A comparative study of metaheuristics algorithms based on their performance of complex benchmark problems

Tithli  Sadhu; Somanth  Chowdhury; Shubham Mondal; Jagannath Roy; Jitamanyu  Chakrabarty; Sandip Kumar  Lahiri

doi:10.31181/dmame0306102022r

Authors

Tithli Sadhu Department of Chemistry, National Institute of Technology Durgapur, West Bengal, India; Department of Biochemistry, School of Agriculture, SR University, Hanumakonda, Telangana, India https://orcid.org/0000-0003-3585-4666
Somanth Chowdhury Department of Chemical Engineering, National Institute of Technology Durgapur, West Bengal, India
Shubham Mondal Department of Computer Science and Engineering, Institute of Engineering and Management Kolkata, West Bengal, India
Jagannath Roy Department of Mathematics, National Institute of Technology Warangal, Telangana, India https://orcid.org/0000-0002-5252-5736
Jitamanyu Chakrabarty Department of Chemistry, National Institute of Technology Durgapur, West Bengal, India
Sandip Kumar Lahiri Department of Chemical Engineering, National Institute of Technology Durgapur, West Bengal, India

DOI:

https://doi.org/10.31181/dmame0306102022r

Keywords:

Metaheuristic, Algorithms, Optimization, Performance, Benchmark problems

Abstract

Metaheuristic approaches with extremely important improvements are very promising in the solution of intractable optimization problems. The objective of the present study is to test the capability of applications and compare the performance of the four selected algorithms from “classical” (simulated annealing (SA), genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE)) and “new generation” (firefly algorithm (FFA), krill herd (KH), grey wolf optimization (GWO), and symbiotic organism search (SOS)) each by solving selected benchmark problems that are used in the literature for algorithm testing purpose. The selected test problems had very complex objective functions and associated constraints with multiple local optima. Among all selected algorithms, the “new generation” SOS and KH algorithm successfully solved most of all the selected benchmark problems and achieved the best solution for most of them. Among four “classical” algorithms, DE, and PSO effectively attained the optimal solution which was very close to the best one. However, the “new generation” algorithm performed much better than the “classical” one. Therefore, no firm conclusion can be done about the universally best algorithm and their performance may be varied for different benchmark problems. However, in this study for the seven selected test problems, SOS and KH exhibited the most promising result and great potential with respect to execution time also. This study gives some insights to use SOS and KH as the best-performing algorithms to the novice user who can easily get lost in the plethora of large optimization algorithms.

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References

Adam, S. P., Alexandropoulos, S. A. N., Pardalos, P. M., & Vrahatis, M. N. (2019). No free lunch theorem: A review. In Demetriou, I., Pardalos, P. (Eds.), Approximation and Optimization. Springer Optimization and Its Applications (pp. 57–82). Springer, Cham.

Bai, Q. (2010). Analysis of particle swarm optimization algorithm. Computer and information science, 3(1), 180–184.

Banzhaf, W., Nordin, P., Keller, R. E., & Francone, F. D. (1998). Genetic programming: an introduction: on the automatic evolution of computer programs and its applications. (1st ed.). Morgan Kaufmann Publishers Inc, (Chapter 5).

Beheshti, Z., & Shamsuddin, S. M. H. (2013). A review of population-based meta-heuristic algorithms. International Journal of Advances in Soft Computing and its Applications, 5(1), 1–35.

Bolaji, A. L. A., Al-Betar, M. A., Awadallah, M. A., Khader, A. T., & Abualigah, L. M. (2016). A comprehensive review: Krill Herd algorithm (KH) and its applications. Applied Soft Computing, 49, 437–446.

Cheng, M. Y., & Prayogo, D. (2014). Symbiotic organisms search: a new metaheuristic optimization algorithm. Computers & Structures, 139, 98–112.

Das, S., Biswas, A., Dasgupta, S., & Abraham, A. (2009). Bacterial foraging optimization algorithm: theoretical foundations, analysis, and applications. In Abraham, A., Hassanien, AE., Siarry, P., Engelbrecht, A. (Eds.), Foundations of Computational Intelligence (pp. 23–55). Springer, Berlin, Heidelberg.

Deb, K. (2000). An efficient constraint handling method for genetic algorithms. Computer methods in applied mechanics and engineering, 186(2–4), 311-338.

Dokeroglu, T., Sevinc, E., Kucukyilmaz, T., & Cosar, A. (2019). A survey on new generation metaheuristic algorithms. Computers & Industrial Engineering, 137, 106040.

Dorigo, M., & Di Caro, G. (1999). Ant colony optimization: a new meta-heuristic, in Proceedings of the 1999 congress on evolutionary computation-CEC99. IEEE, 1470–1477.

Emary, E., Zawbaa, H. M., & Hassanien, A. E. (2016). Binary grey wolf optimization approaches for feature selection. Neurocomputing, 172, 371–381.

Enitan, A. M., & Adeyemo, J. (2011). Food processing optimization using evolutionary algorithms. African Journal of Biotechnology, 10(72), 16120–16127.

Floudas, C., Aggarwal, A., & Ciric, A. (1989). Global optimum search for nonconvex NLP and MINLP problems. Computers & Chemical Engineering, 13(10), 1117–1132.

Gandomi, A. H., & Alavi, A. H. (2012). Krill herd: a new bio-inspired optimization algorithm. Communications in nonlinear science and numerical simulation, 17(12), 4831–4845.

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

Glover, F., & Laguna, M. (1998). Tabu Search. In Du DZ., & Pardalos P.M. (Eds.), Handbook of Combinatorial Optimization (pp. 2093–2229). Springer, Boston, MA.

Goldberg, D.E. (1989). Genetic algorithms in search, Optimization, and Machine Learning. (1st ed.). Addison-Wesley Publishing Company, (Chapter 3).

Ho, Y. C., & Pepyne, D. L. (2001, December). Simple explanation of the no free lunch theorem of optimization, in Proceedings of the 40th IEEE Conference on Decision and Control. IEEE, 4409–4414.

Ho, Y. C., & Pepyne, D. L. (2002). Simple explanation of the no-free-lunch theorem and its implications. Journal of optimization theory and applications, 115(3), 549–570.

Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes university, engineering faculty, computer engineering department.

Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization, in Proceedings of ICNN'95-international conference on neural networks. IEEE, 1942–1948.

Kirkpatrick, S., Gelatt, C.D., & Vecchi, M.P. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680.

Kohli, M., & Arora, S. (2018). Chaotic grey wolf optimization algorithm for constrained optimization problems. Journal of computational design and engineering, 5(4), 458–472.

Lahiri, S. K., & Ghanta, K. C. (2009). Development of a hybrid artificial neural network and genetic algorithm model for regime identification of slurry transport in pipelines. Chemical Product and Process Modeling, 4(1), Article 22. DOI: 10.2202/1934-2659.1343.

Lahiri, S. K., & Ghanta, K. C. (2010). Artificial neural network model with parameter tuning assisted by genetic algorithm technique: study of critical velocity of slurry flow in pipeline. Asia‐Pacific Journal of Chemical Engineering, 5(5), 763–777.

Lahiri, S. K., Khalfe, N. M., & Wadhwa, S. K. (2012). Particle swarm optimization technique for the optimal design of shell and tube heat exchangers. Chemical Product and Process Modeling, 7(1), Article 14. DOI: 10.1515/1934-2659.1612.

Li, B., & Jiang, W. (1997). Chaos optimization method and its application. Control theory and application, 14(4), 613–615.

Marques-Silva, J. P., & Sakallah, K. A. (1999). GRASP: A search algorithm for propositional satisfiability. IEEE Transactions on Computers, 48(5), 506–521.

Michalewicz, Z. (1995). Genetic algorithms, numerical optimization, and constraints. In Eshelman, L. (Eds.), Proceedings of the Sixth International Conference on Genetic Algorithms (pp. 151–158). Morgan Kauffman, San Mateo.

Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in engineering software, 95, 51–67.

Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software, 69, 46–61.

Mirjalili, S., Saremi, S., Mirjalili, S. M., & Coelho, L. D. S. (2016). Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Systems with Applications, 47, 106–119.

Mittal, N., Singh, U., & Sohi, B. S. (2016). Modified grey wolf optimizer for global engineering optimization. Applied Computational Intelligence and Soft Computing, 2016, 7950348.

Mladenović, N., & Hansen, P. (1997). Variable neighborhood search. Computers & operations research, 24(11), 1097–1100.

Niu, P., Niu, S., & Chang, L. (2019). The defect of the Grey Wolf optimization algorithm and its verification method. Knowledge-Based Systems, 171, 37–43.

Qin, H., Fan, P., Tang, H., Huang, P., Fang, B., & Pan, S. (2019). An effective hybrid discrete grey wolf optimizer for the casting production scheduling problem with multi-objective and multi-constraint. Computers & Industrial Engineering, 128, 458–476.

Rangaiah, G.P. (2010). Stochastic Global Optimization: Techniques and Applications in Chemical Engineering. (1st ed.). World Scientific, (Chapter 3).

Rao, S. S. (2019). Engineering optimization: theory and practice. (5th ed.). Wiley, (Chapter 13).

Shopova, E. G., & Vaklieva-Bancheva, N. G. (2006). BASIC- a genetic algorithm for engineering problems solution. Computers and Chemical Engineering, 30(8), 1293–1309.

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.

Summanwar, V., Jayaraman, V., Kulkarni, B., Kusumakar, H., Gupta, K., & Rajesh, J. (2002). Solution of constrained optimization problems by multi-objective genetic algorithm. Computers & Chemical Engineering, 26(10), 1481–1492.

Wang, F. S., & Chen, L. H. (2013). Heuristic optimization. In Dubitzky, W., Wolkenhauer, O., Cho, KH., Yokota, H. (Eds.), Encyclopedia of Systems Biology (pp. 885–885). Springer, New York.

Wolpert, D. H., & Macready, W. G. (1997). No free lunch theorems for optimization. IEEE transactions on evolutionary computation, 1(1), 67–82.

Yang, X. S. (2010a). Firefly algorithm, stochastic test functions and design optimisation. International journal of bio-inspired computation, 2(2), 78–84.

Yang, X. S. (2010b). A new metaheuristic bat-inspired algorithm. In González J.R., Pelta D.A., Cruz C., Terrazas G., & Krasnogor N. (Eds.), Nature Inspired Cooperative Strategies for Optimization (NICSO 2010) (pp. 65–74). Springer, Berlin, Heidelberg.

Yang, X. S., & Deb, S. (2009). Cuckoo search via Lévy flights, in 2009 World congress on nature & biologically inspired computing (NaBIC). IEEE, 210–214.