Method for processing multiple targets of efficiency and fairness in water resource distribution

Abstract

The invention provides a method for processing multiple targets of efficiency and fairness in water resource distribution, and belongs to the field of water resource distribution, and the method comprises the steps: constructing a fairness coefficient according to basin information, and carrying out the calculation of a water resource distribution fairness index based on the Gini impurity of a classification regression tree; performing efficiency loss calculation based on the fairness cost to obtain a water resource distribution and utilization efficiency index; setting necessary constraint conditions for water resource distribution; constructing a water resource distribution multi-target model according to the water resource distribution fairness index and the water resource distribution utilization efficiency index in combination with constraint conditions of water resource distribution; according to the preference information of the decision maker, converting the water resource distribution multi-target model into a water resource distribution single-target model and solving the water resource distribution single-target model to obtain an optimal water resource distribution scheme; the problems that in the existing water resource distribution process, fairness and efficiency are prone to conflict, a multi-target water resource distribution model is complex to solve, and an accurate water resource distribution scheme cannot be provided are solved.

Description

Technical Field

[0001] The present invention belongs to the field of water resource allocation, and particularly relates to a method for processing multi-objectives of efficiency and fairness in water resource allocation. Background Art

[0002] In the resource allocation problems in the real world, there is often a contradiction between fairness and efficiency. How to achieve a reasonable balance between the two is a key challenge; for decision-makers who are concerned about both fairness and efficiency, it is particularly difficult to find an optimal solution; the main challenge lies in modeling the problem and determining the optimal trade-off; first of all, fairness and efficiency are abstract concepts and must be quantified before modeling. Each quantification method has its advantages and disadvantages.

[0003] In research, the gap between the perfect fairness line and the Lorenz curve is often used to calculate fairness. In order to transform this concept into a mathematical expression, researchers usually adopt variants of variance or Gini index; some studies use variants of the Gini index containing absolute value terms, but this may affect the differentiability of the model; in addition, efficiency is usually defined as the total economic benefit, while fairness is calculated through the Gini index, and its value range is , this inconsistency in the measurement scale brings challenges when trying to integrate these objectives into a single objective (such as through the weighting method).

[0004] Therefore, it is necessary to develop new methods to improve the measurement methods of fairness and efficiency, modify the existing methods to maintain the differentiability of the Gini index function, and unify the measurement scales of the two objectives. Summary of the Invention

[0005] In view of the above deficiencies in the prior art, the present invention provides a method for processing multi-objectives of efficiency and fairness in water resource allocation, which solves the problems of easy conflict between fairness and efficiency in the existing water resource allocation process, complex solution of the multi-objective water resource allocation model, and inability to provide an accurate water resource allocation scheme.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a method for processing multi-objectives of efficiency and fairness in water resource allocation, including the following steps: S1. According to the basin information, construct a fairness coefficient, and based on the Gini impurity of the classification regression tree, use the fairness coefficient to calculate the water resource allocation fairness index; S2. Calculate the efficiency loss based on the fairness cost to obtain the water resource allocation utilization efficiency index; S3. Set the necessary constraints for water resource allocation; S4. Based on the trade - off between fairness and efficiency, according to the fairness index of water resource allocation and the efficiency index of water resource allocation and utilization, combined with the constraint conditions of water resource allocation, construct a multi - objective model for water resource allocation; S5. According to the decision - maker's preference information, transform the multi - objective model of water resource allocation into a single - objective model of water resource allocation and solve it to obtain the optimal water resource allocation scheme.

[0007] The beneficial effects of the present invention are as follows: By improving the measurement methods of fairness and efficiency indicators, modifying the existing method to maintain the differentiability of the Gini index function, unifying the measurement scale of objectives, avoiding the deviation of the optimization results caused by dimensional inconsistency, reducing the difficulty of solving the optimization model, improving the solving efficiency of the multi - objective water resource allocation model and the quality of the obtained solutions, and realizing the resolution of the conflict between the two types of objective functions of fairness and efficiency in the process of water resource allocation; and combining the preference information to transform the multi - objective model into a single - objective model for solution, providing an accurate water resource allocation scheme for decision - makers.

[0008] Further, the S1 includes the following steps: S101. Construct a fairness coefficient according to the total population of the sub - region, the water resource demand of the sub - region, and the water resource demand of the water - using department; S102. Normalize the fairness coefficient to obtain the normalized fairness coefficient; S103. Based on the Gini impurity of the classification and regression tree, calculate using the normalized fairness coefficient to obtain the first - stage Gini coefficient; S104. Adjust the first - stage Gini coefficient using a preset adjustment term to obtain the adjusted first - stage Gini coefficient; S105. Calculate the fairness index of water resource allocation according to the adjusted first - stage Gini coefficient and the fairness coefficient.

[0009] Still further, the expression of the normalized fairness coefficient is as follows: ; ; where, represents the fairness coefficient, represents the normalized fairness coefficient, represents the total amount of water resources allocated to the water - using department in the sub - region , represents the sub - region, represents the water - using department, M represents the maximum number of sub - regions, N represents the maximum number of water - using departments, Represents the object participating in the fairness calculation. Indicates there are M sub - regions, and the calculation object is the sub - region. Indicates there are N water - using departments, and the calculation object is the water - using department; when ... represents the total population of the sub - region and the water resource demand of the sub - region, when ... represents the water resource demand of the water - using department.

[0010] Furthermore, the expression for calculating the water resource allocation fairness index is as follows: ; ; ; Among them, represents the adjusted Gini coefficient in the first stage, which is a fairness index. represents part of represents the Gini coefficient in the first stage.

[0011] The beneficial effects of the above - mentioned further solution are as follows: By defining the fairness coefficient and calculating the Gini coefficient based on the Gini impurity of the classification regression tree, on the one hand, the calculation results can reflect the fairness of water resource allocation for the sub - region population, sub - region water resource demand, and water - using department water resource demand. Substituting it into the optimization model as the objective function, an accurate allocation plan that meets the decision - maker's requirements for water resource allocation fairness can be obtained; on the other hand, the obtained Gini coefficient eliminates the non - differentiable nature brought by the traditional calculation method, simplifies the complexity of model solution, and can improve the solution efficiency.

[0012] Furthermore, the specific content of S2 is as follows: Based on the fairness principle, the unit water - using efficiency value of the water - using department in the sub - region, and the maximum unit water - using efficiency value of the water - using department, calculate the efficiency loss based on the fairness cost to obtain the water resource allocation and utilization efficiency index.

[0013] Furthermore, the expression for calculating the efficiency loss based on the fairness cost is as follows: ; Among them, represents the fairness cost of water resource allocation. represents the maximum unit water - using efficiency value for all water - using departments in all sub - regions. represents the sub - region of the water - using department The unit water use efficiency value.

[0014] The beneficial effects of the above further scheme are as follows: By calculating the fairness cost, on the one hand, the economic benefits lost under the water resource allocation considering the fairness goal are obtained, and minimizing the fairness cost is taken as one of the objective functions of the optimization model; on the other hand, compared with directly substituting the economic benefit index, the fairness cost solves the problem of inconsistent dimensions of multiple objectives, thereby reducing the deviation of the optimization results caused thereby. Combining the fairness cost with the aforementioned fairness index, the water resource allocation fairness and efficiency are comprehensively considered to optimize the scheme, providing a water resource allocation scheme with both fairness and efficiency for decision-makers.

[0015] Furthermore, the specific content of S3 is as follows: Set the upper limit of the total water resource allocation of the water use departments in the sub-region according to the planned maximum value of the overall water resource allocation in the basin. Set the upper limit of the total water resource allocation of the economic water use departments in the sub-region according to the planned maximum value of the water resource allocation of the economic water use departments in the sub-region. Set the upper limit of the total water resource allocation of the sub-region according to the water resource supply capacity of the sub-region. Set the lower limit of the total water resource allocation of the water use departments in the sub-region according to the minimum water resource demand of the water use departments in the sub-region.

[0016] Furthermore, the expression of the upper limit of the total water resource allocation of the water use departments in the sub-region is as follows: ; Wherein, C Represents the planned maximum value of the overall water resource allocation in the basin; The expression of the upper limit of the total water resource allocation of the economic water use departments in the sub-region is as follows: ; Wherein, Represents the planned maximum value of the water resource allocation of all sub-region economic water use departments; The expression of the upper limit of the total water resource allocation of the sub-region is as follows: ; Wherein, Represents the sub-region Water resource supply capacity; The expression of the lower limit of the total water resource allocation of the water use departments in the sub-region is as follows: ; Wherein, Represents the sub-region Of the water use department The minimum water resource demand.

[0017] The beneficial effect of the above further scheme is: the present invention sets necessary constraints for water resource allocation and incorporates them into a multi-objective water resource allocation model for optimization, thereby improving the applicability of the resulting water resource allocation scheme in practical problems and making it more able to meet the needs of decision makers for water resource allocation schemes.

[0018] Furthermore, the expression of the multi-objective model of water resources allocation is as follows: ; ; in, represents minimization, represents the adjusted first-stage Gini coefficient.

[0019] The beneficial effect of the above further scheme is: the present invention constructs a multi-objective model for water resource allocation that considers the trade-off between fairness and efficiency, comprehensively evaluates the two conflicting goals of maximizing the fairness of water resource allocation and maximizing the efficiency of water resource allocation, combines the necessary constraints on water resource allocation, and uses multi-objective optimization technology that considers the preferences of decision makers to obtain an accurate water resource allocation plan that meets the needs of decision makers.

[0020] Furthermore, the S5 is specifically: According to the preference information of decision makers, the multi-objective model of water resources allocation is transformed into a single-objective model of water resources allocation by considering the target programming method of different types of preference information. The planning software is used to solve the single-objective model of water resource allocation, obtain the optimal water resource allocation plan, and complete the multi-objective processing of efficiency and fairness in water resource allocation; The target programming methods for different types of preference information include: a weight-based target programming method and an S-type penalty function-based target programming method.

[0021] The beneficial effect of the above further scheme is: based on the multi-objective optimization technology that takes into account the decision maker's preferences, the present invention transforms the multi-objective model of water resources allocation into a single-objective model of water resources allocation for solving, thereby eliminating the complexity of solving caused by the multi-objective structure and avoiding the drawbacks of the traditional heuristic algorithm solution method. That is, the model and method proposed by the present invention can directly solve the only accurate solution without the need for secondary screening. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 The present invention is a flow chart of the method.

[0023] Figure 2 It is a general framework diagram of water resource allocation in this embodiment.

[0024] Figure 3 This is the flowchart for calculating the Gini coefficient in this embodiment.

[0025] Figure 4 This is the result graph of the goal and achievement function of the goal programming method based on weights in this embodiment.

[0026] Figure 5 This is the water resource allocation scheme graph obtained by the goal programming method based on weights in this embodiment.

[0027] Figure 6 This is the S-shaped penalty function graph of the goal in this embodiment.

[0028] Figure 7 This is the result graph of the goal and achievement function of the goal programming method based on the S-shaped interval in this embodiment.

[0029] Figure 8 This is the water resource allocation scheme graph obtained by the goal programming method based on the S-shaped interval in this embodiment. Detailed implementation manners

[0030] The following describes the detailed implementation manners of the present invention to facilitate those skilled in the art of this technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation manners. For those ordinary skilled in the art of this technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0031] Before describing this embodiment, the following terms are first explained: CART: Classification and Regression Tree; POF: Fairness cost; LINGO: Interactive linear and general optimization solver.

[0032] Embodiment 1 As Figure 1 shown, the present invention provides a method for processing multiple objectives of efficiency and fairness in water resource allocation, and its implementation method is as follows: S1. According to the basin information, construct a fairness coefficient, and based on the Gini impurity of the classification and regression tree, use the fairness coefficient to calculate the water resource allocation fairness index, specifically as follows: S101. Construct a fairness coefficient according to the total population of the sub-region, the water resource demand of the sub-region, and the water resource demand of the water use department; S102. Normalize the fairness coefficient to obtain the normalized fairness coefficient; S103. Based on the Gini impurity of the classification and regression tree, use the normalized fairness coefficient for calculation to obtain the Gini coefficient in the first stage; S104. Adjust the Gini coefficient of the first stage using the preset adjustment item to obtain the adjusted Gini coefficient of the first stage; S105. Calculate the water resource allocation fairness index based on the adjusted Gini coefficient of the first stage and the fairness coefficient.

[0033] In this embodiment, as Figure 2 shown, according to the general framework of water resource allocation and the Gini impurity index based on CART, calculate the water resource allocation fairness index, specifically: As Figure 3 shown, the process of calculating the Gini coefficient; Introduce the fairness coefficient : Define the expression of the fairness coefficient as follows: ; Among them, represents the total amount of water resources of the water use department allocated to the sub-region , represents the sub-region, represents the water use department, M represents the maximum number of sub-regions, N represents the maximum number of water use departments, represents the object participating in the fairness calculation, represents a total of M sub-regions, and the calculation object is the sub-region; represents a total of N water use departments, and the calculation object is the water use department; Generally speaking, the variable parameter represents the total population of the sub-region and the water resource demand of the sub-region, represents the water resource demand of the water use department; Normalize the fairness coefficient : Normalize each fairness coefficient to obtain the normalized fairness coefficient ; The expression of the normalization process is as follows: ; Based on the classification and regression tree, calculate the Gini coefficient of the first stage: Based on the concept of Gini impurity introduced in the classification and regression tree, use the normalized fairness coefficient to calculate the Gini coefficient of the first stage, and its expression is as follows: ; Among them, represents the Gini coefficient of the first stage; Adjust the Gini coefficient of the first stage: It is necessary to use the adjustment item , since , take the part of the feature . When or , the Gini coefficient is meaningless, and the minimum value of the Gini coefficient must be 0. Therefore, use the adjustment term to adjust the Gini coefficient in the first stage as follows, and calculate the adjusted Gini coefficient in the first stage as: ; Among them, represents the adjusted Gini coefficient in the first stage, that is, the fairness index, represents part; Combine the adjusted Gini coefficient in the first stage and the fairness coefficient, calculate the adjusted Gini coefficient in the first stage, obtain the water resource allocation fairness index, and feedback it to the water resource allocation plan. The expression for calculating the adjusted Gini coefficient in the first stage based on the fairness multi-objective is as follows: ; .

[0034] S2. Calculate the efficiency loss based on the fairness cost to obtain the water resource allocation and utilization efficiency index, specifically as follows: Calculate the efficiency loss based on the fairness cost according to the fairness principle, the unit water use efficiency value of the water use department in the sub-region, and the maximum unit water use efficiency value of the water use department, and obtain the water resource allocation and utilization efficiency index.

[0035] In this embodiment, considering the efficiency loss when considering the fairness principle, calculate the efficiency loss based on POF to obtain the water resource allocation and utilization efficiency index. The expression for calculating the efficiency loss based on the fairness cost is as follows: ; Among them, represents the fairness cost of water resource allocation, represents the maximum unit water use efficiency value of all water use departments for all sub-regions, represents the sub-region water use department unit water use efficiency value.

[0036] S3. Set the necessary constraints for water resource allocation, specifically as follows: Set the upper limit of the total water resource allocation of the water use department in the sub-region according to the planned maximum value of the overall water resource allocation in the basin; Set the upper limit of the total water resources allocation for the economic water use sectors in the sub-region according to the planned maximum value of the water resources allocation for the economic water use sectors in the sub-region; Set the upper limit of the total water resources allocation for the sub-region according to the water resources supply capacity of the sub-region; Set the lower limit of the total water resources allocation for the water use sectors in the sub-region according to the minimum water resources demand of the water use sectors in the sub-region.

[0037] In this embodiment, set the necessary constraints for water resources allocation, considering the planned maximum values of the water resources allocation plans for all water use sectors in all sub-regions. The specific expression is as follows: ; Among them, C represents the planned maximum value of the overall water resources allocation in the basin. This constraint serves as the upper limit of the total water resources allocation for the water use sectors in the sub-region ; For the upper limit of the total water resources allocation; Consider the planned maximum value of the water resources allocation plan for the economic water use sectors in the sub-region. The specific expression is as follows: ; Among them, represents the planned maximum value of the water resources allocation for all economic water use sectors in all sub-regions. In the formula takes the number of the economic water use sectors among the water use sectors; this constraint serves as the upper limit of the total water resources allocation for all economic water use sectors (i.e., agricultural, industrial, and domestic water use sectors); Consider the maximum resource supply capacity of each sub-region. The specific expression is as follows: ; Among them, represents the water resources supply capacity of the sub-region ; this constraint serves as the upper limit of the total water resources allocation for each sub-region ; Consider the minimum water resources demand of the water use sectors in the sub-region . The specific expression is as follows: ; Among them, represents the minimum water resources demand of the water use sectors in the sub-region ; this constraint serves as the lower limit of the total water resources allocation for the water use sectors in each sub-region ; For the lower limit of the total water resources allocation;

[0038] S4. Based on the trade-off between fairness and efficiency, construct a multi-objective model for water resources allocation according to the water resources allocation fairness index and the water resources allocation utilization efficiency index, in combination with the constraints of water resources allocation; The expression of the multi-objective model for water resource allocation is as follows: ; ; Among them, represents minimization.

[0039] In this embodiment, based on the trade-off between fairness and efficiency, according to the water resource allocation fairness index and the water resource allocation and utilization efficiency index, combined with the constraints of water resource allocation, a multi-objective model for water resource allocation is constructed.

[0040] In this embodiment, the multi-objective model for water resource allocation considering the trade-off between fairness and efficiency is specifically as follows: Calculate the minimized Gini coefficient based on classification and regression tree for population in sub-regions as the first objective, and the expression is as follows: ; The constraints are: ; Among them, represents the water resource allocation fairness index for the population in the sub-region , represents the total population of the sub-region , represents the fairness parameter related to the population of the sub-region , M represents the maximum number of sub-regions, represents the total water resources of the water use department allocated from the basin to the sub-region , N represents the maximum number of water use departments; Calculate the minimized Gini coefficient based on classification and regression tree for resource demand in sub-regions as the second objective, and the expression is as follows: ; The constraints are: ; Among them, represents the water resource allocation fairness index for the water resource demand in the sub-region , represents the total water resource demand of the sub-region , represents the fairness parameter related to the water resource demand of the sub-region ; Considering the maximization of the efficiency index from the perspective of the Gini coefficient, that is, maximizing the difference between the total amount of water resources allocated among water-using sectors and their water demands, so as to maximize the efficiency of water resources allocation, calculate the maximization of the efficiency of water resources allocation as the third objective, and the expression is as follows: ; The constraints are: ; Among them, represents the fairness index of water resources allocation for the water demand of water-using sector , represents the total water demand of water-using sector , represents the fairness parameter related to the water demand of water-using sector ; Calculate the minimization of the fairness cost POF of water resources allocation as the fourth objective, and the expression is as follows: ; According to the first objective, the second objective, the third objective and the fourth objective, combined with the necessary constraints of water resources allocation, realize the construction of a multi-objective model of water resources allocation.

[0041] S5. According to the decision maker's preference information, transform the multi-objective model of water resources allocation to obtain a single-objective model of water resources allocation and solve it to obtain the optimal water resources allocation scheme, which is specifically as follows: According to the decision maker's preference information, considering the goal programming method for different types of preference information, transform the multi-objective model of water resources allocation to obtain a single-objective model of water resources allocation; Use the planning software to solve the single-objective model of water resources allocation to obtain the optimal water resources allocation scheme, and complete the multi-objective processing of efficiency and fairness in water resources allocation; The goal programming method for different types of preference information includes: the goal programming method based on weights and the goal programming method based on the S-shaped penalty function.

[0042] In this embodiment, the multi-objective model is transformed into a single-objective model in combination with the decision maker's preference information and solved using the planning software; the planning software, such as LINGO; this embodiment uses two types of preference information, one is the goal programming method based on weights and the other is the goal programming method based on the S-shaped penalty function.

[0043] Embodiment 2 In this embodiment, as Figure 2 shown, considering the general allocation framework from the basin to sub-regional water-using sectors, select 14 different sub-regions (cities) in the basin of Gansu Province, China as the research objects, as shown in Table 1.

[0044] Table 1

[0045] Referring to statistical materials such as the "Gansu Provincial Water Resources Bulletin", constants required for modeling are obtained, including: the planned maximum water consumption of all water-using departments C 、the planned maximum value of water resources allocation for economic water-using departments 、sub-regions 's water resources supply capacity 、sub-regions 's water-using departments 's minimum water resources demand 、sub-regions 's total population 、sub-regions 's total water resources demand 、water-using departments 's total water resources demand and sub-regions 's water-using departments 's unit water use efficiency value (average economic benefit of water resources allocation); weight information of 20 decision-makers when facing four objectives is collected, as shown in Table 2; when dealing with the multi-objective structure of the original problem, first, the following goal programming model is used to convert the original multi-objective problem into a deterministic single-objective problem for solution, and the expression is as follows: ; ; ; ; ; ; ; Among them, represents the negative deviation of objective i , represents the positive deviation of objective i , represents the expected level of objective i , represents the weight of objective i , i represents the objective, and can take 1, 2, 3, 4.

[0046] Table 2

[0047] In this embodiment, as Figure 4As shown, it presents the multi-objective achievement under different decision-maker preferences. Table 3 listing the objective achievement results calculated based on the weight method is shown. As shown in Table 3, the preference of Decision-maker -7 performs best on Objective 1 with a score of 0.069, while Decision-maker -2 performs worst with a score of 0.075. It is worth noting that all the water resource allocation schemes proposed by the 20 decision-makers show a high degree of fairness on Objective 1, which aims to minimize the differences among the population. Similarly, Objective 2 also shows significant fairness. Decision-maker -3 and Decision-maker -17 perform best with a score of 0.005, while Decision-maker -2 performs worst with a score of 0.01. For Objective 3, the schemes proposed by the 20 decision-makers all show a constant value of 0.235 on Objective 3, indicating that the achievement degree of this objective is not affected by decision-maker preferences. In contrast, for Objective 4, the best score is 0.853 achieved by Decision-maker -2, while the worst result of 0.86 appears in the scheme of Decision-maker -17. The results of Objective 4 are limitedly affected by decision-making preferences. At the same time, this shows that a large part of efficiency is sacrificed in the pursuit of fairness, which further strengthens the concept of fairness-efficiency trade-off. The total penalty value reflects the degree of conflict between objectives caused by decision-maker preferences. The higher the total penalty value, the greater the conflict, and thus the lower the decision-maker's satisfaction with the result. It is worth noting that Decision-maker -5 has the smallest total penalty value of 0.295, and its results on the four objectives are similar to those of Decision-maker -18 (with the largest total penalty value of 2.915). As Figure 5 shown Figure 5 shows the specific water resource allocation schemes obtained by the decision-makers. Taking Decision-maker -1 as an example. It should be noted that in order to ensure Figure 5 the display degree of the listed data, the values less than 0.2 are hidden. It can be seen that in the total water resource allocation scheme, the water resource allocation amounts in the four regions of JQ, ZY, WW, and LZ are the largest, the water resource allocation amounts in the remaining areas are less, and the water resource allocation amount in the GN region is the least; in the water resource allocation of the ecological water use department, except for the regions of JQ, LZ, and WW, the proportion of ecological water use in the other 11 regions is relatively small; in the water resource allocation of the agricultural water use department, the proportion of agricultural water use in the regions of ZY, WW, JQ, and JC is relatively high, and the proportion of agricultural water use in the JYG region is the smallest; on the contrary, in terms of industrial water use, the proportion of industrial water use in the regions of GN, LZ, DX, etc. is relatively high, and the proportion of industrial water use in the regions of JQ, ZY, WW, etc. is relatively low; in terms of domestic water use, the proportion of domestic water use in the JYG region is the lowest.

[0048] Table 3

[0049] In this embodiment, the result calculated by the target programming method based on weights is not greatly affected by the weights of different targets because the preference information that the weights can provide is relatively limited. The following S-shaped interval programming method is used to solve the model for comparison, and the expression is as follows: ; ; ; ; ; ; ; ; ; Among them, represents the i th attribute value of the target j , j takes , represents the deviation of the target i between the attributes and , represents the slope of the target i between the attributes and , represents a binary variable, represents the water resource allocation fairness index for the water resource demand in the sub-region , represents the water resource allocation fairness index for the water resource demand in the sub-region , represents the fairness cost; is a sufficiently large number; the S-shaped penalty function is reorganized according to the decision maker's preference information and adopted in the S-shaped interval target programming model. The S-shaped penalty function is as Figure 6 shown.

[0050] In this embodiment, as a result of the S-shaped interval programming method, as Figure 7 shown, Figure 7It shows the multi-objective achievement under different decision-maker preferences, and Table 4 lists the objective achievement results calculated based on the S-shaped interval programming method. In comparison, the results of the S-shaped interval programming method considering more complex preference information have higher responsiveness because the preference information presented by linear preferences (weight method) may be overly simplified, leading to inaccurate results. It can be seen that the preference of Decision-maker -20 performs best on Objective 1, with a score of 0.071, while the preferences of Decision-makers -1, 2, 4, 5, 6, 10, 11, 13, 17, and 19 perform worst, with a score of 0.078. It is worth noting that the scores of the water resource allocation plans proposed by all 20 decision-makers on Objective 1 are in the range of [0.071, 0.078]. Among them, 78% of the decision-makers' scores are concentrated in 0.076 - 0.078, and 50% of the decision-makers have a score of 0.078, showing relatively high fairness. Objective 2 also shows significant fairness. Decision-maker -20 has the best performance with a score of 0.009, while Decision-makers -1, 2, 4, 5, 6, 10, 13, 17, and 19 perform worst with a score of 0.011. In addition, the performance of Objective 3 shows a polarized trend. The best results are achieved by Decision-makers -2, 4, 10, 11, 13, 14, 15, and 16, with a score of 0.2, while the decision results of the remaining decision-makers are the worst, at 0.235. The results of Objective 4 show slight fluctuations. The best score is 0.849, achieved by Decision-makers -2, 4, 10, 11, 13, 15, and 16, while the worst result of 0.855 appears in the plan of Decision-maker -20. From the perspective of the total penalty value, Decision-maker -5 has the smallest total penalty value, at 0.298, and its results on the four objectives are similar to those of Decision-maker -18 (with the largest total penalty value of 2.923). As Figure 8 shown, Figure 8 it shows the specific water resource allocation plans obtained by the decision-makers, taking Decision-maker -1 as an example. It should be noted that in order to ensure Figure 8 the display of the listed data, the values less than 0.2 are hidden. It can be seen that in the total water resource allocation plan, the water resource allocation amounts in the three regions of JQ, ZY, and WW are the largest, the water resource allocation amounts in the remaining regions are relatively small, and the water resource allocation amount in the GN region is the smallest; in the water resource allocation for the ecological water use department, except for the JC, LZ, and WW regions, the ecological water use amounts in the other 11 regions are relatively small; in the water resource allocation for the agricultural water use department, the agricultural water use ratios in the ZY, WW, JQ, JC, and BY regions are relatively high, and the agricultural water use ratio in the GN region is the smallest; on the contrary, in terms of industrial water use, the industrial water use ratios in the JYG and LZ regions are relatively high, and the industrial water use ratios in the remaining regions are relatively low; in terms of household water use, the household water use amounts in the JQ, JC, and JYG regions are extremely low.

[0051] Table 4

[0052] In this embodiment, considering that Decision Maker - 1 exhibits different preference characteristics during the acquisition processes of two different types of preferences, the resulting allocation schemes vary significantly in terms of numerical values, but the total penalty values achieved are relatively close. The above results do not affect the simplification of the solution process by the "fairness" and "efficiency" indicators proposed in the present invention, and provide an accurate allocation scheme for water resource allocation decision makers. Therefore, the method involved in this application can effectively handle the "fairness" and "efficiency" trade - offs in the multi - objective problem of water resource allocation. While unifying the dimensions of the two types of heterogeneous objectives, it can also eliminate the increased difficulty in solving the original multi - objective problem caused by "non - differentiability".

Claims

1. A method for dealing with multiple objectives of efficiency and fairness in water resource allocation, characterized in that: The following steps are involved: S1. Based on the watershed information, the fairness coefficient is constructed, and based on the Gini impurity of the classification regression tree, the fairness index of water resource allocation is calculated using the fairness coefficient; S2. Calculate the efficiency loss based on the fairness cost and obtain the water resources allocation and utilization efficiency index; S3. Set necessary constraints for water resource allocation; S4. Based on the trade-off between fairness and efficiency, a multi-objective model of water resource allocation is constructed according to the water resource allocation fairness index and water resource allocation utilization efficiency index, combined with the constraints of water resource allocation; S5. According to the decision maker's preference information, the multi-objective model of water resources allocation is transformed into a single-objective model of water resources allocation and solved to obtain the optimal water resources allocation plan.

2. The method for dealing with multiple objectives of efficiency and fairness in water resource allocation according to claim 1, characterized in that: The S1 comprises the following steps: S101. Construct a fairness coefficient based on the total population of the sub-region, the water resource demand of the sub-region, and the water resource demand of the water-using sector; S102, normalizing the fairness coefficient to obtain a normalized fairness coefficient; S103, based on the Gini impurity of the classification and regression tree, the normalized fairness coefficient is used for calculation to obtain the first-stage Gini coefficient; S104, adjusting the first-stage Gini coefficient using a preset adjustment item to obtain an adjusted first-stage Gini coefficient; S105. Calculate the water resources allocation fairness index based on the adjusted first-stage Gini coefficient and fairness coefficient.

3. The method for dealing with multiple objectives of efficiency and fairness in water resource allocation according to claim 2, characterized in that: The expression of the normalized fairness coefficient is as follows: in, represents the fairness coefficient, represents the normalized fairness coefficient, Indicates the allocation of watersheds to sub-regions Water use sector The total amount of water resources, represents a sub-region, Indicates the water use department, M represents the maximum number of sub-regions, N represents the number of the largest water-consuming sectors, Represents the object participating in the fairness calculation, Indicates shared M sub-regions, the calculation object is the sub-region; Indicates shared N The calculation object is the water-using department; hour, represents the total population of the sub-region and the water resource demand of the sub-region. hour, Represents the water resource demand of water-using sectors.

4. The method for dealing with multiple objectives of efficiency and fairness in water resource allocation according to claim 3, characterized in that: The expression of the water resource allocation fairness index calculated is as follows: in, represents the adjusted first-stage Gini coefficient, which is an indicator of fairness. express part, represents the first-stage Gini coefficient.

5. The method for dealing with multiple objectives of efficiency and fairness in water resource allocation according to claim 4, characterized in that: The S2 is specifically: According to the principle of fairness, the unit water use efficiency value of the water use departments in the sub-region and the maximum unit water use efficiency value of the water use departments, the efficiency loss is calculated based on the fairness cost to obtain the water resources allocation and utilization efficiency index.

6. The method for dealing with multiple objectives of efficiency and fairness in water resource allocation according to claim 5, characterized in that: The expression for calculating efficiency loss based on fairness cost is as follows: in, represents the fairness cost of water resource allocation, represents the maximum unit water efficiency value of all water-using departments in all sub-regions, Indicates sub-area Water use sector Unit water efficiency value.

7. The method for dealing with multiple objectives of efficiency and fairness in water resource allocation according to claim 6, characterized in that: The S3 is specifically: According to the planned maximum value of the overall water resources allocation of the basin, set the total water resources allocation limit for the water users in the sub-region; According to the planned maximum value of water resources allocation to the economic water sector of the sub-region, an upper limit of the total amount of water resources allocation to the economic water sector of the sub-region is set; According to the water supply capacity of the sub-region, set the upper limit of the total amount of water resources allocated to the sub-region; Based on the minimum water resource demand of the water-using departments in the sub-region, a lower limit of the total amount of water resources allocated to the water-using departments in the sub-region is set.

8. The method for dealing with multiple objectives of efficiency and fairness in water resource allocation according to claim 7, characterized in that: The expression for the upper limit of the total amount of water resources allocated to the water-using departments in the sub-region is as follows: in, C It represents the planned maximum value of the overall water resource allocation of the basin; The expression for the upper limit of the total amount of water resources allocated to the economic water sector in the sub-region is as follows: in, It represents the planned maximum value of water resource allocation for all economic water-using sectors in all sub-regions; The expression of the upper limit of the total amount of water resources allocated to the sub-region is as follows: in, Indicates sub-area Water supply capacity; The expression for the lower limit of the total amount of water resources allocated to water-using departments in the sub-region is as follows: in, Indicates sub-area Water use sector minimum water demand.

9. The method for dealing with multiple objectives of efficiency and fairness in water resource allocation according to claim 8, characterized in that: The expression of the multi-objective model of water resources allocation is as follows: in, represents minimization, represents the adjusted first-stage Gini coefficient.

10. The method for dealing with multiple objectives of efficiency and fairness in water resource allocation according to claim 1, characterized in that: The S5 is specifically: According to the preference information of decision makers, the multi-objective model of water resources allocation is transformed into a single-objective model of water resources allocation by considering the target programming method of different types of preference information. The planning software is used to solve the single-objective model of water resource allocation, obtain the optimal water resource allocation plan, and complete the multi-objective processing of efficiency and fairness in water resource allocation; The target programming methods for different types of preference information include: a weight-based target programming method and an S-type penalty function-based target programming method.

Images