Cross-regional river water distribution decision-making method and device for balancing fairness and stability

Abstract

The invention discloses a cross-regional river water distribution decision method and device for balancing fairness and stability, and the method comprises the steps: obtaining the basic information data of the cross-regional river water distribution, generating a plurality of water distribution schemes through employing a production breaking theory rule, and enabling each water distribution scheme to comprise a water resource share corresponding to each region main body, and obtaining a fairness index and a stability index of each water distribution scheme based on a Gini index and a Sharpley-Schbi power index, generating a combined index of the fairness index and the stability index of each water distribution scheme by adopting a game theory method, and sorting all the water distribution schemes based on the combined index. And obtaining an optimal water distribution scheme. According to the method, on the basis of quantitative fairness and stability principles, the fairness and stability principles are aggregated by adopting a game theory method, and a practical and feasible water allocation strategy is provided for solving cross-regional river water allocation conflicts under a water shortage situation.

Description

Technical Field

[0001] The present invention relates to the technical field of water allocation, and in particular to a method and device for making decisions on cross-regional river water allocation with balanced fairness and stability. Background Art

[0002] Freshwater resources are the material foundation and energy driving force behind orderly socioeconomic development and the maintenance of a virtuous cycle of ecological and environmental development. As the primary source of freshwater, when the available water volume of interregional rivers cannot meet the total demand of all regional entities, disputes and confrontations may arise over water resources to ensure that economic and social development within their jurisdiction is not harmed by water shortages.

[0003] However, different bankruptcy rules, based on different notions of fairness, may produce different legal water allocation plans, and regional entities may have different preferences for these plans. Therefore, effective evaluation of water allocation plans is necessary to provide decision makers with feasible water allocation strategies. Existing research results typically make decisions about water allocation plans based on bankruptcy theory based on a single performance criterion, and different performance criteria are likely to lead to conflicting decision outcomes.

[0004] Generally, Pareto efficiency, social fairness, and solution stability are the core performance criteria for reaching consensus on resource allocation agreements. Pareto efficiency, from a cooperative game perspective, emphasizes the complete divisibility of resources or their benefits, which can be achieved by incorporating relevant constraints into water allocation models. There is no universal consensus on the definition of social fairness. A generally accepted view is that a fair multilateral environmental agreement should emphasize the concept of distributive justice, based on egalitarianism. The stability criterion emphasizes the sustainability of resource-sharing agreements and focuses on the willingness of all parties to cooperate on water allocation plans. Currently, in the water resources management literature related to bankruptcy theory, water allocation is typically focused solely on Pareto efficiency. Methods that simultaneously consider both fairness and stability criteria, building on Pareto efficiency and balancing these criteria in water allocation decision-making, have yet to emerge. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a cross-regional river water allocation decision-making method and device that balances fairness and stability. On the basis of quantifying fairness and stability rules, the two are combined using game theory to provide a realistic and feasible water allocation strategy for resolving cross-regional river water allocation conflicts.

[0006] Other features and advantages of the present application will become apparent from the following detailed description, or may be learned in part by practice of the present application.

[0007] According to a first aspect of the present application, a cross-regional river water allocation decision-making method that balances fairness and stability is provided, comprising: Obtaining basic information data on inter-regional river water allocation, including allocable water resources, several regional entities, and declared water volumes corresponding to each regional entity; Based on basic information data, the cross-regional river water allocation problem under water shortage is described as a problem of competing demands among multiple regional entities. Several water allocation schemes are generated using bankruptcy theory rules. Each water allocation scheme includes the water resource share corresponding to each regional entity. The fairness index of the water allocation scheme is obtained based on the Gini index formula, and the stability index of the water allocation scheme is obtained based on the Shapley-Shubik power index formula; The game theory method is used to generate a combination index of equilibrium fairness index and stability index for each water allocation scheme. All water allocation schemes are ranked based on the combination index to obtain the optimal water allocation scheme.

[0008] In some embodiments of the present application, based on the aforementioned solution, the cross-regional river water allocation problem under water shortage conditions is described as a problem of competing demands among multiple regional entities based on basic information data. A water allocation scheme comprising several water allocation schemes is generated using bankruptcy theory rules. Each water allocation scheme includes the water resource share corresponding to each regional entity, and further includes: A constraint function is established, and the corresponding water allocation plans are generated using bankruptcy theory rules such as equal proportion, constrained equal benefit, constrained equal loss, adjusted equal proportion, Talmudic or Pin rule.

[0009] In some embodiments of the present application, based on the aforementioned solution, obtaining the fairness index of the water allocation solution based on the Gini index formula includes: Based on the water resource share corresponding to each regional entity under the water allocation plan, the Gini index formula is used to obtain the fairness index of the water allocation plan. The calculation formula is: ; ; Where: It is Fairness index of water allocation scheme; and They are Regional entities under the water allocation plan and share of water resources; It is The average value of water resource shares of all regional entities under this water allocation plan.

[0010] In some embodiments of the present application, based on the aforementioned solution, the method of obtaining the stability index of the water allocation solution based on the Shapley-Shubik power index formula includes: Based on the water resource share obtained by each regional entity under the water allocation plan, the Shapley-Shubik power index of each regional entity in the water allocation plan is obtained based on the Shapley-Shubik power index formula. The calculation formula is: ; ; Where: Is a regional entity The maximum share of water received among all water allocation options; Is a regional entity In the The Shapley-Shubik power index under the water allocation scheme;

[0011] The Shapley-Shubik power index of all regional entities in the water allocation plan is averaged to obtain the average index of the water allocation plan. The calculation formula is: ; ; Based on the arithmetic mean and standard deviation of the above Shapley-Shubik power index, the coefficient of variation of each water allocation scheme is calculated as its stability index. The calculation formula is: ; Where: It is Stability index of the water allocation plan; and They are The arithmetic mean and standard deviation of the Shapley-Shubik power index of all regional entities under the water allocation scheme.

[0012] In some embodiments of the present application, based on the aforementioned solution, the game theory method is used to generate a combination index of the equilibrium fairness index and the stability index for each water allocation solution, and all water allocation solutions are sorted based on the combination index to obtain the optimal water allocation solution: The fairness index and stability index of each water allocation scheme are normalized to obtain the fairness normalized value and stability normalized value of each water allocation scheme. For each water allocation scheme, the fairness normalized value and stability normalized value are weighted using a linear weight coefficient; Game theory is used to process the linear weight coefficients to obtain the optimal linear combination coefficients. For each water allocation plan, a combination index of the equilibrium fairness index and the stability index based on the optimal linear combination coefficient is generated. All combination indexes are sorted, and the smallest combination index is selected. The water allocation plan corresponding to the smallest combination index is taken as the optimal water allocation plan.

[0013] In some embodiments of the present application, based on the aforementioned scheme, the fairness index and stability index of each water allocation scheme are normalized to obtain the fairness normalized value and stability normalized value of each water allocation scheme, and the fairness normalized value and stability normalized value are weighted using a linear weight coefficient, including: The fairness index and stability index of each water allocation scheme are normalized to obtain the fairness normalized value and stability normalized value of each water allocation scheme. The calculation formula is: ; ; Where: and They are The fairness normalized value and stability normalized value of the scheme; The fairness normalized values ​​of all water allocation schemes are aggregated into a fairness index vector, and the stability normalized values ​​of each water allocation scheme are aggregated into a stability index vector; The fairness index vector and the stability index vector are weighted using a linear weight coefficient to obtain a first linear combination vector. The calculation formula of the first linear combination vector is: ; Where: and The linear weight coefficients corresponding to fairness and stability respectively; and They are fairness index vector and stability index vector, Transpose the sign of a vector.

[0014] In some embodiments of the present application, based on the aforementioned solution, the linear weight coefficients are processed using game theory to obtain the optimal linear combination coefficients. For each water allocation scheme, a combination index of the equilibrium fairness index and the stability index based on the optimal linear combination coefficients is generated. All combination indexes are sorted, and the water allocation scheme corresponding to the minimum combination index is selected as the optimal water allocation scheme. The following also includes: By minimizing the deviation between the first linear combination vector and the fairness index vector and the stability index vector, the optimal linear combination coefficient function is obtained. The calculation formula is: ; Where: represents the Euclidean norm symbol; According to the differential properties of the matrix, the optimal condition is obtained by using the first-order derivative of the optimal linear combination coefficient function: ; Solving the optimal conditions, we can get the optimal linear combination coefficient of fairness and stability , get the normalized result of the optimal linear combination coefficient: ; ; Where: and are the normalized results of the optimal linear combination coefficients of fairness and stability respectively; Based on the normalized result of the optimal linear combination coefficient, a second linear combination vector based on the optimal linear combination coefficient is obtained. The second linear combination vector includes the combined index of the equilibrium fairness index and the stability index corresponding to each water allocation scheme. The calculation formula of the second linear combination vector is: .

[0015] Sort all combination indexes in ascending order, and select the water allocation scheme corresponding to the minimum combination index as the optimal water allocation scheme. The calculation formula is: ; Where: It is the optimal water allocation solution; It is The combined index value of the fairness index and stability index of the scheme.

[0016] According to a second aspect of the present application, a cross-regional river water allocation decision-making device that balances fairness and stability is provided, comprising: The first acquisition module is used to obtain basic information data on inter-regional river water allocation, wherein the basic information data includes the amount of allocable water resources, a number of regional entities, and the declared water volume corresponding to each regional entity; The first allocation module is used to describe the cross-regional river water allocation problem under water shortage conditions as a problem of competing demands among multiple regional entities based on basic information data. It uses bankruptcy theory rules to generate several water allocation plans, each of which includes the water resource share corresponding to each regional entity. a second acquisition module, configured to acquire a fairness index of the water allocation scheme based on a Gini index formula, and to acquire a stability index of the water allocation scheme based on a Shapley-Shubik power index formula; The second allocation module is used to generate a combination index of equilibrium fairness index and stability index for each water allocation plan using game theory, and to sort all water allocation plans based on the combination index to obtain the optimal water allocation plan.

[0017] According to the third aspect of the present application, an electronic device is provided, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the above-mentioned cross-regional river water allocation decision-making method that balances fairness and stability when executing the program.

[0018] According to a fourth aspect of the present application, a non-transitory computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the cross-regional river water allocation decision-making method with balanced fairness and stability is implemented.

[0019] Compared with the prior art, the present invention has the following advantages and beneficial effects: The present invention provides a cross-regional river water allocation decision-making method and device that balances fairness and stability, obtains basic information data such as the distributable water resources of cross-regional rivers, several regional entities involved, and the declared water volume corresponding to each regional entity; describes the cross-regional river water allocation problem under water shortage conditions as a problem of competitive demand among multiple regional entities, and uses bankruptcy theory rules to generate several water allocation plans. Starting from the fairness and justice of the distribution, a quantitative method for the fairness of the water allocation plan is proposed based on the Gini index formula; starting from the acceptability at the individual level, a quantitative method for the stability of the water allocation plan is proposed based on the Shapley-Shubik power index formula; uses game theory to propose several water allocation plans that balance fairness and stability, and sorts the several water allocation plans to obtain the optimal water allocation plan. This invention makes decisions on water allocation plans based on bankruptcy theory rules from the perspective of balancing the two criteria of fairness and stability. It innovatively proposes the use of game theory to balance the fairness and stability indexes, and constructs a cross-regional river water allocation decision-making method that can comprehensively consider fairness, justice and individual acceptability. It can avoid the one-sidedness of the decision-making results of a single evaluation criterion and provide decision makers with a realistic and feasible water allocation plan. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The accompanying drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings: Figure 1 This is a flow chart of a cross-regional river water allocation decision-making method that balances fairness and stability in this embodiment; Figure 2Schematic diagram of the fairness normalized value, stability normalized value, and combined index of the equilibrium fairness index and stability index for inter-regional river water allocation schemes under different water inflow frequencies; Figure 3 A schematic diagram of a cross-regional river water allocation decision-making device that balances fairness and stability in this embodiment. DETAILED DESCRIPTION

[0021] In order to make the technical problems, technical solutions and beneficial technical effects to be solved by the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and multiple exemplary embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the scope of protection of the present invention.

[0022] In addition, described feature, structure or characteristic can be combined in one or more embodiments in any suitable manner.In the following description, many specific details are provided so as to provide a full understanding of the embodiments of the present application. However, it will be appreciated by those skilled in the art that the technical scheme of the present application can be put into practice without one or more of the specific details, or other methods, components, devices, steps etc. can be adopted. In other cases, known methods, devices, implementations or operations are not shown or described in detail to avoid blurring the various aspects of the application.

[0023] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically separate entities. That is, these functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0024] The flowcharts shown in the accompanying drawings are for illustrative purposes only and do not necessarily include all contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps may be decomposed, while others may be combined or partially combined. Therefore, the actual execution order may vary depending on the actual situation.

[0025] Figure 1 A flow chart of a cross-regional river water allocation decision-making method that balances fairness and stability is shown in this embodiment.

[0026] According to the first aspect of the present application, this embodiment provides a cross-regional river water allocation decision-making method that balances fairness and stability, including: Step S1: Obtain basic information data on cross-regional river water allocation, which includes allocable water resources, several regional entities, and the declared water volume corresponding to each regional entity.

[0027] In some implementations of this embodiment, the regional entity may be an administrative area entity or a geographical unit at different levels, such as a provincial administrative region, a prefecture-level administrative region, a river basin or a water system unit, which is not limited in this embodiment.

[0028] In some implementations of this embodiment, when the amount of water resources that can be allocated across regions cannot meet the total demand of all regional entities, conflicts may arise between the regional entities due to competition for water.

[0029] Step S2: Based on basic information data, the cross-regional river water allocation problem under water shortage situation is described as a problem of competitive demand among multiple regional entities. Several water allocation plans are generated using bankruptcy theory rules. Each water allocation plan includes the water resource share corresponding to each regional entity.

[0030] In some implementations of this embodiment, the cross-regional river water allocation problem under water shortage is described as a multi-regional subject competition demand problem, that is, a limited number of regional subjects According to its declared water volume Competition for allocable water resources in interregional rivers , the amount of water resources that can be allocated It is difficult to meet the total water volume declared by all regional entities .

[0031] In some implementations of this embodiment, based on basic information data, the cross-regional river water allocation problem under water shortage is described as a problem of competing demands among multiple regional entities. A water allocation plan is generated using bankruptcy theory rules, including several water allocation plans. Each water allocation plan includes the water resource share corresponding to each regional entity, and also includes: A constraint function is established, and the corresponding water allocation plans are generated using bankruptcy theory rules such as equal proportion, constrained equal benefit, constrained equal loss, adjusted equal proportion, Talmudic or Pin rule.

[0032] Among them, the constraint function considers three basic constraints: Pareto effectiveness, statement boundedness and non-negativity.

[0033] Step S3: Obtain the fairness index of the water allocation scheme based on the Gini index formula, and obtain the stability index of the water allocation scheme based on the Shapley-Shubik power index formula.

[0034] In cross-regional water allocation, considering the fairness index can effectively protect regions with low water demand and prevent their social and economic development from being affected by water shortages; and considering the stability index can ensure that water allocation plans are effective in the long term and avoid frequent adjustments that lead to management chaos.

[0035] In some implementations of this embodiment, obtaining the fairness index of the water allocation scheme based on the Gini index formula includes: Based on the water resource share corresponding to each regional entity under the water allocation plan, the Gini index formula is used to obtain the fairness index of the water allocation plan. The calculation formula is: (1); (2); Where: It is Fairness index of water allocation scheme; and They are Regional entities under the water allocation plan and share of water resources; It is The average value of water resource shares of all regional entities under this water allocation plan.

[0036] Therefore, based on the fairness and justice of distribution, a quantitative method for the fairness of water allocation scheme is proposed.

[0037] In some implementations of this embodiment, the stability index of the water allocation scheme is obtained based on the Shapley-Shubik power index formula, including: Based on the water resource share obtained by each regional entity under the water allocation plan, the Shapley-Shubik power index of each regional entity in the water allocation plan is obtained based on the Shapley-Shubik power index formula. The calculation formula is: (3); (4); Where: Is a regional entity The maximum share of water received among all water allocation options; Is a regional entity In the The Shapley-Shubik power index under the water allocation scheme; The Shapley-Shubik power index of all regional entities in the water allocation plan is averaged to obtain the average index of the water allocation plan. The calculation formula is: (5); (6); Based on the arithmetic mean and standard deviation of the above Shapley-Shubik power index, the coefficient of variation of each water allocation scheme is calculated as its stability index. The calculation formula is: (7); Where: It is Stability index of the water allocation plan; and They are The arithmetic mean and standard deviation of the Shapley-Shubik power index of all regional entities under the water allocation scheme.

[0038] Thus, starting from the acceptability at the individual level, a quantitative method for the stability of water allocation schemes is proposed.

[0039] Step S4: Use the game theory method to generate a combination index of the equilibrium fairness index and the stability index for each water allocation plan, sort all water allocation plans based on the combination index, and obtain the optimal water allocation plan.

[0040] In some implementations of this embodiment, a game theory method is used to generate a combination index of a balanced fairness index and a stability index for each water allocation scheme, and all water allocation schemes are sorted based on the combination index to obtain the optimal water allocation scheme, including: Step S401: normalizing the fairness index and stability index of each water allocation scheme to obtain a fairness normalized value and a stability normalized value of each water allocation scheme. For each water allocation scheme, weighting the fairness normalized value and the stability normalized value is performed using a linear weight coefficient. Step S402: Use game theory to process the linear weight coefficients to obtain the optimal linear combination coefficients. For each water allocation plan, generate a combination index of the equilibrium fairness index and the stability index based on the optimal linear combination coefficients. Sorting all the combination indexes, select the water allocation plan corresponding to the minimum combination index as the optimal water allocation plan.

[0041] In some implementations of this embodiment, the fairness index and stability index of each water allocation scheme are normalized to obtain a fairness normalized value and a stability normalized value of each water allocation scheme. For each water allocation scheme, the fairness normalized value and the stability normalized value are weighted using a linear weight coefficient, including: The fairness index and stability index of each water allocation scheme are normalized to obtain the fairness normalized value and stability normalized value of each water allocation scheme. The calculation formula is: (8); (9); Where: and They are The fairness normalized value and stability normalized value of the scheme; The fairness normalized values ​​of all water allocation schemes are aggregated into a fairness index vector, and the stability normalized values ​​of each water allocation scheme are aggregated into a stability index vector;

[0042] The fairness index vector and the stability index vector are weighted using a linear weight coefficient to obtain a first linear combination vector. The calculation formula of the first linear combination vector is: (10); Where: and The linear weight coefficients corresponding to fairness and stability respectively; and They are fairness index vector and stability index vector, Transpose the sign of a vector.

[0043] In some implementations of this embodiment, game theory is used to process the linear weight coefficients to obtain the optimal linear combination coefficients. For each water allocation scheme, a combination index of the equilibrium fairness index and the stability index based on the optimal linear combination coefficients is generated. All combination indexes are sorted, and the water allocation scheme corresponding to the minimum combination index is selected as the optimal water allocation scheme. The following also includes: By minimizing the deviation between the first linear combination vector and the fairness index vector and the stability index vector, the optimal linear combination coefficient function is obtained. The calculation formula is: (11); Where: represents the Euclidean norm symbol; According to the differential properties of the matrix, the optimal condition is obtained by using the first-order derivative of the optimal linear combination coefficient function: (12); Solving the optimal conditions, we can get the optimal linear combination coefficient of fairness and stability , get the normalized result of the optimal linear combination coefficient: (13); (14); Where: and are the normalized results of the optimal linear combination coefficients of fairness and stability respectively; Based on the normalized result of the optimal linear combination coefficient, a second linear combination vector based on the optimal linear combination coefficient is obtained. The second linear combination vector includes the combined index of the equilibrium fairness index and the stability index corresponding to each water allocation scheme. The calculation formula of the second linear combination vector is: (15); Sort all combination indexes in ascending order, and select the water allocation scheme corresponding to the minimum combination index as the optimal water allocation scheme. The calculation formula is: (16); Where: It is the optimal water allocation solution; It is The combined index value of the fairness index and stability index of the scheme.

[0044] In summary, by calculating the fairness and stability of water allocation plans for interregional rivers and applying game theory, we construct a decision-making method that comprehensively considers both fairness and individual acceptability. This method effectively strikes a balance between the two performance criteria of fairness and stability, thus contributing to the scientific and rational implementation of interregional river water allocation decisions under water-scarce conditions. The implementation is simple and the results are straightforward. Compared to existing technologies, this is the first to propose a game-theoretic approach to balance fairness and stability, and thus to develop a corresponding decision-making technique. This is of great significance for coordinating water use conflicts among regional entities in interregional rivers under water-scarce conditions and achieving a relatively favorable and feasible water allocation strategy for each entity.

[0045] Furthermore, this embodiment proposes to use the Gini coefficient and the Shapley-Shubik power index method to quantify the fairness and stability of the water allocation scheme.

[0046] In addition, this embodiment innovatively proposes to use game theory to aggregate fairness and stability criteria, which can avoid the "multiplication effect" of the product normalization method and break through the linear weighted method's reliance on the subjective preferences of the management subject.

[0047] In addition, this embodiment proposes for the first time to make decisions on water bankruptcy water allocation plans from the perspective of balancing the two performance criteria of fairness and stability. This not only helps to resolve the conflicts of interest among regional entities in the allocation of water in cross-regional rivers under water shortage situations, but also enriches the application of bankruptcy theory and game theory in the field of water resources management decision-making.

[0048] In order to make the purpose, technical solution and advantages of this embodiment more clear, the technical solution of this method will be introduced in conjunction with this embodiment. It should be understood that the specific embodiment described here is only used to explain this embodiment and is not used to limit this embodiment.

[0049] See attached Figure 1 The flowchart of the cross-regional river water allocation decision-making method for balancing fairness and stability proposed in this embodiment clearly shows the specific implementation process of this embodiment. The following further introduces the method using a cross-regional river water allocation as an example. The cross-regional river water allocation involves 10 regional entities, namely, regional entity A, regional entity B, regional entity C, regional entity D, regional entity E, regional entity F, regional entity G, regional entity H, regional entity I, and regional entity J. The total water demand at 75% and 95% water inflow frequencies is 13.8068 billion m3 respectively. 3 and 16.324 billion m 3 , the distributable water volume is 13.493 billion m 3 and 11.312 billion m 3 , and the corresponding water shortages are 313.8 million m 3 and 5.012 billion m 3 The water demand of each area of ​​the cross-regional river under different water inflow frequencies is shown in Table 1.

[0050] Table 1 Water demand of each regional entity under different water inflow frequencies Unit: 100 million m³

[0051] When the available water volume of a cross-regional river cannot meet the needs of all regional entities, conflicts may arise between regional entities due to competition for water. This situation is very similar to the situation where a company's remaining assets are insufficient to fully repay its debts and is on the verge of bankruptcy. Therefore, the cross-regional river water allocation problem under water shortage can be described as a problem of competing demands among multiple regional entities, that is, 10 regional entities compete for the limited allocable water volume of the cross-regional river based on their declared water volume (when P = 75%). 100 million m 3 When P=95% 100 million m 3 ), and this amount of water is difficult to meet the total amount of water declared by all regional entities (when P=75%) 100 million m 3 When P=95% 100 million m 3 Taking into account the three basic constraints of Pareto efficiency, boundedness, and non-negativity, this example uses bankruptcy theory rules such as equal proportion (PRO), constrained equal benefit (CEA), constrained equal loss (CEL), adjusted equal proportion (APRO), Talmud (Tal), and Piniles' (Pin) to generate water allocation plans for inter-regional rivers under different water inflow frequencies. The plans are then normalized to obtain the water share of each regional entity. The results are shown in Table 2.

[0052] Table 2 Water allocation shares of various regional entities in cross-regional rivers under different schemes

[0053] The method provided in this embodiment is used to obtain the fairness index (Fai) of each water allocation scheme. The results are shown in Table 3.

[0054] Table 3 Fairness index of water allocation scheme for inter-regional rivers

[0055] The method provided in this embodiment is used to obtain the stability index (Sta) of each water allocation scheme. The results are shown in Table 4.

[0056] Table 4 Stability index of water allocation scheme for inter-regional rivers

[0057] After calculation, the optimal linear combination coefficient of fairness and stability of the water allocation scheme under the 75% water inflow frequency is , get the normalized result of its optimal linear combination coefficient The optimal linear combination coefficient of fairness and stability of the water allocation scheme under 95% water inflow frequency is , get the normalized result of its optimal linear combination coefficient , substituted into formula (15), we get the second linear combination vector , The index includes the combined index (FS) of the equilibrium fairness index and stability index corresponding to each water allocation scheme. Figure 2 , which is a schematic diagram of the fairness normalized value, stability normalized value, and combined index of the equilibrium fairness index and stability index of the cross-regional river water allocation scheme under different water inflow frequencies in this embodiment.

[0058] Depend on Figure 2It can be seen that under a 75% water inflow frequency, the CEA and Pin schemes are the most equitable water allocation schemes for inter-regional rivers, while the CEL scheme is the least equitable. CEL is the most stable water allocation scheme, while CEA / Pin is the least stable. Under a 95% water inflow frequency, the CEA scheme is the most equitable water allocation scheme for inter-regional rivers, while the CEL scheme is the least equitable. The APRO scheme is the most stable water allocation scheme, while CEA is the least stable. This indicates that in the decision-making process for water resource allocation, a certain equilibrium relationship exists between the fairness and stability criteria. Using game theory, from the perspective of the equilibrium between the fairness and stability criteria, the normalized fairness value (Fai) and the normalized stability value (Sta) are aggregated to obtain a combined index (FS) of the equilibrium fairness index and stability index.

[0059] The combined index (FS) of the equilibrium fairness index and the stability index was used to sort the water allocation schemes for inter-regional rivers in ascending order under different water inflow frequencies. The water allocation scheme corresponding to the minimum combined index was selected as the optimal water allocation scheme. The sorting results show that at a water inflow frequency of 75%, the water allocation scheme for inter-regional rivers based on the CEL rule is the best, while the water allocation schemes based on the CEA and Pin rules are the worst. At a water inflow frequency of 95%, the water allocation scheme for inter-regional rivers based on the APRO rule is the best, while the water allocation scheme based on the CEA rule is the worst.

[0060] According to the second aspect of the present application, a cross-regional river water allocation decision-making device is provided that balances fairness and stability, such as Figure 3 Shown, including: The first acquisition module is used to obtain basic information data on inter-regional river water allocation, wherein the basic information data includes the amount of allocable water resources, a number of regional entities, and the declared water volume corresponding to each regional entity; The first allocation module is used to describe the cross-regional river water allocation problem under water shortage conditions as a problem of competing demands among multiple regional entities based on basic information data. It uses bankruptcy theory rules to generate several water allocation plans, each of which includes the water resource share corresponding to each regional entity. a second acquisition module, configured to acquire a fairness index of the water allocation scheme based on a Gini index formula, and to acquire a stability index of the water allocation scheme based on a Shapley-Shubik power index formula; The second allocation module is used to generate a combination index of equilibrium fairness index and stability index for each water allocation plan using game theory, and to sort all water allocation plans based on the combination index to obtain the optimal water allocation plan.

[0061] Specifically, this embodiment corresponds one-to-one to the above method embodiment, and the functions of each module have been described in detail in the corresponding method embodiment, so they will not be repeated here.

[0062] According to the third aspect of the present application, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the cross-regional river water allocation decision-making method with balanced fairness and stability is implemented.

[0063] According to a fourth aspect of the present application, a non-transitory computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the cross-regional river water allocation decision-making method with balanced fairness and stability is implemented.

[0064] The memory in the embodiment of the present invention is used to store various types of data to support the operation of the electronic device. Examples of such data include: any computer program used to operate on the electronic device.

[0065] The cross-regional river water allocation decision-making method for balancing fairness and stability disclosed in the embodiments of the present invention can be applied to or implemented by a processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the cross-regional river water allocation decision-making method for balancing fairness and stability can be completed by hardware integrated logic circuits or software instructions in the processor. The processor may be a general-purpose processor, a digital signal processor (DSP), or other programmable logic device, discrete gate or transistor logic device, discrete hardware component, etc. The processor can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. The general-purpose processor may be a microprocessor or any conventional processor. The steps of the method disclosed in the embodiments of the present invention can be directly implemented and executed by a hardware decoding processor, or by a combination of hardware and software modules in the decoding processor. The software module may be located in a storage medium located in a memory. The processor reads information from the memory and, in conjunction with its hardware, completes the steps of the cross-regional river water allocation decision-making method for balancing fairness and stability provided in the embodiments of the present invention.

[0066] In an exemplary embodiment, the electronic device may be implemented by one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), FPGAs, general-purpose processors, controllers, microcontrollers (MCUs), microprocessors, or other electronic components to perform the aforementioned method.

[0067] It is understood that the memory can be volatile memory or non-volatile memory, or can include both volatile and non-volatile memory. Among them, non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disk, or compact disc read-only memory (CD-ROM); magnetic surface memory can be magnetic disk memory or tape memory. Volatile memory can be random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of RAM are available, such as static random access memory (SRAM), synchronous static random access memory (SSRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous link dynamic random access memory (SLDRAM), and direct rambus random access memory (DRRAM).The memories described in the embodiments of the present invention are intended to include, but are not limited to, these and any other suitable types of memories.

[0068] The above embodiments are merely illustrative of the technical solutions of the present invention. The methods of the present invention are not limited solely to those described in the above embodiments, but are subject to the scope defined by the claims. Any modifications, supplements, or equivalent substitutions made by those skilled in the art based on these embodiments are within the scope of protection claimed in the claims.

Claims

1. A cross-regional river water allocation decision-making method that balances fairness and stability, characterized by: include: Obtaining basic information data on inter-regional river water allocation, including allocable water resources, several regional entities, and declared water volumes corresponding to each regional entity; Based on basic information data, the cross-regional river water allocation problem under water shortage is described as a problem of competing demands among multiple regional entities. Several water allocation schemes are generated using bankruptcy theory rules. Each water allocation scheme includes the water resource share corresponding to each regional entity. The fairness index of the water allocation scheme is obtained based on the Gini index formula, and the stability index of the water allocation scheme is obtained based on the Shapley-Shubik power index formula; The game theory method is used to generate a combination index of equilibrium fairness index and stability index for each water allocation scheme. All water allocation schemes are ranked based on the combination index to obtain the optimal water allocation scheme.

2. The method according to claim 1, characterized in that Based on basic information data, the cross-regional river water allocation problem under water shortage is described as a problem of competitive demand among multiple regional entities. A water allocation plan is generated using bankruptcy theory rules, which includes several water allocation plans. Each water allocation plan includes the water resource share corresponding to each regional entity, and also includes: A constraint function is established, and the corresponding water allocation plans are generated using bankruptcy theory rules such as equal proportion, constrained equal benefit, constrained equal loss, adjusted equal proportion, Talmudic or Pin rule.

3. The method according to claim 1, characterized in that The fairness index of the water allocation scheme obtained based on the Gini index formula includes: Based on the water resource share corresponding to each regional entity under the water allocation plan, the Gini index formula is used to obtain the fairness index of the water allocation plan. The calculation formula is: ； ； Where: It is Fairness index of water allocation scheme; and They are Regional entities under the water allocation plan and share of water resources; It is The average value of water resource shares of all regional entities under this water allocation plan.

4. The method according to claim 1, wherein The stability index of the water allocation scheme obtained based on the Shapley-Shubik power index formula includes: Based on the water resource share obtained by each regional entity under the water allocation plan, the Shapley-Shubik power index of each regional entity in the water allocation plan is obtained based on the Shapley-Shubik power index formula. The calculation formula is: ； ； Where: Is a regional entity The maximum share of water received among all water allocation options; Is a regional entity In the The Shapley-Shubik power index under the water allocation scheme; The Shapley-Shubik power index of all regional entities in the water allocation plan is averaged to obtain the arithmetic mean and standard deviation of the water allocation plan. The calculation formula is: ； ； Based on the arithmetic mean and standard deviation of the above Shapley-Shubik power index, the coefficient of variation of each water allocation scheme is calculated as its stability index. The calculation formula is: ； Where: It is Stability index of the water allocation plan; and They are The arithmetic mean and standard deviation of the Shapley-Shubik power index of all regional entities under the water allocation scheme.

5. The method according to claim 1, wherein The game theory method is used to generate a combination index of the equilibrium fairness index and the stability index for each water allocation scheme, and all water allocation schemes are sorted based on the combination index to obtain the optimal water allocation scheme: The fairness index and stability index of each water allocation scheme are normalized to obtain the fairness normalized value and stability normalized value of each water allocation scheme. For each water allocation scheme, the fairness normalized value and stability normalized value are weighted using a linear weight coefficient; Game theory is used to process the linear weight coefficients to obtain the optimal linear combination coefficients. For each water allocation scheme, a combination index of the equilibrium fairness index and the stability index based on the optimal linear combination coefficient is generated. All combination indexes are ranked, and the water allocation scheme corresponding to the minimum combination index is selected as the optimal water allocation scheme.

6. The method according to claim 5, characterized in that Normalizing the fairness index and stability index of each water allocation scheme to obtain the fairness normalized value and stability normalized value of each water allocation scheme, and weighting the fairness normalized value and stability normalized value using a linear weight coefficient, including: The fairness index and stability index of each water allocation scheme are normalized to obtain the fairness normalized value and stability normalized value of each water allocation scheme. The calculation formula is: ； ； Where: and They are The fairness normalized value and stability normalized value of the scheme; The fairness normalized values ​​of all water allocation schemes are aggregated into a fairness index vector, and the stability normalized values ​​of each water allocation scheme are aggregated into a stability index vector; The fairness index vector and the stability index vector are weighted using a linear weight coefficient to obtain a first linear combination vector. The calculation formula of the first linear combination vector is: ； Where: and The linear weight coefficients corresponding to fairness and stability respectively; and They are fairness index vector and stability index vector, Transpose the sign of a vector.

7. The method according to claim 6, characterized in that The linear weight coefficients are processed using game theory to obtain the optimal linear combination coefficients. For each water allocation plan, a combination index of the equilibrium fairness index and the stability index based on the optimal linear combination coefficients is generated. All combination indexes are sorted, and the smallest combination index is selected. The water allocation plan corresponding to the smallest combination index is used as the optimal water allocation plan. The method also includes: By minimizing the deviation between the first linear combination vector and the fairness index vector and the stability index vector, the optimal linear combination coefficient function is obtained. The calculation formula is: ； Where: represents the Euclidean norm symbol; According to the differential properties of the matrix, the optimal condition is obtained by using the first-order derivative of the optimal linear combination coefficient function: ； Solving the optimal conditions, we can get the optimal linear combination coefficient of fairness and stability , get the normalized result of the optimal linear combination coefficient: ； ； Where: and are the normalized results of the optimal linear combination coefficients of fairness and stability respectively; Based on the normalized result of the optimal linear combination coefficient, a second linear combination vector based on the optimal linear combination coefficient is obtained. The second linear combination vector includes the combined index of the equilibrium fairness index and the stability index corresponding to each water allocation scheme. The calculation formula of the second linear combination vector is: ； Sort all combination indexes in ascending order, and select the water allocation scheme corresponding to the minimum combination index as the optimal water allocation scheme. The calculation formula is: ； Where: It is the optimal water allocation solution; It is The combined index value of the fairness index and stability index of the scheme.

8. A cross-regional river water allocation decision-making device that balances fairness and stability, characterized by: include: The first acquisition module is used to obtain basic information data on inter-regional river water allocation, wherein the basic information data includes the amount of allocable water resources, a number of regional entities, and the declared water volume corresponding to each regional entity; The first allocation module is used to describe the cross-regional river water allocation problem under water shortage conditions as a problem of competing demands among multiple regional entities based on basic information data. It uses bankruptcy theory rules to generate several water allocation plans, each of which includes the water resource share corresponding to each regional entity. a second acquisition module, configured to acquire a fairness index of the water allocation scheme based on a Gini index formula, and to acquire a stability index of the water allocation scheme based on a Shapley-Shubik power index formula; The second allocation module is used to generate a combination index of equilibrium fairness index and stability index for each water allocation plan using game theory, and to sort all water allocation plans based on the combination index to obtain the optimal water allocation plan.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the cross-regional river water allocation decision-making method with balanced fairness and stability as described in any one of claims 1 to 7 is implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the cross-regional river water allocation decision-making method with balanced fairness and stability as described in any one of claims 1 to 7 is implemented.

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