Two-layer robust optimal distribution method considering uncertainty of water resources

Abstract

The invention discloses a two-layer robust optimization allocation method considering uncertainty of water resources, which comprises the following steps: constructing a water resource life cycle model, integrating historical meteorological and hydrological data, and outputting a nominal value of total available water amount; establishing a two-layer robust optimization global model of water resource distribution of the watershed layer according to the nominal value of the total available water amount; an affine adjustable robust peer-to-peer method is adopted to convert the two-layer robust optimization global model into a planning problem which can be directly solved, and an accurate solution is obtained through planning software; and further changing the adjustable robust parameter value, solving the planning model in combination with a policy-driven scene, and generating a dynamic water resource adaptability allocation scheme. Based on the water resource life cycle model, the method can more accurately estimate the nominal value of the total available water consumption, further forms a support set of the total available water consumption for constructing a two-layer robust optimization global model, effectively solves the problem of two-layer water resource distribution under the condition of uncertain water resource availability, and helps a decision maker to obtain an accurate solution.

Description

Technical Field

[0001] The present invention belongs to the technical field of water resource allocation, and in particular relates to a two-layer robust optimization allocation method considering water resource uncertainty. Background Art

[0002] As global climate change intensifies, river basin water resources systems face high uncertainty in the meteorological and hydrological environment, such as fluctuations in precipitation and rising evaporation. At the same time, socioeconomic development has led to supply-demand conflicts, including population growth and expanding industrial demand. Fluctuations in average annual precipitation in some river basins and growing industrial water demand in densely populated areas have caused traditional water allocation schemes to frequently fail. These challenges are particularly severe in developing countries, necessitating a water resources planning approach that can dynamically adapt to these uncertainties.

[0003] Existing technologies attempt to address these issues through mathematical optimization models, but they face numerous limitations in coping with uncertain decision-making. First, traditional deterministic models assume fixed parameters and cannot account for random perturbations in meteorological factors such as precipitation and evaporation. Stochastic optimization methods, on the other hand, rely on precise probability distributions, but in reality, the probability density functions of these meteorological data are difficult to obtain. Fuzzy programming requires pre-set membership functions, which are highly subjective and cannot quantify the risk of abrupt climate change. Second, river basin management agencies must strike a balance between overall fairness and regional efficiency, but single-layer optimization models typically only optimize for a single objective, leading to a conflict between fairness and efficiency. For example, traditional interval robust optimization, in order to ensure worst-case feasibility, may excessively reduce water allocations, thereby sacrificing economic benefits. Furthermore, existing models ignore the dynamic nature of the water resource lifecycle and fail to integrate real-time forecast data and policy adjustments, limiting the flexibility and adaptability of the solutions.

[0004] While recent research has improved to some extent, significant bottlenecks and limitations remain. Many studies are still based on static models. In addition, traditional robust optimization methods use a "boxed" uncertainty set to ensure the feasibility of the solution, resulting in overly conservative allocation schemes and severe loss of benefits. While adjustable robust optimization has reduced conservatism to a certain extent, it fails to incorporate dynamic policy scenarios and cannot assess the effectiveness of technological improvements in alleviating the supply-demand gap. More importantly, existing research focuses primarily on model construction and lacks quantitative analysis of policy variables such as water-saving technologies and resident behavior, resulting in poor implementation of the scheme in practical applications. Summary of the Invention

[0005] To address the aforementioned shortcomings of the existing technology, the present invention provides a two-level robust optimization allocation method that considers water resource uncertainty. This method utilizes the Affine Adjustable Robust Correspondence (AARC) technique to transform complex nonlinear models with uncertain parameters into a directly solvable planning problem. By varying the values ​​of adjustable robust parameters and incorporating policy-driven scenarios, the method quantifies the impact of water-saving technology improvements and residents' willingness to comply with policies on allocation outcomes, generating a dynamic, adaptive water resource allocation solution. Based on a water resource lifecycle model, the present invention more accurately estimates the nominal value of total available water, thereby forming a support set of total available water for constructing a two-level robust optimization global model. The present invention utilizes the Affine Adjustable Robust Correspondence method to address the uncertain parameters in the model, converting the uncertain model into a deterministic model for solution, making it easier to obtain an exact solution. Furthermore, solving the model under different planning scenarios and adjustable robust parameters demonstrates the adaptability and robustness of the resulting exact solution from multiple perspectives. In summary, the present invention effectively addresses two-level water resource allocation problems under uncertain water resource availability and helps decision makers obtain an exact solution.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a two-layer robust optimization allocation method considering the uncertainty of water resources, comprising the following steps: S1. Construct a water resources life cycle model, integrate historical meteorological and hydrological data, output the nominal value of total available water, and then form a support set of total available water; S2. Establish a two-level robust optimization global model for water resource allocation at the basin level based on the support set of total available water; S3. Using the affine adjustable robust equivalence method, the two-layer robust optimization global model is transformed into a directly solvable planning problem, and the exact solution is obtained through the planning software; S4. Further change the values ​​of adjustable robust parameters, solve the planning model in combination with policy-driven scenarios, and generate a dynamic adaptive water resources allocation plan.

[0007] Further: S1 includes the following sub-steps: S11. In the water resource processing stage, the inflow and outflow are paired and expressed to calculate the nominal value of the total available water; S12. Define a support set of the total available water quantity according to the nominal value of the total available water quantity and the adjustable robust parameter.

[0008] Further: In S11, the nominal value of the total available water volume is calculated The specific expression is:

[0009] Where, is the uncertain effective precipitation, is the uncertain upstream inflow, The amount of water that can be recycled, is the overall utilization coefficient of river water resources; In S12, the support set The specific expression is:

[0010] Where, is the total available water, is an adjustable robust parameter.

[0011] Further: S2 includes the following sub-steps: S21. Construct an upper-level leader model and determine the objective function and constraints of the upper-level leader model; S22, constructing a lower-level follower model, and determining the objective function and constraints of the lower-level follower model; S23. Construct a two-layer robust optimization global model for water resources allocation at the basin level based on the upper-layer leader model and the lower-layer follower model.

[0012] Furthermore: In S21, the objective function of the upper leader model is expressed as:

[0013] Where, G For fair distribution of water resources, For partition The effective distribution water volume after deducting the total loss, I is the number of all partitions, Represents a partition u The effective distribution water volume after deducting the total loss, Represents a partition z The effective distribution water volume after deducting the total loss, and Indicates two different partitions among all partitions, For partition Total number of water users, For partition Total number of water users, For partition Total number of water users; The constraints of the upper-level leader model are as follows: The first water resource availability limit is expressed as:

[0014] Where, Assign to partition for upper layer Total water volume; The water demand constraint is expressed as:

[0015] Where, is the minimum water requirement; In S22, the objective function of the lower-level follower model is expressed as:

[0016] Where, max To maximize, P To allocate the total benefits of economic water resources, For industrial water consumption, For domestic water consumption, For agricultural water use, For the unit benefit of industrial water use, For the unit benefit of domestic water use, Unit benefits for agricultural water use; The constraints of the lower-level follower model are as follows: The second water resource availability limit is expressed as:

[0017] Where, It is ecological water consumption; The minimum water demand limit is expressed as:

[0018]

[0019]

[0020] Where, To obtain the minimum function, is the industrial water demand, is the agricultural water demand, Water demand for life; The water conservation policy limit is expressed as:

[0021]

[0022]

[0023] Where, For industrial water quotas, For agricultural water quotas, Allotment of water for domestic use; The ecological water demand limit is expressed as:

[0024]

[0025] Where, is the ecological water demand, is the maximum value function.

[0026] Furthermore: In S23, the two-layer robust optimization global model for water resources allocation at the basin level is expressed as:

[0027] Where, is a constraint condition.

[0028] Further: S3 includes the following sub-steps: S31. Convert the two-level robust optimization global model into a single-level programming model by replacing each follower's problem with a Carlo-Kuhn-Tucker condition. S32. In the typical case of uncertainty in the total available water quantity on the right side of a single-level programming model, its affine adjustable robust equivalent model is solved to obtain a directly solvable programming model.

[0029] Furthermore: In S31, the expression of the single-layer planning model is specifically:

[0030] Where, , , , , , and For the corresponding constraints , , , , , and The dual variable of the original decision variable , , , , is converted into its affine function, including: , , , and ; in, is the nominal value for a given available water quantity, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of the non-adjustable variable.

[0031] Furthermore: In S32, the directly solvable planning model expression is obtained as follows:

[0032] Where, is the time corresponding to the timing uncertainty parameter, is the total time, is an adjustable robust parameter, is the first relevant parameter, is the second relevant parameter, is the third relevant parameter, is the fourth related parameter, is the fifth related parameter, is the sixth related parameter, is the seventh related parameter; is the control parameter of the first related parameter, is the control parameter of the second related parameter, is the control parameter of the third related parameter, is the control parameter of the fourth related parameter, is the control parameter of the fifth related parameter, is the control parameter of the sixth related parameter, is the control parameter of the seventh related parameter; .

[0033] Further: S4 is specifically: According to different scenarios under water resources allocation-related policies, the relevant parameters and adjustable robust parameters in the planning model are changed to obtain water resources allocation plans under different policy-driven scenarios as dynamic water resources adaptive allocation plans.

[0034] The beneficial effects of the present invention are: (1) This invention provides a two-layer robust optimization allocation method that considers water resource uncertainty. Based on the water resource life cycle model, this invention can more accurately estimate the nominal value of the total available water volume, thereby forming a support set of the total available water volume for constructing a two-layer robust optimization global model and effectively handling the two-layer water resource allocation problem under uncertain water resource availability. This provides a more reliable basis for decision-making in the face of water resource uncertainty and enhances the model's ability to reflect the actual water resource situation.

[0035] (2) The two-layer robust optimization global model proposed in this paper effectively balances the fairness and economic benefits of water resource allocation. The upper layer optimizes the Gini coefficient to maximize the fairness of distribution and ensure a reasonable increase in per capita water consumption across regions; the lower layer optimizes water quotas to improve overall water resource utilization efficiency. This dual optimization structure ensures a win-win situation of fairness and efficiency among different stakeholders.

[0036] (3) By combining policy-driven scenario analysis, this paper can quantify the impact of water-saving technology improvements and residents' willingness to follow policies on water resource allocation and generate dynamic adaptive solutions. This not only improves the model's responsiveness to policy changes and technological advances, but also provides in-depth insights and scientific decision-making support for future water resource management, ensuring that the long-term goal of sustainable river basin management is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flow chart of a two-layer robust optimization allocation method considering water resource uncertainty of the present invention.

[0038] Figure 2 It is a comprehensive structural diagram of the macro water resources life cycle model; Figure 3 To directly solve the planning model ( ) is a schematic diagram of the planning results.

[0039] Figure 4 To directly solve the planning model The following is a schematic diagram of the planning results.

[0040] Figure 5 To directly solve the planning model The following is a schematic diagram of the planning results.

[0041] Figure 6 Schematic diagram of water resource allocation under the baseline scenario.

[0042] Figure 7 Schematic diagram of the water resources allocation model planning results under different scenarios. DETAILED DESCRIPTION

[0043] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0044] like Figure 1 As shown, in one embodiment of the present invention, a two-layer robust optimization allocation method considering water resource uncertainty includes the following steps: S1. Construct a water resources life cycle model, integrate historical meteorological and hydrological data, output the nominal value of total available water, and then form a support set of total available water; S2. Establish a two-level robust optimization global model for water resource allocation at the basin level based on the support set of total available water; S3. Using the affine adjustable robust equivalence method, the two-layer robust optimization global model is transformed into a directly solvable planning problem, and the exact solution is obtained through the planning software; S4. Further change the values ​​of adjustable robust parameters, solve the planning model in combination with policy-driven scenarios, and generate a dynamic adaptive water resources allocation plan.

[0045] S1 includes the following sub-steps: S11. In the water resource processing stage, the inflow and outflow are paired and expressed to calculate the nominal value of the total available water; S12. Define a support set of the total available water quantity according to the nominal value of the total available water quantity and the adjustable robust parameter of the random parameter.

[0046] In S11, calculate the nominal value of total available water The specific expression is:

[0047] Where, is the uncertain effective precipitation, is the uncertain upstream inflow, The amount of water that can be recycled, is the overall utilization coefficient of river water resources; In this embodiment, the precipitation history can be used to predict the Without considering extreme natural disasters such as floods, Considered as a steady annual inflow. It is determined by the water use in the previous year, i.e. the total water use, the amount of wastewater generated and treated, and the amount of water effectively recycled. Finally, the overall availability coefficient of river water resources is calculated using It represents the availability of water resources in the basin.

[0048] In S12, the support set The specific expression is:

[0049] Where, is the total available water, is an adjustable robust parameter that represents the degree to which managers are willing to accept uncertainty in climate change.

[0050] S2 includes the following sub-steps: S21. Construct an upper-level leader model and determine the objective function and constraints of the upper-level leader model; S22, constructing a lower-level follower model, and determining the objective function and constraints of the lower-level follower model; S23. Construct a two-layer robust optimization global model for water resources allocation at the basin level based on the upper-layer leader model and the lower-layer follower model.

[0051] In S21, the objective function of the upper leader model is expressed as:

[0052] Where, G For fair distribution of water resources, For partition The effective distribution water volume after deducting the total loss, I is the number of all partitions, Represents a partition u The effective distribution water volume after deducting the total loss, Represents a partition z The effective distribution water volume after deducting the total loss, and Indicates two different partitions among all partitions, For partition Total number of water users, For partition Total number of water users, For partition Total number of water users; In water resource allocation, attention should be paid to equitable access to water resources for all water users in each sub-region, so as to reduce the gap between high water stress areas (large populations sharing limited water resources) and low water stress areas (small populations sharing abundant water resources). , then the water resources distribution among the zones is considered to be completely equal. At this time, there is no difference in the per capita water consumption of each zone, that is, the access to water resources is completely fair.

[0053] The constraints of the upper-level leader model are as follows: To ensure basic feasibility, the upper layer is allocated to the partition The total amount of water cannot exceed the total available water, and the total available water is uncertain. The first water resource availability limit is expressed as:

[0054] Where, Assign to partition for upper layer Total water volume; Before allocating water resources, there is always a trade-off between water supply and demand. Set the range constraint. That is, assign it to the partition The total water volume must be greater than or equal to , the water resource demand constraint is expressed as:

[0055] Where, is the minimum water requirement; Regional managers are more concerned about the overall benefits of allocating water resources to different sectors. For industry, water resources are mainly used for production, manufacturing and other industrial activities, which is recorded as industrial water consumption. Ecological water consumption Ensure the protection of the hydrological environment. and agricultural water use It is vital to local residents.

[0056] In S22, the objective function of the lower-level follower model is expressed as:

[0057] Where, max To maximize, P To allocate the total benefits of economic water resources, For industrial water consumption, For domestic water consumption, For agricultural water use, For the unit benefit of industrial water use, For the unit benefit of domestic water use, Unit benefits for agricultural water use; The constraints of the lower-level follower model are as follows: The second water resource availability limit is expressed as:

[0058] Where, It is ecological water consumption; To ensure the basic needs of industry, agriculture and life, the amount of water allocated should be greater than the minimum water demand. The minimum water demand limit is expressed as:

[0059]

[0060]

[0061] Where, is the minimum value function, which represents the minimum threshold value. is the industrial water demand, is the agricultural water demand, Water demand for life; Water conservation has long been a key issue in water resource management, with local regulations on total water use. In this study, total water use for industry and agriculture is limited by setting a maximum water use quota (i.e., water quota) before the planning year to support water conservation policies. The water conservation policy limit is expressed as:

[0062]

[0063]

[0064] Where, For industrial water quotas, For agricultural water quotas, Allotment of water for domestic use; Ecological water demand has long been squeezed, which is detrimental to the basin's ecological environment. Therefore, a minimum water demand constraint is set to ensure an adequate supply of ecological water. In some cases, overemphasizing ecological water demand may exacerbate water shortages and even affect the basic supply of domestic water. Therefore, another constraint is set on the maximum ecological water demand. The ecological water demand constraint is expressed as:

[0065]

[0066] Where, is the ecological water demand, is the maximum value function.

[0067] In S23, the two-level robust optimization global model for water resources allocation at the basin level is expressed as:

[0068] Where, is a constraint condition.

[0069] S3 includes the following sub-steps: S31. Convert the two-level robust optimization global model into a single-level programming model by replacing each follower's problem with a Carlo-Kuhn-Tucker condition. S32, the total available water volume with uncertainty on the right side of the single-level planning model In the typical case of , solving its affine tunable robust counterpart leads to a directly solvable planning model.

[0070] In S31, the expression of the single-level planning model is specifically:

[0071] Where, , , , , , and For the corresponding constraints , , , , , and The dual variable of the original decision variable , , , , is converted into its affine function, including: , , , and ; in, is the nominal value for a given available water quantity, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of the non-adjustable variable.

[0072] In S32, the directly solvable planning model expression is obtained as follows:

[0073] Where, is the time corresponding to the timing uncertainty parameter, is the total time, is an adjustable robust parameter, is the first relevant parameter, is the second relevant parameter, is the third relevant parameter, is the fourth related parameter, is the fifth related parameter, is the sixth related parameter, is the seventh related parameter; is the control parameter of the first related parameter, is the control parameter of the second related parameter, is the control parameter of the third related parameter, is the control parameter of the fourth related parameter, is the control parameter of the fifth related parameter, is the control parameter of the sixth related parameter, is the control parameter of the seventh related parameter; .

[0074] S4 is specifically: According to different scenarios under water resources allocation-related policies, the relevant parameters and adjustable robust parameters in the planning model are changed to obtain water resources allocation plans under different policy-driven scenarios as dynamic water resources adaptive allocation plans.

[0075] In this embodiment, the present invention provides a specific analysis case, taking 13 prefecture-level cities in Sichuan Province and their corresponding water use as case study objects, and applying a two-layer robust optimization model to solve the water resource allocation problem.

[0076] Case Background As the Tuojiang River flows through industrial cities such as Luzhou, Neijiang, Ziyang, Jianyang, Chengdu, and Deyang in Sichuan Province, it must balance industrial water consumption across regions. Furthermore, the Tuojiang River faces water resource issues such as inefficient water allocation and water pollution.

[0077] Result Analysis according to Figure 2 The water resources life cycle model shown in the figure is used to calculate the water resources in the Sichuan Basin in 2020. The estimated value is 235.035×10 8 cubic meter.

[0078] refer to Figure 3-Figure 5 ,and Figure 3 compared to, Figure 4 and Figure 5 shows how outcomes vary depending on managers’ attitudes toward climate change uncertainty. When , the manager may support the decision to change the water availability within the range [-5%, +5%]. In this case, the worst case is a 5% decrease in total water availability. Similarly, in robust planning, when 、 and The worst case scenario is that the available water volume is reduced by 10%, 15% and 20% respectively. The impact of climate change causes limited changes in the total amount of water allocated to the sub-region and results in proportional changes in the data columns. Figure 4 The broken line in the figure is drawn based on the per capita water consumption under different meteorological disturbance levels. As the water consumption in different regions increases, the gap between them may widen, while the per capita water consumption in backward areas such as Ziyang and Neijiang remains the same. Figure 5 It can be found that as the total available water volume decreases, only the domestic water consumption continues to decrease. This is because the constraints are designed to prioritize the protection of a livable environment for residents.

[0079] In the scenario analysis, consider the following scenarios: Scenario 1 is based on a scenario of rapid population growth and economic development. This scenario faces more risks due to the significant increase in water demand for industry and life. Scenario 2 shows how water-saving technology advancements can alleviate the water resource pressure caused by the increase in water demand in Scenario 1. In this paper, water-saving technology advancements include various measures, namely avoiding unnecessary waste in water resource allocation and improving water recycling efficiency. Specifically, in robust planning, , improve the water resources life cycle model 、 and , with increases of 20%. If the improved value exceeds the range [0,1], the boundary value prevails. Scenario 3 tests citizens' willingness to conserve water under relevant policies. This paper reflects citizens' willingness to conserve water by measuring the effectiveness of policy implementation. Assume that initially, only 60% of water users firmly support the new water-saving policy, while the other 40% do not. Local residents with a strong desire to conserve water strictly adhere to the government-mandated quota; conversely, others maintain their average water consumption prior to the planned year (i.e., 2019). Compared to Scenario 1, Scenario 4 comprehensively considers advances in water-saving technology and citizens' willingness to support the current policy.

[0080] Table 1 Scenario parameter settings

[0081] Scenario S0 serves as a control group. In this scenario, no additional measures are taken to alleviate possible water pressure. Water pressure is reflected by total water consumption, industrial water consumption, domestic water consumption and ecological water consumption. Scenario S1 is set as a rapid population growth and rapid economic development. Since the water demand for industry and life will increase significantly, this scenario will face more risks. Scenario S2 shows how water-saving technology progress can alleviate the water resource pressure caused by the increase in water demand in scenario S1. In this article, water-saving technology progress covers a variety of measures, namely avoiding unnecessary waste in water resource allocation and improving the recycling efficiency of water. Specifically, in robust planning, improving , improve the water resources life cycle model 、 and , with increases of 20%. If the improved value exceeds the range [0,1], the boundary value prevails. Scenario S3 tests citizens' willingness to conserve water under relevant policies. This paper reflects citizens' willingness to conserve water by measuring the effectiveness of policy implementation. Assume that initially, only 60% of water users firmly support the new water-saving policy, while the other 40% do not. Local residents with a strong desire to conserve water strictly adhere to the government-mandated quota; conversely, others maintain their average water consumption prior to the planned year (i.e., 2019). Compared to S1, Scenario S4 comprehensively considers both advances in water-saving technology and citizens' willingness to support the current policy.

[0082] from Figure 6 and Figure 7 The results show that the robust planning results mostly exceed the designated water quotas for each region, with only some regions meeting the baseline water conservation policy established in 2013. This means that the robust planning solutions are not feasible given the water conservation policy designed in 2013. Therefore, current policies must be re-examined in light of current water use patterns. Compared to Chengdu, Ya'an, Meishan, and Liangshan, the gap between projected water use and actual demand in Ziyang, Neijiang, and Luzhou is significantly larger.

[0083] Figure 7 It shows how the actual effects of technological progress and water conservation policies affect these gaps. First, let's look at scenario 1. Figure 7 (a) shows the impact of possible population growth and economic development on future water demand. Figure 6 In this case, the gap between water supply and limited water use is further narrowed, which indicates that the water supply pressure is greater because the growing demand is approaching the actual water supply in the planned year. Next, try to find solutions to alleviate the possible water supply pressure. There are two basic measures, namely the relevant water-saving technological progress and the willingness of citizens to take water-saving actions. The former improves the feasibility of water supply by increasing the available water, and the latter reduces demand through the water-saving actions of citizens. In scenario two, technologies such as reducing unnecessary waste in the production process and improving recycling efficiency were applied. Through technological progress, the total available water volume increased by 2.6%. Figure 7 As shown in (b), water resource pressure has been alleviated to a certain extent, especially in Ziyang, Yibin and Luzhou, but Deyang, Ya'an and Leshan are still facing great water supply pressure. Then, in scenario three, the willingness of citizens to comply with water-saving policies is improved. Figure 7 As shown in (c), the current gap is further narrowed compared to Scenario 2. In this scenario, 80% of local residents are willing to save water in accordance with policy regulations, and only 20% remain unchanged. Obviously, this is more effective than simply promoting technological progress. Finally, Figure 7(d) shows how these two measures work together to alleviate water stress in Scenario 4. It can be seen that the overall effect of these actions in narrowing the gap has doubled, as the overall water stress caused by accelerated population growth and economic development has been significantly alleviated.

[0084] In the description of the present invention, it should be understood that the terms "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only and cannot be understood as indicating or implying the relative importance or the number of technical features implicitly specified. Therefore, the features defined by "first", "second", and "third" may explicitly or implicitly include one or more of such features.

Claims

1. A two-layer robust optimization allocation method considering water resource uncertainty, characterized by: The following steps are involved: S1. Construct a water resources life cycle model, integrate historical meteorological and hydrological data, output the nominal value of total available water, and then form a support set of total available water; S2. Establish a two-level robust optimization global model for water resource allocation at the basin level based on the support set of total available water; S3. Using the affine adjustable robust equivalence method, the two-layer robust optimization global model is transformed into a directly solvable planning problem, and the exact solution is obtained through the planning software; S4. Further change the values ​​of adjustable robust parameters, solve the planning model in combination with policy-driven scenarios, and generate a dynamic adaptive water resources allocation plan.

2. The two-layer robust optimization allocation method considering water resource uncertainty according to claim 1 is characterized in that: S1 includes the following sub-steps: S11. In the water resource processing stage, the inflow and outflow are paired and expressed to calculate the nominal value of the total available water; S12. Define a support set of the total available water quantity according to the nominal value of the total available water quantity and the adjustable robust parameter.

3. The two-layer robust optimization allocation method considering water resource uncertainty according to claim 2 is characterized in that: In S11, calculate the nominal value of total available water The specific expression is: Where, is the uncertain effective precipitation, is the uncertain upstream inflow, The amount of water that can be recycled, is the overall utilization coefficient of river water resources; In S12, the support set The specific expression is: Where, is the total available water, is an adjustable robust parameter.

4. The two-layer robust optimization allocation method considering water resource uncertainty according to claim 3 is characterized in that: S2 includes the following sub-steps: S21. Construct an upper-level leader model and determine the objective function and constraints of the upper-level leader model; S22, constructing a lower-level follower model, and determining the objective function and constraints of the lower-level follower model; S23. Construct a two-layer robust optimization global model for water resources allocation at the basin level based on the upper-layer leader model and the lower-layer follower model.

5. The two-layer robust optimization allocation method considering water resource uncertainty according to claim 4 is characterized in that: In S21, the objective function of the upper leader model is expressed as: Where, G For fair distribution of water resources, For partition The effective distribution water volume after deducting the total loss, I is the number of all partitions, Represents a partition u The effective distribution water volume after deducting the total loss, Represents a partition z The effective distribution water volume after deducting the total loss, and Indicates two different partitions among all partitions, For partition Total number of water users, For partition Total number of water users, For partition Total number of water users; The constraints of the upper-level leader model are as follows: The first water resource availability limit is expressed as: Where, Assign to partition for upper layer Total water volume; The water demand constraint is expressed as: Where, is the minimum water requirement; In S22, the objective function of the lower-level follower model is expressed as: Where, max To maximize, P To allocate the total benefits of economic water resources, For industrial water consumption, For domestic water consumption, For agricultural water use, For the unit benefit of industrial water use, For the unit benefit of domestic water use, Unit benefits for agricultural water use; The constraints of the lower-level follower model are as follows: The second water resource availability limit is expressed as: Where, It is ecological water consumption; The minimum water demand limit is expressed as: Where, To obtain the minimum function, is the industrial water demand, is the agricultural water demand, Water demand for life; The water conservation policy limit is expressed as: Where, For industrial water quotas, For agricultural water quotas, Allotment of water for domestic use; The ecological water demand limit is expressed as: Where, is the ecological water demand, is the maximum value function.

6. The two-layer robust optimization allocation method considering water resource uncertainty according to claim 5 is characterized in that: In S23, the two-level robust optimization global model for water resources allocation at the basin level is expressed as: Where, is a constraint condition.

7. The two-layer robust optimization allocation method considering water resource uncertainty according to claim 6 is characterized in that: S3 includes the following sub-steps: S31. Convert the two-level robust optimization global model into a single-level programming model by replacing each follower's problem with a Carlo-Kuhn-Tucker condition. S32. In the typical case of uncertainty in the total available water quantity on the right side of a single-level programming model, its affine adjustable robust equivalent model is solved to obtain a directly solvable programming model.

8. The two-layer robust optimization allocation method considering water resource uncertainty according to claim 7 is characterized in that: In S31, the expression of the single-level planning model is specifically: Where, , , , , , and For the corresponding constraints , , , , , and The dual variable of the original decision variable , , , , is converted into its affine function, including: , , , and ; in, is the nominal value for a given available water quantity, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of cannot be adjusted variable, is the corresponding decision variable The affine function variable of , is the corresponding decision variable The affine function of the non-adjustable variable.

9. The two-layer robust optimization allocation method considering water resource uncertainty according to claim 8 is characterized in that: In S32, the expression of the planning model that can be directly solved is: Where, is the time corresponding to the timing uncertainty parameter, is the total time, is an adjustable robust parameter, is the first relevant parameter, is the second relevant parameter, is the third relevant parameter, is the fourth related parameter, is the fifth related parameter, is the sixth related parameter, is the seventh related parameter; is the control parameter of the first related parameter, is the control parameter of the second related parameter, is the control parameter of the third related parameter, is the control parameter of the fourth related parameter, is the control parameter of the fifth related parameter, is the control parameter of the sixth related parameter, is the control parameter of the seventh related parameter; 。 10. The two-layer robust optimization allocation method considering water resource uncertainty according to claim 1 is characterized in that: S4 is specifically: According to different scenarios and relevant policies of water resource allocation, by changing the relevant parameters and adjustable robust parameters in the planning model, water resource allocation plans under different scenarios are obtained, namely, dynamic adaptive water resource allocation plans.

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