A water quantity scheduling method based on physical-data dual model convergence

Abstract

The application discloses a water quantity scheduling method based on physical-data double model convergence, and is applied to the technical field of water resource scheduling optimization, and comprises the following steps: a multi-objective optimization model including a water supply target and a convergence target is constructed; wherein the water supply target is the minimum square sum of water shortages of each river section of a trunk stream; the convergence target is the minimum difference of section flow processes of two models of physics and data under a certain water distribution result; an improved NSGA-II algorithm is used to solve the multi-objective optimization model, and a set of non-inferior solution sets are obtained; wherein the improvement comprises the following steps: a Halton sequence is introduced to generate an initial population, and the self-adaptive adjustment of the crossover and mutation probability is based on the comparison of individual fitness and the overall performance of the population; and a fuzzy comprehensive evaluation model is used to determine an optimal water quantity scheduling scheme from the non-inferior solution sets. The application realizes the dynamic collaborative optimization of basin water quantity regulation, and provides a new optimization idea and technical path for the intelligent scheduling of the Yellow River water quantity.

Description

Technical Field

[0001] This invention relates to the field of water resource scheduling and optimization technology, and more specifically to a water allocation method based on convergence of physical and data dual models. Background Technology

[0002] The "87 Plan," forwarded by the General Office of the State Council in 1987, was the core basis for water allocation in the Yellow River Basin before the South-to-North Water Diversion Project took effect, establishing a guiding framework for water allocation in the Yellow River Basin. Based on actual water consumption in 1980, the 87 Plan considered the scale of irrigation development in relevant provinces and municipalities, the growth of industrial and urban water use, and the possibility of constructing large and medium-sized water conservancy projects. However, in the nearly forty years since the plan's implementation, the hydrological situation, economic and social development stage, and ecological protection requirements of the Yellow River Basin have all undergone significant changes, and the eastern and central routes of the South-to-North Water Diversion Project were opened in 2013 and 2014 respectively. The 87 Plan has gradually revealed various uncertainties in its actual operation. These uncertainties stem from the inherent complexity of the Yellow River Basin's water resources system, requiring systematic identification and in-depth analysis from multiple dimensions, including changes in the basin's natural water inflow and changes in provincial water use patterns.

[0003] (a) The uncertainty of the inflow dimension stems from the dual impacts of climate change and human activities: The Yellow River Basin is inherently water-scarce, with a general downward trend in water resources. Its distribution is extremely uneven both annually and interannually. Non-flood season runoff accounts for 30%–40% of the annual total, yet it bears over 60% of the water demand. Furthermore, interannual runoff fluctuations can reach 1–2 times. These fluctuations are driven by both climate system changes and underlying surface variations. Climate-wise, weather events can reduce rainfall in the upper reaches of the Yellow River by more than 10%, leading to a decrease in runoff in the main inflow area upstream of Tangnaihai (accounting for over 35% of the Yellow River's main stream inflow). Abnormal monsoon intensity alters the spatial and temporal distribution of rainfall in the Loess Plateau of the middle reaches, causing the flood season arrival time of tributaries such as the Jinghe and Weihe Rivers to be 1–2 months earlier or later. Regarding the underlying surface, since 2000, vegetation cover in the Yellow River Basin has increased year by year. The interception and transpiration effects of forest and grassland vegetation have reduced the basin's runoff coefficient, directly resulting in a decrease in water yield in the Loess Plateau of the middle reaches. In addition, although the regulation and storage functions of key reservoirs such as Longyangxia and Liujiaxia can smooth short-term runoff fluctuations, in the long run, reservoir siltation will lead to a gradual reduction in beneficial storage capacity, further exacerbating the impact of the uncertainty of the inflow process on the allocation of the 87 scheme.

[0004] (ii) The uncertainty in water use stems from the dynamic changes in the basin's economic and social development and water use structure: When the "87 Plan" was formulated, agriculture was the primary water user in the Yellow River Basin, with industry and domestic water use accounting for less than 20%. By 2024, however, industrial water use had increased to 12%, and domestic water use to 15%. This shift in water use structure has caused a discrepancy between the initial demand assumptions of the "87 Plan" and current actual needs. Agricultural water use, as the core component of the basin's water use (accounting for over 60%), faces uncertainties primarily due to adjustments in planting structures, the promotion of irrigation technologies, and the impact of meteorological conditions. Uncertainties in industrial water use are closely related to industrial upgrading. Uncertainties in domestic water use mainly stem from increased urbanization rates. The rise in urbanization and increased domestic water consumption have led to rapid increases in domestic water consumption in populous provinces such as Henan and Shandong, further squeezing the space for agricultural and ecological water use.

[0005] Over the past 40 years, the water use pattern in the Yellow River Basin has undergone significant changes due to differences in the pace and speed of economic and social development across different regions. Provinces such as Inner Mongolia and Shandong have consistently exceeded their water consumption targets allocated under the "1987 Water Allocation Scheme," while provinces like Shanxi and Henan have failed to meet their allocation targets in most years. The current water allocation scheme deviates to some extent from the actual supply and demand situation in the basin, weakening its guiding role for provincial water use and hindering effective control of total water withdrawal at the basin-wide level. In the 1980s, the utilization rate of surface water resources in the Yellow River Basin reached 69%, and currently it has climbed to 79%, significantly exceeding the carrying capacity of the Yellow River's water resources.

[0006] In summary, the "87 Scheme" provides a macro-level allocation framework and total quantity control, but the static spatiotemporal proportional allocation based on the "2520 Scheme" and other supporting water allocation schemes is difficult to adapt to complex water inflow situations and constantly changing water use patterns, which is the root cause of its "uncertainty".

[0007] Therefore, how to provide a water allocation method based on a physical-data dual-model convergence that can dynamically and in real time optimize the allocation of water over time based on changes in water use patterns under the background of the 87 scheme limiting the total water consumption of the province, so as to improve the efficiency of water allocation for the whole river, is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0008] In view of this, this invention provides a water allocation method based on convergent physical-data dual models. It aims to address the problem that existing watershed water allocation optimization research often focuses on single data-driven or single physical mechanism-driven models, lacking deep integration of data and physical mechanisms. This results in insufficient reliability and rationality of allocation schemes, and difficulty in effectively avoiding the uncertainties brought about by static water allocation patterns. Under the overall framework established by the "87 Plan" and the rigid constraints of strategies such as watershed ecological protection and high-quality development, this invention constructs a water allocation scheme that can dynamically respond to changes in natural water inflow and water use patterns in various regions, and is both forward-looking and operable.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: A water allocation method based on convergent physical-data dual models includes: Step 1: Construct a multi-objective optimization model that includes water supply objectives and convergence objectives; among which, the water supply objective is to minimize the sum of squares of the water shortage rate in each section of the main stream; the convergence objective is to minimize the difference in cross-sectional flow process between the physical and data models under a certain water allocation result. Step 2: Solve the multi-objective optimization model using the improved NSGA-II algorithm to obtain a set of non-dominated solutions; the improvements to the NSGA-II algorithm include: introducing Halton sequences to generate the initial population, and adaptive adjustment of crossover and mutation probabilities based on the comparison of individual fitness and overall population performance. Step 3: Use a fuzzy comprehensive evaluation model to determine the optimal water allocation scheme from the solution set of non-inferior schemes.

[0010] Optionally, in step 1, the objective function for the water supply target is expressed by the following mathematical expression:

[0011] in, This is the sum of squares of the water shortage rates in each section of the main stream; To manage the number of river sections; The number of time units to be divided; For the first Each section of the river Water demand during different time periods; For the first Each section of the river Water consumption allocated over time periods.

[0012] Optionally, in step 1, the objective function for the convergence objective is expressed by the following mathematical expression:

[0013] in, The difference in cross-sectional flow process between physical and data models under a certain water distribution result; The number of time units to be divided; Number of cross sections; For the first The difference weighting coefficients for the entire river flow process in each time period are used to adjust the optimization direction in the time dimension; For the first The weighting coefficients for the differences in flow processes in each river segment are used to adjust the optimization direction in the spatial dimension. , Based on two models, namely physical and data, in the first... Time period, number The flow rate at the cross-section.

[0014] Optionally, in step 1, the physical and data models employ a traffic evolution physical model and a CNN-LSTM hybrid model.

[0015] Optionally, the constraints of the multi-objective optimization model in step 1 are as follows: Water supply constraints in each province and region:

[0016] in, The number of river sections to be dispatched in each province / region; The number of time units to be divided; For the province / region Each section of the river Water consumption allocated over time periods; The annual available water consumption of the main stream allocated to provinces and regions; Water demand constraints:

[0017] in, For the first Each section of the river Water consumption allocated over time periods; No. Each section of the river Water demand during different time periods; Suitable water consumption range constraints: The water consumption of the main stream predicted by the BiLSTM model is close to the actual situation and is used as a constraint for appropriate water consumption, as follows:

[0018] in, The water consumption of the entire main stream is appropriate; The set threshold range; Ecological flow constraints:

[0019] in, for Section Ecological flow during a given time period; for Section Simulated traffic flow over a given time period; Flow rate variation constraints:

[0020] in, for Section The maximum range of change before and after the time period; Reservoir capacity constraints:

[0021] in, , They are respectively reservoir Upper and lower limits of storage capacity for a given time period; for reservoir Water storage volume during a given period; Minimum discharge flow constraint of the reservoir:

[0022] in, for reservoir Minimum allowable outbound flow rate for a given time period; Variable nonnegation constraint:

[0023] Among them, the allocated water volume Cross-sectional flow It should be non-negative.

[0024] Optionally, in step 2, the Halton sequence is introduced to generate the initial population, specifically as follows: In the Halton sequence, let prime number For any integer Both can be used to Represented in base form, see the following formula:

[0025] in, ,base Given a known prime number, in the above formula... Both exist and are unique. Taking a fundamental reversal of the above formula, we get:

[0026] Furthermore, for different integers, the corresponding base can be obtained. The following one-dimensional Halton sequence: .

[0027] Optionally, in step 2, the adaptive adjustment of crossover and mutation probabilities based on the comparison between individual fitness and overall population performance is as follows: First, we introduce the fitness function, which is obtained by comparing individuals. A higher fitness value indicates that the individual is better. The formula is as follows:

[0028] in, Population size; The number of objective functions; The first in the population Individual; For this individual's contribution to the population of the first The sequence number of the objective functions after being arranged; For this individual regarding the first The fitness value of each objective; The overall fitness is obtained by summing the fitness values ​​of all targets; a constant is introduced here to highlight the fitness of outstanding individuals. Based on the comparison between individual fitness and overall population performance, adaptive adjustments to crossover and mutation probabilities are achieved. The adaptive function expressions for these probabilities as a function of fitness are as follows:

[0029] in, , These are the adaptive change values ​​for crossover and mutation probabilities, respectively; The maximum fitness value in the population; This represents the average fitness value. The larger of the fitness values ​​of the two individuals undergoing crossover; To determine the fitness value of the individual to be mutated , These are fixed values ​​for the crossover and mutation probabilities, respectively.

[0030] Optionally, in step 2, an improved NSGA-II algorithm is used to solve the multi-objective optimization model, specifically as follows: Parameter settings: Based on the algorithm's characteristics and the actual needs of water allocation, the following values ​​were determined through parameter calibration and testing: Population size Maximum number of iterations, baseline crossover probability Baseline value of mutation probability ; Initial population generation: After setting the range of decision variables according to the constraints, to balance the randomness and uniformity of the initial population, an integer is randomly selected from the interval [1, 100] as the base to generate the Halton sequence. And use this sequence to construct a structure of size initial population ; Crossover and mutation operations: from the population Two individuals are randomly selected, and their crossover probabilities are determined based on their fitness values. Crossover is performed preferentially using the adaptive crossover rate corresponding to the individual with higher fitness. Then, one individual is randomly selected, and its mutation probability is calculated based on its fitness to perform a mutation operation. Through this adaptive crossover and mutation process, a offspring population is generated. ; Elite strategy selection forms a new parent generation: the parent population With offspring population Merged into a size of Mixed population ;right All individuals are subjected to a fast non-dominated sorting and crowding calculation, and selected according to the fitness assignment rule. The best individuals constitute the next generation of the parent population. ; Termination condition judgment: If the current evolutionary generation has not reached the set upper limit, the newly generated parent population will be terminated. Proceed to crossover and mutation operations to continue iteration; otherwise, terminate the algorithm and output the result.

[0031] Optionally, in step 3, a fuzzy comprehensive evaluation model is used to determine the optimal water allocation scheme from the solution set of non-inferior solutions, specifically as follows: For each planning year, individuals in the population output from the multi-objective optimization model are non-dominated and ranked. A predetermined number of individuals are selected to form a set of alternative solutions. The alternative solutions are evaluated using an index set composed of two indicators: water supply and convergence. The resulting eigenvalue matrix is ​​then obtained. ;in, For the number of indicators; The number of solutions in the solution set; For eigenvalue matrix For standardization, since both objectives of this model are minimization, the evaluation indicators are processed into cost-based indicators using the following membership function:

[0032] in, For the first The plan for the first The characteristic values ​​of the indicator; , The first of all the schemes The maximum and minimum values ​​of the indicator; For the first The plan for the first The membership value of the indicator is determined by... Forming a membership matrix ; exist ,in , Indicates the first option among all solutions. The maximum membership degree of each indicator. It is the maximum membership matrix; there exists ,in , Indicates the first option among all solutions. The minimum membership degree of each indicator. It is the minimum membership matrix; Assuming the system The weight vector of each indicator is , For the goal The weight of; then the weight of the first The progress of the Euclid patch scheme is as follows:

[0033] in, For distance parameters; Representation scheme For the optimal solution of the schedule, according to The size of the values ​​is used to judge the merits of each scheme, and the scheme with the highest value is ultimately selected. The largest possible solution is considered the optimal water allocation solution.

[0034] As can be seen from the above technical solution, compared with the prior art, this invention discloses a water allocation method based on convergence of physical and data dual models. Existing research on water allocation optimization in river basins often focuses on single data-driven or single physical mechanism-driven models, lacking deep integration of data and physical mechanisms. This results in insufficient reliability and rationality of the allocation scheme, making it difficult to effectively avoid the uncertainties brought about by static water allocation patterns. The core of this invention lies in constructing a multi-source model collaborative optimization method. Using the aforementioned flow evolution model as the core simulation engine, through dual-model collaborative verification, when the physical model and data model, driven by the same configuration scheme, show a high degree of convergence in the output cross-sectional flow process, it indicates that different methodologies have reached a consensus on the physical mechanism. This consensus effectively reduces the scheduling uncertainty brought about by static water allocation schemes. The established bidirectional driven allocation model and the innovative collaborative fusion mode of multi-source heterogeneous algorithms realize dynamic collaborative optimization of watershed water allocation, providing a new optimization idea and technical path for intelligent water allocation in the Yellow River. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0036] Figure 1 This is a schematic diagram of the method flow provided by the present invention.

[0037] Figure 2(a) is a schematic diagram of the scatter distribution of the random sequence provided by the present invention.

[0038] Figure 2(b) is a schematic diagram of the scatter distribution of the Halton sequence provided by the present invention.

[0039] Figure 3(a) is a schematic diagram of the simulation results of the traditional NSGA-II algorithm after 50 iterations.

[0040] Figure 3(b) is a schematic diagram of the simulation results of the traditional NSGA-II algorithm after 300 iterations.

[0041] Figure 3(c) is a schematic diagram of the simulation results of the traditional NSGA-II algorithm after 500 iterations.

[0042] Figure 3(d) is a schematic diagram of the simulation results of the traditional NSGA-II algorithm after 800 iterations.

[0043] Figure 4(a) is a schematic diagram of the simulation results of the improved algorithm after 50 iterations.

[0044] Figure 4(b) is a schematic diagram of the simulation results of the improved algorithm iterating 300 times.

[0045] Figure 4(c) is a schematic diagram of the simulation results of the improved algorithm iterating 500 times.

[0046] Figure 4(d) is a schematic diagram of the simulation results of the improved algorithm after 800 iterations.

[0047] Figure 5(a) is a schematic diagram of the population distribution of local optimal solutions after 300 iterations of the traditional NSGA-II algorithm.

[0048] Figure 5(b) is a schematic diagram of the population distribution of local optimal solutions after 500 iterations of the traditional NSGA-II algorithm.

[0049] Figure 6 A schematic diagram illustrating the process of solving multi-objective optimization models using the improved NSGA-II algorithm provided in this invention. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Example 1: Embodiment 1 of this invention discloses a water allocation method based on convergent physical-data dual models, such as... Figure 1 As shown, it includes: Step 1: Construct a multi-objective optimization model that includes water supply objectives and convergence objectives; among them, the water supply objective is to minimize the sum of squares of the water shortage rate in each section of the main stream; the convergence objective is to minimize the difference in cross-sectional flow process between the physical and data models under a certain water allocation result.

[0052] Adhering to the principle of fairness, the water allocation model should ensure that water resources are planned and allocated rationally in both time and space, minimizing the sum of the squares of the water shortage rates of each unit. The water demand is calculated based on the reported water usage for each river section submitted by each province, with the goal of minimizing the sum of the squares of the water shortage rates for each section of the main stream.

[0053] The objective function for the water supply target is expressed by the following mathematical expression:

[0054] in, This is the sum of squares of the water shortage rates in each section of the main stream; To manage the number of river sections; The number of time units to be divided; For the first Each section of the river The water demand for a given period is the declared water usage. For the first Each section of the river The Yellow River's water consumption distribution over a given period of time.

[0055] The optimization process for achieving convergence can be viewed as dynamically searching for a refined spatiotemporal allocation process that best matches the current water inflow situation and water use patterns, under the constraints of the total amount and principles of the "87 Scheme," using a physical model of flow evolution and a CNN-LSTM hybrid model as simulation tools. A water allocation scheme can be considered not only physically feasible but also highly consistent with the actual operating laws of the watershed system if and only if it simultaneously passes the aforementioned dual verification (i.e., the output results of the two models converge). The convergence objective is to minimize the difference in cross-sectional flow processes between the two models under a given water allocation result.

[0056] The objective function for convergence goals is expressed by the following mathematical expression:

[0057] in, The difference in cross-sectional flow process between physical and data models under a certain water distribution result; The number of time units to be divided; Number of cross sections; For the first The difference weighting coefficients for the entire river flow process in each time period are used to adjust the optimization direction in the time dimension; For the first The weighting coefficients for the differences in flow processes in each river segment are used to adjust the optimization direction in the spatial dimension. , Based on two models, namely physical and data, in the first... Time period, number The flow rate at the cross-section, these two flow processes need to be determined in a certain intended water distribution result. The simulation yielded the results.

[0058] The convergence target needs to take into account the weights of different river sections and different time periods. The data model shows a high level in most spatiotemporal simulations, but due to the coverage of basic data, it performs poorly during specific periods such as the autumn flood season in the middle and lower reaches and water and sediment regulation. Meanwhile, the physical model shows a certain degree of stability due to its deep understanding of the physical mechanisms of floods and downstream sediment flushing. Therefore, the corresponding spatiotemporal weights should be increased for the river section below Fugu during the period from July to October.

[0059] Setting conditions: Using 25 regulated sections of the Yellow River main stream as spatial calculation units The year is divided into 36 time units, with each ten-day period serving as a separate period. The convergence objective requires simulating daily-scale cross-sectional flow processes, averaging decadal-scale river segment water consumption over daily periods, and then inputting this data into two models to obtain the convergence objective. (The text then repeats the first instance.) The river section during the time period Water distribution of the Yellow River main stream As decision variables, the model contains a total of 900 (25×36) decision variables.

[0060] Solving the Yellow River water allocation model requires deriving it under numerous constraints, including water quantity constraints, flow process constraints, and reservoir scheduling constraints. Specifically, the constraints for establishing the multi-objective optimization model are as follows: Water supply constraints in each province and region: The water consumption allocated to each province and region should not exceed the available water consumption of the Yellow River main stream in the province and region in the scheduling year as determined by the 87 Plan and other relevant plans, which is 24.665 billion m³.

[0061] in, The number of river sections to be dispatched in each province / region; The number of time units to be divided; For the province / region Each section of the river Water consumption allocated over time periods; The annual available water consumption of the Yellow River main stream allocated to provinces and regions; Water demand constraints: Declaration limit. The declared water demand, i.e., the declared water consumption, is the upper limit of the water allocation for each section of the main stream. The allocated water volume should not exceed the declared water consumption for the corresponding section reported by the province or region.

[0062] in, For the first Each section of the river Water consumption allocated over time periods; No. Each section of the river The water demand for a given period is the declared water usage. Suitable water consumption range constraints: The water consumption of the main stream predicted by the BiLSTM model is close to the actual situation and is used as a constraint for appropriate water consumption, as follows:

[0063] in, Suitable water consumption for the entire main stream; The set threshold range; Ecological flow constraints: For ecological flow control sections, the simulated flow must not be lower than its threshold.

[0064] in, for Section Ecological flow during a given time period; for Section Simulated traffic flow for a given time period, if Less than Then the amount of water allocated to that section of the river needs to be reduced; Flow rate variation constraints: To prevent model divergence due to imbalanced water volume and sudden changes in the data model, the flow rate variation before and after the fault should be controlled within a reasonable range based on historical data to ensure the stability of the evolution.

[0065] in, for Section The maximum range of change before and after the time period; Reservoir capacity constraints: During the operation of a reservoir, the reservoir capacity at any time should not exceed the reservoir capacity limit, including the dead capacity, normal high capacity, and flood limit constraints during routine operations, as well as constraints such as water and sediment regulation and ice prevention during special periods.

[0066] in, , They are respectively reservoir Upper and lower limits of storage capacity for a given time period; for reservoir Water storage volume during a given period; Minimum discharge flow constraint of the reservoir:

[0067] in, for reservoir Minimum allowable outbound flow rate for a given time period; Variable nonnegation constraint:

[0068] Among them, the allocated water volume Cross-sectional flow It should be non-negative.

[0069] Step 2: Solve the multi-objective optimization model using the improved NSGA-II algorithm to obtain a set of non-dominated solutions; the improvements to the NSGA-II algorithm include: introducing Halton sequences to generate the initial population, and adaptive adjustment of crossover and mutation probabilities based on the comparison of individual fitness and overall population performance.

[0070] The Non-Dominated Fast Genetic Algorithm (NSGA-II) with Elite Strategy is one of the most classic and widely used evolutionary algorithms in the field of multi-objective optimization. It can simultaneously optimize multiple conflicting objectives in a single run, obtaining a uniformly distributed Pareto optimal solution set (Pareto Front). NSGA-II mainly introduces core mechanisms such as non-dominated sorting, crowding degree, and elite strategy, providing a solution framework that balances scientific rigor and practicality for water allocation problems in complex large-scale systems like the Yellow River. It can efficiently generate a series of trade-off solutions based on the set objective function and constraints, making it suitable for supporting high-level strategic water resource allocation decisions.

[0071] However, while the NSGA-II algorithm has many advantages, it also has some limitations in its computation. On the one hand, if the distribution of individuals within the population is uneven, especially if the initial population is randomly generated, the algorithm may not be able to fully utilize information about certain superior individuals and the objective function. Limitations in population distribution can easily lead to premature convergence, resulting in a local optimum rather than a globally optimal solution. On the other hand, since the parameters in operations such as crossover and mutation are usually fixed, population diversity is difficult to maintain sustainably, and the limitation of the search space may cause the algorithm to get trapped in local optima in the later stages of iteration and be unable to escape.

[0072] Therefore, the present invention makes the following improvements to the NSGA-II algorithm: The initial population is generated by introducing Halton sequences, specifically as follows: In the NSGA-II algorithm, the initial population is typically generated using random sequences or specific pre-defined sequences. This method can easily lead to uneven distribution and insufficient representativeness within the population. In contrast, using Halton sequences can generate an initial population with better uniformity and lower variability. The resulting initial population is more representative, which helps improve the overall search performance of the algorithm. Halton sequences are simple to execute, using the inverse function of the basic function to generate a low-variability random sequence, ensuring that sequences of any length can be evenly distributed in the constraint space. The uniform distribution of the initial population generated using Halton sequences allows for more comprehensive acquisition of key information about the objective function, ensuring better performance of the algorithm in the early stages.

[0073] In the Halton sequence, let prime number For any integer Both can be used to Represented in base form, see the following formula:

[0074] in, ,base Given a known prime number, in the above formula... Both exist and are unique. Taking a fundamental reversal of the above formula, we get:

[0075] Furthermore, for different integers, the corresponding base can be obtained. The following one-dimensional Halton sequence: .

[0076] Within a unit length, two sets of random numbers of size 20 were generated using a random sequence. Then, two more sets of random numbers were generated using Halton sequences with base 2 and base 3, respectively. The random numbers generated by the two sequences were combined into two-dimensional arrays, and their corresponding scatter plots were plotted, as shown in Figure 2. Figure 2(a) shows the scatter plot of the random sequence, and Figure 2(b) shows the scatter plot of the Halton sequence. Comparative analysis shows that the point set generated by the Halton sequence has better uniformity. Furthermore, thanks to the inherent characteristics of the Halton sequence and the flexibility in selecting its base, this sequence maintains good randomness while ensuring uniform distribution. Therefore, using the Halton sequence can significantly improve the quality of the initial population.

[0077] The adaptive adjustment of crossover and mutation probabilities based on the comparison between individual fitness and overall population performance is as follows: Crossover probability and mutation probability These are key control parameters in the evolution process of genetic algorithms; their values ​​directly affect the algorithm's convergence speed and solution performance. Crossover probability Defined as the ratio of the number of new solutions generated through crossover to the population size, it is used to regulate the rate of genetic evolution. If If the value is too high, it may lead to excessive disruption of the structure of individuals with high fitness; if the value is too low, insufficient new solutions will be generated, the search process will be slow, and it will be easy to get trapped in local optima. Mutation probability This refers to the ratio of the number of mutated genes to the total number of genes in the population; its main function is to maintain population diversity. If If the size is too small, the individual has limited opportunities for variation, making it difficult to introduce new structures and thus reducing population diversity; conversely, if... If the crossover and mutation parameters are too large, the mutation operation may disrupt the inheritance of superior genes, causing the algorithm to degenerate into an approximate random search. To effectively preserve superior individuals in the population and ensure the generation of some better new individuals, this invention improves the crossover and mutation parameters in the NSGA-II algorithm based on the adaptive principle of evolution, making... and It can adapt to change.

[0078] First, we introduce the fitness function, which is obtained by comparing individuals. A higher fitness value indicates that the individual is better. The formula is as follows:

[0079] in, Population size; The number of objective functions; The first in the population Individual; For this individual's contribution to the population of the first The sequence number of the objective functions after being arranged; For this individual regarding the first The fitness value of each objective; The overall fitness is obtained by summing the fitness values ​​of all targets; a constant is introduced here to highlight the fitness of outstanding individuals. (This invention takes) Based on the comparison between individual fitness and overall population performance, adaptive adjustments to crossover and mutation probabilities are achieved. The adaptive function expressions for these probabilities as a function of fitness are as follows:

[0080] in, , These are the adaptive change values ​​for crossover and mutation probabilities, respectively; The maximum fitness value in the population; This represents the average fitness value. The larger of the fitness values ​​of the two individuals undergoing crossover; To determine the fitness value of the individual to be mutated , These are fixed values ​​for crossover and mutation probabilities, respectively. These fixed values ​​are used when an individual's fitness value is less than the average. In later stages of evolution... , The value of has little impact on the final result. However, when an individual is of high fitness, its fitness value will be higher than the average. This individual can obtain a crossover rate and mutation rate corresponding to its fitness, and will also have a greater probability of entering the next generation.

[0081] Improved algorithm performance analysis: A simplified socio-economic water resource allocation model was solved using both the traditional NSGA-II algorithm and the improved NSGA-II algorithm described in this invention to analyze the performance of the improved algorithm. The corresponding Pareto optimal solution was obtained, and a point set graph was plotted. The efficiency and stability of the algorithm were analyzed by observing the point set distribution. The population size was 100, and the number of generations was 800. Simulation calculations were performed using the traditional NSGA-II algorithm and the improved algorithm, with iterations of 50, 300, 500, and 800 times respectively. The results are shown in Figures 3 and 4. Specifically, Figure 3(a) shows the simulation results of the traditional NSGA-II algorithm after 50 iterations; Figure 3(b) shows the simulation results of the traditional NSGA-II algorithm after 300 iterations; Figure 3(c) shows the simulation results of the traditional NSGA-II algorithm after 500 iterations; Figure 3(d) shows the simulation results of the traditional NSGA-II algorithm after 800 iterations; Figure 4(a) shows the simulation results of the improved algorithm after 50 iterations; Figure 4(b) shows the simulation results of the improved algorithm after 300 iterations; Figure 4(c) shows the simulation results of the improved algorithm after 500 iterations; and Figure 4(d) shows the simulation results of the improved algorithm after 800 iterations.

[0082] As can be seen from Figure 3, the population distribution was initially scattered due to the small number of iterations. As the number of generations increased, the population distribution gradually became more orderly. By the 500th generation, the Pareto front outline had appeared, but the population distribution was not uniform and stable enough. By the 800th generation, the population was relatively uniform but still sparse.

[0083] As shown in Figure 4, by generation 50, the population exhibits a relatively regular distribution; by generation 300, the outline of the Pareto front is quite clear; by generation 500, the population begins to extend towards the Pareto boundary, and the curve becomes smoother; by generation 800, the population as a whole is stably and evenly distributed on the Pareto front, indicating that the population evolution process is nearing completion, and the calculated results are reasonable and effective. This demonstrates that the improved algorithm exhibits better uniformity in the early stages of evolution and also best derives the Pareto curve in the later stages. The improved algorithm's convergence speed is significantly better than the traditional algorithm, clearly indicating that the improved algorithm has higher efficiency.

[0084] The stability of the algorithm is analyzed below. Under the same test environment, the traditional algorithm and the improved algorithm were run independently 30 times each. The traditional algorithm showed a Pareto front curve in 12 runs, while the rest resulted in local optima, as shown in Figure 5. Figure 5(a) shows the population distribution of local optima after 300 iterations of the traditional NSGA-II algorithm; Figure 5(b) shows the population distribution of local optima after 500 iterations of the traditional NSGA-II algorithm. In contrast, the improved algorithm showed a Pareto front curve in all 30 tests, without getting trapped in local optima. Getting trapped in local optima means the algorithm simulation has failed, requiring adjustments to the initial population, parameters, or repeated simulations. Clearly, the improved algorithm is significantly more stable than the traditional algorithm.

[0085] The above analysis shows that the improved algorithm has higher efficiency and stability than the traditional algorithm. Under the premise of ensuring rich diversity of the population, it searches smoothly and finds the optimal solution set of multiple objectives by adaptively adjusting the crossover rate and mutation rate. It can be used to solve the "water supply-convergence" multi-objective water quantity optimization configuration model constructed in this paper.

[0086] The improved NSGA-II algorithm is used to solve the multi-objective optimization model, such as... Figure 6 As shown, specifically: Parameter settings: Based on the algorithm's characteristics and the actual needs of water allocation, the following values ​​were determined through parameter calibration and testing: Population size Maximum number of iterations: 5000; Crossover probability baseline value: Baseline value of mutation probability ; Initial population generation: After setting the range of decision variables according to the constraints, to balance the randomness and uniformity of the initial population, an integer is randomly selected from the interval [1, 100] as the base to generate the Halton sequence. And use this sequence to construct a structure of size initial population ; Crossover and mutation operations: from the population Two individuals are randomly selected, and their crossover probabilities are determined based on their fitness values. Crossover is performed preferentially using the adaptive crossover rate corresponding to the individual with higher fitness. Then, one individual is randomly selected, and its mutation probability is calculated based on its fitness to perform a mutation operation. Through this adaptive crossover and mutation process, a offspring population is generated. ; Elite strategy selection forms a new parent generation: the parent population With offspring population Merged into a size of Mixed population ;right All individuals are subjected to a fast non-dominated sorting and crowding calculation, and selected according to the fitness assignment rule. The best individuals constitute the next generation of the parent population. ; Termination condition judgment: If the current evolutionary generation has not reached the set upper limit, the newly generated parent population will be terminated. Proceed to crossover and mutation operations to continue iteration; otherwise, terminate the algorithm and output the result.

[0087] Step 3: Use a fuzzy comprehensive evaluation model to determine the optimal water allocation scheme from the solution set of non-inferior schemes.

[0088] Multi-objective problems often have more than one optimal solution. Using the improved NSGA-II algorithm described above to solve multi-objective models, after 5000 generations of evolution, the corresponding Pareto undominated front curve can be obtained, which corresponds to a set of undominated solutions. This invention employs a fuzzy comprehensive evaluation model to determine the optimal solution from numerous scheduling schemes.

[0089] Taking the Pareto population distribution in 2024-2025 as an example, when the algorithm iterates to the 3000th generation, it begins to show the outline of the Pareto front. When it iterates to the 5000th generation, the population begins to extend towards the Pareto boundary, and the Pareto front curve has become smooth and stable, indicating that the algorithm has basically evolved and obtained a non-dominated solution set containing 50 individuals that considers the water supply target and the convergence target.

[0090] The optimal water allocation scheme is determined from the solution set of non-inferior schemes using a fuzzy comprehensive evaluation model, specifically as follows: For each planning year, the individuals in the population (individuals in a population of size 50 after 5000 iterations) from the final output of the multi-objective optimization model are non-dominated and sorted. A predetermined number of individuals (20 in this embodiment) are selected to form a scheme set. The scheme set is evaluated by an index set composed of two indicators: water supply and convergence. Then, the eigenvalue matrix is ​​obtained. ;in, The number of indicators (taken in this embodiment of the invention) ); The number of schemes in the scheme set (in this embodiment of the invention, the number of schemes is taken as follows). The water allocation schemes for 2024-2025 are shown in Table 1.

[0091] Table 1. Water Allocation Scheme Set for 2024-2025

[0092] To eliminate the influence of different dimensions and orders of magnitude of the eigenvalues, the eigenvalue matrix is... For standardization, since both objectives of this model are minimization, the evaluation indicators are processed into cost-based indicators using the following membership function:

[0093] in, For the first The plan for the first The characteristic values ​​of the indicator; , The first of all the schemes The maximum and minimum values ​​of the indicator; For the first The plan for the first The membership value of the indicator is determined by... Forming a membership matrix ; exist ,in , Indicates the first option among all solutions. The maximum membership degree of each indicator. It is the maximum membership matrix; there exists ,in , Indicates the first option among all solutions. The minimum membership degree of each indicator. It is the minimum membership matrix; Assuming the system The weight vector of each indicator is , For the goal The weight of; then the weight of the first The progress of the Euclid patch scheme is as follows:

[0094] in, For distance parameters; Representation scheme The optimal solution for the timing of the track can also be called the Euclidean distance, according to... The size of the values ​​is used to judge the merits of each scheme, and the scheme with the highest value is ultimately selected. The largest possible solution is considered the optimal water allocation solution.

[0095] Euclidean distance Taking into account the distances between the proposed schemes and both the "positive ideal solution" (optimal scheme) and the "negative ideal solution" (worst scheme), the larger the Euclidean distance, the closer the scheme is to the ideal scheme. The Euclidean distances of each individual scheme in the scheme set were calculated, and the evaluation results of the water allocation scheme set for 2024-2025 were finally obtained, as shown in Table 2.

[0096] Table 2 Evaluation Results of Water Allocation Schemes for 2024-2025

[0097] The scheme with the largest central Euclidean distance among all schemes is selected as the optimal scheme, and is indicated in bold in the evaluation results table above. According to the evaluation results in Table 2, the optimal water allocation scheme for 2024-2025 is Scheme No. 8.

[0098] Two-way driven water allocation results and scheme development mode: Water allocation results: (1) Water allocation by province / region. According to the calculation results of the above model, the total water consumption of the Yellow River main stream in 2024-2025 is 23.838 billion m³, and the water demand is 27.404 billion m³ based on the declared water demand, resulting in a water shortage of 3.566 billion m³. The water allocation results of each province / region in 2024-2025 are shown in Table 3.

[0099] Table 3. Water allocation results for each province and region in 2024-2025 (unit: 100 million m³)

[0100] As shown in Table 3, the total water shortage rate of the Yellow River main stream is 13.0%, which is basically consistent with the predicted water shortage rate of 14.72% before the western route project took effect in the "Comprehensive Water Resources Plan for the Yellow River Basin", thus verifying the overall rationality of this water allocation simulation.

[0101] From the perspective of fairness, the water supply target is set to promote the water shortage situation in each province and region to approach the average level of the basin. However, the water shortage rate of each province and region in the table is significantly different, with the maximum being 26.8% in Shanxi Province and the minimum being 5.2% in Shaanxi Province. This difference is an objective result of the convergence target regulation.

[0102] From a convergence perspective, provinces and regions whose historical actual water consumption has consistently exceeded planned targets will have water shortage rates lower than the basin average under the guidance of convergent goals. Specifically: Inner Mongolia Autonomous Region 8.8% (affected by ecological water replenishment and flood diversion), Shaanxi Province 5.2% (affected by emergency drought relief water replenishment), and Shandong Province 10.1% (major water user in the basin). Conversely, provinces and regions whose historical actual water consumption has consistently fallen below planned targets will have water shortage rates higher than the basin average. Specifically: Qinghai Province 20.6% (advantageous natural water resources), Shanxi Province 26.8% (constrained by complex water intake conditions), and Henan Province 16.1% (affected by river conditions and engineering issues). Other provinces and regions whose historical actual water consumption is consistent with planned targets or declared water consumption have water shortage rates close to the basin average, such as: Gansu 15.4%, Ningxia 13.4%, and Hebei + Tianjin 13.4%.

[0103] Therefore, this water allocation plan is the result of a comprehensive balance between the water supply target representing the "ideal configuration state" of the basin and the convergent target reflecting the "actual water use characteristics" of the region. It not only ensures the fairness and stability of water allocation in the Yellow River Basin, but also achieves dynamic adaptation to the actual water use situation in the region.

[0104] According to the "Announcement on the Implementation of Yellow River Water Allocation in 2024-2025", the planned allocation target for the Yellow River main stream in 2024-2025 was 25.32 billion m³, while the actual water consumption of the entire main stream was 22.355 billion m³. A comparison of the planned allocation target and actual water consumption of the Yellow River main stream in 2024-2025 is shown in Table 4.

[0105] Table 4 Comparison of planned water consumption targets and actual water consumption for 2024-2025 (unit: 100 million m³)

[0106] Table 4 shows that the actual water consumption of the Yellow River main stream was 2.965 billion m³ less than the planned allocation. This is mainly due to abundant rainfall in Ningxia and Shandong that year, resulting in a combined reduction of 1.462 billion m³ in these two provinces. The simulated allocation of 23.838 billion m³ falls between the actual water consumption of 22.355 billion m³ and the published annual plan of 25.32 billion m³, and is within the physical model's predicted water allocation target of 24.665 billion m³. This is close to the suitable water consumption of 23.5 billion m³ predicted by the BiLSTM model, and the allocated water volume for most provinces is slightly higher than the actual water consumption. Within the framework of the "87 Scheme," this ensures the full utilization of water resources. Therefore, the above allocation results are reasonable.

[0107] (2) Water allocation by river section. The total water consumption of the Yellow River main stream in 2024-2025 is 23.838 billion m³, of which 10.934 billion m³ is allocated to the upper reaches, 3.034 billion m³ to the middle reaches, and 9.87 billion m³ to the lower reaches. The annual total water allocation for each river section in 2024-2025 is shown in Table 5.

[0108] Table 5. Water allocation results for river sections in 2024-2025 (unit: 100 million m³)

[0109] After normalizing the water allocation for each river section according to the ten-day process, and comparing it with the actual water consumption process, it can be concluded that the simulated water allocation results for the river sections in 2024-2025 are highly consistent with the spatiotemporal distribution process of the actual water consumption of the entire river, clearly reflecting the water intake pattern and the underlying physical mechanism in the Yellow River Basin, specifically as follows: In the upstream region, the overall water consumption in the river section above Liujiaxia is relatively small. Water demand is concentrated in large irrigation areas downstream of Liujiaxia, such as Jingdian Irrigation Area (Lanzhou-Xiaheyan), Qingtongxia Irrigation Area (Xiaheyan-Qingtongxia), Hetao Irrigation Area (Shizuishan-Bayangol), and the Inner Mongolia Yellow River South Bank Irrigation Area (Sanhuhekou-Toudaoguai). These areas exhibit typical irrigation system characteristics such as spring irrigation, summer irrigation, and autumn irrigation. Meanwhile, in the "Shizuishan-Bayangol" section, the irrigation interval is accompanied by ecological water replenishment processes from Wuliangsuhai, Kubuqi, and Maowusu, while the ice breakup period is accompanied by ice separation processes. Furthermore, in the downstream sections of important water intakes (Qingtongxia-Shizuishan, Bayangol-Sanhuhekou), the water exhibits a deep blue irrigation runoff characteristic, which directly reflects the water cycle process of "water intake-use-runoff".

[0110] The middle reaches region, including the Yumenkou Irrigation Area in Shanxi and the Donglei Irrigation Area (Longmen-Tongguan) in Shaanxi, also exhibit certain irrigation water patterns, but the overall water use scale is significantly smaller than that of the Ningxia-Inner Mongolia Irrigation Area. Due to limitations in topography, arable land area, and water resources, the overall water use intensity is relatively low, and there is basically no water use in the northern main stream canyon section from Wanjiazhai Dam to Longmen due to topographical constraints.

[0111] Downstream areas, including the Shengli Canal (Xixia Yuan-Huayuan Kou) and Zhao Kou (Huayuan Kou-Jiahetan) irrigation districts in Henan Province, and the Weishan (Sun Kou-Aishan), Panzhuang (Aishan-Luokou), and Dayuzhang (Luokou-Lijin) irrigation districts in Shandong Province, all exhibit a high demand for spring irrigation of winter wheat, while summer and autumn irrigation require relatively less water. Spring irrigation is crucial for the greening of winter wheat, resulting in a strong demand for water. Summer and autumn irrigation, however, see a decrease in water consumption due to effective replenishment of soil moisture by downstream rainfall. Furthermore, Hebei and Tianjin regions also exhibit a simultaneous water use pattern of irrigation and ecological water replenishment in autumn and winter, reflecting the complexity of downstream inter-basin water supply.

[0112] In summary, the water allocation results obtained from this simulation are highly consistent with the actual water use situation in the Yellow River Basin. For example, the gradual advancement of spring irrigation time from upstream to downstream, and the timely implementation of ecological water replenishment and ice-breaking scheduling during irrigation breaks, all directly reflect the water intake patterns, irrigation system, and ecological water replenishment needs of the basin. Furthermore, these results corroborate the physical mechanisms of the Yellow River's main channel flow evolution, fully verifying the rationality and reliability of the simulation results.

[0113] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0114] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in this invention may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A water allocation method based on convergent physical-data dual models, characterized in that, include: Step 1: Construct a multi-objective optimization model that includes a water supply objective and a convergence objective; wherein, the water supply objective is to minimize the sum of squares of the water shortage rate in each section of the main stream; the convergence objective is to minimize the difference in cross-sectional flow process between the physical and data models under a certain water allocation result; Step 2: Solve the multi-objective optimization model using the improved NSGA-II algorithm to obtain a set of non-dominated solutions; wherein, the improvement of the NSGA-II algorithm includes: introducing Halton sequences to generate the initial population, and adaptive adjustment of crossover and mutation probabilities based on the comparison of individual fitness and overall population performance; Step 3: Use a fuzzy comprehensive evaluation model to determine the optimal water allocation scheme from the solution set of the non-inferior schemes.

2. The water allocation method based on physical-data dual-model convergence according to claim 1, characterized in that, In step 1, the objective function of the water supply target is expressed by the following mathematical expression: in, This is the sum of squares of the water shortage rates in each section of the main stream; To manage the number of river sections; The number of time units to be divided; For the first Each section of the river Water demand during different time periods; For the first Each section of the river Water consumption allocated over time periods.

3. The water allocation method based on physical-data dual-model convergence according to claim 1, characterized in that, In step 1, the objective function of the convergence objective is expressed by the following mathematical expression: in, The difference in cross-sectional flow process between physical and data models under a certain water distribution result; The number of time units to be divided; Number of cross sections; For the first The difference weighting coefficients for the entire river flow process in each time period are used to adjust the optimization direction in the time dimension; For the first The weighting coefficients for the differences in flow processes in each river segment are used to adjust the optimization direction in the spatial dimension. , Based on two models, namely physical and data, in the first... Time period, number The flow rate at the cross-section.

4. The water allocation method based on physical-data dual-model convergence according to claim 1, characterized in that, In step 1, the physical and data models adopt a traffic evolution physical model and a CNN-LSTM hybrid model.

5. The water allocation method based on physical-data dual-model convergence according to claim 1, characterized in that, In step 1, the constraints of the multi-objective optimization model are specifically as follows: Water supply constraints in each province and region: in, The number of river sections to be dispatched in each province / region; The number of time units to be divided; For the province / region Each section of the river Water consumption allocated over time periods; The annual available water consumption of the main stream allocated to provinces and regions; Water demand constraints: in, For the first Each section of the river Water consumption allocated over time periods; No. Each section of the river Water demand during different time periods; Suitable water consumption range constraints: The water consumption of the main stream predicted by the BiLSTM model is close to the actual situation and is used as a constraint for appropriate water consumption, as follows: in, Suitable water consumption for the entire main stream; The set threshold range; Ecological flow constraints: in, for Section Ecological flow during a given time period; for Section Simulated traffic flow over a given time period; Flow rate variation constraints: in, for Section The maximum range of change before and after the time period; Reservoir capacity constraints: in, , They are respectively reservoir Upper and lower limits of storage capacity for a given time period; for reservoir Water storage volume during a given period; Minimum discharge flow constraint of the reservoir: in, for reservoir Minimum allowable outbound flow rate for a given time period; Non-negativity constraint for variables: Among them, the allocated water volume Cross-sectional flow It should be non-negative.

6. The water allocation method based on physical-data dual-model convergence according to claim 1, characterized in that, In step 2, the Halton sequence is introduced to generate the initial population, specifically as follows: In the Halton sequence, let prime number For any integer Both can be used to Represented in base form, see the following formula: in, ,base Given a known prime number, in the above formula... Both exist and are unique. Taking a fundamental reversal of the above formula, we get: Furthermore, for different integers, the corresponding base can be obtained. The following one-dimensional Halton sequence: 。 7. A water allocation method based on physical-data dual-model convergence according to claim 1, characterized in that, In step 2, the adaptive adjustment of crossover and mutation probabilities based on the comparison between individual fitness and overall population performance is specifically as follows: First, we introduce the fitness function, which is obtained by comparing individuals. A higher fitness value indicates that the individual is better. The formula is as follows: in, Population size; The number of objective functions; The first in the population Individual; For this individual's contribution to the population of the first The sequence number of the objective functions after being arranged; For this individual regarding the first The fitness value of each objective; The overall fitness is obtained by summing the fitness values ​​of all targets; a constant is introduced here to highlight the fitness of outstanding individuals. Based on the comparison between individual fitness and overall population performance, adaptive adjustments to crossover and mutation probabilities are achieved. The adaptive function expressions for these probabilities as a function of fitness are as follows: in, , These are the adaptive change values ​​for crossover and mutation probabilities, respectively; The maximum fitness value in the population; This represents the average fitness value. The larger of the fitness values ​​of the two individuals undergoing crossover; To determine the fitness value of the individual to be mutated , These are fixed values ​​for the crossover and mutation probabilities, respectively.

8. A water allocation method based on physical-data dual-model convergence according to claim 1, characterized in that, In step 2, the improved NSGA-II algorithm is used to solve the multi-objective optimization model, specifically as follows: Parameter settings: Based on the algorithm's characteristics and the actual needs of water allocation, the following values ​​were determined through parameter calibration and testing: Population size Maximum number of iterations, baseline crossover probability Baseline value of mutation probability ; Initial population generation: After setting the range of decision variables according to the constraints, to balance the randomness and uniformity of the initial population, an integer is randomly selected from the interval [1, 100] as the base to generate the Halton sequence. And use this sequence to construct a structure of size initial population ; Crossover and mutation operations: from the population Two individuals are randomly selected, and their crossover probabilities are determined based on their fitness values. Crossover is performed preferentially using the adaptive crossover rate corresponding to the individual with higher fitness. Then, one individual is randomly selected, and its mutation probability is calculated based on its fitness to perform a mutation operation. Through this adaptive crossover and mutation process, a offspring population is generated. ; Elite strategy selection forms a new parent generation: the parent population With offspring population Merged into a size of Mixed population ;right All individuals are subjected to a fast non-dominated sorting and crowding calculation, and selected according to the fitness assignment rule. The best individuals constitute the next generation of the parent population. ; Termination condition judgment: If the current evolutionary generation has not reached the set upper limit, the newly generated parent population will be terminated. Continue iterating using crossover and mutation operations; Otherwise, terminate the algorithm and output the result.

9. A water allocation method based on physical-data dual-model convergence according to claim 1, characterized in that, In step 3, the optimal water allocation scheme is determined from the solution set of the non-inferior schemes using a fuzzy comprehensive evaluation model, specifically as follows: For each planning year, individuals in the population output from the multi-objective optimization model are non-dominated and ranked. A predetermined number of individuals are selected to form a set of alternative solutions. The alternative solutions are evaluated using an index set composed of two indicators: water supply and convergence. The resulting eigenvalue matrix is ​​then obtained. ;in, For the number of indicators; The number of solutions in the solution set; For eigenvalue matrix For standardization, since both objectives of this model are minimization, the evaluation indicators are processed into cost-based indicators using the following membership function: in, For the first The plan for the first The characteristic values ​​of the indicator; , The first of all the schemes The maximum and minimum values ​​of the indicator; For the first The plan for the first The membership value of the indicator is determined by... Forming a membership matrix ; exist ,in , Indicates the first option among all solutions. The maximum membership degree of each indicator. It is the maximum membership matrix; there exists ,in , Indicates the first option among all solutions. The minimum membership degree of each indicator. It is the minimum membership matrix; Assuming the system The weight vector of each indicator is , For the goal The weight of; then the weight of the first The progress of the Euclid patch scheme is as follows: in, For distance parameters; Representation scheme For the optimal solution of the schedule, according to The size of the values ​​is used to judge the merits of each scheme, and the scheme with the highest value is ultimately selected. The largest possible solution is considered the optimal water allocation solution.

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