Method and device for allocating water quantity of cross-region river based on balance of fairness and stability

Abstract

The application discloses a cross-region river water distribution decision method and device balancing fairness and stability, comprising obtaining basic information data of cross-region river water distribution, generating a plurality of water distribution schemes by adopting bankruptcy theory rules, each water distribution scheme including water resource shares respectively corresponding to each regional subject, obtaining fairness indexes and stability indexes of each water distribution scheme based on Gini indexes and Shapley-Shubik power indexes, generating combination indexes of fairness indexes and stability indexes of each water distribution scheme by adopting game theory, sorting all water distribution schemes based on the combination indexes, and obtaining an optimal water distribution scheme. The application aggregates fairness and stability principles by adopting game theory on the basis of quantifying the principles, and provides a practical water distribution strategy for solving cross-region river water distribution conflicts under water shortage situations.

Description

Technical Field

[0001] This invention relates to the field of water allocation technology, specifically to a method and apparatus for cross-regional river water allocation decision-making that balances fairness and stability. Background Technology

[0002] Freshwater resources are the material foundation and energy source for supporting the orderly development of the social economy and maintaining a healthy ecological cycle. As the main source of freshwater supply, when the available water volume of inter-regional rivers cannot meet the total demand of all regional entities, disputes and conflicts may arise among these entities over water resources in order to ensure that the economic and social development within their jurisdictions is not damaged by water shortages.

[0003] However, based on different concepts of fairness, different bankruptcy theories may produce differentiated water allocation schemes, and regional stakeholders may hold different preferences for these schemes. Therefore, effective evaluation of water allocation schemes is needed to provide decision-makers with feasible water allocation strategies. Existing research typically relies on only one performance criterion for decision-making regarding water allocation schemes based on bankruptcy theory, but different performance criteria are highly likely to lead to conflicting decision outcomes.

[0004] Pareto efficiency, social equity, and scheme stability are typically 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 universally accepted definition of social equity. A generally accepted view is that a fair multilateral environmental agreement should emphasize the concept of distributive justice, i.e., based on egalitarianism. The stability criterion emphasizes the sustainability of resource-sharing agreements, focusing on the cooperative willingness of all parties regarding water allocation schemes. Currently, in water resource management literature related to bankruptcy theory, water allocation typically focuses only on Pareto efficiency. A method that, based on Pareto efficiency, simultaneously considers equity and stability criteria and makes water allocation decisions from the perspective of their equilibrium has not yet emerged. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and apparatus for making decisions on the allocation of water volume in inter-regional rivers that balances fairness and stability. Based on quantified rules of fairness and stability, the invention combines the two using game theory to provide a practical and feasible water allocation strategy for resolving conflicts in the allocation of water volume in inter-regional rivers.

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

[0007] According to the first aspect of this application, a method for cross-regional river water allocation decision-making that balances fairness and stability is provided, including:

[0008] Acquire basic information data on the allocation of water volume in inter-regional rivers. The basic information data includes the allocable water resources, several regional entities, and the declared water volume corresponding to each regional entity.

[0009] Based on basic information data, the problem of cross-regional river water allocation under water shortage is described as a multi-regional subject competition demand problem. The bankruptcy theory rules are used to generate several water allocation schemes, each of which includes the water resource share corresponding to each regional subject.

[0010] 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.

[0011] Game theory is used to generate a combined index of equilibrium fairness and stability for each water allocation scheme. Based on the combined index, all water allocation schemes are ranked to obtain the optimal water allocation scheme.

[0012] In some embodiments of this application, based on the aforementioned scheme, the problem of cross-regional river water allocation under water shortage conditions is described as a multi-regional subject competition demand problem based on basic information data. A water allocation scheme comprising several allocation schemes is generated using bankruptcy theory rules. Each allocation scheme includes the water resource share corresponding to each regional subject, and further includes:

[0013] Establish constraint functions and generate corresponding water allocation schemes using bankruptcy theory rules such as equal proportion, constrained equal benefit, constrained equal loss, adjusted equal proportion, Talmud, or Pin rule.

[0014] In some embodiments of this application, based on the foregoing scheme, obtaining the fairness index of the water allocation scheme based on the Gini index formula includes:

[0015] Based on the water resource share corresponding to each regional entity under the water allocation scheme, the fairness index of the water allocation scheme is obtained using the Gini index formula. The calculation formula is as follows:

[0016] ;

[0017] ;

[0018] In the formula: It is the first Fairness index of water allocation scheme; and They are the first Regional main body under the water allocation scheme and The share of water resources; It is the first The average share of water resources in all regions under the water allocation scheme.

[0019] In some embodiments of this application, based on the foregoing scheme, obtaining the stability index of the water allocation scheme based on the Shapley-Shubik power index formula includes:

[0020] Based on the water resource share obtained by each regional entity under the water allocation scheme, the Shapley-Shubik power index of each regional entity in the water allocation scheme is obtained based on the Shapley-Shubik power index formula. The calculation formula is as follows:

[0021] ;

[0022] ;

[0023] In the formula: It is the main body of the region The maximum water share obtained among all water allocation schemes; It is the main body of the region In the The Shapley-Shubik power index under the water allocation scheme;

[0024] The Shapley-Shubik power indices of all regional entities in the water allocation scheme are averaged to obtain the average index of the water allocation scheme. The calculation formula is as follows:

[0025] ;

[0026] ;

[0027] Based on the arithmetic mean and standard deviation of the Shapley-Shubik power index, the coefficient of variation of each water allocation scheme is calculated as its stability index. The calculation formula is as follows:

[0028] ;

[0029] In the formula: It is the first Stability index of the water allocation scheme; and They are the first The arithmetic mean and standard deviation of the Shapley-Shubik power index for all regions under the seed water allocation scheme.

[0030] In some embodiments of this application, based on the aforementioned scheme, the method of using game theory to generate a combined index of equilibrium fairness index and stability index for each water allocation scheme, and ranking all water allocation schemes based on the combined index to obtain the optimal water allocation scheme:

[0031] The fairness index and stability index of each water allocation scheme are normalized to obtain the normalized fairness value and the normalized stability value of each water allocation scheme. For each water allocation scheme, the normalized fairness value and the normalized stability value are weighted by a linear weight coefficient.

[0032] 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 based on the equilibrium fairness index and stability index based on the optimal linear combination coefficients is generated. All combination indices are sorted, and the combination index with the smallest value is selected. The water allocation scheme corresponding to the smallest combination index is taken as the optimal water allocation scheme.

[0033] In some embodiments of this application, based on the aforementioned scheme, the fairness index and stability index of each water allocation scheme are normalized to obtain the normalized fairness value and stability value of each water allocation scheme, and the normalized fairness value and stability value are weighted using linear weighting coefficients, including:

[0034] The fairness and stability indices of each water allocation scheme are normalized to obtain the normalized fairness and stability values ​​for each scheme. The calculation formula is as follows:

[0035] ;

[0036] ;

[0037] In the formula: and They are the first The fairness normalized value and stability normalized value of the scheme;

[0038] The fairness normalized values ​​of all water allocation schemes are set into a fairness index vector, and the stability normalized values ​​of each water allocation scheme are set into a stability index vector.

[0039] The fairness index vector and the stability index vector are weighted using linear weighting coefficients to obtain the first linear combination vector. The formula for calculating the first linear combination vector is as follows:

[0040] ;

[0041] In the formula: and The linear weighting coefficients corresponding to fairness and stability, respectively; and These are the fairness index vector and the stability index vector, respectively. This is the vector transpose symbol.

[0042] In some embodiments of this application, based on the aforementioned scheme, the step of processing the linear weight coefficients using game theory to obtain the optimal linear combination coefficients, generating a combination index of equilibrium fairness index and stability index based on the optimal linear combination coefficients for each water allocation scheme, sorting all combination indices, and selecting the water allocation scheme corresponding to the smallest combination index as the optimal water allocation scheme, further includes:

[0043] The optimal linear combination coefficient function is obtained by minimizing the deviation between the first linear combination vector and the fairness index vector and the stability index vector. The calculation formula is as follows:

[0044] ;

[0045] In the formula: The symbol for the Euclidean norm;

[0046] Based on the differential properties of matrices, the optimal conditions are obtained using the first derivative of the coefficient function of the optimal linear combination:

[0047] ;

[0048] Solving for the optimal conditions yields the optimal linear combination coefficients that ensure both fairness and stability. Obtain the normalized result of the coefficients of the optimal linear combination:

[0049] ;

[0050] ;

[0051] In the formula: and These are the normalized results of the optimal linear combination coefficients for fairness and stability, respectively.

[0052] Based on the normalized result of the optimal linear combination coefficients, a second linear combination vector is obtained. This 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 for the second linear combination vector is as follows:

[0053] .

[0054] Sort all combination indices in ascending order, and select the water allocation scheme corresponding to the smallest combination index as the optimal water allocation scheme. The calculation formula is as follows:

[0055] ;

[0056] In the formula: It is the optimal water allocation scheme; It is the first The combined index value of the fairness index and stability index of the scheme.

[0057] According to a second aspect of this application, a decision-making device for cross-regional river water allocation that balances fairness and stability is provided, comprising:

[0058] The first acquisition module is used to acquire basic information data on the allocation of water volume in cross-regional rivers. The basic information data includes the amount of allocable water resources, several regional entities, and the declared water volume corresponding to each regional entity.

[0059] The first allocation module is used to describe the problem of cross-regional river water allocation under water shortage conditions as a multi-regional subject competitive demand problem based on basic information data, and to generate several water allocation schemes using bankruptcy theory rules. Each water allocation scheme includes the water resource share corresponding to each regional subject.

[0060] The second acquisition module is used to obtain the fairness index of the water allocation scheme based on the Gini index formula and the stability index of the water allocation scheme based on the Shapley-Shubik power index formula.

[0061] The second allocation module is used to generate a combination index of equilibrium fairness index and stability index for each water allocation scheme using game theory. Based on the combination index, all water allocation schemes are ranked to obtain the optimal water allocation scheme.

[0062] According to a third aspect of this application, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aforementioned method for cross-regional river water allocation decision-making with balance, fairness, and stability.

[0063] According to a fourth aspect of this application, a non-transitory computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the above-described method for cross-regional river water allocation decision-making with balance, fairness, and stability.

[0064] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0065] This invention provides a method and apparatus for balancing fairness and stability in cross-regional river water allocation decisions. It acquires basic information data such as the allocable water resources of cross-regional rivers, the involved regional entities, and the declared water volume of each entity. The method describes the cross-regional river water allocation problem under water scarcity as a multi-regional entity competitive demand problem, and uses bankruptcy theory rules to generate several water allocation schemes. Based on the fairness and justice of the allocation, it proposes a quantification method for the fairness of the water allocation schemes using the Gini index formula. Based on the acceptability at the individual level, it proposes a quantification method for the stability of the water allocation schemes using the Shapley-Shubik power index formula. Finally, it uses game theory to propose several water allocation schemes that balance fairness and stability, ranks these schemes, and obtains the optimal water allocation scheme. This invention addresses water allocation schemes based on bankruptcy theory rules from the perspective of balancing fairness and stability. It innovatively proposes using game theory to balance fairness and stability indices, constructing a cross-regional river water allocation decision-making method that comprehensively considers fairness, justice, and individual-level acceptability. This avoids the one-sidedness of decisions based on a single evaluation criterion and provides decision-makers with a realistic and feasible water allocation scheme. Attached Figure Description

[0066] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and are intended to explain the invention, but do not constitute an undue limitation thereof. In the drawings:

[0067] Figure 1 This is a flowchart illustrating a cross-regional river water allocation decision-making method that balances fairness and stability in this embodiment.

[0068] Figure 2 A schematic diagram of the fairness normalized value, stability normalized value, and combined index of equilibrium fairness index and stability index for inter-regional river water allocation schemes under different water inflow frequencies.

[0069] Figure 3 This embodiment presents a schematic diagram of a cross-regional river water allocation decision-making device that balances fairness and stability. Detailed Implementation

[0070] To make the technical problems to be solved, the technical solutions, and the beneficial technical effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and several exemplary embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of protection of this invention.

[0071] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a thorough understanding of embodiments of this application. However, those skilled in the art will recognize that the technical solutions of this application can be practiced without one or more of the specific details, or other methods, components, apparatuses, steps, etc., can be employed. In other instances, well-known methods, apparatuses, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of this application.

[0072] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0073] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily need to be performed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0074] Figure 1 The flowchart illustrates a cross-regional river water allocation decision-making method that balances fairness and stability according to this embodiment.

[0075] According to a first aspect of this application, this embodiment provides a method for balancing fairness and stability in the allocation of water volume across regions of rivers, including:

[0076] Step S1: Obtain basic information data on the allocation of water volume in inter-regional rivers. The basic information data includes the amount of water resources available for allocation, several regional entities, and the declared water volume corresponding to each regional entity.

[0077] In some embodiments of this example, the regional subject can be an administrative region or geographical unit at different levels, such as a provincial-level administrative region, a prefecture-level administrative region, a river basin or water system unit. This example does not limit this.

[0078] In some implementations of this embodiment, when the amount of water resources available across regions cannot meet the total demand of all regional entities, conflicts may occur between the various regional entities due to competition for water.

[0079] Step S2: Based on basic information data, the problem of cross-regional river water allocation under water shortage is described as a multi-regional subject competition demand problem. Several water allocation schemes are generated using bankruptcy theory rules. Each water allocation scheme includes the water resource share corresponding to each regional subject.

[0080] In some embodiments of this example, the problem of inter-regional river water allocation under water shortage conditions is described as a multi-regional subject competition demand problem, i.e., a limited number of regional subjects. Based on its declared water volume Competition for the allocable water resources of inter-regional rivers Available water resources It is difficult to meet the total declared water volume of all regional entities. .

[0081] In some embodiments of this example, based on basic information data, the problem of cross-regional river water allocation under water shortage conditions is described as a multi-regional subject competition demand problem. Bankruptcy theory rules are used to generate a water allocation scheme that includes several water allocation plans. Each water allocation plan includes the water resource share corresponding to each regional subject, and also includes:

[0082] Establish constraint functions and generate corresponding water allocation schemes using bankruptcy theory rules such as equal proportion, constrained equal benefit, constrained equal loss, adjusted equal proportion, Talmud, or Pin rule.

[0083] The constraint functions are three basic constraints that take into account Pareto validity, boundedness, and nonnegativity.

[0084] 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.

[0085] In cross-regional water allocation, considering the fairness index can effectively protect the main entities in areas with lower water demand and prevent them from being affected by water shortages in their socio-economic development; while considering the stability index can ensure that the water allocation plan is effective in the long term and avoid frequent adjustments that lead to management chaos.

[0086] In some embodiments of this example, the fairness index of the water allocation scheme is obtained based on the Gini index formula, including:

[0087] Based on the water resource share corresponding to each regional entity under the water allocation scheme, the fairness index of the water allocation scheme is obtained using the Gini index formula. The calculation formula is as follows:

[0088] (1);

[0089] (2);

[0090] In the formula: It is the first Fairness index of water allocation scheme; and They are the first Regional main body under the water allocation scheme and The share of water resources; It is the first The average share of water resources in all regions under the water allocation scheme.

[0091] Therefore, based on the principle of fairness and justice in the allocation, a quantitative method for assessing the fairness of water allocation schemes is proposed.

[0092] In some embodiments of this example, the stability index of the water allocation scheme is obtained based on the Shapley-Shubik power index formula, including:

[0093] Based on the water resource share obtained by each regional entity under the water allocation scheme, the Shapley-Shubik power index of each regional entity in the water allocation scheme is obtained based on the Shapley-Shubik power index formula. The calculation formula is as follows:

[0094] (3);

[0095] (4);

[0096] In the formula: It is the main body of the region The maximum water share obtained among all water allocation schemes; It is the main body of the region In the The Shapley-Shubik power index under the water allocation scheme;

[0097] The Shapley-Shubik power indices of all regional entities in the water allocation scheme are averaged to obtain the average index of the water allocation scheme. The calculation formula is as follows:

[0098] (5);

[0099] (6);

[0100] Based on the arithmetic mean and standard deviation of the Shapley-Shubik power index, the coefficient of variation of each water allocation scheme is calculated as its stability index. The calculation formula is as follows:

[0101] (7);

[0102] In the formula: It is the first Stability index of the water allocation scheme; and They are the first The arithmetic mean and standard deviation of the Shapley-Shubik power index for all regions under the seed water allocation scheme.

[0103] Therefore, starting from the acceptability at the individual level, a quantitative method for the stability of water allocation schemes is proposed.

[0104] Step S4: Use game theory to generate a combination index of equilibrium fairness index and stability index for each water allocation scheme. Sort all water allocation schemes based on the combination index to obtain the optimal water allocation scheme.

[0105] In some embodiments of this example, game theory is used to generate a combined index of equilibrium fairness and stability for each water allocation scheme. Based on this combined index, all water allocation schemes are ranked to obtain the optimal water allocation scheme, including:

[0106] Step S401: Normalize the fairness index and stability index of each water allocation scheme to obtain the normalized fairness value and the normalized stability value of each water allocation scheme. For each water allocation scheme, use a linear weighting coefficient to weight the normalized fairness value and the normalized stability value.

[0107] Step S402: Use game theory to process the linear weight coefficients to obtain the optimal linear combination coefficients. For each water allocation scheme, generate a combination index based on the equilibrium fairness index and stability index of the optimal linear combination coefficients. Sort all combination indices and select the water allocation scheme corresponding to the smallest combination index as the optimal water allocation scheme.

[0108] In some embodiments of this example, the fairness index and stability index of each water allocation scheme are normalized to obtain the normalized fairness value and the normalized stability value of each water allocation scheme. For each water allocation scheme, the normalized fairness value and the normalized stability value are weighted using a linear weighting coefficient, including:

[0109] The fairness and stability indices of each water allocation scheme are normalized to obtain the normalized fairness and stability values ​​for each scheme. The calculation formula is as follows:

[0110] (8);

[0111] (9);

[0112] In the formula: and They are the first The fairness normalized value and stability normalized value of the scheme;

[0113] The fairness normalized values ​​of all water allocation schemes are set into a fairness index vector, and the stability normalized values ​​of each water allocation scheme are set into a stability index vector.

[0114] The fairness index vector and the stability index vector are weighted using linear weighting coefficients to obtain the first linear combination vector. The formula for calculating the first linear combination vector is as follows:

[0115] (10);

[0116] In the formula: and The linear weighting coefficients corresponding to fairness and stability, respectively; and These are the fairness index vector and the stability index vector, respectively. This is the vector transpose symbol.

[0117] In some embodiments of this example, 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 based on the equilibrium fairness index and stability index of the optimal linear combination coefficients is generated. All combination indices are sorted, and the water allocation scheme corresponding to the smallest combination index is selected as the optimal water allocation scheme. The method also includes:

[0118] The optimal linear combination coefficient function is obtained by minimizing the deviation between the first linear combination vector and the fairness index vector and the stability index vector. The calculation formula is as follows:

[0119] (11);

[0120] In the formula: The symbol for the Euclidean norm;

[0121] Based on the differential properties of matrices, the optimal conditions are obtained using the first derivative of the coefficient function of the optimal linear combination:

[0122] (12);

[0123] Solving for the optimal conditions yields the optimal linear combination coefficients that ensure both fairness and stability. Obtain the normalized result of the coefficients of the optimal linear combination:

[0124] (13);

[0125] (14);

[0126] In the formula: and These are the normalized results of the optimal linear combination coefficients for fairness and stability, respectively.

[0127] Based on the normalized result of the optimal linear combination coefficients, a second linear combination vector is obtained. This 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 for the second linear combination vector is as follows:

[0128] (15);

[0129] Sort all combination indices in ascending order, and select the water allocation scheme corresponding to the smallest combination index as the optimal water allocation scheme. The calculation formula is as follows:

[0130] (16);

[0131] In the formula: It is the optimal water allocation scheme; It is the first The combined index value of the fairness index and stability index of the scheme.

[0132] In summary, by calculating the fairness and stability of inter-regional river water allocation schemes and based on game theory, a decision-making method is constructed that comprehensively considers the fairness and justice of allocation and the acceptability at the individual level. This method can achieve an effective trade-off between the two performance criteria of fairness and stability, thus contributing to the scientific and rational implementation of inter-regional river water allocation decisions under water scarcity conditions. It is simple and easy to implement, and the results are straightforward. Compared with existing technologies, this paper proposes for the first time to use game theory to balance the fairness and stability criteria, and then proposes corresponding decision-making techniques. This is of great significance for coordinating water use conflicts among various regional entities in inter-regional rivers under water scarcity conditions, and achieving a relatively favorable and realistically feasible water allocation strategy for each regional entity.

[0133] Furthermore, this embodiment proposes to use the Gini coefficient and the Shapley-Shubik power index method respectively to quantify the fairness and stability of the water allocation scheme.

[0134] 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 dependence of the linear weighting method on the subjective preferences of the management subject.

[0135] Furthermore, this embodiment proposes for the first time to make decisions on water allocation schemes in the event of water bankruptcy from the perspective of balancing the two performance criteria of fairness and stability. This not only helps to resolve the conflict of interests among various regional entities in the allocation of water in cross-regional rivers under water shortage conditions, but also enriches the application of bankruptcy theory and game theory in the field of water resource management decision-making.

[0136] To make the objectives, technical solutions, and advantages of this embodiment clearer, the technical solution of this method will be described below in conjunction with this embodiment. It should be understood that the specific embodiments described herein are only used to explain this embodiment and are not intended to limit this embodiment.

[0137] See appendix Figure 1 The flowchart of the inter-regional river water allocation decision-making method that balances fairness and stability proposed in this embodiment clearly shows the specific implementation process. The following example uses the water allocation of a specific inter-regional river as an illustration to further introduce the method. This inter-regional river water allocation involves 10 regions: A, B, C, D, E, F, G, H, I, and J. The total water demand under 75% and 95% inflow frequencies is 13.8068 billion m³. 3 and 16.324 billion m 3 The allocable water volume is 13.493 billion m³. 3 and 11.312 billion m 3 The corresponding water shortage is 313.8 million cubic meters. 3 and 5.012 billion m 3 Table 1 shows the water demand of the main body of the cross-regional river under different water inflow frequencies.

[0138] Table 1. Water demand of main areas under different water inflow frequencies (unit: 100 million m³)

[0139]

[0140] When the available water volume of a cross-regional river cannot meet the needs of all regional entities, conflicts may arise among them due to competition for water. This situation is very similar to a company facing bankruptcy because its remaining assets are insufficient to fully cover its debts. Therefore, the problem of water allocation in cross-regional rivers under water scarcity can be described as a multi-regional entity competition problem, where 10 regional entities compete for a limited amount of allocable water in a cross-regional river based on their declared water volume (when P=75%). billion m 3 When P=95% billion m 3 Furthermore, this water volume is insufficient to meet the total declared water volume of all regional entities (when P=75%). billion m 3 When P=95% billion m 3Based on the three basic constraints of Pareto validity, declaration boundedness, and nonnegativity, this embodiment uses bankruptcy theory rules such as Proportional (PRO), Constrained Equal Gain (CEA), Constrained Equal Loss (CEL), Adjusted Proportional (APRO), Talmud (Tal), and Piniles' (Pin) to generate water allocation schemes for inter-regional rivers under different water inflow frequencies, and then normalizes them to obtain the water share of each region's main body. The results are shown in Table 2.

[0141] Table 2. Water allocation share of each region in cross-regional rivers under different scenarios

[0142]

[0143] Using the method provided in this embodiment, the fairness index (Fai) of each water allocation scheme was obtained, and the results are shown in Table 3.

[0144] Table 3 Fairness Index of Water Allocation Scheme for Inter-regional Rivers

[0145]

[0146] Using the method provided in this embodiment, the stability index (Sta) of each water allocation scheme was obtained, and the results are shown in Table 4.

[0147] Table 4. Stability Index of Water Allocation Scheme for Inter-regional Rivers

[0148]

[0149] Calculations show that the optimal linear combination coefficient for the fairness and stability of the water allocation scheme is as follows, under a 75% water inflow frequency: Obtain the normalized result of its optimal linear combination coefficients. The optimal linear combination coefficient for the fairness and stability of the water allocation scheme under a 95% water inflow frequency is: Obtain the normalized result of its optimal linear combination coefficients. Substituting this into formula (15), we obtain the second linear combination vector. , This includes a combined index (FS) of the equilibrium fairness index and the stability index corresponding to each water allocation scheme. For example... Figure 2 The diagram shows the normalized values ​​of fairness, stability, and the combined index of equilibrium fairness index and stability index for the cross-regional river water allocation scheme under different water inflow frequencies in this embodiment.

[0150] Depend on Figure 2It can be seen that, at a 75% water inflow frequency, the CEA and Pin schemes are the fairest water allocation schemes for inter-regional rivers, while the CEL scheme is the most unfair; the CEL scheme is the most stable water allocation scheme, while the CEA / Pin scheme is the most unstable. At a 95% water inflow frequency, the CEA scheme is the fairest water allocation scheme for inter-regional rivers, while the CEL scheme is the most unfair; the APRO scheme is the most stable water allocation scheme, while the CEA scheme is the most unstable. This demonstrates that there is a certain equilibrium relationship between fairness and stability criteria in the water resource allocation scheme decision-making process. Using game theory, from the perspective of the equilibrium between fairness and stability criteria, the normalized value of fairness (Fai) and the normalized value of stability (Sta) are aggregated to obtain the combined index (FS) of equilibrium fairness and stability indices.

[0151] A combined index of equilibrium fairness and stability (FS) was used to rank the water allocation schemes for inter-regional rivers under different inflow frequencies in ascending order. The water allocation scheme corresponding to the smallest combined index was selected as the optimal water allocation scheme. The ranking results show that at a 75% inflow frequency, the water allocation scheme based on the CEL rule is optimal, while the schemes based on the CEA and Pin rules are the worst. At a 95% inflow frequency, the water allocation scheme based on the APRO rule is optimal, while the scheme based on the CEA rule is the worst.

[0152] According to a second aspect of this application, a decision-making device for cross-regional river water allocation that balances fairness and stability is provided, such as... Figure 3 As shown, it includes:

[0153] The first acquisition module is used to acquire basic information data on the allocation of water volume in cross-regional rivers. The basic information data includes the amount of allocable water resources, several regional entities, and the declared water volume corresponding to each regional entity.

[0154] The first allocation module is used to describe the problem of cross-regional river water allocation under water shortage conditions as a multi-regional subject competitive demand problem based on basic information data, and to generate several water allocation schemes using bankruptcy theory rules. Each water allocation scheme includes the water resource share corresponding to each regional subject.

[0155] The second acquisition module is used to obtain the fairness index of the water allocation scheme based on the Gini index formula and the stability index of the water allocation scheme based on the Shapley-Shubik power index formula.

[0156] The second allocation module is used to generate a combination index of equilibrium fairness index and stability index for each water allocation scheme using game theory. Based on the combination index, all water allocation schemes are ranked to obtain the optimal water allocation scheme.

[0157] Specifically, this embodiment corresponds one-to-one with the above method embodiments. The functions of each module have been described in detail in the corresponding method embodiments, so they will not be repeated here.

[0158] According to a third aspect of this application, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the aforementioned method for cross-regional river water allocation decision-making that achieves balance, fairness, and stability.

[0159] According to a fourth aspect of this application, a non-transitory computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the aforementioned method for cross-regional river water allocation decision-making that achieves balance, fairness, and stability.

[0160] The memory in this embodiment of the 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.

[0161] The cross-regional river water allocation decision-making method for balance, fairness, and stability disclosed in this invention can be applied to a processor 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 balance, fairness, and stability can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The processor can implement or execute the methods, steps, and logic block diagrams disclosed in this invention's embodiments. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention's embodiments can be directly manifested as execution by a hardware decoding processor, or execution by a combination of hardware and software modules in the decoding processor. The software modules can be located in a storage medium, specifically 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 balance, fairness, and stability provided in this invention's embodiments.

[0162] 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 methods.

[0163] It is understood that memory can be volatile or non-volatile, or both. 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), ferromagnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc, or compact disc read-only memory (CD-ROM); magnetic surface memory can be disk storage or magnetic tape storage. Volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but 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), Sync Link Dynamic Random Access Memory (SLDRAM), and Direct Rambus Random Access Memory (DRRAM).The memories described in the embodiments of this invention are intended to include, but are not limited to, these and any other suitable types of memories.

[0164] The above embodiments are merely illustrative examples of the technical solutions of the present invention. The methods involved in the present invention are not limited to those described in the above embodiments, but are defined by the scope of the claims. Any modifications, additions, or equivalent substitutions made by those skilled in the art based on these embodiments are within the scope of protection claimed by the claims of the present invention.

Claims

1. A decision-making method for cross-regional river water allocation that balances fairness and stability, characterized in that, include: Acquire basic information data on the allocation of water volume in inter-regional rivers. The basic information data includes the allocable water resources, several regional entities, and the declared water volume corresponding to each regional entity. Based on basic information data, the problem of cross-regional river water allocation under water shortage is described as a multi-regional subject competition demand problem. The bankruptcy theory rules are used to generate several water allocation schemes, each of which includes the water resource share corresponding to each regional subject. 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. Game theory is used to generate a combined index of equilibrium fairness and stability for each water allocation scheme. Based on this combined index, all water allocation schemes are ranked to obtain the optimal water allocation scheme. Specifically: The fairness index and stability index of each water allocation scheme are normalized to obtain the normalized fairness value and the normalized stability value of each water allocation scheme. For each water allocation scheme, the normalized fairness value and the normalized stability value are weighted by 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 equilibrium fairness index and stability index based on the optimal linear combination coefficients is generated. All combination indices are sorted, and the water allocation scheme corresponding to the smallest combination index is selected as the optimal water allocation scheme.

2. The method according to claim 1, characterized in that, Based on basic information data, the problem of cross-regional river water allocation under water shortage conditions is described as a multi-regional subject competition demand problem. Bankruptcy theory rules are used to generate a water allocation scheme including several allocation options. Each allocation scheme includes the water resource share corresponding to each regional subject, and also includes: Establish constraint functions and generate corresponding water allocation schemes using bankruptcy theory rules such as equal proportion, constrained equal benefit, constrained equal loss, adjusted equal proportion, Talmud, 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 scheme, the fairness index of the water allocation scheme is obtained using the Gini index formula. The calculation formula is as follows: ； ； In the formula: It is the first Fairness index of water allocation scheme; and They are the first Regional main body under the water allocation scheme and The share of water resources; It is the first The average share of water resources in all regions under the water allocation scheme.

4. The method according to claim 1, characterized in that, 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 scheme, the Shapley-Shubik power index of each regional entity in the water allocation scheme is obtained based on the Shapley-Shubik power index formula. The calculation formula is as follows: ； ； In the formula: It is the main body of the region The maximum water share obtained among all water allocation schemes; It is the main body of the region In the The Shapley-Shubik power index under the water allocation scheme It is the first Regional main body under the water allocation scheme The share of water resources; The Shapley-Shubik power indices of all regional entities in the water allocation scheme are averaged to obtain the arithmetic mean and standard deviation of the water allocation scheme. The calculation formula is as follows: ； ； Based on the arithmetic mean and standard deviation of the Shapley-Shubik power index, the coefficient of variation of each water allocation scheme is calculated as its stability index. The calculation formula is as follows: ； In the formula: It is the first Stability index of the water allocation scheme; and They are the first The arithmetic mean and standard deviation of the Shapley-Shubik power index for all regions under the seed water allocation scheme.

5. The method according to claim 1, characterized in that, The process involves normalizing the fairness and stability indices of each water allocation scheme to obtain normalized fairness and stability values ​​for each scheme. Then, a linear weighting coefficient is used to weight these normalized fairness and stability values, including: The fairness and stability indices of each water allocation scheme are normalized to obtain the normalized fairness and stability values ​​for each scheme. The calculation formula is as follows: ； ； In the formula: and They are the first The fairness normalized value and stability normalized value of the scheme, It is the first The fairness index of the water allocation scheme. It is the first Stability index of the water allocation scheme; The fairness normalized values ​​of all water allocation schemes are set into a fairness index vector, and the stability normalized values ​​of each water allocation scheme are set into a stability index vector. The fairness index vector and the stability index vector are weighted using linear weighting coefficients to obtain the first linear combination vector. The formula for calculating the first linear combination vector is as follows: ； In the formula: and The linear weighting coefficients corresponding to fairness and stability, respectively; and These are the fairness index vector and the stability index vector, respectively. This is the vector transpose symbol.

6. The method according to claim 5, characterized in that, The process involves using game theory to process the linear weight coefficients to obtain the optimal linear combination coefficients. For each water allocation scheme, a combination index based on the equilibrium fairness index and stability index of the optimal linear combination coefficients is generated. All combination indices are sorted, and the combination index with the smallest value is selected. The water allocation scheme corresponding to the smallest combination index is taken as the optimal water allocation scheme. The process also includes: The optimal linear combination coefficient function is obtained by minimizing the deviation between the first linear combination vector and the fairness index vector and the stability index vector. The calculation formula is as follows: ； In the formula: The symbol for the Euclidean norm; Based on the differential properties of matrices, the optimal conditions are obtained using the first derivative of the coefficient function of the optimal linear combination: ； Solving for the optimal conditions yields the optimal linear combination coefficients that ensure both fairness and stability. Obtain the normalized result of the coefficients of the optimal linear combination: ； ； In the formula: and These are the normalized results of the optimal linear combination coefficients for fairness and stability, respectively. Based on the normalized result of the optimal linear combination coefficients, a second linear combination vector is obtained. This 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 for the second linear combination vector is as follows: ； Sort all combination indices in ascending order, and select the water allocation scheme corresponding to the smallest combination index as the optimal water allocation scheme. The calculation formula is as follows: ； In the formula: It is the optimal water allocation scheme; It is the first The combined index value of the fairness index and stability index of the scheme.

7. A decision-making device for cross-regional river water allocation that balances fairness and stability, applied to the cross-regional river water allocation decision-making method for balancing fairness and stability as described in any one of claims 1-6, characterized in that, include: The first acquisition module is used to acquire basic information data on the allocation of water volume in cross-regional rivers. The basic information data includes the amount of allocable water resources, several regional entities, and the declared water volume corresponding to each regional entity. The first allocation module is used to describe the problem of cross-regional river water allocation under water shortage conditions as a multi-regional subject competitive demand problem based on basic information data, and to generate several water allocation schemes using bankruptcy theory rules. Each water allocation scheme includes the water resource share corresponding to each regional subject. The second acquisition module is used to obtain the fairness index of the water allocation scheme based on the Gini index formula and the stability index of the water allocation scheme based on the 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 scheme using game theory. Based on the combination index, all water allocation schemes are ranked to obtain the optimal water allocation scheme.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the cross-regional river water allocation decision-making method with balanced fairness and stability as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the cross-regional river water allocation decision method as described in any one of claims 1 to 6, which balances fairness and stability.

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