Comparative assessment of five metaheuristic methods on distinct problems

Öz

Metaheuristic algorithms belong to the non-gradient based optimization methods. Accomplished studies in this area reveal that each of these methods mostly has its own affirmative and inconvenient aspects. So that, one might provide a high level of exploration while the other can perform a great level of exploitation. Thus, selecting the proper and efficient algorithm for a problem can highly affect both the convergence rate and the accuracy level. There are several different metaheuristic algorithms have been announced in the technical literature in the last decade. Therefore, performing an objective comparative assessment over some of these methods can provide a fundamental and fair attitude for researchers either to select an algorithm which is more fitted with their target(s) or to develop even more efficient methods. So, the current investigation deals with evaluating and comparing of five different metaheuristic techniques emerged from ten years ago up to now. The selected methods can be sorted chronologically as Firefly Algorithm (FA), Teaching and Learning Based Algorithm (TLBO), Drosophila Food Search (DSO) method, Ions Motion Optimization (IMO) and Butterfly Optimization Algorithm (BOA). Different properties of these algorithms as convergence rate, diversity variation, complexity and accuracy level of the final solutions are compared on both constrained and non-constrained optimization problems include mathematical functions, mechanical and structural problems. The results show that the cited methods show different performance depending on the type of the optimization problem but overally BOA and TLBO outperform the other algorithms on non-constrained and constrained problems, respectively.

Anahtar Kelimeler

• Optimization techniques,Metaheuristic algorithms,Constrained optimization problems

Kaynakça

1. AISC, (1989). American Institute of Steel Construction (AISC). Manual of steel construction allowable stress design. 9th ed. Chicago, IL, 1-360.
2. Arora, S., Singh, S., (2019). Butterfly optimization algorithm: a novel approach for global optimization, Soft Computing,23,3, 715-734.
3. Camp, C.V., Farshchin, M., (2014). Design of space trusses using modified teaching–learning based optimization, Engineering Structures,62–63, 87-97.
4. Das, K.N., Singh, T.K., (2014). Drosophila Food-Search Optimization, Applied Mathematics and Computation,231, 566-580.
5. Degertekin, S.O., Hayalioglu, M.S., (2013). Sizing truss structures using teaching-learning-based optimization, Computers & Structures,119, 177-188.
6. Eker, M.K., Karadeniz, A., (2016). Rüzgar Ve Termik Santrallerden Oluşan Enerji Sistemlerinde Ekonomik Güç Dağılımının Big-Bang Big-Crunch, PSO ve IMO Algoritmaları İile İrdelenmesi, Politeknik Dergisi,19,3.
7. Hasançebi, O., Çarbaş, S., Doğan, E., Erdal, F., Saka, M.P., (2010). Comparison of non-deterministic search techniques in the optimum design of real size steel frames, Computers & Structures,88,17–18, 1033-1048.
8. Javidy, B., Hatamlou, A., Mirjalili, S., (2015). Ions motion algorithm for solving optimization problems, Applied Soft Computing,32, 72-79.

9. Kaveh, A., Zolghadr, A., (2014). Democratic PSO for truss layout and size optimization with frequency constraints, Computers & Structures,130, 10-21.
10. Kennedy, J., Eberhart, R., 1995. Particle swarm optimization, Neural Networks, 1995. Proceedings., IEEE International Conference on. pp. 1942-1948 vol.1944.
11. Lieu, Q.X., Do, D.T.T., Lee, J., (2018). An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints, Computers & Structures,195, 99-112.
12. Lim, W.H., Mat Isa, N.A., (2013). Two-layer particle swarm optimization with intelligent division of labor, Engineering Applications of Artificial Intelligence,26,10, 2327-2348.
13. Lim, W.H., Mat Isa, N.A., (2014). Teaching and peer-learning particle swarm optimization, Applied Soft Computing,18, 39-58.
14. Miguel, L.F.F., Lopez, R.H., Miguel, L.F.F., (2013). Multimodal size, shape, and topology optimisation of truss structures using the Firefly algorithm, Advances in Engineering Software,56, 23-37.
15. Moloodpoor, M., Mortazavi, A., Ozbalta, N., (2019). Thermal analysis of parabolic trough collectors via a swarm intelligence optimizer, Solar Energy,181, 264-275.
16. Mortazavi, A., (2019). Interactive fuzzy search algorithm: A new self-adaptive hybrid optimization algorithm, Engineering Applications of Artificial Intelligence,81, 270-282.
17. Mortazavi, A., Toğan, V., (2017). Triangular units based method for simultaneous optimizations of planar trusses, Advances in Computational Design,2,3, 195-210.
18. Mortazavi, A., Togan, V., Daloğlu, A., Nuhoglu, A., 2016. Simultaneous topology and sizing optimization of trusses with two different optimization algorithms, 12th International Congress on Advances in Civil Engineering. Istanbul, Turkey.
19. Mortazavi, A., Toğan, V., Moloodpoor, M., (2019). Solution of structural and mathematical optimization problems using a new hybrid swarm intelligence optimization algorithm, Advances in Engineering Software,127, 106-123.
20. Mortazavi, A., Toğan, V., Nuhoğlu, A., (2017a). An integrated particle swarm optimizer for optimization of truss structures with discrete variables, Structural Engineering and Mechanics,61, 359-370.
21. Mortazavi, A., Toğan, V., Nuhoğlu, A., (2017b). Weight minimization of truss structures with sizing and layout variables using integrated particle swarm optimizer AU - Mortazavi, Ali, Journal of Civil Engineering and Management,23,8, 985-1001.
22. Rao, R.V., Savsani, V.J., Vakharia, D.P., (2011). Teaching–learning-based optimization: A novel method for constrained mechanical design optimization problems, Computer-Aided Design,43,3, 303-315.
23. Rao, R.V., Waghmare, G.G., (2014). Complex constrained design optimisation using an elitist teaching-learning-based optimisation algorithm, International Journal of Metaheuristics,3,1, 81-102.
24. Ray, T., Liew, K.M., (2003). Society and civilization: An optimization algorithm based on the simulation of social behavior, IEEE Transactions on Evolutionary Computation,7,4, 386-396.
25. Storn, R., Price, K., (1997). Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces, Journal of Global Optimization,11,4, 341-359.
26. Suganthan, P.N., Hansen, N., Liang, J.J., Deb, K., Chen, Y., Auger, A., Tiwari, S., (2005). Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization, Technical Report, Nanyang Technological University, Singapore, May 2005 AND KanGAL Report 2005005, IIT Kanpur, India.
27. Toğan, V., (2012). Design of planar steel frames using Teaching–Learning Based Optimization, Engineering Structures,34, 225-232.
28. Toğan, V., Mortazavi, A., (2017). Sizing optimization of skeletal structures using teaching-learning based optimization, Optimization and Control: Theories Applications,7,2, 12.
29. Yang, X.-S., 2009. Firefly Algorithms for Multimodal Optimization, in: Watanabe, O., Zeugmann, T. (Eds.), Stochastic Algorithms: Foundations and Applications. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 169-178.
30. Yuhui, S., Eberhart, R.C., 2001. Fuzzy adaptive particle swarm optimization, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546). pp. 101-106 vol. 101.