The Study On The Solution Of Probabilistic Boolean Networks Based On HS-DY Conjugate Gradient Algorithm

Probabilistic Boolean networks are probability form change based on Boolean networks. It changes the deterministic of Boolean networks, and it can powerfully simulate some uncertain biological internal system. It means that it makes the gene regulation network become abstraction. Therefore, probabilistic Boolean networks have been widely used in gene regulation networks and biological systems. With the proposed inverse problem of probabilistic Boolean networks, biological problem was pushed to a new field.The steps to solve the inverse problem of probabilistic Boolean networks as follows: firstly, semi Markov decision process model is transformed into the problem of target, then select the optimal control input objective function and make objective function minimum, thus, we need to solve an optimal control problem. The conjugate gradient method (Conjugate Gradient Methods CG) is one of the most commonly and effectively used optimization methods, and has been applied to the probabilistic Boolean networks. Among of them, FR method is a kind of nonlinear conjugate gradient method, this method have good convergence, but its performance is not good; PRP method can effectively avoid continuously produce long step of the FR method, but its convergence is not good; HS have good numerical performance, but when we use line search accurate to the general non convex function, the HS method may not converge; Convergence performance of DY method is good, but its numerical performance is not better than the PRP method.In this paper, we use hybrid HS-DY conjugate gradient method to solve the inverse problem of probabilistic Boolean networks. We use different conjugate gradient method that find that mixed HS-DY conjugate gradient algorithm has better numerical performance and less error than others in the solving process. At the same time, when the coefficient of linear equations is the large sparse matrix, we propose a PSD splitting method that solving rank deficient linear equation, and we use examples to demonstrate the method is feasible.Finally, this paper uses a parameter estimation method-COD method to predict the probabilistic Boolean network structure, when we use the same numerical examples to proved that the method has good convergence and good numerical form.