Analysis Of The Convergence Of The Bat Algorithm

The bats algorithm(BA)is a new heuristic algorithm based on the echolocation of bats,which has been favored by many scholars in recent years.However,the BA also has some problems such as slow convergence,easy to fall into the local extremum under certain conditions.In addition,the theoretical analysis of the algorithm need to be further explored.In this paper,we analyze the convergence of BA by using Markov correlation theory and dynamic matrix correlation theory,then the learning strategies of improvement of algorithm convergence performance are given.The main research works are as follows:(1)In order to improve the convergence theory of the BA,several basic mathematical concepts of the algorithm were defined,and a Markov model were built.Further analysis of the global convergence criterion of stochastic optimization algorithms proved that the BA does not satisfy the convergence conditions.(2)In regard to the problem of slow convergence and accuracy in later stage,and poor optimization performance due to effect of the population,a new updating model of BA is defined by using the correlation theory of dynamic matrix.The dynamic parameter matrix is used to obtain the parameter selection region which makes the algorithm converge quickly in this mode.(3)In order to improve the convergence of the BA,and to overcome the shortcomings of easy to fall into local optimum and premature entry into the stagnation state,the paper introduced time-varying inertia weights into the update model of the BA.On the other hand,the paper introduced strategy of a dynamically varying inertia weight to improve the algorithm.In this paper,a theoretical analysis of the BA has been carried out and presented,which provides further strategies to improve the algorithm.Finally,the main results are summarized and further research topics are discussed.