Cross-regional watershed resource allocation optimization method based on longitudinal ecological compensation
By building a two-layer robust optimization model, the problem of unreasonable allocation of ecological protection costs and pollution discharges in cross-regional watershed management is solved, the fairness and economicality of water environment management is achieved, and the precise allocation of environmental resources is achieved.
Patent Information
- Application Number
- CN202510634971.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-16
- Publication Date
- 2025-08-15
AI Technical Summary
In water conservancy projects, due to uneven distribution of interests in upstream and downstream regions, complex water pollution control in basin management, lack of cross-regional environmental governance agreements and coordination mechanisms, the ecosystem and communities are affected by degradation, and the existing technology cannot effectively alleviate the deterioration of water quality.
A cross-regional basin resource allocation optimization method based on vertical ecological compensation is adopted to build a double-layer robust optimization model. By minimizing the difference between ecological protection costs and vertical ecological compensation parameters and the Gini coefficient of pollution discharge distribution, combined with vertical ecological compensation parameters and ellipsoid uncertain set, it is transformed into a single-layer planning model to solve the optimal ecological protection costs and pollution discharge distribution scheme.
The fairness and economicality of cross-regional water environment management have been achieved, and fair and reasonable decision-making plans have been obtained through the integration of ecological compensation and pollution control mechanisms, and the precise allocation of environmental resources has been achieved.
Smart Images
Figure CN120494408A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of water conservancy projects, and in particular to a method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation. Background Art
[0002] In the field of water conservancy engineering, river basin management, particularly cross-regional water pollution control, has become increasingly complex due to the uneven distribution of benefits between upstream and downstream regions. In upstream regions, regional managers often prioritize economic development over environmental protection, relaxing wastewater discharge regulations and exacerbating water pollution downstream. Consequently, downstream regions face significant challenges in both water governance and environmental protection while coping with the compounding pressures of deteriorating water quality. Due to the lack of effective cross-regional environmental governance agreements and coordinated action mechanisms, regional managers have implemented independent and independent measures, failing to comprehensively mitigate water pollution in the river basin. Consequently, the lack of regional cooperation has hindered progress in improving the overall water environment, leaving ecosystems and local communities increasingly vulnerable to degradation. Summary of the Invention
[0003] In response to the above-mentioned deficiencies in the existing technology, the present invention provides a cross-regional watershed resource allocation optimization method based on vertical ecological compensation, thereby solving technical problems such as the unreasonable distribution of existing ecological protection costs and pollution discharge.
[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation includes the following steps: Obtain cross-regional watershed monitoring data; With minimizing the difference between ecological protection costs and vertical ecological compensation parameters and minimizing the Gini coefficient of pollutant discharge distribution as the upper-level goals, and maximizing the vertical ecological compensation benefits as the lower-level goals, a cross-regional watershed resource allocation optimization model is constructed. The longitudinal ecological compensation parameter uncertainty set and ellipsoid uncertainty set are introduced into the cross-regional watershed resource allocation optimization model to construct a two-layer robust optimization model for cross-regional watershed resource allocation. Robust equivalence transformation is used to convert the uncertain set into deterministic conditions, and then the KKT condition is used to transform the two-layer robust optimization model of cross-regional watershed resource allocation into a single-layer planning model to obtain the optimal ecological protection cost and pollution discharge allocation plan.
[0005] Furthermore, cross-regional watershed monitoring data include industrial sulfur dioxide emissions, sewage discharge, solid waste generation and electricity consumption.
[0006] Furthermore, the objective function of minimizing the difference between ecological protection cost and vertical ecological compensation parameter is:
[0007] in, In order to minimize the objective function of the difference between ecological protection cost and vertical ecological compensation parameters, To obtain the minimum function, for t Period Area i The weight coefficient of for t Period Area i The total ecological protection cost of the basin, for t Periods allocated to regions i Ecological compensation parameters, is the number of regions, is the number of periods.
[0008] Furthermore, the objective function of minimizing the Gini coefficient of pollution discharge distribution is:
[0009] in, To minimize the Gini coefficient objective function of pollution discharge distribution, Assign weight coefficients to pollutant discharge, , for t Periods allocated to regions l pollutants z emissions, for t Periods allocated to regions h pollutants z emissions, for t Period Area l The weight coefficient of for t Period Area h The weight coefficient of for t Periods allocated to regions i pollutants z emissions, for t Period Area i The weight coefficient of for u Periods allocated to regions i pollutants z emissions, for v Periods allocated to regions i pollutants z emissions, for u Period Area iThe weight coefficient of for v Period Area i The weight coefficient of , , , Randomly selected, is the number of regions, is the number of periods.
[0010] Furthermore, the constraint function of the upper-level objective is:
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[0017] in, for t Periods are allocated to sub-regions i Ecological compensation parameters, is the total amount of vertical ecological compensation parameters, for t Period allocated to downstream areas i Ecological compensation parameters, for t Period allocated to upstream areas i Ecological compensation parameters, for t Period allocated to developed regions i Ecological compensation parameters, for t Period allocated to less developed regions i Ecological compensation parameters, Assign lower limit index to eco-compensation parameters, for t Period Area i The total ecological protection cost of the basin, for t Periods allocated to regions i pollutants z emissions, Pollutants that can be allocated to each area z The total amount of emissions, Assign the lower limit of the pollutant discharge amount, Assign an upper limit to the amount of pollutants discharged, is the number of regions, is the number of periods.
[0018] Furthermore, the objective function for maximizing vertical ecological compensation benefits is:
[0019] in, In order to maximize the vertical ecological compensation benefit objective function, To obtain the maximum value function, For the region i The income adjustment factor, for t Period Area i Assigned to Project j Ecological compensation parameters, is the ecological benefit coefficient, is the economic benefit coefficient, is the social benefit coefficient, is the discount rate, The future time point of the project's benefits, The time when the project started, is the number of regions, is the number of items, is the number of periods.
[0020] Furthermore, the constraints of the lower-level objectives are:
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[0024] in, for t Period Area i Assigned to Project j Ecological compensation parameters, for t Periods allocated to regions i Ecological compensation parameters, is the concentration of pollutant z in region i at time t, is the dilution factor that converts the discharge of pollutant z into the concentration of pollutant in region i during period t, for t Periods allocated to regions i pollutants zemissions, for t Period Area i Pollutants affected by other factors z concentration, For the project j In the area i Unit pollutants reduced z The concentration of is the target value of pollutant z concentration in region i during period t, is the number of items.
[0025] Furthermore, when constructing a two-layer robust optimization model for cross-regional watershed resource allocation, the constraint function of the upper layer objective is
[0026] Convert to
[0027] in, , for t Periods allocated to regions i Ecological compensation parameters, is the total amount of ecological compensation parameters, is the total amount of ecological compensation parameters after introducing uncertainty, is the uncertainty set of vertical ecological compensation parameters, for t Total amount of vertical ecological compensation parameters during the period The expected value of for t The disturbance vector of the period, is the uncertainty parameter, is the number of regions.
[0028] Furthermore, when constructing a two-layer robust optimization model for cross-regional watershed resource allocation, the objective function of the lower layer is transformed into:
[0029] in, In order to maximize the vertical ecological compensation benefit objective function, To obtain the maximum value function, The region after introducing uncertainty i Income adjustment factor, for t Period Area i Assigned to Project j Ecological compensation parameters, For the project j In the area i The ecological benefit coefficient, For the project j In the area i The economic benefit coefficient, For the project j In the area i The social benefit coefficient, is the discount rate, For the future time point of project benefits, The time when the project started, is the number of regions, is the number of items, is the number of periods, , is the ellipsoid uncertainty set of the income adjustment coefficient, For the region i The expected value of the earnings adjustment factor, For the region i The perturbation vector, is the radius of the uncertainty set of the ellipsoid, is the bi-norm of the perturbation vector.
[0030] Furthermore, the robust equivalence transformation is used to convert the uncertain set into a deterministic condition, and then the KKT condition is used to transform the two-layer robust optimization model of cross-regional river basin resource allocation into a single-layer planning model, specifically:
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[0057] in, To minimize the Gini coefficient objective function of pollution discharge distribution, Assign weight coefficients to pollutant discharge, for t Periods allocated to regions l pollutants z emissions, for t Periods allocated to regions h pollutants z emissions, for t Period Area l The weight coefficient of for t Period Area h The weight coefficient of for t Periods allocated to regions i pollutants z emissions, for t Period Area i The weight coefficient of foru Periods allocated to regions i pollutants z emissions, for v Periods allocated to regions i pollutants z emissions, for u Period Area i The weight coefficient of for v Period Area i The weight coefficient of is the number of regions, is the number of periods, for t Period Area i The total ecological protection cost of the basin, for t Periods allocated to regions i Ecological compensation parameters, is the maximum allowable value of the difference between the ecological protection cost and the vertical ecological compensation parameter, for t Period Area i The first-class inequality constraint function in the upper layer, for t Total amount of vertical ecological compensation parameters during the period The expected value of is the perturbation weight coefficient after dualization, is the uncertainty parameter, for t The slack variable of the first-type disturbance during period , for t The slack variable of the second type of disturbance during the period, for t Period Area i The second type inequality constraint function of the upper layer, is an auxiliary variable, for t Period Area i The third kind of inequality constraint function in the upper layer, for t Period allocated to downstream areas i Ecological compensation parameters, for t Period allocated to upstream areas i Ecological compensation parameters, for t Period Area i The fourth kind of inequality constraint function in the upper layer, for t Period allocated to developed regionsi Ecological compensation parameters, for t Period allocated to less developed regions i Ecological compensation parameters, for t Period Area i The fifth kind of inequality constraint function in the upper layer, Assign lower limit index to eco-compensation parameters, for t Period Area i The sixth kind of inequality constraint function in the upper layer, for t Period Area i The seventh type of inequality constraint function in the upper layer, Pollutants that can be allocated to each area z The total amount of emissions, for t Period Area i The eighth type of inequality constraint function in the upper layer, Assign the lower limit of the pollutant discharge amount, for t Period Area i The ninth type of inequality constraint function in the upper layer, Assign an upper limit to the amount of pollutants discharged, for t Period Area i For projects j The lower first-kind inequality constraint function of For the region i The expected value of the earnings adjustment factor, for t Period Area i Assigned to Project j Ecological compensation parameters, for t Period Project j In the area i The ecological benefit coefficient, for t Period Project j In the area i The economic benefit coefficient, for t Period Project j In the area i The social benefit coefficient, is the discount rate, The future time point of the project's benefits, The time when the project started, is the radius of the uncertainty set of the ellipsoid, is the introduced substitution variable, fort Period Area i The second kind of inequality constraint function in the lower layer, for t Period Area i project j Targeting pollutants z The equality constraint, is the concentration of pollutant z in region i at time t, is the dilution factor that converts the discharge of pollutant z into pollutant concentration in period t, for t Period Area i Pollutants affected by other factors z concentration, For the project j In the area i Unit pollutants reduced z The concentration of for t Period Area i Targeting pollutants z The lower third-kind inequality constraint function of is the target value of pollutant z concentration in region i during period t, For all upper-level inequality constraint functions, are all the underlying inequality constraint functions.
[0058] The present invention has the following beneficial effects: This paper uses a two-layer, multi-objective robust optimization model to construct a model for allocating eco-compensation costs and pollutant discharges in cross-regional water environment management. This model aims to achieve both fairness and economy while incorporating a pollutant concentration index for eco-compensation. Unlike traditional approaches that address environmental impact parameters and pollution control separately, this paper integrates these two mechanisms into a unified optimization framework, taking into account their interdependence. This approach results in fair and reasonable decision-making solutions and enables precise allocation of environmental resources. BRIEF DESCRIPTION OF THE DRAWINGS
[0059] Figure 1 This is a flow chart of a cross-regional watershed resource allocation optimization method based on vertical ecological compensation. DETAILED DESCRIPTION
[0060] 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.
[0061] like Figure 1 As shown, the embodiment of the present invention provides a method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation, comprising the following steps S1 to S4: S1. Obtain cross-regional watershed monitoring data; In an optional embodiment of the present invention, the cross-regional watershed monitoring data acquired in step S1 includes industrial sulfur dioxide emissions, sewage discharge, solid waste generation and electricity consumption.
[0062] In addition, the original data obtained in this embodiment may further involve per capita GDP, per capita consumer expenditure of residents, the proportion of the secondary industry, the proportion of the tertiary industry, the proportion of college education and above, the number of doctors per 10,000 people, the employment rate, per capita road area, water supply capacity, per capita forest area, per capita wetland area, per capita sown area of grain crops, per capita water resources, and the proportion of environmental protection investment in GDP, thereby improving the multi-source nature of the data.
[0063] S2. Build a cross-regional watershed resource allocation optimization model with minimizing the difference between ecological protection costs and vertical ecological compensation parameters and minimizing the Gini coefficient of pollutant discharge distribution as the upper-level goal and maximizing the vertical ecological compensation benefits as the lower-level goal; In an optional embodiment of the present invention, the objective function for minimizing the difference between the ecological protection cost and the vertical ecological compensation parameter constructed in step S2 is:
[0064] in, In order to minimize the objective function of the difference between ecological protection cost and vertical ecological compensation parameters, To obtain the minimum function, for t Period Area i The weight coefficient of for t Period Area i The total ecological protection cost of the basin, for t Periods allocated to regions i Ecological compensation parameters, is the number of regions, is the number of periods, , Cost of soil and water loss prevention and control, For the cost of ecological migration, Cost of water pollution prevention and control.
[0065] The objective function for minimizing the Gini coefficient of pollution discharge distribution constructed in step S2 is:
[0066] in, To minimize the Gini coefficient objective function of pollution discharge distribution, Assign weight coefficients to pollutant discharge, , for t Periods allocated to regions l pollutants z emissions, for t Periods allocated to regions h pollutants z emissions, for t Period Area l The weight coefficient of for t Period Area h The weight coefficient of for t Periods allocated to regions i pollutants z emissions, for t Period Area i The weight coefficient of for u Periods allocated to regions i pollutants z emissions, for v Periods allocated to regions i pollutants z emissions, for u Period Area i The weight coefficient of for v Period Area i The weight coefficient of , , , Randomly selected, is the number of regions, The Gini coefficient can take any value between 0 and 1. The smaller the Gini coefficient, the fairer the distribution; the higher the Gini coefficient, the more unequal the distribution of emission rights.
[0067] The constraint function of the upper-level target constructed in step S2 is:
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[0074] in, for t Periods are allocated to sub-regions i Ecological compensation parameters, is the total amount of vertical ecological compensation parameters, for t Period allocated to downstream areas i Ecological compensation parameters, for t Period allocated to upstream areas i Ecological compensation parameters, for t Period allocated to developed regions i Ecological compensation parameters, for t Period allocated to less developed regions i Ecological compensation parameters, Assign lower limit index to eco-compensation parameters, for t Period Area i The total ecological protection cost of the basin, for t Periods allocated to regions i pollutants z emissions, Pollutants that can be allocated to each area z The total amount of emissions, Assign the lower limit of the pollutant discharge amount, Assign an upper limit to the amount of pollutants discharged, is the number of regions, is the number of periods.
[0075] The objective function for maximizing vertical ecological compensation benefits constructed in step S2 is:
[0076] in, In order to maximize the vertical ecological compensation benefit objective function, To obtain the maximum value function, For the region i The income adjustment factor, for t Period Area i Assigned to Project j Ecological compensation parameters, is the ecological benefit coefficient, is the economic benefit coefficient, is the social benefit coefficient, is the discount rate, The future time point of the project's benefits, The time when the project started, is the number of regions, is the number of items, is the number of periods.
[0077] The constraints of the lower-level target constructed in step S2 are:
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[0081] in, for t Period Area i Assigned to Project j Ecological compensation parameters, for t Periods allocated to regions i Ecological compensation parameters, is the concentration of pollutant z in region i at time t, is the dilution factor that converts the discharge of pollutant z into the concentration of pollutant in region i during period t, for t Periods allocated to regions i pollutants z emissions, for t Period Area i Pollutants affected by other factors z concentration, For the project j In the area i Unit pollutants reduced z The concentration of is the target value of pollutant z concentration in region i during period t, is the number of items.
[0082] S3. Introducing the uncertainty set of vertical ecological compensation parameters and the uncertainty set of ellipsoid into the optimization model of cross-regional watershed resource allocation, and constructing a two-layer robust optimization model for cross-regional watershed resource allocation; In an optional embodiment of the present invention, when constructing a two-layer robust optimization model for cross-regional watershed resource allocation in step S3, an uncertain set of vertical ecological compensation parameters U is introduced, and the constraint function of the upper layer objective is
[0083] Convert to
[0084] in, , for t Periods allocated to regions i Ecological compensation parameters, is the total amount of ecological compensation parameters, is the total amount of ecological compensation parameters after introducing uncertainty, is the uncertainty set of vertical ecological compensation parameters, for t Total amount of vertical ecological compensation parameters during the period The expected value of for t The disturbance vector of the period, is the uncertainty parameter, is the number of regions. The perturbation vector Affected by parameter uncertainty set Influence determines the decision maker's attitude towards risk. The larger the value, the stronger the risk aversion and the more extreme points of the random vector; the smaller the value, the more optimistic the attitude; Indicates decision certainty.
[0085] When constructing the two-layer robust optimization model for cross-regional watershed resource allocation in step S3, the ellipsoid uncertainty set Q is introduced and the objective function of the lower layer objective is transformed into:
[0086] in, In order to maximize the vertical ecological compensation benefit objective function, To obtain the maximum value function, The region after introducing uncertainty i Income adjustment factor, for t Period Area i Assigned to Project j Ecological compensation parameters, For the project j In the area i The ecological benefit coefficient, For the project j In the area i The economic benefit coefficient, For the project jIn the area i The social benefit coefficient, is the discount rate, For the future time point of project benefits, The time when the project started, is the number of regions, is the number of items, is the number of periods, , is the ellipsoid uncertainty set of the income adjustment coefficient, For the region i The expected value of the earnings adjustment factor, For the region i The perturbation vector, is the radius of the uncertainty set of the ellipsoid, is the bi-norm of the perturbation vector.
[0087] In the lower-level model, there are unknown parameters in the objective function—the benefit coefficients of each project. Therefore, by adding the parameter Φ, the objective function can be transformed into an equivalent constraint equation:
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[0089] S4. Use robust equivalence transformation to convert the uncertain set into deterministic conditions, and then use KKT conditions to transform the two-layer robust optimization model of cross-regional river basin resource allocation into a single-layer planning model to obtain the optimal ecological protection cost and pollution discharge allocation plan.
[0090] In an optional embodiment of the present invention, step S4 uses robust equivalence transformation to convert the uncertainty set into deterministic conditions, and then uses KKT conditions to transform the two-layer robust optimization model for cross-regional watershed resource allocation into a single-layer planning model to form a final solvable global model, specifically:
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[0117] in, To minimize the Gini coefficient objective function of pollution discharge distribution, Assign weight coefficients to pollutant discharge, for t Periods allocated to regions l pollutants z emissions, for t Periods allocated to regions h pollutants z emissions, for t Period Areal The weight coefficient of for t Period Area h The weight coefficient of for t Periods allocated to regions i pollutants z emissions, for t Period Area i The weight coefficient of for u Periods allocated to regions i pollutants z emissions, for v Periods allocated to regions i pollutants z emissions, for u Period Area i The weight coefficient of for v Period Area i The weight coefficient of is the number of regions, is the number of periods, for t Period Area i The total ecological protection cost of the basin, for t Periods allocated to regions i Ecological compensation parameters, is the maximum allowable value of the difference between the ecological protection cost and the vertical ecological compensation parameter, for t Period Area i The first-class inequality constraint function in the upper layer, for t Total amount of vertical ecological compensation parameters during the period The expected value of is the perturbation weight coefficient after dualization, is the uncertainty parameter, for t The slack variable of the first-type disturbance during period , for t The slack variable of the second type of disturbance during the period, for t Period Area i The second type inequality constraint function of the upper layer, is an auxiliary variable, for t Period Area i The third kind of inequality constraint function in the upper layer, for t Period allocated to downstream areas i Ecological compensation parameters, for t Period allocated to upstream areas i Ecological compensation parameters, for t Period Area i The fourth kind of inequality constraint function in the upper layer, for t Period allocated to developed regions i Ecological compensation parameters, for t Period allocated to less developed regions i Ecological compensation parameters, for t Period Area i The fifth kind of inequality constraint function in the upper layer, Assign lower limit index to eco-compensation parameters, for t Period Area i The sixth kind of inequality constraint function in the upper layer, for t Period Area i The seventh type of inequality constraint function in the upper layer, Pollutants that can be allocated to each area z The total amount of emissions, for t Period Area i The eighth type of inequality constraint function in the upper layer, Assign the lower limit of the pollutant discharge amount, for t Period Area i The ninth type of inequality constraint function in the upper layer, Assign an upper limit to the amount of pollutants discharged, for t Period Area i For projects j The lower first-kind inequality constraint function of For the region i The expected value of the earnings adjustment factor, for t Period Area i Assigned to Project j Ecological compensation parameters, for t Period Project j In the area i The ecological benefit coefficient, for t Period Project j In the area iThe economic benefit coefficient, for t Period Project j In the area i The social benefit coefficient, is the discount rate, The future time point of the project's benefits, The time when the project started, is the radius of the uncertainty set of the ellipsoid, is the introduced substitution variable, for t Period Area i The second kind of inequality constraint function in the lower layer, for t Period Area i project j Targeting pollutants z The equality constraint, is the concentration of pollutant z in region i at time t, is the dilution factor that converts the discharge of pollutant z into pollutant concentration in period t, for t Period Area i Pollutants affected by other factors z concentration, For the project j In the area i Unit pollutants reduced z The concentration of for t Period Area i Targeting pollutants z The lower third-kind inequality constraint function of is the target value of pollutant z concentration in region i during period t, For all upper-level inequality constraint functions, are all the underlying inequality constraint functions.
[0118] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.
[0119] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.
[0120] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.
[0121] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.
[0122] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.
Claims
1. A cross-regional watershed resource allocation optimization method based on vertical ecological compensation, characterized in that: The following steps are involved: Access to cross-regional watershed monitoring data; With minimizing the difference between ecological protection costs and vertical ecological compensation parameters and minimizing the Gini coefficient of pollutant discharge distribution as the upper-level goals, and maximizing the vertical ecological compensation benefits as the lower-level goals, a cross-regional watershed resource allocation optimization model is constructed. The longitudinal ecological compensation parameter uncertainty set and ellipsoid uncertainty set are introduced into the cross-regional watershed resource allocation optimization model to construct a two-layer robust optimization model for cross-regional watershed resource allocation. Robust equivalence transformation is used to convert the uncertain set into deterministic conditions, and then the KKT condition is used to transform the two-layer robust optimization model of cross-regional watershed resource allocation into a single-layer planning model to obtain the optimal ecological protection cost and pollution discharge allocation plan.
2. The method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation according to claim 1 is characterized in that: Cross-regional river basin monitoring data include industrial sulfur dioxide emissions, sewage discharge, solid waste generation and electricity consumption.
3. The method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation according to claim 1 is characterized in that: The objective function of minimizing the difference between ecological protection cost and vertical ecological compensation parameter is: in, In order to minimize the objective function of the difference between ecological protection cost and vertical ecological compensation parameters, To obtain the minimum function, for t Period Area i The weight coefficient of for t Period Area i The total ecological protection cost of the basin, for t Periods allocated to regions i Ecological compensation parameters, is the number of regions, is the number of periods.
4. The method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation according to claim 1 is characterized in that: The objective function of minimizing the Gini coefficient of pollution discharge distribution is: in, To minimize the Gini coefficient objective function of pollution discharge distribution, Assign weight coefficients to pollutant discharge, , for t Periods allocated to regions l pollutants z emissions, for t Periods allocated to regions h pollutants z emissions, for t Period Area l The weight coefficient of for t Period Area h The weight coefficient of for t Periods allocated to regions i pollutants z emissions, for t Period Area i The weight coefficient of for u Periods allocated to regions i pollutants z emissions, for v Periods allocated to regions i pollutants z emissions, for u Period Area i The weight coefficient of for v Period Area i The weight coefficient of , , , Randomly selected, is the number of regions, is the number of periods.
5. The method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation according to claim 1 is characterized in that: The constraint function of the upper-level objective is: in, for t Periods are allocated to sub-regions i Ecological compensation parameters, is the total amount of vertical ecological compensation parameters, for t Period allocated to downstream areas i Ecological compensation parameters, for t Period allocated to upstream areas i Ecological compensation parameters, for t Period allocated to developed regions i Ecological compensation parameters, for t Period allocated to less developed regions i Ecological compensation parameters, Assign lower limit index to eco-compensation parameters, for t Period Area i The total ecological protection cost of the basin, for t Periods allocated to regions i pollutants z emissions, Pollutants that can be allocated to each area z The total amount of emissions, Assign the lower limit of the pollutant discharge amount, Assign an upper limit to the amount of pollutants discharged, is the number of regions, is the number of periods.
6. The method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation according to claim 1 is characterized in that: The objective function for maximizing vertical ecological compensation benefits is: in, In order to maximize the vertical ecological compensation benefit objective function, To obtain the maximum value function, For the region i The income adjustment factor, for t Period Area i Assigned to Project j Ecological compensation parameters, is the ecological benefit coefficient, is the economic benefit coefficient, is the social benefit coefficient, is the discount rate, The future time point of the project's benefits, The time when the project started, is the number of regions, is the number of items, is the number of periods.
7. The method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation according to claim 1 is characterized in that: The constraints of the lower-level objectives are: in, for t Period Area i Assigned to Project j Ecological compensation parameters, for t Periods allocated to regions i Ecological compensation parameters, is the concentration of pollutant z in region i at time t, is the dilution factor that converts the discharge of pollutant z into the concentration of pollutant in region i during period t, for t Periods allocated to regions i pollutants z emissions, for t Period Area i Pollutants affected by other factors z concentration, For the project j In the area i Unit pollutants reduced z The concentration of is the target value of pollutant z concentration in region i during period t, is the number of items.
8. The method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation according to claim 1 is characterized in that: When constructing a two-layer robust optimization model for cross-regional watershed resource allocation, the constraint function of the upper layer objective is Convert to in, , for t Periods allocated to regions i Ecological compensation parameters, is the total amount of ecological compensation parameters, is the total amount of ecological compensation parameters after introducing uncertainty, is the uncertainty set of vertical ecological compensation parameters, for t Total amount of vertical ecological compensation parameters during the period The expected value of for t The disturbance vector of the period, is the uncertainty parameter, is the number of regions.
9. The method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation according to claim 1, characterized in that: When constructing a two-layer robust optimization model for cross-regional watershed resource allocation, the objective function of the lower layer is transformed into: in, In order to maximize the vertical ecological compensation benefit objective function, To obtain the maximum value function, The region after introducing uncertainty i Income adjustment factor, for t Period Area i Assigned to Project j Ecological compensation parameters, For the project j In the area i The ecological benefit coefficient, For the project j In the area i The economic benefit coefficient, For the project j In the area i The social benefit coefficient, is the discount rate, For the future time point of project benefits, The time when the project started, is the number of regions, is the number of items, is the number of periods, , is the ellipsoid uncertainty set of the revenue adjustment coefficient, For the region i The expected value of the earnings adjustment factor, For the region i The perturbation vector, is the radius of the uncertainty set of the ellipsoid, is the bi-norm of the perturbation vector.
10. The method for optimizing cross-regional watershed resource allocation based on vertical ecological compensation according to claim 1, characterized in that: Robust equivalence transformation is used to convert the uncertain set into deterministic conditions, and then the KKT condition is used to transform the two-layer robust optimization model of cross-regional river basin resource allocation into a single-layer planning model. Specifically: st in, To minimize the Gini coefficient objective function of pollution discharge distribution, Assign weight coefficients to pollutant discharge, for t Periods allocated to regions l pollutants z emissions, for t Periods allocated to regions h pollutants z emissions, for t Period Area l The weight coefficient of for t Period Area h The weight coefficient of for t Periods allocated to regions i pollutants z emissions, for t Period Area i The weight coefficient of for u Periods allocated to regions i pollutants z emissions, for v Periods allocated to regions i pollutants z emissions, for u Period Area i The weight coefficient of for v Period Area i The weight coefficient of is the number of regions, is the number of periods, for t Period Area i The total ecological protection cost of the basin, for t Periods allocated to regions i Ecological compensation parameters, is the maximum allowable value of the difference between the ecological protection cost and the vertical ecological compensation parameter, for t Period Area i The first-class inequality constraint function in the upper layer, for t Total amount of vertical ecological compensation parameters during the period The expected value of is the perturbation weight coefficient after dualization, is the uncertainty parameter, for t The slack variable of the first-type disturbance during period , for t The slack variable of the second type of disturbance during the period, for t Period Area i The second type inequality constraint function of the upper layer, is an auxiliary variable, for t Period Area i The third kind of inequality constraint function in the upper layer, for t Period allocated to downstream areas i Ecological compensation parameters, for t Period allocated to upstream areas i Ecological compensation parameters, for t Period Area i The fourth kind of inequality constraint function in the upper layer, for t Period allocated to developed regions i Ecological compensation parameters, for t Period allocated to less developed regions i Ecological compensation parameters, for t Period Area i The fifth kind of inequality constraint function in the upper layer, Assign lower limit index to eco-compensation parameters, for t Period Area i The sixth kind of inequality constraint function in the upper layer, for t Period Area i The seventh type of inequality constraint function in the upper layer, Pollutants that can be allocated to each area z The total amount of emissions, for t Period Area i The eighth type of inequality constraint function in the upper layer, Assign the lower limit of the pollutant discharge amount, for t Period Area i The ninth type of inequality constraint function in the upper layer, Assign an upper limit to the amount of pollutants discharged, for t Period Area i For projects j The lower first-kind inequality constraint function of For the region i The expected value of the earnings adjustment factor, for t Period Area i Assigned to Project j Ecological compensation parameters, for t Period Project j In the area i The ecological benefit coefficient, for t Period Project j In the area i The economic benefit coefficient, for t Period Project j In the area i The social benefit coefficient, is the discount rate, The future time point of the project's benefits, The time when the project started, is the radius of the uncertainty set of the ellipsoid, is the introduced substitution variable, for t Period Area i The second kind of inequality constraint function in the lower layer, for t Period Area i project j Targeting pollutants z The equality constraint, is the concentration of pollutant z in region i at time t, is the dilution factor that converts the discharge of pollutant z into pollutant concentration in period t, for t Period Area i Pollutants affected by other factors z concentration, For the project j In the area i Unit pollutants reduced z The concentration of for t Period Area i Targeting pollutants z The lower third-kind inequality constraint function of is the target value of pollutant z concentration in region i during period t, For all upper-level inequality constraint functions, are all the underlying inequality constraint functions.