On the Convergence of Immune Algorithms

Abstract — Immune Algorithms have been used widely and successfully in many computational intelligence areas including optimization. Given the large number of variants of each operator of this class of algorithms, this paper presents a study of the convergence properties of Immune Algorithms in general, conducted by examining conditions which are sufficient to prove their convergence to the global optimum of an optimization problem. Furthermore problem independent upper bounds for the number of generations required to guarantee that the solution is found with a defined probability are derived in a similar manner as performed previously, in literature, for genetic algorithms. Again the independence of the function to be optimised leads to an upper bound which is not of practical interest, confirming the general idea that when deriving time bounds for Evolutionary Algorithms the problem class to be optimised needs to be considered. I