Soft Computing

, Volume 23, Issue 21, pp 10681–10697 | Cite as

A hybrid many-objective cuckoo search algorithm

  • Zhihua Cui
  • Maoqing ZhangEmail author
  • Hui Wang
  • Xingjuan CaiEmail author
  • Wensheng Zhang


Cuckoo search (CS) is an excellent population-based algorithm and has shown promising performance in dealing with single- and multi-objective optimization problems. However, for many-objective optimization problems (MaOPs), CS cannot be directly employed. So far, few paper have been reported to use CS to solve MaOPs. In this paper, we try to propose a hybrid many-objective cuckoo search (HMaOCS) for MaOPs. In HMaOCS, the standard CS is firstly modified to effectively deal with MaOPs. Then, non-dominated sorting and the strategy of reference points are employed to ensure the convergence and diversity. In order to verify the performance of HMaOCS, DTLZ and WFG benchmark sets are utilized in the experiments. Experimental results show that HMaOCS can achieve promising performance compared with five other well-known many-objective optimization algorithms.


Cuckoo search Many-objective optimization problems Non-dominated sorting Reference points 



This study is funded by the National Natural Science Foundation of China under Grant Nos. 61806138, U1636220, 61663028, 71771176, 51775385, 61703279 and 71371142, Natural Science Foundation of Shanxi Province under Grant No. 201801D121127, PhD Research Startup Foundation of Taiyuan University of Science and Technology under Grant No. 20182002, the Distinguished Young Talents Plan of Jiang-xi Province under Grant No. 20171BCB23075, the Natural Science Foundation of Jiang-xi Province under Grant No. 20171BAB202035.

Compliance with ethical standards

Conflict of interest

Author Zhihua Cui declares that he has no conflict of interest. Author Maoqing Zhang declares that he has no conflict of interest. Author Hui Wang declares that he has no conflict of interest. Author Xingjuan Cai declares that she has no conflict of interest. Author Wensheng Zhang 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.


  1. Abdel-Baset M, Zhou Y, Ismail M (2018) An improved cuckoo search algorithm for integer programming problems. Int J Comput Sci Math 9(1):66–81MathSciNetCrossRefGoogle Scholar
  2. Adra S, Fleming P (2011) Diversity management in evolutionary many-objective optimization. IEEE Trans Evol Comput 15(2):183–195CrossRefGoogle Scholar
  3. Bader J, Zitzler E (2011) HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19(1):45–76CrossRefGoogle Scholar
  4. Barthelemy P, Bertolotti J, Wiersma D (2008) A Lévy flight for light. Nature 453(7194):495Google Scholar
  5. Cai X, Gao X, Xue Y (2016) Improved bat algorithm with optimal forage strategy and random disturbance strategy. Int J Bio-inspired Comput 8(4):205–214CrossRefGoogle Scholar
  6. Cai X, Wang H, Cui Z, Cai J, Xue Y, Wang L (2018) Bat algorithm with triangle-flipping strategy for numerical optimization. Int J Mach Learn Cybernet 9(2):199–215CrossRefGoogle Scholar
  7. Chandrasekaran K, Simon S (2012) Multi-objective scheduling problem: hybrid approach using fuzzy assisted cuckoo search algorithm. Swarm Evol Comput 5:1–16CrossRefGoogle Scholar
  8. Coelho L, Guerra F, Batistela N (2013) Multiobjective cuckoo search algorithm based on duffing’s oscillator applied to jiles-atherton vector hysteresis parameters estimation. IEEE Trans Magn 49(5):1745–1748CrossRefGoogle Scholar
  9. Cortés P, Muñuzuri J, Onieva L, Guadix J (2018) A discrete particle swarm optimisation algorithm to operate distributed energy generation networks efficiently. Int J Bio-Inspired Comput 12(4):226–235CrossRefGoogle Scholar
  10. Cui Z, Cao Y, Cai X, Cai J, Chen J (2017a) Optimal LEACH protocol with modified bat algorithm for big data sensing systems in internet of things. J Parallel Distrib Comput 10:1–12. CrossRefGoogle Scholar
  11. Cui Z, Sun B, Wang G, Xue Y, Chen J (2017b) A novel oriented cuckoo search algorithm to improve DV-Hop performance for cyber-physical systems. J Parallel Distrib Comput 103:42–52CrossRefGoogle Scholar
  12. Cui Z, Xue F, Cai X, Cao Y, Wang G, Chen J (2018) Detection of malicious code variants based on deep learning. IEEE Trans Industr Inf 14(7):3187–3196CrossRefGoogle Scholar
  13. Cui Z, Du L, Wang P, Cai X, Zhang W (2019a) Malicious code detection based on CNNs and multi-objective algorithm. J Parallel Distrib Comput 129:50–58CrossRefGoogle Scholar
  14. Cui Z, Li F, Zhang W (2019b) Bat algorithm with principal component analysis. Int J Mach Learn Cybernet 10(3):603–622CrossRefGoogle Scholar
  15. Cui Z, Zhang J, Wang Y, Cao Y, Cai X, Zhang W, Chen J (2019c) A pigeon-inspired optimization algorithm for many-objective optimization problems. Sci China Inf Sci 62(7):070212. CrossRefGoogle Scholar
  16. Das I, Dennis J (2006) Normal-Boundary Intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim 8(3):631–657MathSciNetzbMATHCrossRefGoogle Scholar
  17. Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, Part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601CrossRefGoogle Scholar
  18. Deb K, Kalyanmoy D (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New YorkzbMATHGoogle Scholar
  19. Deb K, Thiele L, Laumanns M, Zitzler E (2002a) Scalable multi-objective optimization test problems. In: Proceedings of the 2002 congress on IEEE evolutionary computation. CEC ‘02, pp 825–830Google Scholar
  20. Deb K, Pratap A, Agarwal S, Meyarivan T (2002b) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  21. Deb K, Mohan M, Mishra S (2005) Evaluating the ε-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions. Evol Comput 13(4):501–525CrossRefGoogle Scholar
  22. Fan J, Li Y, Tang L, Wu G (2018) RoughPSO: rough set-based particle swarm optimization. Int J Bio-Inspired Comput 12(4):245–253CrossRefGoogle Scholar
  23. Hanoun S, Nahavandi S, Creighton D, Kull H (2012) Solving a multiobjective job shop scheduling problem using Pareto archived cuckoo search. Emerg Technol Factory Autom IEEE 43:1–8Google Scholar
  24. Huband S, Hingston P, Barone L, While L (2006) A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans Evol Comput 10(5):477–506zbMATHCrossRefGoogle Scholar
  25. Hughes E (2003) Multiple single objective Pareto sampling. In: The 2003 congress on IEEE evolutionary computation (CEC), vol 4, pp 2678–2684Google Scholar
  26. Jain H, Deb K (2014) An Evolutionary Many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput 18(4):602–622CrossRefGoogle Scholar
  27. Laumanns M, Thiele L, Deb K, Zitzler E (2002) Combining convergence and diversity in evolutionary multi- objective optimization. MIT Press, Cambridge, pp 263–282Google Scholar
  28. Li M, Zheng J (2009) Spread assessment for evolutionary multi-objective optimization. In: International conference on evolutionary multi-criterion optimization, Springer, pp 216–230Google Scholar
  29. Li M, Zheng J, Li K, Yuan Q, Shen R (2010) Enhancing diversity for average ranking method in evolutionary many-objective optimization. In: Parallel problem solving from nature, PPSN XI. Springer, Berlin, pp. 647–656Google Scholar
  30. Li M, Yang S, Liu X (2014) Shift-based density estimation for Pareto-based algorithms in many-objective optimization. IEEE Trans Evol Comput 18(3):348–365CrossRefGoogle Scholar
  31. Niu Y, Tian Z, Zhang M, Cai X, Li J (2018) Adaptive two-SVM multi-objective cuckoo search algorithm for software defect prediction. Int J Comput Sci Math 9(6):547–554MathSciNetCrossRefGoogle Scholar
  32. Pandey H, Chaudhary A, Mehrotra D (2018) Bit mask-oriented genetic algorithm for grammatical inference and premature convergence. Int J Bio-Inspired Comput 12(1):54–69CrossRefGoogle Scholar
  33. Pooja P, Chaturvedi P, Kumar P, Tomar A (2018) A novel differential evolution approach for constraint optimization. Int J Bio-Inspired Comput 12(4):254–265CrossRefGoogle Scholar
  34. Raja B, Jhala R, Patel V (2017) Many-objective optimization of cross-flow plate-fin heat exchanger. Int J Therm Sci 118:320–339CrossRefGoogle Scholar
  35. Rani K, Malek M, Neoh S (2013) Hybrid multiobjective optimization using modified cuckoo search algorithm in linear array synthesis. In: IEEE antennas and propagation conference, pp 1–4Google Scholar
  36. Reynolds AM, Frye MA (2007) Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search. PLoS ONE 2(4):e354CrossRefGoogle Scholar
  37. Shan X, Ye B, Zhang L (2018) Analysis of flow field of hydrodynamic suspension polishing disk based on multi-fractal method. Int J Comput Sci Math 9(1):13–20MathSciNetCrossRefGoogle Scholar
  38. Sun B, Cui Z, Dai C (2014) DV-hop localization algorithm with cuckoo search. Sensor Lett 12(2):444–447CrossRefGoogle Scholar
  39. Tozer B, Mazzuchi T, Sarkani S (2017) Many-objective stochastic path finding using reinforcement learning. Expert Syst Appl. CrossRefGoogle Scholar
  40. Wang Z, Li Y (2015) Irreversibility analysis for optimization design of plate fin heat exchangers using a multi-objective cuckoo search algorithm. Energy Convers Manag 101:126–135CrossRefGoogle Scholar
  41. Wang Q, Liu S, Wang H (2012) Multi-objective cuckoo search for the optimal design of water distribution systems. In: International conference on civil engineering and urban planning.
  42. Wang H, Wang W, Zhou X, Sun H, Zhao J, Yu X, Cui Z (2017) Firefly algorithm with neighborhood attraction. Inf Sci 382(383):374–387CrossRefGoogle Scholar
  43. Wang H, Wang W, Cui Z, Zhou X, Zhao J, Li Y (2018) A new dynamic firefly algorithm for demand estimation of water resources. Inf Sci 438:95–106MathSciNetCrossRefGoogle Scholar
  44. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82CrossRefGoogle Scholar
  45. Yang X, Deb S (2010a) Cuckoo search via Lévy flights. In: Nature and biologically inspired computing 2009, NaBIC 2009, world congress on IEEE, pp 210–214Google Scholar
  46. Yang X, Deb S (2010b) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1(4):330–343zbMATHGoogle Scholar
  47. Yang S, Li M, Liu X, Zheng J (2013) A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 17(5):721–736CrossRefGoogle Scholar
  48. Yigit T, Unsal O, Deperlioglu O (2018) Using the metaheuristic methods for real-time optimisation of dynamic school bus routing problem and an application. Int J Bio-Inspired Comput 11(2):123–133CrossRefGoogle Scholar
  49. Zhang QF, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRefGoogle Scholar
  50. Zhang X, Tian Y, Jin Y (2015) A knee point-driven evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 19(6):761–776CrossRefGoogle Scholar
  51. Zhang M, Wang H, Cui Z, Chen J (2018) Hybrid multi-objective cuckoo search with dynamical local search. Memet Comput 10(2):199–208CrossRefGoogle Scholar
  52. Zhao B, Xue Y, Xu B, Ma T, Liu J (2018) Multi-objective classification based on NSGA-II. Int J Comput Sci Math 9(6):539–546MathSciNetCrossRefGoogle Scholar
  53. Zhou X, Liu Y, Li B (2016) A multi-objective discrete cuckoo search algorithm with local search for community detection in complex networks. Mod Phys Lett B 30(07):1650080MathSciNetCrossRefGoogle Scholar
  54. Zitzler E, Kunzli S (2004) Indicator-based selection in multi objective search. In: Lecture notes in computing science, pp 832–842Google Scholar
  55. Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou K, et al. (eds) EUROGEN 2001. International Center for Numerical Methods in engineering (CIMNE), pp 95–100Google Scholar
  56. Zou X, Chen Y, Liu M, Kang L (2008) A new evolutionary algorithm for solving many-objective optimization problems. IEEE Trans Syst Man Cybern B Cybern 38(5):1402–1412CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Complex System and Computational Intelligence LaboratoryTaiyuan University of Science and TechnologyTaiyuanChina
  2. 2.School of Electronics and InformationTongji UniversityShanghaiChina
  3. 3.School of Information EngineeringNanchang Institute of TechnologyNanchangChina
  4. 4.Institute of Automation, Chinese Academy of SciencesBeijingChina

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