供水系统调度问题的凸化及其优化算法

Convexification and Optimization Algorithm of Water Distribution System

前言含蓄水池城市供水系统的优化调度问题是一个大规模非线性的静态优化问题。由于该问题的数学模型中含有非线性等式约束,因此,它是一个大规模的非凸优化问题。求解的方法一种是将该问题的数学模型转化成具有凸结构的优化问题,然后利用基于拉格朗日函数法的分解-协调优化技术求解。但所建模型有时很难被用户接受。另一种方法是基于增广拉格朗日函数法的基本原理,直接求解大规模非凸优化问题的局部最优解。后一种方法目前在理论上还不够成熟,成功的应用实例也不多见。

The optimal distribution problem of urban water supply system with reservoirs is a large-scale and noncoavex optimization problem. Based on the special structure of the mathematical model of this problem, a convexification method of the problem and the decomposition-coordination algorithm of solving this problem are proposed in this paper. With this algorithm, a real urban water supply system has been simulated, and the satisfactory results are obtained.