Testing Soccer League Competition Algorithm in Comparison with Ten Popular Meta-heuristic Algorithms for Sizing Optimization of Truss Structures


1 Department of Civil Engineering, University of British Columbia, Applied Science Lane, Vancouver, BC, Canada

2 Department of Civil Engineering (Structural Engineering), Sharif University of Technology, Tehran, Iran


Recently, many meta-heuristic algorithms are proposed for optimization of various problems. Some of them originally are presented for continuous optimization problems and some others are just applicable for discrete ones. In the literature, sizing optimization of truss structures is one of the discrete optimization problems which is solved by many meta-heuristic algorithms. In this paper, in order to discover an efficient and reliable algorithm for optimization of truss structures, a discrete optimizer, entitled Soccer League Competition (SLC) algorithm and ten popular and powerful solvers are examined and statistical analysis is carried out for them. The fundamental idea of SLC algorithm is inspired from a professional soccer league and based on the competitions among teams to achieve better ranking and players to be the best. For optimization purpose and convergence of the initial population to the global optimum, different teams compete to take the possession of the best rating positions in the league table and the internal competitions are taken place between players in each team for personal improvements. Recently, SLC as a multi-population algorithm with developed operators has been applied for optimization of various problems. In this paper, for demonstrating the performance of the different solvers for optimal design of truss structures, five numerical examples will be optimized and the results show that proposed SLC algorithm is able to find better solutions among other algorithms. In other words, SLC can discover new local optimal solutions for some examples where other algorithms fail to find that one.


  1. Templeman, A. B. and Yates, D. F., “A segmental method for the discrete optimum design of structures”, Engineering Optimization, Vol. 6, No. 3, (1983), 145-155.
  2. Zhu, D. M., “An improved Templeman's algorithm for the optimum design of trusses with discrete member sizes”, Engineering Optimization, Vol. 9, No. 4, (1986), 303-312.
  3. John, K. V., Ramakrishnan, C. V. and Sharma, K. G., “Minimum weight design of trusses using improved move limit method of sequential linear programming”, Computers & Structures, Vol. 27, No. 5, (1987), 583-591.
  4. Mehdizadeh, E. and Fatehi Kivi, A., “Three Meta-heuristic Algorithms for the Single-Item Capacitated Lot-sizing Problem”, International Journal of Engineering (IJE) Transactions B: Applications, Vol. 27, No. 8, (2014), 1223-1232.
  5. Tavakkoli-Moghaddam, R., Torabi, N. and Ghaseminejad, A., “A Quaternion Firefly Algorithm to Solve a Multi-Row Facility Layout Problem”, International Journal of Engineering (IJE), TRANSACTIONS B: Applications, Vol. 28, No. 11, (2015), 1605-1613.
  6. Ghodratnamaa, A., Tavakkoli-Moghaddam, R. and Baboli, A., “Comparing Three Proposed Meta-heuristics to Solve a New P-Hub Location allocation Problem”, International Journal of Engineering (IJE), TRANSACTIONS C: Aspects, Vol. 26, No. 9, (2013), 1043-1058.
  7. Jenkins, W. M., “Towards structural optimization via the genetic algorithm”, Computers & Structures, Vol. 40, No. 5, (1991), 1321-1327.
  8. Rajeev, S. and Krishnamoorthy, C., “Discrete optimization of structures using genetic”, Journal of Structural Engineering ASCE, Vol. 118, No. 5, (1992), 1123–1250.
  9. Adeli, H. and Cheng, N., “Integrated Genetic Algorithm for Optimization of Space Structures”, Journal of Aerospace Engineering, Vol. 6, No. 4, (1993), 315-328.
  10. Camp, C., Pezeshk, S. and Cao, G., “Optimized Design of Two-Dimensional Structures Using a Genetic Algorithm”, Journal of Structural Engineering, Vol. 124, No. 5, (1998), 551-559.
  11. Hasançebi, O. and Erbatur, F., “Constraint handling in genetic algorithm integrated structural optimization”, Acta Mechanica, Vol. 139, No. 1, (2000), 15-31.
  12. Sarma, K. and Adeli, H., “Fuzzy Genetic Algorithm for Optimization of Steel Structures”, Journal of Structural Engineering, Vol. 126, No. 5, (2000), 596-604.
  13. Lee, K., S. and Geem, Z., W., “A new structural optimization method based on the harmony search algorithm”, Computers & Structurs, Vol. 82, No. 9-10, (2004), 781–798.
  14. Li, L. J., Huang, B. Z. and Liu, F., “A heuristic particle swarm optimization method for truss structures with discrete variables”, Computers & Structures, Vol. 87, No. 7-8, (2009), 435-443.
  15. Camp, C. V. and Bichon, B. J., “Design of space trusses using ant colony optimization”, Journal of Structural Engineering, ASCE, Vol. 130, (2004), 741–751.
  16. Kaveh, A. and Talataheri, S., “Size optimization of space trusses using Big Bang–Big Crunch algorithm”, Computers & Structures, Vol. 87, No. 17-18, (2009), 1129-1140.
  17. Kaveh, A. and Talataheri, S., “A particle swarm optimization for truss structures with discrete variables”, Journal of Constructional Steel Research, Vol. 65, No. 8-9, (2009), 1558-1568.
  18. Sonmez, M., “Discrete optimum design of truss structures using artificial bee colony algorithm”, Structural and Multidisciplinary Optimization, Vol. 43, No. 1, (2011), 85-97.
  19. Sadollah, A. and Bahreininejad, A., “Mine blast algorithm for optimization of truss structures with discrete variables”, Computers & Structures, Vol. 102-103, No. 8-9, (2012), 49-63.
  20. Kaveh, A. and Mahdavi, V. R., “Colliding Bodies Optimization method for optimum discrete design of truss structures”, Computers & Structures, Vol. 139, (2014), 43-53.
  21. Bekdaş, G., Nigdeli, S. M. and Yang, X. S., “Sizing optimization of truss structures using flower pollination algorithm”, Applied Soft Computing, Vol. 37, (2015), 322-331.
  22. Hasançebi, O. and Kazemzadeh Azad, S., “Adaptive dimensional search: A new metaheuristic algorithm for discrete truss sizing optimization”, Computers & Structures, Vol. 154, (2015), 1-16.
  23. Gonçalves, M., S., Lopez, R. H. and Miguel, L. F. F., “Search group algorithm: A new metaheuristic method for the optimization of truss structures”, Computers & Structures, Vol. 153, (2015), 165-184.
  24. Wolpert, D. H. and Macready, W. G., “No free lunch theorems for optimization”, IEEE Transactions on Evolutionary Computation, Vol. 1, No. 1 (1997), 67-82.
  25. Mirjalili, S., “Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm”, Knowledge-Based Systems, Vol. 89, (2015), 228-249.
  26. Moosavian, N. and Roodsari, B. K., “Soccer league competition algorithm, a new method for solving systems of nonlinear equations”, International Journal of Intelligence Science, Vol. 4, (1), 7-16.
  27. Moosavian, N. and Roodsari, B. K., “Soccer league competition algorithm: a novel meta-heuristic algorithm for optimal design of water distribution networks”, Swarm and Evolutionary Computation, Swarm and Evolutionary Computation, Vol. 17, (2014), 14–24.
  28. Moosavian, N., “Soccer league competition algorithm for solving knapsack problems”, Swarm and Evolutionary Computation, Vol. 20, (2015), 14-22.
  29. Jaramillo, A., Crawford, B., Soto, R. and Misra, S., “An Approach to Solve the Set Covering Problem with the Soccer League Competition Algorithm”, Computational Science and Its Applications – ICCSA 2016, Vol. 9786, (2016), 373-385.
  30. Goldberg, D. E., “Genetic Algorithms in Search, Optimization, and Machine Learning” , Mishigan, Addison-Wesley Publishing Company, (1989).
  31. Kirkpatrick, S., Gelatt, C. D. and Vecchi, M. P., “Optimization by Simulated Annealing”, Science, Vol. 220, No. 4595, (1983), 671-680.
  32. Dorigo, M., Maniezzo, V. and Colorni, A., “Ant system: optimization by a colony of cooperating agents”, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), Vol. 26, No. 1, (1996), 29-41.
  33. Geem, Z. W., Kim, H. and Loganathan, G. V., “A new heuristic optimization algorithm: harmony search”, Simulation, Vol. 76, No. 2, (2001), 60-68.
  34. Storn, R., “On the usage of differential evolution for function optimization”, Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS), (1996).
  35. Storn, R. and Price, K., “Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces”, Journal of Global Optimization, Vol. 11, (1997), 341-359.
  36. Kennedy, J. and Eberhart, R., “Particle Swarm Optimization”, Proceedings of IEEE International Conference on Neural Networks, (1995).
  37. Mirjalili, S., “A new hybrid PSOGSA algorithm for function optimization”, Computer and Information Application (ICCIA), Tianjin, (2010).
  38. Karaboga, D., “An idea based on honey bee swarm for numerical optimization”, Technical Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, (2005).
  39. Egea, J. A., Marti, R. and Banga, J. R., “An Evolutionary Method for Complex-process Optimization”, Computers and Operations Research, Vol. 37, No. 2, (2010), 315-324.
  40. Hansen, N., “The CMA Evolution Strategy: A Comparing Review”, Towards a New Evolutionary Computation, Vol. 192, Springer Berlin Heidelberg, (2006), 1769-1776.
  41. Guistolisi, O. and Moosavian, N., “Testing linear solvers for global gradient algorithm”, Journal of Hydroinformatics, Vol. 16, No. 5,  (2014), 1178-1193.
  42. Wu, S. and Chow, P., W., “Steady-state genetic algorithms for discrete optimization of trusses”, Computers & Structurs, Vol. 56, No. 6, (1995), 919-991.
  43. Hasançebia, O., Çarbaş, S., Doğan, E., Erdal, F. and Saka, M. P., “Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures”, Computers & Structures, Vol. 87, No. 5-6, (2009), 284-302.