Optimal Control Rules for Random Boolean Networks

  • Matthew R. KarlsenEmail author
  • Sotiris K. MoschoyiannisEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 812)


A random Boolean network (RBN) may be controlled through the use of a learning classifier system (LCS) – an eXtended Classifier System (XCS) can evolve a rule set that directs an RBN from any state to a target state. However, the rules evolved may not be optimal, in terms of minimising the total cost of the paths used to direct the network from any state to a specified attractor. Here we uncover the optimal set of control rules via an exhaustive algorithm. The performance of an LCS (XCS) on the RBN control problem is assessed in light of the newly uncovered optimal rule set.


  1. 1.
    Bianconi, G., Pin, P., Marsili, M.: Assessing the relevance of node features for network structure. Proc. Natl. Acad. Sci. 106(28), 11433–11438 (2009).
  2. 2.
    Butz, M.V., Wilson, S.W.: An algorithmic description of XCS. In: International Workshop on Learning Classifier Systems, pp. 253–272. Springer (2000)Google Scholar
  3. 3.
    Cornelius, S.P., Kath, W.L., Motter, A.E.: Realistic control of network dynamics. Nat. Commun. 4, 1942 (2013)Google Scholar
  4. 4.
    Dutot, A., Guinand, F., Olivier, D., Pigné, Y.: Graphstream: A tool for bridging the gap between complex systems and dynamic graphs. In: Emergent Properties in Natural and Artificial Complex Systems. 4th European Conference on Complex Systems (ECCS’2007) (2007)Google Scholar
  5. 5.
    Fornasini, E., Valcher, M.E.: Optimal control of Boolean control networks. IEEE Trans. Autom. Control 59(5), 1258–1270 (2014)Google Scholar
  6. 6.
    Fornasini, E., Valcher, M.E.: Recent developments in Boolean networks control. J. Control Decis. 3(1), 1–18 (2016)Google Scholar
  7. 7.
    Gates, A.J., Rocha, L.M.: Control of complex networks requires both structure and dynamics. Sci. Rep. 6, 24456 (2016)Google Scholar
  8. 8.
    Haghighi, R., Namazi, H.: Algorithm for identifying minimum driver nodes based on structural controllability. Math. Probl. Eng. 2015 (2015)Google Scholar
  9. 9.
    Karlsen, M.R., Moschoyiannis, S.: Evolution of control with learning classifier systems. Appl. Netw. Sci. 3(1), 30 (2018).
  10. 10.
    Karlsen, M.R., Moschoyiannis, S.: Learning condition–action rules for personalised journey recommendations. In: RuleML+RR: Rules and Reasoning. LNCS, vol. 11092, pp. 293–301 (2018)Google Scholar
  11. 11.
    Kauffman, S.: The Origins of Order. Oxford University Press, New York, NY (1993)Google Scholar
  12. 12.
    Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22(3), 437–467 (1969)Google Scholar
  13. 13.
    Kim, J., Park, S.M., Cho, K.H.: Discovery of a kernel for controlling biomolecular regulatory networks. Sci. Rep. 3, 2223 (2013).
  14. 14.
    Kovacs, T.: XCS classifier system reliably evolves accurate, complete, and minimal representations for Boolean functions. In: Soft Computing in Engineering Design and Manufacturing, pp. 59–68. Springer (1998)Google Scholar
  15. 15.
    Liu, Y.Y., Slotine, J.J., Barabási, A.L.: Controllability of complex networks. Nature 473(7346), 167 (2011)Google Scholar
  16. 16.
    Moschoyiannis, S., Elia, N., Penn, A., Lloyd, D.J.B., Knight, C.: A web-based tool for identifying strategic intervention points in complex systems. In: Proceedings of the Games for the Synthesis of Complex Systems (CASSTING’16 @ ETAPS 2016), EPTCS, vol. 220, pp. 39–52 (2016)Google Scholar
  17. 17.
    Savvopoulos, S., Moschoyiannis, S.: Impact of removing nodes on the controllability of complex networks. In: 6th Conference on Complex Networks and Applications, pp. 361–363 (2017)Google Scholar
  18. 18.
    Savvopoulos, S., Penn, A., Moschoyiannis, S.: On the interplay between topology and controllability of complex networks. In: Conference on Complex Systems (CCS’17) (2017)Google Scholar
  19. 19.
    Urbanowicz, R.J., Moore, J.H.: Learning classifier systems: a complete introduction, review, and roadmap. J. Artif. Evol. Appl. 2009(1), 1–25 (2009)Google Scholar
  20. 20.
    Wilson, S.W.: Classifier fitness based on accuracy. Evol. Comput. 3(2), 149–175 (1995)Google Scholar
  21. 21.
    Wilson, S.W.: Generalization in the XCS classifier system. In: Koza, J., Banzhaf, W., Chellapilla, K., Deb, K., Dorigo, M., Fogel, D., Garzon, M., Goldberg, D., Iba, H., Riolo R. (eds.) Genetic Programming 1998: Proceedings of the Third Annual Conference. Morgan Kaufmann, San Francisco, CA (1998)Google Scholar
  22. 22.
    Wilson, S.W.: Compact rulesets from XCSI. In: International Workshop on Learning Classifier Systems, pp. 197–208. Springer (2001)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Engineering and Physical Sciences, Department of Computer ScienceUniversity of SurreyGuildfordUK

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