Skip to main content
Log in

A hybrid method based on krill herd and quantum-behaved particle swarm optimization

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

A novel hybrid Krill herd (KH) and quantum-behaved particle swarm optimization (QPSO), called KH–QPSO, is presented for benchmark and engineering optimization. QPSO is intended for enhancing the ability of the local search and increasing the individual diversity in the population. KH–QPSO is capable of avoiding the premature convergence and eventually finding the function minimum; especially, KH–QPSO can make all the individuals proceed to the true global optimum without introducing additional operators to the basic KH and QPSO algorithms. To verify its performance, various experiments are carried out on an array of test problems as well as an engineering case. Based on the results, we can easily infer that the hybrid KH–QPSO is more efficient than other optimization methods for solving standard test problems and engineering optimization problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

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

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

    Article  Google Scholar 

  3. 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 

  4. 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 

  5. 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 

  6. 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 

  7. 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 

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

    Article  Google Scholar 

  9. 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 

  10. Yang XS (2010) 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 IntelligenceSpringer, Heidelberg, pp 65–74. doi:10.1007/978-3-642-12538-6_6

    Chapter  Google Scholar 

  11. 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

    Google Scholar 

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

    Google Scholar 

  13. 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 

  14. Gandomi AH, Yang X-S, Talatahari S, Deb S (2012) Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization. Comput Math Appl 63(1):191–200. doi:10.1016/j.camwa.2011.11.010

    Article  MathSciNet  MATH  Google Scholar 

  15. Zou D, Wu J, Gao L, Li S (2013) A modified differential evolution algorithm for unconstrained optimization problems. Neurocomputing 120:469–481. doi:10.1016/j.neucom.2013.04.036

    Article  Google Scholar 

  16. 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 

  17. Yang XS (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspired Comput 2(2):78–84. doi:10.1504/IJBIC.2010.032124

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Li X, Yin M (2012) Multi-operator based biogeography based optimization with mutation for global numerical optimization. Comput Math Appl 64(9):2833–2844. doi:10.1016/j.camwa.2012.04.015

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  22. Lin J (2014) Parameter estimation for time-delay chaotic systems by hybrid biogeography-based optimization. Nonlinear Dyn 77(3):983–992. doi:10.1007/s11071-014-1356-7

    Article  Google Scholar 

  23. Lin J, Xu L, Zhang H (2014) Hybrid biogeography based optimization for constrained optimal spot color matching. Color Res Appl 39(6):607–615. doi:10.1002/col.21836

    Article  Google Scholar 

  24. Yang XS, Deb S Cuckoo search via Lévy flights. In: Abraham A, Carvalho A, Herrera F, Pai V (eds) Proceeding of world congress on nature & biologically inspired computing (NaBIC 2009), Coimbatore, India, Dec 2009. IEEE Publications, USA, pp 210–214

  25. Li X, Wang J, Yin M (2013) Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Comput Appl 24(6):1233–1247. doi:10.1007/s00521-013-1354-6

    Article  MathSciNet  Google Scholar 

  26. 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 

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

    Google Scholar 

  28. Li X, Yin M (2015) A particle swarm inspired cuckoo search algorithm for real parameter optimization. Soft Comput. doi:10.1007/s00500-015-1594-8

    Google Scholar 

  29. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471. doi:10.1007/s10898-007-9149-x

    Article  MathSciNet  MATH  Google Scholar 

  30. Li X, Yin M (2014) Parameter estimation for chaotic systems by hybrid differential evolution algorithm and artificial bee colony algorithm. Nonlinear Dyn 77(1–2):61–71. doi:10.1007/s11071-014-1273-9

    Article  MathSciNet  Google Scholar 

  31. Li X, Yin M (2012) Self-adaptive constrained artificial bee colony for constrained numerical optimization. Neural Comput Appl 24(3–4):723–734. doi:10.1007/s00521-012-1285-7

    Google Scholar 

  32. Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98. doi:10.1016/j.advengsoft.2015.01.010

    Article  Google Scholar 

  33. Mirjalili S, Mirjalili SM, Hatamlou A (2015) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl. doi:10.1007/s00521-015-1870-7

    Google Scholar 

  34. Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213(3–4):267–289. doi:10.1007/s00707-009-0270-4

    Article  MATH  Google Scholar 

  35. Kaveh A, Talatahari S (2012) Charged system search for optimal design of frame structures. Appl Soft Comput 12(1):382–393. doi:10.1016/j.asoc.2011.08.034

    Article  Google Scholar 

  36. Kaveh A, Talatahari S (2010) A charged system search with a fly to boundary method for discrete optimum design of truss structures. Asian J Civil Eng 11(3):277–293

    Google Scholar 

  37. Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248. doi:10.1016/j.ins.2009.03.004

    Article  MATH  Google Scholar 

  38. Mirjalili S, Wang G-G, Coelho LdS (2014) Binary optimization using hybrid particle swarm optimization and gravitational search algorithm. Neural Comput Appl 25(6):1423–1435. doi:10.1007/s00521-014-1629-6

    Article  Google Scholar 

  39. Mirjalili S, Lewis A (2014) Adaptive gbest-guided gravitational search algorithm. Neural Comput Appl 25(7–8):1569–1584. doi:10.1007/s00521-014-1640-y

    Article  Google Scholar 

  40. 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 

  41. Gandomi AH (2014) Interior search algorithm (ISA): a novel approach for global optimization. ISA Trans 53(4):1168–1183. doi:10.1016/j.isatra.2014.03.018

    Article  Google Scholar 

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

    Article  Google Scholar 

  43. Mirjalili S (2015) How effective is the Grey Wolf optimizer in training multi-layer perceptrons. Appl Intell. doi:10.1007/s10489-014-0645-7

    Google Scholar 

  44. 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 

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

    Google Scholar 

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

    Article  Google Scholar 

  47. 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 

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

    Google Scholar 

  49. Khatib W, Fleming P (1998) The stud GA: A mini revolution? In: Eiben A, Bäck T, Schoenauer M, Schwefel H-P (eds) Parallel problem solving from nature—PPSN V, vol 1498., Lecture Notes in Computer ScienceSpringer, Berlin Heidelberg, pp 683–691. doi:10.1007/BFb0056910

    Chapter  Google Scholar 

  50. Zhang G, Gheorghe M, Li Y (2012) A membrane algorithm with quantum-inspired subalgorithms and its application to image processing. Nat Comput 11(4):701–717. doi:10.1007/s11047-012-9320-2

    Article  MathSciNet  MATH  Google Scholar 

  51. Lu T-C, Yu G-R (2013) An adaptive population multi-objective quantum-inspired evolutionary algorithm for multi-objective 0/1 knapsack problems. Inf Sci 243:39–56. doi:10.1016/j.ins.2013.04.018

    Article  MathSciNet  MATH  Google Scholar 

  52. Duan H-B, Xu C-F, Xing Z-H (2010) A hybrid artificial bee colony optimization and quantum evolutionary algorithm for continuous optimization problems. Int J Neural Syst 20(1):39–50. doi:10.1142/S012906571000222X

    Article  Google Scholar 

  53. Sun J, Feng B, Xu W Particle swarm optimization with particles having quantum behavior. In: Proceedings of congress on evolutionary computation (CEC 2004), Portland, USA, June 19–23 2004. IEEE, pp 325–331. doi:10.1109/CEC.2004.1330875

  54. Van Den Bergh F (2006) An analysis of particle swarm optimizers. University of Pretoria, South Africa

    Google Scholar 

  55. Tian N, Lai C-H (2013) Parallel quantum-behaved particle swarm optimization. Int J Mach Learn Cybern 5(2):309–318. doi:10.1007/s13042-013-0168-2

    Article  Google Scholar 

  56. Wang G, Guo L, Wang H, Duan H, Liu L, Li J (2014) 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

    Article  Google Scholar 

  57. Li J, Tang Y, Hua C, Guan X (2014) An improved krill herd algorithm: krill herd with linear decreasing step. Appl Math Comput 234:356–367. doi:10.1016/j.amc.2014.01.146

    Article  MathSciNet  MATH  Google Scholar 

  58. Wang G-G, Gandomi AH, Alavi AH, Hao G-S (2014) 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

    Article  Google Scholar 

  59. Wang G-G, Gandomi AH, Alavi AH (2014) 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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  61. Wang G, Guo L, Gandomi AH, Cao L, Alavi AH, Duan H, Li J (2013) Lévy-flight krill herd algorithm. Math Probl Eng 2013:1–14. doi:10.1155/2013/682073

    Google Scholar 

  62. 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 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  66. Wang G-G, Gandomi AH, Yang X-S, Alavi AH (2014) A novel improved accelerated particle swarm optimization algorithm for global numerical optimization. Eng Comput 31(7):1198–1220. doi:10.1108/EC-10-2012-0232

    Article  Google Scholar 

  67. Zhao X, Lin W, Zhang Q (2014) 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

    Article  MathSciNet  Google Scholar 

  68. Mirjalili S, Mohd Hashim SZ, Moradian Sardroudi H (2012) Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl Math Comput 218(22):11125–11137. doi:10.1016/j.amc.2012.04.069

    Article  MathSciNet  MATH  Google Scholar 

  69. Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73. doi:10.1109/4235.985692

    Article  Google Scholar 

  70. Jamil M, Yang X-S (2013) A literature survey of benchmark functions for global optimisation problems. Int J Math Model Numer Optim 4(2):150–194. doi:10.1504/IJMMNO.2013.055204

    MATH  Google Scholar 

  71. Vanaret C, Gotteland J-B, Durand N, Alliot J-M (2014) Certified global minima for a benchmark of difficult optimization problems. hal-00996713, https://hal-enac.archives-ouvertes.fr/hal-00996713

  72. Li X, Yin M (2013) 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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gai-Ge Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, GG., Gandomi, A.H., Alavi, A.H. et al. A hybrid method based on krill herd and quantum-behaved particle swarm optimization. Neural Comput & Applic 27, 989–1006 (2016). https://doi.org/10.1007/s00521-015-1914-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-015-1914-z

Keywords

Navigation