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.
- F. M. Burnet. The Clonal Selection Theory of Acquired Immunity. Cambridge University Press, 1959.Google ScholarCross Ref
- E. Clark, A. Hone, and J. Timmis. A Markov chain model of the b-cell algorithm. In International Conference on Artificial Immune Systems (ICARIS), pages 318--330. Springer, 2005. Google ScholarDigital Library
- N. C. Cortés and C. A. C. Coello. Multiobjective optimization using ideas from the clonal selection principle. In Genetic and Evolutionary Computation Conference (GECCO), pages 158--170. Springer, 2003. Google ScholarDigital Library
- V. Cutello, G. Nicosia, and M. Pavone. Exploring the capability of immune algorithms: A characterization of hypermutation operators. In International Conference on Artificial Immune Systems (ICARIS), pages 263--276. Springer, 2004.Google ScholarCross Ref
- V. Cutello, G. Nicosia, M. Romeo, and P. S. Oliveto. On the convergence of immune algorithms. In IEEE Symposium on Foundations of Computational Intelligence (FOCI), pages 409--415. IEEE Press, 2007.Google ScholarCross Ref
- D. Dasgupta. Artificial Immune Systems and Their Applications. Springer, 1998. Google ScholarDigital Library
- L. N. de Castro and J. Timmis. Artificial Immune Systems: A New Computational Intelligence Approach. Springer, 2002. Google ScholarDigital Library
- L. N. de Castro and F. J. V. Zuben. Learning and optimization using the clonal selection principle. IEEE Transactions on Evolutionary Computation, 6(3):239--251, 2002. Google ScholarDigital Library
- S. Droste, T. Jansen, and I. Wegener. On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science, 276(1-2):51--81, 2002. Google ScholarDigital Library
- T. Hagerup and C. Rüb. A guided tour of Chernoff bounds. Information Processing Letters, 33(6):305--308, 1990. Google ScholarDigital Library
- T. Jansen and I. Wegener. On the utility of populations. In Genetic and Evolutionary Computation Conference (GECCO), pages 1034--1041. Morgan Kaufmann, 2001.Google Scholar
- T. Jansen and I. Wegener. A comparison of simulated annealing with a simple evolutionary algorithm on pseudo-Boolean functions of unitation. Theoretical Computer Science, 386(1-2):73--93, 2007. Google ScholarDigital Library
- J. Kelsey and J. Timmis. Immune inspired somatic contiguous hypermutation for function optimisation. In Genetic and Evolutionary Computation Conference (GECCO), pages 207--218. Springer, 2003. Google ScholarDigital Library
- T. Storch. On the choice of the population size. In Genetic and Evolutionary Computation Conference (GECCO), pages 748--760. Springer, 2004.Google ScholarCross Ref
- J. Timmis, A. Hone, T. Stibor, and E. Clark. Theoretical advances in artificial immune systems. Theoretical Computer Science, 403(1):11--32, 2008. Google ScholarDigital Library
- M. Villalobos-Arias, C. A. C. Coello, and O. Hernández-Lerma. Convergence analysis of a multiobjective artificial immune system algorithm. In International Conference on Artificial Immune Systems (ICARIS), pages 226--235. Springer, 2004.Google ScholarCross Ref
- C. Witt. Runtime analysis of the (µ+1) EA on simple pseudo-Boolean functions. Evolutionary Computation, 14(1):65--86, 2006. Google ScholarDigital Library
- C. Witt. Population size versus runtime of a simple evolutionary algorithm. Theoretical Computer Science, 403(1):104--120, 2008. Google ScholarDigital Library
- C. Zarges. Rigorous runtime analysis of inversely fitness proportional mutation rates. In International Conference on Parallel Problem Solving from Nature (PPSN), pages 112--122. Springer, 2008.Google ScholarCross Ref
Index Terms
- On the utility of the population size for inversely fitness proportional mutation rates
Recommendations
The choice of the offspring population size in the (1,λ) EA
GECCO '12: Proceedings of the 14th annual conference on Genetic and evolutionary computationWe extend the theory of non-elitist evolutionary algorithms (EAs) by considering the offspring population size in the (1,λ) EA. We establish a sharp threshold at λ = log{\frac{e}{e-1}} n ≈5 log10 n between exponential and polynomial running times on ...
The choice of the offspring population size in the (1,λ) evolutionary algorithm
We extend the theory of non-elitist evolutionary algorithms (EAs) by considering the offspring population size in the (1,@l) EA. We establish a sharp threshold at @l=log"e"e"-"1n~5log"1"0n between exponential and polynomial running times on OneMax. For ...
Population size versus runtime of a simple evolutionary algorithm
Evolutionary algorithms (EAs) find numerous applications, and practical knowledge on EAs is immense. In practice, sophisticated population-based EAs employing selection, mutation and crossover are applied. In contrast, theoretical analysis of EAs often ...
Comments