Advertisement

Neural Computing and Applications

, Volume 31, Issue 8, pp 4385–4405 | Cite as

Chaotic grasshopper optimization algorithm for global optimization

  • Sankalap AroraEmail author
  • Priyanka Anand
Original Article

Abstract

Grasshopper optimization algorithm (GOA) is a new meta-heuristic algorithm inspired by the swarming behavior of grasshoppers. The present study introduces chaos theory into the optimization process of GOA so as to accelerate its global convergence speed. The chaotic maps are employed to balance the exploration and exploitation efficiently and the reduction in repulsion/attraction forces between grasshoppers in the optimization process. The proposed chaotic GOA algorithms are benchmarked on thirteen test functions. The results show that the chaotic maps (especially circle map) are able to significantly boost the performance of GOA.

Keywords

Grasshopper optimization algorithm Chaotic maps Global optimization problem Multimodal function 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest. This manuscript does not contain any studies with human participants or animals performed by any of the authors. Authors have carefully checked the “Instructions for Authors” and certify that the manuscript complies with the Ethical Rules applicable for this journal.

References

  1. 1.
    Yang X-S (2008) Introduction to mathematical optimization: from linear programming to metaheuristics. Cambridge International Science Publishing, CambridgezbMATHGoogle Scholar
  2. 2.
    Brownlee J (2011) Clever algorithms: nature-inspired programming recipes. 1st edn. Lulu, North CarolinaGoogle Scholar
  3. 3.
    Yang X-S, Gandomi AH, Talatahari S, Alavi AH (eds) (2012) Metaheuristics in water, geotechnical and transport engineering. Elsevier, NewnesGoogle Scholar
  4. 4.
    Yildiz AR (2009) An effective hybrid immune-hill climbing optimization approach for solving design and manufacturing optimization problems in industry. J Mater Process Technol 209(6):2773–2780CrossRefGoogle Scholar
  5. 5.
    Jordehi AR (2015) Chaotic bat swarm optimisation (cbso). Appl Soft Comput 26:523–530CrossRefGoogle Scholar
  6. 6.
    Skalak DB (1994) Prototype and feature selection by sampling and random mutation hill climbing algorithms. In: Proceedings of the eleventh international conference on machine learning, pp 293–301Google Scholar
  7. 7.
    Aarts E, Korst J (1988) Simulated annealing and Boltzmann machines. Wiley, New YorkGoogle Scholar
  8. 8.
    dos Coelho L Santos, Mariani VC (2006) Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect. IEEE Trans Power Syst 21(2):989CrossRefGoogle Scholar
  9. 9.
    Storn R (1996) Differential evolution design of an IIR filter. In: Proceedings of IEEE international conference on evolutionary computation, pp 268–273Google Scholar
  10. 10.
    Arora S, Singh S (2017) Node localization in wireless sensor networks using butterfly optimization algorithm. Arab J Sci Eng 42:3325–3335CrossRefGoogle Scholar
  11. 11.
    Sayed GI, Hassanien AE, Azar AT (2017) Feature selection via a novel chaotic crow search algorithm. Neural Comput Appl.  https://doi.org/10.1007/s00521-017-2988-6 CrossRefGoogle Scholar
  12. 12.
    Ilonen J, Kamarainen J-K, Lampinen J (2003) Differential evolution training algorithm for feed-forward neural networks. Neural Process Lett 17(1):93–105CrossRefGoogle Scholar
  13. 13.
    Eberhart RC, Kennedy J et al (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, New York, vol 1, pp 39–43Google Scholar
  14. 14.
    Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95–99CrossRefGoogle Scholar
  15. 15.
    Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Arora S, Singh S, Singh S, Sharma B (2014) Mutated firefly algorithm. In: International conference on parallel, distributed and grid computing (PDGC), pp 33–38Google Scholar
  17. 17.
    Yang X-S (2010) Firefly algorithm, levy flights and global optimization. In: Research and development in intelligent systems XXVI, pp 209–218Google Scholar
  18. 18.
    Arora S, Singh S (2013) The firefly optimization algorithm: convergence analysis and parameter selection. Int J Comput Appl 69(3):48–52Google Scholar
  19. 19.
    Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) Gsa: a gravitational search algorithm. Inf Sci 179(13):2232–2248zbMATHCrossRefGoogle Scholar
  20. 20.
    Geem ZW, Kim JH, Loganathan G (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68CrossRefGoogle Scholar
  21. 21.
    Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9(2):159–195CrossRefGoogle Scholar
  22. 22.
    Arora S, Singh S (2015) Butterfly algorithm with levy flights for global optimization. In: International conference on signal processing, computing and control (ISPCC), pp 220–224Google Scholar
  23. 23.
    Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61CrossRefGoogle Scholar
  24. 24.
    Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47CrossRefGoogle Scholar
  25. 25.
    Yang D, Li G, Cheng G (2007) On the efficiency of chaos optimization algorithms for global optimization. Chaos Solitons Fractals 34(4):1366–1375MathSciNetCrossRefGoogle Scholar
  26. 26.
    Gandomi A, Yang X-S, Talatahari S, Alavi A (2013) Firefly algorithm with chaos. Commun Nonlinear Sci Numer Simul 18(1):89–98MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Gandomi AH, Yun GJ, Yang X-S, Talatahari S (2013) Chaos-enhanced accelerated particle swarm optimization. Commun Nonlinear Sci Numer Simul 18(2):327–340MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Arora S, Singh S (2017) An improved butterfly optimization algorithm with chaos. J Intell Fuzzy Syst 32(1):1079–1088zbMATHCrossRefGoogle Scholar
  29. 29.
    Kohli M, Arora S (2017) Chaotic grey wolf optimization algorithm for constrained optimization problems. J Comput Design Eng.  https://doi.org/10.1016/j.jcde.2017.02.005
  30. 30.
    Han X, Chang X (2013) An intelligent noise reduction method for chaotic signals based on genetic algorithms and lifting wavelet transforms. Inf Sci 218:103–118CrossRefGoogle Scholar
  31. 31.
    Jordehi AR (2014) A chaotic-based big bang-big crunch algorithm for solving global optimisation problems. Neural Comput Appl 25(6):1329–1335CrossRefGoogle Scholar
  32. 32.
    Jia D, Zheng G, Khan MK (2011) An effective memetic differential evolution algorithm based on chaotic local search. Inf Sci 181(15):3175–3187CrossRefGoogle Scholar
  33. 33.
    Heidari AA, Abbaspour RA, Jordehi AR (2017) An efficient chaotic water cycle algorithm for optimization tasks. Neural Comput Appl 28(1):57–85CrossRefGoogle Scholar
  34. 34.
    Talatahari S, Azar BF, Sheikholeslami R, Gandomi A (2012) Imperialist competitive algorithm combined with chaos for global optimization. Commun Nonlinear Sci Numer Simul 17(3):1312–1319MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Jordehi AR (2015) A chaotic artificial immune system optimisation algorithm for solving global continuous optimisation problems. Neural Comput Appl 26(4):827–833CrossRefGoogle Scholar
  36. 36.
    Chuang L-Y, Tsai S-W, Yang C-H (2011) Chaotic catfish particle swarm optimization for solving global numerical optimization problems. Appl Math Comput 217(16):6900–6916MathSciNetzbMATHGoogle Scholar
  37. 37.
    Saremi S, Mirjalili S, Lewis A (2014) Biogeography-based optimisation with chaos. Neural Comput Appl 25(5):1077–1097CrossRefGoogle Scholar
  38. 38.
    Han X, Chang X (2012) A chaotic digital secure communication based on a modified gravitational search algorithm filter. Inf Sci 208:14–27CrossRefGoogle Scholar
  39. 39.
    Naanaa A (2015) Fast chaotic optimization algorithm based on spatiotemporal maps for global optimization. Appl Math Comput 269:402–411MathSciNetzbMATHGoogle Scholar
  40. 40.
    Lu H, Wang X, Fei Z, Qiu M (2014) The effects of using chaotic map on improving the performance of multiobjective evolutionary algorithms. Math Prob Eng 2014:16.  https://doi.org/10.1155/2014/924652
  41. 41.
    He D, He C, Jiang L-G, Zhu H-W, Hu G-R (2001) Chaotic characteristics of a one-dimensional iterative map with infinite collapses. IEEE Trans Circuits Syst I Fundam Theory Appl 48(7):900–906MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Tavazoei MS, Haeri M (2007) Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl Math Comput 187(2):1076–1085MathSciNetzbMATHGoogle Scholar
  43. 43.
    Zheng W-M (1994) Kneading plane of the circle map. Chaos Solitons Fractals 4(7):1221–1233zbMATHCrossRefGoogle Scholar
  44. 44.
    Wang G, Guo L (2013) A novel hybrid bat algorithm with harmony search for global numerical optimization. J Appl Math 2013:21.  https://doi.org/10.1155/2013/696491
  45. 45.
    Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102CrossRefGoogle Scholar
  46. 46.
    Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18CrossRefGoogle Scholar
  47. 47.
    García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms behaviour: a case study on the cec2005 special session on real parameter optimization. J Heuristics 15(6):617–644zbMATHCrossRefGoogle Scholar
  48. 48.
    Wilcoxon F, Katti S, Wilcox RA (1970) Critical values and probability levels for the Wilcoxon rank sum test and the Wilcoxon signed rank test. Sel Tables Math Stat 1:171–259zbMATHGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.DAV UniversityJalandharIndia
  2. 2.Lovely Professional UniversityJalandharIndia

Personalised recommendations