Abstract: Genetic regulatory networks (GRNs) are the fundamental and significant biological networks,and the biologi-cal system function can be regulated by controlling them.In the field of biological system,one of the significant research topics is to construct the control theory of genetic regulatory networks by applying external intervention control.Currently,as an important network model,the context-sensitive probabilistic Boolean network with perturbation (CS-PBNp) has been widely used for the research of optimal control problem of GRNs.With respect to the infinite-horizon optimal control problem,this paper proposed an approach of approximate optimal control strategy based on probabilistic model checking and genetic algorithm.Firstly,the total expected cost defined in infinite-horizon control is reduced to the steady-state reward in a discrete-time Markov chain.Then,the model of CS-PBNp containing stationary control policy should be constructed,the cost of the fixed control strategy is represented by the temporal logic with reward property,and the automatic calculation is carried out by using probabilistic model checker PRISM.Next,stationary control policy is encoded as an individual in the solution space of genetic algorithm.The fitness of the individual can be computed by PRISM,and the optimal solution can be obtained by making use of the genetic algorithm to execute genetic operations iteratively.The experimental results generated by utilizing the proposed approach into the WNT5A network illustrate the correctness and effectiveness of this approach.

Key words: Genetic algorithm, Genetic regulatory networks, Optimal control, Probabilistic model checking