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

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.

[1]  Carsten Witt,et al.  Runtime Analysis of the ( + 1) EA on Simple Pseudo-Boolean Functions , 2006, Evolutionary Computation.

[2]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[3]  Tobias Storch,et al.  On the Choice of the Population Size , 2004, GECCO.

[4]  F. Burnet.  The clonal selection theory of acquired immunity , 1959 .

[5]  Carsten Witt,et al.  Runtime Analysis of the ( μ +1) EA on Simple Pseudo-Boolean Functions , 2006 .

[6]  Carlos A. Coello Coello,et al.  Convergence Analysis of a Multiobjective Artificial Immune System Algorithm , 2004, ICARIS.

[7]  Carsten Witt,et al.  Population size versus runtime of a simple evolutionary algorithm , 2008, Theor. Comput. Sci..

[8]  Christine Zarges,et al.  Rigorous Runtime Analysis of Inversely Fitness Proportional Mutation Rates , 2008, PPSN.

[9]  Jonathan Timmis,et al.  A Markov Chain Model of the B-Cell Algorithm , 2005, ICARIS.

[10]  Vincenzo Cutello,et al.  Exploring the Capability of Immune Algorithms: A Characterization of Hypermutation Operators , 2004, ICARIS.

[11]  Jonathan Timmis,et al.  Immune Inspired Somatic Contiguous Hypermutation for Function Optimisation , 2003, GECCO.

[12]  Thomas Jansen,et al.  A comparison of simulated annealing with a simple evolutionary algorithm on pseudo-boolean functions of unitation , 2007, Theor. Comput. Sci..

[13]  D. Dasgupta.  Artificial Immune Systems and Their Applications , 1998, Springer Berlin Heidelberg.

[14]  F. Azuaje.  Artificial Immune Systems: A New Computational Intelligence Approach , 2003 .

[15]  Torben Hagerup,et al.  A Guided Tour of Chernoff Bounds , 1990, Inf. Process. Lett..

[16]  Fernando José Von Zuben,et al.  Learning and optimization using the clonal selection principle , 2002, IEEE Trans. Evol. Comput..

[17]  Carlos A. Coello Coello,et al.  Multiobjective Optimization Using Ideas from the Clonal Selection Principle , 2003, GECCO.

[18]  Jonathan Timmis,et al.  Artificial immune systems - a new computational intelligence paradigm , 2002 .

[19]  Jonathan Timmis,et al.  Theoretical advances in artificial immune systems , 2008, Theor. Comput. Sci..

[20]  Thomas Jansen.  On the utility of populations , 2004 .

[21]  Pietro Simone Oliveto,et al.  On the Convergence of Immune Algorithms , 2007, 2007 IEEE Symposium on Foundations of Computational Intelligence.