Abstract
Metaheuristics play a major role in the important domain of global optimization. Since they are problem independent, they can be effectively used in constrained and higher-dimension problems and in real-world applications also. In this paper, one novel two-phase trigonometric algorithm is presented to obtain optimal/ near-optimal solutions for different optimization problems. In this work, the main focus is given to solving real-world engineering problems with constraints. The proposed algorithm effectively explores and exploits the search space to arrive at the solutions. Benchmarks analyzed include unconstrained (unimodal and multimodal) functions, constrained special functions, constrained engineering problems and ten problems of the "100 digit challenge", Institute of Electrical and Electronics Engineers (IEEE) Congress on Evolutionary Computation (CEC2019) totaling fifty-nine problem instances. The problems include functions with continuous variables, discrete variables and both continuous and discrete variables. They are all single-objective functions that are suitably modelled and simulated in MATLAB environment. The obtained results are compared with recent and time-tested popular algorithms including Differential Evolution (DE), Improved Teaching–Learning-Based Optimization (ITLBO), Social Network Search (SNS), Firefly Algorithm (FA), Cuckoo Search (CS) and Whale Optimization Algorithm (WOA). Analyses of the results obtained from TP-AB against the performance of the well-known algorithms indicate the superiority and competitiveness of the proposed algorithm in providing quality solutions.
Similar content being viewed by others
Data availability
The codes used in this paper are not available online and can be provided to potential researchers on request.
References
Abualigah, L., Diabat, A., Mirjalili, S., AbdElaziz, M., & Gandomi, A. H. (2021). The arithmetic optimization algorithm. Computer Methods in Applied Mechanics and Engineering, 376, 113609.
Azizi, M., Talatahari, S., & Giaralis, A. (2021). Optimization of engineering design problems using atomic orbital search algorithm. IEEE Access, 9, 102497–102519.
Baskar, A. (2022a). Sine (B): A single randomized population-based algorithm for solving optimization problems. In Materials today: Proceedings
Baskar, A. (2022b). New simple trigonometric algorithms for solving optimization problems. Journal of Applied Science and Engineering, 25(6), 1105–1120.
Bayzidi, H., Talatahari, S., Saraee, M., & Lamarche, C. P. (2021). Social network search for solving engineering optimization problems. In Computational Intelligence and Neuroscience (2021).
Deb, K., & Goyal, M. (1997, July). Optimizing engineering designs using a combined genetic search. In ICGA (pp. 521–528).
Deb, K. (2000). An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 186(2–4), 311–338.
Dehghani, M., Hubálovský, Š, & Trojovský, P. (2022). A new optimization algorithm based on average and subtraction of the best and worst members of the population for solving various optimization problems. PeerJ Computer Science, 8, e910.
Dhadwal, M. K., Jung, S. N., & Kim, C. J. (2014). Advanced particle swarm assisted genetic algorithm for constrained optimization problems. Computational Optimization and Applications, 58, 781–806.
Eskandar, H., Sadollah, A., Bahreininejad, A., & Hamdi, M. (2012). Water cycle algorithm—A novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & Structures, 110, 151–166.
Fesanghary, M., Mahdavi, M., Minary-Jolandan, M., & Alizadeh, Y. (2008). Hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems. Computer Methods in Applied Mechanics and Engineering, 197(33–40), 3080–3091.
Gandomi, A. H., Yang, X. S., & Alavi, A. H. (2011). Mixed variable structural optimization using firefly algorithm. Computers & Structures, 89(23–24), 2325–2336.
Himmelblau, D. M. (1972). Applied nonlinear programming. New York: McGraw-Hill Book Company.
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, 549–570.
Holland, J. H. (1992). Genetic Algorithms. Scientific American, 267(1), 66–73.
https://in.mathworks.com/help/gads/solving-a-mixed-integer-engineering-design-problem-using-the-genetic-algorithm.html. Accessed on 11 Nov. 2022
Hu, X., Eberhart, R. C., & Shi, Y. (2003, April). Engineering optimization with particle swarm. In Proceedings of the 2003 IEEE swarm intelligence symposium. SIS'03 (Cat. No. 03EX706) (pp. 53–57). IEEE.
Hu, G., Yang, R., Qin, X., & Wei, G. (2023). MCSA: Multi-strategy boosted chameleon-inspired optimization algorithm for engineering applications. Computer Methods in Applied Mechanics and Engineering, 403, 115676.
Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization (Vol. 200, pp. 1–10). Technical report-tr06, Erciyes university, engineering faculty, computer engineering department.
Kaveh, A., & Eslamlou, A. D. (2020, June). Water strider algorithm: A new metaheuristic and applications. In Structures (Vol. 25, pp. 520–541). Elsevier.
Kennedy, J., & Eberhart, R. (1995, November). Particle swarm optimization. In Proceedings of ICNN'95-international conference on neural networks (Vol. 4, pp. 1942–1948). IEEE
Kuri-Morales, A. F., & Gutiérrez-García, J. (2002). Penalty function methods for constrained optimization with genetic algorithms: A statistical analysis. In A. de Albornoz, L. E. Sucar, & O. C. Battistutti (Eds.), CA Coello Coello (pp. 108–117). Mexican international conference on artificial intelligence. Berlin: Springer.
Long, W., Wu, T., Liang, X., & Xu, S. (2019). Solving high-dimensional global optimization problems using an improved sine cosine algorithm. Expert Systems with Applications, 123, 108–126.
Mehta, V. K., & Dasgupta, B. (2012). A constrained optimization algorithm based on the simplex search method. Engineering Optimization, 44(5), 537–550.
MiarNaeimi, F., Azizyan, G., & Rashki, M. (2018). Multi-level cross entropy optimizer (MCEO): An evolutionary optimization algorithm for engineering problems. Engineering with Computers, 34(4), 719–739.
Mirjalili, S. (2016). SCA: A sine cosine algorithm for solving optimization problems. Knowledge-Based Systems, 96, 120–133.
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.
Mohammed, H. M., Umar, S. U., & Rashid, T. A. (2019). A systematic and meta-analysis survey of whale optimization algorithm. Computational Intelligence and Neuroscience, 2019.
Mohammed, H., & Rashid, T. (2020). A novel hybrid GWO with WOA for global numerical optimization and solving pressure vessel design. Neural Computing and Applications, 32(18), 14701–14718.
Price, K. V., Awad, N. H., Ali, M. Z., & Suganthan, P. N. (2018). The 100-digit challenge: Problem definitions and evaluation criteria for the 100-digit challenge special session and competition on single objective numerical optimization. Nanyang: Nanyang Technological University.
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.
Rashedi, E., Nezamabadi-Pour, H., & Saryazdi, S. (2009). GSA: A gravitational search algorithm. Information Sciences, 179(13), 2232–2248.
Sarhani, M., Voß, S., & Jovanovic, R. (2023). Initialization of metaheuristics: Comprehensive review, critical analysis, and research directions. International Transactions in Operational Research, 30(6), 3361–3397.
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.
Talatahari, S., & Azizi, M. (2020). Optimization of constrained mathematical and engineering design problems using chaos game optimization. Computers & Industrial Engineering, 145, 106560.
Wang, X., Haynes, R. D., He, Y., & Feng, Q. (2019). Well control optimization using derivative-free algorithms and a multiscale approach. Computers & Chemical Engineering, 123, 12–33.
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., & Deb, S. (2010). Engineering optimisation by cuckoo search. International Journal of Mathematical Modelling and Numerical Optimisation, 1(4), 330–343.
Yeniay, Ö. (2005). Penalty function methods for constrained optimization with genetic algorithms. Mathematical and Computational Applications, 10(1), 45–56.
Yu, K., Wang, X., & Wang, Z. (2016). An improved teaching–learning-based optimization algorithm for numerical and engineering optimization problems. Journal of Intelligent Manufacturing, 27(4), 831–843.
Zhu, G., & Kwong, S. (2010). Gbest-guided artificial bee colony algorithm for numerical function optimization. Applied Mathematics and Computation, 217(7), 3166–3173.
Acknowledgements
The authors are grateful to the Editor and the anonymous reviewers for their constructive comments and suggestions to improve the quality and presentation of this paper.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
A. Baskar, M. Anthony Xavior and P. Jeyapandiarajan declares that they have no conflict of interests. Andre Batako is one of the ISPEM Conference Co-Chairs. Anna Burduk is the ISPEM Conference Chair.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Baskar, A., Xavior, M.A., Jeyapandiarajan, P. et al. A novel two-phase trigonometric algorithm for solving global optimization problems. Ann Oper Res (2024). https://doi.org/10.1007/s10479-024-05837-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10479-024-05837-5