On the utility of the population size for inversely fitness proportional mutation rates

Abstract

Artificial Immune Systems (AIS) are an emerging new field of research in Computational Intelligence that are used in many areas of application, e. g. optimization, anomaly detection and classification. For optimization tasks usually hypermutation operators are used. In this paper, we show that the use of populations can be essential for the utility of such operators by analyzing the runtime of a simple population-based immune inspired algorithm on a classical example problem. The runtime bounds we prove are tight for the problem at hand. Moreover, we derive some general characteristics of the considered mutation operator as well as properties of the population, which hold for a class of pseudo-Boolean functions.