Viscous gravitational algorithm for ptimization

Abstract

Optimization is one of the most important tools for controlling systems of various nature. Along with the optimization problems that have become classic in decision making and control of technical systems, the search for the extremum of a function is an important tool for machine learning. The role of effective optimization algorithms is especially significant in solving dynamic problems, when the solution must be found in real time. At the same time, the problem of fast numerical optimization has not yet received a universal solution and requires additional development and improved approaches. The paper proposes a new optimization method based on a modification of the gravity search algorithm. It uses an analogy with the gravitational attraction of masses depending on the value of the objective function. The disadvantage of conventional gravitational search is the manifestation of inertia effects during its operation, which complicate the optimization process. To improve the performance of the algorithm, we proposed to use the model of viscous motion of effective particles. The basic equations describing the operation of the presented modification of the gravitational search are discussed. The viscous gravity search algorithm is described and its implementation in pseudocode is given. The features of the algorithm operation are analyzed on the examples of Rastrigin and Schwefel reference objective functions with many local minima in comparison with the genetic algorithm and the standard gravity search algorithm using programs implemented in the Python language. We have studied the speed of work and the accuracy of determining the minimum of functions with a different number of variables by a viscous gravitational algorithm. The results obtained allow us to conclude that the viscous gravity search is highly efficient and that it is expedient to apply it to solving multidimensional optimization problems.