生化系统稳态优化的双层规划模型与求解方法

Bi-level Programming Model and Solution Algorithm for Steady-State Optimization of Biochemical Systems

针对一类生化系统的稳态优化问题，建立了一种具有二层递阶结构的双层规划优化模型，其上层和下层问题的优化目标分别为最大化产物产率（或代谢物浓度）和最小化生化系统的代谢物浓度之和．模型的生物意义是在尽可能小的代谢成本条件下使产物的产率或浓度达到最大．为了有效求解所建立的NP—hard、非凸双层规划问题，在S-系统建模框架下应用等价变换策略提出了一种可求其最优解的优化算法．算法具有操作简便和计算成本低的优点．最后，将所提双层规划模型与求解方法应用于两个生化系统的稳态优化中．结果表明，方法可行且有效．

An optimization model is established for steady-state optimization problem of a class of biochemical systems. This model is a bi-level programming that has a two layer hierarchical structure. The optimized objectives for the upper and lower level problems are respectively to maximize the production rate of some product or the concentration of some metabolite, and minimize the total sum of metabolite concentrations of biochemical systems. The biological significance of the proposed model is to maximize the production rate or concentration of the considered product under a lower metabolic cost of biochemical system. The established bi-level programming is a NP-hard and nonconvex problem. In the modelling framework of S-system, an optimization algorithm is proposed to efficiently solve it by using the equivalence transformation strategies. This algorithm takes advantages of easy implementation and low computational burden model and solution algorithm are applied to the systems. The results show the tractability and Finally, the proposed hi-level programming steady-state optimization of two biochemical effectiveness of the presented method.