Method for determining priority target in multi-objective regulation of water conservancy and hydropower resources

Abstract

The application discloses a determination method, in particular to a determination method for priority target in multi-target regulation of water conservancy and hydropower resources, and belongs to the technical field of water conservancy and hydropower resource utilization distribution process. The application provides a determination method for priority target in multi-target regulation of water conservancy and hydropower resources, which can select priority target based on the conflict relationship among various targets in numerous targets. The determination method is based on a plurality of single-target optimal solution sets obtained by solving each target respectively, constructs a directional fuzzy conflict matrix through degeneration analysis, then based on the directional fuzzy conflict matrix and the overall conflict intensity requirement, constructs a multi-target priority determination function on the basis of the fusion of subjective and objective weights by using the DEMATEL structure analysis method, finally sorts each target from large to small according to the calculation results of the Priority function, and determines the priority order of each target in the multi-target according to the sorting results.

Description

Technical Field

[0001] This invention relates to a determination method, and more particularly to a method for determining priority targets in multi-objective regulation of water conservancy and hydropower resources, belonging to the field of water conservancy and hydropower resource utilization and allocation technology. Background Technology

[0002] In the process of optimizing water resource system scheduling and making multi-objective engineering decisions, it is usually necessary to consider multiple conflicting objectives such as power generation, flood control, sediment regulation, and ecological protection. Due to the significant resource competition and functional coupling relationships among these objectives, how to scientifically characterize the conflict relationships between objectives and rationally determine their priorities has always been a key issue in the field of multi-objective optimization.

[0003] Traditional multi-objective decision-making methods mainly include weighted summation, Analytic Hierarchy Process (AHP), Fuzzy Analytic Hierarchy Process (FAHP), TOPSIS, and the Dematel method based on system analysis. Among these, AHP and FAHP methods primarily determine objective weights by constructing a judgment matrix through experts, thereby achieving a ranking driven by subjective preferences. The Dematel method, on the other hand, analyzes the causal structure of the system by constructing an influence relationship matrix between factors to identify key driving and influenced factors. In addition, some studies employ conflict matrices or Pareto front-based multi-objective analysis methods to describe the competitive or substitution relationships between objectives. These methods can reflect the mutual constraints among multiple objectives to a certain extent.

[0004] However, the above methods still have the following shortcomings:

[0005] 1) Most methods rely on expert experience or static evaluation indicators, lack objective data support based on system optimization results, and are difficult to reflect the target conflict mechanism in the real operation process;

[0006] 2) Existing conflict analysis methods are usually based on differences in objective functions or Pareto dominance, which makes it difficult to characterize the directional conflict feature of "the improvement of one objective's performance leading to the degradation of another objective's performance";

[0007] 3) The conflict relationship analysis and weight determination processes are relatively separate, failing to form a unified multi-objective priority decision-making framework;

[0008] 4) Although system structure analysis methods (such as DEMATEL) can characterize causal relationships, they are usually not combined with the optimization degradation process, resulting in a disconnect between structure analysis and actual optimization behavior.

[0009] As mentioned earlier, existing methods mainly include weighted summation, analytic hierarchy process (AHP), fuzzy analytic hierarchy process (FAHP), TOPSIS, and Dematel structural analysis. Among them, FAHP and Dematel methods mainly rely on expert experience to construct judgment matrices or influence relationship matrices to calculate target weights and analyze system structure; while conflict matrix and Pareto front analysis methods mainly characterize the competitive relationships between multiple objectives based on differences or dominance relationships in objective functions.

[0010] Therefore, existing methods for determining this still have the following structural shortcomings:

[0011] 1) Lack of conflict generation mechanism based on optimization process: Existing methods usually construct the target relationship based on static indicators or expert assignments, and fail to extract the real performance degradation information between targets from the single-objective optimization results;

[0012] 2) Difficulty in characterizing the directional conflict relationship between objectives: Existing conflict analysis methods are mostly symmetrical relationships or static difference measures, which cannot reflect the asymmetric impact characteristics of "optimization of one objective leading to performance degradation of another objective";

[0013] 3) Lack of a unified framework for expressing conflict relationships, weighting mechanisms and system structure analysis: Existing methods usually conduct conflict analysis, weight determination and causal structure analysis independently, and there is a lack of internal consistency and coupling mechanism among the three.

[0014] 4) The lack of a multi-objective priority generation mechanism based on optimization degradation information leads to the multi-objective ranking results relying on a single weight system, resulting in insufficient stability and interpretability. Summary of the Invention

[0015] The technical problem to be solved by the present invention is to provide a method for determining priority targets in multi-objective regulation of water conservancy and hydropower resources, which can optimize the selection of priority targets based on the objective conflict relationship between various targets and the subjective judgment of professionals.

[0016] The technical solution adopted to solve the above-mentioned technical problems is: a method for determining priority targets in multi-objective regulation of water conservancy and hydropower resources. This method is based on multiple sets of optimal solutions for each single objective obtained by solving each objective separately. A directional fuzzy conflict matrix is ​​constructed through degradation analysis. Then, based on this directional fuzzy conflict matrix, the overall conflict intensity of each objective is determined. Finally, by integrating objective conflict analysis and subjective weights, the Dematel structural analysis method is used to construct a multi-objective priority determination function. Finally, the objectives are sorted from largest to smallest according to the Priority function calculation results, and the priority order of each objective in the multi-objective system is determined based on the sorting results.

[0017] in, This is the comprehensive weight after correcting the subjective weights of FAHP based on objective conflict analysis; Net impact; This is the structural influence adjustment coefficient, which can be set to 1.

[0018] Furthermore, the process of finding the optimal solution set for a single objective is as follows: taking each objective in the multi-objective system as the object, a single-objective optimization model is constructed for each objective, and the optimal operating scheme corresponding to each objective is solved separately, finally obtaining the optimal solution set for each objective.

[0019] The optimal solution set is the set of single-objective solutions that are independently optimized for each objective.

[0020] The preferred approach to the above scheme is as follows: The process of constructing the directional fuzzy conflict matrix through degradation analysis is as follows:

[0021] First, define the performance degradation function between targets. Then, based on the introduction of engineering tolerance threshold and conflict threshold, a fuzzy membership function is constructed. The directional conflict degree between targets is obtained. Finally, based on the degree of directional conflict between targets, a directional fuzzy conflict matrix is ​​formed. ,

[0022] Among them, the performance degradation function The value in the table represents the index value of the i-th solution relative to the j-th objective. , Let be the maximum and minimum index values ​​of the j-th objective, respectively. Characterize the degradation rate of objective j under solution / scheme i. This indicates that there has been no degradation. This indicates that objective j suffers complete loss under the optimal solution for objective i;

[0023] Fuzzy membership functions The engineering fuzzy membership degree of solution / scheme i to target j is represented by a, where a represents the engineering allowable degradation threshold and b represents the complete conflict threshold, both of which are determined by engineers based on experience.

[0024] In directional conflict degree, when the degradation rate When smaller, ,at this time This indicates that the directional conflict between target i and target j is relatively weak; conversely, when the degradation rate exceeds the engineering tolerance range, 1. The degree of conflict is close to the actual degradation rate;

[0025] In the directional fuzzy conflict matrix, n represents the total number of targets. This matrix is ​​used to characterize the directional conflict influence relationship between target i and target j.

[0026] Furthermore, before defining the performance degradation function between objectives, in the process of solving the set of optimal solutions for a single objective, each solution is first substituted into the objective function according to the single objective solution optimized independently for each objective, and the index value of each solution for each objective is calculated. Then, the optimal solution of a certain objective is used as a reference benchmark to analyze the degree of performance degradation of other objectives under the condition of the optimal solution and define the performance degradation function between objectives.

[0027] The preferred approach to the above scheme is that the overall conflict intensity is calculated using the following formula:

[0028] ,

[0029] in, It is used to characterize the degree of conflict participation of the target in the system; the larger the CI, the more likely the target is to conflict with other targets, and the smaller the CI, the stronger the compatibility of the target.

[0030] Furthermore, the subjective weights are FAHP subjective weights of each objective obtained by constructing a judgment matrix based on fuzzy hierarchical analysis and then performing fuzzy consistency processing and defuzzification calculation.

[0031] The preferred method for the above scheme is as follows: The process for calculating the FAHP subjective weights is as follows:

[0032] First, obtain the triangular fuzzy number of each target according to the triangular fuzzy number standard mapping table, and denote the set of each evaluation target as... Let the triangular fuzzy number representing the importance of target j relative to target k be . The triplet of the triangular fuzzy number These correspond to conservative estimates, core judgments, and optimistic estimates, respectively.

[0033] Then, the fuzzy comprehensive evaluation value of each objective is determined based on the triangular fuzzy number. When the total number of targets Fuzzy comprehensive evaluation value of target j according to Calculate when the total number of targets Fuzzy comprehensive evaluation value of target j The algorithm was adjusted to ,in, The initial fuzzy weights are generally taken as... ; To select the smaller operator, the triplet of two triangular fuzzy numbers is... Take the minimum value respectively; To obtain the largest operator, for The triplet of multiple triangular fuzzy numbers takes the maximum value respectively; For multiplication operators, the triplet of two triangular fuzzy numbers Calculate the product separately; For the summation operator, for Sum the triples of multiple triangular fuzzy numbers respectively

[0034] Next, the fuzzy basic weights of each objective are determined based on the fuzzy comprehensive evaluation values. ,in, For fuzzy multiplication, the triples of triangular fuzzy numbers Perform multiplication on each tuple separately; This represents the fuzzy addition of the comprehensive fuzzy evaluation values ​​of all targets, and the addition of the triples of multiple triangular fuzzy numbers respectively; Indicates a fuzzy reciprocal, such as ;

[0035] Finally, the FAHP subjective weights are determined based on the fuzzy basic weights, and the triples of the fuzzy basic weights for target j correspond to... The clear weights after defuzzification using the centroid method After normalization, the FAHP subjective weights are obtained. .

[0036] Furthermore, after the FAHP subjective weights are calculated, the conflict-driven weights need to be corrected to obtain a comprehensive weight that reflects the actual importance of the target in a conflict environment. The process is as follows:

[0037] First, define the conflict penalty coefficient. ,in, This is an adjustable parameter and can be set to 1; the greater the total conflict intensity of objective j, the more likely the achievement of this objective will harm other objectives, and the heavier the penalty will be.

[0038] Then, based on the conflict analysis, the combined weight of subjective weight and conflict intensity is calculated and corrected according to the post-formula. .

[0039] The preferred approach to the above scheme is as follows, based on the structural impact analysis process of DEMATEL:

[0040] First, construct the output influence based on the fuzzy conflict matrix. and input impact The system impact relationships are then considered, and based on a comprehensive assessment of the structural roles of each objective in the overall trade-off system, a net impact value based on the DEMATEL framework is introduced and defined. , used to characterize the systemic causal properties of a target.

[0041] The beneficial effects of this invention are as follows: The determination method provided in this application first solves for each objective separately and obtains the optimal solution set corresponding to each objective. Then, it quantifies directional conflict through degradation analysis and a directional fuzzy conflict matrix, corrects the subjective weights of FAHP based on conflict intensity, and finally uses a priority determination function constructed by the DEMATEL structural analysis method to calculate and sort the priorities of each objective, thereby achieving the goal of determining the priority order of each objective based on the ranking. This effectively solves many defects of the single-objective analysis in the prior art, and achieves the goal of selecting priority objectives based on the conflict relationships between various objectives and the subjective judgment of professionals among numerous objectives. It solves the optimal selection problem in power generation, flood control, sediment regulation, and ecological protection during the optimal scheduling and multi-objective engineering decision-making process of water resource systems. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating the optimal solution determination method for determining priority objectives in multi-objective regulation of water conservancy and hydropower resources according to the present invention. Detailed Implementation

[0043] like Figure 1 This invention presents a method for determining priority objectives in multi-objective regulation of water conservancy and hydropower resources. This method optimizes the selection of priority objectives based on objective conflict relationships among various objectives and the subjective judgment of professionals. The method is based on multiple sets of optimal solutions obtained by solving each objective separately. A directional fuzzy conflict matrix is ​​constructed through degradation analysis. Then, based on this matrix, the overall conflict intensity requirement for each objective is determined. Finally, by integrating objective conflict analysis and subjective weighting, the Dematel structural analysis method is used to construct a multi-objective priority determination function. Finally, the objectives are sorted from largest to smallest according to the Priority function calculation results, and the priority order of each objective in the multi-objective system is determined based on the sorting results.

[0044] in, This is the comprehensive weight after correcting the subjective weights of FAHP based on objective conflict analysis; Net impact; The structural influence adjustment coefficient can be set to 1. The method provided in this application first solves for each objective separately and obtains the optimal solution set for each objective. Then, it quantifies directional conflict through degradation analysis and a directional fuzzy conflict matrix, corrects the FAHP subjective weights based on conflict intensity, and finally uses a priority determination function constructed by the DEMATEL structural analysis method to calculate and sort the priorities of each objective. This effectively solves many shortcomings of existing technologies that use single-objective analysis, and achieves the goal of selecting priority objectives based on the conflict relationships between various objectives and the subjective judgment of professionals. It solves the optimal selection problem in power generation, flood control, sediment regulation, and ecological protection during the optimal scheduling and multi-objective engineering decision-making process of water resource systems.

[0045] Accordingly, to facilitate the computation and solution of each objective and the construction of short matrices, the solution process for the single-objective optimal solution set in this application is as follows: taking each objective in the multi-objective system as the object, a single-objective optimization model is constructed for each objective, and the optimal running scheme corresponding to each objective is solved separately, finally obtaining the optimal solution set for each objective.

[0046] The optimal solution set can be either a multi-objective Pareto solution set or a single-objective solution set where each objective is independently optimized. The process of constructing the directional fuzzy conflict matrix through degradation analysis is as follows:

[0047] First, define the performance degradation function between targets. Then, based on the introduction of engineering tolerance threshold and conflict threshold, a fuzzy membership function is constructed. The directional conflict degree between targets is obtained. Finally, based on the degree of directional conflict between targets, a directional fuzzy conflict matrix is ​​formed. ,

[0048] Among them, the performance degradation function Let be the index value of the i-th solution relative to the j-th objective. , Let be the maximum and minimum index values ​​of the j-th objective, respectively. Characterize the degradation rate of objective j under solution / scheme i. This indicates that there has been no degradation. This indicates that objective j suffers complete loss under the optimal solution for objective i;

[0049] Fuzzy membership functions The engineering fuzzy membership degree of solution / scheme i to target j is represented by a, where a represents the engineering allowable degradation threshold and b represents the complete conflict threshold, both of which are determined by engineers based on experience.

[0050] In directional conflict degree, when the degradation rate When smaller, ,at this time This indicates that the directional conflict between target i and target j is relatively weak; conversely, when the degradation rate exceeds the engineering tolerance range, 1. The degree of conflict is close to the actual degradation rate;

[0051] In the directional fuzzy conflict matrix, n represents the total number of targets. This matrix characterizes the directional conflict influence of target i on target j. Before defining the performance degradation function between targets, during the process of solving the single-target optimal solution set, each independently optimized single-target solution is first substituted into its respective objective function to calculate the index value of each solution for each target. Then, using the optimal solution of a certain target as a reference benchmark, the performance degradation degree of other targets under that optimal solution condition is analyzed, and the performance degradation function between targets is defined. The corresponding overall conflict intensity is calculated using the following formula.

[0052] ,

[0053] in, It is used to characterize the degree of conflict participation of the target in the system; the larger the CI, the more likely the target is to conflict with other targets, and the smaller the CI, the stronger the compatibility of the target.

[0054] Furthermore, the subjective weights in this application are obtained by constructing a judgment matrix based on fuzzy hierarchical analysis, and then calculating the FAHP subjective weights of each objective through fuzzy consistency processing and defuzzification. The process of calculating the FAHP subjective weights is as follows:

[0055] First, obtain the triangular fuzzy number of each target according to the triangular fuzzy number standard mapping table, and denote the set of each evaluation target as... Let the triangular fuzzy number representing the importance of target j relative to target k be . The triplet of the triangular fuzzy number These correspond to conservative estimates, core judgments, and optimistic estimates, respectively.

[0056] Then, the fuzzy comprehensive evaluation value of each objective is determined based on the triangular fuzzy number. When the total number of targets Fuzzy comprehensive evaluation value of target j according to Calculate when the total number of targets Fuzzy comprehensive evaluation value of target j The algorithm was adjusted to ,in, The initial fuzzy weights are generally taken as follows: ; To select the smaller operator, the triplet of two triangular fuzzy numbers is... Take the minimum value respectively; To obtain the largest operator, for The triplet of multiple triangular fuzzy numbers takes the maximum value respectively; For multiplication operators, the triplet of two triangular fuzzy numbers Calculate the product separately; For the summation operator, for Sum the triples of multiple triangular fuzzy numbers respectively

[0057] Next, the fuzzy basic weights of each objective are determined based on the fuzzy comprehensive evaluation values. , among which, Fuzzy multiplication, triples of triangular fuzzy numbers Perform multiplication on each tuple separately; This represents the fuzzy addition of the comprehensive fuzzy evaluation values ​​of all targets, and the addition of the triples of multiple triangular fuzzy numbers respectively; Indicates a fuzzy reciprocal, such as ;

[0058] Finally, the FAHP subjective weights are determined based on the fuzzy basic weights, and the triples of the fuzzy basic weights for target j correspond to... The clear weights after defuzzification using the centroid method After normalization, the FAHP subjective weights are obtained. .

[0059] More specifically, after the FAHP subjective weights are calculated, the conflict-driven weights need to be corrected to obtain a comprehensive weight that reflects the actual importance of the target in a conflict environment. The process is as follows:

[0060] First, define the conflict penalty coefficient. ,in, This is an adjustable parameter and can be set to 1; the greater the total conflict intensity of objective j, the more likely the achievement of this objective will harm other objectives, and the heavier the penalty will be.

[0061] Then, based on the conflict analysis, the combined weight of subjective weight and conflict intensity is calculated and corrected according to the post-formula. The structural impact analysis process based on DEMATEL is as follows:

[0062] First, construct the output influence based on the fuzzy conflict matrix. and input impact The system impact relationships are then considered, and based on a comprehensive assessment of the structural roles of each objective in the overall trade-off system, a net impact value based on the DEMATEL framework is introduced and defined. , used to characterize the systemic causal properties of a target.

[0063] In summary, this application proposes a multi-objective priority determination method that starts from optimization degradation information and integrates fuzzy conflict modeling, subjective weight evaluation, and system structure analysis. By introducing optimization solution degradation information to construct directional fuzzy conflict relationships and integrating subjective weights and system structure analysis, it achieves integrated determination of multi-objective priorities. Its advantages are as follows:

[0064] 1. Enhanced objectivity: This invention constructs fuzzy conflict relationships between objectives based on performance degradation information between optimal solutions of a single objective. Compared with traditional methods that rely on expert experience or static evaluation indicators, it realizes the transformation from subjective empowerment to an objective conflict identification mechanism driven by optimization results, thereby improving the authenticity and interpretability of the target conflict characterization.

[0065] 2. Enhanced Quantification of Directional Conflict: By introducing a directional conflict measurement mechanism based on performance degradation, this invention can characterize the asymmetric relationship where “the performance improvement of one target leads to the performance decline of another target”, overcoming the limitations of traditional conflict matrices and Pareto analysis methods that can only express symmetric or static relationships, and improving the precision of multi-target relationship description.

[0066] 3. Enhanced consistency and integrity in multi-objective decision-making process modeling: This invention integrates fuzzy conflict modeling, subjective weight determination, and system structure analysis methods to construct an integrated multi-objective priority decision-making framework. This effectively solves the problem of the separation between conflict analysis and weight analysis in existing technologies, and improves the consistency and integrity of the multi-objective decision-making process.

[0067] 4. Enhanced coupling between structural analysis and optimization process: This invention combines system structural analysis methods such as DEMATEL with optimization degradation processes, so that causal relationship analysis is no longer limited to static influence relationships, but can reflect dynamic structural characteristics based on the evolution of optimization behavior, thereby enhancing the matching between system analysis results and actual optimization processes.

[0068] 5. More stable and reliable priority determination: By comprehensively considering optimization degradation information, subjective weight information, and the influence of system structure, this invention can obtain more stable and interpretable multi-objective priority ranking results, reducing the result bias caused by a single method.

[0069] 6. Strong applicability and scalability: The method of this invention is not only applicable to dual-objective conflict problems such as sand control and power generation, but can also be extended to multi-objective coupled systems such as joint scheduling of multiple reservoirs, ecological flow control, and energy optimization scheduling, and has strong versatility and engineering applicability.

[0070] 7. High interpretability of the method: By constructing an analysis path of "degradation-driven - fuzzy conflict - structural coupling", this invention enables the multi-objective priority generation process to have a clear causal chain, which significantly improves the interpretability and engineering acceptability of the results compared with the traditional black box weighted method.

[0071] The technical solution of this application will be further described below through specific embodiments:

[0072] This invention, based on the technical route of "single-objective optimal solution degradation analysis—fuzzy conflict modeling—subjective and objective weight fusion—DEMATEL structural analysis," constructs a multi-objective priority determination framework. The technical solution is as follows: Figure 1 As shown.

[0073] Specifically, it includes the following steps:

[0074] (I) Solving for the optimal solution of a single objective

[0075] For each objective in a multi-objective system, a single-objective optimization model is constructed to solve for the optimal operating scheme corresponding to each objective, thereby obtaining the optimal solution set for each objective.

[0076] (II) Construction of Directional Fuzzy Conflict Matrix Based on Degradation Analysis

[0077] Based on the unweighted, independently optimized multi-objective Pareto solution set or the single-objective solution with each objective independently optimized, each solution is substituted into the respective objective function to calculate the index value of each solution for each objective. The following method construction uses the following conventions. Let be the index value of the i-th solution relative to the j-th objective. , These are the maximum and minimum index values ​​for the j-th objective, respectively.

[0078] Using the optimal solution of a certain objective as a benchmark, we analyze the performance degradation of other objectives under the condition of that optimal solution, and define the "performance degradation function (trade-off loss)" between objectives as follows:

[0079] (1)

[0080] in, The characterization represents the degradation rate of objective j under solution / scheme i. This indicates that there has been no degradation. This indicates that objective j suffers complete loss under the optimal solution for objective i.

[0081] Based on this, an engineering tolerance threshold and a conflict threshold are introduced, and the fuzzy membership function is constructed as follows:

[0082] (2)

[0083] in, The engineering fuzzy membership degree of solution / scheme i to target j is represented by a, where a represents the engineering allowable degradation threshold and b represents the complete conflict threshold, both of which are determined by engineers based on experience.

[0084] By further combining the performance degradation function and the fuzzy membership function, the directional conflict degree between targets is obtained, defined as follows:

[0085] (3)

[0086] When degradation rate When smaller, ,at this time This indicates that the directional conflict between target i and target j is relatively weak; conversely, when the degradation rate exceeds the engineering tolerance range, 1. The degree of conflict is close to the actual degradation rate. Therefore, the directional conflict degree FC under this definition retains both the target degradation analysis (trade-off analysis) and takes into account engineering fuzziness.

[0087] Based on the directional conflict degree between targets, a directional fuzzy conflict matrix is ​​formed:

[0088] (4)

[0089] Where n is the total number of targets, this matrix is ​​used to characterize the directional conflict influence relationship between target i and target j.

[0090] (III) Calculation of Overall Conflict Intensity

[0091] The overall conflict intensity of the objective is defined as follows:

[0092] (5)

[0093] in, CI is used to characterize the degree of conflict involvement of the target in the system. The larger the CI, the more likely the target is to conflict with other targets; the smaller the CI, the stronger the compatibility of the target.

[0094] (iv) Calculation of FAHP Subjective Weights

[0095] A judgment matrix is ​​constructed using fuzzy hierarchical analysis. The subjective weights of each objective are obtained through fuzzy consistency processing and defuzzification. The specific calculation steps are as follows:

[0096] 1. First, obtain the triangular fuzzy number corresponding to the expert evaluation based on the triangular fuzzy number standard mapping table. Let the evaluation target set be denoted as . Let the triangular fuzzy number representing the importance of target j relative to target k be . The triplet of the triangular fuzzy number These correspond to conservative estimates, core judgments, and optimistic estimates, respectively.

[0097] 2. Next, determine the fuzzy comprehensive evaluation value of each objective based on the triangular fuzzy number:

[0098] When the total number of targets When, the fuzzy comprehensive evaluation value of target j Calculate as follows:

[0099] (6)

[0100] in: The initial fuzzy weights are generally taken as follows: ; To select the smaller operator, the triplet of two triangular fuzzy numbers is... Take the minimum value respectively; To obtain the largest operator, for The triplet of the multiple triangular fuzzy numbers takes the maximum value.

[0101] When the total number of targets At that time, the above The calculation method only retains the most conservative minimum value information, completely losing the information for judging strength and weakness. It is only suitable for multi-index hierarchical structures and not suitable for pairwise comparisons. Therefore, referring to the FAHP standard for water resources, the fuzzy comprehensive evaluation value of target j is determined. The algorithm has been adjusted as follows:

[0102] (7)

[0103] in: For multiplication operators, the triplet of two triangular fuzzy numbers Calculate the product separately; For the summation operator, for Sum the triples of multiple triangular fuzzy numbers respectively.

[0104] 3. Determine the fuzzy basic weights of each objective again based on the fuzzy comprehensive evaluation values:

[0105] (8)

[0106] in: For fuzzy multiplication, the triples of triangular fuzzy numbers Perform multiplication on each tuple separately; This represents the fuzzy addition of the comprehensive fuzzy evaluation values ​​of all targets, and the addition of the triples of multiple triangular fuzzy numbers respectively; Indicates a fuzzy reciprocal, such as .

[0107] 4. Finally, determine the FAHP subjective weights based on the fuzzy basic weights:

[0108] Let the triplet of the fuzzy basic weights of target j correspond to... The clear weights after defuzzification using the centroid method for:

[0109] (10)

[0110] Normalized FAHP subjective weights for:

[0111] (11)

[0112] (v) Conflict-driven weight adjustment

[0113] The FAHP subjective weights are integrated and corrected with conflict intensity to obtain a comprehensive weight, which reflects the actual importance of the target in a conflict environment. The specific steps are as follows:

[0114] 1. Determine the conflict penalty coefficient.

[0115] The conflict penalty coefficient is defined as follows:

[0116] (12)

[0117] in , is an adjustable parameter, which can be set to 1. The greater the total conflict intensity of objective j, the more likely the achievement of this objective will harm other objectives, and the heavier the penalty will be.

[0118] 2. Determine the comprehensive weight that integrates subjective weight and conflict intensity.

[0119] The comprehensive weight, adjusted based on conflict analysis, is calculated using the following formula:

[0120] (13)

[0121] This definition indicates that if achieving objective j would lead to a serious deterioration of another objective, then its weight should be further reduced based on subjective judgment weights in order to ensure the coordinated operation of the system.

[0122] (vi) Structural Influence Analysis Based on DEMATEL

[0123] Based on the fuzzy conflict matrix, the system influence relationship is constructed, and the following calculations are performed:

[0124] ① Output impact:

[0125] (14)

[0126] ② Input impact level:

[0127] (15)

[0128] Furthermore, to further consider the structural role of each objective in the overall trade-off system, a net impact based on the DEMATEL framework is introduced, and the net impact is defined as follows:

[0129] (16)

[0130] Used to characterize the systemic causal properties of a target.

[0131] (vii) Determining the priority of multiple objectives

[0132] Constructing a comprehensive priority function:

[0133] (17)

[0134] in, The structural influence moderating coefficient can be set to 1. This is used to balance the relationship between conflict intensity and the system's causal structure. Objectives are ranked from highest to lowest priority to determine the priority order of multiple objectives.

[0135] The above methods can solve the problems of insufficient characterization of conflict relationships, inadequate integration of subjective and objective information, and difficulty in uniformly determining the priority of multiple objectives in the decision-making of multi-objective order and weight in the optimization scheduling of existing water resource systems.

[0136] Example 1

[0137] Dual-objective system calculation example of sand control and power generation

[0138] To verify the effectiveness of the method of the present invention, an example is given of two conflicting objectives: sand control and power generation.

[0139] A control reservoir with annual regulation capacity is designated as the upper reservoir, and a diversion-type power station is located downstream of this reservoir, forming a cascade system of control reservoir and diversion-type power station. To meet the water diversion and sand control safety requirements of the downstream diversion-type power station, the coarse sand content in the power generation flow of the downstream reservoir should be minimized. At the same time, considering the cascade power generation benefits, the total power generation of the cascade reservoirs should be maximized.

[0140] First, the single-objective optimization models for sand control and power generation of the downstream reservoir-diversion power station cascade are constructed to minimize the coarse sand content passing through the turbines and maximize the total power generation of the cascade, respectively. The optimal solutions for each model are obtained by using a certain intelligent optimization algorithm. The corresponding operating indicators of each optimal solution are shown in Table 1.

[0141] Table 1. Optimal Operation Solution and Operation Indicators for a Certain Controlled Reservoir-Hydropower Station Cascade Sand Control and Power Generation

[0142]

[0143] Based on the optimal solution of a single objective and its operational indicators, the performance degradation relationship between the two objectives is analyzed. The performance loss of the power generation objective under the optimal solution for sand control and the performance loss of the sand control objective under the optimal solution for power generation are calculated, and a directional fuzzy conflict degree matrix is ​​constructed. The overall conflict intensity of each objective is further calculated, and subjective weights are obtained using the FAHP method. Simultaneously, the DEMATEL method is introduced to calculate the system structure influence relationship, determining the order of the two objectives: sand control and power generation. The calculation results are shown in Table 2. Considering the subjectivity of expert evaluation, this table assumes two scenarios: expert evaluation of sand control being more important than power generation (AHP scale = 6) and sand control being extremely important than power generation (AHP scale = 8).

[0144] Table 2. Calculation Results of Weights and Orders of Cascade Sand Control and Power Generation Targets for a Certain Control Reservoir-Hydropower Station

[0145]

[0146] Note: In the calculations above, the allowable degradation threshold 'a' is taken as 0.1, and the complete conflict threshold 'b' is taken as 0.4. The conflict penalty coefficient is calculated as follows: Set to 1, the adjustment coefficient is influenced by objective information. Set to 1, structural influence adjustment coefficient Take 1.

[0147] Compared with the subjective weights based on FAHP, the weight of the sand control target is significantly improved after considering the directional conflict analysis. The final comprehensive weights of the sand control and power generation targets are 0.92 and 0.08 (Scenario 1 AHP ​​scale = 6), and 0.94 and 0.06 (Scenario 2 AHP scale = 8), respectively.

[0148] Based on the comprehensive weight and DEMATEL impact analysis, the overall priority of each objective is as follows: the priority of sand control is higher than that of power generation.

[0149] The results show that the method of the present invention can effectively characterize the conflict relationship between multiple objectives and achieve reasonable priority ranking.

Claims

1. A method for determining priority objectives in multi-objective regulation of water conservancy and hydropower resources, characterized in that: The aforementioned method is based on multiple sets of optimal solutions for each single objective obtained by solving each objective separately. A directional fuzzy conflict matrix is ​​constructed through degradation analysis. Then, based on this matrix, the overall conflict intensity requirement for each objective is determined. Finally, by integrating objective conflict analysis and subjective weighting, the Dematel structural analysis method is used to construct a multi-objective priority determination function. Finally, the objectives are sorted from largest to smallest according to the Priority function calculation results, and the priority order of each objective in the multi-objective system is determined based on the sorting results. in, This is the comprehensive weight after correcting the subjective weights of FAHP based on objective conflict analysis; Net impact; This is the structural influence adjustment coefficient, which can be set to 1.

2. The method for determining priority objectives in multi-objective regulation of water conservancy and hydropower resources according to claim 1, characterized in that: The process of finding the optimal solution set for a single objective is as follows: taking each objective in the multi-objective system as the object, constructing a single-objective optimization model for each objective, solving for the optimal operating scheme corresponding to each objective, and finally obtaining the optimal solution set for each objective. The optimal solution set is the set of single-objective solutions that are independently optimized for each objective.

3. The method for determining priority targets in multi-objective regulation of water conservancy and hydropower resources according to claim 1 or 2, characterized in that: The process of constructing a directional fuzzy conflict matrix through degradation analysis is as follows: First, define the performance degradation function between targets. Then, based on the introduction of engineering tolerance threshold and conflict threshold, a fuzzy membership function is constructed. The directional conflict degree between targets is obtained. Finally, based on the degree of directional conflict between targets, a directional fuzzy conflict matrix is ​​formed. , Among them, the performance degradation function Let be the index value of the i-th solution relative to the j-th objective. , Let be the maximum and minimum index values ​​of the j-th objective, respectively. Characterize the degradation rate of objective j under solution / scheme i. This indicates that there has been no degradation. This indicates that objective j suffers complete loss under the optimal solution for objective i; Fuzzy membership functions The engineering fuzzy membership degree of solution / scheme i to target j is represented by a, where a represents the engineering allowable degradation threshold and b represents the complete conflict threshold, both of which are determined by engineers based on experience. In directional conflict degree, when the degradation rate When smaller, ,at this time This indicates that the directional conflict between target i and target j is relatively weak; conversely, when the degradation rate exceeds the engineering tolerance range, 1. The degree of conflict is close to the actual degradation rate; In the directional fuzzy conflict matrix, n represents the total number of targets. This matrix is ​​used to characterize the directional conflict influence relationship between target i and target j.

4. The method for determining priority targets in multi-objective regulation of water conservancy and hydropower resources according to claim 3, characterized in that: Before defining the performance degradation function between objectives, in the process of solving the set of optimal solutions for a single objective, each solution is first substituted into the objective function according to the single objective solution optimized independently for each objective, and the index value of each solution for each objective is calculated. Then, the optimal solution of a certain objective is used as a reference benchmark to analyze the degree of performance degradation of other objectives under the condition of the optimal solution and define the performance degradation function between objectives.

5. The method for determining priority targets in multi-objective regulation of water conservancy and hydropower resources according to claim 4, characterized in that: The overall intensity of the conflict is calculated using the following formula: ， in, It is used to characterize the degree of conflict participation of the target in the system; the larger the CI, the more likely the target is to conflict with other targets, and the smaller the CI, the stronger the compatibility of the target.

6. The method for determining priority targets in multi-objective regulation of water conservancy and hydropower resources according to claim 5, characterized in that: Subjective weights are the FAHP subjective weights of each objective obtained by constructing a judgment matrix based on fuzzy hierarchical analysis and then performing fuzzy consistency processing and defuzzification calculation.

7. The method for determining priority targets in multi-objective regulation of water conservancy and hydropower resources according to claim 6, characterized in that: The process of calculating the FAHP subjective weights is as follows: First, obtain the triangular fuzzy number of each target according to the triangular fuzzy number standard mapping table, and denote the set of each evaluation target as... Let the triangular fuzzy number representing the importance of target j relative to target k be . The triplet of the triangular fuzzy number These correspond to conservative estimates, core judgments, and optimistic estimates, respectively. Then, the fuzzy comprehensive evaluation value of each objective is determined based on the triangular fuzzy number. When the total number of targets Fuzzy comprehensive evaluation value of target j according to Calculate when the total number of targets Fuzzy comprehensive evaluation value of target j The algorithm was adjusted to ,in, The initial fuzzy weights are generally taken as follows: ; To select the smaller operator, the triplet of two triangular fuzzy numbers is... Take the minimum value respectively; To obtain the largest operator, for The triplet of multiple triangular fuzzy numbers takes the maximum value respectively; For multiplication operators, the triplet of two triangular fuzzy numbers Calculate the product separately; For the summation operator, for Sum the triples of multiple triangular fuzzy numbers respectively Next, the fuzzy basic weights of each objective are determined based on the fuzzy comprehensive evaluation values. ,in, For fuzzy multiplication, the triples of triangular fuzzy numbers Perform multiplication on each tuple separately; This represents the fuzzy addition of the comprehensive fuzzy evaluation values ​​of all targets, and the addition of the triples of multiple triangular fuzzy numbers respectively; Indicates a fuzzy reciprocal, such as ; Finally, the FAHP subjective weights are determined based on the fuzzy basic weights, and the triples of the fuzzy basic weights for target j correspond to... The clear weights after defuzzification using the centroid method After normalization, the FAHP subjective weights are obtained. .

8. The method for determining priority targets in multi-objective regulation of water conservancy and hydropower resources according to claim 7, characterized in that: After the FAHP subjective weights are calculated, the conflict-driven weights need to be corrected to obtain a comprehensive weight that reflects the actual importance of the target in a conflict environment. The process is as follows: First, define the conflict penalty coefficient. ,in, This is an adjustable parameter and can be set to 1; the greater the total conflict intensity of objective j, the more likely the achievement of this objective will harm other objectives, and the heavier the penalty will be. Then, based on the conflict analysis, the combined weight of subjective weight and conflict intensity is calculated and corrected according to the post-formula. .

9. The method for determining priority targets in multi-objective regulation of water conservancy and hydropower resources according to claim 8, characterized in that: The structural impact analysis process based on DEMATEL is as follows. First, construct the output influence based on the fuzzy conflict matrix. and input impact The system impact relationships are then considered, and based on a comprehensive assessment of the structural roles of each objective in the overall trade-off system, a net impact value based on the DEMATEL framework is introduced and defined. , used to characterize the systemic causal properties of a target.

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