A new convergence rate estimation of general artificial immune algorithm

Abstract

Artificial immune algorithm has been used widely and successfully in many computational optimization areas, but the theoretical research exploring the convergence rate characteristics of artificial immune algorithm is yet inadequate. In this paper, instead of the traditional eigenvalue estimation of state transition matrix, stochastic processes theory is introduced to study the convergence rate of general artificial immune algorithm. The method begins by analyzing the necessary condition for convergence of artificial immune algorithm and takes it as the sufficient condition for a class of general artificial immune algorithm. Through the definition of Markov chain convergence rate, a probability strong convergence rate estimation method of general artificial immune algorithm is proposed. This method is judged by the final convergence of the best antibody, which overcomes the conservative defect of traditional estimation methods. The simulation results show the correctness of the proposed estimation method, and the estimation method can be used to judge the convergence and convergence rate of a class of artificial immune algorithms. This research has a certain theoretical reference value to optimize the convergence rate in the practical application of artificial immune algorithm.