Convergence Analysis Of Gravitational Search Algorithm Based On Markov Chain

Gravitational Search Algorithm(GSA)is a heuristic optimization algorithm that has been widely used in various fields of numerical optimization problems.In order to overcome the limitations of the standard gravitational search algorithm,scholars have proposed many improved gravitational search algorithms to effectively solve the problem of the standard gravitational search algorithm being too early.And the improved gravitational search algorithm was applied to real life and good results were obtained.However,there are few studies on the theoretical analysis of gravitational search algorithm.This paper focuses on the convergence problem of gravitational search algorithm.The specific work is as follows:1.Convergence analysis of gravitational search algorithm based on markov chain.In this paper,the particle state space and sample space are defined,the Markov chain nature of the state sequence is analyzed,and the state transition probability is estimated.Based on the properties of Markov chain,it is proved that the standard GSA algorithm converges to the optimal solution with probability 1 under certain conditions.2.Aiming at the shortcomings of the gravitational search algorithm,such as low precision and easy precocity,an improved gravitational search algorithm was proposed.In order to balance the development and exploration capabilities of the algorithm,we introduce two mutation operators: one operator enhances the ability to develop the algorithm;the other operator enhances the ability to explore the algorithm.Finally,13 standard test functions were used to compare the improved gravitational search algorithm with the standard GSA algorithm and other intelligent optimization algorithms.Experimental results show that the proposed algorithm has better performance in solving nonlinear function optimization problems.