Abstract
In this work we address the issue of designing a Boolean network such that its attractors are maximally distant. The design objective is converted into an optimisation problem, that is solved via an iterated local search algorithm. This technique proves to be effective and enables us to design networks with size up to 200 nodes. We also show that the networks obtained through the optimisation technique exhibit a mixture of characteristics typical of networks in the critical and chaotic dynamical regime.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aldana, M., Balleza, E., Kauffman, S., Resendiz, O.: Robustness and evolvability in genetic regulatory networks. Journal of Theoretical Biology 245, 433–448 (2007)
Balleza, E., Alvarez-Buylla, E., Chaos, A., Kauffman, S., Shmulevich, I., Aldana, M.: Critical dynamics in genetic regulatory networks: Examples from four kingdoms. PLoS ONE 3(6), e2456 (2008)
Bastolla, U., Parisi, G.: Closing probabilities in the Kauffman model: An annealed computation. Physica D 98, 1–25 (1996)
Benedettini, S.: The Boolean network toolkit, http://booleannetwork.sourceforge.net (viewed: November 2010)
Bernasconi, A., Codenotti, B.: Sensitivity of Boolean functions, harmonic analysis, and circuit complexity. Tech. rep., International Computer Science Institute, Berkley, CA (June 1993), http://www.icsi.berkeley.edu/cgi-bin/pubs/publication.pl?ID=000818
Chambers, J.: Graphical Methods for Data Analysis. Springer, Berlin (1983)
Derrida, B., Pomeau, Y.: Random networks of automata: a simple annealed approximation. Europhysics Letters 1(2), 45–49 (1986)
Esmaeili, A., Jacob, C.: Evolution of discrete gene regulatory models. In: Keijzer, M. (ed.) Proceedings of GECCO 2008 – Genetic and Evolutionary Computation Conference, Atlanta, GA, pp. 307–314 (2008)
Graudenzi, A., Serra, R.: A new model of genetic network: the gene protein boolean network. In: Serra, R., Villani, M., Poli, I. (eds.) Artificial Life and Evolutionary Computation – Proceedings of WIVACE 2008, pp. 283–291. World Scientific Publishing, Singapore (2008)
Kaneko, K.: Life: An Introduction to Complex System Biology. Springer, Berlin (2006)
Kauffman, S.: Adaptive automata based on Darwinian selection. Physica D 22, 68–82 (1986)
Kauffman, S.: The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, UK (1993)
Kauffman, S.: A proposal for using the ensemble approach to understand genetic regulatory networks. Journal of Theoretical Biology 230, 581–590 (2004)
Kesseli, J., Rämö, P., Yli-Harja, O.: On spectral techniques in analysis of Boolean networks. Physica D: Nonlinear Phenomena 206(1-2), 49–61 (2005), http://www.sciencedirect.com/science/article/B6TVK-4G7X9CX-3/2/16eb18c3acca5123aed298e6769b1afa
Lemke, N., Mombach, J., Bodmann, B.: A numerical investigation of adaptation in populations of random Boolean networks. Physica A 301, 589–600 (2001)
Lourenço, H., Martin, O., Stützle, T.: Iterated local search. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 57, pp. 320–353. Springer, New York (2003)
Mihaljev, T., Drossel, B.: Evolution of a population of random Boolean networks. The European Physical Journal B - Condensed Matter and Complex Systems 67, 259–267 (2009)
Fretter, C., Szejka, A., Drossel, B.: Perturbation propagation in random and evolved Boolean networks. New Journal of Physics 11(3), 033005:1–13
Nolfi, S., Floreano, D.: Evolutionary robotics. The MIT Press, Cambridge (2000)
Nykter, M., Price, N., Aldana, M., Ramsey, S., Kauffman, S., Hood, L., Yli-Harja, O., Shmulevich, I.: Gene expression dynamics in the macrophage exhibit criticality. Proceedings of the National Academy of Sciences 105(6), 1897–1900 (2008)
Ribeiro, A., Kauffman, S., Lloyd-Price, J., Samuelsson, B., Socolar, J.: Mutual information in random Boolean models of regulatory networks. Physical Review E 77, 011901:1–10 (2008)
Roli, A., Benedettini, S., Serra, R., Villani, M.: Analysis of attractor distances in random Boolean networks. In: Apolloni, B., Bassis, S., Esposito, A., Morabito, C. (eds.) Neural Nets WIRN10 – Proceedings of the 20th Italian Workshop on Neural Nets, Frontiers in Artificial Intelligence and Applications, vol. 226, pp. 201–208 (2011), also available as arXiv:1011.4682v1 [cs.NE]
Serra, R., Villani, M., Barbieri, A., Kauffman, S., Colacci, A.: On the dynamics of random Boolean networks subject to noise: attractors, ergodic sets and cell types. Journal of Theoretical Biology 265(2), 185–193 (2010)
Serra, R., Villani, M., Semeria, A.: Genetic network models and statistical properties of gene expression data in knock-out experiments. Journal of Theoretical Biology 227, 149–157 (2004)
Shmulevich, I., Dougherty, E.: Probabilistic Boolean Networks: The Modeling and Control of Gene Regulatory Networks. SIAM, Philadelphia (2009)
Shmulevich, I., Kauffman, S.: Activities and sensitivities in Boolean network models. Phys. Rev. Lett. 93(4), 048701:1–10 (2004)
Szejka, A., Drossel, B.: Evolution of Boolean networks under selection for a robust response to external inputs yields an extensive neutral space. Phys. Rev. E 81(2), 021908:1–9 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Benedettini, S., Roli, A., Serra, R., Villani, M. (2011). Stochastic Local Search to Automatically Design Boolean Networks with Maximally Distant Attractors. In: Di Chio, C., et al. Applications of Evolutionary Computation. EvoApplications 2011. Lecture Notes in Computer Science, vol 6624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20525-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-20525-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20524-8
Online ISBN: 978-3-642-20525-5
eBook Packages: Computer ScienceComputer Science (R0)