Abstract
Artificial immune systems can be applied to a variety of very different tasks including classical function optimization. There are even artificial immune systems tailored specifically for this task. In spite of the successful application there is little knowledge and hardly any theoretical investigation about how and why they perform well. Here a rigorous analysis for a specific type of mutation operator introduced for function optimization called somatic contiguous hypermutation is presented. While there are serious limitations to the performance of this operator even for simple optimization tasks it is proven that for some types of optimization problems it performs much better than standard bit mutations most often used in evolutionary algorithms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aarts, E., Lenstra, J.K. (eds.): Local Search in Combinatorial Optimization. Princeton University Press, Princeton (2003)
Bull, P., Knowles, A., Tedesco, G., Hone, A.: Diophantine benchmarks for the B-cell algorithm. In: Bersini, H., Caarneiro, J. (eds.) ICARIS 2006. LNCS, vol. 4163, pp. 267–279. Springer, Heidelberg (2006)
Burnet, F.M.: The Clonal Selection Theory of Acquired Immunity. Cambridge University Press, Cambridge (1959)
Clark, E., Hone, A., Timmis, J.: A Markov chain model of the b-cell algorithm. In: Jacob, C., et al. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 318–330. Springer, Heidelberg (2005)
Cortés, N.C., Coello, C.A.C.: Multiobjective optimization using ideas from the clonal selection principle. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 158–170. Springer, Heidelberg (2003)
Cutello, V., Nicosia, G., Pavone, M.: Exploring the capability of immune algorithms: A characterization of hypermutation operators. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 263–276. Springer, Heidelberg (2004)
Dasgupta, D., Niño, L.F.: Immunological Computation: Theory and Applications. Auerbach (2008)
de Castro, L.N., Timmis, J.: Artificial Immune Systems: A New Computational Intelligence Approach. Springer, Heidelberg (2002)
de Castro, L.N., Zuben, F.J.V.: Learning and optimization using the clonal selection principle. IEEE Trans. on Evolutionary Computation 6(3), 239–251 (2002)
de Jong, K.A.: Evolutionary Computation: A Unified Approach. MIT Press, Cambridge (2006)
Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276, 51–81 (2002)
Droste, S., Jansen, T., Wegener, I.: Upper and lower bounds for randomized search heuristics in black-box optimization. Theory of Computing Systems 39, 525–544 (2006)
Droste, S., Wiesmann, D.: On the design of problem-specific evolutionary algorithms. In: Ghosh, A., Tsutsui, S. (eds.) Advances in Evolutionary Computing, pp. 153–173. Springer, Heidelberg (2003)
He, J., Yao, X.: A study of drift analysis for estimating computation time of evolutionary algorithms. Natural Computing 3(1), 21–35 (2004)
Jansen, T., Wiegand, R.P.: The cooperative coevolutionary (1+1) EA. Evolutionary Computation 12(4), 405–434 (2004)
Kelsey, J., Timmis, J.: Immune inspired somatic contiguous hypermutations for function optimisation. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 207–218. Springer, Heidelberg (2003)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Oliveto, P.S., Witt, C.: Simplified drift analysis for proving lower bounds in evolutionary optimization. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 82–91. Springer, Heidelberg (2008)
Wegener, I.: Methods for the analysis of evolutionary algorithms on pseudo-boolean functions. In: Sarker, R., et al. (eds.) Evolutionary Optimization. Kluwer Academic Publishers, Dordrecht (2001)
Zarges, C.: Rigorous runtime analysis of inversely fitness proportional mutation rates. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 112–122. Springer, Heidelberg (2008)
Zarges, C.: On the utility of the population size for inversely fitness proportional mutation rates. In: Garibay, I., et al. (eds.) Foundations of Genetic Algorithms (FOGA), pp. 39–46. ACM Press, New York (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jansen, T., Zarges, C. (2009). A Theoretical Analysis of Immune Inspired Somatic Contiguous Hypermutations for Function Optimization. In: Andrews, P.S., et al. Artificial Immune Systems. ICARIS 2009. Lecture Notes in Computer Science, vol 5666. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03246-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-03246-2_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03245-5
Online ISBN: 978-3-642-03246-2
eBook Packages: Computer ScienceComputer Science (R0)