Appropriate Paremeters Setting of League Championship Algorithm: Continuous Optimization Problems


  • Pupong Pongcharoen
  • Anothai Klakankhai


League Championship Algorithm, Optimal Parameters, Numerical Function Optimization, Fractional Factorial Experiment, Analysis of Variance


Manufacturing and service businesses need to increase their competitive always.  A business decision making tool is algorithms, and most business problems are NP-Hard. Therefore, the objectives of this article are to review League Championship Algorithm (LCA), to find the optimal parameters of the 10 different benchmarked functions and to design and analysis of experiments with the fractional factorial experiment (2k-p) and analysis of variance (ANOVA). The results of this experiments show that f1(x), f2(x), f9(x) and f10(x) have a P-value less than 0.05, indicating that the value of the factor responds. So the best parameter of the league championship algorithm should be as follows, for f1(x) set a retreat coefficient (c1)  to 6, for f2(x) and f10(x) set the league size (L) x Seasonality (S) to 56x1, the retreat coefficient (c1) and the approach coefficient (c2) is 6, and the probability of success (pc) is 0.99999 and f9(x)  set a retreat coefficient (c1)  to 6, the approach coefficient (c2) is 6 and the probability of success (pc) is 0.99999.


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Author Biographies

Pupong Pongcharoen

Department of Industrial Engineering, Faculty of Engineering, Naresuan University

Anothai Klakankhai

Department of Industrial Engineering, Faculty of Engineering, Naresuan University


1] Bozorg Haddad, O., "Advanced Optimization by Nature-Inspired Algorithms". Omid Bozorg-Haddad ed, Vol. 720. 2018: Springer Nature Singapore Pte Ltd, pp.166.

[2] Kashan, A.H, "League Championship Algorithm: A new algorithm for numerical function optimization", in SoCPaR 2009 - Soft Computing and Pattern Recognition. 2009.

[3] Kashan, A.H. and B. Karimi, "A new algorithm for constrained optimization inspired by the sport league championships". in 2010 IEEE World Congress on Computational Intelligence, WCCI 2010 - 2010 IEEE Congress on Evolutionary Computation, CEC 2010, 2010.

[4] Kashan, A.H., et al, "A modified League Championship Algorithm for numerical function optimization via artificial modeling of the 'between two halves analysis", in 6th International Conference on Soft Computing and Intelligent Systems, and 13th International Symposium on Advanced Intelligence Systems, SCIS/ISIS 2012, 2012.

[5] Yadav, S. and S.J. Nanda, "League Championship Algorithm for clustering". in 2015 IEEE Power, Communication and Information Technology Conference, PCITC 2015 - Proceedings. 2015.

[6] Shishira, S.R., A. Kandasamy, and K. Chandrasekaran, "Survey on meta heuristic optimization techniques in cloud computing". in 2016 International Conference on Advances in Computing, Communications and Informatics, ICACCI 2016, 2016.

[7] Kashan, A.H., A. Abbasi-Pooya, and S. Karimiyan, A New Mathematical Model and a League Championship Algorithm to Determine the Helicopter Routes in Offshore Gas Fields. 2016.

[8] Husseinzadeh Kashan, A., "An efficient algorithm for constrained global optimization and application to mechanical engineering design: League championship algorithm (LCA)". CAD Computer Aided Design, Vol. 43, No. 12, pp. 1769-1792, 2011.

[9] Husseinzadeh Kashan, A., B. Rezaee, and S. Karimiyan, "An efficient approach for unsupervised fuzzy clustering based on grouping evolution strategies". Pattern Recognition, Vol. 46, No.5, pp. 1240-1254, 2013.
[10] Husseinzadeh Kashan, A., "League Champion-
ship Algorithm (LCA): An algorithm for global optimization inspired by sport championships", Applied Soft Computing Journal, Vol. 16, pp. 171-200, 2014.

[11] Bouchekara, H.R.E.H., et al., "Optimal power flow using the league championship algorithm: A case study of the Algerian power system", Energy Conversion and Management, Vol. 87, pp. 58-70, 2014.

[12] Kalra, M. and S. Singh, "A review of metaheuristic scheduling techniques in cloud computing", Egyptian Informatics Journal, Vol. 16, No. 3, pp. 275-295, 2015.

[13] Noktehdan, A., S. Seyedhosseini, and M. Saidi-Mehrabad, "A Metaheuristic algorithm for the manufacturing cell formation problem based on grouping efficacy", International Journal of Advanced Manufacturing Technology, Vol. 82, No. 1-4, pp. 25-37, 2016.

[14] Abdulhamid, S.M., et al., "Secure scientific applications scheduling technique for cloud computing environment using global league championship algorithm". PLoS ONE, Vol. 11, No. 7 , 2016.

[15] Bingol, H. and B. Alatas, "Chaotic League Championship Algorithms". Arabian Journal for Science and Engineering, Vol. 41, No. 12, pp. 5123-5147, 2016.

[16] Seyyarer, A., et al, Overcurrent relay coordination of 154/34,5 kV Hasançelebi substation by League Championship Algorithm. in IDAP 2017 - International Artificial Intelligence and Data Processing Symposium, 2017.

[17] Karagöz, S. and A.R. Yildiz, "A comparison of recent metaheuristic algorithms for crashworthiness optimisation of vehicle thin-walled tubes considering sheet metal forming effects", International Journal of Vehicle Design, Vol. 73, No. 1, pp. 179-188, 2017.

[18] Tezcan, B.M. and O. Pekcan, League Championship Algorithm for Backcalculation of Conventional Flexible Pavements Using Artificial Neural Networks, 2017.

[19] Jalili, S., A.H. Kashan, and Y. Hosseinzadeh, "League Championship Algorithms for Optimum Design of Pin-Jointed Structures". Journal of Computing in Civil Engineering,Vol. 31, No. 2 , 2017.

[20] Alatas, B., "Sports inspired computational intelligence algorithms for global optimization", Artificial Intelligence Review, pp. 1-49, 2017.

[21] Ebrahimi, M., S.H. Vakilipour, and M.E.I. Shahverdi, "A novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem". Journal of Computational Applied Mechanics. Vol. 48, No. 2, pp. 285-296, 2017.

[22] Rezaei, H., O. Bozorg-Haddad, and X. Chu, "League championship algorithm (LCA)", in Studies in Computational Intelligence, pp. 19-30, 2018.

[23] Xu, W., R.F. Wang, and J.R. Yang, "An improved league championship algorithm with free search and its application on production scheduling". Journal of Intelligent Manufacturing, Vol. 29, No.1, pp. 165-174, 2018.

[24] Beheshtinia, M.A. and A. Ghasemi, "A multi-objective and integrated model for supply chain scheduling optimization in a multi-site manufacturing system". Engineering Optimization, Vol. 50, No. 9, pp. 1415-1433, 2018.

[25] Guchhait, A., B. Maji, and D. Kandar, "A hybrid V2V system for collision-free high-speed internet access in intelligent transportation system". Transactions on Emerging Telecommunications Technologies, Vol. 29, No. 3 , 2018.

[26] Soto, R., et al., "Solving the MCDP using a league championship algorithm", in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 447-453, 2018.

[27] Pourali, Z. and M. Aminnayeri, "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 (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 139-146, 2011.

[28] Sun, J., et al., An auction and league championship algorithm based resource allocation mechanism for distributed cloud, in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 334-346, 2013.

[29] Abdulhamid, S.M., M.S.A. Latiff, and I. Idris, "Tasks scheduling technique using League Championship Algorithm for makespan minimization in IaaS cloud". ARPN Journal of Engineering and Applied Sciences, Vol. 9,
No. 12, pp. 2528-2533, 2014.

[30] Sajadi, S.M., A.H. Kashan, and S. Khaledan. "A new approach for permutation flow-shop scheduling problem using league championship algorithm". in CIE 2014 - 44th International Conference on Computers and Industrial Engineering and IMSS 2014 - 9th International Symposium on Intelligent Manufacturing and Service Systems, Joint International Symposium on "The Social Impacts of Developments in Information, Manufacturing and Service Systems" - Proceedings, 2014.

[31] Seyedhosseini, S.M., H. Badkoobehi, and A. Noktehdan, "Machine-Part Cell Formation Problem Using a Group Based League Championship Algorithm". Journal of Promotion Management, Vol. 21, No. 1, pp. 55-63, 2015.

[32] Abdulhamid, S.M., et al., "A survey of league championship algorithm: Prospects and challenges", Indian Journal of Science and Technology, Vol. 8, pp. 101-110, 2015.

[33] Bouchekara, H.R.E.H., M. Nahas, and H.M. Kaouach, "Optimal design of electromagnetic devices using the league championship algorithm", Applied Computational Electromagnetics Society Journal, Vol. 32,
No. 6, pp. 484-490, 2017.

[34] Saraswathi, D. and E. Srinivasan, "Mammogram analysis using league championship algorithm optimized ensembled FCRN classifier", Indonesian Journal of Electrical Engineering and Computer Science, Vol. 5, No. 2,
pp. 451-461, 2017.

[35] KARCI, A., "Differential Evolution Algorithm and Its Variants", Anatolian Science-Bilgisayar Bilimleri Dergisi, Vol. 2, pp. 10-14, 2017.

[36] Ghahremani Nahr, J., R. Kian, and H. Rezazadeh, "A Modified Priority-Based Encoding for Design of a Closed-Loop Supply Chain Network Using a Discrete League Championship Algorithm", Mathematical Problems in Engineering, 2018.

[37] Alimoradi, M.R. and A. Husseinzadeh Kashan, "A league championship algorithm equipped with network structure and backward Q-learning for extracting stock trading rules", Applied Soft Computing Journal,Vol. 68, pp. 478-493, 2018.

[38] Karakoc, M.M., "Prediction of electroencephalogram time series via artificial neuro-fuzzy inference system trained by league championship algorithm", in Nature-Inspired Intelligent Techniques for Solving Biomedical Engineering Problems, pp. 232-248, 2018.

[39] Maharana, D., S. Maheshka, and P. Kotecha, "Multi-objective league championship algorithms and its applications to optimal control problems", in Advances in Intelligent Systems and Computing, pp. 35-46, 2019.

[40] Pholdee, N. and S. Bureerat, "Structural health monitoring through meta-heuristics - comparative performance study", Advances in Computational Design, Vol. , 2019 1, No. 4,pp. 315-327, 2016.

[41] Abdulhamid, S.M. and M.S.A. Latiff, "A checkpointed league championship algorithm-based cloud scheduling scheme with secure fault tolerance responsiveness", Applied Soft Computing Journal, Vol. 61, pp. 670-680, 2017.

[42] Abdulhamid, S.M., et al., "Fault tolerance aware scheduling technique for cloud computing environment using dynamic clustering algorithm", Neural Computing and Applications, Vol. 29, No. 1, pp. 279-293, 2018.

[43] Kejani, T., "A new approach for reliability optimization based on league championship algorithm (LCA)", Iran: Najaf Abad Branch, Azad University, 2013.

[44] Fister Jr, I., et al., "A brief review of nature-inspired algorithms for optimization", arXiv preprint arXiv:1307.4186, 2013.

[45] Stephen, M.J. and P.R. PV, "Simple league championship algorithm", International Journal of Computer Applications, Vol. 75, No. 6 , 2013.

[46] Lenin, K., B.R. Reddy, and M.S. Kalavathi, "League championship algorithm (LCA) for solving optimal reactive power dispatch problem", International Journal of Computer and Information Technologies, Vol. 1, No. 3, pp. 254-272, 2013.

[47] Sebastián, A.R. and L.R. Isabel, "Scheduling to job shop configuration minimizing the make span using champions league algorithm", Tunja: Division de Arquitectura e Ingenierias, Universidad Santo, 2014.

[48] Kahledan, S., "A league championship algorithm for travelling salesman problem", Iran: Najaf Abad Branch, Azad University, 2014.

[49] Abdulhamid, S.M. and M.S.A. Latiff, "League Championship Algorithm based job scheduling scheme for infrastructure as a service cloud", arXiv preprint arXiv:1410.2208, 2014.

[50] Abdullahi, M., Job Scheduling Technique for Infrastructure as a Service Cloud Using an Enhanced League Championship Algorithm. 2015.

[51] Khoshalhan, F., "A new play-off approach in league championship algorithm for solving large-scale support vector machine problems", International Journal of Industrial Engineering & Production Research, Vol. 27, No. 1,
pp. 61-68, 2016.

[52] Yildiz, B.S., "A comparative investigation of eight recent population-based optimisation algorithms for mechanical and structural design problems", International Journal of Vehicle Design,Vol. 73, No. 1, pp. 208-218, 2017.

[53] Wangchamhan, T., S. Chiewchanwattana, and K. Sunat, "Efficient algorithms based on the k-means and Chaotic League Championship Algorithm for numeric, categorical, and mixed-type data clustering", Expert Systems with Applications, Vol. 90, pp. 146-167, 2017.

[54] Husseinzadeh Kashan, A., A. Abbasi-Pooya, and S. Karimiyan, "A rig-based formulation and a league championship algorithm for helicopter routing in offshore transportation", in Advances in Intelligent Systems and Computing, pp. 23-38, 2019.