  This paper deals with the infinite-horizon optimal control problem for
Boolean control networks (BCNs) with a discounted-cost criterion. This problem
has been investigated in existing studies with algorithms characterized by high
computational complexity. We thus attempt to develop more efficient approaches
for this problem from a deterministic Markov decision process (DMDP)
perspective. First, we show the eligibility of a DMDP to model the control
process of a BCN and the existence of an optimal solution. Next, two approaches
are developed to handle the optimal control problem in a DMDP. One approach
adopts the well-known value iteration algorithm, and the other resorts to the
Madani's algorithm specifically designed for DMDPs. The latter approach can
find an exact optimal solution and outperform existing methods in terms of time
efficiency, while the former value iteration based approach usually obtains a
near-optimal solution much faster than all others. The 9-state-4-input
\textit{ara} operon network of the bacteria \textit{E. coli} is used to verify
the effectiveness and performance of our approaches. Results show that both
approaches can reduce the running time dramatically by several orders of
magnitude compared with existing work.
