Design of a new meta-heuristic algorithm based on the behavior of mathematical functions xCos(x) and tanh(x)

Document Type : Original Article


1 Ph.D., Shahid Beheshti University.

2 Associate Professor, Shahid Beheshti University.


Today, the use of meta-heuristic methods to obtain satisfying responses in compound optimization has grown dramatically. Due to the approach of problems to real-world situations due to the increasing complexity of the problems and the inability of current mathematical methods to provide optimal points with reasonable resources, this has intensified. The development of meta-heuristic methods is usually done by exploring the nature of optimization and its inspiration, including the ant algorithm and refrigeration simulation. The proposed algorithm of this paper is developed by investigating the interesting behavior of two functions x(Cos)(x) and tanh(x) in iterative loops and presents a method for finding neighborhoods in continuous functions that resembles the optimization algorithm. Refrigeration Modeling and Cloud Theory Based Refrigeration Simulation Algorithm performs better in terms of accuracy and speed. The superiority of the proposed algorithm to the two mentioned algorithms was proved by comparing the performance of these algorithms to find the optimal point (points) of seven known continuous functions.


1. Blum, C., & Roli, A. (2003). Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Comput. Surv., 35(3), 268-308. doi: 10.1145/937503.937505
2. Blum, C., & Roli, A. (2008). Hybrid Metaheuristics: An Introduction. In C. Blum, M. J. e. B. Aguilera, A. Roli & M. Sampels (Eds.), Hybrid Metaheuristics (pp. 1-30). Berlin: Springer-Verlag.
3. Borenstein, Y., & Poli, R. (2006). Structure and metaheuristics. Paper presented at the Proceedings of the 8th annual conference on Genetic and evolutionary computation, Seattle, Washington, USA.
4. Burke, E. K., & Kendall, G. (2005). Introduction. In E. K. Burke & G. Kendall (Eds.), Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques (pp. 5-18). New York: Springer.
5. Ferland, J. A., Hertz, A., & Lavoie, A. (1996). An Object-Oriented Methodology for Solving Assignment-Type Problems with Neighborhood Search Techniques. Operations Research, 44(2), 347-359.
6. Gonzalez, T. F. (2007). Basic Methodologies. In T. F. Gonzalez (Ed.), Handbook of Approximation Algorithms and Metaheuristics (pp. 1.1-1.17). Boca Raton, FL, USA: Chapman and Hall/CRC.
7. Hendrix, E. M. T., & G.-Tóth, B. (2010). Goodness of optimization algorithms Introduction to Nonlinear and Global Optimization (Vol. 37, pp. 67-90): Springer New York.
8. Liu, J. (1999). The impact of neighbourhood size on the process of simulated annealing: Computational experiments on the flowshop scheduling problem. [doi: DOI: 10.1016/S0360-8352(99)00075-3]. Computers & Industrial Engineering, 37(1-2), 285-288.
9. LV, P., Yuan, L., & Zhang, J. (2009). Cloud theory-based simulated annealing algorithm and application. Engineering Applications of Artificial Intelligence, 22, 742–749.
10. Metaheuristics. (2011), 2011, from
12. Wang, X. (2010). Solving Six-Hump Camel Back Function Optimization Problem by Using Thermodynamics Evolutionary Algorithm.
13. Weise, T. (2007). Global Optimization Algorithm: Theory and Application
14. Xin, Y. (1991). Simulated Annealing with Extended Neighborhood. International Journal of Computer Mathematics, 40(3-4), 169-189.