WO2022012093A1 - 一种基于"分区-分级"理论的复杂水资源系统优化配置方法 - Google Patents

一种基于"分区-分级"理论的复杂水资源系统优化配置方法 Download PDF

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WO2022012093A1
WO2022012093A1 PCT/CN2021/085198 CN2021085198W WO2022012093A1 WO 2022012093 A1 WO2022012093 A1 WO 2022012093A1 CN 2021085198 W CN2021085198 W CN 2021085198W WO 2022012093 A1 WO2022012093 A1 WO 2022012093A1
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water
population
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郭玉雪
许月萍
程伟平
于欣廷
尤延锋
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Zhejiang University
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    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
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Definitions

  • the invention belongs to the field of water resource allocation, and in particular relates to an optimal allocation method for a complex water resource system based on the "zoning-grading" theory.
  • the gray wolf optimization algorithm proposed by Mirjalili et al. (2014) has been proved to be significantly better than the particle swarm algorithm (PSO) and the difference algorithm in the accuracy and stability of the function solution.
  • PSO particle swarm algorithm
  • GA Genetic Algorithm
  • the purpose of the present invention is to provide a method for optimal configuration of complex water resources system, which is based on the "partition-grading" theory to construct an optimal configuration model for water resources, and at the same time improves the gray wolf algorithm, and applies it to model solving to determine the optimal configuration. Collection of water distribution schemes.
  • the method can simplify the multi-dimensional optimization solution process, avoid falling into local optimization, improve the calculation efficiency, and ensure the fairness of each water user and improve the water supply guarantee rate.
  • the technical scheme of the present invention is:
  • Step 1 Acquire basic information data of the water resources system, including the relationship curve of reservoir water level-storage capacity, basic characteristic parameters of reservoirs, pumping stations, river courses, water pipelines, water plants, geographic location information, etc.;
  • Step 2 generalize the complex water resources system into different units, including nodes and directed line segments;
  • Step 3 Divide the entire complex water resources system into areas, and establish a digital matrix of hydraulic relationships in different areas;
  • Step 4 Build and solve a multi-level water resource system optimal allocation model according to the type of water supply source, and determine a reasonable set of water resource optimal allocation schemes.
  • the reservoirs, pumping stations, river channels and water plants in the system are respectively generalized as nodes, and the water pipelines are generalized as directed line segments.
  • the division principle in the step 3 is that the water plant is the division center, and the area is divided according to the hydraulic relationship between the reservoir, the pumping station, the river, the water transmission pipeline and the water plant.
  • the intersections between different partitions are generalized as virtual nodes.
  • the hydraulic relationship is represented digitally by 0, -1 and 1, wherein 0 represents no hydraulic relationship, -1 represents outflow, and 1 represents inflow.
  • the water supply source in the step 4 includes local water and externally transferred water, wherein the local water includes reservoir and river water.
  • step 4 constructs and solves the optimal configuration model of the multi-level water resource system according to the type of water supply source, including the following steps:
  • Step 4-1 only considering the local water, establish a single-objective optimal allocation model of the first-level water resources. Taking the regional water resources system as the object, constructing the water resource unit with the maximum water supply guarantee rate of the water plant as the objective function and the water balance, the available water supply of the local water source, the overcurrent capacity of the pumping station, and the water delivery capacity of the pipeline as the constraints.
  • the objective optimization configuration model where the objective function is:
  • Q j is the water demand of the j water plant (m 3 )
  • x ij is the water supply amount (m 3 ) of the i-th reservoir to the j-th water plant.
  • Step 4-3 consider both local water and external water transfer, and establish a multi-objective optimal allocation model for the second-level water resources.
  • the objective function With the maximum water supply guarantee rate and the minimum total operating cost of the system, and the distribution of external water to each water plant is not less than the water shortage WQ i of each water plant, the water balance, and the water supply from local water sources.
  • the multi-objective optimal configuration model of water resources is constrained by the amount of water available for external transfer, the water supply capacity of the external transfer water source, the overcurrent capacity of the pumping station, and the water delivery capacity of the pipeline.
  • the objective function is:
  • k 1,2, .., K is the number of partitions
  • M i the local water use charges ( ⁇ ), M e to transfer water usage fee ( ⁇ ), M b of gains ( ⁇ ).
  • the local water supply fee includes the electricity fee for the operation of the pumping station, the government water resource fee, and the water resource purchase fee for the non-self-owned reservoir;
  • the external water transfer includes the government water resource fee and the electricity fee for the operation of the pumping station.
  • Steps 4-4 according to the calculation of each partition, use the improved multi-objective gray wolf algorithm to solve the multi-objective optimal configuration model, obtain the Pareto scheme set, and determine the water distribution and external transfer amount of each reservoir under different schemes.
  • step 4-2 adopts the improved single-objective gray wolf algorithm to solve the single-objective optimization model of each partition, including the following steps:
  • Step 4-2-1 initialize algorithm parameters and population.
  • Step 4-2-2 Calculate the fitness of each individual in the population. The larger the water supply guarantee rate of the water plant, the larger the returned fitness; sort according to the fitness, and select and save the three individuals with the largest fitness : X ⁇ , X ⁇ , X ⁇ , where X ⁇ is the globally optimal gray wolf;
  • Step 4-2-3 use X ⁇ , X ⁇ , X ⁇ to update all gray wolf individuals in the population, and the update method is:
  • Step 4-2-4 determine whether the number of iterations has reached MAXGEN, if so, terminate the operation and output the water shortage of the water plant; if not, return to step 4-2-2 to continue the evolution;
  • Step 4-2-5 determine the water shortage of all water plants in the system.
  • the convergence factor a adopts the nonlinear convergence method based on the parabola to converge, and the equation is:
  • t is the current number of iterations
  • MAXGEN is the maximum number of iterations
  • steps 4-4 adopt the improved multi-objective gray wolf algorithm to solve the system multi-objective optimal configuration model, including the following steps:
  • Step 4-4-1 initialize algorithm parameters and population.
  • the size of the population is N p
  • the number of external archive sets is N e
  • the maximum number of iterations is N gen
  • the number of decision variables is N d
  • the value range of the decision variables is [Lb, Ub], according to the value range of the decision variables
  • Step 4-4-2 calculate the fitness value of each individual in the population, and calculate the non-dominated ranking level of all individuals according to the fitness value and crowding distance
  • the three individuals with the largest distance are taken as X' ⁇ , X' ⁇ , X' ⁇ , where X' ⁇ is the globally optimal gray
  • Step 4-4-4 according to X' ⁇ , X' ⁇ , X' ⁇ using formula (4)-(5) to update all gray wolf individuals in the population;
  • Step 4-4-5 calculate the fitness value of each individual in the population, merge the updated new population with the external archive set NEA, and update the external archive set NEA according to the selection rules described in step 4-4-2;
  • Step 4-4-6 judge whether the number of iterations has reached MAXGEN, if so, terminate the operation and output the Pareto non-inferior solution set in the external archive set NEA; if not, return to step 4-4-3 to continue the evolution;
  • Step 4-4-7 Arrange and output the water supply volume of the reservoir, the volume of river turning water and the volume of externally transferred water corresponding to different non-inferior solutions.
  • the present invention has the following beneficial effects:
  • the water resources system is divided according to the water supply relationship, which can simplify the high-dimensional optimization and solution process of the complex water resources system;
  • the initial attenuation of the convergence factor a can be reduced to ensure a better search for the global optimal solution; the later attenuation is increased, and the local optimal solution can be found more accurately, which can effectively balance
  • the gray wolf algorithm has global search and local search capabilities to improve the efficiency of model solving;
  • Fig. 1 is the method flow chart of the present invention
  • Fig. 2 is the concrete flow chart of step 4-2 in the present invention.
  • Fig. 3 is the nonlinear convergence diagram of parameter a in step 4-2-3 of the present invention.
  • Fig. 4 is the concrete flow chart of step 4-4 in the present invention.
  • a method for optimal allocation of complex water resources system based on the "zoning-grading" theory includes the following steps:
  • Step 1 Acquire basic information data of the water resources system, including the relationship curve of reservoir water level-storage capacity, basic characteristic parameters of reservoirs, pumping stations, river courses, water pipelines, water plants, geographic location information, etc.;
  • Step 2 generalize the complex water resources system into different units, including nodes and directed line segments;
  • Step 3 Divide the entire complex water resources system into areas, and establish a digital matrix of hydraulic relationships in different areas;
  • Step 4 Build and solve a multi-level water resource system optimal allocation model according to the type of water supply source, and determine a reasonable set of water resource optimal allocation schemes.
  • the reservoirs, pumping stations, river channels and water plants in the system are respectively generalized as nodes, and the water pipelines are generalized as directed line segments.
  • step 3 the zoning principle is to take the water plant as the zoning center, and divide the area according to the water supply relationship between the reservoir, pump station, river, water pipeline and the water plant.
  • step 3 the junctions between different partitions are generalized as virtual nodes.
  • step 3 the hydraulic relationship matrix is represented digitally by 0, -1 and 1, where 0 means no hydraulic relationship, -1 means outflow, and 1 means inflow.
  • the water supply sources in the step 4 include local water and externally transferred water, wherein the local water includes reservoir and river water.
  • Step 4-1 only considering the local water, establish a single-objective optimal allocation model of the first-level water resources. Taking the regional water resources system as the object, constructing the water resource unit with the maximum water supply guarantee rate of the water plant as the objective function and the water balance, the available water supply of the local water source, the overcurrent capacity of the pumping station, and the water delivery capacity of the pipeline as the constraints.
  • the objective optimization configuration model where the objective function is:
  • Q j is the water demand of the j water plant (m 3 )
  • x ij is the water supply amount (m 3 ) of the i-th reservoir to the j-th water plant.
  • Step 4-3 consider both local water and external water transfer, and establish a multi-objective optimal allocation model for the second-level water resources.
  • the objective function With the maximum water supply guarantee rate and the minimum total operating cost of the system, and the distribution of external water to each water plant is not less than the water shortage WQ i of each water plant, the water balance, and the water supply from local water sources.
  • the multi-objective optimal configuration model of water resources is constrained by the amount of water available for external transfer, the water supply capacity of the external transfer water source, the overcurrent capacity of the pumping station, and the water delivery capacity of the pipeline.
  • the objective function is:
  • k 1,2, .., K is the number of partitions
  • M i the local water use charges ( ⁇ ), M e to transfer water usage fee ( ⁇ ), M b of gains ( ⁇ ).
  • the local water supply fee includes the electricity fee for the operation of the pumping station, the government water resource fee, and the water resource purchase fee for the non-self-owned reservoir;
  • the external water transfer includes the government water resource fee and the electricity fee for the operation of the pumping station.
  • Steps 4-4 according to the calculation of each partition, use the improved multi-objective gray wolf algorithm to solve the multi-objective optimal configuration model, obtain the Pareto scheme set, and determine the water distribution and external transfer amount of each reservoir under different schemes.
  • step 4-2 the improved single-objective gray wolf algorithm is used to solve the single-objective optimization model of each partition.
  • the flow chart is shown in Figure 2, and the specific steps are as follows:
  • Step 4-2-1 initialize algorithm parameters and population.
  • Step 4-2-2 Calculate the fitness of each individual in the population. The larger the water supply guarantee rate of the water plant, the larger the returned fitness; sort according to the fitness, and select and save the three individuals with the largest fitness : X ⁇ , X ⁇ , X ⁇ , where X ⁇ is the globally optimal gray wolf;
  • Step 4-2-3 update the convergence factors A, C and a, and update all gray wolf individuals in the population according to X ⁇ , X ⁇ , X ⁇ , and the update method is:
  • Step 4-2-4 determine whether the number of iterations has reached MAXGEN, if so, terminate the operation and output the water shortage of the water plant; if not, return to step 4-2-2 to continue the evolution;
  • Step 4-2-5 determine the water shortage of all water plants in the system.
  • the convergence factor a adopts a nonlinear convergence method based on parabola, and the equation is:
  • t is the current number of iterations
  • MAXGEN is the maximum number of iterations
  • Step 4-4 using the improved multi-objective gray wolf algorithm to solve the multi-objective optimal configuration model of the whole system, obtain the Pareto scheme set, and determine the water distribution and external transfer amount of each reservoir under different schemes.
  • the flow chart is shown in Figure 4. Specific steps are as follows:
  • Step 4-4-1 initialize algorithm parameters and population.
  • the size of the population is N p
  • the number of external archive sets is N e
  • the maximum number of iterations is N gen
  • the number of decision variables is N d
  • the value range of the decision variables is [Lb, Ub], according to the value range of the decision variables
  • Step 4-4-2 calculate the fitness value of each individual in the population, and calculate the non-dominated ranking level of all individuals according to the fitness value and crowding distance
  • the level selects the three individuals with the largest crowding distance as X' ⁇ , X' ⁇ , X' ⁇ , where X' ⁇ is the globally optimal gray wolf;
  • Step 4-4-4 according to X' ⁇ , X' ⁇ , X' ⁇ using formula (4)-(5) to update all gray wolf individuals in the population;
  • Step 4-4-5 calculate the fitness value of each individual in the population, merge the updated new population with the external archive set NEA, and update the external archive set NEA according to the selection rules described in step 4-4-2;
  • Step 4-4-6 judge whether the number of iterations has reached MAXGEN, if so, terminate the operation and output the Pareto non-inferior solution set in the external archive set NEA; if not, return to step 4-4-3 to continue the evolution;
  • Step 4-4-7 Arrange and output the water supply volume of the reservoir, the volume of river turning water and the volume of externally transferred water corresponding to different non-inferior solutions.
  • the study area involves 27 reservoirs, 22 pumping stations, and 4 water supply plants: A, B, C, and D water plants.
  • This area can be divided into 3 areas, D 1 , D 2 and D 3 , according to the water supply relationship between pump stations, reservoirs and water plants, where A and B water plants are located in D 1 district, C water plant is located in D 2 district, The D water plant is located in the D 3 subdivision.
  • Overview of the system as a system overview of the partition D 2 shown in FIG. 5; the Area Analysis of Hydraulic relationship to establish digital matrix, as shown in Table 1 as D 2 partitions hydraulic relation digitizing part of the information matrix.
  • the calculation period was selected as June 1, 2016, and the optimal configuration model of the multi-level water resources system in the study area was constructed and solved according to the type of water supply. According to the water distribution scheme, it can be seen that under various schemes, the water supply guarantee rate of the four water plants on June 1 all met 100%.
  • the R 1 reservoir in the D 1 sub-area stores water for external transfer, and is responsible for supplying water to the three water plants A, B and C.

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Abstract

一种基于"分区-分级"理论的复杂水资源系统优化配置方法，步骤如下：首先获取水资源系统基本信息数据，其次对复杂水资源系统进行概化；然后按照水库、泵站、河道、输水管道与水厂之间的供给水关系对整个水资源系统进行分区，并建立不同分区水力关系数字化矩阵；最后按照供水水源类型构建和求解多级水资源系统优化配置模型，确定合理的优化配置方案集合。本方法可实现复杂水资源系统的简单化，为水资源高效利用提供新的途径。

Description

一种基于“分区-分级”理论的复杂水资源系统优化配置方法 技术领域
本发明属于水资源配置领域，具体涉及一种基于“分区-分级”理论的复杂水资源系统优化配置方法。
背景技术
为了解决水资源分布时空不均问题导致的水资源短缺问题，开展水资源优化配置研究能够提高水资源利用率，具有明显的社会和经济效益。然而随着社会经济的快速发展，水资源优化配置需要考虑的因素日益增多，尤其是针对复杂水资源系统，在优化配置模型的构建和求解过程中，容易出现维数灾难问题，因此有必要对系统进行分区处理，实现系统的有效降维，以提高计算效率。同时，以往的水资源优化配置模型通常以全区域的总供水保证率最大为社会效益目标，难以保证各分区用水户效益的公平性。另外，在优化配置模型的求解方面，Mirjalili等人(2014)提出的灰狼优化算法(GWO)已被证明在对函数求解精度和稳定性上要明显优于粒子群算法(PSO)、差分算法(DE)和遗传算法(GA)等优化算法，但也存在着收敛速度慢、全局搜索能力弱、容易陷入局部最优的缺陷。
发明内容
本发明的目的在于提供一种复杂水资源系统优化配置方法，该方法基于“分区-分级”理论进行水资源优化配置模型构建，同时对灰狼算法进行改进，并应用于模型求解，确定最优配水方案集合。该方法能够简化多维优化求解过程，避免陷入局部优化提高计算效率，且保证各用水户的公平性及提高供水保证率。
为实现上述目的，本发明的技术方案是：
一种基于“分区-分级”理论的复杂水资源系统优化配置方法，包括以下步骤：
步骤1，获取水资源系统基本信息数据，包括水库水位-库容关系曲线，水库、泵站、河道、输水管道、水厂的基本特征参数、地理位置信息等；
步骤2，将复杂水资源系统概化为不同单元，包括节点和有向线段；
步骤3，对整个复杂水资源系统进行片区划分，分别建立不同分区水力关系数字化矩阵；
步骤4，按照供水水源类型构建和求解多级水资源系统优化配置模型，确定合理的水资源优化配置方案集合。
上述技术方案中，进一步地，所述步骤2中将系统中的水库、泵站、河道、水厂分别概化为节点，输水管道概化为有向线段。
进一步地，所述步骤3中分区原则是以水厂为分区中心，按照水库、泵站、河道、输水管道与水厂之间的水力关系进行片区划分。
更进一步地，所述步骤3中将不同分区之间的交汇处概化为虚拟节点。
进一步地，所述步骤3中水力关系均以0，-1和1数字化表示，其中0表示无水力关系，-1表示出流，1表示入流。
进一步地，所述步骤4中的供水水源包括本地水和外调水，其中本地水包括水库和河道水。
进一步地，所述步骤4按照供水水源类型构建和求解多级水资源系统优化配置模型，包括以下步骤：
步骤4-1，仅考虑本地水，建立第一级水资源单目标优化配置模型。以分区水资源系统为对象，分别构建各分区以水厂供水保证率最大为目标函数，以水量平衡、本地水源可供水量、泵站过流能力、管道输水能力等为约束的水资源单目标优化配置模型，其中，目标函数：
Figure PCTCN2021085198-appb-000001
式中，Q j为j水厂的需水量(m 3)，x ij为第i水库向第j水厂的供水量(m 3)。
步骤4-2，采用改进的单目标灰狼算法进行上述模型求解，确定各个水厂的缺水量WQ i(i＝1,2,...,M)，M为整个水资源系统内的水厂个数；
步骤4-3，同时考虑本地水和外调水，建立第二级水资源多目标优化配置模型。以整个水资源系统为对象，构建以系统供水保证率最大、运营总成本最小为目标函数，以外调水分配到各个水厂不小于各水厂缺水量WQ i、水量平衡、本地水源可供水量、外调水水源可供水量、泵站过流能力、管道输水能力等为约束的水资源多目标优化配置模型，其中，目标函数为：
供水保证率最大
Figure PCTCN2021085198-appb-000002
运营总成本最小Min f 2(x)＝M e+M i-M b      (3)
式中，k＝1,2,..,K为分区个数，M i为本地水使用费用(￥)，M e为外调水使用费用(￥)，M b为收益(￥)。其中，本地供水费用包括泵站运行电费、政府水资源费用、非自有水库水资源购置费；外调水包括政府水资源费、以及泵站运行电费。
步骤4-4，按照各分区计算，采用改进的多目标灰狼算法求解多目标优化配置模型，获得Pareto方案集合，确定不同方案下各个水库的配水量和外调水量。
进一步地，所述步骤4-2采用改进的单目标灰狼算法求解各个分区单目标优化模型，包括以下步骤：
步骤4-2-1，初始化算法参数和种群。种群规模大小为Popsize，最大迭代次数Maxgen，决策变量个数Dimension，决策变量取值范围[Lb,Ub]，按照决策变量的取值范围初始化灰狼种群X＝[X 1,X 2,...,X i,...,X Popsize]；
步骤4-2-2，计算种群中每个个体的适应度，其中水厂供水保证率越大，返回的适应度越大；按照适应度大小进行排序，选择并保存适应度最大的三个个体：X α、X β、X δ，其中X α为全局最优的灰狼；
步骤4-2-3，采用X α、X β、X δ对种群中的所有灰狼个体进行更新，更新方式为：
Figure PCTCN2021085198-appb-000003
其中，t为迭代次数，A＝2a×r 1-a，C＝2×r 2；A、C和a均为收敛因子，r 1、r 2为随机变量，r 1、r 2∈(0，1)，D α、D β、D δ表示个体X α、X β、X δ与个体X i之间的距离。
步骤4-2-4，判断迭代次数是否已达到MAXGEN，若是，则终止运行并输出水厂的缺水量；若否，返回步骤4-2-2继续进化；
步骤4-2-5，确定系统内所有水厂的缺水量。
进一步地，所述步骤4-2-3中收敛因子a采用基于抛物线的非线性收敛方式收敛，方程为：
a＝2-2(t /MAXGEN) 2    (5)
其中，t为当前迭代次数，MAXGEN为最大迭代次数。
进一步地，所述步骤4-4采用改进的多目标灰狼算法求解系统多目标优化配置模型，包括以下步骤：
步骤4-4-1，初始化算法参数和种群。种群规模大小为N p，外部归档集个数为N e，最大迭代次数为N gen，决策变量个数为N d，决策变量取值范围为[Lb,Ub]，按照决策变量的取值范围初始化灰狼种群X；
步骤4-4-2，计算种群中每个个体的适应度值，按照适应度值计算所有个体的非支配排序等级
Figure PCTCN2021085198-appb-000004
和拥挤距离
Figure PCTCN2021085198-appb-000005
按照以下规则选取N e个个体作为初始的外部归档集NEA：选取非支配排序等级为rank＝1的个体，若等级为1的个体数量大于N e，则选择拥挤距离较大的前N e个体；若不足，则依此选择排序等级为rank＝rank+1中拥挤距离较大的个体，直至外部归档集NEA包含个体数为N e，以保证种群的多样性；
步骤4-4-3，在外部归档集NEA中按照以下规则选择X' α、X' β、X' δ三个个体作为优先等级：若非支配排序的等级均为非占优等级或第一等级，分别选取拥挤距离最大的前三个个体作为X' α、X' β、X' δ；若非支配排序的等级个数等于2，分别在rank＝1的等级中选取拥挤距离最大的前两个个体作为X' α、X' β，在rank＝2的等级中选取拥挤距离最大的个体作为X' δ；若非支配排序的等级个数大于2，分别在rank＝1、2、3等级选取拥挤距离最大的三个个体作为X' α、X' β、X' δ，其中X' α为全局最优的灰狼；
步骤4-4-4，按照X' α、X' β、X' δ采用式(4)-(5)对种群中的所有灰狼个体进行更新；
步骤4-4-5，计算种群中每个个体的适应度值，将更新后的新种群与外部归档集NEA进行合并，按照步骤4-4-2所述的选取规则更新外部归档集NEA；
步骤4-4-6，判断迭代次数是否已达到MAXGEN，若是，则终止运行并输出外部归档集NEA中的Pareto非劣解集合；若否，返回步骤4-4-3继续进化；
步骤4-4-7，整理输出不同非劣解对应的水库供水量、河道翻水量和外调水量。
本发明与现有技术相比，具有以下有益效果：
(1)以水厂为中心，按照供水关系对水资源系统进行分区处理，能够简化复杂水资源系统的高维优化求解过程；
(2)按照供水水源类型构建和求解多级水资源优化配置模型，可在提高供水保证率的前提下，实现经济效益最大化和水资源利用最大化；
(3)建立水力关系数字化矩阵，能够直观展示复杂水资源系统单元之间的水力联系，简化模型构建与求解过程；
(4)以各分区供水保证率最大化为目标函数计算缺水量，能够保障各用水户的供水公平性；
(5)采用基于抛物线的非线性收敛方式，可使收敛因子a初期衰减程度降低，确保更好地寻找全局最优解；后期衰减程度提高，更加精确地寻找局部最优解，能够有效地平衡灰狼算法全局搜索和局部搜索能力，提高模型求解效率；
附图说明
图1是本发明的方法流程图；
图2是本发明中步骤4-2的具体流程图；
图3是本发明中步骤4-2-3中的参数a非线性收敛图；
图4是本发明中步骤4-4的具体流程图；
图5是实施案例中D 2分区系统概化图；
具体实施方式
下面结合具体实施例，进一步阐明本发明，应理解这些实施例仅用于说明本发明而不用于限制本发明的范围，在阅读了本发明之后，本领域技术人员对本发明的各种等价形式的修改均落于本申请所附权利要求所限定的范围。
如图1所示，一种基于“分区-分级”理论的复杂水资源系统优化配置方法，具体包括以下步骤：
步骤1，获取水资源系统基本信息数据，包括水库水位-库容关系曲线，水库、泵站、河道、输水管道、水厂的基本特征参数、地理位置信息等；
步骤2，将复杂水资源系统概化为不同单元，包括节点和有向线段；
步骤3，对整个复杂水资源系统进行片区划分，分别建立不同分区水力关系数字化矩阵；
步骤4，按照供水水源类型构建和求解多级水资源系统优化配置模型，确定合理的水资源优化配置方案集合。
所述步骤2中将系统中的水库、泵站、河道、水厂分别概化为节点，输水管道概化为有向线段。
步骤3中分区原则是以水厂为分区中心，按照水库、泵站、河道、输水管道与水厂之间的供给水关系进行片区划分。
步骤3中将不同分区之间的交汇处概化为虚拟节点。
步骤3中水力关系矩阵均以0，-1和1数字化表示，其中0表示无水力关系，-1表示出流，1表示入流。
所述步骤4中的供水水源包括本地水和外调水，其中本地水包括水库和河道水。
步骤4-1，仅考虑本地水，建立第一级水资源单目标优化配置模型。以分区水资源系统为对象，分别构建各分区以水厂供水保证率最大为目标函数，以水量平衡、本地水源可供水量、泵站过流能力、管道输水能力等为约束的水资源单目标优化配置模型，其中，目标函数：
Figure PCTCN2021085198-appb-000006
式中，Q j为j水厂的需水量(m 3)，x ij为第i水库向第j水厂的供水量(m 3)。
步骤4-2，采用改进的单目标灰狼算法进行上述模型求解，确定各个水厂的缺水量WQ i(i＝1,2,...,M)，M为整个水资源系统内的水厂个数；
步骤4-3，同时考虑本地水和外调水，建立第二级水资源多目标优化配置模型。以整个水资源系统为对象，构建以系统供水保证率最大、运营总成本最小为目标函数，以外调水分配到各个水厂不小于各水厂缺水量WQ i、水量平衡、本地水源可供水量、外调水水源可供水量、泵站过流能力、管道输水能力等为约束的水资源多目标优化配置模型，其中，目标函数为：
供水保证率最大
Figure PCTCN2021085198-appb-000007
运营总成本最小Min f 2(x)＝M e+M i-M b     (3)
式中，k＝1,2,..,K为分区个数，M i为本地水使用费用(￥)，M e为外调水使用费用(￥)，M b为收益(￥)。其中，本地供水费用包括泵站运行电费、政府水资源费用、非自有水库水资源购置费；外调水包括政府水资源费、以及泵站运行电费。
步骤4-4，按照各分区计算，采用改进的多目标灰狼算法求解多目标优化配置模型，获得Pareto方案集合，确定不同方案下各个水库的配水量和外调水量。
步骤4-2的采用改进的单目标灰狼算法求解各个分区单目标优化模型，其流程图如图2所示，具体步骤如下：
步骤4-2-1，初始化算法参数和种群。种群规模大小为Popsize，最大迭代 次数Maxgen，决策变量个数Dimension，决策变量取值范围[Lb,Ub]，按照决策变量的取值范围初始化灰狼种群X＝[X 1,X 2,...,X i,...,X Popsize]；
步骤4-2-2，计算种群中每个个体的适应度，其中水厂供水保证率越大，返回的适应度越大；按照适应度大小进行排序，选择并保存适应度最大的三个个体：X α、X β、X δ，其中X α为全局最优的灰狼；
步骤4-2-3，更新收敛因子A、C和a，按照X α、X β、X δ对种群中的所有灰狼个体进行更新，更新方式为：
Figure PCTCN2021085198-appb-000008
其中，t为迭代次数，A＝2a×r 1-a，C＝2×r 2；A、C和a均为收敛因子，r 1、r 2为随机变量，r 1、r 2∈(0，1)，D α、D β、D δ表示个体X α、X β、X δ与个体X i之间的距离。
步骤4-2-4，判断迭代次数是否已达到MAXGEN，若是，则终止运行并输出水厂的缺水量；若否，返回步骤4-2-2继续进化；
步骤4-2-5，确定系统内所有水厂的缺水量。
如图3所示，所述的收敛因子a采用基于抛物线的非线性收敛方式，方程为：
a＝2-2(t/MAXGEN) 2        (5)
其中，t为当前迭代次数，MAXGEN为最大迭代次数。
步骤4-4，采用改进的多目标灰狼算法求解整个系统的多目标优化配置模型，获得Pareto方案集合，确定不同方案下各个水库的配水量和外调水量，其流程图如图4所示，具体步骤如下：
步骤4-4-1，初始化算法参数和种群。种群规模大小为N p，外部归档集个数为N e，最大迭代次数为N gen，决策变量个数为N d，决策变量取值范围为[Lb,Ub]，按照决策变量的取值范围初始化灰狼种群X；
步骤4-4-2，计算种群中每个个体的适应度值，按照适应度值计算所有个体的非支配排序等级
Figure PCTCN2021085198-appb-000009
和拥挤距离
Figure PCTCN2021085198-appb-000010
按照以下规则选取N e个个体作为初始的外部归档集NEA：选取非支配排序等级为rank＝1的 个体，若等级为1的个体数量大于N e，则选择拥挤距离较大的前N e个体；若不足，则依此选择排序等级为rank＝rank+1中拥挤距离较大的个体，直至外部归档集NEA包含个体数为N e，以保证种群的多样性；
步骤4-4-3，在外部归档集NEA中按照以下规则选择X' α、X' β、X' δ三个个体作为优先等级：若非支配排序的等级均为非占优等级或第一等级，分别选取拥挤距离最大的前三个个体作为X' α、X' β、X' δ、X δ；若非支配排序的等级个数等于2，分别在rank＝1的等级中选取拥挤距离最大的前两个个体作为X' α、X' β，在rank＝2的等级中选取拥挤距离最大的个体作为X' δ；若非支配排序的等级个数大于2，分别在rank＝1、2、3等级选取拥挤距离最大的三个个体作为X' α、X' β、X' δ，其中X' α为全局最优的灰狼；
步骤4-4-4，按照X' α、X' β、X' δ采用式(4)-(5)对种群中的所有灰狼个体进行更新；
步骤4-4-5，计算种群中每个个体的适应度值，将更新后的新种群与外部归档集NEA进行合并，按照步骤4-4-2所述的选取规则更新外部归档集NEA；
步骤4-4-6，判断迭代次数是否已达到MAXGEN，若是，则终止运行并输出外部归档集NEA中的Pareto非劣解集合；若否，返回步骤4-4-3继续进化；
步骤4-4-7，整理输出不同非劣解对应的水库供水量、河道翻水量和外调水量。
现以某城市复杂水资源系统优化配置为例，说明发明方法的有效性与合理性。该研究地区涉及27个水库、22个泵站以及4个供水水厂：A、B、C和D水厂。按照泵站、水库与水厂的供给水关系可将此区域划分为3个片区，D 1、D 2和D 3，其中A和B水厂位于D 1分区，C水厂位于D 2分区，D水厂位于D 3分区。对系统进行概化，如图5所示为D 2分区系统概化图；分析各片区的水力关系，建立数字化矩阵，如表1为D 2分区的水力关系数字化矩阵的部分信息。选取计算时段为2016年6月1日，按照供水水源类型构建和求解研究区多级水资源系统优化配置模型，表2为以6月1日为例，在多目标解集中选择的多组水库配水方案，可知，在多种方案下四个水厂于6月1日供水保证率均满足100％。其中所在D 1分区的R 1水库存储外调水，并负责对A、B、C三个水厂进行供水。
表1 D 2分区的水力关系数字化矩阵的部分信息
Figure PCTCN2021085198-appb-000011
Figure PCTCN2021085198-appb-000012
表2 6月1日多组水库供水水量方案
Figure PCTCN2021085198-appb-000013
Figure PCTCN2021085198-appb-000014

Claims (8)

  1. 一种基于“分区-分级”理论的复杂水资源系统优化配置方法，其特征在于，包括以下步骤：
    步骤1，获取水资源系统基本信息数据，包括水库水位-库容关系曲线，水库、泵站、河道、输水管道、水厂的基本特征参数、地理位置信息；
    步骤2，将水资源系统概化为不同单元，包括节点和有向线段；
    步骤3，对整个水资源系统进行片区划分，分别建立不同分区水力关系数字化矩阵；
    步骤4，按照供水水源类型构建和求解多级水资源系统优化配置模型，确定合理的水资源优化配置方案集合；
    所述步骤4中的供水水源包括本地水和外调水，其中本地水包括水库和河道水；所述步骤4按照供水水源类型构建和求解多级水资源系统优化配置模型，包括以下步骤：
    步骤4-1，仅考虑本地水，建立第一级水资源单目标优化配置模型：以分区水资源系统为对象，分别构建各分区以水厂供水保证率最大为目标函数，以水量平衡、本地水源可供水量、泵站过流能力、管道输水能力为约束的水资源单目标优化配置模型；
    步骤4-2，采用改进的单目标灰狼算法求解步骤4-1建立的各个分区单目标优化配置模型，确定各个水厂的缺水量WQ i，其中，i＝1,2,...,M，M为整个水资源系统内的水厂个数；
    步骤4-3，同时考虑本地水和外调水，建立第二级水资源多目标优化配置模型：以整个水资源系统为对象，构建以系统供水保证率最大、运营总成本最小为目标函数，以外调水分配到各个水厂不小于各水厂缺水量WQ i、水量平衡、本地水水源可供水量、外调水水源可供水量、泵站过流能力、管道输水能力为约束的水资源多目标优化配置模型；
    步骤4-4，采用改进的多目标灰狼算法求解步骤4-3建立的系统多目标优化配置模型，获得Pareto方案集合，确定不同方案下各个水库的配水量和外调水量。
  2. 如权利要求1所述的基于“分区-分级”理论的复杂水资源系统优化配置方法，其特征在于，所述步骤2中将系统中的水库、泵站、河道、水厂分别概化为节点，输水管道概化为有向线段。
  3. 如权利要求1所述的基于“分区-分级”理论的复杂水资源系统优化配置方法，其特征在于，所述步骤3中分区原则是以水厂为分区中心，按照水库、泵站、河道、输水管道与水厂之间的水力关系进行片区划分。
  4. 如权利要求3所述的基于“分区-分级”理论的复杂水资源系统优化配置方法，其特征在于，所述步骤3中将不同分区之间的交汇处概化为虚拟节点。
  5. 如权利要求3所述的基于“分区-分级”理论的复杂水资源系统优化配置方法，其特征在于，所述步骤3中水力关系均以0，-1和1数字化表示，其中0表示无水力关系，-1表示出流，1表示入流。
  6. 如权利要求1所述的基于“分区-分级”理论的复杂水资源系统优化配置方法，其特征在于，所述步骤4-2采用改进的单目标灰狼算法求解各个分区单目标优化模型，包括以下步骤：
    步骤4-2-1，初始化算法参数和种群，其中，种群规模大小为Popsize，最大迭代次数为Maxgen，决策变量个数为Dimension，决策变量取值范围为[Lb,Ub]，按照决策变量的取值范围初始化灰狼种群X＝[X 1,X 2,...,X i,...,X Popsize]；
    步骤4-2-2，计算种群中每个个体的适应度，其中水厂供水保证率越大，返回的适应度越大；按照适应度大小进行排序，选择并保存适应度最大的三个个体：X α、X β、X δ，其中X α为全局最优的灰狼；
    步骤4-2-3，采用X α、X β、X δ对种群中的所有灰狼个体进行更新，更新方程为：
    Figure PCTCN2021085198-appb-100001
    其中，t为迭代次数，A＝2a×r 1-a，C＝2×r 2；A、C和a均为收敛因子，r 1、r 2为随机变量，r 1、r 2∈(0，1)，D α、D β、D δ表示个体X α、X β、X δ与个体X i之间的距离；
    步骤4-2-4，判断迭代次数是否已达到MAXGEN，若是，则终止运行并输出水厂的缺水量；若否，返回步骤4-2-2；
    步骤4-2-5，确定系统内所有水厂的缺水量。
  7. 如权利要求6所述的基于“分区-分级”理论的复杂水资源系统优化配 置方法，其特征在于，所述步骤4-2-3中，收敛因子a采用基于抛物线的非线性收敛方式收敛，方程为：
    a＝2-2(t/MAXGEN) 2  (2)
    。
  8. 如权利要求7所述的基于“分区-分级”理论的复杂水资源系统优化配置方法，其特征在于，所述步骤4-4采用改进的多目标灰狼算法求解系统多目标优化配置模型，包括以下步骤：
    步骤4-4-1，初始化算法参数和种群，其中，种群规模大小为N p，外部归档集个数为N e，最大迭代次数为N gen，决策变量个数为N d，决策变量取值范围为[Lb,Ub]，按照决策变量的取值范围初始化灰狼种群X；
    步骤4-4-2，计算种群中每个个体的适应度值，按照适应度值计算所有个体的非支配排序等级
    Figure PCTCN2021085198-appb-100002
    和拥挤距离
    Figure PCTCN2021085198-appb-100003
    其中，j＝1,2,...,N p，
    Figure PCTCN2021085198-appb-100004
    为迭代t次后第j个体的非支配排序等级，
    Figure PCTCN2021085198-appb-100005
    为迭代t次后第j个体的拥挤距离，按照以下规则选取N e个个体作为初始的外部归档集NEA：选取非支配排序等级为rank＝1的个体，若等级为1的个体数量大于N e，则选择拥挤距离较大的前N e个体；若不足，则依次选择排序等级为rank＝rank+1中拥挤距离较大的个体，直至外部归档集NEA包含个体数为N e，以保证种群的多样性；
    步骤4-4-3，在外部归档集NEA中按照以下规则选择X' α、X' β、X' δ三个个体作为优先等级：若非支配排序的等级均为非占优等级或第一等级，分别选取拥挤距离最大的前三个个体作为X' α、X' β、X' δ；若非支配排序的等级个数等于2，分别在rank＝1的等级中选取拥挤距离最大的前两个个体作为X' α、X' β，在rank＝2的等级中选取拥挤距离最大的个体作为X' δ；若非支配排序的等级个数大于2，分别在rank＝1、2、3等级选取拥挤距离最大的三个个体作为X' α、X' β、X' δ，其中X' α为全局最优的灰狼；
    步骤4-4-4，按照X' α、X' β、X' δ采用式(1)-(2)对种群中的所有灰狼个体进行更新；
    步骤4-4-5，计算种群中每个个体的适应度值，将更新后的新种群与外部归档集NEA进行合并，按照步骤4-4-2所述的选取规则更新外部归档集NEA；
    步骤4-4-6，判断迭代次数是否已达到MAXGEN，若是，则终止运行并输出外部归档集NEA中的Pareto非劣解集合；若否，返回步骤4-4-3；
    步骤4-4-7，整理输出不同非劣解对应的水库供水量、河道翻水量和外调水量。
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