High-dimensional multi-target water resource scheduling control method based on multi-view sampling

Abstract

The invention relates to the field of multi-objective optimization algorithms, and discloses a high-dimensional multi-objective water resource scheduling control method based on multi-view sampling, which comprises the following steps of: executing initialization, and storing an initial solution and a real objective function value thereof into a database; constructing an agent model; executing an internal multi-objective optimization algorithm on the proxy model, and outputting a candidate solution set; executing a multi-view-angle-based sampling strategy, and screening out a part of solutions from the candidate solution set; executing the true evaluation on the partial solution, and updating the database; and executing termination judgment, and checking whether the number of evaluation times reaches a preset maximum number of evaluation times or not. According to the method, the sampling strategy based on multiple view angles is executed, and only the partial solution is actually evaluated, so that the total number of times of the actual evaluation is reduced; non-dominated sorting is executed by calculating the Euclidean distance and the included angle of the candidate solution, and evaluation resources are concentrated in an area where prediction of the proxy model is not accurate.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of multi-objective optimization algorithm, and particularly to a high-dimensional multi-objective water resources scheduling control method based on multi-view sampling. BACKGROUND

[0002] In the field of engineering optimization such as water resources scheduling, many high-dimensional multi-objective optimization problems rely on high-cost computational simulation to evaluate objective functions. The computational overhead of evaluating a single scheduling scheme is huge, which limits the total number of real evaluations that optimization algorithms can perform within a practical acceptable time.

[0003] To address this challenge, surrogate model assisted evolutionary algorithms are a major technical path currently adopted. Such methods use computationally inexpensive surrogate models, such as Gaussian process models, to fit expensive objective functions. Optimization algorithms mainly search on surrogate models, and select a small number of solutions to perform real evaluations through sampling strategies, and then update the surrogate model with the newly obtained real data.

[0004] However, existing sampling strategies mostly aim to select the solution with the best performance on the current surrogate model. This approach often ignores the contribution of the selected solution as a training sample to improving the prediction accuracy of the surrogate model. The surrogate model can better fit regions where the objective function changes smoothly, but in regions where the function changes dramatically or discontinuously, the prediction accuracy of the model will decrease. Therefore, how to effectively select samples to improve the fitting accuracy of the surrogate model in these complex regions is a problem that needs to be solved in the field. SUMMARY

[0005] To address the shortcomings of the prior art, the present application provides a high-dimensional multi-objective water resources scheduling control method based on multi-view sampling, which solves the problem that existing sampling strategies mostly aim to select the solution with the best performance, without fully considering the contribution of the selected solution to improving the prediction accuracy of the surrogate model in regions where the function changes dramatically, resulting in difficulty in improving the fitting accuracy of the surrogate model.

[0006] To achieve the above purpose, the present application is implemented by the following technical solution: a high-dimensional multi-objective water resources scheduling control method based on multi-view sampling, specifically comprising the following steps: S1, initialization is performed, Latin hypercube sampling is used to generate a specified number of initial solutions, real evaluations are performed on the initial solutions, and the initial solutions and their real objective function values are stored in a database; S2, a surrogate model is constructed, all current training samples are read from the database, and Gaussian process models are trained for m objective functions respectively; S3, algorithm optimization is performed, the internal multi-objective optimization algorithm is executed on the surrogate model constructed in the S2 step, the optimal solution set on the current model is searched, and the candidate solution set is output. S4. Execute a multi-view sampling strategy to select a portion of the solutions from the candidate solution set output in step S3. S5. Perform the true evaluation on the partial solutions selected in step S4. After the evaluation is completed, add or update these new solutions and their true objective function values ​​to the database. S6. Execute the termination judgment, check the number of evaluations. If the number of evaluations is less than the preset maximum number of evaluations, the process returns to step S2.

[0007] The S3 step (the internal multi-objective optimization algorithm) employs a reference vector-guided evolutionary mechanism to balance the convergence and diversity of the population. This step may specifically include: S31. Set a population evolution generation count, initially set to 0, and initialize a specified number of reference vectors; S32. Perform population initialization to obtain the initial population; S33. Generate offspring population using genetic algorithms; S34. Merge the initial population and the offspring population into a merged population, and use the Gaussian process model to predict the objective function value of the solution in the merged population. S35. Perform the step of maintaining population diversity: associate the solutions in the merged population with the corresponding reference vectors according to the angle to form multiple solution groups; S36. Perform the step to enhance population convergence: Select individuals from the multiple solutions formed in step S35 to form the next generation population; S37. Update the reference vector; S38. The population generation count is incremented by 1; S39. Termination condition: When the population evolution generation count is less than the preset maximum population evolution generation, return to step S32 to continue execution; otherwise, stop the search and output the optimized population as the candidate solution set.

[0008] Step S4, based on a multi-view sampling strategy, is used to locate and filter candidate solutions located in regions of drastic change in the objective function. Selecting these solutions helps improve the prediction accuracy of the surrogate model at the Pareto front. This step may specifically include: S41. Receive the candidate solution set output in step S3; S42. Find the sample in the decision space that is closest to the candidate solution in the candidate solution set in the database, and record the Euclidean distance between the candidate solution and the closest sample; S43. Calculate the angle between the predicted target value of the candidate solution and the true objective function value of the nearest sample in the target space; S44. Using the negative values ​​of the Euclidean distance and the included angle of the candidate solutions as two indicators, perform a non-dominated sorting of the solutions in the candidate solution set. This sorting divides the solutions into one or more levels, and selects the partial solutions from the solutions located in the first level.

[0009] The technical principle behind this strategy is to analyze the differences in the performance of solutions in the decision space and the target space. In regions where the objective function changes gradually, solutions that are similar in the decision space will also have similar performance (objective function values) in the target space. Conversely, in regions where the objective function changes drastically or is discontinuous, the performance of solutions in the two spaces will diverge. The sampling strategy described herein is used to quantify this divergence.

[0010] In the implementation of steps S42 and S43, this strategy targets candidate solutions in the candidate solution set. First, it searches the database for the nearest sample in the decision space. Then, two quantitative indicators were calculated: First, calculate the candidate solutions. With the nearest sample Euclidean distance in decision space : Secondly, calculate the candidate solutions. With the nearest sample Angle in the target space .

[0011] In step S44, these two metrics are used. All candidate solutions are non-dominated and sorted. The solutions in the first layer are those with the greatest difference in performance between the decision space and the target space; this difference is manifested as follows: large and Small, or Small Large. These solutions are selected as the partial solutions and subjected to true evaluation.

[0012] Furthermore, the internal multi-objective optimization algorithm in step S3 employs a reference vector-guided evolutionary mechanism to balance the convergence and diversity of the population.

[0013] In the implementation of step S35, when the number of solutions in a certain group in the merged population is greater than a preset threshold, the algorithm can use a clustering method to divide the individuals in that group into a predetermined number of groups while maintaining population diversity. In the implementation of step S36, individuals closest to the ideal point are selected from each group formed in step S35 to enter the next generation population.

[0014] This invention provides a high-dimensional, multi-objective water resource scheduling and control method based on multi-view sampling. It has the following beneficial effects: 1. The present invention reduces the total number of real evaluations required in the entire optimization process by executing an internal multi-objective optimization algorithm on the surrogate model to search for a candidate solution set and executing a multi-view sampling strategy to select a partial solution from the candidate solution set, and then performing a real evaluation only on the partial solution.

[0015] 2. This invention calculates the Euclidean distance between candidate solutions in the decision space and the angle between them in the target space, and performs non-dominated ranking on these two indicators. This enables effective screening of solutions with large differences in performance between the decision space and the target space, thereby concentrating limited real evaluation resources on areas where the surrogate model prediction is inaccurate.

[0016] 3. This invention performs steps to maintain population diversity and enhance population convergence in the internal multi-objective optimization algorithm, and uses reference vectors and ideal points to guide population evolution, so that the output candidate solution set has good diversity and convergence in the surrogate model. Attached Figure Description

[0017] Figure 1 This is a general flowchart of an embodiment of the present invention; Figure 2 The MSEMOEA algorithm framework; Figure 3 Select an example to fill the sample; Figure 4 The statistical results of the MSEMOEA algorithm on the DTLZ and WFG test sets are shown. Detailed Implementation

[0018] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] In the field of water resource allocation, this type of high-dimensional multi-objective optimization problem (MaOP) can be formally described by the following mathematical model: ; in: It is a set of dimensions A decision vector represents a set of scheduling schemes. It is a dimension of The decision-making space; It represents the objective function to be optimized; This indicates that the goal of the optimization problem is to simultaneously minimize all One objective function.

[0020] See attached document Figure 1 and attached Figure 2 This invention provides a high-dimensional, multi-objective water resource scheduling and control method based on multi-view sampling, specifically including the following steps: S1. Perform initialization, using Latin hypercube sampling (LHS) to generate a specified number of (e.g., ...) in the decision space. (Number) initial solutions. These initial solutions are then evaluated using a true evaluation method, and the solutions and their true objective function values ​​are stored in a database.

[0021] S2. Construct a proxy model, read all current training samples from the database, and then... indivual( Gaussian process models are trained for each objective function (target number) to generate the surrogate model for the current iteration.

[0022] S3. Execute the algorithm for optimization. On the surrogate model (Gaussian process model) constructed in step S2, execute the internal multi-objective optimization algorithm to search for the optimal solution set on the current model, and output the optimal solution set as the candidate solution set C.

[0023] S4. Execute a multi-view sampling strategy (filling criterion) and receive the candidate solution set C output from step S3. By comparing the differences in performance between the solutions in the candidate solution set C and their nearest neighbors in the database in the decision space and target space, select a subset of solutions.

[0024] S5. Perform a true evaluation on the solutions selected in step S4. After the evaluation is completed, add or update these new solutions and their true objective function values ​​to the database.

[0025] S6. Execute the termination check and check if the number of evaluations has reached the preset maximum number of evaluations. If the number of evaluations is less than the preset maximum number of evaluations, the process returns to step S2 and starts a new round of iteration using the updated database. If the number of evaluations is greater than or equal to the preset maximum number of evaluations, the algorithm terminates, extracts and outputs all non-dominated solutions from the database, and outputs them as the optimization result.

[0026] The specific implementation methods of steps S1 to S6 described above will be explained in detail below.

[0027] Step S1 is the initialization step of the method of the present invention, which is to generate training sample data required to build the initial agent model.

[0028] In practice, the Latin hypercube sampling (LHS) method is used to generate [the necessary data] in the decision space. There are several initial solutions (i.e., decision vectors). The dimension of the decision space, and the number of initial solutions. Can be set to .

[0029] In the field of surrogate model-assisted evolutionary algorithms, the following is typically used: (i.e., 10 times the dimension) was used as the baseline sampling size for constructing the Gaussian process model to ensure coverage of the initial space. To further improve the fitting accuracy of the initial model in high-dimensional space, this invention appropriately expanded the baseline sampling size, selecting... This serves as the baseline value. Meanwhile, considering the high computational cost of accurately evaluating water resource allocation issues and the upper limit on the total number of evaluations, the final initial sampling size was slightly adjusted to... Experimental results show that this specific setting can optimize the allocation of computational resources while ensuring the initial accuracy of the model, thereby achieving a balance between convergence speed and solution set quality within a limited computational budget.

[0030] For each initial solution generated in step S1, the system calls a real evaluation function (e.g., performs a complete water resource scheduling simulation) to evaluate it in order to obtain the m-dimensional real objective function value corresponding to that solution.

[0031] all Each initial solution and its corresponding true objective function value are stored in the database as (decision vector, true objective vector) data pairs. This is the initial solution. The database of samples is then invoked in step S2 as initial training data for training the Gaussian process model.

[0032] Step S2 is the step of constructing the surrogate models. This step utilizes all the currently accumulated (decision vector, true target vector) data pairs in the database to construct surrogate models for each of the m expensive objective functions.

[0033] In specific implementation, the present invention preferably uses a Gaussian process (GP) model as a surrogate model. Step S2 reads all training samples from the database.

[0034] For each of the m objectives, the objective function (in , (For the decision vector), each step independently uses all sample data in the database to train a corresponding Gaussian process model. .

[0035] The constructed Each Gaussian process model is a computationally fitted version of the true objective function. These models are then invoked in step S3 for low-cost fitness evaluation during the optimization process. When the process returns to step S2 in a subsequent iteration, this step retrains or updates the Gaussian process models using an updated (i.e., more samples) database.

[0036] Step S3 is the step of performing the algorithm optimization. Its function is to execute an internal multi-objective evolutionary optimization algorithm on the surrogate model (Gaussian process model) constructed in step S2. The goal of this algorithm is to search for and output the optimal solution set on the current surrogate model, which will be submitted as a candidate solution set C to step S4.

[0037] The specific implementation steps of the optimization algorithm within this step are as follows: S31, Settings The number of generations in the population, initially .initialization reference vectors .

[0038] S32. Population Initialization: When t=0, associate the samples in the database with the reference vector. For each vector, select the solution closest to the ideal point. If the predetermined number is not reached... Then, for each reference vector, select the solution that is second closest to the ideal point, until the number of selected solutions reaches a certain threshold. Greater than or equal to To control the population size, if it is greater than... It will select only the reference vector with the smallest distance from the ideal point in the last traversal. The solutions form the initial population. .

[0039] S33, Initial Population The offspring population is generated using genetic algorithms (e.g., simulated binary crossover SBX and polynomial mutation PM). .

[0040] S34, Parental population and offspring population Merge (denoted as) ), and use a trained Gaussian process model to predict the population. The objective function value of the solution.

[0041] S35. Maintaining population diversity: [This refers to] population... The solution is associated with the corresponding reference vector based on the angle. Above. When the number of a certain set of solutions in the population... Larger than the population When 2 / 3 of the individuals are in the group, K-means clustering is used to divide the group into μ / 3 groups.

[0042] S36. Enhance population convergence: In each group formed in step S35, select the individual closest to the ideal point to enter the next generation of the population (denoted as P(t+1)).

[0043] S37. Update the reference vector according to formula (2) so that as many solutions as possible in the population are evenly associated with the reference vector.

[0044] ; in, yes The first generation Reference vectors, It is the initial reference vector. and Let represent the vectors formed by the maximum and minimum values ​​of each objective function found during the population optimization process. It represents the generation number of a population's evolution.

[0045] S38 .

[0046] S39. Termination Condition: When Less than the preset number of generations of population evolution If successful, return to step S3.2 and continue execution. Otherwise, stop the search and output the optimized population. We use it as the candidate solution set C.

[0047] Step S4 is the step of implementing a multi-view sampling strategy. Its function is to receive the candidate solution set C output from step S3. The core task of this step is to analyze all candidate solutions in the candidate solution set C and filter out solutions located in regions where the objective function changes drastically, to be submitted to step S5 for true evaluation.

[0048] The technical principle behind this step is based on the analysis of the differences in performance between the decision space and the objective space. In regions where the objective function changes gradually, solutions that are close to each other in the decision space also have similar performance (i.e., objective function values) in the objective space.

[0049] Conversely, in regions where the objective function changes drastically (such as inflection points of the Pareto front or discontinuous regions), the performance of solutions in the two spaces will diverge. This divergence manifests in two ways: solutions that are close in the decision space are far apart in the objective space; or solutions that are far apart in the decision space are close together in the objective space. This step aims to locate and filter out these two types of solutions by quantifying this performance difference.

[0050] See attached document Figure 3The figure illustrates a one-dimensional function graph. Triangles (A, C, and E) represent training data from the database; circles (B, D, and F) represent solutions in the population. When the function changes relatively smoothly, for example, points A and B are close in the decision space, and their values ​​in the target space are also similar. For points C and D, their values ​​in the target space are similar, but they are far apart in the decision space. For points E and F, they are close in the decision space, but their values ​​differ significantly in the target space. Therefore, choosing solutions D and F, which show greater differences in the decision and target spaces, is beneficial for improving the model's prediction accuracy.

[0051] The specific steps of this sampling strategy are as follows: S41. After optimizing the model using a multi-objective optimization algorithm, a candidate solution set is obtained. .

[0052] S42. Decision Space Analysis: Finding candidate solutions in the decision space from the training set (database). Recent samples And record the Euclidean distance between them. .

[0053] S43. Objective Space Analysis: Calculating Candidate Solutions and Angle in the target space .

[0054] S44. Non-dominated sorting and screening: Two indicators for all candidate solutions and A non-dominated sort is performed, which divides the solutions into one or more levels. Solutions located in the first level are those that exhibit significant differences in performance between the decision space and the objective space (i.e.,...). Large value and Small value, or Small value and (The value is large). Subsequently, half of the individuals were selected for real evaluation, and the results were updated in the database.

[0055] Step S5 is the step of performing a real evaluation and updating the database.

[0056] The filtered solution output from step S4 is fed into the true evaluation function. In water resource allocation applications, this evaluation corresponds to a complete hydrological and hydrodynamic simulation.

[0057] After the evaluation is completed, the system obtains the true objective function values ​​corresponding to these solutions. These new (decision vector, true objective vector) data pairs are added to or updated in the database.

[0058] This step increases the number of samples in the database, providing new data support for the S2 step to build a more accurate surrogate model in the next iteration.

[0059] Step S6 is the termination judgment step, which is used to control the loop and termination of the entire optimization process.

[0060] In this step, the system checks whether the number of evaluations has reached the preset maximum number of evaluations.

[0061] If the number of evaluations is less than the preset maximum number of evaluations, it indicates that computing resources have not been exhausted, and the process returns to step S2. Step S2 will use the database updated in step S5 to rebuild the agent model and begin a new round of iterative optimization.

[0062] If the number of evaluations is greater than or equal to the preset maximum number of evaluations, it indicates that the computational budget limit has been reached, and the algorithm terminates. The system then extracts and outputs all non-dominated solutions from the database as the optimization result.

[0063] To verify the effectiveness of the proposed algorithm MSEMOEA, the DTLZ and WFG function test sets and the water resources planning and management problem were used for validation. Five excellent algorithms of the same type proposed in recent years—AB-SAEA, EDN-ARMOEA, KTA2, PA-EMaOEA, and K-RVEA—were selected as comparison algorithms to verify the effectiveness of the proposed algorithm.

[0064] Parameter settings: 1. The algorithm MSEMOEA of this invention was tested on the widely used test functions DTLZ and WFG, with 6, 10, and 20 targets respectively. When the number of targets was 6 and 10, the number of decision variables was set to 10, and the maximum number of evaluations was set to 300. When the number of targets was 20, the number of decision variables was set to 20, and the maximum number of evaluations was set to 400.

[0065] 2. The crossover probability and mutation probability are set to 1 and 1 / D, respectively, where D is the number of decision variables, and the distribution factor for both is set to 20. The maximum number of iterations is set to 100.

[0066] 3. The improved inverse generation distance (IGD+) is selected as the evaluation index. A smaller value indicates better algorithm optimization results. Hypervolume (HV) is used to evaluate the algorithm's performance in solving the water resource allocation optimization problem; a larger value indicates better results.

[0067] 4. All experiments were conducted independently 20 times on the PlatEMO 2.8 platform. The Wilcoxon rank-sum test was used to compare the experimental results. The symbols +, -, and = represent that the performance of the algorithm MSEMOEA in this paper is better than, worse than, or similar to other comparative algorithms, respectively.

[0068] Ablation experiment: To verify the effectiveness of the proposed multi-view sampling strategy, the following ablation experiments were conducted: MSEMOEA-Obj represents the sampling strategy based solely on the solution's performance in the target space; MSEMOEA-Dec represents the sampling strategy based solely on the solution's performance in the decision space. Furthermore, the DTLZ test functions selected for verification included DTLZ2, DTLZ3 (with multimodal characteristics), DTLZ4 (with bias characteristics), and DTLZ7 (with an irregular Pareto front).

[0069] Table 1: IGD+ statistics for MSEMOEA-Obj, MSEMOEA-Dec, and MSEMOEA on DTLZ2, DTLZ3, DTLZ4, and DTLZ7 for 6, 10, and 20 targets. Table 1 details the IGD+ values ​​of algorithms MSEMOEA-Obj, MSEMOEA-Dec, and MSEMOEA on four test functions (DTLZ2, DTLZ3, DTLZ4, and DTLZ7). Among the 12 test functions, MSEMOEA outperforms MSEMOEA-Obj in all 12 functions. MSEMOEA outperforms MSEMOEA-Dec in 8 functions, with no significant difference in the remaining 4. In summary, the multi-view sampling strategy proposed in this paper can more comprehensively evaluate the performance of the solution. The selected solution improves model performance, thereby enhancing the overall algorithm performance.

[0070] Comparative analysis of experimental results with other algorithms: 1. Analysis of experimental results on the DTLZ test function set: Table 2: IGD+ test results of AB-SAEA, EDN-ARMOEA, KTA2, PA-EMaOEA, K-RVEA and MSEMOEA on 6, 10 and 20 target DTLZ test functions. Table 2 presents the optimization results of MSEMOEA and five comparative algorithms on DTLZ test sets with 6, 10, and 20 objectives, respectively. The specific analysis is as follows: In 21 test functions, MSEMOEA outperforms algorithms AB-SAEA, EDN-ARMOEA, KTA2, PA-EMaOEA, and K-RVEA on 17, 18, 17, 13, and 15 functions, respectively; the number of functions with poor performance is 1, 2, 3, 5, and 2; the number of functions with no significant difference is 3, 1, 1, 3, and 4, respectively. Overall, MSEMOEA outperforms other algorithms in solving expensive, high-dimensional multi-objective problems.

[0071] 2. Analysis of experimental results on the WFG test function set: Table 3: HV Test Results of AB-SAEA, EDN-ARMOEA, KTA2, PA-EMaOEA, K-RVEA and MSEMOEA on 6, 10 and 20 target WFG test functions Table 3 shows the optimization results of MSEMOEA and five comparative algorithms on WFG test sets with 6, 10, and 20 targets, respectively. The table shows that among the 27 test functions, MSEMOEA performs better than algorithms AB-SAEA, EDN-ARMOEA, KTA2, PA-EMaOEA, and K-RVEA on 21, 25, 19, 27, and 24 functions, respectively; the number of functions with poor performance is 1, 0, 1, 0, and 0; the number of functions with no significant difference is 5, 2, 7, 0, and 3, respectively.

[0072] See attached document Figure 4 The figure presents the statistical results of the algorithm on the DTLZ and WFG test sets. Specifically, bars labeled "good performance" indicate that MSEMOEA outperforms the comparison algorithms; bars labeled "no significant difference" indicate that there is no significant difference in experimental results between MSEMOEA and the comparison algorithms; and bars labeled "poor performance" indicate that MSEMOEA performs worse than the comparison algorithms. Figure 4 It can be seen that MSEMOEA outperforms similar comparison algorithms.

[0073] Engineering example optimization issues: To verify the effectiveness of MSEMOEA in solving practical problems, this paper tests it on the water resource scheduling optimization problem and compares it with other algorithms. This problem includes five optimization objectives.

[0074] Table 4: Test results of AB-SAEA, EDN-ARMOEA, KTA2, PA-EMaOEA, K-RVEA, and MSEMOEA, HV As can be seen from Table 4, MSEMOEA achieves the best optimization result. Therefore, the algorithm proposed in this invention can effectively solve expensive multi-objective optimization problems in engineering practice.

[0075] Time complexity analysis: In the surrogate model-assisted evolutionary algorithm, each iteration consists of two parts: training the surrogate model and model-based optimization search.

[0076] Table 5: Algorithm Complexity of AB-SAEA, EDN-ARMOEA, KTA2, PA-EMaOEA, K-RVEA, MSEMOEA Table 5 shows the computational complexity of the algorithms. It can be seen from the table that KTA2 has a higher computational complexity due to its use of an ensemble model. AB-SAEA, K-RVEA, and MSEMOEA all build Gaussian process models for each objective function; therefore, the computational complexity of model construction is the same for these algorithms. The main difference in complexity lies in the different search algorithms. EDN-ARMOEA, however, has the highest complexity because it uses a Dropout network with many neurons and the more complex evolutionary algorithm AR-MOEA to optimize the model.

Claims

1. A high-dimensional, multi-objective water resource scheduling and control method based on multi-view sampling, characterized in that, Specifically, the following steps are included: S1. Latin hypercube sampling is used in dimension [missing information]. A predetermined number of initial solutions are generated in the decision space, the initial solutions are evaluated, and the initial solutions and the true objective function values ​​are stored in the database. S2. Read all current training samples from the database, for Each objective function is used to train a Gaussian process model to generate the surrogate model for the current iteration; S3. Execute the internal multi-objective optimization algorithm on the proxy model constructed in step S2, search for the optimal solution set on the current model, and output the optimal solution set as a candidate solution set; S4. Select a subset of solutions from the candidate solution set output in step S3; S5. Perform the real evaluation on the partial solutions selected in step S4. After the evaluation is completed, add or update these new solutions and the real objective function values ​​to the database. S6. Execute termination judgment, check whether the number of evaluations has reached the preset maximum number of evaluations. If the number of evaluations is less than the preset maximum number of evaluations, the process returns to step S2. If the number of evaluations is greater than or equal to the preset maximum number of evaluations, the algorithm terminates and extracts and outputs all non-dominated solutions from the database.

2. The high-dimensional multi-objective water resource scheduling and control method based on multi-view sampling according to claim 1, characterized in that, The S4 step specifically includes: S41. Receive the candidate solution set output in step S3; S42. Find the sample in the decision space that is closest to the candidate solution in the candidate solution set in the database, and record the Euclidean distance between the candidate solution and the closest sample; S43. Calculate the angle between the predicted target value of the candidate solution and the true objective function value of the nearest sample in the target space; S44. Using the negative values ​​of the Euclidean distance and the included angle of the candidate solutions as two indicators, perform a non-dominated sort on the solutions in the candidate solution set. The non-dominated sort divides the solutions into one or more levels and selects some solutions from the solutions located in the first level.

3. The high-dimensional multi-objective water resource scheduling and control method based on multi-view sampling according to claim 2, characterized in that, In step S44, selecting the partial solution specifically means selecting half of the solutions from the solutions located in the first layer.

4. The high-dimensional multi-objective water resource scheduling and control method based on multi-view sampling according to claim 1, characterized in that, The internal multi-objective optimization algorithm in step S3 specifically includes the following steps: S31. Set a population evolution generation count, initially set to 0, and initialize a specified number of reference vectors; S32. Perform population initialization to obtain the initial population; S33. Generate offspring population using genetic algorithms; S34. Merge the initial population and the offspring population into a merged population, and use the Gaussian process model to predict the objective function value of the solution in the merged population. S35. Perform the step of maintaining population diversity: associate the solutions in the merged population with the corresponding reference vectors according to the angle to form multiple solution groups; S36. Perform the step to enhance population convergence: Select individuals from the multiple solutions formed in step S35 to form the next generation population; S37. Update the reference vector; S38. The population generation count is incremented by 1; S39. Termination condition: When the population evolution generation count is less than the preset maximum population evolution generation, return to step S32 to continue execution; otherwise, stop the search and output the optimized population as the candidate solution set.

5. The high-dimensional multi-objective water resource scheduling and control method based on multi-view sampling according to claim 4, characterized in that, In step S35, the step of maintaining population diversity further includes: when the number of solutions in a certain group in the merged population is greater than a preset threshold, then a clustering method is used to divide the individuals in that group into a predetermined number of groups.

6. The high-dimensional multi-objective water resource scheduling and control method based on multi-view sampling according to claim 5, characterized in that, In step S36, the step of enhancing population convergence specifically involves selecting the individual closest to the ideal point from each group formed in step S35 to enter the next generation of the population.

7. The high-dimensional multi-objective water resource scheduling and control method based on multi-view sampling according to claim 6, characterized in that, In step S33, the genetic algorithm uses a crossover probability of 1 and a mutation probability of 1. .

8. A high-dimensional multi-objective water resource scheduling and control method based on multi-view sampling according to claim 4, characterized in that, In step S37, the update of the reference vector is performed based on the initial reference vector and the vector composed of the maximum and minimum values ​​of each objective function found during the population optimization process.

9. A high-dimensional multi-objective water resource scheduling and control method based on multi-view sampling according to claim 4, characterized in that, In step S32, the population initialization specifically involves: When the population's generation count reaches 0, the samples in the database are associated with the reference vector, and the solution closest to the ideal point is selected on each vector. If the predetermined number is not reached... Then, for each reference vector, select the solution that is second closest to the ideal point, until the number of selected solutions reaches a certain threshold. Greater than or equal to To control the population size, if it is greater than... It will select only the reference vector with the smallest distance from the ideal point in the last traversal. One solution.

10. A high-dimensional multi-objective water resource scheduling and control method based on multi-view sampling according to claim 1, characterized in that, In step S1, the specified quantity is .

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