Multi-agent evolutionary game method and system for generating annual scheduling plan of water transfer project

Abstract

The invention discloses a multi-subject evolutionary game method and system for generating an annual scheduling plan of a water transfer project, and the method comprises the steps: collecting the data of a research region, dividing the research region into a water source region and a water receiving region, and making a water plan strategy set of the water receiving region; constructing a three-dimensional joint distribution function of the current-moment water diversion amount of the water source area, the current-moment water inflow amount of the water receiving area and the previous-moment water inflow amount of the water receiving area, and generating random samples of the water diversion amount and the water inflow process of the water receiving area; constructing a water transfer project annual water quantity scheduling plan making model, and calculating the water supply quantity of each water receiving area; calculating an expected profit value of the water receiving area; and carrying out water use plan strategy adjustment and iteration on the water receiving area until the probability of selecting a specific water use plan strategy by the water receiving area approaches 1, and obtaining a stable decision combination of the annual water use plan of the water receiving area corresponding to the random sample. According to the method, a stable strategy for making an annual water use plan in a water receiving area under different water incoming conditions and uncertain risks is obtained.

Description

Technical Field

[0001] This invention belongs to the field of water resource scheduling, and relates to the generation and decision-making of annual scheduling plans for water diversion projects. In particular, it relates to a multi-agent evolutionary game method and system for generating annual scheduling plans for water diversion projects. Background Technology

[0002] The annual water allocation plan is a prerequisite for the operation of inter-regional and inter-basin water transfer projects. The goal of preparing the annual water allocation plan is to formulate a time-by-time water storage and supply plan based on the predicted water inflow situation of the water source area and the water receiving area, the annual water use plan suggestions proposed by each water receiving area, and the regulation and storage function of the reservoirs along the project route, in order to allocate water in a timely and appropriate manner throughout the year, achieve a reasonable allocation of water among different regions and industries under different water inflow conditions, and ultimately improve water allocation efficiency and achieve the designed water supply target of the water transfer project.

[0003] On the one hand, water diversion projects involve a wide geographical area, with uneven spatial distribution of water inflow between the source and receiving areas, presenting a superposition of uncertainties. This poses a risk of deviation from the water supply plan target to the strict implementation of the annual water allocation. A reasonable water diversion project scheduling plan should be formulated under the premise of considering the dual uncertainties of water inflow to enhance the adaptability of scheduling operations to risks and improve the water supply security. On the other hand, the determination of the water supply plan for each time period of the water diversion project is the result of a comprehensive balance of water demand in each receiving area based on the annual water use plan proposal. Therefore, the water supply benefits and water costs borne by the receiving area are affected by its own proposed water use plan, as well as the water use plan proposals of other receiving areas. If the receiving areas are regarded as decision-making entities representing the interests of different regions, then the process of each receiving area proposing water use plan proposals involves a competitive game relationship. Furthermore, the water use plan formulation strategy of each receiving area will be adjusted with reference to the actual water supply effect of the previous year, thus it is an evolutionary game process.

[0004] In summary, modeling and analyzing the evolutionary game process of generating annual water allocation plans for water diversion projects under uncertain conditions can help optimize and determine stable water use plans for water-receiving areas that are adaptable to uncertainty risks. Existing methods involve the analysis of rainfall abundance and scarcity in water source and water-receiving areas, modeling of multi-source joint water supply scheduling under uncertain conditions, and cooperative game theory in water resource allocation. However, there is still a lack of evolutionary game decision-making methods and systems for proposing annual water use plans for water-receiving areas under uncertain conditions.

[0005] This invention proposes a multi-agent evolutionary game method and system for generating annual scheduling plans for water diversion projects, which solves the aforementioned problems and provides technical support for further research on water resource supply and demand balance, water pricing, and market-based allocation of water rights in water network projects. Summary of the Invention

[0006] Objective: To provide a multi-agent evolutionary game method for generating annual scheduling plans for water diversion projects, thereby addressing the aforementioned problems in existing technologies. Furthermore, to provide a multi-agent evolutionary game system for generating annual scheduling plans for water diversion projects.

[0007] Technical Solution: A multi-agent evolutionary game method for generating annual scheduling plans for water diversion projects, comprising the following steps: Collect data on the study area, divide the study area into water source area and water receiving area, and formulate a set of water use planning strategies for the water receiving area; Construct a three-dimensional joint distribution function of the current water diversion volume in the water source area, the current water inflow volume in the water receiving area, and the previous water inflow volume in the water receiving area, and generate random samples of the divertable water volume and the water inflow process in the water receiving area. Random samples are extracted and combined with the water use planning strategies (taken from the water use planning strategy set) of the water receiving area. The samples are then input into the annual water volume scheduling plan compilation model of the water diversion project to obtain the water supply volume of each water receiving area in each time period under the combination of water use planning strategies. Based on the water supply, a multi-objective benefit vector of the water-receiving area under the combination of water use planning strategies is generated, the comprehensive benefit value of the water-receiving area is calculated, and the expected benefit value of the water-receiving area is calculated after traversing the combination of water use planning strategies. The water use planning strategy for the water-receiving area is adjusted and iterated until the probability of the water-receiving area selecting a specific water use planning strategy approaches 1, thus obtaining a stable decision combination of the annual water use plan for the water-receiving area corresponding to the random sample.

[0008] According to one aspect of this application, the adjustment and iteration of water use planning strategies for the water-receiving area includes: A replication dynamic equation incorporating learning ability coefficients and risk preference coefficients is used to calculate risk-adjusted utility based on the expected return of the water-receiving area. The probability of selecting each water use plan strategy in the water-receiving area is updated based on the difference between risk-adjusted utility and average expected return, combined with the learning ability coefficient. The strategy selection probability is iteratively updated until the probability of the water-receiving area selecting a specific water use plan strategy approaches 1, and the probability of selecting other strategies approaches 0, thus obtaining a stable decision combination.

[0009] According to one aspect of this application, the calculation of the risk-adjusted utility includes: Calculate the variance of revenue from the water-receiving area's water use planning strategy, and multiply the variance of revenue by the risk preference coefficient to obtain the risk adjustment term; The risk-adjusted utility is obtained by subtracting the risk adjustment term from the expected return. The probability of selecting each water use plan strategy for the updated water-receiving area includes: Calculate the difference between the risk-adjusted utility and the average expected return of the water-receiving area. Multiply the difference by the learning ability coefficient and the current strategy selection probability to obtain the probability update. Adjust the strategy selection probability based on the probability update.

[0010] According to one aspect of this application, obtaining a stable decision combination includes: Set a convergence threshold for the probability of strategy selection. When the probability of a water-receiving area selecting a certain water use plan strategy exceeds the convergence threshold, the strategy is determined as the stable strategy for that water-receiving area. Once a stable strategy has been determined for all water-receiving areas, a stable decision combination corresponding to the random sample is formed. Based on the annual water inflow levels of the water-receiving areas in the random sample, the stable decision combination is classified into annual water use planning strategies corresponding to wet years, normal years, and dry years.

[0011] According to one aspect of this application, the three-dimensional joint distribution function of the current water diversion volume of the water source area, the current water inflow volume of the water receiving area, and the previous water inflow volume of the water receiving area includes: Historical water diversion data of the water source area and historical water inflow data of the water receiving area were extracted from the data of the study area. Marginal distributions of water diversion volume in the water source area, current water inflow volume in the water receiving area, and previous water inflow volume in the water receiving area were fitted respectively. A two-dimensional Copula function is used to construct the joint distribution of water diversion from the water source area and the current water inflow from the water receiving area, thereby obtaining the conditional distribution of the current water inflow from the water receiving area under the given water diversion from the water source area. Based on conditional distribution, a three-dimensional joint distribution function is constructed by connecting the water inflow volume of the water receiving area at the previous moment using a conditional Copula function.

[0012] According to one aspect of this application, the use of a conditional Copula function to connect the water inflow volume of the receiving area at the previous moment includes: The marginal distribution of water diversion volume in the water source area and the marginal distribution of water inflow in the water receiving area at the current moment are transformed into a uniform distribution. The Kendall rank correlation coefficient is calculated and the parameters of the two-dimensional Copula function are determined. By taking the partial derivative of the two-dimensional Copula function, we can obtain the conditional distribution function of the water inflow to the water-receiving area at the current moment under the given water diversion volume from the water source area. Based on the conditional distribution function and the marginal distribution of water inflow in the water-receiving area at the previous moment, the conditional Kendall rank correlation coefficient is calculated, the parameters of the conditional Copula function are determined, and a complete three-dimensional joint distribution is constructed.

[0013] According to one aspect of this application, the generation of random samples of the water drawable volume and the water inflow process in the receiving area includes: An initial random number matrix is ​​generated based on a three-dimensional joint distribution function, where rows represent time periods and columns represent water source areas and water receiving areas. Calculate the temporal correlation matrix between adjacent months in historical data, and construct the type correlation matrix for different water-receiving areas; An improved Latin hypercube sampling method is adopted to reorder the initial random number matrix based on the temporal correlation matrix and the typological correlation matrix, thereby generating random samples that maintain spatiotemporal correlation.

[0014] According to one aspect of this application, the calculation of the time-series correlation matrix and the construction of the typological correlation matrix include: Extract the water volume series for each month from the historical data, calculate the Pearson correlation coefficient between adjacent months, and form a 12×12 time series correlation matrix; Spatial distance weights are calculated based on the geographical location of the water-receiving areas, and a type association matrix between the water-receiving areas is constructed by combining the similarity of water supply characteristics of the water-receiving areas. The temporal correlation matrix and the typological correlation matrix are decomposed by Cholesky to obtain lower triangular matrices. The initial random number matrix is ​​multiplied by the lower triangular matrix to generate random samples under correlation constraints.

[0015] According to one aspect of this application, the calculation of the comprehensive benefit value of the water-receiving area includes: Based on the water supply volume, the water supply security target, water use efficiency target, water transfer cost target and equity target of the water receiving area are calculated, forming a four-dimensional benefit vector and then normalized. The water supply guarantee target is measured by the water supply guarantee rate, which is calculated as the ratio of the number of time periods that meet water demand to the total number of time periods. The water use efficiency target is calculated by weighted summation of the benefits from power generation, water supply, etc. The target water diversion cost is calculated by multiplying the actual water supply volume by the water diversion cost coefficient; The fairness objective is measured by the difference in the level of water supply guarantee between this water-receiving area and other areas; Pareto non-dominated sorting is performed on the multi-objective payoff vector set to determine the non-dominated level of each strategy combination, and crowding distance is calculated within the same non-dominated level. The strategy dispersion of the water use planning strategy combination is calculated. The non-dominance level, congestion distance and strategy dispersion are weighted and combined to obtain the comprehensive benefit value.

[0016] According to one aspect of this application, the calculation of the strategy dispersion includes: The frequency of occurrence of each strategy in the statistical water use planning strategy combination is calculated, the strategy distribution entropy is calculated, and the strategy distribution entropy is divided by the maximum possible entropy value to obtain the normalized strategy dispersion. The formula for calculating the comprehensive return value is as follows: the reciprocal of the non-dominance level is used as the level score, the crowding distance is normalized and used as the distance score, the level score, the distance score and the strategy dispersion are assigned weight coefficients a, b and c respectively, and the comprehensive return value is obtained by weighted summation.

[0017] According to one aspect of this application, the generation of random samples of the divertable water volume and the water inflow process in the receiving area using a master-slave calculation method includes: From the three-dimensional joint distribution function, firstly, uniformly distributed random numbers of water diversion volume in the water source area are generated by inverse transformation sampling. Based on the generated water diversion volume of the water source area, the current water inflow volume of the water receiving area is generated through the conditional distribution function. Based on the water diversion volume of the water source area and the current water inflow volume of the receiving area, the water inflow volume of the receiving area at the previous moment is generated through the conditional Copula function. The uniformly distributed random numbers are then inversely transformed back to the original variable space to form random samples that maintain spatiotemporal correlation.

[0018] According to one aspect of this application, it also includes a classification process for stable decision combinations: Based on the total annual water inflow to the water-receiving areas in the random sample, the stable decision combination is divided into three categories: high-water year, normal-water year, and low-water year. Statistical analysis was conducted on the frequency distribution of water use planning strategies selected by the water-receiving areas under each type of water inflow condition, and the degree of strategy difference between different water inflow conditions was calculated. When the strategy difference exceeds the set threshold, stable decision combinations under different water inflow conditions are stored as classified scheduling plans; otherwise, a unified stable decision combination is used as the annual scheduling plan.

[0019] According to one aspect of this application, the improved Latin hypercube sampling method includes: The local weighted regression method was used to perform seasonal-trend decomposition on the historical water use series, extracting the trend term, seasonal term and residual term, and clarifying the water use benchmark range for different months; The ARIMA model was used to fit the time-series relationship between monthly water consumption, and a 12×12 time-series correlation matrix was constructed. Calculate the Pearson correlation coefficient of water consumption of different types during the same period, and use the Archimedes Copula function to fit the joint distribution for those with weak linear correlation to obtain the inter-type correlation matrix; Divide the marginal distribution of each month-water type dimension into N equally probable intervals, where N is the sampling size of the random strategy and N≥50; Samples are randomly drawn from N strata based on the first month, and the sampling strata of subsequent months are constrained according to the time-series correlation matrix to ensure that the samples of each month are dependent on the previous months. Calculate the current association matrix for different types of water use samples for each month. When the association deviation from the inter-type association matrix is ​​greater than 5%, use Cholesky decomposition to embed the target association matrix into the sample for correction.

[0020] According to another aspect of this application, a multi-agent evolutionary game system for generating annual scheduling plans for water diversion projects is provided, comprising: At least one processor; and A memory communicatively connected to at least one of the processors; wherein, The memory stores instructions that can be executed by the processor. These instructions are used by the processor to implement the multi-agent evolutionary game method for generating annual scheduling plans for water diversion projects as described in any of the above technical solutions.

[0021] Beneficial effects: The multi-stakeholder evolutionary game method for generating annual water transfer project scheduling plans can reflect the dynamic game relationship between different water-receiving areas in the process of proposing annual water use plans, which is consistent with the actual situation of multi-stakeholder participation in decision-making for cross-regional and cross-basin water transfer management. By optimizing the water use evolutionary game decision-making model based on random samples of water diversion from the input water source area and water inflow from the receiving area, it helps to obtain stable strategies for water-receiving areas to formulate annual water use plans under different water inflow conditions and uncertainties, achieving a comprehensive balance between water supply benefits and water use costs in the receiving areas and between different water-receiving areas meeting water demand, thus more effectively ensuring the realization of water supply benefits of water transfer projects. Attached Figure Description

[0022] Figure 1 This is a flowchart of the present invention.

[0023] Figure 2 This is a flowchart provided by the present invention for adjusting and iterating the water use planning strategy of the water-receiving area.

[0024] Figure 3 This is a flowchart of the three-dimensional joint distribution function of the water diversion volume of the water source area at the current moment, the water inflow volume of the water receiving area at the current moment, and the water inflow volume of the water receiving area at the previous moment, provided by the present invention.

[0025] Figure 4 This is a flowchart of the process of generating random samples of water diversion volume and water inflow process in the receiving area, provided by the present invention.

[0026] Figure 5 This is a flowchart for calculating the comprehensive benefit value of the water-receiving area provided by the present invention.

[0027] Figure 6 This is a flowchart of the classification process for stable decision combinations provided by the present invention. Detailed Implementation

[0028] like Figure 1 As shown, the following technical solution is proposed. According to one aspect of this application, a multi-agent evolutionary game method for generating annual scheduling plans for water diversion projects is provided, characterized by comprising the following steps: Collect data on the study area, divide the study area into water source area and water receiving area, and formulate a set of water use planning strategies for the water receiving area; Construct a three-dimensional joint distribution function of the current water diversion volume in the water source area, the current water inflow volume in the water receiving area, and the previous water inflow volume in the water receiving area, and generate random samples of the divertable water volume and the water inflow process in the water receiving area. Random samples are extracted and combined with the water use planning strategies of the water-receiving areas. The samples are then input into the annual water volume scheduling plan compilation model of the water diversion project to obtain the water supply volume of each water-receiving area in each time period under the water use planning strategy combination. Based on the water supply, a multi-objective benefit vector of the water-receiving area under the combination of water use planning strategies is generated, the comprehensive benefit value of the water-receiving area is calculated, and the expected benefit value of the water-receiving area is calculated after traversing the combination of water use planning strategies. The water use planning strategy for the water-receiving area is adjusted and iterated until the probability of the water-receiving area selecting a specific water use planning strategy approaches 1, thus obtaining a stable decision combination of the annual water use plan for the water-receiving area corresponding to the random sample.

[0029] This embodiment provides a multi-agent evolutionary game method for generating annual scheduling plans for water diversion projects, which can be used to solve the annual water use planning decision-making problem of water diversion projects under uncertain conditions.

[0030] Data from the study area were collected, and the study area was divided into a water source area and a water receiving area. A set of water use planning strategies for the water receiving area was formulated. A three-dimensional joint distribution function was constructed for the current water diversion volume of the water source area, the current water inflow volume of the water receiving area, and the previous water inflow volume of the water receiving area. Random samples of the available water diversion volume and the water inflow process of the water receiving area were generated.

[0031] In this embodiment, the study area refers to the entire water supply area covered by the water diversion project, including the water source area and the receiving areas. The water source area is usually a river, lake, or reservoir with relatively abundant water resources, while the receiving areas are water-scarce regions. Based on geographical location and water supply characteristics, these areas can be divided into upstream receiving areas, direct reservoir supply areas, and downstream receiving areas. The water use planning strategy set refers to the set of annual water use plans that each receiving area can choose from. Each strategy includes monthly water use for 12 months, covering four categories of water use: domestic, industrial, agricultural, and ecological. The three-dimensional joint distribution function is used to describe the temporal and spatial correlation between the water diversion volume of the water source area and the water inflow volume of the receiving areas. The random samples generated by this distribution function can reflect the uncertainty characteristics of the incoming water.

[0032] Water use plans for water-receiving areas should be based on historical water consumption records, and monthly planned water consumption has temporal correlation. In view of these characteristics, this invention proposes an improved Latin hypercube sampling method driven by big data and coupled with time to generate a water use plan strategy set for water-receiving areas. Compared with the conventional Latin hypercube sampling method, this method can highlight the advantages of high efficiency and good coverage of high-dimensional variable sampling, and can generate a more realistic monthly water use plan strategy set that meets the temporal correlation through anchoring and embedding of historical data, thus providing high-quality input samples for evolutionary game decision-making.

[0033] In one embodiment, specifically: Based on the actual needs of the water-receiving areas of the water diversion project, we collected more than 10 years of monthly historical data on domestic, industrial, agricultural irrigation and ecological water use, as well as hydrological and meteorological data, local water resource availability, related engineering data, population, economic and social data, etc. We used time-series interpolation methods to fill in missing values ​​and established a three-dimensional database according to water-receiving area-month-water use type. For a single water use type, the water use series was decomposed using the locally weighted regression (STL) method of seasonal-trend decomposition, extracting the trend term, seasonal term, and residual term to clarify the water use benchmark range for different months. The time-series relationship between monthly water consumption was fitted using the ARIMA model to obtain a 12-month time-series correlation matrix. For different water use types (residential, industrial, agricultural, and ecological), the Pearson correlation coefficients of water consumption of different types in the same period were calculated. For those with weak linear correlation, the Archimedes Copula function was used to fit the joint distribution to obtain the inter-type correlation matrix. The marginal distribution of the 48-dimensional monthly-water use type combination was fitted using kernel density estimation (KDE) or parametric distribution and passed the KS test (p>0.05). Determine the sampling size N (N > 50) for the random strategy, and divide the marginal distribution of each month's water use type dimension into N equally probable intervals. Taking January as the baseline, randomly sample from the N strata, and constrain the sampling layers of subsequent months according to the time-series correlation matrix to ensure the dependence of each month's samples on the preceding months, resulting in an initial sampling matrix of 12 months × 4 water use types. Calculate the current correlation matrix for each month's different water use types, compare it with the inter-type correlation matrix, and if the correlation deviation is > 5%, use Cholesky decomposition to embed the target correlation matrix into the samples for correction. Based on the constraints that the water diversion project must meet, such as the annual total water consumption control target, water balance constraints, project water supply capacity constraints, ecological discharge constraints, water supply priority constraints, and project operation stability constraints, the sampled strategies are verified one by one, invalid strategies are eliminated, and supplementary sampling is carried out until the number of feasible strategies reaches N, forming a candidate strategy set. The candidate strategy set is verified in three aspects: distribution consistency (KS test), temporal rationality (ACF error between candidate set and historical data ≤10%), and scenario diversity (calculated minimum Euclidean distance between samples is not lower than the set threshold). If the distribution consistency and temporal rationality verification fails, the fitting of the temporal correlation matrix and the inter-type correlation matrix is ​​readjusted. If the diversity is insufficient, the sampling size is increased or the stratification interval is adjusted, and the strategy set is regenerated.

[0034] Random samples are extracted and combined with the water use planning strategies of the water-receiving areas. The samples are then input into the annual water volume scheduling plan model of the water diversion project to obtain the water supply volume of each water-receiving area in each time period under the water use planning strategy combination.

[0035] Specifically, each water-receiving area independently selects a water use planning strategy from its strategy set to form a strategy combination. The annual water volume scheduling plan preparation model of the water diversion project determines the actual water supply to each water-receiving area at each time period through optimization calculation based on the water diversion capacity of the water source area, the water inflow of the water-receiving area, the water use plan demand, and the project constraints. This model considers multiple constraints such as water balance constraints, project water supply capacity constraints, ecological discharge constraints, and water supply priority constraints.

[0036] The decision variables include: W _supply (i, t, k) represents the water supply volume for the i-th water-receiving area of ​​type k during time period t; S _res (j, t) represents the water storage capacity of the j-th reservoir at the end of time period t; Q channel (l, t) represents the water flow rate of the l-th water conveyance channel during time period t; W _spill (j, t) represents the amount of water discharged from the j-th reservoir during time period t; The main objective function is to minimize the total water deficit: minF1 = Σ t Σ i Σ k [D(i,t,k)-W _supply [(i, t, k)], where D(i, t, k) is the water demand; Secondary objectives include: minimizing the water supply imbalance F2=Σ t Σ i [(W _supply (i,t) / D(i,t)-W avg / D avg ) 2 ]; where W _supply (i, t) represents the water supply to the i-th water-receiving area during time period t; D(i, t) represents the water demand of the i-th water-receiving area during time period t; Q channel (l, t) represents the water flow rate of the l-th water conveyance channel during time period t; W avg / D avgLet F3 be the ratio of the total water supply to the total water demand of all water-receiving areas; minimize the water transfer cost F3 = Σ t Σ _l C unit (l)×Q channel (l, t) × Δt, where C unit (l) represents the unit water diversion cost; maximizing the year-end reservoir storage capacity F_4 = Σ j S _res (j, T) end ); A hierarchical sequential approach is adopted to handle multiple objectives, optimizing them in order of priority: first, ensuring basic water supply needs, then considering fairness, and finally optimizing economic efficiency.

[0037] Water balance constraint: For reservoir j, S _res (j, t) = S _res (j, t-1) + I natural (j,t)+I transfer (j,t)-O _supply (j,t)-O ecology (j,t)-E(j,t)-W _spill (j, t), where I natural It is natural water, I transfer To adjust the water volume, O _supply For water supply, O ecology E represents the ecological discharge, and E represents the evaporation loss. Reservoir capacity constraint: S dead (j)≤S_res(j,t)≤S normal (j), where S dead For dead storage capacity, S normal This is the reservoir capacity corresponding to the normal water level. During special periods, it can be temporarily over-stored to S... _flood The flood control limit water level corresponds to the reservoir capacity; Channel water conveyance capacity constraint: 0 ≤ Q channel (l, t) ≤ Q max (l)×η(l,t), where Q max (l) represents the design water conveyance capacity, and η(l,t) is the time-varying water conveyance efficiency coefficient, which is generally taken as 0.85-0.95 considering factors such as canal maintenance and ice season. Ecological flow constraints: Q ecology (j, t) ≥ max(Q) eco-min (j), β×Q natural (j, t)), where Q eco-min β is the minimum ecological flow, and β is the ecological flow proportionality coefficient, which is usually taken as 0.1-0.2; Water supply priority constraint: When water supply is insufficient, water is supplied according to priority order, defined by priority coefficient ω(k): domestic water ω(1)=1.0, industrial water ω(2)=0.9, ecological water ω(3)=0.7, agricultural water ω(4)=0.5. Actual water supply rate satisfies: W _supply (i,t,k) / D(i,t,k)≥ω(k)×W _supply (i, t, k') / D(i, t, k'), when ω(k)>ω(k').

[0038] Linearizing the nonlinear constraints, for the evaporation loss E(j,t)=e _rate (t)×A(S _res (j, t)), where A is the water surface area of ​​the reservoir; piecewise linearization is adopted: the reservoir capacity interval [S min S max The reservoir is divided into K segments. Within each segment, the relationship between water surface area and reservoir capacity is approximated by a linear function. A 0-1 variable δ(j, t, k) is introduced to represent the reservoir capacity falling in the k-th segment, satisfying Σ k δ(j, t, k) = 1; The branch and bound algorithm is used to solve the problem, with a solution accuracy of ε = 0.01 and a maximum number of iterations N. max =10000, the initial solution is obtained using a greedy algorithm: sorted by priority and economy, each demand is satisfied in turn until the water is exhausted; In some alternative implementations, dynamic programming can be used to solve the problem, decomposing it into T stages. The state variables are the water storage capacity of each reservoir, and the decision variables are the water supply and water transfer. The state transition equation is: V t (S t )=min{C t (S t U t )+V t+1 (S t+1 )}, where V t Let C be the optimal value function for time period t. t For current period costs, U t For the set of decision variables; Furthermore, stochastic optimization can be introduced to handle uncertainty. The future water volume is treated as a random variable, and the scenario tree method is used to describe its uncertainty evolution. The objective function is modified to the expected value form: minE[F(x,ξ)], where ξ is a random variable. The two-stage stochastic programming problem is solved using the L-shaped algorithm or the asymptotic hedging algorithm.

[0039] Verify that all constraints are strictly satisfied, with an allowable error range of 0.1%. For solutions that violate the constraints, correct them through local adjustments: prioritize adjusting the amount of water wasted and the supply of non-critical water, while keeping the critical water supply unchanged. Calculate the water supply guarantee rate index: P _guarantee (i, k) = Σ t I(W _supply (i, t, k)≥α×D(i, t, k)) / T, where I(·) is the indicator function, α is the satisfaction rate threshold, generally taken as 0.9-0.95, the guarantee rate for domestic and industrial water use should not be less than 95%, and the guarantee rate for agricultural water use should not be less than 75%; Output a complete scheduling plan, including: the water storage and release process of each reservoir in each time period; the water conveyance process of each channel; the water supply process of each water receiving area; and a summary of key indicators (total water supply, water shortage, guarantee rate, etc.). This plan serves as the optimal scheduling result under a given strategy combination, providing basic data for subsequent revenue calculation.

[0040] Based on the water supply, a multi-objective benefit vector is generated for the water-receiving area under the combination of water use planning strategies. The comprehensive benefit value of the water-receiving area is calculated. After traversing the combination of water use planning strategies, the expected benefit value of the water-receiving area is calculated.

[0041] The multi-objective benefit vector comprises four dimensions: water supply security reflects water supply reliability, measured by the water supply guarantee rate; water use efficiency reflects economic benefits, calculated by a weighted sum of the benefits of power generation, water supply, etc.; water diversion cost reflects economic costs, calculated by the product of the actual water supply volume and the water diversion cost coefficient; and equity reflects regional equilibrium, measured by the difference in water supply security between the receiving area and other areas. The comprehensive benefit value is calculated using the Pareto non-dominated ranking method, avoiding the influence of subjective weight settings. The expected benefit value is the average benefit obtained by the receiving area under all possible strategy combinations.

[0042] The water use planning strategy for the water-receiving area is adjusted and iterated until the probability of the water-receiving area selecting a specific water use planning strategy approaches 1, thus obtaining a stable decision combination of the annual water use plan for the water-receiving area corresponding to the random sample.

[0043] In this embodiment, strategy adjustment is implemented using a replicating dynamic equation to simulate the evolution of the probability of strategy selection by the water-receiving areas based on historical returns. When the return of a certain strategy is higher than the average expected return, the probability of selecting that strategy increases; conversely, it decreases. Through multiple iterations, each water-receiving area eventually converges to a stable strategy, forming a stable decision combination under Nash equilibrium. This combination represents the equilibrium state reached after the water-receiving areas interact with each other under given water conditions.

[0044] Through the above steps, this embodiment realizes the evolutionary game decision-making of the annual water use plan of the water transfer project under uncertain conditions. The resulting stable decision combination not only takes into account the uncertainty of the incoming water, but also reflects the interest game relationship between different water receiving areas, providing a scientific basis for the actual operation and management of the water transfer project.

[0045] like Figure 2 As shown, according to one aspect of this application, the adjustment and iteration of the water use planning strategy for the water-receiving area includes: A replication dynamic equation incorporating learning ability coefficients and risk preference coefficients is used to calculate risk-adjusted utility based on the expected return of the water-receiving area. The probability of selecting each water use plan strategy in the water-receiving area is updated based on the difference between risk-adjusted utility and average expected return, combined with the learning ability coefficient. The strategy selection probability is iteratively updated until the probability of the water-receiving area selecting a specific water use plan strategy approaches 1, and the probability of selecting other strategies approaches 0, thus obtaining a stable decision combination.

[0046] In one embodiment, specifically: Initialize the strategy probability distribution for each water-receiving area, assuming area i has n i There are several optional strategies, with an initial probability vector p. i (0)=[p i，1 (0), p i，2 (0), ..., p i，ni (0)], using a uniform distribution p i，j (0) = 1 / n i This indicates that the probability of each strategy being chosen is equal in the initial stage, and a small perturbation ε is introduced. j Let ~N(0, σε²), where σε = 0.01, and let the initial probability be p. i，j (0)=(1+ε j ) / n i and normalization ensures Σ j p i，j =1; The expected return of strategy j for region i is: π i，j (t)=Σ_{k≠i}Σ_{s k}p k ,s k (t)×V i (j, s_ -i ), where p k s k (t) represents the selection strategy for region k at time t. k The probability, V i (j, s_ -i For region i, strategy j is selected, while other regions select strategy combinations s_. -i The benefits at that time; The average expected return for region i is: π¯ i (t)=Σ_ j p i，j (t)×π i，j (t); The dynamic equation for replication is: dp i，j / dt=p i，j (t)×[π i，j (t)-π¯ i [t], this equation shows that when the payoff of strategy j is higher than the average payoff, its probability of being chosen increases; conversely, it decreases. The discretized form is: p i，j (t+1)=p i，j (t)+δ×p i，j (t)×[π i，j (t)-π¯ i [(t)], where δ is the learning rate, ranging from 0.01 to 0.1.

[0047] Introducing a noise term to simulate the uncertainty of decision-making: p i，j (t+1)=p i，j (t)+δ×p i，j (t)×[π i，j (t)-π¯ i (t)]+η i，j (t), where η i，j (t)~N(0,σ) η 2 ), σ η =0.001, noise intensity decreases with the number of iterations: σ η (t)=σ η (0)×exp(-t / τ decay ), τ decay =100 is the decay time constant; Different water-receiving areas have different risk preferences; a risk-adjusted utility function is defined as: U i (π)=π^(1-r i ) / (1-r i ), where r i Let r1 be the relative risk aversion coefficient of area i. The upstream water-receiving area depends on water diversion and has a high degree of risk aversion, r1=0.8; the reservoir direct supply area has storage capacity and is risk-neutral, r2=0.5; the downstream water-receiving area has diverse water sources and a risk preference, r3=0.2.

[0048] The corrected replication dynamic equation is: dp i，j / dt=p i，j (t)×[U i (π i，j (t))-U¯ i [(t)], where U¯ i (t)=Σjp i，j (t)×U i (π i，j (t) represents the risk-adjusted average utility; Furthermore, we introduce the bounded rationality assumption and adopt Logit response dynamics: p i，j (t+1)=exp(β i ×π i，j (t)) / Σ k exp(β i ×π i ,k(t)), where β i β is a parameter representing the degree of rationality. i →∞ indicates perfect rationality, immediately choosing the optimal strategy; β i →0 indicates random selection, set β i =β0×(1+t / T max This allows the level of rationality to gradually increase during the learning process, β0=1, T max =500.

[0049] Convergence condition defined as follows: when the probability of choosing a certain strategy in all regions exceeds a threshold θ. conv When convergence is achieved, it is formally expressed as: for any i, there exists j: p i，j (t)≥θ conv , where θ conv =0.95.

[0050] Auxiliary convergence criteria include: the probability change rate criterion: max i，j |p i，j (t)-p i，j (t-1)|<ε_p, where ε_p=0.001; max i，j This represents the maximum value of the probability change for all regions and all strategies; p i，j (t) represents the probability that the i-th region chooses the j-th strategy at time t; p i，j (t-1) represents the probability that the i-th region chooses the j-th strategy at time t-1; Moving average criterion: |P¯ i，j (t)-P¯ i，j (t-τ)|<ε avg , where P¯ i，j (t)=(1 / τ)Σ_{k=0}^{τ-1}p i，j (tk) is the moving average over period τ, τ=20; Entropy criterion: H i (t)=—Σ_jp i，j (t)×log(p i，j (t)) <H threshold H threshold =0.1 indicates that the uncertainty of the policy distribution is sufficiently small.

[0051] Set the maximum number of iterations T max=1000. If convergence is not achieved after reaching the maximum number of iterations, the strategy with the highest probability is selected as the result and marked as a weak convergence state.

[0052] An adaptive learning rate is adopted: δ(t)=δ0 / (1+α_δ×t), where δ0=0.1 is the initial learning rate and α_δ=0.01 is the decay coefficient. When oscillation is detected (the policy probability changes repeatedly in 5 consecutive iterations), the learning rate is halved.

[0053] Applying the momentum method accelerates convergence: p i，j (t+1)=p i，j (t)+δ×[p i，j (t)×(π i，j (t)-π¯ i (t))+γ m ×Δp i，j [(t-1)], where γ m =0.9 is the momentum coefficient, Δp i，j (t-1)=p i，j (t)-p i，j (t-1) represents the change in the previous step.

[0054] In some optional implementations, a parallel evolution strategy is adopted to group the water-receiving areas, with synchronous updates within each group and asynchronous updates between groups. Specifically, I areas are divided into G groups, each containing I / G areas. The g-th group is updated at time t_g = t0 + g × Δt. group Update, where Δt group This method reduces computational complexity by setting the inter-group update interval to O(I0). 2 ×n 2 The value decreased to O((I / G)). 2 ×n 2 ).

[0055] Alternatively, reinforcement learning can be used to replace the copy dynamics, modeling policy selection as a multi-agent reinforcement learning problem, with each region representing one agent and the state space S. i Includes information such as historical water supply, current inventory, and season; Action Space A i The policy set; reward function R i =V i It employs independent Q-learning or the Actor-Critic algorithm to learn the optimal strategy through interaction with the environment.

[0056] Record the convergent policy combination S*={s1*, s2*, ..., s i *}, where s i For the stable strategy of region i, calculate the Nash equilibrium property of the combination: verify for any i, any s i':V i (s i ,s_-i*)≥V i (s i ',s_-i*), meaning that unilateral deviation cannot yield higher returns.

[0057] Sensitivity analysis was conducted on key parameters (learning rate δ, risk coefficient r). i rational parameter β i The evolution process is rerun by subjecting the parameters to a ±20% perturbation. The changes in the stable strategy are statistically analyzed. If more than 90% of the parameter combinations converge to the same strategy, the result is considered to have good robustness.

[0058] According to one aspect of this application, the calculation of the risk-adjusted utility includes: Calculate the variance of revenue from the water-receiving area's water use planning strategy, and multiply the variance of revenue by the risk preference coefficient to obtain the risk adjustment term; The risk-adjusted utility is obtained by subtracting the risk adjustment term from the expected return. The probability of selecting each water use plan strategy for the updated water-receiving area includes: Calculate the difference between the risk-adjusted utility and the average expected return of the water-receiving area. Multiply the difference by the learning ability coefficient and the current strategy selection probability to obtain the probability update. Adjust the strategy selection probability based on the probability update.

[0059] In one embodiment, specifically: Construct a four-dimensional profit vector R i =[R_ reliability (i), R _benefit (i), R cost (i), R equity (i)], which correspond to the four objectives of water supply security, water use efficiency, water transfer cost and equity, respectively.

[0060] Water supply security target R _reliability Calculation of (i): R _reliability (i)=Σ k w k ×P k (i), where P k (i)=Σ tmin (W _supply (i, t, k) / D(i, t, k), 1) / T is the water supply satisfaction rate for the k-th type of water use, w k The weighting coefficient has a value of w. life =0.4, w industry =0.3, w ecology =0.2, w agriculture =0.1, considering the differences in importance between time periods, a time period weight can be introduced: Pk (i)=Σ t γ t ×min(W _supply (i,t,k) / D(i,t,k),1) / Σ t γ t , where γ t The importance coefficient for time period t is 1.2 for the dry season and 0.8 for the wet season.

[0061] Water use efficiency target R _benefit Calculation of (i): R _benefit (i)=Σ k Σ t B -unit (i, k)×W _supply (i,t,k)×(1-L_ rate (i, k, t)), where B -unit (i, k) represents the benefit generated per unit of water volume, with domestic water costing 50 yuan / m³. 3 Industrial water: 120 yuan / m³ 3 Agricultural water cost 3 yuan / m³ 3 Ecological water use is calculated at 15 yuan / m³ based on its environmental value. 3 ;L_ rate (i, k, t) represents the loss rate, reflecting the loss of benefits caused by insufficient water supply. The calculation formula is L_ rate (i, k, t) = a k ×[1-W _supply (i, t, k) / D(i, t, k)]^b k , where a k and b k For empirical parameters, a=0.8 and b=2 are used for industrial water use, and a=0.6 and b=1.5 are used for agricultural water use.

[0062] Water transfer cost target R cost Calculation of (i): R cost (i)=-[C_ water (i)+C energy (i)+C maintain (i)], where C_ water (i)=Σ t c_ w ×W transfer (i, t) represents the water resource fee, and c_ w Take 0.5-2 yuan / m 3 C energy (i)=Σ t c e ×H(i,t)×W transfer (i, t) × g / (η_ pump(×3600) represents the energy cost of water lifting, H(i,t) represents the head, and g=9.8m / s 2 η_ pump For pump station efficiency; C maintain (i)=c m ×L(i)×T represents the channel maintenance cost, c m L(i) represents the maintenance cost per unit length, and L(i) represents the channel length.

[0063] Fairness objective R equity Calculation of (i): R equity (i)=-σ _supply (i) / μ _supply , where σ _supply (i)=sqrt(Σ_j≠i[P _guarantee (i)-P _guarantee (j)] 2 / (N-1)) represents the standard deviation of the water supply guarantee rate between this area and other areas, μ _supply =Σ_jP _guarantee (j) / N represents the average water supply guarantee rate. The smaller this indicator is, the fairer the water supply is.

[0064] Define a dominance relationship: Policy A dominates Policy B if and only if A is no worse than B on all objectives and is strictly superior to B on at least one objective. Formally, this is expressed as: A > B, which is (for any m:R) m (A)≥R m (B))∧(Existence m:R) m (A)>R m (B)).

[0065] Execute the fast non-dominated sorting algorithm: Initialize the number of dominated members n_ for each strategy p p =0 and the dominating set S_ p Not zero; for any two policies p and q, if p dominates q, then S_ p =S_ p ∪{q},n_ q =n_ q +1; if n_ p =0, then p belongs to the first non-dominated layer F1; for each policy p in F1, traverse its dominance set S_ p In the strategy q, let n_ q =n_ q -1, if n_ q If q = 0, then q is added to F2; repeat this process until all strategies are layered.

[0066] Calculate the crowding distance: For policies within the same undominated layer, calculate their crowding level in the target space. For the k-th target, sort the policies according to the target value. The crowding distance contribution of policy i is: d k (i)=[R k (i+1)-R k (i-1)] / [R k max -R k min ], where R k max and R k min For the maximum and minimum values ​​of this objective, the total congestion distance D(i) = Σ k d k (i).

[0067] The overall return value is calculated as follows: V(i) = α / rank(i) + β × D(i), where rank(i) is the non-dominated level of the strategy, α = 0.7 is the level weight, and β = 0.3 is the diversity weight. This formula ensures that the frontier solution obtains a high return value, while rewarding sparsely distributed solutions in the target space.

[0068] Iterate through all possible strategy combinations, and let the size of the strategy set for each water-receiving area be n1, n2, ..., n i The total number of combinations is N total =∏ i n i For region i, the number of strategy combinations for other regions is N_ -i =N total / n i .

[0069] Calculate the conditional expected return when choosing strategy s for region i: E[V i |s i =s]=(1 / N_ -i )×Σ_{s_ -i}V i (s,s_ -i ), where s_ -i V represents the strategy combination for other regions. i (s,s_ -i ) represents region i in the complete strategy combination (s, s_ -i The overall return value under )

[0070] Optionally, the Monte Carlo method can be used to approximate the expected value. When the number of combinations is too large, randomly sampling M=10000 strategy combinations yields an approximate expected return of: E[V i |s i =s]≈(1 / M)×Σ_{m=1}^MVi (s,s_ -i ^(m)). Importance sampling is used to improve efficiency, and the sampling probability distribution is set based on historical experience or prior knowledge.

[0071] Furthermore, risk adjustment is introduced to calculate the variance of returns, Var[V]. i |s i =s] and CVaR (Conditional Value at Risk): CVaR _α (V i )=E[V i |V i ≤VaR _α ], where VaR _α Given the α quantile, the risk-adjusted expected return is: E[V] i ]-λ _risk ×sqrt(Var[V i ]), where λ _risk The risk aversion coefficient is set at 0.5-1.0 for conservative decisions and 0-0.3 for aggressive decisions.

[0072] According to one aspect of this application, obtaining a stable decision combination includes: Set a convergence threshold for the probability of strategy selection. When the probability of a water-receiving area selecting a certain water use plan strategy exceeds the convergence threshold, the strategy is determined as the stable strategy for that water-receiving area. Once a stable strategy has been determined for all water-receiving areas, a stable decision combination corresponding to the random sample is formed. Based on the annual water inflow levels of the water-receiving areas in the random sample, the stable decision combination is classified into annual water use planning strategies corresponding to wet years, normal years, and dry years.

[0073] like Figure 3 As shown, according to one aspect of this application, the three-dimensional joint distribution function of the current water diversion volume of the water source area, the current water inflow volume of the water receiving area, and the previous water inflow volume of the water receiving area includes: Historical water diversion data of the water source area and historical water inflow data of the water receiving area were extracted from the data of the study area. Marginal distributions of water diversion volume in the water source area, current water inflow volume in the water receiving area, and previous water inflow volume in the water receiving area were fitted respectively. A two-dimensional Copula function is used to construct the joint distribution of water diversion from the water source area and the current water inflow from the water receiving area, thereby obtaining the conditional distribution of the current water inflow from the water receiving area under the given water diversion from the water source area. In one embodiment, specifically: Collect monthly historical hydrological data for no less than 30 years from the water source area and each water-receiving area, and set X as... t Y represents the amount of water available for diversion in the water source area at time t.i,t Y represents the inflow volume of the i-th water-receiving area at time t. i，t-1 This represents the water inflow to the area at time t-1. For each water-receiving area i, a three-dimensional random vector Z is constructed. i =(X t Y i ,t,Y i , t-1); For the water diversion capacity X t Density estimation is performed using the Gaussian kernel function with adaptive bandwidth: f x (x)=(1 / (n×h x ))×Σ_ j K((x-x_ j ) / h x ), where n is the number of samples, h x Let K(·) be the bandwidth parameter, K(·) be the standard normal kernel function, and h be the bandwidth. x The Silverman rule is used to determine: h x =1.06×σ x ×n^(-1 / 5), where σ x The standard deviation is the sample standard deviation. For the water inflow Y of the water-receiving area i，t Considering its seasonality, kernel density estimation is performed monthly. Historical data are grouped by month, and the inflow sequence Y for each month m is calculated. i m={y i，m，1 y i，m，2 , ..., y i，m，k Fit the marginal distributions F respectively Y，i，m (y), during the fitting process, for months with zero or extreme values, a mixed distribution model is used: F Y，i，m (y)=p0×I(y=0)+(1-p0)×F continuous (y|y>0), where p0 is the zero probability, I(·) is the indicator function, and F continuous The distribution function for the continuous portion; Calculate the Kendall rank correlation coefficient τ and tail correlation coefficient λ between each pair of the three variables, and select the Copula family of functions based on the correlation characteristics: when τ xY When τ > 0.5 and upper tail correlation exists, select GumbelCopula; when τ < 0.5, select GumbelCopula. xY When the correlation coefficient is greater than 0.5 and a lower tail correlation exists, choose Clayton Copula; when there is no obvious tail correlation, choose Frank Copula; when the correlation is weak (|τ|<0.3), consider Independent Copula. Specifically, a three-dimensional Archimedean Copula function C(u1, u2, u3; θ) = φ^(-1)(φ(u1) + φ(u2) + φ(u3)) is used, where φ is the generating function and θ is the dependent parameter. For Frank Copula, the generating function φ(t) = -ln((exp(-θt)-1) / (exp(-θ)-1)); the parameter θ is estimated using the maximum likelihood method: θ mLE =argmax_θΣ k lnc(F X (x k ), F Y，i，t (y i，t，k ), F Y，i，t-1 (y i，t-1，k ); θ), where c(·) is the Copula density function; In some alternative implementations, a vine (VineCopula) structure can be used to capture more complex dependencies, constructing a C-vine structure: First layer construction X t With Y i，t Two-dimensional CopulaC 12 and X t With Y i，t-1 Two-dimensional CopulaC 13 Second-layer structural conditions CopulaC 23|1 Describe a given X t Condition Y i，t With Y i，t-1 This method allows for flexible selection of different Copula function types for different variable pairs, based on their dependencies. Relevant random samples are generated using conditional sampling. First, a uniform random number u1 is generated on [0, 1]. Then, u2 is generated according to the conditional distribution C2|1(u2|u1)=ΞC12(u1, u2) / Ξu1. Finally, u3 is generated according to C3|12(u3|u1, u2)=Ξ²C123(u1, u2, u3) / (Ξu1Ξu2), where Ξ is the partial derivative. The original sample space is obtained through inverse transformation: x=F x ^(-1)(u1), y i，t =F Y，i，t^(-1)(u2) y i，t-1 =F Y，I，t-1^(-1)(u3) ; To improve sampling efficiency, a quasi-Monte Carlo method is used instead of the traditional Monte Carlo method. A low-bias point set is generated using Sobol or Halton sequences within the range [0, 1]. 3 Spatially uniform distribution, generating M=1000 sets of random samples {(x m y i , t my i，t-1 m )}, m=1,2,...,M, forming a set of water inflow scenarios; To test whether the statistical characteristics of the sample are consistent with historical data, including: mean test |μ _sample -μ _history | / μ _history <0.05; Standard deviation test | σ _sample -σ _history | / σ _history <0.1; Correlation coefficient test |ρ _sample -ρ _history |<0.1; Extreme value testing ensures that the maximum value of the sample does not exceed 1.2 times the historical maximum value; For samples that do not meet the testing criteria, a new sample is generated using the accept-rejection method, and the acceptance probability p is defined. accept =exp(-d² / 2σ d ²), where d is the distance metric between the sample and the target distribution, and σ d This is the tolerance parameter. Through multiple iterations, it is ensured that the generated sample set maintains both the interdependence structure between variables and conforms to the physical laws of the hydrological sequence; Furthermore, climate change scenarios can be introduced, and trend adjustments can be made to the marginal distribution based on the climate change projections published by the IPCC: F _future (x)=F _history (x / α), where F_ history (·) represents the cumulative distribution function of historical water inflow; F _future (·) represents the cumulative distribution function of future water inflow; x represents the random variable of future water inflow; α represents the coefficient of variation, reflecting the trend of future water inflow. The random samples generated by this method can reflect the potential impact of climate change on water resources.

[0074] Based on conditional distribution, a three-dimensional joint distribution function is constructed by connecting the water inflow volume of the water receiving area at the previous moment using a conditional Copula function.

[0075] According to one aspect of this application, the use of a conditional Copula function to connect the water inflow volume of the receiving area at the previous moment includes: The marginal distribution of water diversion volume in the water source area and the marginal distribution of water inflow in the water receiving area at the current moment are transformed into a uniform distribution. The Kendall rank correlation coefficient is calculated and the parameters of the two-dimensional Copula function are determined. By taking the partial derivative of the two-dimensional Copula function, we can obtain the conditional distribution function of the water inflow to the water-receiving area at the current moment under the given water diversion volume from the water source area. Based on the conditional distribution function and the marginal distribution of water inflow in the water-receiving area at the previous moment, the conditional Kendall rank correlation coefficient is calculated, the parameters of the conditional Copula function are determined, and a complete three-dimensional joint distribution is constructed.

[0076] like Figure 4 As shown, according to one aspect of this application, the generation of random samples of the water drawable volume and the water inflow process in the receiving area includes: An initial random number matrix is ​​generated based on a three-dimensional joint distribution function, where rows represent time periods and columns represent water source areas and water receiving areas. Calculate the temporal correlation matrix between adjacent months in historical data, and construct the type correlation matrix for different water-receiving areas; According to one aspect of this application, the calculation of the time-series correlation matrix and the construction of the typological correlation matrix include: Extract the water volume series for each month from the historical data, calculate the Pearson correlation coefficient between adjacent months, and form a 12×12 time series correlation matrix; Spatial distance weights are calculated based on the geographical location of the water-receiving areas, and a type association matrix between the water-receiving areas is constructed by combining the similarity of water supply characteristics of the water-receiving areas. The temporal correlation matrix and the typological correlation matrix are decomposed by Cholesky to obtain lower triangular matrices. The initial random number matrix is ​​multiplied by the lower triangular matrix to generate random samples under correlation constraints.

[0077] like Figure 5 As shown, according to one aspect of this application, the calculation of the comprehensive benefit value of the water-receiving area includes: Based on the water supply volume, the water supply security target, water use efficiency target, water transfer cost target and equity target of the water receiving area are calculated, forming a four-dimensional benefit vector and then normalized. The water supply guarantee target is measured by the water supply guarantee rate, which is calculated as the ratio of the number of time periods that meet water demand to the total number of time periods. The water use efficiency target is calculated by weighted summation of the benefits from power generation, water supply, etc. The target water diversion cost is calculated by multiplying the actual water supply volume by the water diversion cost coefficient; The fairness objective is measured by the difference in the level of water supply guarantee between this water-receiving area and other areas; Pareto non-dominated sorting is performed on the multi-objective payoff vector set to determine the non-dominated level of each strategy combination, and crowding distance is calculated within the same non-dominated level. The strategy dispersion of the water use planning strategy combination is calculated. The non-dominance level, congestion distance and strategy dispersion are weighted and combined to obtain the comprehensive benefit value.

[0078] According to one aspect of this application, the calculation of the strategy dispersion includes: The frequency of occurrence of each strategy in the statistical water use planning strategy combination is calculated, the strategy distribution entropy is calculated, and the strategy distribution entropy is divided by the maximum possible entropy value to obtain the normalized strategy dispersion. The formula for calculating the comprehensive return value is as follows: the reciprocal of the non-dominance level is used as the level score, the crowding distance is normalized and used as the distance score, the level score, the distance score and the strategy dispersion are assigned weight coefficients a, b and c respectively, and the comprehensive return value is obtained by weighted summation.

[0079] According to one aspect of this application, the generation of random samples of the divertable water volume and the water inflow process in the receiving area using a master-slave calculation method includes: From the three-dimensional joint distribution function, firstly, uniformly distributed random numbers of water diversion volume in the water source area are generated by inverse transformation sampling. Based on the generated water diversion volume of the water source area, the current water inflow volume of the water receiving area is generated through the conditional distribution function. Based on the water diversion volume of the water source area and the current water inflow volume of the receiving area, the water inflow volume of the receiving area at the previous moment is generated through the conditional Copula function. The uniformly distributed random numbers are then inversely transformed back to the original variable space to form random samples that maintain spatiotemporal correlation.

[0080] like Figure 6 As shown, according to one aspect of this application, it also includes a classification process for stable decision combinations: Based on the total annual water inflow to the water-receiving areas in the random sample, the stable decision combination is divided into three categories: high-water year, normal-water year, and low-water year. Statistical analysis was conducted on the frequency distribution of water use planning strategies selected by the water-receiving areas under each type of water inflow condition, and the degree of strategy difference between different water inflow conditions was calculated. When the strategy difference exceeds the set threshold, stable decision combinations under different water inflow conditions are stored as classified scheduling plans; otherwise, a unified stable decision combination is used as the annual scheduling plan.

[0081] According to one aspect of this application, the improved Latin hypercube sampling method includes: The local weighted regression method was used to perform seasonal-trend decomposition on the historical water use series, extracting the trend term, seasonal term and residual term, and clarifying the water use benchmark range for different months; The ARIMA model was used to fit the time-series relationship between monthly water consumption, and a 12×12 time-series correlation matrix was constructed. Calculate the Pearson correlation coefficient of water consumption of different types during the same period, and use the Archimedes Copula function to fit the joint distribution for those with weak linear correlation to obtain the inter-type correlation matrix; Divide the marginal distribution of each month-water type dimension into N equally probable intervals, where N is the sampling size of the random strategy and N≥50; Samples are randomly drawn from N strata based on the first month, and the sampling strata of subsequent months are constrained according to the time-series correlation matrix to ensure that the samples of each month are dependent on the previous months. Calculate the current association matrix for different types of water use samples for each month. When the association deviation from the inter-type association matrix is ​​greater than 5%, use Cholesky decomposition to embed the target association matrix into the sample for correction.

[0082] An improved Latin hypercube sampling method is adopted to reorder the initial random number matrix based on the temporal correlation matrix and the typological correlation matrix, thereby generating random samples that maintain spatiotemporal correlation.

[0083] First, historical monthly data for domestic, industrial, agricultural irrigation, and ecological water use in the study area were collected for more than 10 years, specifically including: monthly domestic water consumption series W_ for each water-receiving area. life (i, t), where i represents the water-receiving area number and t represents the month; monthly industrial water consumption sequence W industry (i, t); Monthly agricultural irrigation water consumption sequence W_ agriculture (i, t); Monthly ecological water consumption sequence W ecology (i,t), and simultaneously collect hydrological and meteorological data including monthly precipitation P(i,t) and monthly average temperature T(i,t); local water resource availability data including surface water resources SW(i,t) and groundwater resources GW(i,t); relevant engineering data including reservoir storage S(i,t) and canal water conveyance capacity C(i); population, economic and social data including population Pop(i,t), GDP G(i,t), and irrigated area A(i,t), etc.

[0084] For each water consumption sequence W(i,t), perform STL decomposition: W(i,t) = T(i,t) + S(i,t) + R(i,t), where T(i,t) is the trend term, reflecting the long-term trend of water consumption; S(i,t) is the seasonal term, reflecting the periodic variation within the year; R(i,t) is the residual term, reflecting random fluctuations. The trend term is fitted using local weighted regression with a window width of 13 months; the seasonal term is extracted using the moving average method with a period of 12 months; and the residual term is the remaining part after subtracting the trend term and the seasonal term from the original sequence.

[0085] Time-series correlation matrix M temporal It is a 12×12 matrix with element M temporal (m,n) represents the correlation coefficient between water consumption in month m and month n, calculated using the formula: M temporal (m, n) = Cov(W m Wn ) / (σ m ×σ n ), where Cov represents the covariance, σ represents the standard deviation, and W m This represents the water consumption sequence for month m of all years.

[0086] Inter-type correlation matrix M type It is a 4×4 matrix with element M type (p, q) represents the correlation coefficient between water use type p and water use type q. For water use type pairs with strong linear correlation (correlation coefficient greater than 0.7), the Pearson correlation coefficient is used directly. For non-linearly correlated type pairs, the Frank Copula function is used to fit their joint distribution, and the correlation strength is calculated by the Kendall rank correlation coefficient τ: τ = 4∫∫C(u, v)dC(u, v)-1, where C(u, v) is the Copula function.

[0087] The sampling size N=100 is set to ensure sufficient diversity in the strategy set. For each of the 48 dimensions (12 months × 4 types of water use), its marginal distribution F is first fitted. d (x), where d∈{1,2,...,48}. Divide the range [0,1] of the cumulative distribution function into N intervals: [0,1 / N], [1 / N,2 / N],...,[(N-1) / N,1]. Randomly select a uniformly distributed random number u in each interval. d , k, where k∈{1,2,...,N} represents the k-th sample. Through inverse transformation x d k=F d ^(-1)(u d ,k) to obtain the sample values ​​of the original space.

[0088] Initial sampling matrix X init This is an N×48 matrix, where each row represents a candidate strategy and each column represents a month-water type combination. To maintain temporal relevance, samples are randomly drawn from N strata, using January as the baseline, and then analyzed according to the temporal relevance matrix M. temporal The sampling stratum selection for subsequent months is constrained. Specifically, if a certain type of water consumption in January is located in the k-th stratum, then the sampling stratum k' for that type of water consumption in February is determined by the conditional probability P(k'|k)=exp(-|k'-k| / λ) / Σexp(-|jk| / λ), where λ is the relevant intensity parameter, based on M. temporal The value of the corresponding element is determined.

[0089] Annual water consumption control constraints: Σ t Σ type W(t, type)≤W total W totalThe annual water consumption control target; water balance constraint: for any time period t, the water supply shall not exceed the available water supply; engineering water supply capacity constraint: the water supply in each time period shall not exceed the channel water conveyance capacity C. max Ecological discharge constraints: ensuring the ecological base flow Q of the river channel eco The following constraints are met: Water supply priority: domestic water use > industrial water use > ecological water use > agricultural water use; Engineering operation stability constraint: Water supply variation in adjacent time periods does not exceed the threshold ΔW. max .

[0090] For the initial sampling matrix X init Each candidate strategy undergoes constraint testing, and strategies that do not meet the constraints are eliminated. If the number of feasible strategies is less than N, supplementary sampling is performed until N feasible strategies are reached, resulting in the final strategy set S. i ={P i 1 P i 2 , ..., P i N}, where P i j This represents the j-th water use planning strategy for the i-th water-receiving area.

[0091] The improved Latin hypercube sampling method described above generates a strategy set that maintains the temporal and typological correlation of historical water use, while ensuring the diversity and representativeness of strategies through stratified sampling, providing high-quality input for subsequent evolutionary game analysis.

[0092] In another embodiment, a more comprehensive decision-making framework is constructed by comprehensively considering the uncertainties of water inflow, demand, and model parameters, specifically as follows: The uncertainty of incoming water is handled using the method described in Example 3. The demand uncertainty is modeled as: D_ actual (i, t, k) = D_ plan (i, t, k) × (1 + ξ) demand ), where ξ demand ~N(0, σ d 2 ), σ d Based on historical demand forecasting errors, the domestic water consumption σ is determined. d =0.05, σ for industrial water d =0.10, agricultural water use σ d =0.20.

[0093] The uncertainty of the model parameters is handled using a Bayesian method, for the benefit coefficient B. unit (i, k), let the prior distribution B be... unit ~Gamma(α _B ,β_B ), where the shape parameter α _B and scale parameter β _B Based on historical data estimation, the posterior sample {B} of the parameters generated by the MCMC method is estimated. unit m}, m=1, ...,M _param .

[0094] Phase 1 (beginning of the year): Each water-receiving area determines its annual water use plan through evolutionary game theory based on historical information and forecasts; Phase 2 (within the year): Adaptive adjustments are implemented based on actual water inflow and demand.

[0095] Define information set I t ={X τ Y τ D τ : τ≤t} represents all historical information available at time t, and the policy mapping σ i :I t →A i (t), where A i (t) represents the actionable set at time t. Information value analysis is introduced: VOI = E[V|perfect] info ]-E[V|current info ] Quantify the value of complete information.

[0096] The annual planning period T is divided into K decision-making stages, each stage containing T / K time periods. At the beginning of the k-th stage, based on the latest information I... k Update the strategy for the next stage.

[0097] Prediction-Correction Mechanism: The prediction step uses historical models to generate future scenarios; the correction step updates model parameters based on actual observations and uses Kalman filtering for state estimation: x k |k=x k |k-1+K k ×(z k -H×x k |k-1), where x is the system state, z is the observed value, and K k This is the Kalman gain.

[0098] Adaptive policy adjustment: Δs i k=f_ adjust (e k , σ e ,k), where e k =actual k -forecast k For the prediction error, σ e k is the standard deviation of the error, and the adjustment function is f_ adjustUsing piecewise linear form: when |e k |<σ e When k, Δs=0; when σ e , k≤|e k |<2σ e When k, Δs=sign(e k )×λ1×|e k |;when|e k |≥2σ e When k is reached, the emergency response mechanism is triggered.

[0099] Generate N_ scenario =500 future scenarios, covering different hydrological year types (abundant, normal, and dry and their combinations), demand growth patterns (high, medium, and low), and climate change impacts (RCP2.6, RCP4.5, and RCP8.5).

[0100] For each scenario s, run the complete evolutionary game process to obtain the stable policy S_s*, and construct the scenario-policy matrix M_ scenario Element M ij This represents the performance of strategy i in scenario j.

[0101] A robust optimization strategy is used to select the final policy: min_smax_scenarioRegret(s, scenario), where Regret(s, scenario) = V_ best (scenario)-V(s,scenario) is the regret value. Optionally, the CVaR criterion can be used: min_sCVaR_α(Loss(s)) to focus on tail risk.

[0102] Establish a trigger-response mechanism and define a trigger indicator set T. indicator ={Inventory water level, inflow deviation, demand deviation, water supply guarantee rate}, when the indicators exceed the threshold, the corresponding management response is triggered: Level 1 response (yellow warning): strengthen monitoring and increase forecast frequency; Level 2 response (orange warning): activate backup water sources and implement restricted water supply; Level 3 response (red warning): activate emergency plan and re-engage in strategic game.

[0103] Learning and updating mechanism: Establish a case library to store historical decisions and their effects; use the case reasoning (CBR) method to find similar historical cases for new situations; generate initial strategy suggestions based on similarity weighted average; and continuously improve decision rules through incremental learning.

[0104] In some alternative implementations, a sub-Bruker bar optimization is introduced, which does not assume an exact probability distribution, but instead considers an uncertain set P of the distribution: min_ssup_P∈PE_P[Loss(s, ξ)], where the uncertain set is constrained by moments or by a Wasserstein sphere.

[0105] Furthermore, deep reinforcement learning can be used to process high-dimensional state spaces. Deep Q-Network (DQN) or Proximal Policy Optimization (PPO) algorithms can be used to learn policies directly from the raw data. The network inputs include historical hydrological data, current inventory, seasonal information, etc.; the outputs are the Q-values ​​or selection probabilities of each policy. The learning stability can be improved through experience replay and target networks.

[0106] This embodiment maintains the spatiotemporal correlation of hydrological sequences during the random sample generation process, ensuring that the generated random scenarios reflect both uncertainty and the inherent regularity of the hydrological process. Specifically: First, we analyze the spatiotemporal correlation characteristics of historical hydrological data. For M water source areas and N time periods, we construct a complete correlation matrix R with dimensions (M×N)×(M×N).

[0107] Time correlation analysis employed the autocorrelation function (ACF) and partial autocorrelation function (PACF) for the inflow sequence Q of the water source area m. m (t), calculate the autocorrelation coefficient with a lag of k periods: ρ m (k)=Cov[Q m (t), Q m (tk)] / Var[Q m [t] In practice, it has been found that monthly runoff sequences usually exhibit significant annual periodicity, ρ(12)≈0.6-0.8; the lag-1 correlation coefficient of seasonal runoff is ρ(1)≈0.3-0.5.

[0108] Spatial correlation is characterized by the cross-correlation function (CCF). For water source areas i and j, the spatial correlation coefficient is calculated as: ρ ij =Cov[Q i (t), Q j (t)] / (σ i ×σ j The correlation coefficient between upstream and downstream water source areas is usually between 0.7 and 0.9, while the correlation coefficient between adjacent watersheds is about 0.4 to 0.6, and the correlation between watersheds that are geographically far apart drops to below 0.2.

[0109] Constructing a block-related matrix: R=[R 11 R 12 ...R 1N ]; [R21 R 22 ...R 2N ]; [............]; [R n1 R n2 ...R nN ]; Where the submatrix R ij This represents the cross-correlation matrix of all water source areas between time periods i and j, with dimensions M×M. The diagonal block R... ii Reflecting spatial correlation within the same time period, off-diagonal block R ij (i≠j) reflects the spatiotemporal cross-correlation between different time periods.

[0110] To ensure numerical stability, the original correlation matrix is ​​corrected for positive definiteness using eigenvalue decomposition R = QΛQ. T Set the negative eigenvalues ​​to zero or to a small positive number ε = 10^-6, and reconstruct the matrix R' = QΛ'Q. T Another approach is to add a regularization term: R_ reg =(1-α)R+αI, where α=0.01 is the regularization parameter.

[0111] The corrected correlation matrix R' is decomposed using Cholesky: R' = LL^T, where L is a lower triangular matrix. Since the matrix dimension is large (typically 60×60 to 120×120), a block-based Cholesky algorithm is used to improve computational efficiency.

[0112] Block-based recursive algorithm implementation: Divide R' into blocks: R'=[AB] T ]; [BC]; Where A is a k×k principal submatrix.

[0113] Recursive calculation: L_A=chol(A), performing Cholesky decomposition on A; L_B=B×(L A T ) -1 Solve by forward substitution; L c =chol(CL B ×L B T ), decompose Schur complement; Assembly: L=[L A0 ];[L B L c ].

[0114] For sparsity optimization, when |ρij When <threshold (such as 0.05), set the correlation coefficient to zero, store the sparse matrix in Compressed Sparse Column (CSC) format, and use the CHOLMOD or SuiteSparse library for sparse Cholesky decomposition. The computational complexity is reduced from O(n 3 ) to O(n 1.5 ).

[0115] Numerical precision control: Use double-precision floating-point numbers (float64) for calculations; after each column vector calculation, check the numerical stability: ||LL T - R'||_F / ||R'||_F < 10^-10; if numerical instability occurs, use modified Cholesky decomposition or LDL T decomposition.

[0116] Standardized random number generation: Generate independent and identically distributed standard normal random vectors Z ~ N(0, I), with dimensions M×N. Use the Mersenne Twister algorithm (MT19937) as the random number generator, with a period of 2^19937 - 1. To ensure reproducibility, set the random seed seed = hash(scenario i d + timestamp).

[0117] Correlated random vector generation: Y = LZ + μ, where μ is the mean vector, and Y preserves the correlation structure of the original data: E[Y] = μ, Cov[Y] = LL T = R'. <00,01063>Inverse standardization transformation: Convert the standard normal distributed Y back to the original distribution. For the inflow, usually use the lognormal distribution: Q = exp(σY + μ_log), where μ_log and σ are determined based on the logarithmic mean and standard deviation of historical data. For precipitation, use the Gamma distribution and achieve it through quantile mapping: P = F_ gamma ^(-1)[Φ(Y)], where Φ is the standard normal CDF, and F gamma -1 is the inverse CDF of the Gamma distribution.

[0119] Split the random vector X into the known part X o (observed) and the unknown part X u (unobserved): X = [X o , μ = [μ o , Σ = [Σ oo Σ ou ; [X u [μu [Σ uo Σ uu ; The conditional distribution is: X u |X o ~N(μ u |o, Σ u |o), where: The conditional mean: μ u |o = μ u + Σ uo × Σ oo -1 × (X o - μ o ); The conditional covariance: Σ u |o = Σ uu - Σ uo × Σ oo -1 × Σ ou ; Implementation steps: Perform Cholesky decomposition on the conditional covariance matrix: Σ u |o = L c × L c T ; Generate an independent standard normal random vector: Z c ~N(0, I); Calculate the conditional random sample: X u = μ u |o + L c × Z c ; Examples of application scenarios: Given the measured inflow of the upstream reservoir, it is necessary to generate the random flow of each downstream section; given the precipitation of the current month, predict the possible scenarios for the next few months.

[0120] After generating the samples, it is necessary to verify whether their spatio-temporal correlation is maintained.

[0121] Correlation test: Calculate the empirical correlation matrix R of the generated samples emp =(1 / N _sample )× Σ(X i - μ)(X i - μ) T ; Compare the theoretical correlation matrix and the empirical correlation matrix: ||R emp - R target ||_F / ||R target ||_F < tolerance (such as 5%); Use the Kolmogorov-Smirnov test to check the consistency of the marginal distributions.

[0122] Correlation Adjustment: If the correlation deviation is large, an iterative adjustment algorithm is used, defining the objective function as: f(θ) = ||R emp (θ)-R target || F 2 The parameter θ is optimized using the quasi-Newton method (L-BFGS). The adjustment methods include fine-tuning the elements of the L matrix or performing post-processing transformations on the generated samples.

[0123] Multi-scale correlations are maintained: Annual scale: maintain the correlation of annual total runoff; Seasonal scale: maintain the correlation structure between flood season and non-flood season; Monthly scale: maintain the correlation of monthly processes; Extreme value correlation: maintain the spatial synchronicity of flood peak and dry season.

[0124] In some alternative implementations, the Copula function method can be used, selecting a suitable Copula function (such as GaussianCopula, t-Copula, ArchimedeseanCopula) to describe the dependency structure between variables; separating the marginal distribution from the modeling of the dependency structure; generating uniformly distributed random numbers that maintain dependency through the Copula function; and then obtaining the final sample through the inverse transformation of the marginal distribution.

[0125] Furthermore, for non-stationary time series, detrending and deperiodic processing can be performed first: separating the trend term T(t), the periodic term S(t), and the random term R(t); applying a correlation-preserving sampling method to the random term; and superimposing the generated random term with the deterministic component to restore the complete series.

[0126] To achieve refined scheduling and management of the reservoir group, this embodiment constructs reservoir scheduling rules based on a reservoir scheduling rule system with six restricted water supply lines and one restricted water diversion line, specifically as follows: Establish a scheduling diagram consisting of six restricted water supply lines and one restricted water diversion line. The six restricted water supply lines, from top to bottom, are: The first limiting water supply line (normal water supply line) Z1(t): When the reservoir water level is higher than this line, each water user will be supplied with 100% of the planned water supply. The principle for setting this line is: Z1(t) = Z_ flood (t)-ΔH_ safety Z_ flood (t) represents the flood control limit water level, ΔH_ safety For safety reasons, the water level is set at 2-3m during the flood season and 1-2m during the non-flood season. The annual variation is considered as follows: gradually lowering the water level before the flood season (March-May) to reserve reservoir capacity for flood control; maintaining a lower water level during the flood season (June-September); rapidly rising the water level after the flood season (October); and maintaining a high water level during the dry season (November-February of the following year). Second restricted water supply line (mild restriction line) Z2(t): When the water level drops to this line, agricultural water use is reduced by 10%, and other water uses are normal. It is set 3 - 5 m below the normal water supply line to ensure a certain buffer space. The calculation formula is: Z2(t)=Z1(t)-V_ buffer1 / A(Z), where V_ buffer1 is the first - level buffer storage capacity, usually the normal water supply for 0.5 - 1 months, and A(Z) is the water level - area relationship; Third restricted water supply line (moderate restriction line) Z3(t): Trigger the second - level water restriction measures, agricultural water use is reduced by 25%, industrial water use is reduced by 5%, and domestic water use is normal. Location determination: Z3(t)=Z dead +0.7×(Z1(t)-Z dead ), ensuring that the remaining storage capacity can support the basic water use for 2 - 3 months; Fourth restricted water supply line (severe restriction line) Z4(t): Implement the third - level water restriction, agricultural water use is reduced by 40%, industrial water use is reduced by 15%, and domestic water use is reduced by 5%. Set based on probability analysis: P(Z<Z4)=0.05, that is, the water level corresponding to a 95% guarantee rate; Fifth restricted water supply line (special restriction line) Z5(t): Enter the emergency state, agricultural water use is reduced by 60%, industrial water use is reduced by 30%, and domestic water use is reduced by 10%. Priority is given to ensuring urban water supply. Setting principle: Ensure the basic domestic water use during the critical period (such as 3 consecutive dry months). Calculation: Z5(t)=Z dead +V emergency / A(Z), V emergency =3×W_ lifemin ; Sixth restricted water supply line (extreme water supply line) Z6(t): Only ensure the most basic domestic water use and ecological base flow, and all other water uses are stopped. Usually set 5 - 10 m above the dead water level, Z6(t)=Z dead +ΔH extreme , ensuring that the water pump can still draw water normally; Restricted water diversion line Z transfer (t): Control the start time of cross - basin water diversion, set between the second and third restricted water supply lines: Z transfer (t)=Z2(t)-α×(Z2(t)-Z3(t)), where α = 0.3 - 0.5. When the water level is lower than this line, start emergency water diversion; the water diversion volume Q transfer =β×(Z transfer -Z_actual)×A(Z) / Δt, where β is the adjustment coefficient.

[0127] Determine the water supply and water diversion strategies according to the interval where the current reservoir water level Z(t) is located.

[0128] Decision logic implementation: if Z(t)≥Z1(t): Normal water supply area; W _supply =W_ plan ×1.0; Q transfer =0; elif Z2(t)≤ Z(t) <Z1(t): Level 1 Water Restriction Zone: W _agriculture =W _agr_plan ×0.9; W industry =W ind_plan ×1.0; W _life =W _life_plan ×1.0; Q transfer =0; elif Z3(t)≤Z(t) <Z2(t): Level II water restriction zone: W _agriculture =W _agr_plan ×0.75; W industry =W ind_plan ×0.95; W _life =W _life_plan ×1.0; ifZ(t) <Z transfer (t): Q transfer =min(Q transfer-capacity Q transfer-needed ); And so on for other intervals.

[0129] Water supply priority will be dynamically adjusted: the basic priority is: domestic > ecological > industrial > agricultural; adjustments will be made during special periods, such as increasing the priority of agriculture during the spring irrigation season; users with high water efficiency per unit volume will be given priority, taking into account economic benefits; and emergency water supply plans will be established to ensure water supply to key users.

[0130] Multi-reservoir joint operation rules: Compensational operation principle: when upstream reservoirs have high water levels, more water is supplied to reduce downstream pressure; Balanced drawdown principle: each reservoir experiences a synchronous drawdown in proportion to its upstream water level. i -Z idead ) / (Z inormal- Z idead )≈constant; The principle of staggered scheduling means that different reservoirs stagger their peak water supply periods.

[0131] Based on historical operational data and simulation results, the scheduling rule line is optimized.

[0132] Parameter optimization model: minF=Σ t Σ i [α_ shortage ×D_ shortage (i, t) + α spill ×W_ spill [(i, t)]; st water balance constraint; Water level constraints; Water supply capacity constraints; Decision variables: Coordinates of control points for each limiting water supply line {Z} k (t, j)}; Genetic algorithm optimization is used: chromosomes are encoded as the coordinates of key points of each rule line; the fitness function includes water shortage loss, water abandonment loss and operating cost; the crossover operation adopts simulated binary crossover (SBX); the mutation operation adopts polynomial mutation; the population size is 100 and the number of generations is 500.

[0133] Sensitivity analysis: The impact of ±1m changes in the position of each rule line on system performance was analyzed; critical scheduling periods and critical control points were identified; the results showed that the third and fourth limiting water supply lines had the greatest impact on the water supply guarantee rate.

[0134] The scheduling rules are dynamically adjusted based on real-time information to improve adaptability.

[0135] Forward-looking adjustments based on forecasts: Obtain water inflow forecasts for the next 15-30 days; if the forecast indicates a large inflow, restrictions can be appropriately relaxed; if the forecast indicates continued drought, water supply should be tightened in advance; Correction amount: ΔZ k (t)=f(Q _forecast P confidence ), where P confidence For forecast confidence level.

[0136] State-based feedback adjustment: Define the system state index S = (S_ water S demand S ecology When S deviates from the normal range, adjust the rule line; the adjustment range is proportional to the degree of deviation: ΔZ = K_p × (S) target -S_ actual Set upper and lower limits to prevent over-adjustment.

[0137] Seasonal correction factor: Spring (March-May): k_ spring =1.1, appropriately raise water supply standards to support spring plowing; Summer (June-August): k_ summer =0.9, reserved flood control capacity; Autumn (September-November): k_ autumn=1.0, running normally; Winter (December-February): k_ winter =0.95, taking into account the effects of the glacial period.

[0138] The scheduling rules are coordinated with other objectives to form a comprehensive scheduling scheme.

[0139] Coordination between flood control and water supply: Dynamically control the flood limit water level during the flood season and increase water storage on the premise of ensuring flood control safety; adopt forecast scheduling and pre-release or impound water according to rainfall forecasts; set graded flood control limit water levels and adopt different flood limit water levels for different flood levels.

[0140] Water supply and power generation coordination: Optimize power generation scheduling while ensuring water supply; increase power generation during periods of high electricity prices by utilizing time-of-use pricing; and set minimum discharge flow to ensure the operation of downstream cascade power stations.

[0141] Ecological and economic coordination: Ensuring ecological base flow: Q ecology ≥max(0.1×Q_ annualmean Q minimum_history ); implement pulsed water release during critical ecological periods (fish spawning season); establish an ecological compensation mechanism to balance the economic losses from ecological water use.

[0142] Emergency Response Rules: In the event of a major flood, all rules will be temporarily invalidated, and the flood control plan will be followed; in the event of an extreme drought, the emergency water supply plan will be activated, and water will be supplied in a fixed quantity; in the event of an engineering failure, backup water intakes or emergency water diversion channels will be activated.

[0143] In some alternative implementations, machine learning can be introduced to optimize the rules, using an LSTM network to learn historical scheduling decision patterns; the input is the current state (water level, inflow, and demand), and the output is the suggested water supply ratio; the neural network output is used as a reference for correcting the rule-based scheduling.

[0144] Furthermore, adaptive scheduling rules can be implemented, defining the performance index PI = w1 × water supply guarantee rate + w2 × reservoir fullness rate - w3 × water shortage loss; PI is evaluated at the end of each scheduling period; the rule parameters are updated using reinforcement learning algorithms (such as Q-learning); and the learning rate α = 0.01 is set to ensure gradual optimization of the rules.

[0145] Visualization of scheduling rules: Develop an interactive scheduling chart system to display water levels and various limit lines in real time; use color coding to indicate different water supply statuses (green for normal, yellow for warning, and red for restriction); provide historical comparisons and future trend predictions; support hypothetical scenario analysis to assess the impact of different decisions.

[0146] According to another aspect of this application, a multi-agent evolutionary game system for generating annual scheduling plans for water diversion projects is provided, comprising: At least one processor; and A memory communicatively connected to at least one of the processors; wherein, The memory stores instructions that can be executed by the processor to implement the multi-agent evolutionary game method for generating annual scheduling plans for water diversion projects as described above.

[0147] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A multi-agent evolutionary game method for generating a water transfer project annual operation plan, characterized in that, The method comprises the following steps: Collecting research area data, dividing the research area into water source area and water receiving area, and formulating water use plan strategy set of the water receiving area; Constructing three-dimensional joint distribution function of water diversion amount of the water source area at current time, water inflow amount of the water receiving area at current time and water inflow amount of the water receiving area at last time, and generating random samples of water diversion amount and water inflow process of the water receiving area; Extracting the random samples and combining with the water use plan strategy combination of the water receiving area, inputting an annual water amount scheduling plan compiling model, and obtaining water supply amount of each water receiving area at each time period under the water use plan strategy combination; Based on the water supply amount, generating multi-objective benefit vector of the water receiving area under the water use plan strategy combination, calculating comprehensive benefit value of the water receiving area, and calculating expected benefit value of the water receiving area after traversing the water use plan strategy combination; Adjusting and iterating the water use plan strategy of the water receiving area until the probability of the water receiving area selecting a specific water use plan strategy approaches to 1, and obtaining stable decision combination of the annual water use plan of the water receiving area corresponding to the random samples.

2. The method according to claim 1, wherein, The adjusting and iterating the water use plan strategy of the water receiving area comprises: Using a replication dynamic equation containing learning ability coefficient and risk preference coefficient, calculating risk adjustment utility based on the expected benefit value of the water receiving area; According to the difference between the risk adjustment utility and the average expected benefit, updating the probability of the water receiving area selecting each water use plan strategy combined with the learning ability coefficient; Iteratively updating the strategy selection probability until the probability of the water receiving area selecting a specific water use plan strategy approaches to 1 and the probability of selecting other strategies approaches to 0, and obtaining the stable decision combination.

3. The method according to claim 2, wherein, The calculation of the risk adjustment utility comprises: Calculating the benefit variance of the water receiving area selecting the water use plan strategy, multiplying the benefit variance by the risk preference coefficient to obtain the risk adjustment term; Subtracting the risk adjustment term from the expected benefit value to obtain the risk adjustment utility; The updating of the probability of the water receiving area selecting each water use plan strategy comprises: Calculating the difference between the risk adjustment utility and the average expected benefit of the water receiving area, multiplying the difference by the learning ability coefficient and the current strategy selection probability to obtain the probability update amount, and adjusting the strategy selection probability according to the probability update amount.

4. The method according to claim 2 or 3, wherein, The obtaining of the stable decision combination comprises: Setting a convergence threshold of the strategy selection probability, when the probability of the water receiving area selecting a specific water use plan strategy exceeds the convergence threshold, determining the strategy as the stable strategy of the water receiving area; After all the water receiving areas determine the stable strategies, forming the stable decision combination corresponding to the random samples; According to the annual water inflow level of the water receiving area of the random samples, classifying the stable decision combination into annual water use plan strategies corresponding to wet years, normal years and dry years.

5. The method according to claim 1, wherein, The construction of the three-dimensional joint distribution function of the water diversion amount of the water source area at current time, the water inflow amount of the water receiving area at current time and the water inflow amount of the water receiving area at last time comprises: Extracting historical water diversion data of the water source area and historical water inflow data of the water receiving area from the research area data, and fitting the water diversion amount edge distribution of the water source area, the water inflow amount edge distribution of the water receiving area at current time and the water inflow amount edge distribution of the water receiving area at last time; The two-dimensional Copula function is used to construct a joint distribution of water diversion quantity of a water source area and current water inflow of a water receiving area, so as to obtain a conditional distribution of the current water inflow of the water receiving area under a given water diversion quantity of the water source area; Based on the conditional distribution, a conditional Copula function is used to connect the water inflow of the water receiving area at a previous time, so as to construct a three-dimensional joint distribution function.

6. The method according to claim 5, wherein, The connecting of the water inflow of the water receiving area at the previous time by the conditional Copula function comprises: The edge distribution of the water diversion quantity of the water source area and the edge distribution of the current water inflow of the water receiving area are converted into uniform distributions, a Kendall rank correlation coefficient is calculated, and parameters of the two-dimensional Copula function are determined; Partial derivatives of the two-dimensional Copula function are calculated, so as to obtain a conditional distribution function of the current water inflow of the water receiving area under a given water diversion quantity of the water source area; Based on the conditional distribution function and the edge distribution of the water inflow of the water receiving area at the previous time, a conditional Kendall rank correlation coefficient is calculated, parameters of the conditional Copula function are determined, and a complete three-dimensional joint distribution is constructed.

7. The method according to claim 1, wherein, The generating of random samples of the water diversion quantity and the water inflow process of the water receiving area comprises: An initial random number matrix is generated based on the three-dimensional joint distribution function, a row of the matrix represents a time period, and a column of the matrix represents the water source area and the water receiving area; A time series correlation matrix between adjacent months in historical data is calculated, and a type association matrix between different water receiving areas is constructed; An improved Latin hypercube sampling method is used to reorder the initial random number matrix according to the time series correlation matrix and the type association matrix, so as to generate random samples that maintain the spatio-temporal correlation.

8. The method according to claim 7, wherein, The calculation of the time series correlation matrix and the construction of the type association matrix comprise: Water quantity sequences of each month in the historical data are extracted, Pearson correlation coefficients between adjacent months are calculated, and a 12*12 time series correlation matrix is formed; Spatial distance weights are calculated according to geographical positions of the water receiving areas, and a type association matrix between the water receiving areas is constructed in combination with supply water feature similarities of the water receiving areas; Cholesky decomposition is respectively performed on the time series correlation matrix and the type association matrix, so as to obtain lower triangular matrices, the initial random number matrix is multiplied by the lower triangular matrices, and random samples under the correlation constraint are generated.

9. The method according to claim 1, wherein, The calculation of the comprehensive benefit value of the water receiving area comprises: Based on the supply water quantity, a water supply guarantee target, a water use benefit target, a water diversion cost target and a fairness target of the water receiving area are calculated, a four-dimensional benefit vector is formed, and normalization processing is performed; The water supply guarantee target is measured by a water supply guarantee rate, and is calculated as a ratio of a number of time periods that meet water demand to a total number of time periods; The water use benefit target is calculated by weighted summation of benefits for use, including power generation and water supply; The water diversion cost target is calculated by a product of an actual supply water quantity and a water diversion cost coefficient; The fairness target is measured by a difference between a water supply guarantee degree of the water receiving area and water supply guarantee degrees of other areas; A Pareto non-dominated sorting is performed on a multi-target benefit vector set, a non-dominated level of each strategy combination is determined, and a crowding distance is calculated in a same non-dominated level; A strategy dispersion degree of the water use plan strategy combination is calculated, a comprehensive benefit value is obtained by weighted combination of the non-dominated level, the crowding distance and the strategy dispersion degree.

10. The method according to claim 9, wherein, The calculation of the strategy dispersion degree comprises: The strategy distribution entropy is calculated, the strategy distribution entropy is divided by the maximum possible entropy value to obtain a normalized strategy dispersion degree; The calculation formula of the comprehensive benefit value is: the reciprocal of the non-dominated level is taken as the level score, the congestion distance is normalized as the distance score, the level score, the distance score and the strategy dispersion degree are respectively given the weight coefficients of a, b and c, and the comprehensive benefit value is obtained by weighted summation.

11. The method according to claim 1, wherein, The generation of the random sample of the water intake and the water receiving area inflow process adopts a master-slave calculation method, which comprises the following steps: Firstly, the uniform distribution random number of the water source area water intake is generated by inverse transformation sampling from the three-dimensional joint distribution function; Based on the generated water source area water intake, the water receiving area current time inflow is generated by the conditional distribution function; According to the water source area water intake and the water receiving area current time inflow, the water receiving area last time inflow is generated by the conditional Copula function, the uniform distribution random number is inversely transformed into the original variable space, and the random sample maintaining the space-time correlation is formed.

12. The method according to claim 1 or 2, wherein, It also includes the classification processing of the stable decision combination: According to the annual water inflow of the water receiving area in the random sample, the stable decision combination is divided into three categories of wet year, normal year and dry year; The frequency distribution of the water receiving area selecting each water plan strategy under each type of water inflow condition is counted, and the strategy difference degree between different water inflow conditions is calculated; When the strategy difference degree exceeds the set threshold, the stable decision combination under different water inflow conditions is stored respectively as the classified scheduling plan; otherwise, the unified stable decision combination is used as the annual scheduling plan.

13. The method of claim 7, wherein the method further comprises: The improved Latin hypercube sampling method comprises the following steps: The local weighted regression method is used to seasonally-trend decompose the historical water consumption sequence, the trend item, the seasonal item and the residual item are extracted, and the water consumption benchmark range of different months is determined; An ARIMA model is used to fit the time sequence relationship between the monthly water consumption, and a 12*12 time sequence correlation matrix is constructed; The Pearson correlation coefficient of the same period and different types of water consumption is calculated, the Archimedean Copula function is used to fit the joint distribution of the weak linear correlation, and the inter-type correlation matrix is obtained; The marginal distribution of each month-water type dimension is divided into N equal probability intervals, N is the sampling sample size of the random strategy and N is greater than or equal to 50; The first month is taken as the benchmark to randomly sample from N layers, and the sampling layer of the subsequent month is constrained according to the time sequence correlation matrix, so that the dependence of the sample of each month on the previous month is ensured; The current correlation matrix of each month and different types of water samples is calculated, and when the correlation deviation from the inter-type correlation matrix is greater than 5%, the target correlation matrix is embedded in the sample by Cholesky decomposition for correction.

14. A multi-agent evolutionary game system for generating an annual operation plan of a water diversion project, characterized in that, It comprises: At least one processor; And The memory is in communication connection with the at least one processor; wherein The memory stores instructions executable by the processor, and the instructions are executed by the processor to implement the water diversion project annual scheduling plan generation multi-agent evolutionary game method of any one of claims 1 to 13.

Images