Title: Finding optimal control policy in probabilistic Boolean Networks with hard constraints by using integer programming and dynamic programming

Authors: Xi Chen; Tatsuya Akutsu; Takeyuki Tamura; Wai-Ki Ching

Addresses: Advanced Modelling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong ' Bioinformatics Center, Institute for Chemical Research, Kyoto University, Japan Gokasho, Uji, Kyoto 611-0011, Japan ' Bioinformatics Center, Institute for Chemical Research, Kyoto University, Japan Gokasho, Uji, Kyoto 611-0011, Japan ' Advanced Modelling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

Abstract: Boolean Networks (BNs) and Probabilistic Boolean Networks (PBNs) are studied in this paper from the viewpoint of control problems. For BN CONTROL, by applying external control, we propose to derive the network to the desired state within a few time steps. For PBN CONTROL, we propose to find a control sequence such that the network will terminate in the desired state with a maximum probability. Also, we propose to minimise the maximum cost of the terminal state to which the network will enter. We also present a hardness result suggesting that PBN CONTROL is harder than BN CONTROL.

Keywords: Boolean networks; PBN; probabilistic Boolean networks; optimal control; integer linear programming; dynamic programming.

DOI: 10.1504/IJDMB.2013.053306

International Journal of Data Mining and Bioinformatics, 2013 Vol.7 No.3, pp.321 - 343

Received: 29 Apr 2011
Accepted: 29 Apr 2011
Published online: 07 Jun 2013 *

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