Finding Optimal Control Policy in Probabilistic Boolean Networks with Hard Constraints by Using Integer Programming and Dynamic Programming

In this paper, we study control problems of Boolean Networks (BNs) and Probabilistic Boolean Networks (PBNs). 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 minimize the maximum cost of the terminal state to which the network will enter. Integer linear programming and dynamic programming in conjunction with hard constraints are then employed to solve the above problems. Numerical experiments are given to demonstrate the effectiveness of our algorithms. We also present a hardness result suggesting that PBN CONTROL is harder than BN CONTROL.