Sampling algorithm strategy set construction method based on experimental problem feature matching

Abstract

The invention relates to a sampling algorithm strategy set construction method based on experimental problem feature matching. The method comprises the following steps: acquiring at least one experimental problem feature; according to the at least one experimental problem feature, calculating the number of samples required to be generated by the comprehensive experimental method; and selecting a target sampling algorithm from the sampling algorithm strategy set according to the sample number, and performing experiment arrangement according to the target sampling algorithm. According to the method, a proper sampling algorithm is adopted, an effective experiment design tool is provided, the number of times of simulation experiments can be effectively reduced, efficiency is improved, and analysis of simulation results is allowed to follow.

Description

Technical Field

[0001] The present application belongs to the technical field of sampling algorithm strategies, and in particular relates to a method for constructing a sampling algorithm strategy set based on experimental problem feature matching. Background Art

[0002] Experimental design is the application and development of experimental design methodology in the field of computer simulation. Its purpose is to improve the efficiency and effectiveness of simulation experiments. Experimental sampling algorithms are an important component of experimental design. The selection and implementation of sampling algorithms are crucial in experimental design. An appropriate sampling algorithm can ensure that representative experimental samples are obtained from the experimental sample space, thereby supporting the experimenter's accurate analysis of experimental results. The design of the sampling algorithm needs to consider factors such as the number, distribution, and sampling frequency of samples to ensure that the experimental sample data truly reflects the characteristics and patterns of the experimental sample space. The choice of experimental plan will influence the selection and implementation of the sampling algorithm, and the performance and results of the sampling algorithm will also be fed back into the design of the experimental plan. During the experimental process, the experimenter needs to continuously adjust and optimize the experimental plan and sampling algorithm based on the experimental progress and results to ensure the reliability and effectiveness of the experiment. Summary of the Invention

[0003] Based on this, it is necessary to provide a sampling algorithm strategy set construction method based on experimental problem feature matching to address the above technical issues.

[0004] A method for constructing a sampling algorithm strategy set based on experimental problem feature matching, the method comprising:

[0005] Obtain at least one experimental question feature;

[0006] Calculate the number of samples required for a comprehensive experimental method based on at least one characteristic of the experimental question;

[0007] According to the number of samples, the target sampling algorithm is selected from the sampling algorithm strategy set, and the experiment is arranged according to the target sampling algorithm.

[0008] Among them, according to the number of samples, the target sampling algorithm is selected from the sampling algorithm strategy set, including:

[0009] Determine whether the number of samples is greater than a preset threshold;

[0010] If the number of samples is greater than or equal to the preset threshold, the target optimization algorithm is selected from the sampling algorithm strategy set as the target sampling algorithm.

[0011] Among them, the target optimization algorithm is the Bayesian optimization algorithm.

[0012] The target optimization algorithm is a combination of one or more of an EI-based Bayesian optimization algorithm, a PI-based Bayesian optimization algorithm, a UCB-based Bayesian optimization algorithm, a Turbo-based Bayesian optimization algorithm, and a Hebo-based Bayesian optimization algorithm.

[0013] If the number of samples is less than a preset threshold, the method further includes:

[0014] Determine whether the experimental sample can match the number in the specific design table;

[0015] If the experimental samples can match the number in the specific design table, the target sampling algorithm is selected based on the specific design table.

[0016] The specific design table is an orthogonal design table or a uniform design table.

[0017] The method further includes:

[0018] If the experimental sample cannot match the specific design table, the comprehensive experiment method is used as the target sampling algorithm.

[0019] This invention relates to a method for constructing a sampling algorithm strategy set based on experimental problem feature matching. Based on the experimental problem's characteristics, including the experimenter's requirements for the size of the simulation sample space, the method automatically selects an appropriate sampling algorithm from the sampling algorithm strategy set and directly provides experimental arrangements. By employing appropriate sampling algorithms and providing effective experimental design tools, the method can effectively reduce the number of simulation experiments, improve efficiency, and provide a methodical approach to analyzing simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Flowchart of a method for constructing a sampling algorithm strategy set based on experimental problem feature matching in one embodiment;

[0021] Figure 2 A flowchart of a method for constructing a sampling algorithm strategy set based on experimental problem feature matching in another embodiment;

[0022] Figure 3 A schematic diagram of Hebo optimal sample combination scores in one embodiment;

[0023] Figure 4 Schematic diagram of Turbo optimal sample combination score in one embodiment;

[0024] Figure 5 Schematic diagram of the EI optimal sample combination score in one embodiment;

[0025] Figure 6 Schematic diagram of POI optimal sample combination scores in one embodiment;

[0026] Figure 7 Schematic diagram of the optimal UCB sample combination score in one embodiment. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0028] like Figure 1 As shown, an embodiment of the present invention provides a method for constructing a sampling algorithm strategy set based on experimental problem feature matching, the method comprising:

[0029] S110, obtaining at least one experimental question feature;

[0030] In this embodiment, the experimenter can input basic experimental information through an input system. This basic experimental information can include experimental problem characteristics such as at least one experimental factor and the combination of experimental factor levels. This allows the experimenter's needs to be readily received and interpreted, ensuring the accuracy and pertinence of subsequent design. For example, when choosing a tourist destination, it is necessary to comprehensively consider multiple experimental factors such as the tourist destination's consumption level, the scenic beauty, traffic conditions, and personal income to extract experimental problem characteristics. The levels of the experimental factors can be specific numerical values, such as 0, 1, etc.

[0031] S120. Calculate the number of samples required to generate a comprehensive experimental method based on at least one experimental problem feature;

[0032] Among them, the comprehensive experimental design method is a design strategy that comprehensively considers various possible factors. By covering all factors and combinations of factor levels, the comprehensive experimental design method can ensure the comprehensiveness and robustness of the system design. For experimental designers, they can find the experimental samples that best meet their needs within a wider range of choices. However, the number of samples in the comprehensive experimental method usually increases exponentially with the increase in the combination of experimental factors and their factor levels. Therefore, it is necessary to consider the effective use of computing resources and the optimization of algorithms. The embodiment of the present invention calculates the number of samples required to be generated by the comprehensive experimental method based on at least one experimental problem feature, and finds the number of experimental samples that meets the experimental needs by comprehensively considering factors such as computing resources and algorithm optimization.

[0033] S130. Select a target sampling algorithm from a sampling algorithm strategy set based on the number of samples, and arrange experiments based on the target sampling algorithm.

[0034] The method of this embodiment can automatically select an appropriate sampling algorithm from a set of sampling algorithm strategies based on the experimental problem characteristics, such as the experimenter's requirements for the simulation sample space size, and directly provide experimental arrangements. Thus, by adopting an appropriate sampling algorithm and providing an effective experimental design tool, the number of simulation experiments can be effectively reduced, efficiency can be improved, and the analysis of simulation results can be organized in a systematic manner.

[0035] Among them, the sampling algorithms of the sampling algorithm strategy set can include Bayesian optimization algorithm, orthogonal design sampling algorithm, uniform design sampling algorithm, etc. Among them, the Bayesian optimization algorithm is an effective method suitable for global optimization problems, especially in the optimization of black box functions with high evaluation costs. The Bayesian optimization algorithm pays more attention to updating the model and approximating the true functional relationship. It is suitable for complex optimization problems and performs well when the number of samples is relatively large. The Bayesian optimization algorithm is a method suitable for continuous parameter optimization problems. By continuously selecting new experimental points in the experimental space, the algorithm can find the global optimal solution within a limited number of experiments. This method can provide personalized design suggestions when the experimental designer has specific preferences or constraints, ensuring that the design scheme is more in line with the actual needs of the experimental designer. The principles of the Bayesian optimization algorithm are as follows:

[0036] The core idea of ​​Bayesian optimization is to construct a proxy model (usually a Gaussian process or other probabilistic model) and use it to select the next sampling point, thereby finding the global optimal solution within a limited number of evaluations. The Bayesian theorem formula is as follows:

[0037]

[0038] Among them, the prior probability model is p(f); the observation model describes the mechanism of generating observation data, that is, the likelihood distribution p(D 1:t |f). Updating the probabilistic surrogate model means obtaining a posterior probability distribution that contains more data information according to the Bayesian formula.

[0039] The acquisition function is constructed based on the posterior probability distribution, and the next evaluation point with the greatest potential is selected by maximizing the acquisition function. At the same time, an effective acquisition function can ensure that the total loss of the selected evaluation point sequence is minimized.

[0040] The Bayesian optimization workflow can be divided into the following key steps:

[0041] (1) Selecting the initial point: The initial point is usually selected randomly, but can also be based on some heuristic rules.

[0042] (2) Constructing a surrogate model: Use the evaluated data points to construct a surrogate model of the objective function.

[0043] (3) Optimize the acquisition function: The next evaluation point is selected based on the proxy model, and the acquisition function is used to balance exploration and exploitation.

[0044] (4) Update the proxy model: Evaluate the new data point and update the proxy model, repeating steps 2) and 3) until the termination condition is met.

[0045] A surrogate model is a simplified model used to simulate a complex and computationally expensive objective function. In Bayesian optimization, a surrogate model is used to predict the value and uncertainty of the objective function, thereby determining the next evaluation point. Surrogate models effectively balance exploration (seeking new information) and exploitation (using known information for optimization). Common surrogate models include Gaussian processes, random forests, and neural networks.

[0046] The acquisition function is used to select the next evaluation point based on the surrogate model. By balancing exploration and exploitation, the acquisition function guides the optimization process to find the global optimal solution within the minimum number of function evaluations. Common acquisition functions include expected improvement (EI), probability of improvement (PI), upper confidence bound (UCB), and trust region (Trust Region Bayesian Optimization, TuRBO). Based on this, Bayesian optimization algorithms can be divided into EI-based Bayesian optimization algorithms, PI-based Bayesian optimization algorithms, UCB-based Bayesian optimization algorithms, Turbo-based Bayesian optimization algorithms, and Hebo-based Bayesian optimization algorithms.

[0047] The orthogonal design sampling algorithm is a design strategy that considers the interactions between factors. By selecting a set of orthogonal experimental conditions, the orthogonal experimental design method can help experimental designers better understand the independent contribution of each factor, allowing for more targeted selection. The orthogonal design sampling algorithm selects representative points based on the orthogonality criterion, ensuring that these points reflect the relationships between factors and indicators within the experimental range. It uses orthogonal tables to scientifically arrange and analyze multifactor experiments, and is suitable for experiments with a large number of factors and a limited number of factor levels.

[0048] The uniform design sampling algorithm, similar to the orthogonal design sampling algorithm, is a method for scientifically arranging and analyzing multifactorial experiments using a uniform table. The uniform design sampling method focuses on evenly distributing experimental points within the design space to ensure reliable and consistent results. This method can help experimenters avoid over-concentration in specific areas, thereby gaining a more comprehensive understanding.

[0049] In order to construct the above-mentioned sampling algorithm strategy set, the method of the embodiment of the present invention analyzes and compares the applicability and optimal factor combination evaluation scores of sampling methods such as orthogonal design sampling algorithm, uniform design sampling algorithm and Bayesian optimization algorithm, so as to assist experimenters in selecting the optimal solution suitable for the intended experiment.

[0050] like Figure 2 As shown, an embodiment of the present invention provides a method for constructing a sampling algorithm strategy set based on experimental problem feature matching, the method comprising:

[0051] S210, obtaining basic experimental information selected by the experimenter to obtain at least one experimental problem feature;

[0052] S220. Calculate the number of samples required to generate a comprehensive experimental method based on at least one experimental problem feature;

[0053] S230: Determine whether the number of samples is greater than a preset threshold; for example, the preset threshold may be 200,000.

[0054] If the number of samples is greater than or equal to the preset threshold, step S240 is executed to select a target optimization algorithm from the sampling algorithm strategy set as the target sampling algorithm, wherein the target optimization algorithm is a Bayesian optimization algorithm. That is, when the number of samples is greater than or equal to the preset threshold (e.g., 200,000), the Bayesian optimization algorithm is selected as the target sampling algorithm.

[0055] The Bayesian optimization algorithm can be an EI-based Bayesian optimization algorithm, a PI-based Bayesian optimization algorithm, a UCB-based Bayesian optimization algorithm, a Turbo-based Bayesian optimization algorithm, or a Hebo-based Bayesian optimization algorithm.

[0056] (1) The core of EI-based Bayesian optimization is to select the experimental factor combinations with the largest expected improvement, which are used to select the next most promising improvement point based on the currently known proxy model. The characteristic of EI Bayesian is that it is suitable for situations where the experimenter is mainly concerned with the size of the improvement. It helps the optimization algorithm to quickly converge to the global optimal solution by finding a balance between exploring unknown areas and utilizing known information. The working principle of EI is based on the following key steps:

[0057] 1) Surrogate model prediction: In Bayesian optimization, a surrogate model (usually a Gaussian process or other regression model) is used to estimate the probability distribution of the objective function in the entire search space. The surrogate model gives the predicted value μ(x) and variance σ for each point. 2 (x), which reflects the uncertainty of the objective function value.

[0058] 2) Current optimal value: During the optimization process, the optimal objective function value f(x+ ).

[0059] 3) EI calculation: For each candidate point x, the EI calculation formula is as follows:

[0060] EI(x)=E[max(0,f(x)-f(x + ))]

[0061] Where E[·] represents the expected operation, and f(x) is the predicted value of the objective function at point x. The formula means to calculate the optimal value f(x + ), how much can the predicted objective function value f(x) be improved. If f(x)>f(x + ), then max(0,f(x)-f(x + )) is greater than zero, otherwise it is zero.

[0062] If the predicted distribution of the target function at x is a Gaussian distribution N(μ(x),σ 2 (x)), then EI can be further expressed as:

[0063] EI(x)=(μ(x)-f(x + )-ξ)Φ(Z)+σ(x)φ(Z)

[0064] Among them, ξ is a non-negative adjustment parameter used to balance exploration and exploitation; Φ is the cumulative distribution function of the standard normal distribution, and φ is its probability density function.

[0065] (2) Bayesian optimization based on PI. The characteristic of Bayesian optimization based on PI is to select experimental factor combinations that have a higher probability of obtaining improvement than the current optimal value. It is suitable for experimenters who are mainly concerned with the probability of improvement, without considering the size of the improvement. It quantifies the current optimal value f(x + ) and the new candidate point x to guide the search. Specifically, if f(x)>f(x + ), the new point x is considered to have the potential to become the new optimal solution.

[0066] The working principle of PI is based on the following key steps:

[0067] 1) Calculate the predicted value and variance: First, you need to use a surrogate model (usually a Gaussian process) to predict the target function value μ(x) and variance σ at the current point x. 2 (x). These predictions are based on a Gaussian process model constructed from previously evaluated data points.

[0068] 2) Calculate the improvement threshold: Set the threshold ξ of the improvement probability, which can be a small non-negative value to adjust the balance between exploration and exploitation. Usually, ξ can be set to zero or a small positive number to ensure that the candidate point x has a significantly higher predicted value μ(x) than the current optimal value f(x). + ) is selected.

[0069] 3) Calculate the improvement probability: The improvement probability PI(x) can be calculated using the following formula:

[0070]

[0071] Where Φ is the cumulative distribution function of the standard normal distribution. This formula reflects the probability that a new point x is selected as the next evaluation point based on its predicted value μ(x) and the current optimal value f(x + ) and its variance σ(x).

[0072] 4) Select the next evaluation point: Based on the calculated improvement probability PI(x), the point x with the highest probability is selected as the next point to be evaluated. Typically, the acquisition function calculates the improvement probabilities of multiple candidate points in each iteration and selects the point with the highest probability for actual evaluation.

[0073] (3) Bayesian optimization based on UCB not only considers the mean, variance, or confidence interval of the predicted value, but also provides a trade-off coefficient, allowing the experimenter to adjust the algorithm according to actual needs during the optimization process to balance between exploring new areas and utilizing known information, thereby ensuring that while exploring new areas, the search is conducted as close to the known optimal solution as possible. The characteristic of Bayesian optimization based on UCB is that it is suitable for situations where the experimenter has a good understanding of the data distribution and wants to maintain search diversity while efficiently utilizing existing data.

[0074] The UCB working principle is based on the following key steps:

[0075] 1) Calculate the predicted value and variance: First, the surrogate model is used to predict the mean μ(x) and variance σ of the objective function value at the current point. 2 (x). These predictions are based on a Gaussian process model constructed from previously evaluated data points.

[0076] 2) Calculate the upper bound of the confidence interval: According to the mathematical expression of UCB, the upper bound of the confidence interval of each candidate point x can be calculated:

[0077] UCB(x)=μ(x)+κσ(x)

[0078] Here, κ is a non-negative tuning parameter that controls the balance between exploration and exploitation. Typically, κ can be tuned based on the nature of the problem to achieve optimal performance in practical applications.

[0079] 3) Select the next evaluation point: Based on the calculated UCB value, select the point x that maximizes the UCB value as the next point to be evaluated. The UCB method tends to select points with large uncertainty in the predicted value, thus achieving a balance between exploring new areas and leveraging known information.

[0080] 4) Update the surrogate model: After selecting the next evaluation point x, the actual function evaluation is performed and the surrogate model is updated based on the new observations. The updated surrogate model will reflect the new data point and affect the next round of UCB calculations.

[0081] (4) Turbo-based Bayesian optimization can significantly improve the efficiency of global optimization by transforming the global optimization problem into a series of local optimization problems and efficiently solving each local problem using the trust region. This can also significantly improve the efficiency of experimenters in finding more optimal experimental factor combinations. The characteristic of Turbo-based Bayesian optimization is that it is suitable for solving higher-dimensional and more complex global optimization problems. It combines the trust region optimization strategy with the concept of Bayesian optimization, aiming to minimize the number of objective function evaluations by effectively exploring and utilizing the search space, thereby quickly finding the global optimal solution.

[0082] The working principle of Turbo is based on the following key steps:

[0083] 1) Construct candidate points: Based on the current evaluation point set x, f(x), construct a proxy model and obtain the model's length_scale value as the weight. Take the point corresponding to the current optimal function value min(f(x)) as the center point x center , construct a new hypercube sphere, the upper and lower bounds of the hypercube sphere are defined by the following formula (length is the trust region radius):

[0084] lb=np.clip(x center -weights*length / 2.0,0.0,1.0)

[0085] ub=np.clip(x center -weights*length / 2·0,0·0,1·0)

[0086] Generate n cand Quasi-random sequence candidate points, calling the proxy model for n cand Perform maximum likelihood estimation on candidate points and output n cand candidate points and their corresponding function values ​​Xcand ,y cand , and select the best candidate points.

[0087] 2) Adjust the trust region radius: According to the minimum value min(y cand )Adjust the radius of the trust region:

[0088] If the current optimal value min(y cand ) <y best , the number of successful searches increases by 1, otherwise the number of failed searches increases by 1;

[0089] Trust region radius expansion condition (multiplied by 2): If the current number of successes is equal to the preset threshold;

[0090] Trust region radius reduction condition (divided by 2): If the current number of failures is equal to the preset threshold.

[0091] (5) Hebo-based Bayesian optimization, through input and output data transformation, Gaussian kernel function optimization, and multi-objective acquisition function construction, can quickly locate the optimal solution of the objective function within a small number of iterations, combining the characteristics of EI, PI, and UCB. The working principle of Hebo is based on the following key steps:

[0092] 1) Output transformation: Use power transformation (Γ ζ (·)) to reduce heteroskedasticity, rather than the commonly used linear normalization. Specifically, if the target is strictly positive or strictly negative, a Box-Cox transformation is used, otherwise a Yeo-Johnson transformation is followed. For each transformation, the hyperparameters for stabilizing variance and minimizing skewness are estimated via maximum likelihood. Note that this is performed before minimizing the negative log-marginal likelihood of the GP.

[0093] 2) Input transformation: The distorted Gaussian process can be used to handle non-stationary functions for the input parameters. A nonlinear monotonic transformation is performed by using the cumulative distribution function of the Kumaraswamy distribution, which is given by the following formula: The transformation is performed component-wise, and Θ = {a, b} represents the additional parameters introduced. When performing these transformations, power_transform from sklearn and InputWarpedGP from the GPy package were used.

[0094] 3) Gaussian kernel function optimization: Sample efficiency is important, so a Gaussian process with an additive kernel is used, which is given by the following formula:

[0095]

[0096] Here, θ1 and θ2 are kernel hyperparameters.

[0097] 4) Multi-objective acquisition function construction: The common EI, PI, and UCB acquisition functions in Bayesian optimization are aggregated and sampled on the Pareto front of these three acquisition functions. This not only avoids the universality issues of a single acquisition function, but also supports parallel exploration. An evolutionary optimizer NSGA-II that supports mutation and crossover is called from the multi-objective optimization library pymoo to implement the aggregate optimization of the EI, PI, and UCB acquisition functions:

[0098]

[0099] In summary, these methods each have their own advantages and disadvantages, and are applicable to different simulation sample space sizes. Orthogonal and uniform sampling algorithms are traditional experimental design methods that focus on the selection and uniformity of experimental point distribution. They are suitable for simple, low-dimensional optimization problems, resulting in smaller sample sizes. Bayesian optimization methods, on the other hand, focus more on model updating and approximating true functional relationships, and are suitable for complex, high-dimensional optimization problems, resulting in larger sample sizes. Choosing an experimental design method depends on the specific characteristics and requirements of the problem.

[0100] Continue to see Figure 2 If the number of samples is less than a preset threshold, step S250 is executed to determine whether the experimental samples match the number in a specific design table; the specific design table is an orthogonal design table or a uniform design table. That is, when the number of samples is less than a preset threshold (e.g., 200,000), a determination is made as to whether the experimental samples match the corresponding orthogonal design table of the orthogonal design sampling algorithm, or whether the experimental samples match the corresponding uniform design table of the uniform design sampling algorithm.

[0101] If the experimental samples can match the number in the specific design table, step S260 is executed to select the target sampling algorithm based on the specific design table. That is, when the number of experimental samples is less than a preset threshold and the experimental samples can match the number in the orthogonal design table, the orthogonal design sampling algorithm is selected as the target sampling algorithm. Alternatively, when the number of experimental samples is less than a preset threshold and the experimental samples can match the number in the uniform design table, the uniform design sampling algorithm is selected as the target sampling algorithm. This involves designing an intelligent matching algorithm that can establish an effective association between the experimental samples and the design table. This includes technical means such as fuzzy matching and feature extraction to ensure the accuracy and efficiency of the matching.

[0102] Further, if the experimental sample can not match the specific design table, then step S270 is executed, and the comprehensive experimental method is used as the target sampling algorithm. That is, if the number of experimental samples is less than a preset threshold value (such as 200,000), and the experimental sample can not match the orthogonal design table or the uniform design table, then the construction of the sampling strategy is carried out based on the comprehensive experimental method. If the number of experimental factors and the number of each experimental factor level can not match the number given in the orthogonal design table and the uniform design table, then the comprehensive experimental method is adopted, considering all experimental factors and factor level combinations to carry out the construction of the sampling algorithm strategy. This needs to ensure that the implementation of the comprehensive experimental method can effectively cover all possible situations, while ensuring the economy and feasibility of the experiment. Now it is necessary to design a kind of efficient experimental scheme generation algorithm, considering factors such as resource consumption and time cost in the experimental process.

[0103] Overall, the key technical aspects of the sampling algorithm strategy set based on experimental problem feature matching involve accurately capturing the experimenter's needs, effectively calculating the sample size, selecting and integrating optimization algorithms, and matching experimental samples with the design table. By combining these technical approaches, it is possible to automatically select the appropriate experimental design method based on the experimenter's requirements for the size of the simulation sample space and directly provide experimental arrangements, effectively improving the efficiency and accuracy of experimental design.

[0104] The following examples illustrate various experimental settings and experimental results:

[0105] 1. Experimental Setup

[0106] (1) Orthogonal design: using L 18 (2 1 ×3 7 ), taking 8 factors as an example, the orthogonal design table is shown in Table 1, where the horizontal header indicates the type of experimental factor, the vertical header indicates that there are 18 combinations of experimental factor levels using the orthogonal design, and the content in the table indicates the level of each experimental factor. For example, experimental factor 8 has two factor levels, 0 and 1. The orthogonal design table of 8 factors is shown in Table 1 below:

[0107] Table 1 Orthogonal design table

[0108]

[0109]

[0110] (2) Uniform design: using U 60 (6 8 ) uniform table, the uniform design table of 8 factors is shown in Table 2 below:

[0111] Table 2 Uniform design table

[0112]

[0113]

[0114] (3)EI / PI / UCB:

[0115] 1) Initial point: The traditional Bayesian sampling initial point is randomly generated, and the corresponding score is generated based on the objective function. This is modified to use the current round of sample points and corresponding scores as the sampling initial point;

[0116] 2) Sample training: After the first round of GP model training, the model is saved. In the subsequent rounds of sampling, a new proxy model is not established. Instead, the model saved in the previous round is loaded. After the training is completed, the proxy model is updated and saved.

[0117] (4) Turbo: The original turbo algorithm randomly generates the initial point and initial trust region. In the system algorithm, it is necessary to sample backward based on the real sample points and corresponding scores of the previous round. Therefore, the initial point of the turbo algorithm is set to the n sample points and corresponding scores of the previous round. Modifications are made to the allocation of the trust region of the initial sample points, the generation of the upper and lower bounds of the initial trust region, and the selection of the final sample points.

[0118] (5)Hebo:

[0119] 1) Initial point: The initial point generation part of the HEBO algorithm itself is skipped, and the sample points and corresponding scores of the previous round are used as the initial points of the next round of sampling;

[0120] 2) Sample training: When using the HEBO algorithm for multiple rounds of sample sampling, the model is saved after the first round of GP model training. In subsequent rounds of sampling, a new proxy model is not established. Instead, the model saved in the previous round is loaded. After the training is completed, the proxy model is updated and saved.

[0121] 2. Experimental Results

[0122] The score is a single extreme point objective function, as follows:

[0123]

[0124] The score is adjusted to a percentage system, score = score / 6.06

[0125] Among them, x i is the experimental factor, x1,…,x6 are the system target selection factors, and their values ​​range from 20 to 50.

[0126] x7 is the task execution timing factor, with a value range of (0, 1, 2, 3, 4, 5). x8 is the policy preference setting factor, with a value range of (0, 1).

[0127] The experimental results of each algorithm in the above experimental settings are as follows Figure 3-Figure 7 As shown in Table 3, the evaluation scores of each algorithm in the above experimental settings are shown in Table 3.

[0128] Table 3 Algorithm comparison experiment results score table

[0129] Optimal sample combination Highest score Running time / s Orthogonal design [20,35,35,35,35,35,3,0] 83.00 / Uniform design [26,26,44,38,44,38,2,1] 74.42 / Turbo [35,38,36,34,35,35,2,0] 98.53 50.42649221420288 Hebo [35,35,35,35,35,35,5,1] 100.0 59.1706759929657 EI [34,34,31,34,33,34,4,1] 98.07 410.97965717315674 POI [42,35,24,32,37,28,2,0] 82.32 174.25713658332825 UCB [34,37,33,34,30,31,2,1] 95.76 1638.7709040641785

[0130] As can be seen, in all experiments, the orthogonal and uniform designs were static single-round experiments. The experimental score plots and runtimes in Table 3 are not recorded. The remaining algorithms all used 10 real samples per round to train the proxy model. Except for Turbo, the other four algorithms (Hebo, EI, POI, and UCB) all achieved convergence within 20 rounds, while Turbo required more rounds, typically converging after around 30 to 40 rounds.

[0131] From the experimental result score chart, we can see that except Turbo, the other four algorithms (Hebo, EI, POI, UCB) converge within 20 rounds, while Turbo requires more rounds, usually converging in about 30 to 40 rounds.

[0132] Hebo performed the best, taking 59 seconds and achieving an optimal sample combination score of 100. Turbo, despite requiring more rounds to converge, was the fastest at 50 seconds, achieving an optimal sample combination score of 98.53. The EI algorithm took 410 seconds and achieved an optimal sample combination score of 98.07. UCB took the longest to run, taking 1638 seconds, achieving an optimal sample combination score of 95.76. POI ran for 874 seconds, achieving an optimal sample combination score of 85.32.

[0133] In summary, orthogonal and uniform designs are more suitable for exploratory sampling in small sample spaces due to the size limitations of the orthogonal and uniform matching tables. Hebo performs best in terms of optimal sample combination score and convergence speed, quickly finding the optimal solution and being suitable for experimental designs that demand high time and accuracy. Although Turbo requires more rounds to converge, its optimal sample combination score is close to full and its run time is the shortest, making it suitable for efficient experimental designs requiring a larger number of experimental rounds. EI has a higher optimal sample combination score, but exhibits significant fluctuations during convergence and has the longest run time, making it less stable and less efficient than the other two algorithms. UCB has the second lowest optimal sample combination score, but also has a longer run time and the second lowest efficiency. POI performs the worst in all aspects, with the lowest score and the second longest run time. Compared to Hebo and Turbo, EI, POI, and UCB have lower optimal sample combination scores and may serve as alternative experimental design options.

[0134] This paper provides a method for constructing a sampling algorithm strategy set based on experimental problem feature matching. Based on the experimental problem's characteristics, such as the experimenter's requirements for the size of the simulation sample space, the method automatically selects an appropriate sampling algorithm from the sampling algorithm strategy set and directly provides experimental arrangements. By employing appropriate sampling algorithms and providing effective experimental design tools, the method can effectively reduce the number of simulation experiments, improve efficiency, and provide a methodical approach to analyzing simulation results.

[0135] The above embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A method for constructing a sampling algorithm strategy set based on experimental problem feature matching, characterized in that: The method comprises: Obtain at least one experimental question feature; Calculate the number of samples required for a comprehensive experimental method based on at least one characteristic of the experimental question; According to the number of samples, the target sampling algorithm is selected from the sampling algorithm strategy set, and the experiment is arranged according to the target sampling algorithm.

2. The method according to claim 1, characterized in that The target sampling algorithm is selected from the sampling algorithm strategy set according to the number of samples, including: Determining whether the sample size is greater than a preset threshold; If the number of samples is greater than or equal to a preset threshold, a target optimization algorithm is selected from the sampling algorithm strategy set as the target sampling algorithm.

3. The method according to claim 2, characterized in that The target optimization algorithm is a Bayesian optimization algorithm.

4. The method according to claim 2, characterized in that The target optimization algorithm is a combination of one or more of an EI-based Bayesian optimization algorithm, a PI-based Bayesian optimization algorithm, a UCB-based Bayesian optimization algorithm, a Turbo-based Bayesian optimization algorithm, and a Hebo-based Bayesian optimization algorithm.

5. The method according to claim 2, characterized in that If the number of samples is less than a preset threshold, the method further includes: Determine whether the experimental sample can match the number in the specific design table; If the experimental samples can match the number in the specific design table, a target sampling algorithm is selected based on the specific design table.

6. The method according to claim 5, characterized in that The specific design table is an orthogonal design table or a uniform design table.

7. The method according to claim 5, characterized in that The method further comprises: If the experimental samples cannot match the specific design table, the full experiment method is used as the target sampling algorithm.

8. The method according to any one of claims 1 to 7, characterized in that The method further comprises: The applicability of various sampling algorithms in the sampling algorithm strategy set is analyzed and compared, and the optimal factor combination and evaluation score corresponding to each sampling algorithm are obtained to assist experimenters in selecting the optimal solution suitable for the intended experiment.

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