Skip to main content
SpringerLink
Log in

Chaotic League Championship Algorithms

  • Research Article - Computer Engineering and Computer Science
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Classical optimization algorithms are insufficient in large-scale combinatorial problems and in nonlinear problems. Hence, heuristic optimization algorithms have been proposed. General purposed metaheuristic methods are evaluated in nine different groups: biology-based, physics-based, social-based, music-based, chemical-based, sports-based, mathematics-based, and hybrid methods which are combinations of these. Recently, a sports-based search and optimization algorithm entitled as league championship algorithm (LCA) has been proposed. LCA is a population-based, metaheuristic optimization algorithm that simulates a championship for general optimization with artificial teams and artificial league for several weeks. In this algorithm, according to the league program, a number is given to the couple of teams that will match and the result of match is determined as loser or winner. Winning or losing the game is closely related to power of teams. Teams are intended to improve the formation of the current team throughout the season to win the game in the coming weeks. Chaotic maps seem to improve the convergence speed and accuracy of optimization algorithms. Increasing global convergence speed and prevention of getting stuck on local solutions of LCA with chaos have been proposed for the first time in this study. In this paper, six different chaotic LCAs have been proposed and explained in detail. Comparative performance results have been examined in complex benchmark functions. Promising results have been obtained from the experimental results. Combining results appeared in different fields like LCA and complex dynamics can increase quality in some optimization problems and the chaos can be the wanted process.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alatas B., Akin E., Ozer A.B.: Chaos embedded particle swarm optimization algorithms. Chaos Soliton Fractals 40(4), 1715–1734 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bingol H., Alatas B.: Sports based a novel approach to metaheuristic optimization techniques: League Championship Algorithm. Fırat Univ. J. Sci. 27(1), 1–11 (2015)

    Google Scholar 

  3. Kashan A.H.: League Championship Algorithm (LCA): an algorithm for global optimization inspired by sport championships. Appl. Soft Comput. 16, 171–200 (2014)

    Article  Google Scholar 

  4. Kashan, A.H.: League Championship Algorithm: a new algorithm for numerical function optimization. In: International Conference on Soft Computing and Pattern Recognition (2009). doi:10.1109/SoCPaR.2009.21

  5. Bouchekara, H.; Dupré, L.; Kherrab, H.; Mehasni, R.: Design optimization of electromagnetic devices using the League Championship Algorithm. In: Optimization and Inverse Problems in Electromagnetism (OIPE) (2014)

  6. Bouchekara H.R.E.H., Abido M.A., Chaib A.E., Mehasni R.: Optimal power flow using the League Championship Algorithm: a case study of the Algerian power system. Energy Convers. Manag. 87, 58–70 (2014)

    Article  Google Scholar 

  7. Sajadi, S.M.; Kashan, A.H.; Kahledan, S.: A new approach for permutation flow-shop scheduling problem using League Championship Algorithm. In: Joint International Symposium on CIE44 and IMSS’14 (2014)

  8. Sun J., Wang X., Li K., Wu C., Huang M., Wang X.: An auction and League Championship Algorithm based resource allocation mechanism for distributed cloud. Adv. Parallel Process. Technol. 8299, 334–346 (2013)

    Article  Google Scholar 

  9. Xu, W.; Wang, R.; Yang, J.: An improved League Championship Algorithm with free search and its application on production scheduling. J. Intell. Manuf. (2015). doi:10.1007/s10845-015-1099-4

  10. Caponetto R., Fortuna L., Fazzino S., Xibilia M.G.: Chaotic sequences to improve the performance of evolutionary algorithms. IEEE Trans. Evol. Comput. 7(3), 289–304 (2003)

    Article  Google Scholar 

  11. Tan Y., Tan G.Z., Deng S.G.: Hybrid particle swarm optimization with chaotic search for solving integer and mixed integer programming problems. J. Cent. South Univ. Technol. 21(7), 2731–2742 (2014)

    Article  Google Scholar 

  12. Dai Q.W., Jiang F.B., Dong L.: Nonlinear inversion for electrical resistivity tomography based on chaotic DE-BP algorithm. J. Cent. South Univ. Technol. 21(5), 2018–2025 (2014)

    Article  Google Scholar 

  13. Tan Y., Tan G.Z., Deng S.G.: Hybrid particle swarm optimization with differential evolution and chaotic local search to solve reliability-redundancy allocation problems. J. Cent. South Univ. Technol. 20(6), 1572–1581 (2013)

    Article  Google Scholar 

  14. Brannstrom, A.: Modelling animal populations. Umea University, PhD Thesis (2004)

  15. Arena P., Caponetto R., Fortuna L., Rizzo A., La Rosa M.: Self organization in non-recurrent complex system. Int. J. Bifurc. Chaos 10(5), 1115–1125 (2000)

    Article  Google Scholar 

  16. Behnia S., Ahadpour S., Ayubi P.: Design and implementation of coupled chaotic maps in watermarking. Appl. Soft Comput. 21, 481–490 (2014)

    Article  Google Scholar 

  17. Gana L., Duan H.: Biological image processing via chaotic differential search and lateral inhibition. Optik Int. J. Light Electron Opt. 125(9), 2070–2075 (2014)

    Article  Google Scholar 

  18. Alatas B.: Chaotic bee colony algorithms for global numerical optimization. Expert Syst. Appl. 37(8), 5682–5687 (2010)

    Article  Google Scholar 

  19. Alatas B.: Chaotic harmony search algorithms. Appl. Math. Comput. 216(9), 2687–2699 (2010)

    MATH  Google Scholar 

  20. Saremi S., Mirjalili S., Lewis A.: Biogeography-based optimisation with chaos. Neural Comput. Appl. 25(5), 1077–1097 (2014)

    Article  Google Scholar 

  21. Dhal K.G., Quraishi I., Das S: A chaotic Lévy flight approach in bat and firefly algorithm for gray level image enhancement. I. J. Image Graph. Signal Process. 7, 69–76 (2015)

    Article  Google Scholar 

  22. Wagih K.A.: A chaotic bat algorithm for solving definite integral. Int. J. Comput. Technol. 14(4), 5592–5598 (2015)

    Google Scholar 

  23. Alatas B.: Uniform big bang—chaotic big crunch optimization. Commun. Nonlinear Sci. 16(9), 3696–3703 (2011)

    Article  MATH  Google Scholar 

  24. Schuster H.G., Just W.: Deterministic Chaos: An Introduction. Wiley, New York (2006)

    MATH  Google Scholar 

  25. Peitgen H., Jurgens H., Saupe D.: Chaos and Fractals. Springer Science & Business Media, Berlin (2006)

    MATH  Google Scholar 

  26. Zheng W.M.: Kneading plane of the circle map. Chaos Soliton Fractals 4, 1221 (1994)

    Article  MATH  Google Scholar 

  27. May, R.M.: Simple mathematical models with very complicated dynamics. In: Hunt, B.R.; Li, T.; Kennedy, J.A.; Nusse H.E. (eds.) The Theory of Chaotic Attractors, pp. 85–93. Springer, New York (2004)

  28. http://en.wikipedia.org/wiki/Rastrigin_function (2015). Accessed 11 Feb

  29. Rastrigin, L.A.: Extremal control systems. In: Theoretical Foundations of Engineering Cybernetics Series. Nauka, Moscow (1974)

  30. Adorio, E.P.; Diliman, U.P.: Mvf—Multivariate Test Functions Library in C for Unconstrained Global Optimization. http://www.geocities.ws/eadorio/mvf.pdf (2015). Accessed 11 Feb

  31. Molga, M.; Smutnicki, C.: Test Functions for Optimization Needs. http://www.robertmarks.org/Classes/ENGR5358/Papers/functions.pdf (2015). Accessed 11 Feb

  32. De Jong, K.: An analysis of the behaviour of a class of genetic adaptive systems. PhD Thesis, University of Michigan (1975)

  33. Digalakis J.G., Margaritis K.G.: An experimental study of benchmarking functions for genetic algorithms. Int. J. Comput. Math. 79(4), 403–416 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  34. Griewangk A.O.: Generalized descent of global optimization. J. Optim. Theory Appl. 34(1), 11–39 (1981)

    Article  MathSciNet  Google Scholar 

  35. http://mathworld.wolfram.com/GriewankFunction.html (2015). Accessed 11 Feb

  36. Gavana, A.: Test Functions Index. http://infinity77.net/global_optimization/test_functions.html (2015). Accessed 20 Dec

Download references

Author information

Authors and Affiliations

  1. Department of Computer Programming, Vocational School of Technical Sciences, Bingol University, 12000, Bingol, Turkey

    Harun Bingol

  2. Department of Software Engineering, Firat University, 23100, Elazig, Turkey

    Bilal Alatas

Authors
  1. Harun Bingol
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bilal Alatas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bilal Alatas.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bingol, H., Alatas, B. Chaotic League Championship Algorithms. Arab J Sci Eng 41, 5123–5147 (2016). https://doi.org/10.1007/s13369-016-2200-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-016-2200-9

Keywords

Search

Navigation