线性信赖域算法在给水管网优化设计中的应用

Application of linear-trust region programming method on optimization design of water distribution networks

提出了将给水管网优化设计分解成管径优化和流量优化的方法。对于管径优化，以不同管径管长为优化变量，建立某一流量分配下的线性规划模型。利用管道造价公式和水力计算公式，建立以流量分配为优化变量的非线性规划模型。在计算过程中，采用单纯型法求解线性规划模型，用带有约束的信赖域法求解非线性规划模型，两种算法交替计算。算例表明这一方法是可行的，能得到管网的优化设计方案。

In this paper, the optimization design of water distribution network was divided into the pipe diameter optimization design and flow rate optimization design. To set up the linear planning model under a certain flow rate distribution, the optimization variance should be determined according to different pipe diameters. Using pipeline construction cost equation and hydraulic calcu- lation equation, a non-linear planning model was set up based on flow rate distribution optimization variance. In the process of optimization calculation, simplex method was used to solve the linear programming model and trust region with constraints is used to solve the nonlinear programming model. Two algorithms were carried out alternatively. Case study showed that this method was feasible in network optimization design.