图论在水资源系统建模与配置计算中的应用  

Application of graph theory in modeling and allocation calculation of water resources system

作　　者：郭聪 游进军[1] 林鹏飞[1] GUO Cong;YOU Jinjun;LING Pengfei(State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin,China Institute of Water Resources and Hydropower Research,Beijing 100038,China)

机构地区：[1]中国水利水电科学研究院流域水循环模拟与调控国家重点实验室,北京100038

出　　处：《中国水利水电科学研究院学报（中英文）》2023年第3期295-306,共12页Journal of China Institute of Water Resources and Hydropower Research

基　　金：国家自然科学基金项目(52079143);国家重点研发计划项目(2018YFC0407705,2022YFC3204601)。

摘　　要：为提高复杂水资源系统的供排水关系识别与模型构建计算能力,本文基于系统网络图探讨了图论在模拟水资源系统复杂水量传输过程、确定网络遍历顺序与系统配水计算中的应用。利用图论中的拓扑排序算法与深度优先搜索算法对水资源系统网络关系进行不同目标的分析识别。综合两种算法,进行一次供水、供水还原与二次供水的多次网络分水过程设计和迭代计算,结合最大最小公平算法等水量分配原则,设计基于网络系统的复杂水量分配计算过程,将用户需水、工程可供水量和供水网络关系结合进行供需自适应配置,解决多水源多用户对应关系下的水源供给不均衡问题。以三亚市地表水资源配置开展实例研究,结果表明通过图论算法在系统拓扑关系遍历和配水计算过程中的应用,系统枯水年城镇缺水率从3.42%降至1.63%,供需均衡度从0.38提高至0.71,提高了配置的计算效率与合理性。In order to improve the calculation ability of model construction and water supply and drainage relationship identification in complex water resources system,this paper discusses the application of graph theory in simulating complex water resources system,determining network traversal order,and calculating system water distribution based on the network.The topological sorting algorithm and depth first search algorithm in graph theory are used to analyze the network relationship of water resources system.The two algorithms are integrated to design the network water distribution process into three phases:first water supply,water supply restoration and secondary water supply.The complex water distribution calculation process based on network system is designed by combining the water distribution principles such as the maximum and minimum fair algorithm,and the relationship between user water demand,project water supply and water supply network is combined for supply and demand adaptive configuration.To solve the problem of water supply imbalance under the relationship of multi-source and multi-user,a case study was carried out on the allocation of surface water resources in Sanya City.The results show that the urban water shortage rate decreases from 3.42%to 1.63%and the equilibrium degree of supply and demand increases from 0.38 to 0.71,which improves the calculation efficiency and rationality of the allocation through the application of graph theory algorithm in the traversal of the topological relationship and the calculation process of water distribution.

关 键 词：图论 拓扑排序 深度优先搜索 水资源系统 水资源配置 系统网络图 

分 类 号：TV214[水利工程—水文学及水资源]