A Meta-heuristic Algorithm for Global Numerical Optimization Problems inspired by Vortex in fluid physics

One of the most important issues in engineering is to find the optimal global points of the functions used. It is not easy to find such a point in some functions due to the reasons such as large number of dimensions or inability to derive them from the function. Also in engineering modeling, we do not have the relationships of many functions, but we can input and output them as a black box. Therefore, the meta-heuristic algorithms are presented. In this paper, a meta-heuristic algorithm based on the behavior of vortices in fluid physics is presented. Technically, the algorithm is made up of vortices. Each vortex contains some particles. The particles move by the presented rotation matrix. This movement causes the local search. Also by selecting another vortex through the selection algorithm, each vortex attempts to escape the local optima and reach the global optima. The algorithm will explore and exploit the given function using its operators. Another innovation of this paper is the introduction of two new evaluation criteria for optimization algorithms. These two criteria show the behavior and convergence of algorithms along the way to reach the global optimal point or fall into the local optima. The proposed algorithm has been implemented, evaluated and compared with the numerical optimization state of the art algorithms. It was observed that the proposed method was able to achieve better results than most of the other methods in the major of twenty-four standard functions in different dimensions.  (All codes available at http://web.nit.ac.ir/ h.omranpour/.).