A water resources optimization allocation method based on improved NSGA-Ⅱ multi-objective genetic algorithm

Abstract

This invention discloses a method for optimizing water resource allocation based on an improved NSGA-II multi-objective genetic algorithm. The method comprises the following steps: first, obtaining basic data and relevant parameters of the target watershed and rationally generalizing the target watershed; second, analyzing the specific tasks of water resource optimization, determining the objective function and constraints of the optimization configuration model, and constructing a multi-objective water resource optimization configuration model for the watershed; third, using the improved NSGA-II genetic algorithm to solve the multi-objective water resource optimization configuration model for the watershed and obtain a Pareto non-inferior solution set; and finally, determining the optimal water resource allocation scheme for the watershed within the Pareto solution set. This method achieves efficient iteration, global optimization, and effective identification of high-quality solutions for multi-objective problems, meeting the requirements for autonomous selection of the optimal water resource allocation scheme.

Description

Technical Field

[0001] This invention belongs to the field of water resource allocation technology, specifically relating to a water resource optimization allocation method based on an improved NSGA-II multi-objective genetic algorithm. Background Art

[0002] By employing both engineering and non-engineering measures, the scientific allocation of limited water resources of different forms among various water users can achieve optimal water resource allocation. This is a crucial scientific approach to realizing the scientific development and rational utilization of water resources and ensuring their sustainable use. Multi-objective genetic algorithms, through the use of fast non-dominated sorting algorithms, significantly reduce computational complexity and can effectively solve complex system problems. However, some intelligent optimization algorithms are prone to getting trapped in local searches or failing to find the optimal solution when solving high-dimensional multi-objective optimization problems. Therefore, how to select reasonable and efficient optimization algorithms or improve existing algorithms for solving complex multi-objective water resource optimization allocation models warrants further research.

[0003] The NSGA-II algorithm is an improvement on the NSGA algorithm and has certain advantages: it adopts a fast non-dominated sorting algorithm, which greatly reduces the computational complexity; it uses crowding degree and crowding degree comparison operators instead of specifying the shared radius, so that individuals in the quasi-Pareto domain can be expanded to the entire Pareto domain and evenly distributed, maintaining the diversity of the population; it introduces an elite strategy, expands the sampling space, prevents the loss of the best individuals, and improves the computational speed and anti-interference ability of the algorithm. However, the traditional NSGA-II algorithm still has the following problems in practical applications: (1) it uses random generation when initializing the population. Randomness represents uncertainty, and the randomly generated population is uneven in the entire space, affecting the distribution of the solution set; (2) the parent individual selection method of the traditional NSGA-II algorithm is usually binary tournament selection. In terms of the tournament implementation, the parent selection is close to random selection, which will affect the evolution speed of the entire population, thus making the search ability of the evolution process unreliable and affecting the convergence of the solution set. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a water resource optimization allocation method based on an improved NSGA-II multi-objective genetic algorithm, so as to achieve efficient iteration, global optimization, effective identification of high-quality solution sets for multi-objective problems, and meet the requirement of autonomously selecting the best water resource allocation scheme.

[0005] Technical solution: The water resource optimization allocation method based on the improved NSGA-II multi-objective genetic algorithm described in this invention includes the following steps:

[0006] S1. Obtain basic data and relevant parameters of the target watershed, including: basic characteristic parameters of each water conveyance unit, water level-storage capacity relationship curve of water source project, and generalize the watershed water resource allocation system based on the hydraulic connection between each water source and water conveyance and distribution project.

[0007] S2. Analyze the specific tasks of water resource optimization and construct a multi-objective optimization model for watershed water resources with the objective functions of minimizing water shortage and maximizing the ecological water supply guarantee rate of each irrigation area, and with constraints of water balance, maximum agricultural water supply, minimum ecological water supply and non-negativity of variables.

[0008] S3. The improved NSGA-II genetic algorithm is used to solve the multi-objective optimization allocation model of watershed water resources and obtain the Pareto non-dominated solution set. Each individual in the solution set represents a watershed water resources allocation scheme.

[0009] S4. Determine the optimal watershed water resource allocation scheme in the Pareto solution set.

[0010] Furthermore, the multi-objective optimization allocation model for water resources in the basin constructed in S2 is as follows:

[0011] Objective function 1: Minimize the total water shortage in the basin;

[0012]

[0013] Where f1(x,y) represents the total water shortage in the basin, n represents the total number of irrigation districts, and W xi Let x be the agricultural water demand of the i-th irrigation district; i For agricultural water supply in irrigation district i; W yi The ecological water demand of irrigation district i; y i This refers to the ecological water supply for the i-th irrigation district.

[0014] Objective function 2: Maximize the satisfaction rate of ecological water supply in each irrigation district;

[0015]

[0016] Where f2(y) represents the satisfaction level with ecological water supply in each irrigation district;

[0017] Constraint 1: Water balance constraint;

[0018]

[0019] Among them, W u Available water volume; W i For watershed inflow; W e Ecological baseline flow for key water supply rivers;

[0020] Constraint 2: Maximum agricultural water supply constraint;

[0021] x i ≤W xi

[0022] Constraint 3: Minimum ecological water demand constraint;

[0023] y i ≥αW yi

[0024] Where α is a parameter between 0 and 1, used to calculate the minimum water requirement necessary to ensure the survival of ecological vegetation;

[0025] Constraint 4: Non-negativity constraint;

[0026] x i ≥0; y i ≥0.

[0027] Furthermore, S3 includes the following steps:

[0028] S3-1. Based on the basic water resources situation of the basin, select decision variables, divide the basin into various water conveyance units according to the control hydrological sections of the main water supply rivers, determine the upper and lower limits of water demand for each water conveyance unit, and determine the upper and lower bounds of the search domain for the improved NSGA-II genetic algorithm; the independent variables are agricultural water supply and ecological water supply in each irrigation district, the number of independent variables nVar is twice the number of irrigation districts, and the maximum number of iterations t max Crossover ratio Pc, variation ratio Pm, lower bound of independent variable varmin is a vector dataset consisting of the minimum agricultural water supply and minimum ecological water supply of each irrigation district, upper bound of independent variable varmax is a vector dataset consisting of the maximum agricultural water supply and maximum ecological water supply of each irrigation district, and parent selection parameters ud and up.

[0029] S3-2. Let the number of iterations be t=0, and use the optimal point set theory to generate the first generation population P0;

[0030] S3-3. Calculate the target value of individuals in the population according to the objective function, that is, the total water shortage of the watershed and the ecological water supply satisfaction of each irrigation district for each scheme. Perform a fast non-dominated ranking of individuals and calculate the crowding degree.

[0031] S3-4. Sort individuals in ascending order based on dominance level, then sort them in descending order based on crowding distance. Calculate the probability of each sorted individual becoming a parent and generate a parent population P. t ;

[0032] S3-5. Perform crossover and mutation operations on the parent population after the selection operation to obtain the offspring population P. t+1 ;

[0033] S3-6. Check if the number of generations of genetic evolution has reached the maximum number of iterations. If yes, terminate the operation and output the result; otherwise, let t = t + 1 and return to S3-3 to continue.

[0034] Furthermore, S3-2 includes the following steps:

[0035] S3-2-1. If the spatial dimension of the population is s and the population size is N, calculate the value of each point in the point set r according to the following formula:

[0036] r = (r1, r2, r3, ..., r N )

[0037]

[0038] Where, r j Let J be a good point in the point set R, where J = 1, 2, ..., N; N i Let i represent the i-th individual in the population, where i = 1, 2, ..., N;

[0039] S3-2-2, Construct a set of N ideal points P N (i):

[0040] P N (i)={(r1i1,r2i2,r3i3,…,r N i N )}, i = 1, 2, ..., N

[0041] Where 1≤i j ≤N, j=1,2,…,N;

[0042] S3-2-3, P N (i) Mapping to the feasible region where the population resides:

[0043]

[0044] in, This refers to the optimal location within the feasible region, representing a water resource allocation scheme; a j This represents the lower bound of the current dimension, namely the minimum agricultural water supply and minimum ecological water supply for each irrigation district, b. j This represents the upper limit of the current dimension, namely the maximum agricultural water supply and the maximum ecological water supply of each irrigation district.

[0045] Furthermore, S3-4 includes the following steps:

[0046] S3-4-1. After performing non-dominated sorting and crowding calculation, the population is first sorted in ascending order according to dominance level, and then sorted in descending order according to crowding distance.

[0047] S3-4-2. The N individuals in the new population obtained after sorting are x1, x2, ..., x n Each individual represents a water resource allocation scheme; among them, x1 is the highest-ranked individual with the largest fitness value, x n The individual with the lowest ranking has the lowest fitness value;

[0048] S3-4-3, Assume that the probability of x1 becoming the parent individual is p1, x n The probability of becoming a parent individual is p. n Then the expected number of x1 after the selection operation, i.e., the parent selection parameter up, is:

[0049] up = N * p1

[0050] x n The expected number after the selection operation, i.e., the parent selection parameter ud, is:

[0051] ud = N*p n

[0052] S3-4-4. To ensure that individuals with higher rank in the parent population have a higher probability of becoming parents, using an arithmetic sequence, the probability of the i-th individual in the population becoming a parent is:

[0053]

[0054] If the sum of individual selection expectations in the population is N, then ud + up = 2, 0 ≤ ud ≤ 1, and up = 2 - ud.

[0055] The system corresponding to the method includes:

[0056] The parameter acquisition unit is used to acquire basic data and relevant parameters of the target watershed, including: basic characteristic parameters of each water conveyance unit, water level-storage capacity relationship curves of water source projects, and generalize the watershed water resource allocation system based on the hydraulic connection between each water source and water conveyance and distribution project.

[0057] The model building unit is used to analyze the specific tasks of water resource optimization and allocation, and to build a watershed water resource multi-objective optimization and allocation model with the objective functions of minimizing water shortage and maximizing the ecological water supply guarantee rate of each irrigation area, and with constraints of water balance, maximum agricultural water supply, minimum ecological water supply and non-negativity of variables.

[0058] The model solving unit is used to solve the multi-objective optimization allocation model of watershed water resources using the improved NSGA-II genetic algorithm, and obtain the Pareto non-dominated solution set. Each individual in the solution set represents a watershed water resources allocation scheme.

[0059] The optimal solution determination unit is used to determine the optimal watershed water resource allocation scheme in the Pareto solution set.

[0060] The preferred method for solving the model is as follows:

[0061] S3-1. Based on the basic water resources situation of the basin, select decision variables, divide the basin into various water conveyance units according to the control hydrological sections of the main water supply rivers, determine the upper and lower limits of water demand for each water conveyance unit, and determine the upper and lower bounds of the search domain for the improved NSGA-II genetic algorithm; the independent variables are agricultural water supply and ecological water supply in each irrigation district, the number of independent variables nVar is twice the number of irrigation districts, and the maximum number of iterations t max Crossover ratio Pc, variation ratio Pm, lower bound of independent variable varmin is a vector dataset consisting of the minimum agricultural water supply and minimum ecological water supply of each irrigation district, upper bound of independent variable varmax is a vector dataset consisting of the maximum agricultural water supply and maximum ecological water supply of each irrigation district, and parent selection parameters ud and up.

[0062] S3-2. Let the number of iterations be t=0, and use the optimal point set theory to generate the first generation population P0;

[0063] S3-3. Calculate the target value of individuals in the population according to the objective function, that is, the total water shortage of the watershed and the ecological water supply satisfaction of each irrigation district for each scheme. Perform a fast non-dominated ranking of individuals and calculate the crowding degree.

[0064] S3-4. Sort individuals in ascending order based on dominance level, then sort them in descending order based on crowding distance. Calculate the probability of each sorted individual becoming a parent and generate a parent population P. t ;

[0065] S3-5. Perform crossover and mutation operations on the parent population after the selection operation to obtain the offspring population P. t+1 ;

[0066] S3-6. Check if the number of generations of genetic evolution has reached the maximum number of iterations. If yes, terminate the operation and output the result; otherwise, let t = t + 1 and return to S3-3 to continue.

[0067] More preferably, S3-2 includes the following steps:

[0068] S3-2-1. If the spatial dimension of the population is s and the population size is N, calculate the value of each point in the point set r according to the following formula:

[0069] r = (r1, r2, r3, ..., r N )

[0070]

[0071] Where, rj Let J be a good point in the point set R, where J = 1, 2, ..., N; N i Let i represent the i-th individual in the population, where i = 1, 2, ..., N;

[0072] S3-2-2, Construct a set of N ideal points P N (i):

[0073] P N (i)={(r1i1,r2i2,r3i3,…,r N i N )}, i = 1, 2, ..., N

[0074] Where 1≤i j ≤N, j=1,2,…,N;

[0075] S3-2-3, P N (i) Mapping to the feasible region where the population resides:

[0076]

[0077] in, This refers to the optimal location within the feasible region, representing a water resource allocation scheme; a j This represents the lower bound of the current dimension, namely the minimum agricultural water supply and minimum ecological water supply for each irrigation district, b. j This represents the upper limit of the current dimension, namely the maximum agricultural water supply and the maximum ecological water supply of each irrigation district.

[0078] More preferably, S3-4 includes the following steps:

[0079] S3-4-1. After performing non-dominated sorting and crowding calculation, the population is first sorted in ascending order according to dominance level, and then sorted in descending order according to crowding distance.

[0080] S3-4-2. The N individuals in the new population obtained after sorting are x1, x2, ..., x n Each individual represents a water resource allocation scheme; among them, x1 is the highest-ranked individual with the largest fitness value, x n The individual with the lowest ranking has the lowest fitness value;

[0081] S3-4-3, Assume that the probability of x1 becoming the parent individual is p1, x n The probability of becoming a parent individual is p. n Then the expected number of x1 after the selection operation, i.e., the parent selection parameter up, is:

[0082] up = N * p1

[0083] x nThe expected number after the selection operation, i.e., the parent selection parameter ud, is:

[0084] ud = N*p n

[0085] S3-4-4. To ensure that individuals with higher rank in the parent population have a higher probability of becoming parents, using an arithmetic sequence, the probability of the i-th individual in the population becoming a parent is:

[0086]

[0087] If the sum of individual selection expectations in the population is N, then ud + up = 2, 0 ≤ ud ≤ 1, and up = 2 - ud.

[0088] An electronic device for storing and executing the method includes a memory and a processor, wherein:

[0089] Memory is used to store computer programs that can run on a processor;

[0090] A processor is configured to execute the steps of the water resource optimization allocation method based on the improved NSGA-II multi-objective genetic algorithm when running the computer program.

[0091] Beneficial effects: Compared with the prior art, the significant technical effects of this invention are as follows: (1) In view of the problem that the global search capability is not guaranteed and the algorithm is prone to getting trapped in local optimization during the evolution process of the traditional NSGA-II algorithm, the theory of optimal point set is introduced to generate the first generation population, so that the first generation population is evenly distributed and avoids getting trapped in local optima; the improvement effectively improves the distribution of the solution set and improves the diversity of the population, which can further promote the application of genetic algorithm in multi-objective optimization problems; (2) In view of the problem that the traditional NSGA-II algorithm has high computational complexity and low efficiency in handling large-scale problems, a parent selection strategy based on linear pressure is proposed to make the optimal point set more evenly distributed and avoid getting trapped in local optima. The probability of a superior individual becoming a parent individual increases, improving the optimization efficiency of the algorithm; the improvement effectively improves the convergence of the solution set, reduces the computational complexity, and further promotes the application of genetic algorithms in large-scale multi-objective optimization problems; (3) By system generalizing the target watershed, a multi-objective water resource optimization allocation model for the watershed is constructed, and the improved NSGA-II genetic algorithm is used to solve the model to determine the watershed water resource optimization allocation scheme; As an innovative method in the field of water resource optimization allocation, this invention can provide a scientific basis for watershed water resource management, provide technical support for the sustainable development of water resources, and fully guarantee the rational utilization and protection of water resources. Attached Figure Description

[0092] Figure 1 This is a flowchart of the method of the present invention;

[0093] Figure 2A simplified diagram of the watershed water resources allocation system;

[0094] Figure 3 Flowchart of the improved NSGA-II algorithm;

[0095] Figure 4 The diagram shows the spatial distribution of the ZDT test function scheme set, where (a), (b), (c), and (d) are comparisons of the spatial distribution of test functions ZDT1, ZDT2, ZDT3, and ZDT6 before and after improvement, respectively.

[0096] Figure 5 Figure 1 shows the water distribution before and after the optimization of water resources allocation in the main stream of the Tarim River. Figure 2(a) compares the agricultural water supply allocation schemes, and Figure 3(b) compares the ecological water supply allocation schemes. Detailed Implementation

[0097] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only for illustrating the present invention and are not intended to limit the scope of the present invention. Modifications of the present invention in various equivalent forms by those skilled in the art fall within the scope defined by the appended claims.

[0098] This invention addresses the shortcomings of the traditional NSGA-II algorithm in practical applications, such as poor distribution of the solution set, unreliable search capability, and slow convergence speed. It proposes a water resource optimization allocation method based on an improved NSGA-II multi-objective genetic algorithm. This method uses a best point set strategy for population initialization and utilizes a parent selection strategy based on linear pressure to adjust the elite population selection method.

[0099] like Figure 1 As shown, the water resource optimization allocation method based on the improved NSGA-II multi-objective genetic algorithm of the present invention includes the following steps:

[0100] S1. Obtain basic information data for the watershed, including: basic characteristic parameters of each water source project (reservoir or lake), water level-storage capacity relationship curves of the water source projects, and generalize the watershed water resource allocation system based on the hydraulic and hydrological connections between each water source and water transmission and distribution project (pump, sluice gate or water pipeline). See the generalized diagram below. Figure 2 ;

[0101] S2. Analyze the watershed water resources allocation task and construct a multi-objective optimization allocation model for watershed water resources with the objective functions of minimizing water shortage and maximizing the ecological water supply guarantee rate of each irrigation district, and constraints such as water balance, maximum agricultural water supply, minimum ecological water supply, and non-negativity of variables:

[0102] Objective function 1: Minimize the total water shortage in the watershed

[0103]

[0104] Where f1(x,y) represents the total water shortage in the basin, n represents the total number of irrigation districts, and W xi Let x be the agricultural water demand of the i-th irrigation district; i For agricultural water supply in irrigation district i; W yi The ecological water demand of irrigation district i; y i This refers to the ecological water supply for the i-th irrigation district.

[0105] Objective function 2: Maximize the satisfaction level of ecological water supply in each irrigation district.

[0106]

[0107] Where f2(y) represents the satisfaction level with ecological water supply in each irrigation district;

[0108] Constraint 1: Water Balance Constraint

[0109]

[0110] Among them, W u Available water volume; W i For watershed inflow; W e Ecological baseline flow for key water supply rivers;

[0111] Constraint 2: Maximum agricultural water supply constraint

[0112] x i ≤W xi (4)

[0113] Constraint 3: Minimum ecological water demand constraint

[0114] y i ≥αW yi (5)

[0115] Where α is a parameter between 0 and 1, used to calculate the minimum water requirement necessary to ensure the survival of ecological vegetation;

[0116] Constraint 4: Non-negativity constraint

[0117] x i ≥0; y i ≥0 (6)

[0118] S3. An improved NSGA-II genetic algorithm is used to solve the multi-objective water resources optimization allocation model of the watershed, obtaining a Pareto non-dominated solution set. Each individual in the solution set represents a watershed water resources allocation scheme; for example... Figure 3 As shown, the steps are as follows:

[0119] S3-1. Based on the basic water resources situation of the basin, select decision variables, divide the basin into various water conveyance units according to the control hydrological sections of the main water supply rivers, determine the upper and lower limits of water demand for each water conveyance unit, and determine the upper and lower bounds of the search domain for the improved NSGA-II genetic algorithm. Define the initial generation population as P0, and the parent population after t iterations as P... t The offspring population is P t+1 Set the population size N, the independent variables to agricultural water supply and ecological water supply in each irrigation district, the number of independent variables nVar to be twice the number of irrigation districts, and the maximum number of iterations t. max Crossover ratio Pc, variation ratio Pm, lower bound of independent variable varmin is a vector dataset consisting of the minimum agricultural water supply and minimum ecological water supply of each irrigation district, upper bound of independent variable varmax is a vector dataset consisting of the maximum agricultural water supply and maximum ecological water supply of each irrigation district, and parent selection parameters ud and up.

[0120] S3-2. Let the number of iterations be t=0, and use the optimal point set theory to generate the initial population P0, which includes the following steps:

[0121] S3-2-1. If the spatial dimension of the population is s and the population size is N, calculate the value of each point in the point set r according to formulas (7) to (8):

[0122] r = (r1, r2, r3, ..., r N (7)

[0123]

[0124] Where, r j Let J be a good point in the point set R, where J = 1, 2, ..., N; N i Let i represent the i-th individual in the population, where i = 1, 2, ..., N;

[0125] S3-2-2, Construct a set of N ideal points P N (i):

[0126] P N (i)={(r1i1,r2i2,r3i3,…,r N i N )},i=1,2,…,N (9)

[0127] Where 1≤i j ≤N, j=1,2,…,N;

[0128] S3-2-3, P N (i) Mapping to the feasible region where the population resides:

[0129]

[0130] in, This refers to the optimal location within the feasible region, representing a water resource allocation scheme; a j This represents the lower bound of the current dimension, namely the minimum agricultural water supply and minimum ecological water supply for each irrigation district, b. j This represents the upper limit of the current dimension, namely the maximum agricultural water supply and the maximum ecological water supply of each irrigation district.

[0131] S3-3. Calculate the target values ​​of individuals in the population according to objective functions 1 and 2, namely the total water shortage in the watershed and the ecological water supply satisfaction of each irrigation district for each scheme, perform rapid non-dominated sorting of individuals and calculate the crowding degree.

[0132] S3-4. Sort individuals in ascending order based on dominance level, then sort them in descending order based on crowding distance. Calculate the probability of each sorted individual becoming a parent and generate a parent population P. t Specifically, it includes the following steps:

[0133] S3-4-1. After performing non-dominated sorting and crowding calculation, the population is first sorted in ascending order according to dominance level, and then sorted in descending order according to crowding distance.

[0134] S3-4-2. The N individuals in the new population obtained after sorting are x1, x2, ..., x n Each individual represents a water resource allocation scheme. Among them, x1 is the highest-ranked individual with the highest fitness value, x... n The individual with the lowest ranking has the lowest fitness value;

[0135] S3-4-3, Assume that the probability of x1 becoming the parent individual is p1, x n The probability of becoming a parent individual is p. n Then the expected number of x1 after the selection operation (i.e., the parent selection parameter up) is:

[0136] up=N*p1 (11)

[0137] x n The expected number after the selection operation (i.e., the parent selection parameter ud) is:

[0138] ud = N*p n (12)

[0139] S3-4-4. To ensure that individuals with higher rank in the parent population have a higher probability of becoming parents, using an arithmetic sequence, the probability of the i-th individual in the population becoming a parent is:

[0140]

[0141] If the sum of individual selection expectations in the population is N, then ud + up = 2, 0 ≤ ud ≤ 1, and up = 2 - ud.

[0142] S3-5. Perform crossover and mutation operations on the parent population after the selection operation to obtain the offspring population P. t+1 ;

[0143] S3-6. Check if the number of generations of genetic evolution has reached the maximum number of iterations t. max If yes, terminate the process and output the result; otherwise, set t = t + 1 and return to S3-3 to continue.

[0144] S4. Determine the optimal watershed water resource allocation scheme in the Pareto solution set.

[0145] The system corresponding to the method includes:

[0146] The parameter acquisition unit is used to acquire basic data and relevant parameters of the target watershed, including: basic characteristic parameters of each water conveyance unit, water level-storage capacity relationship curves of water source projects, and generalize the watershed water resource allocation system based on the hydraulic connection between each water source and water conveyance and distribution project.

[0147] The model building unit is used to analyze the specific tasks of water resource optimization and allocation, and to build a watershed water resource multi-objective optimization and allocation model with the objective functions of minimizing water shortage and maximizing the ecological water supply guarantee rate of each irrigation area, and with constraints of water balance, maximum agricultural water supply, minimum ecological water supply and non-negativity of variables.

[0148] The model solving unit is used to solve the multi-objective optimization allocation model of watershed water resources using the improved NSGA-II genetic algorithm, and obtain the Pareto non-dominated solution set. Each individual in the solution set represents a watershed water resources allocation scheme.

[0149] The optimal solution determination unit is used to determine the optimal watershed water resource allocation scheme in the Pareto solution set.

[0150] An electronic device for storing and executing the method includes a memory and a processor, wherein:

[0151] Memory is used to store computer programs that can run on a processor;

[0152] A processor is configured to execute the steps of the water resource optimization allocation method based on the improved NSGA-II multi-objective genetic algorithm when running the computer program.

[0153] Experimental verification:

[0154] The improved test results were compared with the results obtained by the traditional NSGA-II algorithm with the same parameter settings to verify the feasibility and superiority of the algorithm. Figure 4 This is the Pareto curve of the ZDT test function based on the improved and traditional NSGA-II algorithm. Figure 4 As can be seen from (a) to (d), for the ZDT test function, the improved NSGA-II converges faster and obtains a solution set closer to the known Pareto optimal solution when the number of iterations is the same. The improved NSGA-II algorithm is significantly better than the traditional NSGA-II algorithm. The rationality and effectiveness of the invented method are now illustrated using the optimal allocation of water resources in the main stream of the Tarim River as an example. The main stream of the Tarim River is located on the north side of the Tarim Basin, starting at Xiaojiahe, the confluence of the Aksu River, Yarkand River, and Hotan River, and ending at Taitma Lake. The main stream is 1321 km long, with a drainage area of ​​17,600 km². 2 The Tarim River is geographically located between 81°51' and 88°30' east longitude and 39°30' and 41°35' north latitude. The main stream of the Tarim River is divided into three sections—upper, middle, and lower reaches—based on its geomorphological characteristics. Table 1 shows the actual water resource allocation plan for the Tarim River main stream in 2020.

[0155] Table 1. Actual Water Resources Allocation Plan for the Main Stream Area of ​​the Tarim River in 2020 (Unit: 100 million m³) 3

[0156]

[0157] This invention uses agricultural and ecological water supply in each irrigation district as decision variables and employs an improved NSGA-II algorithm for optimal allocation. The goal is to maximize the total water shortage in the watershed and the ecological water supply guarantee rate in each irrigation district, with constraints including water balance, maximum agricultural water supply, minimum ecological water supply, and non-negativity. The specific parameters of the improved NSGA-II algorithm are set as follows: population size N = 100, global iterations are set to 500, and 2020 is selected for optimization. A comparison of the water supply guarantee rate between the optimized and actual allocation schemes in the Tarim River main stream area in 2020 is shown below. Figure 5 (a) and (b). Under the condition that the total regional water supply remains unchanged, compared with the actual allocation scheme, the optimized scheme improves the problem of excessive water supply in the U-A irrigation area and the A-Qia irrigation area, thus alleviating the problem of water waste in the region. At the same time, the agricultural and ecological water supply guarantee rates of the A-Xin irrigation area, Xin-Ying irrigation area, Ying-U irrigation area, and Qia-Da irrigation area are all improved. By using the improved NSGA-II algorithm for optimization allocation, the water shortage problem in the Tarim River main stream area is effectively improved, and the water supply guarantee rate of each irrigation area is improved. The optimized allocation scheme, while making full use of the water inflow at the Alar section, fully guarantees the ecological base flow and the outflow from the Daixihai Lake, so that water resources are rationally allocated. Therefore, the set of watershed water resource optimization allocation schemes solved by the improved NSGA-II algorithm is reasonable and effective.

Claims

1. A water resource optimization allocation method based on an improved NSGA-II multi-objective genetic algorithm, characterized in that, Includes the following steps: S1. Obtain basic data and relevant parameters of the target watershed, including: basic characteristic parameters of each water conveyance unit, water level-storage capacity relationship curve of water source project, and generalize the watershed water resource allocation system based on the hydraulic connection between each water source and water conveyance and distribution project. S2. Analyze the specific tasks of water resource optimization and construct a multi-objective optimization model for watershed water resources with the objective functions of minimizing water shortage and maximizing the ecological water supply guarantee rate of each irrigation area, and with constraints of water balance, maximum agricultural water supply, minimum ecological water supply and non-negativity of variables. S3. The improved NSGA-II genetic algorithm is used to solve the multi-objective optimization allocation model of watershed water resources, and the Pareto non-dominated solution set is obtained. Each individual in the solution set represents a watershed water resources allocation scheme; including the following steps: S3-1. Based on the basic water resources situation of the basin, select decision variables, divide the basin into various water conveyance units according to the control hydrological sections of the main water supply rivers, determine the upper and lower limits of water demand for each water conveyance unit, and determine the upper and lower bounds of the search domain for the improved NSGA-II genetic algorithm; the independent variables are agricultural water supply and ecological water supply in each irrigation district, the number of independent variables nVar is twice the number of irrigation districts, and the maximum number of iterations t max Crossover ratio Pc, variation ratio Pm, lower bound of independent variable varmin is a vector dataset consisting of the minimum agricultural water supply and minimum ecological water supply of each irrigation district, upper bound of independent variable varmax is a vector dataset consisting of the maximum agricultural water supply and maximum ecological water supply of each irrigation district, and parent selection parameters ud and up. S3-2. Let the iteration number be t = 0, and use the optimal point set theory to generate the initial population P0; including the following steps: S3-2-1. If the spatial dimension of the population is s and the population size is N, calculate the value of each point in the point set r according to the following formula: r＝(r1,r2,r3,…,r N ) Where, r j Let J be a good point in the point set R, where J = 1, 2, ..., N; N i Let i represent the i-th individual in the population, where i = 1, 2, ..., N; S3-2-2, Construct a set of N ideal points P N (i): P N (i)={(r1i1,r2i2,r3i3,…,r N i N )},i=1,2,…,N Where 1≤i j ≤N, j=1,2,…,N; S3-2-3, P N (i) Mapping to the feasible region where the population resides: in, This refers to the optimal location within the feasible region, representing a water resource allocation scheme; a j This represents the lower bound of the current dimension, namely the minimum agricultural water supply and minimum ecological water supply for each irrigation district, b. j This indicates the upper limit of the current dimension, namely the maximum agricultural water supply and the maximum ecological water supply of each irrigation district; S3-3. Calculate the target value of individuals in the population according to the objective function, that is, the total water shortage of the watershed and the ecological water supply satisfaction of each irrigation district for each scheme. Perform a fast non-dominated ranking of individuals and calculate the crowding degree. S3-4. Sort individuals in ascending order based on dominance level, then sort them in descending order based on crowding distance. Calculate the probability of each sorted individual becoming a parent and generate a parent population P. t ; S3-5. Perform crossover and mutation operations on the parent population after the selection operation to obtain the offspring population P. t+1 ; S3-6. Check if the number of generations of genetic evolution has reached the maximum number of iterations. If yes, terminate the operation and output the result; otherwise, let t = t + 1 and return to S3-3 to continue. S4. Determine the optimal watershed water resource allocation scheme in the Pareto solution set.

2. The water resource optimization allocation method based on the improved NSGA-II multi-objective genetic algorithm according to claim 1, characterized in that, The multi-objective optimization allocation model for water resources in the basin constructed in S2 is as follows: Objective function 1: Minimize the total water shortage in the basin; Where f1(x,y) represents the total water shortage in the basin, n represents the total number of irrigation districts, and W xi Let x be the agricultural water demand of the i-th irrigation district; i For agricultural water supply in irrigation district i; W yi The ecological water demand of irrigation district i; y i This refers to the ecological water supply for the i-th irrigation district. Objective function 2: Maximize the satisfaction rate of ecological water supply in each irrigation district; Where f2(y) represents the satisfaction level with ecological water supply in each irrigation district; Constraint 1: Water balance constraint; Among them, W u Available water volume; W i For watershed inflow; W e Ecological baseline flow for key water supply rivers; Constraint 2: Maximum agricultural water supply constraint; x i ≤W xi Constraint 3: Minimum ecological water demand constraint; and i ≥αW yi Where α is a parameter between 0 and 1, used to calculate the minimum water requirement necessary to ensure the survival of ecological vegetation; Constraint 4: Non-negativity constraint; x i ≥0; and i ≥0.

3. The water resource optimization allocation method based on the improved NSGA-II multi-objective genetic algorithm according to claim 1, characterized in that, S3-4 includes the following steps: S3-4-1. After performing non-dominated sorting and crowding calculation, the population is first sorted in ascending order according to dominance level, and then sorted in descending order according to crowding distance. S3-4-2. The N individuals in the new population obtained after sorting are x1, x2, ..., x n Each individual represents a water resource allocation scheme; among them, x1 is the highest-ranked individual with the largest fitness value, x n The individual with the lowest ranking has the lowest fitness value; S3-4-3, Assume that the probability of x1 becoming the parent individual is p1, x n The probability of becoming a parent individual is p. n Then the expected number of x1 after the selection operation, i.e., the parent selection parameter up, is: up = N * p1 x n The expected number after the selection operation, i.e., the parent selection parameter ud, is: out=N*p n S3-4-4. To ensure that individuals with higher rank in the parent population have a higher probability of becoming parents, using an arithmetic sequence, the probability of the i-th individual in the population becoming a parent is: If the sum of individual selection expectations in the population is N, then ud + up = 2, 0 ≤ ud ≤ 1, and up = 2 - ud.

4. A water resource optimization allocation system based on an improved NSGA-II multi-objective genetic algorithm, characterized in that, include: The parameter acquisition unit is used to acquire basic data and relevant parameters of the target watershed, including: basic characteristic parameters of each water conveyance unit, water level-storage capacity relationship curves of water source projects, and generalize the watershed water resource allocation system based on the hydraulic connection between each water source and water conveyance and distribution project. The model building unit is used to analyze the specific tasks of water resource optimization and allocation, and to build a watershed water resource multi-objective optimization and allocation model with the objective functions of minimizing water shortage and maximizing the ecological water supply guarantee rate of each irrigation area, and with constraints of water balance, maximum agricultural water supply, minimum ecological water supply and non-negativity of variables. The model solving unit is used to solve the multi-objective optimization allocation model of watershed water resources using the improved NSGA-II genetic algorithm, and to obtain the Pareto non-dominated solution set. Each individual in the solution set represents a watershed water resources allocation scheme; it includes: S3-1. Based on the basic water resources situation of the basin, select decision variables, divide the basin into various water conveyance units according to the control hydrological sections of the main water supply rivers, determine the upper and lower limits of water demand for each water conveyance unit, and determine the upper and lower bounds of the search domain for the improved NSGA-II genetic algorithm; the independent variables are agricultural water supply and ecological water supply in each irrigation district, the number of independent variables nVar is twice the number of irrigation districts, and the maximum number of iterations t max Crossover ratio Pc, variation ratio Pm, lower bound of independent variable varmin is a vector dataset consisting of the minimum agricultural water supply and minimum ecological water supply of each irrigation district, upper bound of independent variable varmax is a vector dataset consisting of the maximum agricultural water supply and maximum ecological water supply of each irrigation district, and parent selection parameters ud and up. S3-2. Let the iteration number be t=0, and use the optimal point set theory to generate the initial population P0; including: S3-2-1. If the spatial dimension of the population is s and the population size is N, calculate the value of each point in the point set r according to the following formula: r＝(r1,r2,r3,…,r N ) Where, r j Let J be a good point in the point set R, where J = 1, 2, ..., N; N i Let i represent the i-th individual in the population, where i = 1, 2, ..., N; S3-2-2, Construct a set of N ideal points P N (i): P N (i)={(r1i1,r2i2,r3i3,...,r N i N )},i=1,2,…,N Where 1≤i j ≤N, j=1,2,…,N; S3-2-3, P N (i) Mapping to the feasible region where the population resides: in, This refers to the optimal location within the feasible region, representing a water resource allocation scheme; a j This represents the lower bound of the current dimension, namely the minimum agricultural water supply and minimum ecological water supply for each irrigation district, b. j This indicates the upper limit of the current dimension, namely the maximum agricultural water supply and the maximum ecological water supply of each irrigation district; S3-3. Calculate the target value of individuals in the population according to the objective function, that is, the total water shortage of the watershed and the ecological water supply satisfaction of each irrigation district for each scheme. Perform a fast non-dominated ranking of individuals and calculate the crowding degree. S3-4. Sort individuals in ascending order based on dominance level, then sort them in descending order based on crowding distance. Calculate the probability of each sorted individual becoming a parent and generate a parent population P. t ; S3-5. Perform crossover and mutation operations on the parent population after the selection operation to obtain the offspring population P. t+1 ; S3-6. Check if the number of generations of genetic evolution has reached the maximum number of iterations. If yes, terminate the operation and output the result; otherwise, let t = t + 1 and return to S3-3 to continue. The optimal solution determination unit is used to determine the optimal watershed water resource allocation scheme in the Pareto solution set.

5. The water resource optimization allocation system based on the improved NSGA-II multi-objective genetic algorithm according to claim 4, characterized in that, S3-4 includes the following steps: S3-4-1. After performing non-dominated sorting and crowding calculation, the population is first sorted in ascending order according to dominance level, and then sorted in descending order according to crowding distance. S3-4-2. The N individuals in the new population obtained after sorting are x1, x2, ..., x n Each individual represents a water resource allocation scheme; among them, x1 is the highest-ranked individual with the largest fitness value, x n The individual with the lowest ranking has the lowest fitness value; S3-4-3, Assume that the probability of x1 becoming the parent individual is p1, x n The probability of becoming a parent individual is p. n Then the expected number of x1 after the selection operation, i.e., the parent selection parameter up, is: up = N * p1 x n The expected number after the selection operation, i.e., the parent selection parameter ud, is: out=N*p n S3-4-4. To ensure that individuals with higher rank in the parent population have a higher probability of becoming parents, using an arithmetic sequence, the probability of the i-th individual in the population becoming a parent is: If the sum of individual selection expectations in the population is N, then ud + up = 2, 0 ≤ ud ≤ 1, and up = 2 - ud.

6. An electronic device, characterized in that, Includes memory and processor, wherein: Memory is used to store computer programs that can run on a processor; A processor, configured to, while running the computer program, execute the steps of the water resource optimization allocation method based on the improved NSGA-II multi-objective genetic algorithm as described in any one of claims 1-3.

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