Multi-target water resource distribution method based on non-linear precision preference of decision maker

Abstract

The invention provides a multi-target water resource distribution method based on non-linear precision preference of a decision maker, and relates to the technical field of water resource distribution, and the method comprises the steps: constructing an initial multi-target water resource distribution model; analyzing the nonlinear precise preference of the decision maker to obtain a piecewise linear penalty function; adjusting the initial multi-target water resource distribution model by using a piecewise linear penalty function to obtain a multi-target water resource distribution model; and the multi-target water resource distribution model is utilized to analyze the target drainage basin water resource data, a water resource distribution result is obtained, and multi-target water resource distribution is completed. The problem that multi-target water resources are difficult to distribute reasonably is solved.

Description

Technical Field

[0001] This specification relates to the technical field of water resource allocation, and particularly to a multi-objective water resource allocation method based on the non-linear precise preferences of decision-makers. Background Art

[0002] The fairness-efficiency trade-off in water resource allocation is a major challenge, especially when decision-makers hope to obtain a deterministic optimal solution. Although these two objectives are equally important in some cases, due to the inevitable "cost of choice", they often conflict. This means that achieving fairness usually comes at the expense of efficiency, and vice versa. It is particularly difficult for decision-makers who are concerned about both fairness and efficiency to find an optimal solution.

[0003] In methods for processing multi-objective problems using non-linear precise preference information of decision-makers, the modeling method based on rough preferences uses weights to represent the preferences of water resource managers. Representative methods include the weighted method and the goal programming model. The modeling method based on precise preferences uses relatively complex penalty functions, such as the interval goal programming model. Compared with the goal programming model that uses limited weight information, the interval goal programming model provides richer preference information through interval-type penalty functions and can be adjusted according to the different needs of water resource managers.

[0004] Since the behavior of decision-makers is often non-linear, especially when the decision involves risks, when we consider the choice of decision-makers between two conflicting objectives as risky, their preferences are likely to be non-linear. However, there is currently no research discussing how to select an appropriate type of penalty function in the modeling method based on precise non-linear preferences. In addition, due to this technical gap, only a small number of numerical cases use the modeling method based on precise preferences to solve multi-objective optimization problems, lacking its application in real cases. Summary of the Invention

[0005] In view of the above deficiencies in the prior art, a multi-objective water resource allocation method based on the non-linear precise preferences of decision-makers provided by the present invention solves the problem of difficult rational allocation of multi-objective water resources.

[0006] To achieve the above invention objective, the technical solution adopted by the present invention is: a multi-objective water resource allocation method based on the non-linear precise preferences of decision-makers, including: S1: Construct an initial multi-objective water resource allocation model; S2: Analyze the non-linear precise preferences of decision-makers to obtain a piecewise linear penalty function; S3: Use the piecewise linear penalty function to adjust the initial multi-objective water resource allocation model to obtain a multi-objective water resource allocation model; S4: Analyze the water resource data of the target basin using the multi-objective water resource allocation model to obtain the water resource allocation result, and complete the multi-objective water resource allocation.

[0007] The beneficial effects of the present invention are as follows: A multi-objective water resource allocation method based on the non-linear precise preference of decision-makers. (1) It can handle any penalty function, thus solving the multi-objective optimization problem and effectively dealing with the refined penalty function generated based on the real and non-linear preferences of decision-makers. (2) By adopting the precise non-linear preferences of decision-makers, it can reduce the total penalty value added by decision-making based on rough preferences, thereby helping water resource allocation decision-makers obtain a deterministic optimal and satisfactory allocation plan.

[0008] Furthermore, the initial multi-objective water resource allocation model includes: The initial multi-objective water resource allocation model includes: Maximization fairness objective function for the population of each sub-region: ; ; Wherein, represents the maximization fairness for the population of each sub-region, represents the fairness parameter related to the population of the sub-region, represents the th sub-region of the target basin, represents the number of sub-regions in the target basin, represents the resource allocation of the th water use department in the th sub-region, represents the th water use department, represents the number of water use departments, represents the total population of the th sub-region of the target basin; Maximization fairness objective function for the water resource demand of each sub-region: ; ; Wherein, represents the maximization fairness for the water resource demand of each sub-region, represents the fairness parameter related to the water resource demand of the sub-region, represents the total water resource demand of the th sub-region of the target basin; Maximization efficiency objective function for maximizing the difference in water allocation for each water use department: ; ; Among them, represents the maximum efficiency of maximizing the difference in water volume allocation to each water-using department, represents the fairness parameter related to the difference in water volume allocation to water-using departments, represents the th water-using department's total water resource demand; Maximum efficiency objective function: ; Among them, represents the maximum efficiency, represents the maximum average economic benefit of all resource allocations, represents the average economic benefit of resource allocation for the th water-using department in the th sub-region of the target basin; Technical constraints for water resource allocation:

[0009]

[0010]

[0011]

[0012] Among them, represents the planned maximum water resource usage, represents the economic water-using department, represents the planned maximum water resource usage of the economic water-using department, represents the maximum water resource supply capacity, represents the th sub-region of the target basin and the th water-using department's minimum resource demand.

[0013] The beneficial effects of Weight 2 are as follows: (1) By introducing multiple objective functions for maximizing the fairness of water resource allocation and maximizing the efficiency of water resource allocation, a multi-objective model that simultaneously considers the two decision-making objectives of fairness and efficiency is constructed. (2) By adding the necessary technical constraints for water resource allocation, the feasibility and interpretability of the obtained solution are enhanced, making the obtained water resource allocation plan more persuasive. (3) Based on the above objective functions and constraints, an initial multi-objective water resource allocation model that can be solved can be constructed.

[0014] Furthermore, the expression of the piecewise linear penalty function is: ; The expression of the piecewise linear penalty function constraint is as follows: ; ; ; ; ; ; Among them, represents the minimum value function, represents the weight of the th objective function, represents the penalty value corresponding to the th objective function value on the piecewise linear penalty function, represents the vector composed of the positive continuous variables of the corresponding penalty function segment, represents the th objective function, represents the number of objective functions, represents the th objective function value, represents the th th attribute value of the th objective function, represents the positive continuous variable, represents the th attribute value, represents the number of attribute values of the th objective function, represents the piecewise linear penalty function of the th objective function, represents the penalty value corresponding to the attribute value represents the binary variable, represents the first positive continuous variable, represents the first binary variable, represents the th positive continuous variable, represents the th binary variable, represents the th binary variable.

[0015] The beneficial effects of claim 3 are as follows: (1) It can convert the non-linear preference of the abstract water resource allocation decision into a mathematical model with a definite form. (2) By considering any piecewise linear penalty function, the penalty values corresponding to the objective function values can be calculated, which can flexibly reflect the decision-maker's preference at different levels of objective function realization. (3) Combined with the initial multi-objective water resource allocation model, the obtained model can effectively handle the multi-objective structure in the water resource allocation decision problem.

[0016] Further, the S3 includes: Adding the water resource allocation technical constraint conditions in the initial multi-objective water resource allocation model to the piecewise linear penalty function to obtain an improved interval goal programming algorithm; Based on the improved interval goal programming algorithm, adjusting the initial multi-objective water resource allocation model to obtain a multi-objective water resource allocation model.

[0017] The beneficial effects of claim 4 are as follows: (1) It can effectively eliminate the possible non-linear components in the model based on the improved interval goal programming algorithm. (2) It can improve the solution efficiency of the original water resource allocation model and enhance the decision-maker's satisfaction with the obtained solution.

[0018] Further, the expression of the multi-objective water resource allocation model is: ; Wherein, Represents the minimum value function, Represents the objective function value; The expression of the constraint conditions of the multi-objective water resource allocation model is: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; Among them, represents the weight of the th objective function, represents the penalty value corresponding to the th objective function value on the piecewise linear penalty function, represents the vector composed of the positive continuous variables of the corresponding penalty function segment, represents the th objective function, represents the number of objective functions, represents the th th attribute value of the th objective function, represents the positive continuous variable, represents the th th attribute value, represents the fairness of water resources allocation for the population in each sub-region, represents the fairness of water resources allocation for the water demand in each sub-region, represents the fairness of water resources allocation for the difference in water volume allocated to water use sectors, represents the water resources allocation efficiency, represents the piecewise linear penalty function of the th objective function, represents the penalty value corresponding to the attribute value, represents the binary variable, represents the first positive continuous variable, represents the first binary variable, represents the th positive continuous variable, represents the th binary variable, represents the th binary variable.

[0019] The beneficial effects of the weight 5 are: (1) It can integrate the initial multi-objective water resources allocation model and the piecewise linear function, and form a deterministic programming model that can obtain an accurate optimal solution. (2) It can efficiently solve the final model using a linear programming solver and obtain an accurate optimal solution that comprehensively considers the non-linear preferences of decision-makers. Description of the Drawings

[0020] This specification will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not restrictive. In these embodiments, the same numbers represent the same structures, where: Figure 1 is an exemplary flowchart of a multi-objective water resources allocation method based on the non-linear precise preference of decision-makers shown in some embodiments of this specification. Detailed implementation manners

[0021] 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 of ordinary skill 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 created using the concept of the present invention are within the scope of protection.

[0022] Embodiment Figure 1 is an exemplary flowchart of a multi-objective water resources allocation method based on the non-linear precise preference of decision-makers shown in some embodiments of this specification. As Figure 1 shown, the process includes the following steps. In some embodiments, the process can be executed by a processor.

[0023] S1: Construct an initial multi-objective water resources allocation model.

[0024] The initial multi-objective water resources allocation model is a mathematical model used to provide a target optimization direction for water resources allocation. For example, the initial multi-objective water resources allocation model can include a maximization fairness objective function for the population of each sub-region, a maximization fairness objective function for the water resources demand of each sub-region, a maximization efficiency objective function for maximizing the difference in the allocated water volume among each water use department, a maximization efficiency objective function, and water resources allocation technical constraints.

[0025] In some embodiments, the expression of the maximization fairness objective function for the population of each sub-region can be: ; ; where, represents the maximization fairness for the population of each sub-region, represents the fairness parameter related to the population of the sub-region, represents the th sub-region of the target basin, represents the number of sub-regions in the target basin, represents the th sub-region of the target basin and the Resource allocation for each water - using department Denote the th water - using department Denote the number of water - using departments Denote the total population of the th sub - region in the target basin

[0026] In some embodiments, the expression of the maximized fairness objective function for the water resource demands of each sub - region can be: ; ; Wherein, Denote the maximized fairness for the water resource demands of each sub - region Denote the fairness parameter related to the water resource demands of the sub - region Denote the th sub - region in the target basin

[0027] In some embodiments, the expression of the maximized efficiency objective function for the maximized difference in water volume allocation for each water - using department can be: ; ; Wherein, Denote the maximized efficiency for the maximized difference in water volume allocation for each water - using department Denote the fairness parameter related to the difference in water volume allocation for the water - using department Denote the th water - using department

[0028] In some embodiments, the expression of the maximized efficiency objective function can be: ; Wherein, Denote the maximized efficiency Denote the maximum average economic benefit of all resource allocations Denote the th sub - region in the target basin th water - using department

[0029] In some embodiments, the expression of the technical constraints for water resource allocation can be:

[0030]

[0031]

[0032]

[0033] Among them, represents the planned maximum water resource usage, represents the economic water use sector, represents the planned maximum water resource usage of the economic water use sector, represents the maximum water resource supply capacity, represents the th th sub-region in the target basin, and the minimum resource demand of the

[0034] S2: Analyze the non-linear precise preference of the decision maker to obtain a piecewise linear penalty function.

[0035] The non-linear precise preference of the decision maker is the decision preference reflected by the decision maker for each realization level of different objectives when facing multi-objective water resource allocation decisions. For example, corresponding to the th th attribute value of the th objective function, there is a corresponding penalty value to form a

[0036] non-linear function correspondence.

[0037] In some embodiments, the processor can obtain the non-linear precise preference of the decision maker regarding multi-objective water resource allocation decisions through expert interviews.

[0038] The piecewise linear penalty function is a piecewise function form reflecting the non-linear precise preference of the decision maker. and the penalty value ; By synthesizing the attribute values and penalty values of each segment, a piecewise linear penalty function is obtained.

[0039] In some embodiments, the expression of the piecewise linear penalty function can be: ; Among them, represents the minimum value function, represents the weight of the th objective function, represents the penalty value corresponding to the th objective function value on the piecewise linear penalty function, represents the positive continuous variable of the corresponding penalty function segment represents the An objective function, represents the number of objective functions.

[0040] In some embodiments, the expression of the piecewise linear penalty function constraint can be: ; ; ; ; ; ; where represents the value of the th objective function, represents the th attribute value of the th objective function, represents a positive continuous variable, represents the th attribute value, represents the number of attribute values of the th objective function, represents the piecewise linear penalty function of the th objective function, represents the penalty value corresponding to the attribute value , represents a binary variable, represents the first positive continuous variable, represents the first binary variable, represents the th positive continuous variable, represents the th binary variable, represents the th binary variable.

[0041] S3: Using the piecewise linear penalty function, adjust the initial multi-objective water resources allocation model to obtain a multi-objective water resources allocation model.

[0042] The multi-objective water resources allocation model is a model for planning the water resources allocation in the target area.

[0043] In some embodiments, the processor can implement S3 based on the following steps: Add the water resources allocation technical constraints in the initial multi-objective water resources allocation model to the piecewise linear penalty function to obtain an improved interval goal programming algorithm; Based on the improved interval goal programming algorithm, adjust the initial multi-objective water resources allocation model to obtain a multi-objective water resources allocation model.

[0044] The improved interval goal programming algorithm is an algorithm that adjusts the initial multi-objective water resources allocation model based on a piecewise linear penalty function.

[0045] In some embodiments, the expression of the multi-objective water resources allocation model can be: ; where, represents the minimum value function, represents the objective function value.

[0046] In some embodiments, the expression of the constraint conditions of the multi-objective water resources allocation model can be: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; where, represents the weight of the th objective function, represents the penalty value corresponding to the th objective function value on the piecewise linear penalty function, represents the vector composed of the positive continuous variables of the corresponding penalty function segment, represents the th objective function, represents the number of objective functions, represents the th attribute value of the th objective function, represents a positive continuous variable, represents the th attribute value, represents the number of attribute values of the th objective function, represents the fairness of water resources allocation for the population in each sub-region, represents the fairness of water resources allocation for the water demand in each sub-region, represents the fairness of water resources allocation for the difference in water volume allocated to water-using sectors, represents the th piecewise linear penalty function of the th objective function, represents the penalty value corresponding to the attribute value represents a binary variable, represents the first positive continuous variable, represents the first binary variable, represents the th positive continuous variable, represents the th binary variable, represents the th binary variable.

[0047] In some embodiments, the performance comparison results of the multi-objective water resources allocation model are shown in Table 1.

[0048] Table 1 Performance comparison results of the multi-objective water resources allocation model

[0049] S4: Using the multi-objective water resources allocation model, analyze the water resources data of the target basin to obtain the water resources allocation result and complete the multi-objective water resources allocation.

[0050] The water resources data of the target basin is data reflecting the division situation and water resources allocation situation of the target basin. For example, the water resources data of the target basin may include the resource allocation situations of the sub-regions of the target basin and each water-using sector.

[0051] The water resources allocation result is the actual water resources allocation result of each water-using sector in each sub-region of the target basin.

[0052] In some embodiments, the processor may input the water resources data of the target basin into the multi-objective water resources allocation model, calculate the optimal water resources allocation method, and obtain the water resources allocation result.

[0053] In some embodiments of this specification, a multi-objective water resource allocation method based on the non-linear precise preference of decision-makers is proposed. (1) It can handle any penalty function, thus solving multi-objective optimization problems and effectively dealing with the fine penalty function generated based on the real and non-linear preferences of decision-makers. (2) By adopting the precise non-linear preferences of decision-makers, it can reduce the total penalty value added by decision-making based on rough preferences, thereby helping decision-makers of water resource allocation obtain a deterministic optimal and satisfactory allocation plan.

Claims

1. A multi-objective water resources allocation method based on nonlinear exact preferences of decision makers, characterized by: include: S1: Construct an initial multi-objective water resources allocation model; S2: Analyze the nonlinear exact preferences of decision makers and obtain a piecewise linear penalty function; S3: using the piecewise linear penalty function, adjusting the initial multi-objective water resource allocation model to obtain a multi-objective water resource allocation model; S4: Analyze the water resource data of the target river basin using the multi-objective water resource allocation model to obtain water resource allocation results and complete the multi-objective water resource allocation.

2. The multi-objective water resources allocation method based on decision maker's nonlinear precise preference according to claim 1 is characterized in that: The initial multi-objective water resources allocation model includes: The objective function for maximizing fairness for the population of each sub-region is: ； ； in, represents the maximum fairness for the population of each sub-region, represents the fairness parameter related to the sub-region population, Indicates the target watershed sub-regions, represents the number of sub-regions in the target watershed, Indicates the target watershed In the sub-area resource allocation to each water-using sector, Indicates water use departments, represents the number of water-using sectors, Indicates the target watershed The total population of each sub-region; The objective function of maximizing fairness for water resource demand in each sub-region is: ； ； in, represents the maximum fairness of water resource demand in each sub-region, represents the fairness parameter related to the water resource demand of the sub-region, Indicates the target watershed Total water demand in each sub-region; The maximum efficiency objective function for maximizing the difference in water allocation to each water user is: ； ； in, represents the maximum efficiency of maximizing the difference in water allocation to each water user, represents the equity parameter related to differences in water allocation between water users, Indicates Total water demand of each water-using sector; Maximize efficiency objective function: ； in, represents maximum efficiency, represents the maximum average economic benefit of all resource allocations, Indicates the target watershed In the sub-area Average economic benefits of resource allocation to each water-using sector; Technical constraints on water resource allocation: in, represents the planned maximum water resource usage, represents the economic water use sector, It represents the maximum water resource usage planned by the economic water-using sector. represents the maximum water supply capacity, Indicates the target watershed In the sub-area minimum resource requirements for each water-using sector.

3. The multi-objective water resources allocation method based on decision maker's nonlinear precise preference according to claim 1 is characterized in that: The expression of the piecewise linear penalty function is: ； The expression of the piecewise linear penalty function constraint is: ； ； ； ； ； ； in, represents the minimum value function, Indicates The weight of the objective function, Indicates The penalty value corresponding to the objective function value on the piecewise linear penalty function, Represents a positive continuous variable corresponding to the penalty function segment The vector formed by Indicates The objective function, represents the number of objective functions, Indicates The objective function value, Indicates The objective function attribute values, represents a positive continuous variable, Indicates attribute values, Indicates The number of attribute values ​​of the objective function, Indicates A piecewise linear penalty function for the objective function, Represents attribute value The corresponding penalty value is represents a binary variable, represents the first positive continuous variable, represents the first binary variable, Indicates A positive continuous variable, Indicates binary variables, Indicates A binary variable.

4. The multi-objective water resources allocation method based on decision maker's nonlinear precise preference according to claim 2 is characterized in that: The S3 includes: Adding the water resource allocation technical constraints in the initial multi-objective water resource allocation model to the piecewise linear penalty function to obtain an improved interval objective programming algorithm; Based on the improved interval objective programming algorithm, the initial multi-objective water resource allocation model is adjusted to obtain a multi-objective water resource allocation model.

5. The multi-objective water resources allocation method based on decision maker's nonlinear precise preference according to claim 4 is characterized in that: The expression of the multi-objective water resources allocation model is: ； in, represents the minimum value function, represents the objective function value; The expression of the constraint condition of the multi-objective water resources allocation model is: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； in, Indicates The weight of the objective function, Indicates The penalty value corresponding to the objective function value on the piecewise linear penalty function, Represents a positive continuous variable corresponding to the penalty function segment The vector formed by Indicates The objective function, represents the number of objective functions, Indicates The objective function attribute values, represents a positive continuous variable, Indicates attribute values, Indicates The number of attribute values ​​of the objective function, represents the fairness of water resource allocation for the population of each sub-region, represents the fairness of water resource allocation for each sub-region’s water resource demand, represents the fairness of water resource allocation in terms of water allocation differences among water users, represents the efficiency of water resource allocation, Indicates A piecewise linear penalty function for the objective function, Represents attribute value The corresponding penalty value is represents a binary variable, represents the first positive continuous variable, represents the first binary variable, Indicates A positive continuous variable, Indicates binary variables, Indicates A binary variable.

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