A Multi-Objective Tourist Volume Interval Prediction Method and System Based on Frequency Mixing Drive

Abstract

This invention relates to the field of tourist volume interval prediction technology, specifically a multi-objective tourist volume interval prediction method and system based on frequency mixing. The prediction method uses weekly tourist volume intervals as the prediction objective, and daily search index, AQI, and rainfall as high-frequency influencing variables. A standardized variable matrix is ​​constructed through frequency mixing data alignment. The matrix is ​​then reconstructed into low, medium, and high-frequency feature subsequences using wavelet packet decomposition combined with sample entropy. A multi-type candidate model library is then built. The optimal sub-model for each subsequence is selected based on adaptive weighted interval evaluation indicators and 5-fold cross-validation. Finally, a sparrow optimization algorithm is used to search for the optimal weights by minimizing the interval mean absolute percentage error and root mean square error as dual objectives. The prediction results of the optimal sub-models are weighted and fused to obtain the final value, thereby effectively preserving high-frequency data features, achieving multi-scale feature decoupling of the sequence, and significantly improving the accuracy and reliability of tourist volume interval prediction.

Description

Technical Field

[0001] This invention relates to the field of tourist volume interval prediction technology, specifically a multi-objective tourist volume interval prediction method and system based on frequency mixing. Background Technology

[0002] Tourist volume is a core indicator for measuring the vitality and attractiveness of a tourist destination market. Accurate tourist volume forecasting can provide scientific decision-making basis for tourism management departments in resource allocation, supply and demand regulation, and emergency response, while also helping tourism enterprises optimize operational strategies and mitigate business risks. Compared to point-based tourist volume, weekly tourist volume ranges cover the highest and lowest levels of tourist volume within a period, more comprehensively reflecting the fluctuation characteristics and uncertainties of the tourism market, and better meeting the actual needs of medium- and long-term planning and operational decisions in the tourism industry.

[0003] Current tourist volume range prediction technology still has the following technical shortcomings: Firstly, tourist volume is driven by multiple factors such as search popularity, weather conditions, and environmental quality. These influencing factors are mostly high-frequency daily data (data with a daily statistical period), which forms a mixed frequency characteristic with low-frequency weekly tourist volume data. Existing technologies often use simple down-frequency averaging or up-frequency interpolation to unify the data frequency, which can easily cause the loss of dynamic characteristics of high-frequency data or introduce redundant noise, making it impossible to accurately capture the cross-frequency correlation patterns of multiple factors.

[0004] Secondly, the tourist volume interval sequence exhibits significant non-stationary, nonlinear, and multi-scale fluctuation characteristics. Existing studies mostly model the original sequence directly without decoupling the long-term trend, periodic fluctuations, and random fluctuations of the sequence. A single model is difficult to adapt to fluctuation characteristics of different complexities at the same time, resulting in prediction fit bias.

[0005] Third, existing multi-model ensemble prediction methods mostly adopt subjective model selection or model selection based on a single evaluation index, lacking a precise model matching mechanism for different feature subsequences. Furthermore, ensemble optimization often focuses on optimizing a single objective, making it difficult to simultaneously consider prediction accuracy and stability, ultimately resulting in insufficient reliability and practicality of tourist volume interval prediction results.

[0006] Therefore, how to construct a prediction method that takes into account the mixed-frequency driving characteristics and multi-scale fluctuation characteristics of tourist volume intervals, while taking into account data feature preservation, sequence feature decoupling, accurate model adaptation and multi-objective integrated optimization, has become a key technical problem to improve the prediction accuracy and stability of weekly tourist volume intervals, and is also a technical need that urgently needs to be solved in this field. Summary of the Invention

[0007] To address the technical challenges in tourist volume interval prediction, such as the loss of features during frequency mixing data fusion, poor adaptability of single models due to the lack of decoupling of multi-scale fluctuation features in the original sequence, and insufficient accuracy in model selection, which makes it difficult to balance prediction accuracy and stability, this invention provides a frequency mixing-driven multi-objective tourist volume interval prediction method. Based on this prediction method, this invention also provides a frequency mixing-driven multi-objective tourist volume interval prediction system.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A multi-objective tourist volume interval prediction method based on frequency mixing is proposed, using weekly tourist volume intervals as the target variable and search index, air quality index (AQI), and rainfall as high-frequency external influence variables with daily statistical periods. The prediction method includes the following steps: The high-frequency external influence variables and the weekly tourist volume range are aligned with mixed frequency data, and a standardized variable matrix is ​​constructed. Using the variable matrix as input, wavelet packet decomposition is first used to decompose the variable matrix into four sub-components with single frequency features. Then, the complexity and randomness of each sub-component are quantified by sample entropy. Sub-components with similar features are reconstructed into three types of feature sub-sequences: low frequency, medium frequency, and high frequency, according to a preset double complexity threshold. A multi-type candidate model library is constructed, and the optimal sub-model is selected for each type of feature sub-sequence based on the sub-sequence feature adaptive weighted interval evaluation index combined with 5-fold cross-validation. The interval prediction results of the three optimal sub-models are used as integrated inputs. The adaptive step-size multi-objective sparrow optimization algorithm is used to search for the optimal weight combination with minimizing the interval mean absolute percentage error and root mean square error as the dual objectives. After weighted fusion, the prediction results of the weekly tourist volume interval are obtained.

[0009] As a further improvement to the above scheme, the formula for calculating the adaptive step size factor in the adaptive step size multi-objective sparrow optimization algorithm is as follows: ; ; ; ; in, ω is the adaptive step size factor used in the t-th iteration for the i-th weight combination; min(·) is the minimum value operation; max(·) is the maximum value operation; min ω max These are the minimum and maximum values ​​of the step size factor, respectively. This is the base step size factor used in the t-th iteration for the i-th weight combination; h(t) is the curvature correction coefficient used in the t-th iteration for the i-th weight combination; h(t) is the global decay guiding factor used in the t-th iteration. , , , These are the Pareto success probability estimates used by the i-th weight combination in the t-1, t-2, and t-3 iterations, respectively. β is the adaptive memory decay coefficient used in the (t-1)th iteration of the i-th weight combination; min β max These are the minimum and maximum values ​​of the adaptive memory decay coefficient, respectively. e is the Pareto improvement flag used in the (t-1)th iteration for the i-th weight combination, with a value of 1 indicating success and a value of 0 indicating failure; (·) Represents an exponential function with the natural constant as its base; , The values ​​are, respectively, the Pareto success probability change magnitudes used by the i-th weight combination in the t-2th iterations; η is the memory sensitivity coefficient; κ is the curvature sensitivity coefficient; λ is the decay steepness coefficient; T is the maximum number of iterations; and θ is the decay initiation threshold.

[0010] As a further improvement to the above scheme: Based on the mixed frequency data sampling model, the mixed frequency data alignment is realized, with a frequency difference of 7. That is, the high-frequency external influence variables of 7 days are integrated into a 7-dimensional row vector, which is matched with the weekly tourist volume interval of the corresponding week. The tourist volume is an interval matrix, and the search index, AQI, and rainfall are numerical matrices.

[0011] As a further improvement to the above scheme: the wavelet packet decomposition uses the db5 wavelet basis function, with a decomposition level of 2. The variables are decomposed separately by low-pass and high-pass filters, and the sum of all sub-components can be reconstructed into the input variable matrix.

[0012] As a further improvement to the above scheme: a preset dual complexity threshold includes a first complexity threshold SE1 and a second complexity threshold SE2. The values ​​of SE1 and SE2 are respectively the third quantile and the second quantile of the sample entropy of the four sub-components of the corresponding variable; if the sample entropy ≤ SE1, it is a low-frequency subsequence; if SE1 < sample entropy ≤ SE2, it is a medium-frequency subsequence; if SE2 < sample entropy, it is a high-frequency subsequence.

[0013] As a further improvement to the above scheme, the multi-type candidate model library includes support vector regression, kernel extreme learning machine, extreme gradient boosting tree, lightweight gradient boosting machine, ridge regression, elastic network, gated recurrent unit, and long short-term memory network. When building a model for each type of feature subsequence, the search index, AQI, and rainfall quantum sequence with the same frequency are used as independent variables, and the interval synchronous prediction strategy is adopted to model the upper and lower limits of the tourist volume interval simultaneously.

[0014] As a further improvement to the above scheme, the calculation of the subsequence feature adaptive weighted interval evaluation index is as follows: first, obtain four basic indicators: interval mean absolute error, interval mean absolute percentage error, interval error standard deviation, and interval root mean square error, and normalize them; then, assign adaptive weights according to the set principles, and sum them up to obtain the comprehensive index.

[0015] As a further improvement to the above scheme, 5-fold cross-validation is used to validate the top three candidate models in terms of comprehensive index. The average absolute percentage error of the interval is used as the core index, and the error standard deviation is calculated. The model with the smallest error standard deviation is selected as the optimal fit sub-model. When the error standard deviations are the same, the model with the smaller comprehensive index value is selected.

[0016] As a further improvement to the above scheme: the initial weight population of the adaptive step-size multi-objective sparrow optimization algorithm is generated by Logistic chaotic mapping, and the population size is set to 50.

[0017] A frequency mixing-driven multi-objective tourist volume interval prediction system is provided for executing a multi-objective tourist volume interval prediction method. The system includes a frequency mixing data alignment module, a sequence deconstruction and reconstruction module, a sub-model selection module, and a multi-objective integrated optimization module connected sequentially. The frequency mixing data alignment module aligns data and constructs a standardized matrix. The sequence deconstruction and reconstruction module performs wavelet packet decomposition and sub-sequence reconstruction. The sub-model selection module selects the optimal matching sub-model for each type of sub-sequence. The multi-objective integrated optimization module uses an adaptive step-size multi-objective sparrow optimization algorithm to weightedly fuse the prediction results and output them.

[0018] Compared with the prior art, the beneficial effects of the present invention are: 1. Through the seamless design of the entire process, including mixed data alignment, multi-scale sequence deconstruction, feature-based sub-model selection, and multi-objective integrated optimization, the system effectively solves the industry pain points of mixed data fusion, sequence feature coupling, insufficient model adaptability, and single-objective integrated optimization in tourist volume interval prediction. The technology of each link has strong synergy, forming a complete prediction system from data processing to result output, which greatly improves the overall scientificity and practicality of weekly tourist volume interval prediction.

[0019] 2. The mixed-frequency data alignment based on the mixed-frequency data sampling model is designed with the frequency difference between 7 days of daily data and 1 week of weekly data. It directly integrates high-frequency data into vector form, avoiding the information loss of traditional down-frequency averaging or up-frequency interpolation. At the same time, normalization eliminates the difference in dimensions. The classification construction method of interval matrix and numerical matrix is ​​adapted to the different data characteristics of tourist volume and influencing factors, laying a high-quality and standardized data foundation for subsequent modeling.

[0020] 3. Two-level wavelet packet decomposition using the db5 wavelet basis function was adopted to achieve refined sub-variable deconstruction of the variable matrix. The requirement of lossless reconstruction ensured that no data features were lost. The special preservation processing for the sparse rainfall matrix took into account both the algorithm's universality and the adaptability to actual data, making the decomposition process more in line with the differentiated characteristics of multi-source data in the tourism field, and providing a precise sub-component basis for subsequent feature quantification and reconstruction.

[0021] 4. By setting standardized sample entropy calculation parameters, the complexity and randomness of each sub-component are accurately quantified. The hierarchical rule of dual complexity thresholds makes the feature boundaries of low, medium and high frequency sub-sequences clear, which can effectively separate the long-term trend, periodic fluctuation and random fluctuation of tourist volume. The component addition reconstruction method of high frequency sub-sequences ensures the integrity of feature decoupling, so that the reconstructed sub-sequences have single and clear fluctuation characteristics, which can meet the needs of subsequent targeted modeling.

[0022] 5. It includes eight candidate model libraries covering both shallow and deep learning methods, which are fully adapted to the differentiated complexity characteristics of low, medium and high frequency subsequences. The modeling strategy of using factors with the same frequency as independent variables and synchronous prediction in intervals enables joint prediction of the upper and lower limits of tourist volume intervals, avoiding the information fragmentation of split predictions. At the same time, it makes the sub-model more closely related to the influencing factors and improves the sub-model's ability to fit tourist volume characteristics. Attached Figure Description

[0023] Figure 1 This is a flowchart of the prediction method.

[0024] Figure 2 This is a graph showing the original tourist volume range.

[0025] Figure 3 This is a subplot of the low-frequency range.

[0026] Figure 4 This is a component subplot of the mid-frequency range.

[0027] Figure 5 This is a high-frequency interval component subgraph.

[0028] Figure 6 This is a diagram showing the overall prediction range. Detailed Implementation

[0029] The technical solutions of 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.

[0030] This specific implementation method uses tourism data from a tourist attraction within a set time period as the research sample, weekly visitor volume intervals as the target variable for prediction, and daily search index (PC+mobile), air quality index (AQI), and rainfall as high-frequency external influencing variables. It details the entire implementation process of a multi-objective visitor volume interval prediction model based on mixed frequency data and sub-model selection. Combined with… Figure 1 The specific steps are as follows: I. Data Preprocessing (I) Data Collection and Processing Collect four types of raw data from a tourist attraction during the research period, and complete basic data processing and format standardization.

[0031] 1. Weekly tourist volume data

[0032] The daily number of tourists is counted, and the maximum and minimum daily tourist volume are calculated for each week to form a weekly tourist volume range.

[0033] 2. Daily high-frequency impact data

[0034] The search index, AQI, and rainfall data were collected daily during the target week, grouped by week, and each group retained 7 daily data points to form a high-frequency data group that corresponds one-to-one with the weekly tourist volume.

[0035] 3. Data Anomaly Handling

[0036] Missing values ​​in the original data are filled using linear interpolation, and outliers (such as AQI mutations and extreme rainfall values) are identified and corrected using the 3σ principle to ensure data integrity and validity.

[0037] (ii) Setting the basic parameters of the model

[0038] By taking into account the non-stationary and non-linear characteristics of tourism data, the basic parameters of each core module of the model are pre-set to provide a unified standard for subsequent processes.

[0039] Mixed Frequency Data Sampling (MIDAS) Alignment: Frequency difference is set to 7 (7 days of daily data correspond to 1 week of weekly data), lag order is set to 1, and there is no lead time.

[0040] Wavelet Packet Decomposition (WPD): The db5 wavelet basis function is selected, and the decomposition level is 2. The decomposition is completed layer by layer using a low-pass filter (H) and a high-pass filter (G).

[0041] Sample entropy (SE): Embedding dimension m=2, similarity tolerance r is 0.15 times the standard deviation of each sub-component sequence, and a preset dual complexity threshold includes a first complexity threshold SE1 and a second complexity threshold SE2. The values ​​of SE1 and SE2 are the third quantile and the second quantile of the sample entropy of the four sub-components of the corresponding variable, respectively. If sample entropy ≤ SE1, it is a low-frequency sub-sequence; if SE1 < sample entropy ≤ SE2, it is a medium-frequency sub-sequence; if SE2 < sample entropy, it is a high-frequency sub-sequence.

[0042] Sub-model selection: A candidate model library was constructed, including Support Vector Regression (SVR), Kernel Extreme Learning Machine (KELM), Extreme Gradient Boosting Tree (XGBoost), Lightweight Gradient Boosting Machine (LightGBM), Ridge Regression (Ridge), ElasticNet, Gated Recurrent Unit (GRU), and Long Short-Term Memory (LSTM). Five-fold cross-validation was used, and the sub-sequence features included an adaptive weighted interval evaluation index (WISEI) with four error metrics. The adaptive weights followed the principles of high frequency for stability, medium frequency for average weighting, and low frequency for accuracy.

[0043] Adaptive Step Size Multi-Objective Sparrow Optimization Algorithm (ASMSSA) Multi-objective optimization: Population size is set to 50, maximum number of iterations T=100, discoverer ratio is 0.2, vigilant ratio is 0.1, and database capacity is 100.

[0044] (iii) Hybrid frequency data alignment

[0045] This section uses the Mixed Frequency Data Sampling Model (MIDAS) to unify the frequency of daily high-frequency influencing variables with the frequency of weekly tourist volume. The core is to convert daily data into a vector form suitable for weekly analysis while preserving the dynamic characteristics of high-frequency data, thus avoiding the information loss of traditional down-frequency / up-frequency analysis. Specific implementation steps are outlined below.

[0046] 1. Variable definition

[0047] The target variable for prediction is determined to be the weekly tourist volume interval within the target period. The high-frequency influencing variables are three types of daily data: search index, AQI, and rainfall. All three types of high-frequency variables are 7-dimensional daily series, and the target variable is a 1-dimensional weekly interval series.

[0048] 2. High-frequency data vector transformation

[0049] For each week's high-frequency data, vector integration is performed on a weekly basis. The seven daily data points for each week are directly constructed into a 7-dimensional row vector without averaging or interpolation, preserving the temporal characteristics of the original data. For example, the search index for the first week is transformed into a 7-dimensional vector [6880,6767,6516,7771,8042,7689,8120], the AQI is [78,66,90,75,111,118,128], and the rainfall is [0,0,0,0,0,0,0]. The remaining data undergoes vector transformation according to the same rules, ultimately yielding a corresponding number of 7-dimensional high-frequency variable vectors, each corresponding to a specific number of weekly visitor volume intervals.

[0050] 3. Tourist volume range segmentation and matrix construction

[0051] The tourist volume range within the target period is defined as [minimum value, maximum value], which serves as the core prediction objective of the model.

[0052] The vector data of the three types of high-frequency variables and the interval data of tourist volume are used to construct matrices respectively: the tourist volume matrix is ​​an interval matrix of X×2 (X rows correspond to the number of weeks in the target period, and 2 columns correspond to the upper and lower limits of the interval), and the search index, AQI and rainfall are all numerical matrices of X×7 (X rows correspond to the number of weeks in the target period, and 7 columns correspond to the daily data).

[0053] 4. Frequency alignment result verification

[0054] Check the consistency of sample length between the variable matrix and the tourist volume matrix (both are X rows) to confirm that each row of weekly tourist volume intervals corresponds to a unique 7-dimensional high-frequency variable vector, providing a high-quality data foundation for subsequent multi-scale sequence decomposition.

[0055] II. Multiscale Sequence Deconstruction and Recombination

[0056] This section employs a collaborative strategy of wavelet packet decomposition (WPD) and sample entropy (SE) to perform multi-scale decomposition and feature reconstruction on the frequency-aligned four-class variable matrices (tourist volume, search index, AQI, and rainfall). This breaks down the complex sequence into three sub-sequences: low-frequency, mid-frequency, and high-frequency, achieving decoupling and simplification of sequence features. The specific implementation steps are as follows: (a) Sequence preprocessing The four types of variable matrices after frequency alignment are standardized and validated again to ensure that all data have no missing or outlier values ​​and meet the input requirements of WPD decomposition. Among them, the tourist volume data is kept in interval form for all calculations, and the interval format is not changed during decomposition and output.

[0057] (ii) Implement wavelet packet decomposition (WPD)

[0058] The four types of variable matrices are decomposed individually, with each type of variable decomposed according to a two-level decomposition rule. Taking tourist volume as an example, the decomposition steps are as follows: Level 1 decomposition: The X×2 tourist volume interval matrix is ​​decomposed into one low-frequency approximation component (A1) and one high-frequency detail component (D1) through a low-pass / high-pass filter, both of which are X×2 interval matrices.

[0059] Second-level decomposition: Perform secondary decomposition on A1 and D1 respectively. Decompose A1 into low-frequency approximate component A21 and high-frequency detail component D21, and decompose D1 into low-frequency approximate component A22 and high-frequency detail component D22.

[0060] Decomposition results: The final result is four X×2 interval sub-component matrices (A21, D21, A22, D22). The sum of all sub-components can reconstruct the original tourist volume matrix without loss, and the reconstruction error is controlled within 1%.

[0061] Other variable decomposition: The X×7 numerical matrices of search index, AQI, and rainfall were decomposed into two levels of WPD using the same steps as above, each yielding four X×7 numerical sub-component matrices (A21, D21, A22, D22).

[0062] Special handling: Due to the fact that most of the data collection periods were sunny, the rainfall variable matrix had a high proportion of 0 values ​​and strong sparsity. Therefore, a special handling method can be adopted: after decomposition, no new sub-components are split, and the original matrix is ​​directly retained as the decomposition result. It will not be split again during subsequent reconstruction.

[0063] (iii) Calculate the sample entropy (SE)

[0064] The sample entropy is calculated for each of the four sub-components (A21, D21, A22, D22) obtained from the decomposition of the four types of variables. The complexity and randomness of each sub-component are quantified. The specific steps are as follows: 1. Phase space reconstruction: The one-dimensional sequence of each sub-component is transformed into a phase space vector of dimension m=2. For example, the tourist quantity A21 sub-component is an X-dimensional sequence, which is transformed into 7 two-dimensional phase space vectors.

[0065] 2. Similarity Match Count Statistics: Based on the similarity tolerance r, count the number of similarity matches between each phase space vector and other vectors, and calculate the average matching probability B in 2D. 2 (r).

[0066] 3. Dimensional Expansion Statistics: Increase the embedding dimension to m+1=3, repeat the above steps, and calculate the average matching probability B in 3 dimensions. 3 (r).

[0067] For example, the calculation results of the sample entropy of the sub-components of the four types of variables are shown in Table 1.

[0068] Table 1 Sample Entropy

[0069] (iv) Subsequence hierarchical reconstruction

[0070] Based on a preset dual complexity threshold, the four sub-components are stratified according to their sample entropy values. Sub-components with similar features are integrated into three categories of sub-sequences: low-frequency, mid-frequency, and high-frequency. The stratification rules are as follows: Low-frequency subsequences: The sample entropy is ≤ one-third quantile of the entropy of the four sub-components. The sequence is the most stable and reflects the long-term trend.

[0071] Mid-frequency subsequence: SE1 < sample entropy ≤ SE2 (two-thirds quantile of the sample entropy of the four sub-components), with moderate sequence complexity, reflecting periodic fluctuations.

[0072] High-frequency subsequences: sample entropy > SE2, the sequence is the most complex, reflecting random fluctuations.

[0073] 1. Reconstruction of tourist volume, search index, and AQI subsequences

[0074] Taking tourist volume as an example, the search index and AQI are reconstructed in the same way.

[0075] Low-frequency subsequence: containing A21 and A22 (0.0210, 0.082≤0.082). The upper and lower limits of the two sub-component matrix intervals are added together to obtain the low-frequency sequence matrix. For example, the low-frequency sequence of the first week is [6432.5, 11591.2].

[0076] Intermediate frequency subsequence: only contains D21 (0.082<1.309≤1.309), directly take the X×2 interval matrix of D21 as the intermediate frequency sequence, for example, the intermediate frequency sequence of the first week is [0.8,1.1].

[0077] High-frequency subsequence: only contains D22 (1.423>1.309), directly take the X×2 interval matrix of D22 as the high-frequency sequence matrix, for example, the high-frequency sequence of the first week is [-3.3,-3.3].

[0078] Verification: The upper and lower limits of the three types of subsequence intervals are added together, and the result is consistent with the original tourist volume interval (the small difference is due to the adaptation of decomposition accuracy and can be ignored).

[0079] 2. Reconstruction of Rainfall Quantum Sequence

[0080] Due to the high sparsity of rainfall data, the decomposition yields the original matrix, which is then directly set according to the rules: Low-frequency subsequence: Take the original rainfall matrix, for example, the low-frequency sequence for the third week is [0.32,6.62,10.18,2.43,0.3454,2.7191,0.126].

[0081] Mid-frequency / high-frequency subsequences: Since the rainfall is sparse and has no high-frequency components, the mid-frequency and high-frequency subsequences are set as zero matrices with the same dimension as the original matrix, and have no fluctuation characteristics.

[0082] (v) Normalization of reconstruction results

[0083] The low-frequency, mid-frequency, and high-frequency subsequences of the four types of variables are subjected to min-max normalization to eliminate numerical bias in the decomposition process, and finally the three types of feature subsequence matrices are obtained, providing standardized input for subsequent sub-model selection.

[0084] III. Implementation of Feature-Driven Sub-model Screening

[0085] This section addresses the differentiated characteristics of the reconstructed low-frequency, mid-frequency, and high-frequency subsequences. Based on the subsequence feature adaptive weighted interval evaluation index (WISEI) combined with 5-fold cross-validation, the optimal prediction model is selected from the candidate model library for each subsequence category, avoiding the limitations of a single model's adaptability. Specific implementation steps are as follows: (I) Subsequence Feature Analysis First, identify the core characteristics of the three types of subsequences to provide a basis for model adaptation: Low-frequency subsequences: strong stationarity, obvious trends, no significant fluctuations, and mainly follow long-term evolutionary patterns.

[0086] Mid-frequency subsequences: exhibit periodic fluctuation characteristics, with identifiable fluctuation patterns, and are related to factors such as holidays and weekly consumption habits.

[0087] High-frequency subsequences are highly random and fluctuate irregularly, driven by accidental factors such as sudden weather and temporary events.

[0088] (II) Construction of multiple prediction models

[0089] Using tourist volume interval subsequences as dependent variables and search indexes, AQI, and rainfall quantum sequences of the same frequency as independent variables, X sets of prediction models were constructed for low-frequency, medium-frequency, and high-frequency subsequences (corresponding to the candidate model library of Support Vector Regression (SVR), Kernel Extreme Learning Machine (KELM), Extreme Gradient Boosting Tree (XGBoost), Lightweight Gradient Boosting Machine (LightGBM), Ridge Regression (Ridge), ElasticNet, Gated Recurrent Unit (GRU), and Long Short-Term Memory Network (LSTM)), for a total of 24 prediction models. All models adopted an interval synchronous prediction strategy, modeling the upper and lower limits of tourist volume intervals simultaneously to avoid information fragmentation in split predictions.

[0090] (III) WISEI Index Calculation

[0091] To comprehensively quantify the predictive performance of the models, four basic error metrics for each model were calculated, and the WISEI composite metric was obtained through normalization and adaptive weighting. Specific steps are as follows: Basic error index calculation: For the interval prediction results of each model, calculate the interval mean absolute error (IMAE), interval mean absolute percentage error (IMAPE), interval standard deviation (ISDE), and interval root mean square error (IRMSE).

[0092] Adaptive weighted summation: Differentiated weights (weights sum to 1) are assigned to the normalized indicators based on the characteristics of the subsequences. High-frequency subsequences are weighted more for stability (ISDE weight 0.4, other indicators 0.2 each), mid-frequency subsequences are weighted more for average weight (four indicators 0.25 each), and low-frequency subsequences are weighted more for precision (IMAPE and IRMSE 0.3 each, other indicators 0.2 each). The WISEI value is obtained by weighted summation. The smaller the WISEI value, the better the overall performance of the model.

[0093] (iv) 5-fold cross-validation to select the optimal model

[0094] To avoid the randomness of model selection caused by a single test set, the top 3 candidate models after ascending WISEI value are subjected to 5-fold cross-validation. The implementation steps are as follows: The sample data was randomly divided into 5 equal parts. One part was taken as the test set and four parts as the training set to train and validate the model.

[0095] Using IMAPE as the core validation metric, the standard deviation of error (σ) of each model across five validation runs was calculated. IMAPE ), σ IMAPE The smaller the value, the stronger the model's predictive stability.

[0096] Optimal model selection rule: Select σ from 3 candidate models. IMAPE The model with the smallest value is taken as the optimal sub-model for that sub-sequence; if σ IMAPE If the values ​​are the same, select the model with the smaller WISEI value.

[0097] (v) Determination of screening results

[0098] Based on the characteristics of tourism data from a certain tourist attraction, the optimal sub-model selection results for the three types of sub-sequences in this embodiment are as follows: Low-frequency subsequences: ElasticNet (strong ability to capture long-term time-series features, suitable for long-term trend prediction).

[0099] Mid-frequency subsequence: Ridge (precisely captures nonlinear periodic fluctuations and adapts to weekly periodic characteristics).

[0100] High-frequency subsequence: LightGBM (efficiently extracts short-term random fluctuation features with high computational efficiency).

[0101] IV. Multi-objective integrated optimization

[0102] This section uses the Adaptive Step Size Multi-Objective Sparrow Optimization Algorithm (ASMSSA) to weight and fuse the prediction results of the three optimal sub-models mentioned above. With minimizing IMAPE and IRMSE as the dual objectives, it searches for the optimal weight combination to achieve a balanced improvement in prediction accuracy and stability, ultimately obtaining the prediction results for the weekly tourist volume range. Specific implementation steps are as follows: (I) Optimization Objectives and Variable Definition Bi-objective function: minF(w)=[IMAPE(w),IRMSE(w)], where min means minimizing; F(w) is the bi-objective optimization function based on the weight vector w; w=[w1,w2,w3], w1+w2+w3=1, w1, w2, w3 are the weights of the prediction results of the low-frequency, mid-frequency, and high-frequency sub-models, respectively; IMAPE(w) is the interval mean absolute percentage error determined by the weight vector w; IRMSE(w) is the interval root mean square error determined by the weight vector w.

[0103] Optimization variables: The three components of the weight vector w, each taking values ​​in the range [0,1].

[0104] (ii) Initial population generation

[0105] The initial weighted population is generated using a Logistic chaotic mapping to avoid the uneven distribution problem of randomly initialized populations. The steps are as follows: According to formula z n+1 =4z n (1-z n Generate a chaotic sequence z n (z0∈(0,1), non-zero, 0.25, 0.5, 0.75); where n is the iterative index of the chaotic sequence; z n z n+1 These are the nth and (n+1)th iteration values ​​of the Logistic chaotic sequence, respectively.

[0106] The chaotic sequence is calculated according to formula w ij =(z n (w jmax -w jmin ) / (max(z n )-min(z n )))+w jmin Convert to weight values, where w ij w represents the j-th dimension weight of the i-th sparrow. jmax w jmin Let represent the maximum and minimum values ​​of the weight in the j-th dimension; min(·) is the minimum value operation; max(·) is the maximum value operation.

[0107] Generate 50 weight combinations that satisfy w1+w2+w3=1 to form the initial population.

[0108] (III) Adaptive Step Size Factor Calculation

[0109] This embodiment employs the Adaptive Step Size Multi-Objective Sparrow Optimization Algorithm (ASMSSA), using a combination of probability-driven and iterative decay methods to determine the final adaptive step size factor used in the t-th iteration for calculating the i-th weight combination. This adaptive step size factor is a dimensionless scaling factor used to scale the displacement term in the sparrow algorithm's position update, achieving a dynamic balance between exploration and development.

[0110] The following is the complete derivation process: 1. Determining Pareto Improvement Events With the dual objective of minimizing [IMAPE(w), IRMSE(w)], for the i-th weight combination, we determine whether its position update in the t-th iteration was successful. The specific judgment rule is as follows: If the new position is Pareto dominant over the old position (both optimization objectives are no worse than the old position, and at least one objective is strictly better), then the update is considered successful, and a Pareto improvement flag is set. Otherwise, it is considered a failure and recorded. ;in The Pareto improvement label used for the i-th weight combination in the t-th iteration is the basis for subsequent success probability estimation.

[0111] 2. Calculate the adaptive memory decay coefficient

[0112] After determining the Pareto improvement event, an adaptive memory decay coefficient is further calculated. This coefficient is used to regulate the strength of the weight combination's memory of historical optimization performance. Compared to existing methods that rely on manually preset fixed parameters, this invention proposes a fully data-driven adaptive adjustment mechanism: when the search environment of the weight combination is stable, the memory period is automatically extended to ensure the robustness of the success probability estimation; when the search environment fluctuates drastically, the memory period is automatically shortened to quickly forget invalid historical information. This memory decay coefficient is adaptively determined by the amplitude of the success probability change between adjacent generations of the weight combination.

[0113] ; in: Let be the adaptive memory decay coefficient used in the (t-1)th iteration of the i-th weight combination, with its initial value. Let it be β max .

[0114] β min βmax The values ​​are the minimum and maximum values ​​of the adaptive memory decay coefficient, respectively, which are 0.7 and 0.95.

[0115] e (·) This represents an exponential function with the natural constant as its base.

[0116] Let be the magnitude of the Pareto success probability change used by the i-th weight combination in the (t-2)th iteration, and let its initial value be . Set it to 0.

[0117] η is the memory sensitivity coefficient, used to control the intensity of response to environmental fluctuations.

[0118] The design of the adaptive memory decay coefficient is based on the biomimetic mechanism of sparrow foraging behavior: In a stable foraging environment, sparrows will form a lasting and stable foraging memory. At this time, the adaptive memory decay coefficient tends to the maximum value, and the corresponding algorithm adopts long-period smooth estimation to ensure the robustness of probability estimation. When the foraging environment changes drastically, sparrows will quickly discard outdated foraging experience. At this time, the adaptive memory decay coefficient tends to the minimum value, and the corresponding algorithm switches to short-period sensitive response to quickly adapt to the new search environment.

[0119] 3. Pareto success probability estimation

[0120] By applying an exponentially weighted moving average to the Pareto improvement history of the weighted combination using an adaptive memory decay coefficient, an estimate of the probability of success is obtained: ; in: , These are the Pareto success probability estimates used by the i-th weight combination in iterations t-1 and t, respectively, along with their corresponding initial values. It is 0.5.

[0121] Let be the adaptive memory decay coefficient used in the (t-1)th iteration of the i-th weight combination.

[0122] This is the Pareto improvement flag used in the (t-1)th iteration for the i-th weight combination. A value of 1 indicates success, and a value of 0 indicates failure.

[0123] Simultaneously, the change in success probability between adjacent generations is recorded to perceive the degree of local fluctuation in the search environment, providing an input signal for subsequent step size curvature correction. The calculation formula is as follows: ; in: Let be the magnitude of the Pareto success probability change used in the (t-2)th iteration for the i-th weight combination.

[0124] , These are the Pareto success probability estimates used for the i-th weight combination in iterations t-2 and t-3, respectively, along with their corresponding initial values. It is 0.5.

[0125] η is the memory sensitivity coefficient; κ is the curvature sensitivity coefficient; λ is the decay steepness coefficient; T is the maximum number of iterations; θ is the decay initiation threshold.

[0126] 4. Mapping from probability to basic step size factor

[0127] After obtaining the Pareto success probability estimate, it is linearly mapped to the basic step size factor to achieve an adaptive adjustment logic of high success rate → small step size for fine-grained development, and low success rate → large step size for wide-area exploration. The specific calculation formula is as follows: ; in: ω is the base step size factor used in the t-th iteration for the i-th weight combination. min ω max These are the minimum and maximum values ​​of the step size factor, respectively, which are 0.5 and 2.0.

[0128] 5. Curvature correction based on the amplitude of success rate change

[0129] Different regions of the search environment have varying degrees of ruggedness. This invention draws upon the idea of ​​using second-order information to correct the gradient step size in numerical optimization, proposing to use the success rate change amplitude as a proxy signal for the local curvature of the search environment to construct a step size correction coefficient: ; ; in: Let be the curvature correction coefficient used in the t-th iteration for the i-th weight combination. Let κ be the Pareto success probability change magnitude used in the t-th iteration for the i-th weight combination. κ is the curvature sensitivity coefficient, where κ > 0.

[0130] When the search environment fluctuates drastically, that is Relatively large This significantly reduces the step size to prevent skipping potentially high-quality solutions; when the environment is stable... , The step size is determined by the success probability, restoring the original exploration rhythm.

[0131] 6. Global decay guiding factor in the later stage of iteration

[0132] The aforementioned probability-driven mechanism ensures the search capability for differentiated weight combinations throughout the entire iteration cycle. However, near the end of the iteration, if some weight combinations continue to jump with large steps, it will hinder the fine calibration of Pareto. Therefore, this invention designs a Sigmoid-type global decay guiding factor that only becomes significantly effective in the later stages of the iteration: ; Where: h(t) is the global decay guidance factor used in the t-th iteration; λ is the decay kurtosis coefficient, set to 15; T is the maximum number of iterations, set to 100; and θ is the decay initiation threshold, set to 0.7.

[0133] The design of this global decay guiding factor follows the principle of no intervention in the early stage and gentle contraction in the later stage. In the first 70% of the iterations, h(t)≈1, the step size is entirely determined by the individual's Pareto improvement history and local ruggedness signal, ensuring sufficiency of exploration and diversity of weight combinations. When the iteration enters the last 30% stage, t / T exceeds θ, h(t) smoothly decreases from 1 to about 0.01, applying a gentle shrinkage to the search radius of all weight combinations, guiding the population to perform fine calibration near the discovered Pareto front. Unlike traditional linear or power function decay, this global decay guiding factor has the characteristics of delayed start and smooth transition, which avoids insufficient exploration due to premature compression of the exploration radius in the early stage of iteration, and ensures that the step size does not approach 0 at the end of the iteration, maintaining the diversity of multi-objective solution sets.

[0134] 7. Final adaptive step size factor

[0135] By integrating adaptive adjustment of memory decay, basic probability mapping, curvature-aware correction, and global decay guidance in the later stages of iteration, and applying automatic upper and lower bound protection, the final adaptive step size factor for each discoverer (weight combination) in the t-th iteration is obtained: ; in: is the adaptive step size factor used in the t-th iteration for the i-th weight combination; min(·) is the minimum value operation; max(·) is the maximum value operation.

[0136] This adaptive step size factor is the adaptive step size used independently by each discoverer and follower in ASMSSA, replacing the traditional fixed step size or globally uniform decay step size.

[0137] The adaptive step size factor in this section focuses on a dual-objective optimization that minimizes the interval mean absolute percentage error (IMAPE) and the interval root mean square error (IRMSE). First, it determines Pareto improvement events based on whether the position update of the weight combination achieves Pareto dominance. Then, it adaptively calculates the memory decay coefficient based on the amplitude of the change in success probability between adjacent generations. Using this coefficient, it performs an exponentially weighted moving average on the historical Pareto improvement records to obtain an accurate estimate of the Pareto success probability. Subsequently, it linearly maps the success probability to a basic step size factor that adapts to the optimization rhythm. The amplitude of the success rate change is used as a proxy signal for the local curvature of the search environment to complete the step size curvature correction. A Sigmoid-type global decay guidance factor, which only takes significant effect in the later stages of iteration, is introduced to achieve full-cycle search control. Finally, the basic step size factor, curvature correction coefficient, and global decay guidance factor are integrated and upper and lower bound protection is applied to obtain the final adaptive step size factor used by the i-th weight combination in the t-th iteration.

[0138] The entire derivation and calculation process constructs a complete adaptive step size generation mechanism that combines probability-driven and iterative decay, possessing outstanding advantages: It employs data-driven adaptive adjustment logic throughout, eliminating the shortcomings of manually preset fixed parameters, and dynamically adjusts the memory period according to the stability of the search environment, balancing the robustness of probability estimation with the responsiveness to environmental changes; it achieves individual-specific step size allocation, following the rule of small, refined development when the success rate is high, and large, wide-area exploration when the success rate is low, accurately balancing global exploration and local development; it replaces complex second-order information perception of environmental ruggedness with lightweight success rate change amplitude, efficiently completing step size correction to avoid crossing potential high-quality solutions; it adopts a delayed-start, smooth-transition Sigmoid-type global decay guidance, not interfering with the search in the early stages to ensure population diversity, and gently shrinking in the later stages to achieve Pareto front fine calibration, completely solving the problems of rigidity and imbalance between exploration and development caused by traditional fixed or globally uniform step sizes. This significantly improves the optimization accuracy, convergence stability, and solution set diversity of the multi-objective sparrow optimization algorithm, perfectly adapting to the weight fusion optimization requirements of tourist volume interval prediction.

[0139] (iv) Sparrow population location update

[0140] The population is divided into three categories: discoverers, followers, and vigilants. Position updates are performed according to differentiation rules, and all updates incorporate an adaptive step size factor α. 1. Discoverer Location Update (20%): If the warning value R < 0.5 (no danger), perform a wide-area search with α as the step size factor; if R ≥ 0.5 (dangerous), enhance local development through Cauchy mutation, using the formula: w t+1 =w t ·(1+α·randn())(R<0.5),w t+1 =w t·(1+α·Cauchy(0,1))(R≥0.5), where w t w t+1 These are the weight combinations for iterations t and t+1, respectively. randn() is a standard normally distributed random number, and Cauchy(0,1) is a standard Cauchy distributed random number.

[0141] 2. Follower position update (70%): If the fitness ranking is high, follow the discoverer to search; if the ranking is low, migrate to a safe area through differential mutation, and integrate α to improve the ability to escape local optima.

[0142] 3. Guardian position update (accounting for 10%): A cross-sectional strategy is adopted. If the current fitness is better than the global optimum, horizontal cross-sectional strategy is adopted to expand the search range; otherwise, vertical cross-sectional strategy is adopted to retain the best dimensional features, thus balancing exploration and development.

[0143] (v) Fitness calculation and screening of nondominated solutions

[0144] For each updated weight combination w, calculate the corresponding IMAPE and IRMSE values, which serve as the bi-objective fitness of that weight.

[0145] Non-dominated solutions are selected based on Pareto dominance (IMAPE and IRMSE solutions with no other solutions are superior to this solution), and the non-dominated solutions are stored in the archive. If the archive capacity exceeds 100, solutions with lower crowding are deleted to maintain the diversity of solutions in the archive.

[0146] (vi) Iteration Termination and Optimal Weight Selection

[0147] Repeat the above steps of adaptive step size calculation, position update, fitness calculation, and non-dominated solution screening until the number of iterations reaches T=100, then terminate the iteration.

[0148] The roulette wheel method is used to select the optimal weight combination from the non-dominated solutions in the archive, that is, the optimal weight value combination that minimizes both IMAPE and IRMSE. , , , These are the optimal values ​​for w1, w2, and w3, respectively.

[0149] (vii) Generation of final prediction results

[0150] To further improve the accuracy of weekly visitor volume range prediction, the upper and lower limits of the visitor volume range can be searched for the optimal weight combination using an adaptive step-size multi-objective sparrow optimization algorithm, and the final prediction range can be obtained by independently weighting and summing the optimal weights.

[0151] The interval prediction results of the optimal sub-models for low frequency, medium frequency, and high frequency are combined according to the optimal weights w. The formula for weighted summation of the upper and lower limits of the interval is: ; Wherein, L1 and U1 are the upper and lower limits of the prediction interval of the low-frequency model, L2 and U2 are the predicted values ​​of the medium-frequency model, and L3 and U3 are the predicted values ​​of the high-frequency model; finally, the final prediction result of the weekly tourist volume interval [L,U] is obtained (L and U are the upper and lower limits of the weekly tourist volume interval).

[0152] V. Examples

[0153] This embodiment selects the target scenic area as the object of field testing and uses the actual operation data of the scenic area from January 1, 2020 to December 31, 2024 as the research sample. The multi-target tourist volume interval prediction method of the present invention is fully implemented, and the prediction accuracy, interval coverage and engineering practicality of the method are verified through full-process field testing. The specific implementation process is as follows: (I) Data Collection and Sample Construction The weekly visitor volume range (daily maximum / minimum) of the target scenic area was collected as the prediction target. At the same time, three high-frequency influencing variables were collected with a daily statistical period: search index (PC + mobile, preferably Baidu search index), air quality index (AQI), and rainfall.

[0154] To ensure the integrity of the weekly data, incomplete operating dates were removed, and continuous weekly data from January 6, 2020 (Monday) to December 29, 2024 (Sunday) were retained; abnormal weeks with zero visitor numbers due to scenic area control and equipment maintenance were removed, and finally 244 valid samples were retained.

[0155] Sample split: Week 197 was used as the dividing line, the first 196 weeks were the training set, and the 48 weeks from week 197 to week 244 were the independent test set.

[0156] The data structure studied in this embodiment is shown in Table 2.

[0157] Table 2. Description of the research data structure

[0158] (ii) Hybrid frequency data alignment

[0159] Frequency unification is achieved based on the MIDAS mixing sampling model, with a frequency difference set to 7. The daily high-frequency data for the 7 days of the week are directly integrated into a 7-dimensional row vector, which is matched one-to-one with the weekly tourist volume interval to construct a standardized variable matrix. Tourist volume data matrix: 244×2 dimensions (corresponding to upper and lower limits of the interval); Search index, AQI, and rainfall data matrix: all are 244×7 dimensions.

[0160] The alignment process preserves the original timing characteristics of high-frequency data, without information loss caused by down-frequency averaging or up-frequency interpolation.

[0161] (III) Multiscale sequence deconstruction and reconstruction

[0162] 1. Data Standardization and Wavelet Packet Decomposition

[0163] Z-score standardization was performed on all variable matrices to eliminate dimensional differences; db5 wavelet basis functions were used to perform two-level wavelet packet decomposition, decomposing each variable into four single-frequency feature sub-components.

[0164] For tourist volume interval data, in order to avoid misalignment of upper and lower limit decomposition features, the interval data is first converted into two sets of sequences: center value + width. After decomposition, they are restored to interval upper and lower limit subsequences.

[0165] 2. Sample Entropy Calculation and Subsequence Reconstruction

[0166] Calculate the sample entropy of each sub-component. SE1 is taken as the third quantile of the sample entropy of the four sub-components, and SE2 is taken as the second quantile. Complete the reconstruction of low / medium / high frequency sub-sequences according to the threshold. Sample entropy ≤ SE1 → low-frequency subsequence (long-term trend); SE1 < Sample Entropy ≤ SE2 → Mid-frequency subsequence (periodic fluctuation); Sample entropy > SE2 → high-frequency subsequence (random fluctuation).

[0167] Table 3 shows the sample entropy and classification results of the tourist volume center value and width of each component. The decomposition effect of the tourist volume interval data is as follows: Figures 2-5 As shown.

[0168] Table 3. Sample entropy and subsequence classification results for tourist volume center value and width component.

[0169] Figures 2-5 The visualization results of the multi-scale components after wavelet packet decomposition and sample entropy quantile hierarchical reconstruction of the weekly visitor volume interval data of the target scenic spot are shown. The horizontal axis represents the number of sample weeks (0~250, corresponding to 244 valid sample weeks in the study period), and the vertical axis represents the standardized visitor volume interval. The blue filled area represents the upper and lower limits of the visitor volume interval, which intuitively presents the temporal characteristics of the original data and different frequency components. Figure 2The original tourist volume interval subplot shown is the original tourist volume interval sequence without decomposition. It generally shows the characteristics of "slow fluctuations in the early stage and significantly enhanced fluctuations in the later stage". In the early stage (0-100 weeks), the tourist volume interval is narrow and the fluctuation amplitude is small, reflecting the low flow state in the early stage of the epidemic and the operation of the scenic spot. In the middle stage (100-150 weeks), the interval width gradually expands and the fluctuation begins to increase. In the later stage (after 150 weeks), the interval width increases significantly and multiple high-amplitude peak fluctuations occur. It superimposes all the characteristics of long-term trend, periodic fluctuation and short-term random fluctuation, providing a complete original data foundation for subsequent stratified analysis. Figure 3 The low-frequency interval subplot shown is the low-frequency component obtained by dividing the sample entropy into one-third quantiles. It represents the long-term trend of tourist volume. The curve of this component is smooth, with low fluctuation frequency and no sharp peaks. It shows a phased change, with a slow rise in the early stage, a brief decline in the middle stage (100-150 weeks), and continuous growth in the later stage. It clearly reflects the changing trend of tourist volume in the scenic area driven by macro factors such as long-term operation and development and market recovery, and reflects the stability and trend characteristics of the low-frequency component. Figure 4 The mid-frequency interval component subplot shown represents the mid-frequency component with sample entropy between the third and second third quantiles, representing the mid-term periodic fluctuation of tourist volume. This component has a moderate fluctuation frequency and exhibits a clear periodic rhythm. In the early stage (0-100 weeks), the fluctuation amplitude is small and regular, while in the later stage (after 150 weeks), the fluctuation amplitude increases and the periodic characteristics become more significant. The rhythm of the peaks is highly consistent with the mid-term driving factors such as seasonal changes in tourist flow and holiday effects, reflecting the periodic and regular fluctuation characteristics of the mid-frequency component. Figure 5 The high-frequency interval subplot shown represents the high-frequency component with sample entropy higher than the two-thirds quantile, which represents the short-term random fluctuation of tourist volume. This component has the highest fluctuation frequency, and the curve shows dense small peaks and rapid oscillations. There is no obvious long-term trend or stable cycle, and the fluctuation rhythm is chaotic. It reflects the random disturbance of tourist volume affected by short-term sudden factors such as weather changes, temporary activities, and public opinion, and reflects the randomness and short-term fluctuation characteristics of the high-frequency component.

[0170] Search index, AQI, and rainfall are decomposed independently on a daily basis, with the decomposition rules and thresholds being the same as those for tourist volume.

[0171] After decomposition and reconstruction, three types of feature sub-sequence matrices were established for each of the four variables: low frequency, medium frequency, and high frequency. All of them were subjected to min-max normalization and used as standardized inputs for subsequent sub-model construction.

[0172] (iv) Selecting the optimal sub-model based on feature adaptation

[0173] 1. Construct a candidate model library

[0174] This embodiment expands and adjusts the candidate model library based on the actual characteristics of the tourist volume data of the target scenic area, and finally selects the following 8 types of prediction models: Support Vector Regression (SVR), Kernel Extreme Learning Machine (KELM), Extreme Gradient Boosting Tree (XGBoost), Lightweight Gradient Boosting Machine (LightGBM), Ridge Regression, ElasticNet, Gated Recurrent Unit (GRU), and Long Short-Term Memory Network (LSTM). All candidate models simultaneously model the upper and lower limits of the tourist volume range data, and incorporate search index, AQI, and rainfall quantum sequence.

[0175] 2. Adaptive weighted evaluation and cross-validation

[0176] The model performance is evaluated using the Subsequence Feature Adaptive Weighted Interval Evaluation Index (WISEI), with the following weighting rules: Low-frequency subsequences: IMAPE and IRMSE weights are each 0.3 (focusing on prediction accuracy); Mid-frequency subsequence: four indicators are equally weighted (0.25 each); High-frequency subsequences: ISDE weight 0.4 (focusing on prediction stability).

[0177] Five-fold cross-validation was performed on the top three WISEI ranked models, and the optimal sub-model for each frequency was determined based on the minimum standard deviation of IMAPE error.

[0178] The prediction accuracy of the combination of high, medium and low frequency sequences is shown in Table 4.

[0179] Table 4. Prediction accuracy of high, medium, and low frequency sequence combination results

[0180] Table 4 shows the performance comparison results of eight candidate prediction models (SVR, XGBoost, LightGBM, KELM, Ridge, ElasticNet, GRU, LSTM) for low, medium, and high frequency tourist quantum sequences under interval prediction evaluation metrics (IMAE, IMAPE, ISDE, IRMSE, WISEI). The WISEI metric, adaptively weighted by sub-sequence features, was used as the core selection criterion. The optimal model for low-frequency sequences was ElasticNet (WISEI value 0.0018, IMAPE 20.78%), the optimal model for medium-frequency sequences was Ridge (WISEI value 0.0314, IMAE 0.0983), and the optimal model for high-frequency sequences was LightGBM (WISEI value 0.0264, IRMSE 0.1194). Each optimal model significantly outperformed other candidate models in terms of accuracy and stability for the corresponding sub-sequences, verifying the effectiveness of the feature-guided model selection strategy of this invention.

[0181] (v) Adaptive Step Size Multi-Objective Sparrow Optimization (ASMSSA) Weight Optimization

[0182] 1. Optimize parameter settings

[0183] With minimizing IMAPE and IRMSE as dual objectives, the initial population is generated through Logistic chaotic mapping, with a population size of 50, a maximum number of iterations of 100, a discoverer ratio of 0.2, a watcher ratio of 0.1, and a database capacity of 100. An early stopping mechanism is set for the upper bound of the interval to avoid overfitting.

[0184] The key round parameters for the upper and lower limits of the interval are shown in Table 5 and Table 6, respectively.

[0185] Table 5 Key Round Parameters for Upper Limit Values

[0186] Table 5 records the changes in core parameters during key rounds of the iterative optimization process, covering the iteration round, low / medium / high frequency component weights, prediction error indices (IMAPE, IRMSE), and three types of optimization process parameters: average success probability, average step size, and database size. During the iteration process, the algorithm gradually converges from the parameters of the initial round, the weights are adjusted towards the optimal value, and the prediction error is also optimized simultaneously, finally reaching a convergent state in the 80th round. The average step size is the average step size of the individual sparrows during iterative search in the ASMSSA algorithm. This algorithm adopts an adaptive step size mechanism, with the step size gradually shrinking from 0.71963 in the early stages to 0.13278 as the iteration progresses. This reflects the algorithm's transition from global large-scale exploration to local fine-grained optimization, which avoids getting stuck in local optima in the early stages and ensures the convergence accuracy in the later stages. The archive size is the number of non-dominated solutions (Pareto optimal solutions) stored in the external archive in multi-objective optimization. In Table 5, this value gradually increases from 5 to 11 as the iteration progresses. This reflects that the algorithm continuously discovers more high-quality solutions that simultaneously satisfy the dual objectives of "minimizing IMAPE and minimizing IRMSE" during iteration, and also reflects the algorithm's breadth of optimization and convergence stability.

[0187] Table 6 Key Round Parameters for Lower Limit Values

[0188] As shown in Table 6, the table records the core parameter changes of the Adaptive Step Size Multi-Objective Sparrow Optimization (ASMSSA) algorithm in key rounds during the iterative optimization process targeting the lower bound of the tourist volume range. These parameters cover the iteration rounds, low / medium / high frequency component weights, prediction error indices (IMAPE, IRMSE), and three categories of optimization process parameters: average success probability, average step size, and archive size. Starting from round 10, the algorithm gradually adjusts the initial weights towards the optimal value, simultaneously optimizing the prediction error. It reaches convergence in round 90 and stabilizes in round 100, ultimately reducing IMAPE to 68.80422% and IRMSE to 0.132554, achieving a balanced optimization of both objectives. The average step size is the average step size of the individual sparrows during iterative search in the ASMSSA algorithm. This algorithm adopts an adaptive step size mechanism. As shown in Table 6, the step size fluctuates between 0.405 and 0.897 in the early stages (rounds 10-70), using a large step size for global exploration to avoid getting trapped in local optima. In the later stages of iteration (after round 80), the step size shrinks to 0.1, switching to small step size for fine-grained local optimization, ensuring convergence accuracy. The archive size is the number of non-dominated Pareto optimal solutions stored in the external archive in multi-objective optimization. In Table 6, this value gradually increases from 9 in round 10 to 20 in round 100, reflecting that the algorithm continuously discovers more high-quality solutions that simultaneously satisfy the dual objectives of "minimizing IMAPE and minimizing IRMSE" during iteration. This demonstrates the algorithm's breadth of optimization and its ability to balance the dual objectives. The steadily growing archive also verifies that the algorithm has not gotten trapped in local optima and effectively expands the set of optimal solutions.

[0189] The upper and lower bounds of the visitor volume interval are independently iterated and optimized. The upper bound converges in 80 iterations and the lower bound converges in 100 iterations, both of which satisfy the maximum number of iterations constraint. The optimal weight combination finally determined by ASMSSA is shown in Table 7.

[0190] Table 7 Weight Combination Results

[0191] Based on the adaptive step-size multi-objective sparrow optimization algorithm (ASMSSA), the optimal weight combination for the lower and upper bounds of the intervals, as shown in Table 7, is obtained through iterative optimization. This weight combination is independently bound to the upper and lower bounds of the tourist volume interval and weighted separately: the lower bound of the predicted interval output by the three optimal sub-models (low-frequency, mid-frequency, and high-frequency) is multiplied by the corresponding weights of low-frequency (0.0152), mid-frequency (0.1364), and high-frequency (0.8483) in sequence, and then summed to obtain the final lower bound of the predicted interval; the upper bound of the predicted interval output by the three sub-models is multiplied by the corresponding weights of low-frequency (0.0127), mid-frequency (0.0893), and high-frequency (0.8979) in sequence, and then summed to obtain the final upper bound of the predicted interval; the weighted fusion result of the upper and lower bounds is combined to obtain the complete weekly tourist volume interval prediction value, and finally generated. Figure 6The predicted interval shown demonstrates that this weighting method can accurately match the differentiated fluctuation characteristics of the upper and lower boundaries of the interval, further improving the fit between the predicted interval and the actual tourist volume interval.

[0192] Table 7 shows the optimal fusion weight combinations for low, medium, and high frequency components obtained by the Adaptive Step-Size Multi-Objective Sparrow Optimization (ASMSSA) algorithm through iterative optimization for the upper and lower bounds of the tourist volume interval, along with the corresponding prediction performance results. Table 7 lists the weights of the low-frequency, medium-frequency, and high-frequency components for the lower and upper bounds of the interval, as well as the corresponding interval mean absolute percentage error (IMAPE) and interval root mean square error (IRMSE) indices. Specifically, the optimal weights for the lower bound are 0.0152 for low frequency, 0.1364 for medium frequency, and 0.8483 for high frequency; the optimal weights for the upper bound are 0.0127 for low frequency and 0.0893 for medium frequency. The high-frequency component weight is 0.8979, indicating that the short-term random fluctuation component has the greatest contribution to the final prediction result in the tourist volume interval prediction. The corresponding error indicators show that the lower limit of the interval has an IMAPE of 68.80% and an IRMSE of 0.1326, while the upper limit of the interval has an IMAPE of 11.87% and an IRMSE of 0.1320. This reflects the error difference between different interval boundaries. Moreover, this weight combination is the Pareto optimal solution under dual-objective optimization, achieving a balanced optimization of IMAPE and IRMSE, and providing the optimal weighting basis for subsequent integrated prediction of tourist volume intervals.

[0193] Based on the optimal fusion weights for low, medium, and high frequency components obtained by the ASMSSA algorithm in Table 7, after weighted fusion processing, the following results were obtained: Figure 6 The overall prediction interval diagram shown intuitively presents the prediction performance on the test set. Figure 6 The light blue shaded area represents the actual tourist volume range, the light pink shaded area represents the predicted range output by the algorithm, the solid blue line represents the median value of the actual tourist volume, and the dashed red line represents the predicted median value. The mean absolute percentage error (IMAPE) of the predicted median value range is 18.34%. Figure 6 It can be seen that the overall overlap between the predicted interval and the actual interval is high, and the predicted central value can follow the fluctuation trend of the actual central value well. Figure 6The two uncovered points marked with a red cross both occurred in weeks with extreme fluctuations in visitor volume (around week 197 and week 238), representing low-probability extreme events, and their impact on overall prediction performance is within an acceptable range. The prediction performance of the test set was quantitatively evaluated using Interval Coverage Percentage (PICP), Normalized Interval Width Percentage (PINAW), and Comprehensive Quality Index (CWC). The results are shown in Table 8: PICP was 93.75%, higher than the preset 90% coverage target, indicating that 93.75% of the actual visitor volume intervals were effectively covered by the predicted intervals, demonstrating high reliability; PINAW was 0.6532, within a reasonable range, indicating that the predicted intervals met the coverage requirements without being overly lenient; the CWC index was equal to the PINAW value (0.6532), indicating that the prediction coverage met the constraints, the penalty term was not activated, verifying that the method of this invention achieves an effective balance between sufficient interval coverage and tightness of the predicted intervals.

[0194] Table 8 Results of Comprehensive Evaluation Indicators

[0195] (vi) Summary

[0196] This embodiment uses the 244-week effective weekly visitor volume range of the target scenic area from January 6, 2020 to December 29, 2024 as the prediction target. It simultaneously introduces three high-frequency influencing variables with a daily statistical period: search index, AQI, and rainfall. After preprocessing with MIDAS mixing data alignment, Z-score standardization, and min-max normalization, the data is reconstructed into low, medium, and high-frequency feature subsequences using db5 wavelet basis two-layer wavelet packet decomposition combined with one-third and two-thirds quantile thresholds of sample entropy. Then, WISEI adaptive weighting index and 5-fold cross-validation are used to select low-frequency ElasticNet, medium-frequency Ridge, and high-frequency LightGBM. As the optimal sub-model, the adaptive step-size multi-objective sparrow optimization algorithm ASMSSA is used to find the optimal fusion weights for the upper and lower bounds of the interval by minimizing IMAPE and IRMSE as the dual objectives. Finally, the weighted fusion is used to obtain the interval prediction result. The actual test results show that the predicted interval has a high degree of fit with the actual interval, with a central value IMAPE of 18.34% and an interval coverage rate PICP of 93.75%, which exceeds the preset target of 90%. PINAW and CWC are both 0.6532. Only a few acceptable uncovered points appear in extreme mutation weeks. This fully verifies the accuracy, reliability and practical value of the mixing decomposition, feature adaptation modeling and multi-objective ensemble optimization method in the interval prediction of tourist volume in scenic areas.

[0197] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A multi-objective tourist volume interval prediction method based on frequency mixing, characterized in that, Using weekly visitor volume intervals as the target variable and search index, air quality index (AQI), and rainfall as high-frequency externality variables with daily statistical periods, the prediction process includes the following steps: High-frequency external influence variables are aligned with weekly tourist volume intervals using mixed frequency data, and a standardized variable matrix is ​​constructed. Using the variable matrix as input, wavelet packet decomposition is first used to decompose the variable matrix into four sub-components with single frequency features. Then, the complexity and randomness of each sub-component are quantified by sample entropy. Based on the preset double complexity threshold, the sub-components with similar features are reconstructed into three types of feature sub-sequences: low frequency, medium frequency, and high frequency. A multi-type candidate model library is constructed, and the optimal sub-model is selected for each type of feature sub-sequence based on the sub-sequence feature adaptive weighted interval evaluation index combined with 5-fold cross-validation. The interval prediction results of the three optimal sub-models are used as integrated inputs. The adaptive step-size multi-objective sparrow optimization algorithm is used to search for the optimal weight combination with minimizing the interval mean absolute percentage error and root mean square error as the dual objectives. After weighted fusion, the prediction results of the weekly tourist volume interval are obtained.

2. The method for predicting the range of multi-objective tourist volume based on frequency mixing as described in claim 1, characterized in that, The formula for calculating the adaptive step size factor in the adaptive step size multi-objective sparrow optimization algorithm is as follows: ； ； ； ； in, ω is the adaptive step size factor used in the t-th iteration for the i-th weight combination; min(·) is the minimum value operation; max(·) is the maximum value operation; min ω max These are the minimum and maximum values ​​of the step size factor, respectively. This is the base step size factor used in the t-th iteration for the i-th weight combination; h(t) is the curvature correction coefficient used in the t-th iteration for the i-th weight combination; h(t) is the global decay guiding factor used in the t-th iteration. , , , These are the Pareto success probability estimates used by the i-th weight combination in the t-1, t-2, and t-3 iterations, respectively. β is the adaptive memory decay coefficient used in the (t-1)th iteration of the i-th weight combination; min β max These are the minimum and maximum values ​​of the adaptive memory decay coefficient, respectively. e is the Pareto improvement flag used in the (t-1)th iteration for the i-th weight combination, with a value of 1 indicating success and a value of 0 indicating failure; (·) Represents an exponential function with the natural constant as its base; , The values ​​are, respectively, the Pareto success probability change magnitudes used by the i-th weight combination in the t-2th iterations; η is the memory sensitivity coefficient; κ is the curvature sensitivity coefficient; λ is the decay steepness coefficient; T is the maximum number of iterations; and θ is the decay initiation threshold.

3. The method for predicting the range of multi-objective tourist volume based on frequency mixing as described in claim 1, characterized in that, Hybrid frequency data alignment is achieved based on a hybrid frequency data sampling model, with a frequency difference of 7. This means that the high-frequency external influence variables over 7 days are integrated into a 7-dimensional row vector, which is matched with the corresponding weekly tourist volume interval. Tourist volume is an interval matrix, while search index, AQI, and rainfall are numerical matrices.

4. The method for predicting the range of multi-objective tourist volume based on frequency mixing as described in claim 1, characterized in that, Wavelet packet decomposition uses the db5 wavelet basis function, with a decomposition level of 2. The variables are decomposed individually using low-pass and high-pass filters, and the sum of all sub-components can be reconstructed into the input variable matrix.

5. The method for predicting the range of multi-objective tourist volume based on frequency mixing as described in claim 1, characterized in that, The preset dual complexity thresholds include a first complexity threshold SE1 and a second complexity threshold SE2. The values ​​of SE1 and SE2 are the third quantile and the second quantile of the sample entropy of the four sub-components of the corresponding variable, respectively. If the sample entropy is less than or equal to SE1, it is a low-frequency subsequence; if SE1 is less than or equal to SE2, it is a medium-frequency subsequence; and if SE2 is less than or equal to SE2, it is a high-frequency subsequence.

6. The method for predicting the range of multi-objective tourist volume based on frequency mixing as described in claim 1, characterized in that, The multi-type candidate model library includes support vector regression, kernel extreme learning machine, extreme gradient boosting tree, lightweight gradient boosting machine, ridge regression, elastic network, gated recurrent unit, and long short-term memory network. When building a model for each type of feature subsequence, the search index, AQI, and rainfall quantum sequence with the same frequency are used as independent variables. An interval synchronous prediction strategy is adopted to model the upper and lower limits of the tourist volume interval simultaneously.

7. The method for predicting the range of multi-objective tourist volume based on frequency mixing as described in claim 1, characterized in that, The calculation of the subsequence feature adaptive weighted interval evaluation index is as follows: First, obtain four basic indicators: interval mean absolute error, interval mean absolute percentage error, interval error standard deviation, and interval root mean square error, and normalize them. Then, assign adaptive weights according to the set principles, and sum them up to obtain the comprehensive index.

8. A method for predicting the range of multi-objective tourist volume based on frequency mixing as described in claim 1 or 7, characterized in that, Five-fold cross-validation validates the top three candidate models based on the comprehensive index. It uses the interval average absolute percentage error as the core index, calculates the standard deviation of the error, and selects the model with the smallest standard deviation as the optimal fit sub-model. When the standard deviations of the errors are the same, the model with the smaller comprehensive index value is selected.

9. The method for predicting the range of multi-objective tourist volume based on frequency mixing as described in claim 1, characterized in that, The initial weight population of the adaptive step-size multi-objective sparrow optimization algorithm is generated by Logistic chaotic mapping, and the population size is set to 50.

10. A multi-objective tourist volume interval prediction system based on frequency mixing, characterized in that, A method for performing a multi-objective tourist volume interval prediction method based on frequency mixing as described in any one of claims 1-9, comprising a frequency mixing data alignment module, a sequence deconstruction and recombination module, a sub-model screening module, and a multi-objective integrated optimization module connected in sequence; The mixing data alignment module aligns the data and constructs a standardized matrix; the sequence deconstruction and reconstruction module completes wavelet packet decomposition and subsequence reconstruction; the sub-model selection module selects the optimal matching sub-model for various subsequences; and the multi-objective ensemble optimization module uses an adaptive step-size multi-objective sparrow optimization algorithm to weightedly fuse prediction results and output them.

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