Optimal finite-horizon control for probabilistic Boolean networks with hard constraints

Abstract

In this paper, we study optimal control policies for Probabilistic Boolean Networks (PBNs) with hard constraints. Boolean Networks (BNs) and PBNs are useful and effective tools for modelling genetic regulatory networks. A PBN is essentially a collection of BNs driven by a Markov chain process. It is well-known that the control/intervention of a genetic regulatory network is useful for avoiding undesirable states associated with diseases like cancer. Therefore both optimal finite-horizon control and infinite-horizon control policies have been proposed to achieve the purpose. Actually the optimal control problem can be formulated as a probabilistic dynamic programming problem. In many studies, the optimal control problems did not consider the case of hard constraints, i.e., to include a maximum upper bound for the number of controls that can be applied to the PBN. The main objective of this paper is to introduce a new formulation for the optimal finite-horizon control problem with hard constraints. Experimental results are given to demonstrate the efficiency of our proposed formulation.