Abstract
An exact Markov chain model of the B-cell algorithm (BCA) is constructed via a novel possible transit method. The model is used to formulate a proof that the BCA is convergent absolute under a very broad set of conditions. Results from a simple numerical example are presented, we use this to demonstrate how the model can be applied to increase understanding of the performance of the BCA in optimizing function landscapes as well as giving insight into the optimal parameter settings for the BCA.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Kelsey, J., Timmis, J.: Immune Inspired Somatic Contiguous Hypermutation for Function Optimisation. In: CantuPaz, et al. (eds.) Proc. of Genetic and Evolutionary Computation Conference (GECCO). LNCS, vol. 2723, pp. 207–218. Springer, Heidelberg (2003)
Kelsey, J., Timmis, J., Hone, A.: Chasing Chaos. In: Sarker, R., Reynolds, R., Abbass, H., Kay-Chen, T., McKay, R. (eds.) Proceedings of the Congress on Evolutionary Computation, Canberra, Australia, December 2003, pp. 413–419. IEEE, Los Alamitos (2003)
Rosin-Arbesfeld, R., Townsley, F., Bienz, M.: The APC tumour suppressor has a nuclear export function. Letters to Nature 406, 1009–1012 (2000)
Hone, A., Kelsey, J.: Optima, extrema, and artificial immune systems. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 80–90. Springer, Heidelberg (2004)
Farmer, J.D., Packard, N.H., Perelson, A.S.: The Immune System, Adaptation, and Machine Learning. Physica D 22, 187–204 (1986)
Grimmett, G.R., Stirzaker, D.R.: Probability and Random Processes. Oxford University Press, Oxford (1982)
Villalobos-Arias, M., Coello Coello, C.A., Hernández-Lerma, O.: Convergence analysis of a multiobjective artificial immune system algorithm. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 226–235. Springer, Heidelberg (2004)
Seneta, E.: Non-Negative Matrices and Markov Chains. Springer, New York (1981)
Nix, A.E., Vose, M.D.: Modeling genetic algorithms with Markov chains. Annals of Mathematics and Artificial Intelligence 5, 79–88 (1992)
Vose, M.D.: Modeling Simple Genetic Algorithms. Evolutionary Computation 3(4) (1996)
De Jong, K.A., Spears, W.M., Gordon, D.F.: Using Markov Chains to Analyze GAFOs. In: Proceedings of FOGA 1994, Estes Park, CO, pp. 115–137. Morgan Kaufmann, San Francisco (1994)
de Castro, L., Von Zuben, F.J.: Learning and optimization using the clonal selection principle. IEEE Transactions on Evolutionary Computation, Special Issue on Artificial Immune Systems 6, 239–251 (2002)
de Castro, L., Timmis, J.: Artificial Immune Systems: A New Computational Intelligence Approach. Springer, Heidelberg (2002)
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)
Brzezniak, Z., Zastawniak, T.: Basic Stochastic Processes. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clark, E., Hone, A., Timmis, J. (2005). A Markov Chain Model of the B-Cell Algorithm. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J.I. (eds) Artificial Immune Systems. ICARIS 2005. Lecture Notes in Computer Science, vol 3627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11536444_24
Download citation
DOI: https://doi.org/10.1007/11536444_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28175-7
Online ISBN: 978-3-540-31875-0
eBook Packages: Computer ScienceComputer Science (R0)