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

Abstract

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.

Keywords

• meta-heuristic
• neighborhood search
• continuous optimization
• simulated annealing