossRefGoogle Scholar
  25. Tiwari V (2012) Face recognition based on cuckoo search algorithm. Indian J Comput Sci Eng 3:401–405Google Scholar
  26. Valian E, Tavakoli S, Mohanna S, Haghi A (2013) Improved cuckoo search for reliability optimization problems. Comput Ind Eng 64:459–468. CrossRefGoogle Scholar
  27. Walton S, Hassan O, Morgan K, Brown MR (2011) Modified cuckoo search: a new gradient free optimisation algorithm. Chaos, Solitons Fractals 44:710–718. CrossRefGoogle Scholar
  28. Walton S, Hassan O, Morgan K (2013) Selected engineering applications of gradient free optimisation using cuckoo search and proper orthogonal decomposition. Arch Comput Methods Eng 20:123–154. CrossRefGoogle Scholar
  29. Wang Y, Cai ZX, Zhang QF (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15:55–66. CrossRefGoogle Scholar
  30. Wang F, He XS, Wang Y, Yang SM (2012) Markov model and convergence analysis based on cuckoo search algorithm. Comput Eng 38:180–182Google Scholar
  31. Wang LJ, Yin YL, Zhong YW (2013) Cuckoo search algorithm with dimension by dimension improvement. J Softw 24:2687–2698MathSciNetCrossRefGoogle Scholar
  32. Wang GG, Gandomi AH, Zhao XJ, Chu HCE (2016) Hybridizing harmony search algorithm with cuckoo search for global numerical optimization. Soft Comput 20:273–285. CrossRefGoogle Scholar
  33. Wang H, Wang WJ, Sun H, Cui ZH, Rahnamayan S, Zeng SY (2017) A new cuckoo search algorithm with hybrid strategies for flow shop scheduling problems. Soft Comput 21:4297–4307. CrossRefGoogle Scholar
  34. Xiao H, Duan Y (2014) Cuckoo search algorithm based on differential evolution. J Comput Appl 19:3181Google Scholar
  35. Xin-She Y, Deb S (2010) Engineering optimisation by cuckoo search. Int J Mat Model Numer Optim 1:330–343. CrossRefzbMATHGoogle Scholar
  36. Yang XS (2010) A new metaheuristic bat-inspired algorithm. Comput Knowl Technol 284:65–74zbMATHGoogle Scholar
  37. Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC). IEEE, pp 210–214Google Scholar
  38. Yang XS, Deb S (2013) Multiobjective cuckoo search for design optimization. Comput Oper Res 40:1616–1624MathSciNetCrossRefGoogle Scholar
  39. Yang XS, Deb S (2014) Cuckoo search: recent advances and applications. Neural Comput Appl 24:169–174. CrossRefGoogle Scholar
  40. Yong W, Zhang Q (2012) Enhancing the search ability of differential evolution through orthogonal crossover. Inf Sci 185:153–177MathSciNetCrossRefGoogle Scholar
  41. Zhang XM (2017) Parameter estimation of shallow wave equation via cuckoo search. Neural Comput Appl 28:4047–4059. CrossRefGoogle Scholar
  42. Zhong Y, Liu X, Wang L, Wang C (2012) Particle swarm optimisation algorithm with iterative improvement strategy for multi-dimensional function optimisation problems. Int J Innovative Comput Appl 4:223–232CrossRefGoogle Scholar
  43. Zong WG, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simul Trans Soc Model Simul Int 76:60–68Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Field Engineering CollegeArmy Engineering University of PLANanjingChina
  2. 2.Automobile NCO AcademyArmy Military Transportation UniversityBengbuChina
  3. 3.School of Economics and ManagementNanjing Institute of TechnologyNanjingChina

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