Water resource multi-objective optimization configuration method considering mixing uncertainty

Abstract

The invention provides a water resource multi-objective optimization configuration method considering mixing uncertainty, which comprises the following steps: introducing a fuzzy random variable to quantify the mixing uncertainty in a water resource system, and taking a quantization result as input data of a water resource optimization configuration model, each water department is a lower-layer decision maker, the lower-layer decision maker is a follower of an upper-layer decision maker, the upper-layer decision maker corresponds to a plurality of lower-layer decision makers as followers, and a multi-target hierarchical master-slave interaction optimization configuration model with the upper-layer decision maker as a dominator and the lower-layer decision makers as followers is constructed. According to the method, the water resource system of the research area is analyzed, and the mixed water distribution mechanism is constructed, so that the state of each component element of the water resource system in each time period is clearer and more visual, and an effective reference basis is provided for actual water resource configuration.

Description

Technical Field

[0001] The present invention relates to the technical field of water resource scheduling and configuration, and in particular to a water resource multi-objective optimization configuration method considering mixed uncertainty. Background Art

[0002] Water resources not only play a vital role in maintaining the natural ecology, but also are the basic resources for human reproduction and sustainable development. Especially in the context of rapid population growth, accelerated urbanization, and increasingly tight water resources, sustainable and efficient water resources management is of great significance to a region or country. Due to the limited regional water resources, there will be demand conflicts between water-using departments, especially in the dry season. Establishing an efficient and reasonable water allocation mechanism is one of the important measures to alleviate the contradiction between water supply and demand. In addition, due to the uncertainty of rainfall runoff and the combined influence of social and economic factors, regional water resources allocation faces the challenge of complex uncertainty, which directly threatens the water security of various regions in the region. Therefore, in the context of limited available water resources and difficult prediction, how to adopt a reasonable and efficient water resources allocation method to deal with water shortage is an urgent problem to be solved at present.

[0003] As a public resource that is vital to economic development and social life, water resources cannot be rationally allocated solely on the water market. A water allocation mechanism should be established with the macro-control of decision-makers under regional unified management as the main body and water market allocation as the auxiliary, so as to ensure that water resources can be used in a unified, coordinated and sustainable manner, and ensure that water resources can maintain their long-term stable ecological and environmental functions while meeting the needs of economic development and society. For decision-makers, water environment and ecological water demand issues must be regarded as key issues, and coordination between different water transmission and distribution projects must be considered. For specific water resource zoning, the optimal economy is often pursued. The regional water resources allocation system is a complex system involving multiple subjects, and subjects with different goals often have a hierarchical relationship, such as the upper-level basin water resources management department and the lower-level industry water use department. If the decision-making needs of any party are simply ignored, the fairness and rationality of the water resources allocation process may be undermined. In existing studies, the study area is regarded as an independent individual, ignoring the hydraulic connection between the study area and other surrounding areas. For example, the Han-Wei Diversion Project in the Weihe River Basin, the water transport volume is one of the important water sources for some cities or regions. When constructing a complex stratified water system model, it is necessary to take into account inter-basin water transfer projects, which play a vital role in the water resource allocation process between basins. From the perspective of basin water resource system managers, it is necessary to consider the multi-objective needs of different entities in the complex water resource system. Summary of the invention

[0004] In view of the increasingly prominent contradiction between water supply and demand, and the particularly obvious water use conflicts among different water-using departments, the present invention provides a multi-objective hierarchical master-slave interactive optimization configuration method for a regional complex water resources system considering mixed uncertainties.

[0005] The solution adopted by the present invention to solve its technical problem is: a multi-objective optimization configuration method for water resources considering mixed uncertainty, which introduces fuzzy random variables to quantify the mixed uncertainty in the water resources system, and uses the quantified results as input data of the water resources optimization configuration model, wherein the river basin manager in the water resources system is the upper decision maker, the water use departments are the lower decision makers, the lower decision makers are the followers of the upper decision makers, and the upper decision makers correspond to multiple lower decision makers as followers, and a multi-objective hierarchical master-slave interactive optimization configuration model with multiple followers, in which the upper decision makers are the leaders and the lower decision makers are the followers, is constructed.

[0006] Each follower is independent of each other, and the optimization of each follower only involves its own variables and upper-level variables. Therefore, the lower-level decision optimization objective in the multi-objective hierarchical master-slave interactive optimization configuration model is the sum of multiple lower-level decision optimization objective functions.

[0007] The upper-level decision optimization objective function is:

[0008]

[0009] in

[0010]

[0011] is the objective function of sustainable development demand,

[0012]

[0013] is the user satisfaction objective function,

[0014]

[0015] The objective function is to reduce the water cost of water use departments;

[0016] For any water resource partition w∈W, the lower-level decision variables are The lower-level decision optimization objective function is:

[0017]

[0018] It indicates that the net economic benefit is the largest;

[0019] Among them, t is the time index, r is the reservoir index, w is the water resource partition index, k is the water use industry index, T is the time set, R is the reservoir set, W is the water resource partition set, K is the water use industry set, R is the reservoir set, r The set of reservoirs connected to reservoir r, W r The set of water resource partitions connected to reservoir r, K w The set of water-using industries within the water resource zone w, The inflow of reservoir r in time period t, The total water demand of industry k in water resource zone w during time period t, The economic benefits per unit of water obtained by industry k in water resource zone w during time period, The upper limit of the fee per unit of water charged by industry k in water resource zone w during time period t, Initial reservoir available water volume, L rr Dead water capacity of reservoir r, U rr The beneficial storage capacity of reservoir r, L rw The minimum capacity of the channel connecting the reservoir r and the water resource zone w, if it is a river channel, needs to meet the ecological flow, U rw The maximum capacity of the channel connecting the reservoir r and the water resource partition w, The water storage capacity of reservoir r at the end of period t is, Flow from reservoir r to reservoir in time period t The amount of water, The amount of water flowing from reservoir r to water resource partition w during time period t, The amount of seawater flowing out of reservoir r during time period t, The deficit storage capacity of reservoir r in period t, From reservoir r to reservoir r in time period t The loss of the minimum ecological flow requirement of the river, The outflow from reservoir r to the sea during time period t is insufficient. The price charged per unit of water by industry k in water resource zone w during time period t, The amount of water allocated to industry k in water resource zone w during time period t;

[0020] In the process of solving the above-mentioned multi-objective hierarchical master-slave interactive optimization configuration model, the equivalent KKT condition is introduced to transform the multi-objective and multi-user two-level optimization problem of the multi-objective hierarchical master-slave interactive optimization configuration model into an equivalent multi-objective mixed integer single-level model, so as to find a suitable water resources optimization configuration plan.

[0021] Furthermore, the constraints of the upper-level decision optimization objective function are:

[0022]

[0023] System water balance,

[0024]

[0025] Minimum reservoir storage capacity limit,

[0026]

[0027] Minimum requirements for water inflow,

[0028]

[0029] Minimum ecological flow limit for connecting rivers between reservoirs,

[0030]

[0031] Maximum reservoir capacity,

[0032]

[0033] The water storage capacity limit of the water diversion channel system,

[0034]

[0035] The upper limit of water supply price,

[0036]

[0037] The variable is non-negative.

[0038] Furthermore, the constraints of the lower-level decision optimization objective function are:

[0039]

[0040] The amount of water allocated to a specific water resource division,

[0041]

[0042] The actual water supply is less than the water demand.

[0043]

[0044] The variable is non-negative.

[0045] Furthermore, the upper-level decision-making optimization goals include sustainable development demand goals, user satisfaction goals, and reducing water costs for water-using departments. The priorities of the above three goals decrease layer by layer.

[0046] Furthermore, the quantification of mixed uncertainty factors in water resource systems based on fuzzy random variables includes discrete fuzzy random reservoir inflow quantification and continuous random fuzzy water demand quantification.

[0047] Among them, the discrete fuzzy random reservoir inflow quantification is to convert the discrete fuzzy random variables into trapezoidal fuzzy numbers.

[0048]

[0049]

[0050] The expectation of the trapezoidal fuzzy number is:

[0051]

[0052] The trapezoidal fuzzy number obtained by this transformation is processed by Me fuzzy processing, and the reservoir inflow can be obtained as follows:

[0053]

[0054] Among them, λ1∈[0,1] is the optimistic coefficient. The larger λ1 is, the The bigger,

[0055] In the model, the reservoir inflow is recorded as make represents the inflow of reservoir r in time period t;

[0056] In the continuous random fuzzy water demand quantification, the water demand of water use department i is in , according to the random fuzzy expected value operator, the trapezoidal fuzzy number can be obtained:

[0057]

[0058] The Me fuzzy processing is used for the trapezoidal fuzzy number, and the determined departmental water demand can be obtained as follows:

[0059]

[0060] Among them, λ2∈[0,1] is the optimistic coefficient. The larger λ2 is, the The larger the value, the water demand of each industry in the model is recorded as make represents the water demand of industry k in time period t.

[0061] Beneficial effects of the invention: The invention provides a multi-objective optimization configuration method for water resources taking into account mixed uncertainties, introduces fuzzy random variables into the water resource system, analyzes the mixed uncertainty factors in the water resource system, and uses the results as the input of the water resource optimization configuration model; introduces machine learning, uses BP neural network to fit the water use benefit function, and uses historical data to calibrate the model parameters, the model calibration period fitting accuracy is 0.93, and the verification period fitting accuracy is 0.89.

[0062] By analyzing the water resources system in the study area, a mixed water allocation mechanism dominated by administrative allocation and supplemented by water market regulation is constructed, and a multi-objective hierarchical master-slave interactive optimization configuration model is established with basin managers as upper-level decision makers and various water-using departments as lower-level followers. The upper level aims to meet ecological water needs, maximize water user satisfaction and minimize water use costs, and the lower level aims to maximize economic benefits. In the process of model construction, the water resources system is split into various independent element formulas (such as water use units, reservoirs, water diversion projects, etc.), and they are connected according to actual hydraulic connections. The model can not only solve the water resources optimization configuration plan, but also obtain the discharge volume and reservoir status of each reservoir in the basin at each time period, making the status of each component element of the water resources system at each time period clearer and more intuitive, providing an effective reference for actual water resources allocation. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is a principle block diagram of the multi-objective optimization configuration method of water resources considering mixed uncertainty according to the present invention;

[0064] Figure 2 is the transformation diagram of discrete fuzzy random reservoir inflow;

[0065] Figure 3 It is a schematic diagram of the BP neural network structure;

[0066] Figure 4 It is a schematic diagram of the model structure and variables of the present invention;

[0067] Figure 5 This is the water use structure diagram of the Weihe River section in the Shaanxi Basin;

[0068] Figure 6 This is the water resources allocation node diagram of the Shaanxi section of the Weihe River Basin;

[0069] Figure 7 This is a map of the annual water supply in the Shaanxi section of the Weihe River Basin;

[0070] Figure 8 This is a diagram of the annual operating status of the Linjiacun Reservoir in the Weihe River Basin in Shaanxi Province. DETAILED DESCRIPTION

[0071] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be described in detail below.

[0072] Example 1: The present invention provides a multi-objective optimization configuration method for water resources taking into account mixed uncertainties, adopts fuzzy number and fuzzy interval theory, introduces fuzzy random variables, and describes the uncertainty of water supply and demand in the water system; in addition, in the water resource system, different water use zones and water use industries have different ratios of converting water resources into economic benefits during the production process, which is affected by economic development, regional geographical location, etc., and this conversion relationship cannot be simply reduced to a simple linear function. Therefore, the present invention introduces a nonlinear BP neural network algorithm in machine learning to construct a water use efficiency function, so as to more accurately and conveniently express the complex relationship between water resources and economic benefits.

[0073] By collecting and analyzing measured data on water conservancy projects, hydrological data, meteorological data, human activities, etc., the water resources management model, ecological environment and water conservancy project operation mode, water supply in the basin, and water network topology are determined. The impact of the series and parallel operation mode of reservoirs in the basin and the scheduling scheme of cross-basin water transfer projects on the water resources management system are considered, and the hydraulic connection between the analysis elements in the region is analyzed to construct a complex water resources system in the basin. Based on the multiple water use goals of the basin water resources managers and supplemented by the water use goals of the lower-level water use departments, a generalized multi-objective hierarchical master-slave interactive optimization configuration model for the water system is constructed. The Karush-Kuhn-Tucker theorem is used to solve the constructed two-level optimization model, and the multi-objective and multi-user two-level optimization problem is converted into an equivalent multi-objective mixed integer single-level model to find the most suitable water resources optimization configuration plan.

[0074] like Figure 1 As shown, in the present invention, firstly, considering the uncertainty of the water resource system, fuzzy number and fuzzy interval theory are used to describe the uncertainty of water supply and demand in the water system; machine learning is introduced, and BP neural network is used to characterize the complex relationship between water resources and economic benefits, so as to quantify the impact of water resource uncertainty on the configuration of the water resource system.

[0075] Secondly, based on the uncertainty analysis of the water resources system, the optimal allocation of water resources between the internal interest competitors of the water resources system in the basin is discussed, and a multi-objective hierarchical master-slave interactive optimization configuration model is proposed. The model takes the realization of the decision-making requirements of the dominant formula (basin management department) as the main goal, and takes the response of the subordinate department formula (demand point manager) to the decision-making goal as a constraint. In the construction of the model, the role of the inter-basin water transfer project in the allocation of water resources between different basins is considered at the same time. From the perspective of the basin water resources manager, a multi-objective hierarchical master-slave interactive optimization configuration model of the regional complex water resources system considering mixed uncertainty is constructed. The constructed two-level optimization model is solved by using the Karush-Kuhn-Tucker theorem, and the multi-objective and multi-user two-level optimization problem is transformed into an equivalent multi-objective mixed integer single-level model to find the most suitable water resources optimization configuration scheme.

[0076] Affected by the natural environment, economic society and other factors, there is a large uncertainty in the external water supply and internal demand in the regional planning level year. In the process of optimizing the allocation of water resources system, the mixed uncertainty of the combination of two main uncertain factors, randomness and fuzziness, should be comprehensively considered. The present invention considers the reservoir inflow and water demand of each water-using department as different types of uncertain variables. At the same time, considering the complex relationship between water resources and economic benefits, machine learning is introduced to construct the water resources economic benefit function.

[0077] When optimizing the water resource optimization model considering economic factors, water consumption as a decision variable is constantly changing, and this change is affected by economic benefits; changes in water consumption also affect economic benefits. That is, water volume and economic benefits affect each other during the model solution process, and it is impossible to optimize one of them first to optimize the other. Therefore, machine learning is embedded in the water resource optimization model, and the uncertainty relationship between the water efficiency coefficient and water consumption is used as one of the constraints of the water resource optimization model, and finally the optimal solution for water consumption and economic benefits is found.

[0078] The quantification of uncertainty factors of water supply and demand based on fuzzy theory includes discrete fuzzy random reservoir inflow quantification method and continuous random fuzzy water demand quantification method.

[0079] In the discrete fuzzy random reservoir inflow quantification method, the discrete fuzzy random reservoir inflow conversion process is as follows: Figure 2 As shown, firstly, the discrete fuzzy random variables are transformed into trapezoidal fuzzy numbers.

[0080]

[0081] The expectation of the trapezoidal fuzzy number is:

[0082]

[0083] The trapezoidal fuzzy number obtained by the transformation is processed by Me fuzzy processing method, and the reservoir inflow can be obtained as follows:

[0084]

[0085] Among them, λ1∈[0,1] is the optimistic coefficient. The larger λ1 is, the For the convenience of representation, the reservoir inflow in the model is recorded as make represents the inflow of reservoir r in time period t.

[0086] In the continuous random fuzzy water demand quantification method, the water demand of water use department i is in According to the random fuzzy expected value operator, the trapezoidal fuzzy number can be obtained:

[0087]

[0088] For the processing of trapezoidal fuzzy numbers, M is also used. e Using the fuzzy processing method, the departmental water demand can be determined as:

[0089]

[0090] Among them, λ2∈[0,1] is the optimistic coefficient. The larger λ2 is, the For the convenience of representation, the water demand of each industry in the model is recorded as make represents the water demand of industry k in time period t.

[0091] Water resource system water use efficiency assessment based on machine learning, such as Figure 3 As shown, the water use benefit function is a mathematical model to measure the economic benefits of the water use industry, and is the key to the water resource allocation process dominated by the water market. When constructing a water use benefit function, not only the production cost should be considered, but also the impact of potential factors such as region, industry, and technical conditions. Without a reasonable analysis of the influencing mechanism of the water use benefit function, blindly ignoring potential factors will affect the accuracy of the water use benefit function. Therefore, the present invention uses a machine learning method to perform feature analysis on large-scale data, extract the internal laws between variables that cannot be obtained through principle analysis, and then construct a more reasonable water use benefit function.

[0092] c=g(X;θ) (7)

[0093] Among them, X is the input data, that is, water consumption, c is the output data, that is, the economic benefits generated by water consumption X, and function g represents the mapping relationship, which is obtained by training the BP neural network. This method constructs a black box model, which makes the relationship between water resources and economic benefits invisible.

[0094] When optimizing the water resource optimization model considering economic factors, water consumption as a decision variable is constantly changing, and this change is affected by economic benefits; changes in water consumption also affect economic benefits. That is, water volume and economic benefits affect each other during the model solution process, and it is impossible to optimize one of them first to optimize the other. Therefore, machine learning is embedded in the water resource optimization model, and the uncertainty relationship between the water efficiency coefficient and water consumption is used as one of the constraints of the water resource optimization model, and finally the optimal solution for water consumption and economic benefits is found.

[0095] Starting from the relationship between policies and water markets, this paper explores the master-slave relationship of mutual coordination and mutual restraint between the upper-level policies and the lower-level markets in complex water systems, and constructs a multi-objective hierarchical master-slave interactive optimization configuration model under complex water systems. In the process of model solution, the equivalent KKT condition is introduced to transform the multi-objective and multi-user two-level optimization problem into an equivalent multi-objective mixed integer single-level model to find a suitable water resource optimization configuration scheme.

[0096] The present invention proposes a two-layer hybrid water allocation mechanism with administrative water allocation mechanism as the main mechanism and water market water allocation mechanism as the auxiliary mechanism. On the one hand, a representative decision-maker or water system supervisor is allowed to decide the total amount of water allocated to each water resource partition. Its goal is to allocate water based on environmental factors and the overall satisfaction of user needs, and allow fees to be charged for the water allocated to users. On the other hand, the managers of the water resource partitions decide on the different uses of the allocated water, that is, the amount of water allocated to water users is determined based on the maximum net benefit. The two decision-making levels make decisions according to a hierarchical structure. There are two decision-making levels in the two-layer hybrid water allocation mechanism. The goal of the upper decision-maker is to optimize his own objective function under a set of constraints. These constraints take into account the response of the lower decision-makers to the leader's plan. Incorporating the response of the lower decision-makers into the decision-making process can be used to evaluate the impact of different available water allocation strategies and the results of different simulation scenarios. Therefore, the two-level programming problem is formulated as an optimization problem that constrains another optimization problem. In addition, the model enables high-level decision-makers to use fees to influence the decisions made by decision-makers who do not directly belong to their authority decision-making level. The present invention constructs a multi-objective hierarchical master-slave interactive optimization configuration model with satisfying ecological water demand, maximizing water user satisfaction and minimizing water cost as the upper-level objectives and maximizing economic benefits as the lower-level objectives.

[0097] In order to express the modeling process more clearly, the variables and parameters used in the model are explained, as shown in Table 1:

[0098] Table 1 Description of model variables and parameters

[0099]

[0100]

[0101] In order to more clearly show the evolution of model variables and system states over time, Figure 4 The above is a simple water resource system and the variable transfer relationship between two time periods.

[0102] When exploring this two-tier hybrid water allocation mechanism in depth, we must first clarify its complex decision-making structure. The core of this mechanism lies in its two-tier decision-making system, that is, the coordination and interaction between upper-level decision makers and lower-level decision makers. The upper-level decision makers play the role of controlling the overall situation, and their goal is to optimize one or more objective functions that maximize system benefits or meet specific needs under strictly set constraints. These constraints are not simply set, but in-depth consideration of the feedback and reactions of lower-level decision makers to the plans proposed by upper-level leaders. This consideration reflects the flexibility of the mechanism and the complexity of actual operations. By incorporating the reactions of lower-level decision makers, upper-level decision makers can more accurately evaluate the effects of different water allocation strategies in actual operations and the possible consequences of different simulation scenarios.

[0103] Specifically, the two-level planning problem is a nested optimization structure. The upper-level decision makers first formulate a preliminary water distribution plan, and then based on this plan, the lower-level decision makers will make corresponding feedback and adjustments according to their own interests and needs. These feedbacks and adjustments will be reconsidered by the upper-level decision makers, and then the initial water distribution plan will be optimized and adjusted. This process will continue to iterate until an optimal solution is found that can meet the global goals of the upper-level decision makers and take into account the actual needs of the lower-level decision makers.

[0104] In addition, this two-tier mixed water distribution mechanism also gives the upper-level decision-makers a unique means of regulation - influencing the behavior of lower-level decision-makers by charging fees. This regulation method enables the upper-level decision-makers to influence decisions that are not within their direct decision-making authority to a certain extent, thereby achieving global coordination and optimization. Through reasonable fee setting and adjustment, the upper-level decision-makers can guide the lower-level decision-makers to develop in a direction that is more conducive to the overall interests of the system.

[0105] To facilitate understanding of the solution method of the two-level optimization model, the following content takes a leader and a follower as an example to briefly introduce the processing method and solution process of the problem. In this case, the two-level optimization model can be expressed as:

[0106]

[0107] Where, for any x, there is a variable y:

[0108]

[0109] In the formula, represents the upper-level variables controlled by the leader, Represents the lower-level variables controlled by followers; F, f: represents the objective function of the upper and lower layers; G j (x, y) and g h (x, y) represents the constraints of the upper and lower optimization models.

[0110] The two-level optimization problem is essentially a problem for the leader, so the upper decision maker must predict the response of the lower decision maker when finding the best decision. Once the leader sets the value of the upper variable, the followers are free to optimize their objective function. For a given x, the followers can solve the lower problem:

[0111]

[0112] If V = {(x, y): G j (x,y)≤0,j=1,…,q,g h (x, y)≤0, h=1,…,p}, M(x) is the optimal solution set of formula (2), T={(x, y):(x, y)∈V, y∈M(x)}, then (x, y)∈T can be called a bi-level feasible solution. If (x, y)∈T exists, then x is a permissible solution. Therefore, the double-layer formula (1) can be equivalently expressed as:

[0113]

[0114] Generally speaking, the two-level optimization problem is non-convex, which often makes it difficult to solve. In actual use, when there are multiple optimal values ​​in the lower level problem, that is, because there are multiple possible values ​​of y, the M(x) corresponding to a specific x is not unique, which makes the problem complicated. If the objective function of the upper level is sensitive to different y∈M(x), it is necessary to formulate corresponding rules to screen out y. * ∈M(x), used to calculate the objective function value F. The present invention adopts an optimistic approach, assuming that the upper-level decision makers have the power to influence the lower-level decision makers, so the latter are allowed to choose y *To calculate F. Even if all the functions involved in the bilevel optimization problem are linear, the problem is still a strong NP-hard problem.

[0115] Based on the above content, the present invention constructs a model. In this two-layer mixed water distribution mechanism, the decision-maker plays the role of a leader, controlling the operation mode of the reservoir and the water allocation ratio between different water resource zones. The manager of the water resource zone acts as a follower, controlling the allocation of water among industries within the zone. The two-layer optimization model can be expressed as follows:

[0116]

[0117] st

[0118]

[0119]

[0120] In addition, for any water resource partition w∈W, the decision variable is t∈T, which can be expressed as:

[0121]

[0122] st

[0123]

[0124] The three goals of the decision-makers are ranked in order by optimizing the objective function formulas (12) to (14) in sequence, so that the importance of the goals decreases layer by layer. For the decision-makers, the highest priority goal is to meet the needs of sustainable development, that is, to minimize the sum of the water deficit in the reservoir, the water deficit in the sea, and the downstream ecological deficit. If there is an extremely dry year, coefficients can be added in front of the three deficit variables to represent different weights. The second priority goal is user satisfaction, that is, the ratio of the actual allocated water volume to the required water volume. The main purpose of the decision-maker to charge for water supply is to influence the actual allocation of water resources rather than to obtain profits. Therefore, the model introduces the third objective function formula (14) to reduce the water use cost of each water-using department. Due to the inherent complexity of the two-layer model, the objective function is made as linear as possible in the present invention. Therefore, the third objective function selects the minimum sum of prices instead of the total amount paid by the water-using department. The objective function formula (25) of the lower model indicates that the net economic benefit is maximized.

[0125] In the upper model, constraint formula (15) represents the conservation of the overall water volume in the system; constraint formula (16) represents the minimum storage limit of the reservoir; constraint formula (17) represents the minimum requirement for the amount of water entering the sea; constraint formula (18) represents the minimum ecological flow limit of the river connecting the reservoirs; constraint formula (19) represents that the water storage of the reservoir cannot exceed its maximum capacity; constraint formulas (20) and (21) represent the water storage limit of the water diversion channel system; constraint formula (22) constrains the upper limit of the water supply price; constraint formulas (23) and (24) ensure that the variables are non-negative. In the lower model, constraint formula (26) represents that the amount of water allocated to a specific water resource zone can only be used for industries within the water resource zone; constraint formula (27) represents that the actual water supply cannot exceed the water demand; constraint formula (28) ensures that the variables are non-negative.

[0126] The above model function is a multi-objective hierarchical master-slave interactive optimization configuration model with |W| followers, where |W| represents the number of W. Each follower is independent of each other, so the optimization problem of the follower only involves its own variables and upper-level variables. The two-level programming model with multiple independent followers is transformed into a multi-objective hierarchical master-slave interactive optimization configuration model with a single follower. The lower-level problem after transformation is the objective function f of the original |W| lower-level problem. 2w After adding and considering the corresponding constraints, it can be expressed as follows:

[0127]

[0128] The constraints are the same as above formulas (15) to (27);

[0129] The lower-level decision variables are The underlying problem is stated as:

[0130]

[0131] st

[0132]

[0133] There are two decision-making levels in this two-level hybrid water allocation mechanism. The goal of the upper-level decision makers is to optimize their own objective function under a set of constraints that take into account the reactions of the lower-level decision makers to the leader's plan. Incorporating the reactions of the lower-level decision makers into the decision-making process can be used to evaluate the impact of different available water allocation strategies and the consequences of different simulation scenarios. Therefore, the two-level programming problem is formulated as an optimization problem involving another optimization problem in the constraint set. In addition, the model enables high-level decision makers to use fees to influence the decisions made by decision makers who do not directly belong to their authority decision level.

[0134] For solving the above-mentioned multi-objective hierarchical master-slave interactive optimization configuration model, the two-layer structure has the ability to model the hierarchical decision-making process, so even the simplest problem (linear function) is a strong NP-hard problem. The solution to the two-layer problem usually uses the feasibility conditions of the original problem and the dual problem and the strong dual equation or equivalent KKT conditions to replace the lower-level problem, thereby converting the original two-layer problem into a single-layer problem for solution. The present invention will use the KKT condition to replace the lower-level problem, and then convert formula (29) and formula (31) into a single-layer optimization model. The KKT condition is a necessary and sufficient condition for linear optimization problems. Therefore, formulas (32)-(34) can be converted into an equivalent problem.

[0135] First, introduce the variable and are used to represent the dual variables related to constraints (33) and (34), respectively. Then the dual problem corresponding to formulas (32)-(34) is

[0136]

[0137] st

[0138]

[0139] According to the application conditions of the KKT theorem, the necessary and sufficient conditions for the KKT condition to be established are as follows:

[0140]

[0141] Since (39)-(41) are nonlinear constraints, in order to simplify the solution process and improve the model solution efficiency, the binary variable Convert nonlinear constraints to linear constraints:

[0142]

[0143] in, are all sufficiently large constants, and are also the effective upper bounds of the original variables and the dual variables in the lower-level problem. The following formula is the mixed integer linear optimization problem after the original two-level optimization problem is transformed,

[0144]

[0145] st(50)

[0146] (16)-(24), (32)-(34), (36)-(38), (42)-(49)

[0147] Since the values ​​of these sufficiently large constants will affect the model output, all the lower-level optimal points are retained to ensure the optimality of the model solution. If the KKT theorem and its complementary conditions are used, combined with the classical large-M method linearization, to solve a given two-level optimization problem, it is necessary to study the effective upper bound of the dual variable in the lower-level problem (the effective upper bound of the original variable is relatively easy to determine due to its unique properties). Considering the characteristics of the original problem and the dual problem, the following conclusions can be obtained through proof.

[0148]

[0149] The present invention is mainly based on the mixed uncertainty conditions of discrete random fuzzy runoff and continuous random fuzzy water demand, with administrative allocation as the main factor, supplemented by a mixed water allocation mechanism regulated by the water market. On the basis of considering the water use satisfaction, environmental protection goals and economic benefit goals of water use departments in the basin, a multi-objective hierarchical master-slave interactive optimization configuration model of regional complex water resources system considering mixed uncertainty is constructed, and the model is simplified and solved using equivalent KKT conditions. At the same time, machine learning is introduced to embed the BP neural network model into the optimization configuration model, which is used to concisely and accurately characterize the water use benefit function.

[0150] The present invention introduces fuzzy random variables into the water resource system, analyzes the mixed uncertainty factors in the water resource system, and uses the results as the input of the water resource optimization allocation model; introduces machine learning, uses BP neural network to fit the water use benefit function, and uses historical data to calibrate the model parameters. The fitting accuracy of the model during the calibration period is 0.93, and the fitting accuracy during the verification period is 0.89.

[0151] By analyzing the water resources system in the study area, a mixed water allocation mechanism dominated by administrative allocation and supplemented by water market regulation is constructed, and a multi-objective hierarchical master-slave interactive optimization configuration model is established with basin managers as upper-level decision makers and various water-using departments as lower-level followers. The upper level aims to meet ecological water needs, maximize water user satisfaction and minimize water use costs, and the lower level aims to maximize economic benefits. In the process of model construction, the water resources system is split into various independent elements (such as water use units, reservoirs, water diversion projects, etc.), and they are connected according to actual hydraulic connections. The model can not only solve the water resources optimization configuration plan, but also obtain the discharge volume and reservoir status of each reservoir in the basin at each time period, making the status of each component element of the water resources system at each time period clearer and more intuitive, providing an effective reference for actual water resources allocation.

[0152] Example 2: This example uses the Shaanxi section of the Weihe River Basin as an example to simulate the water resource system and verify the water resource allocation plan.

[0153] According to the water resources zoning in the National Water Resources Comprehensive Plan, the Shaanxi section of the Weihe River Basin is divided into the following 9 fourth-level water resources zones. The total area, surface water resources, groundwater resources and total water resources of each zone are obtained by consulting the data. See Table 2 below for details.

[0154] Table 2 Summary of water resources in water resource divisions in the Weihe River Basin in Shaanxi Province

[0155]

[0156] The water supply and use in the Shaanxi section of the Weihe River Basin in 2022 are shown in Tables 3 and 4. In general, the total water supply in the Shaanxi section of the Weihe River Basin reached 6.325 billion m 3 , of which surface water supply is 4.046 billion m 3 , accounting for 63.97% of the total water supply; groundwater supply is 1.928 billion m 3 , accounting for 30.48% of the total water supply; the water supply of other types of water sources is 351 million m 3 , accounting for only 5.55% of the basin’s water supply. From an industry analysis, agricultural water consumption is 4.139 billion m 3 , occupying 64.50% of the water volume, and industrial water consumption of 71,500 m 3 , occupying 11.14% of the water volume.

[0157] Table 3 Water supply results for the Weihe River Basin in Shaanxi Province in 2020 Unit: billion m 3

[0158]

[0159]

[0160] Table 4 Water use results for the Weihe River Basin in Shaanxi Province in 2020 Unit: billion m 3

[0161]

[0162] In terms of water use structure, agricultural water use accounts for more than 50% in the Shaanxi section of the Weihe River Basin, showing a gradually decreasing trend; water use for secondary and tertiary industries accounts for more than 30%, and water use efficiency continues to improve; domestic water use accounts for nearly 15%, and is showing an increasing trend. Figure 5 shown.

[0163] The measured runoff data used in this example are all from the Basin Hydrological Yearbook from 2000 to 2020. Through field research in the study area, basic information data of water conservancy projects (mainly including reservoir location, dead storage capacity, total storage capacity, water level storage capacity curve, flood limit water level, normal water storage level and other data, as well as reservoir operation and scheduling rules, water diversion channel water capacity and other data) are obtained.

[0164] The average annual flow of important rivers in the basin is set as a discrete fuzzy random variable. The specific parameters are shown in Table 5. The acquisition steps are as follows:

[0165] 1) The average annual flow levels of important rivers in the basin from 2000 to 2020 are divided into five categories;

[0166] 2) Estimate the range of annual average flow levels for each type of river based on historical data;

[0167] 3) The probability of each category occurring is formed based on historical data aggregation.

[0168] Table 5 Annual average runoff of fuzzy random river channels

[0169]

[0170] At the same time, the water demand of each department is set as a continuous fuzzy random variable. The specific parameters are shown in Table 6. The acquisition steps are as follows:

[0171] 1) Assume that the water demand of industries in each region approximately follows a normal distribution, and perform maximum likelihood estimation on the distribution parameters;

[0172] 2) Prove the rationality of normal distribution in modeling observed data through normality test;

[0173] 3) By making a fuzzy evaluation of future trends, the mean of the probability distribution is considered as a fuzzy number, and the minimum value, maximum value and most likely interval are given.

[0174] Table 6 Random fuzzy water demand

[0175]

[0176]

[0177]

[0178] The BP neural network is used to accurately predict the water use efficiency of each area in the Shaanxi section of the Weihe River Basin. By inputting the relevant water use data from 2000 to 2020, and continuously optimizing and adjusting the network weights and thresholds in the hidden layer, when the error between the predicted value and the actual value is within the preset error range, the predicted value is output to the output layer. After repeated calibration and calibration, the model determined two hidden layers, including 6 and 3 hidden layer nodes respectively. The specific parameters are shown in Table 7. Finally, the fitting results of the model reached the best state, with the model calibration period fitting accuracy (R2) of 0.93 and the validation period fitting accuracy of 0.89.

[0179] Table 7 Model parameter settings

[0180]

[0181] This embodiment divides the Shaanxi section of the Weihe River into eight calculation units. Six large reservoirs and 53 medium-sized reservoirs have been built in the basin. In order to allocate and manage water resources more effectively, some representative reservoirs and water diversion projects are selected as basic engineering nodes for drawing the network diagram of the water resources allocation system according to the characteristics of the basin. At the same time, the actual distribution of the water system in the basin is fully considered, and according to the actual water supply and use situation of the Shaanxi section of the Weihe River and the spatial distribution of water conservancy projects such as reservoirs, water diversion projects, and canal systems (rivers), etc. Figure 6 As described above, computing units, reservoirs, channels, etc. are all generalized into elements to form a network diagram of the water resources allocation system.

[0182] The discrete fuzzy random variable method described in the present invention is used to transform discrete fuzzy random variables and continuous random fuzzy variables, and the water demand data and water inflow data of the water resources system in the Shaanxi section of the Weihe River Basin are obtained, which lays the foundation for model solution. By considering the important reservoirs and inter-basin water diversion projects in the study area, the topological relationship of the complex water system in the Shaanxi section of the Weihe River Basin is established, and a multi-objective hierarchical master-slave interactive optimization configuration model of the regional complex water resources system under uncertain conditions in the Shaanxi section of the Weihe River Basin is constructed. At the same time, the BP neural network is embedded in the configuration model to concisely express the water use benefit function in the water resources system in the model. Afterwards, the constructed model is solved based on the mathematical linear programming solver (Gurobi 10.0.3) and the machine learning solution library (Scikit-learn), and the water resources configuration plan and the discharge flow process of each reservoir are output.

[0183] According to the water conservancy connection and economic development of the Shaanxi section of the Weihe River Basin, the water resources allocation plan for the Weihe River Basin in Shaanxi Province can be obtained by analyzing and calculating the multi-objective hierarchical master-slave interactive optimization configuration model of regional complex water resources system under uncertain conditions. See Table 8 for details.

[0184] Table 8 Water resources allocation plan for the Weihe River Basin in Shaanxi Province

[0185]

[0186]

[0187]

[0188] The water demand in the study area is 6.323 billion m 3 , the water supply is 6.186 billion m 3 , the water shortage is 137 million m 3The water shortage rate in the study area is 2.17%. All the water shortage in the region is basically concentrated in the two areas of Baojixia to Xianyang North and Xianyang to Tongguan North, with water shortages of 20 million m 3 and 117 million m 3 . Agricultural water shortage: 124 million m 3 , accounting for 90.40% of the total water shortage, and the industrial water shortage is 13 million m 3 , accounting for 9.60% of the total water shortage.

[0189] Among the various areas in the Weihe River Basin in Shaanxi Province, the supply and demand are basically balanced in the areas above the south city of Beiluo River, the south area of ​​the Weihe River above Linjia Village, and the area above Zhangjiashan of Jinghe River; the water shortage rates from Baojixia to the north of Xianyang, from Xianyang to the north of Tongguan, and the north area of ​​the Weihe River above Linjia Village are 1.04%, 6.70%, and 1.61% respectively, which will have a certain impact on the GDP of these areas; the supply and demand are basically balanced from Xianyang to the south of Tongguan and from Baojixia to the south of Xianyang.

[0190] In the total water supply of the study area, surface water accounts for 76.31% and groundwater accounts for 23.69%. In each sub-area, groundwater accounts for a large proportion from Baojixia to Xianyang North and Xianyang to Tongguan North, which are 36.90% and 41.06% respectively, and the amount of groundwater exploitation is relatively large.

[0191] like Figure 7 As shown in the data, the maximum damage depth of the water resource system in the Weihe River Basin in Shaanxi Province is 15.6% in terms of the whole year. Among them, there is water shortage in June, July and August, with water shortage rates of 6.1%, 10.6% and 15.6% respectively. This is because the precipitation in the Shaanxi section of the Weihe River Basin is unevenly distributed throughout the year, and some areas often experience a sudden decrease in water inflow in June, July and August. This is because important rivers such as the Weihe River and the Beiluo River are subject to a large amount of pumping and interception when they flow through cities and regions with large demand for agricultural irrigation water in the upper reaches such as Gansu, resulting in a reduction in river runoff when reaching the Shaanxi section of the Weihe River Basin, which directly leads to a water shortage in the water resource system of the entire Shaanxi section of the Weihe River Basin.

[0192] Since the model takes into account the reservoirs, water users and other elements in the water resources system separately, the model not only solves the water resources allocation plan, but also reflects the operation status of each reservoir in the water resources system. The following analysis takes the Linjia Village Reservoir on the Weihe River as an example.

[0193] The annual discharge of Linjiacun Reservoir in the Weihe River Basin presents a typical bell shape. July and August are the main flood seasons, with a large amount of water discharged; January, February and December are the non-flood seasons, with a small amount of water discharged. Figure 8As shown in the figure, it can be seen from the changes in reservoir capacity that the reservoir capacity decreases between May and September. This is because as summer approaches, the water demand for agricultural irrigation continues to increase, and the reservoir needs to discharge more water to provide water resources for agricultural irrigation.

[0194] From this, it can be seen that the water shortage rate in the Shaanxi section of the Weihe River Basin is 2.17%, of which agricultural water shortage accounts for 90.40% of the water shortage in the entire basin; the water shortage in the Shaanxi section of the Weihe River Basin is mainly in the areas from Jixia to North Xianyang and from Xianyang to North Tongguan, and the water shortage is basically concentrated in the agricultural field.

[0195] Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Claims

1. A multi-objective optimization configuration method for water resources considering mixed uncertainty, characterized in that: By introducing fuzzy random variables to quantify the mixed uncertainty in the water resources system, the quantified results are used as the input data of the water resources optimization configuration model, in which the river basin managers in the water resources system are the upper decision makers, the water use departments are the lower decision makers, the lower decision makers are the followers of the upper decision makers, and the upper decision makers correspond to multiple lower decision makers as followers, so as to construct a multi-objective hierarchical master-slave interactive optimization configuration model with multiple followers and upper decision makers as leaders and lower decision makers as followers. Each follower is independent of each other, and the optimization of each follower only involves its own variables and upper-level variables. Therefore, the lower-level decision optimization objective in the multi-objective hierarchical master-slave interactive optimization configuration model is the sum of multiple lower-level decision optimization objective functions. The upper-level decision optimization objective function is: in is the objective function of sustainable development demand, is the user satisfaction objective function, The objective function is to reduce the water cost of water use departments; For any water resource partition w∈W, the lower-level decision variables are The lower-level decision optimization objective function is: It indicates that the net economic benefit is the largest; Among them, t is the time index, r is the reservoir index, w is the water resource partition index, k is the water use industry index, T is the time set, R is the reservoir set, W is the water resource partition set, K is the water use industry set, R is the reservoir set, r The set of reservoirs connected to reservoir r, W r The set of water resource partitions connected to reservoir r, K w The set of water-using industries within the water resource zone w, The inflow of reservoir r in time period t, The total water demand of industry k in water resource zone w during time period t, The economic benefits per unit of water obtained by industry k in water resource zone w during time period t, The upper limit of the fee per unit of water charged by industry k in water resource zone w during time period t, Initial reservoir available water volume, L rr Dead water capacity of reservoir r, U rr The beneficial storage capacity of reservoir r, L rw The minimum capacity of the channel connecting the reservoir r and the water resource zone w, if it is a river channel, needs to meet the ecological flow, U rw The maximum capacity of the channel connecting the reservoir r and the water resource partition w, The water storage capacity of reservoir r at the end of period t is, Flow from reservoir r to reservoir in time period t The amount of water, The amount of water flowing from reservoir r to water resource partition w during time period t, The amount of seawater flowing out of reservoir r during time period t, The deficit storage capacity of reservoir r in period t, From reservoir r to reservoir r in time period t The loss of the minimum ecological flow requirement of the river, The outflow from reservoir r to the sea during time period t is insufficient. The price charged per unit of water by industry k in water resource zone w during time period t, The amount of water allocated to industry k in water resource zone w during time period t; In the process of solving the above-mentioned multi-objective hierarchical master-slave interactive optimization configuration model, the equivalent KKT condition is introduced to transform the multi-objective and multi-user two-level optimization problem of the multi-objective hierarchical master-slave interactive optimization configuration model into an equivalent multi-objective mixed integer single-level model, so as to find a suitable water resources optimization configuration plan.

2. The multi-objective optimization configuration method of water resources considering mixed uncertainty according to claim 1 is characterized in that: The constraints of the upper-level decision optimization objective function are: System water balance, Minimum storage capacity of reservoirs, Minimum requirements for water inflow, Minimum ecological flow limit for connecting rivers between reservoirs, Maximum reservoir capacity, The water storage capacity limit of the water diversion channel system, The upper limit of water supply price, The variable is non-negative.

3. The multi-objective optimization configuration method of water resources considering mixed uncertainty according to claim 1 is characterized in that: The constraints of the lower-level decision optimization objective function are: The amount of water allocated to a specific water resource division, The actual water supply is less than the water demand. The variable is non-negative.

4. The multi-objective optimization configuration method of water resources considering mixed uncertainty according to claim 1 is characterized in that: The upper-level decision-making optimization goals include sustainable development demand goals, user satisfaction goals, and reducing water costs for water-using departments. The priorities of the above three goals decrease layer by layer.

5. The multi-objective optimization configuration method of water resources considering mixed uncertainty according to claim 1 is characterized in that: The quantification of mixed uncertainty factors in water resource systems based on fuzzy random variables includes the quantification of reservoir inflow uncertainty and water demand uncertainty. Among them, the uncertainty quantification of reservoir inflow is to introduce discrete fuzzy random variables and transform them into trapezoidal fuzzy numbers. The expectation of the trapezoidal fuzzy number is: The trapezoidal fuzzy number obtained by the transformation is processed by Me fuzzy processing, and the reservoir inflow can be obtained as follows: Among them, λ1∈[0,1] is the optimistic coefficient. The larger λ1 is, the The bigger, In the model, the reservoir inflow is recorded as make represents the inflow of reservoir r in time period t; In the quantification of water demand uncertainty, the water demand of water-using sector i is in According to the random fuzzy expected value operator, the trapezoidal fuzzy number can be obtained: The Me fuzzy processing is used for the trapezoidal fuzzy number, and the determined departmental water demand can be obtained as follows: Among them, λ2∈[0,1] is the optimistic coefficient. The larger λ2 is, the The larger the value, the water demand of each industry in the model is recorded as make represents the water demand of industry k in time period t.

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