Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

An improved league championship algorithm with free search and its application on production scheduling

  • 344 Accesses

  • 7 Citations


An improved league championship algorithm with free search (LCAFS) is proposed to avoid the drawbacks of basic LCA, such as premature convergence, slow convergence speed. The parameters of the algorithm vary linearly along with iteration. A novel match schedule is designed to improve the competition capability for the sport teams. Furthermore, the free search operation is introduced to promote the diversity of the league. Inspired by the real league degradation, degradation mechanism is used to preserve the team elites. It is convinced by using benchmark functions that LCAFS is superior to other compared algorithms in the global searching performance and convergence speed. The proposed algorithm is finally employed as learning method of parameters in neural network to establish the shop floor production scheduling model and achieves good results.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13


  1. Abharian, A. E., Sarabi, S. Z., & Yomi, M. (2014). Optimal sigmoid nonlinear stochastic control of HIV-1 infection based on bacteria foraging optimization method. Biomedical Signal Processing and Control, 10, 184–191.

  2. Askarzadeh, A. (2013). A discrete chaotic harmony search-based simulated annealing algorithm for optimum design of PV/wind hybrid system. Solar Energy, 97, 93–101.

  3. Chen, M. Y. (2013). A hybrid ANFIS model for business failure prediction utilizing particle swarm optimization and subtractive clustering. Information Sciences, 220, 180–195.

  4. Dorigo, M., & Blum, C. (2005). Ant colony optimization theory: A survey. Theoretical Computer Science, 344, 243–278.

  5. Eberhart, R. C., & Shi, Y. (2000). Comparing inertia weights and constriction factors in particle swarm optimization. In Proceedings of IEEE international congress on evolutionary computation, vol. 1. San Diego, CA, pp. 84–88.

  6. Formato, R. A. (2007). Central force optimization: A new metaheuristic with applications in applied electromagnetics. Progress in Electromagnetics Research, 77, 425–491.

  7. Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A new heuristic optimization algorithm: Harmony search. Simulation, 76(2), 60–68.

  8. Holland, J. H. (1975). Adaptation in natural and artificial system. Ann Arbor: Michigan University Press.

  9. Kalin, P. (2009). Free search—a model of adaptive intelligence. In 2009 International conference on adaptive and intelligent systems, pp. 92–97.

  10. Kalin, P., & Guy, L. (2005). Free search—a comparative analysis. Information Sciences, 172, 173–193.

  11. Kashan, A. H. (2009). League championship algorithm: A new algorithm for numerical function optimization. In 2009 IEEE international conference of soft computing and pattern recognition, pp. 43–48, Dec. 4–9, Malacca.

  12. Kashan, A. H., & Karimi, B. (2010). A new algorithm for constrained optimization inspired by the sport league championships. In 2010 IEEE congress on evolutionary computation, pp. 1–8, July 18–23, Barcelona.

  13. Kashan, A. H., Karimi, B., & Jolai, F. (2006). Effective hybrid genetic algorithm for minimizing makespan on a single-batch processing machine with non-identical job sizes. International Journal of Production Research, 44(12), 2337–2360.

  14. Kashan, A. H. (2011). An efficient algorithm for constrained global optimization and application to mechanical engineering design: League championship algorithm (LCA). Computer-Aided Design, 43(12), 1769–1792.

  15. Kennedy, J., & Eberhart, R. C. (1995). Particle swarm optimization. In Proceedings of IEEE international conference on neural networks. Piscataway, NJ, USA, 4(2), 1942–1948.

  16. Lenin, K., Reddy, B. R., & Kalavathi, M. S. (2013). League championship algorithm (LCA) for solving optimal reactive power dispatch problem. International Journal of Computer and Information Technologies, 1(3), 254–272.

  17. Metaxiotis, K. S., Askounis, D., & Psarras, J. (2002). Expert systems in production planning and scheduling: A state-of-the-art survey. Journal of Intelligent Manufacturing, 13(4), 253–260.

  18. Morad, N., & Zalzala, A. (1999). Genetic algorithms in integrated process planning and scheduling. Journal of Intelligent Manufacturing, 10(2), 169–179.

  19. Niu, B., Zhu, Y., He, X., & Wu, H. (2007). MCPSO: A multi-swarm cooperative particle swarm optimizer. Applied Mathematics and Computation, 185, 1050–1062.

  20. Passino, K. M. (2002). Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Systems Magazine, 22(3), 52–67.

  21. Pourali, Z., & Aminnayeri, M. (2012). A novel discrete league championship algorithm for minimizing earliness/tardiness penalties with distinct due dates and batch delivery consideration. In Lecture notes in computer science, vol. 6838, pp. 139–146.

  22. Ramin, R. (2011). Cuckoo optimization algorithm. Applied Soft Computing, 11, 5508–5518.

  23. Shi, Y., & Eberhart, R. C. (2001). Fuzzy adaptive particle swarm optimization. In Proceedings of IEEE international congress on evolutionary computation, vol. 1. Seoul, Korea, pp. 101–106.

  24. Stacey, A., Jancic, M., & Grundy, I. (2003). Particle swarm optimization with mutation. In The 2003 congress on evolutionary computation, Dec. 8–12, vol. 2, pp. 1425–1430.

  25. Sun, J., Wang, X., & Li, K., et al. (2013). An auction and league championship algorithm based resource allocation mechanism for distributed cloud. In Lecture notes in computer science, vol. 8299, pp. 334–346.

  26. Wang, L., & Shen, W. (2003). DPP: An agent-based approach for distributed process planning. Journal of Intelligent Manufacturing, 14(5), 429–439.

  27. Yang, X. S. (2009). Firefly algorithms for multimodal optimization. In O. Watanabe & T. Zeugmann (Eds.), Stochastic algorithms: Foundations and applications, SAGA 2009, lecture notes in computer science, vol. 5792. Berlin: Springer (pp. 169–78)

Download references


This paper is supported by Shanghai Project of Absorption and Innovation of Imported Technologies (14XI-2-04).

Author information

Correspondence to Wei Xu.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xu, W., Wang, R. & Yang, J. An improved league championship algorithm with free search and its application on production scheduling. J Intell Manuf 29, 165–174 (2018). https://doi.org/10.1007/s10845-015-1099-4

Download citation


  • League championship algorithm
  • Match schedule
  • Free search
  • Production scheduling