Advertisement

Neural Computing and Applications

, Volume 31, Supplement 1, pp 653–670 | Cite as

A hybridization of cuckoo search and particle swarm optimization for solving optimization problems

  • Rui Chi
  • Yi-xin SuEmail author
  • Dan-hong Zhang
  • Xue-xin Chi
  • Hua-jun Zhang
Original Article

Abstract

A new hybrid optimization algorithm, a hybridization of cuckoo search and particle swarm optimization (CSPSO), is proposed in this paper for the optimization of continuous functions and engineering design problems. This algorithm can be regarded as some modifications of the recently developed cuckoo search (CS). These modifications involve the construction of initial population, the dynamic adjustment of the parameter of the cuckoo search, and the incorporation of the particle swarm optimization (PSO). To cover search space with balance dispersion and neat comparability, the initial positions of cuckoo nests are constructed by using the principle of orthogonal Lation squares. To reduce the influence of fixed step size of the CS, the step size is dynamically adjusted according to the evolutionary generations. To increase the diversity of the solutions, PSO is incorporated into CS using a hybrid strategy. The proposed algorithm is tested on 20 standard benchmarking functions and 2 engineering optimization problems. The performance of the CSPSO is compared with that of several meta-heuristic algorithms based on the best solution, worst solution, average solution, standard deviation, and convergence rate. Results show that in most cases, the proposed hybrid optimization algorithm performs better than, or as well as CS, PSO, and some other exiting meta-heuristic algorithms. That means that the proposed hybrid optimization algorithm is competitive to other optimization algorithms.

Keywords

Cuckoo search Particle swarm optimization Hybrid optimization Orthogonal Lation squares Step size 

Notes

Acknowledgments

The authors would like to thank the Associate Editor and the reviewers for their detailed comments and valuable suggestions which considerably improved the presentation of the paper. The work is supported by the Natural Science Foundation of Hubei Province, China (#2015CFB586 and #2016CFB502), and the Fundamental Research Funds for the Central Universities (#163111005).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. International Journal of Mathematical Modelling and Numerical Optimisation 1(4):330–343CrossRefzbMATHGoogle Scholar
  2. 2.
    Sun DI, Ashley B, Brewer B et al (1984) Optimal power flow by Newton approach. IEEE Transactions on Power Apparatus and Systems 103(10):2864–2880CrossRefGoogle Scholar
  3. 3.
    Dommel HW, Tinney WF (1968) Optimal power flow solutions. IEEE Transactions on Power Apparatus and Systems 87(10):1866–1876CrossRefGoogle Scholar
  4. 4.
    Capitanescu F, Wehenkel L (2013) Experiments with the interior-point method for solving large scale optimal power flow problems. Electric Power Systems Research, vol 95:276–283CrossRefGoogle Scholar
  5. 5.
    Diez M, Peri D (2010) Robust optimization for ship conceptual design. Ocean Eng 37(11–12):966–977CrossRefGoogle Scholar
  6. 6.
    Sekhar P, Mohanty S (2016) An enhanced cuckoo search algorithm based contingency constrained economic load dispatch for security enhancement. Int J Electr Power Energy Syst 75:303–310CrossRefGoogle Scholar
  7. 7.
    Li X, Yin M (2013) A hybrid cuckoo search via Lévy flights for the permutation flow shop scheduling problem. Int J Prod Res 51(16):4732–4754CrossRefGoogle Scholar
  8. 8.
    Nagano MS, Moccellin JV (2002) A high quality solution constructive heuristic for flow shop sequencing. J Oper Res Soc 53(12):1374–1379CrossRefzbMATHGoogle Scholar
  9. 9.
    Mitchell M (1998) An introduction to genetic algorithms. MIT press, LondonzbMATHGoogle Scholar
  10. 10.
    Tang O (2004) Simulated annealing in lot sizing problems. Int J Prod Econ 88(2):173–181CrossRefGoogle Scholar
  11. 11.
    Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization. In: Proceedings of the 2007 I.E. Swarm Intelligence Symposium, pp 120–127Google Scholar
  12. 12.
    Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of the IEEE International joint conference on neural networks, pp 1942–1948Google Scholar
  13. 13.
    Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Dorigo M, Di Caro G (1999) The ant colony optimization meta-heuristic. In: New ideas in optimization, pp 11–32Google Scholar
  15. 15.
    Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. SIMULATION 76(2):60–68CrossRefGoogle Scholar
  16. 16.
    Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization, studies in computational intelligence, pp 65–74Google Scholar
  17. 17.
    Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput & Applic 27(4):1053–1073CrossRefGoogle Scholar
  18. 18.
    Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: World Congress on Nature and Biologically Inspired Computing, pp 210–214Google Scholar
  19. 19.
    Nearchou AC (2004) A novel metaheuristic approach for the flow shop scheduling problem. Eng Appl Artif Intell 17(3):289–300CrossRefGoogle Scholar
  20. 20.
    Alikhani MG, Javadian N, Tavakkoli-Moghaddam R (2009) A novel hybrid approach combining electromagnetism-like method with Solis and wets local search for continuous optimization problems. J Glob Optim 44(2):227–234MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Costa L, Santo I, Fernandes E (2012) A hybrid genetic pattern search augmented Lagrangian method for constrained global optimization. Appl Math Comput 218(18):9415–9426MathSciNetzbMATHGoogle Scholar
  22. 22.
    Yildiz AR (2009) A novel hybrid immune algorithm for optimization of machining parameters in milling operations. Robot Comput Integr Manuf 25(2):261–270CrossRefGoogle Scholar
  23. 23.
    De Melo VCV, Carosio GLC (2013) Investigating multi-view differential evolution for solving constrained engineering design problems. Expert Syst Appl 40(9):3370–3377CrossRefGoogle Scholar
  24. 24.
    Su Y, Chi R (2017) Multi-objective particle swarm-differential evolution algorithm. Neural Comput & Applic 28(2):407–418CrossRefGoogle Scholar
  25. 25.
    Kanagaraj G, Ponnambalam SG, Jawahar N et al (2013) An effective hybrid cuckoo search and genetic algorithm for constrained engineering design optimization. Eng Optim 46(10):1331–1351MathSciNetCrossRefGoogle Scholar
  26. 26.
    Kanagaraj G, Ponnambalam SG, Gandomi AH (2016) Hybridizing cuckoo search with bio-inspired algorithms for constrained optimization problems. International Conference on Swarm, Evolutionary, and Memetic Computing, pp260–273Google Scholar
  27. 27.
    Huang J, Gao L, Li X (2015) An effective teaching-learning-based cuckoo search algorithm for parameter optimization problems in structure designing and machining processes. Appl Soft Comput 36:349–356CrossRefGoogle Scholar
  28. 28.
    Mohamad AB, Zain AM, Bazin NEN (2014) Cuckoo search algorithm for optimization problems—a literature review and its applications. Appl Artif Intell 28(5):419–448CrossRefGoogle Scholar
  29. 29.
    Mohapatra P, Chakravarty S, Dash PK (2015) An improved cuckoo search based extreme learning machine for medical data classification. Swarm and Evolutionary Computation 24:25–49CrossRefGoogle Scholar
  30. 30.
    Ouaarab A, Ahiod B, Yang XS (2014) Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput & Applic 24(7–8):1659–1669CrossRefGoogle Scholar
  31. 31.
    Hu X, Eberhart R (2002) Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: Congress on Evolutionary Computation, pp1677–1681Google Scholar
  32. 32.
    Shokrian M, High KA (2014) Application of a multi objective multi-leader particle swarm optimization algorithm on NLP and MINLP problems. Comput Chem Eng 60:57–75CrossRefGoogle Scholar
  33. 33.
    Shlesinger MF, Zaslavsky GM, Frisch U (1995) Lévy flights and related topics in physics. Lecture Notes in Physics, BerlinCrossRefzbMATHGoogle Scholar
  34. 34.
    Brown CT, Liebovitch LS, Glendon R (2007) Lévy flights in dobe ju/’hoansi foraging patterns. Hum Ecol 35(1):129–138CrossRefGoogle Scholar
  35. 35.
    Pavlyukevich I (2007) Lévy flights, non-local search and simulated annealing. J Comput Phys 226(1):1830–1844MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Chen K, Zhang Y, Chen G et al (2016) Further results on mutually nearly orthogonal Latin squares. Acta Mathematicae Applicatae Sinica, English Series 32(1):209–220MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Valian E, Tavakoli S, Mohanna S et al (2013) Improved cuckoo search for reliability optimization problems. Comput Ind Eng 64(1):459–468CrossRefGoogle Scholar
  38. 38.
    Valian E, Mohanna S, Tavakoli S (2011) Improved cuckoo search algorithm for feed-forward neural network training. International Journal of Artificial Intelligence & Applications 2(3):36–43CrossRefGoogle Scholar
  39. 39.
    Bulatović RR, Bošković G, Savković MM et al (2014) Improved cuckoo search (ICS) algorithm for constrained optimization problems. Latin American Journal of Solids and Structures 11(8):1349–1362CrossRefGoogle Scholar
  40. 40.
    Walton S, Hassan O, Morgan K et al (2011) Modified cuckoo search: a new gradient free optimisation algorithm. Chaos, Solitons Fractals 44(9):710–718CrossRefGoogle Scholar
  41. 41.
    Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214(1):108–132MathSciNetzbMATHGoogle Scholar
  42. 42.
    Hedar AR, Fukushima M (2006) Tabu search directed by direct search methods for nonlinear global optimization. Eur J Oper Res 170(2):329–349MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Wang L, Zou F, Hei X et al (2014) A hybridization of teaching-learning-based optimization and differential evolution for chaotic time series prediction. Neural Computing and Application 25(6):1407–1422CrossRefGoogle Scholar
  44. 44.
    Suganthan PN, Hansen N, Liang JJ, et al (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real parameter optimization. Technical Report, Nanyang Technological University, Singapore and KanGAL Report Number 2005005Google Scholar
  45. 45.
    Cagnina LC, Esquivel SC, Coello CAC (2008) Solving engineering optimization problems with the simple constrained particle swarm optimizer. Informatica 32(3):319–326zbMATHGoogle Scholar
  46. 46.
    Bazaraa MS, Sherali HD, Shetty CM (1979) Nonlinear programming, theory and algorithm. Academic Press, New YorkzbMATHGoogle Scholar
  47. 47.
    Belegundu AD (1985) A study of mathematical programming methods for structural optimization, PhD thesis, Department of Civil and Environmental Engineering, University of Iowa, IowaGoogle Scholar
  48. 48.
    Coello CAC, Montes EM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203CrossRefGoogle Scholar
  49. 49.
    Eskandar H, Sadollah A, Bahreininejad A et al (2012) Water cycle algorithm–a novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & Structures, vol 110-111:151–166CrossRefGoogle Scholar
  50. 50.
    Ma W, Wang M, Zhu X (2014) Improved particle swarm optimization based approach for bilevel programming problem—an application on supply chain model. Int J Mach Learn Cybern 5(2):281–292CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • Rui Chi
    • 1
  • Yi-xin Su
    • 1
    Email author
  • Dan-hong Zhang
    • 1
  • Xue-xin Chi
    • 1
  • Hua-jun Zhang
    • 1
  1. 1.School of AutomationWuhan University of TechnologyWuhanChina

Personalised recommendations