Method and system for predicting urban computing power scale based on sled dog optimization of MLP

Abstract

This invention relates to the field of computing power scale prediction technology, specifically disclosing a method and system for predicting urban computing power scale based on a sled dog-optimized MLP. This invention constructs a parameter optimization architecture for an MLP driven by a sled dog optimization algorithm, encoding the number of hidden layer neurons, truncation quantiles, and year-specific switch variables as decision vectors. It designs a multi-objective fitness function that integrates training set error, validation set error, generalization gap penalty, model complexity penalty, and stability penalty. This simulates the dynamic selection, movement, obstacle avoidance, disorientation, training, and retirement behaviors of a sled dog population through iterative optimization. This solves the problems of traditional grid search and random search easily getting trapped in local optima, and the reliance on human experience for key MLP parameter configuration. It also overcomes the shortcomings of insufficient fitting of statistical models and overfitting of conventional neural networks in small sample scenarios, achieving improved accuracy in urban computing power scale prediction and enhanced model generalization performance.

Description

Technical Field

[0001] This invention relates to the field of computing power scale prediction technology, and in particular to a method and system for predicting urban computing power scale based on sled dog optimized MLP. Background Technology

[0002] Against the backdrop of the deep development of the digital economy and the comprehensive advancement of the "Eastern Data, Western Computing" project, urban computing infrastructure has become a core component of new infrastructure construction. In recent years, the digital transformation of various cities has accelerated, leading to a rapid expansion of computing power. This has created an increasingly urgent need for accurate and efficient prediction of urban computing power. However, current specialized research on predicting urban-level computing power is still in its initial stages, and existing research on computing power prediction is scarce, making it difficult to meet the demand for accurate prediction of urban computing power.

[0003] Urban computing power data is generally characterized by small sample sizes due to limitations in statistical dimensions, collection scope, and development cycle. Traditional statistical prediction models are insufficient for fitting small sample scenarios, and conventional neural network models are prone to overfitting. Multilayer perceptron (MLP) neural networks have natural advantages such as simple structure, high training efficiency, and adaptability to modeling small sample data. However, their predictive performance is highly dependent on the selection of key model parameters. Relying solely on traditional parameter optimization methods such as grid search and random search is insufficient to obtain globally optimal parameter combinations, severely limiting the application effectiveness of MLP in urban computing power prediction scenarios. Furthermore, among existing intelligent optimization algorithms, the sled dog optimization algorithm has gradually gained attention due to its strong global search capability and fast convergence speed. However, research on its application to MLP parameter optimization combined with urban computing power scale prediction is scarce, lacking targeted model construction and methodological design, making it difficult to provide effective technical support for accurate prediction of urban computing power scale.

[0004] Therefore, there is an urgent need to provide a technical solution to address the above problems. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method and system for predicting urban computing power scale based on sled dog-optimized MLP.

[0006] Firstly, this invention provides a method for predicting the scale of urban computing power based on sled dog-optimized MLP, the technical solution of which is as follows: Acquire urban computing power scale data, urban development status data, and policy data, and perform logarithmic transformation on the urban computing power scale data and the urban development status data to obtain input feature data and output data under logarithmic scale; A multilayer perceptron model comprising an input layer, a hidden layer, and an output layer is constructed. Training, validation, and test sets are divided based on the input feature data and the output data at the logarithmic scale. The multilayer perceptron model is trained using the backpropagation algorithm. The input layer receives the input feature data; the hidden layer performs weighted summation and nonlinear transformation on the input feature data to obtain the hidden layer output features; and the output layer performs weighted summation on the hidden layer output features to output a predicted value of computing power scale at the logarithmic scale. Define a decision vector, which includes the number of neurons in the hidden layer, the quantiles for truncating the output data in the training set, and a switch variable for whether to add year features; construct a total objective function, which includes a training set error term, a validation set error term, a generalization gap penalty term, a model complexity penalty term, and a stability penalty term; set constraints on the number of neurons and the quantiles. The sled dog optimization algorithm is used to optimize the decision vector under the constraints of the number of neurons and the quantile. The total objective function is used as the fitness function. The position of the individuals in the population is updated iteratively by simulating the initialization, dynamic selection, movement mechanism, obstacle avoidance, disorientation, training mechanism and retirement mechanism of the sled dog population. The optimal decision vector is output when the iteration termination condition is met. Based on the optimal decision vector, configure the number of neurons in the hidden layer of the multilayer perceptron model, the truncated quantile, and the on / off variables of the year feature. Retrain the configured multilayer perceptron model using the training set and the validation set through the backpropagation algorithm to obtain a trained multilayer perceptron model. Use the trained multilayer perceptron model to predict the input feature data of the city to be predicted to obtain the predicted value of computing power scale at the logarithmic scale. Perform an exponential transformation on the predicted value of computing power scale at the logarithmic scale to obtain the predicted result of computing power scale at the original scale.

[0007] The beneficial effects of the urban computing power scale prediction method based on sled dog-optimized MLP of the present invention are as follows: The method of this invention constructs a sled dog optimization algorithm-driven MLP parameter optimization architecture, encodes the number of hidden layer neurons, truncation quantiles, and year feature switch variables into decision vectors, and designs a multi-objective fitness function that integrates training set error, validation set error, generalization gap penalty, model complexity penalty, and stability penalty. It simulates the dynamic selection, movement, obstacle avoidance, disorientation, training, and retirement behaviors of the sled dog population for iterative optimization, solving the problems of traditional grid search and random search easily getting trapped in local optima and the reliance on human experience for key MLP parameter configuration. At the same time, it overcomes the defects of insufficient fitting of statistical models and overfitting of conventional neural networks in small sample scenarios, and achieves improved accuracy in predicting urban computing power scale and enhanced model generalization performance.

[0008] Based on the above scheme, the urban computing power scale prediction method based on sled dog optimized MLP of the present invention can be further improved as follows.

[0009] In one alternative approach, the hidden layer employs a hyperbolic tangent sigmoid function as the activation function; both the training set error term and the validation set error term are root mean square errors on a logarithmic scale, and the expression for the root mean square error is: ;in, This serves as the identifier for the training or validation set. For set The number of samples in Let be the decision vector. For parameters The multilayer perceptron model described below applies to samples The log-scale prediction output, For the sample The output data at the logarithmic scale.

[0010] The advantages of adopting the above optional approach are as follows: it further clarifies that the hidden layer uses the hyperbolic tangent sigmoid function as the activation function, and standardizes the error terms of the training set and the error terms of the validation set to be root mean square errors under logarithmic scale, making the error measurement in the model training process more uniform, improving the accuracy of data fitting after logarithmic transformation, and providing a reliable evaluation benchmark for subsequent parameter optimization.

[0011] In one alternative approach, the expression for the generalization gap penalty term is: ;in, Weighting for the difference penalty For the verification set error term, The training set error term, The allowed generalization gap threshold; The expression for the model complexity penalty term is: ,in This is the complexity penalty coefficient. These are the parameters of the multilayer perceptron model. The maximum allowed number of parameters is the threshold. The expression for the stability penalty term is: ;in, To stabilize the penalty weight, It is a function of standard deviation. For the first The validation set error is obtained by randomly initializing the training data. This represents the number of repetitions for training.

[0012] The beneficial effects of adopting the above optional approach are as follows: further construct specific mathematical expressions for the generalization gap penalty term, model complexity penalty term, and stability penalty term, balance the model fitting ability and generalization performance through multi-dimensional penalty constraints, avoid the risk of overfitting, enhance the stability of the model training process, and make the optimization results more robust and reliable.

[0013] In one alternative approach, the constraint on the number of neurons is: ; The number of neurons in the hidden layer. This represents the minimum number of neurons. This represents the maximum number of neurons. The constraint condition of the quantile is: ; The quantile point of the truncation. The minimum value at the quantile. This represents the maximum value of the quantile.

[0014] The advantages of adopting the above optional approach are: further setting constraints on the number of neurons and quantiles, defining reasonable search boundaries for key parameters in the decision vector, preventing extreme parameter configurations during optimization, ensuring the rationality of the MLP model structure, and improving the search efficiency and solution quality of the sled dog optimization algorithm.

[0015] In one alternative approach, the sled dog population is initialized using a random generation method, wherein the expression for random generation is: ;in, The lower boundary of the search space, The upper boundary of the search space, For interval Random numbers generated internally.

[0016] The advantages of adopting the above optional method are as follows: further specifying that the initialization of the sled dog population adopts a random generation method, so that the individuals in the population are evenly distributed in the search space, enhancing the diversity of the initial population, laying a good foundation for subsequent iterative optimization, and helping the algorithm to quickly locate the potential optimal solution region.

[0017] In one alternative approach, the dynamic selection involves the number of sled dogs participating in the core search task. The expression is: ;in, This refers to the total number of sled dog populations. For the range of values ​​in random variables, For the range of values ​​in A random variable.

[0018] The advantages of adopting the above optional approach are: further defining the formula for calculating the number of sled dogs participating in the core search task in dynamic selection, introducing random variables to realize the dynamic adjustment of the number of core individuals, balancing global exploration and local development capabilities, and enabling the algorithm to adaptively respond to the optimization needs at different stages.

[0019] In one alternative approach, the marching mechanism includes: speed update at the head of the queue, speed update in the middle of the queue, and speed update at the tail of the queue; The expression for updating the speed of the queue head is: ,in , For the first The speed of a sled dog For inertial weights, and As a learning factor, and For interval Internally generated random numbers, For the first The best historical position for a sled dog. The reference position is randomly selected from multiple optimal positions. For the first The location of the sled dogs; The expression for the velocity update in the queue is: ,in , Individuals generated randomly. For interval Integers within; The expression for updating the tail velocity is: ,in , The value can be 0 or 1. For interval Internally generated random numbers, Indicates the position of the other sled dogs in the same group.

[0020] The beneficial effects of adopting the above-mentioned optional approach are as follows: further refine the speed update strategy of the sled dogs at the front, middle and rear of the procession mechanism, simulate the cooperative behavior of real sled dog groups through differentiated movement rules, make full use of swarm intelligence information to guide the search direction, accelerate the convergence speed and improve the global optimality of the solution.

[0021] Secondly, this invention provides a city computing power scale prediction system based on sled dog optimized MLP, the technical solution of which is as follows: The processing module is used to acquire urban computing power scale data, urban development status data, and policy data, and to perform logarithmic transformation on the urban computing power scale data and the urban development status data to obtain input feature data and output data under logarithmic scale. A construction module is used to construct a multilayer perceptron model comprising an input layer, a hidden layer, and an output layer. Based on the input feature data and the output data at the logarithmic scale, a training set, a validation set, and a test set are divided. The multilayer perceptron model is trained using a backpropagation algorithm. The input layer receives the input feature data; the hidden layer performs weighted summation and nonlinear transformation on the input feature data to obtain the hidden layer output features; and the output layer performs weighted summation on the hidden layer output features to output a predicted value of computing power scale at the logarithmic scale. A setting module is used to set a decision vector, which includes the number of neurons in the hidden layer, the quantiles for truncating the output data in the training set, and a switch variable for whether to add year features; constructing a total objective function, which includes a training set error term, a validation set error term, a generalization gap penalty term, a model complexity penalty term, and a stability penalty term; and setting constraints on the number of neurons and the quantiles. The iterative module is used to optimize the decision vector under the constraints of the number of neurons and the quantiles using the sled dog optimization algorithm. The overall objective function is used as the fitness function. The position of the individuals in the population is updated iteratively by simulating the initialization, dynamic selection, movement mechanism, obstacle avoidance, disorientation, training mechanism and retirement mechanism of the sled dog population. The optimal decision vector is output when the iteration termination condition is met. The prediction module is used to configure the number of neurons in the hidden layer of the multilayer perceptron model, the truncated quantile, and the on / off variables of the year feature according to the optimal decision vector. It then retrains the configured multilayer perceptron model using the training set and the validation set through a backpropagation algorithm to obtain a trained multilayer perceptron model. The trained multilayer perceptron model is then used to predict the input feature data of the city to be predicted to obtain a predicted value of computing power scale at a logarithmic scale. Finally, the predicted value of computing power scale at the logarithmic scale is subjected to an exponential transformation to obtain the predicted result of computing power scale at the original scale.

[0022] The beneficial effects of the urban computing power scale prediction system based on sled dog-optimized MLP of the present invention are as follows: The system of this invention constructs an MLP parameter optimization architecture driven by the sled dog optimization algorithm. It encodes the number of hidden layer neurons, truncation quantiles, and year feature switch variables into decision vectors. It designs a multi-objective fitness function that integrates training set error, validation set error, generalization gap penalty, model complexity penalty, and stability penalty. It simulates the dynamic selection, movement, obstacle avoidance, disorientation, training, and retirement behaviors of the sled dog population and iteratively optimizes these behaviors. This solves the problems of traditional grid search and random search easily getting trapped in local optima and the reliance on human experience for key MLP parameter configuration. At the same time, it overcomes the defects of insufficient fitting of statistical models and overfitting of conventional neural networks in small sample scenarios, and achieves improved accuracy in predicting urban computing power scale and enhanced model generalization performance.

[0023] Thirdly, the technical solution of an electronic device according to the present invention is as follows: It includes a memory, a processor, and a program stored in the memory and running on the processor, wherein the processor executes the program to implement the steps of the urban computing power scale prediction method based on sled dog optimized MLP of the present invention.

[0024] Fourthly, the technical solution of a computer-readable storage medium provided by the present invention is as follows: The computer-readable storage medium stores instructions that, when read, cause the computer-readable storage medium to perform the steps of the urban computing power scale prediction method based on sled dog optimized MLP of the present invention.

[0025] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0026] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a flowchart illustrating an embodiment of the urban computing power scale prediction method based on sled dog optimized MLP of the present invention. Figure 2 This is a schematic diagram of the neural network operating framework; Figure 3 Here is the flowchart for the Sled Dog Algorithm (SDO). Figure 4 The convergence curve of the Sled Dog Algorithm (SDO) is shown. Figure 5 A graph comparing the actual and predicted values ​​in the test set; Figure 6 This is a schematic diagram of an embodiment of the urban computing power scale prediction system based on sled dog optimized MLP according to the present invention. Figure 7 This is a schematic diagram of an embodiment of an electronic device according to the present invention. Detailed Implementation

[0027] Exemplary embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0028] Figure 1 This diagram illustrates a flowchart of an embodiment of a city computing power scale prediction method based on sled dog optimized MLP provided by the present invention. This method can be executed by electronic devices such as terminal devices or servers. The terminal device can be any fixed or mobile terminal, such as user equipment (UE), mobile device, user terminal, terminal, cellular phone, cordless phone, personal digital assistant (PDA), handheld device, computing device, vehicle-mounted device, or wearable device. The server can be a single server or a server cluster consisting of multiple servers. Any electronic device can implement the city computing power scale prediction method based on sled dog optimized MLP by having its processor call computer-readable instructions stored in its memory. Figure 1 As shown, it includes the following steps: S100: Obtain urban computing power scale data, urban development status data, and policy data, and perform logarithmic transformation on the urban computing power scale data and the urban development status data to obtain input feature data and output data under logarithmic scale.

[0029] Among them, urban computing power scale data refers to: quantitative indicators used to characterize the development status of urban computing power, including urban computing power scale or computing power scale proxy data; for example, the number of urban artificial intelligence enterprises is used as a proxy variable for urban computing power scale. The number of artificial intelligence enterprises in city A from 2013 to 2023 was 120, 145, 178, 210, 256, 310, 375, 420, 480, 540 and 610 respectively.

[0030] Among them, urban development status data refers to various indicators reflecting the level of urban economic and social development, including urban GDP, urban secondary industry growth value, urban tertiary industry growth value, and the number of urban internet users; for example, city A's GDP from 2013 to 2023 was 850 billion yuan, 930 billion yuan, 1020 billion yuan, 1120 billion yuan, 1230 billion yuan, 1350 billion yuan, 1480 billion yuan, 1620 billion yuan, 1780 billion yuan, 1950 billion yuan, and 2150 billion yuan respectively, and its urban secondary industry growth value was 320 billion yuan, 350 billion yuan, and 380 billion yuan respectively. The figures are as follows: 410 billion yuan, 450 billion yuan, 490 billion yuan, 530 billion yuan, 580 billion yuan, 630 billion yuan, 690 billion yuan, and 760 billion yuan. The growth value of the urban tertiary industry is 480 billion yuan, 530 billion yuan, 590 billion yuan, 650 billion yuan, 720 billion yuan, 790 billion yuan, 860 billion yuan, 940 billion yuan, 1030 billion yuan, 1130 billion yuan, and 1240 billion yuan. The number of urban internet users is 1.8 million, 1.95 million, 2.1 million, 2.28 million, 2.45 million, 2.65 million, 2.85 million, 3.1 million, 3.35 million, 3.65 million, and 4 million.

[0031] Among them, policy data refers to national policy initiation status data expressed using the dummy variable method; for example, taking 2022 as the year the national "East Data West Calculation" policy was initiated, city A's policy data value was 0 during the period from 2013 to 2021, and its policy data value was 1 during the period from 2022 to 2023.

[0032] Logarithmic transformation refers to: using The formula transforms the original data; for example, performing a logarithmic transformation on city A's GDP of 2.15 trillion yuan in 2023 yields... Logarithmic transformation was performed on the number of artificial intelligence companies in city A in 2023, which was 610, to obtain... .

[0033] The input feature data refers to the feature vector used as input to the multilayer perceptron model after logarithmic transformation. The input feature data consists of the logarithmically transformed values ​​of city A's 2023 GDP (9.98), secondary industry growth (8.94), tertiary industry growth (9.43), and number of internet users (5.99), along with policy data 1. The output data on a logarithmic scale refers to the city's computing power scale data after logarithmic transformation. For example, the number of AI companies in city A in 2023 (610) becomes 6.42 after logarithmic transformation; this value is the output data on a logarithmic scale.

[0034] S200. Construct a multilayer perceptron model comprising an input layer, a hidden layer, and an output layer. Divide the input feature data and the output data at the logarithmic scale into training, validation, and test sets, and train the multilayer perceptron model using the backpropagation algorithm. The input layer receives the input feature data, the hidden layer performs weighted summation and nonlinear transformation on the input feature data to obtain hidden layer output features, and the output layer performs weighted summation on the hidden layer output features to output a predicted value of computing power scale at the logarithmic scale.

[0035] Among them, the multilayer perceptron model refers to an artificial neural network model that includes an input layer, a hidden layer, and an output layer; for example, constructing a multilayer perceptron model with 5 input layer nodes, 14 hidden layer nodes, and 1 output layer node.

[0036] The training set refers to the set of data samples used to train the multilayer perceptron model; for example, data from 24 cities (Cities A, B, C, etc.) from 2013 to 2023, totaling 264 samples, is used as the training set. The validation set refers to the set of data samples used to evaluate the model's generalization ability during training; for example, data from three cities (Cities D, E, F, etc.) from 2013 to 2023, totaling 33 samples, is used as the validation set. The test set refers to the set of data samples used to evaluate the final prediction performance after model training is complete. Test set data is not used in model training and hyperparameter optimization; for example, data from three cities (Cities G, H, I, etc.) from 2013 to 2023, totaling 33 samples, is used as the test set.

[0037] Backpropagation refers to an optimization algorithm that updates parameters by calculating the gradient of the loss function with respect to the weights and biases of each layer and propagating it back along the network. For example, a Bayesian regularized backpropagation algorithm can be used to train a multilayer perceptron model, with 400 iterations and a minimum gradient threshold of [value missing]. .

[0038] In this model, the input layer refers to the network layer that receives input feature data. For example, the input layer receives a 5-dimensional input feature vector containing the logarithmic transformation values ​​of the city's GDP, the secondary industry growth rate, the tertiary industry growth rate, the number of internet users, and policy data. The hidden layer is the network layer located between the input and output layers that performs weighted summation and nonlinear transformation on the input features. For example, a hidden layer contains 14 neurons, each of which performs a weighted summation of the 5-dimensional features output from the input layer and then performs a nonlinear transformation using a hyperbolic tangent sigmoid function to obtain the hidden layer output features. The hidden layer output features are the feature vectors output by the hidden layer neurons after weighted summation and nonlinear transformation. For example, the 14 neurons in the hidden layer each output 14 feature values, forming a 14-dimensional hidden layer output feature vector.

[0039] The predicted computing power scale refers to the predicted computing power scale of a city on a logarithmic scale output by the multilayer perceptron model. For example, the multilayer perceptron model predicts the computing power scale of city A in 2024 based on the input feature data, and outputs a predicted computing power scale of 6.05 on a logarithmic scale.

[0040] S300. Set a decision vector, which includes the number of neurons in the hidden layer, the quantiles for truncating the output data in the training set, and a switch variable for whether to add year features; construct a total objective function, which includes a training set error term, a validation set error term, a generalization gap penalty term, a model complexity penalty term, and a stability penalty term; set constraints on the number of neurons and the quantiles.

[0041] Here, the decision vector refers to a set of vectors containing the hyperparameters to be optimized; for example, the decision vector... Number of neurons in the hidden layer truncated quantiles and year feature switch variables Three elements.

[0042] Here, the number of neurons refers to the number of neurons contained in the hidden layer of a multilayer perceptron model; for example, the number of neurons in the hidden layer. The value is 14. The truncated quantile refers to the quantile threshold selected when truncating the output data in the training set; for example, the truncated quantile. A value of 0.98 indicates that only data points below the 98th percentile in the training set output are retained for training. Year features refer to additional variables that incorporate the year as an input feature into the multilayer perceptron model; for example, encoding the years 2013 to 2023 as discrete features and adding them to the input feature vector. Switch variables are binary decision variables used to control whether to include year features; for example, switch variables... A value of 0 indicates that the year feature is not included, while a value of 1 indicates that the year feature is included.

[0043] Here, the overall objective function refers to the comprehensive evaluation function used to assess the merits of decision vectors; for example, the overall objective function. It consists of the validation set error term multiplied by a weight of 0.85, the training set error term multiplied by a weight of 0.15, the generalization gap penalty term, the model complexity penalty term, and the stability penalty term.

[0044] The training set error term refers to the model prediction error calculated on the training set; for example, the training set error term... The root mean square error on the logarithmic scale on the training set is calculated to be 0.015. The validation set error term refers to the model prediction error calculated on the validation set; for example, the validation set error term... The root mean square error on the logarithmic scale on the validation set is calculated to be 0.020. The generalization gap penalty term is a term that penalizes excessively large differences between the training set error and the validation set error; for example, the generalization gap penalty term... In the calculation, the difference penalty weight Set to 1.5, the allowable generalization gap threshold. Set to 0.06. The model complexity penalty term refers to a term that penalizes multilayer perceptron model parameters when they exceed a set threshold; for example, the model complexity penalty term... In the calculation, the complexity penalty coefficient Set as Maximum number of parameters allowed Set to 180. The stability penalty term refers to a term that penalizes the error fluctuation of the validation set obtained from multiple repeated training sessions under the same decision vector; for example, the stability penalty term... In the calculation, the number of repeated training times Set to 3 for stable penalty weight Set it to 0.4.

[0045] The constraint on the number of neurons refers to a restriction on the range of values ​​for the number of neurons in the hidden layer; for example, the constraint on the number of neurons is... ,in The value is 4. The value is 20. The constraint condition for the quantile refers to the restriction on the range of values ​​for the truncated quantile; for example, the constraint condition for the quantile is... ,in The value is 0.95. The value is 0.995.

[0046] S400. The sled dog optimization algorithm is used to optimize the decision vector under the constraints of the number of neurons and the quantile. The total objective function is used as the fitness function. The position of the individuals in the population is iteratively updated by simulating the initialization, dynamic selection, movement mechanism, obstacle avoidance, disorientation, training mechanism and retirement mechanism of the sled dog population. The optimal decision vector is output when the iteration termination condition is met.

[0047] The Sled Dog Optimization Algorithm (SDO) refers to an intelligent optimization algorithm that simulates the cooperative behavior of Arctic sled dogs. For example, the SDO algorithm is used to optimize the decision vector, with a population size of 30 and a maximum number of iterations of 80. This embodiment applies the SDO algorithm to the hyperparameter optimization of an MLP model. Unlike the fixed sampling strategies of traditional grid search and random search, the SDO algorithm simulates the behaviors of the sled dog population, such as alpha dog guidance, energy consumption adaptation, and echelon rotation, to achieve a dynamic balance between exploration and development in the search space. This effectively avoids local optima traps and is particularly suitable for scenarios where the MLP hyperparameter search space has multi-peak and non-convex characteristics. The fitness function refers to a quantitative function used to evaluate the quality of individuals in the population; for example, the overall objective function... As a fitness function, the fitness value corresponding to each decision vector is calculated.

[0048] The initialization of the sled dog population refers to the process of randomly generating initial population individuals within the search space; for example, within a search space consisting of 4 to 20 hidden layer neurons, 0.95 to 0.995 truncated quantiles, and a year feature switch variable of 0 or 1, 30 initial decision vectors are randomly generated as the initial population. Dynamic selection refers to the mechanism of dynamically determining the number of sled dogs participating in the core search task based on their fitness values; for example, according to the formula... Calculate the number of sled dogs participating in the core search task, including the total population. It is 30. For interval Random numbers within, For interval The movement mechanism refers to the motion rules that simulate the speed updates of the sled dog team during movement; for example, the speed update of the lead sled dog combines the individual's historical best position with the global best reference position, the speed update of the middle sled dogs combines the position of the sled dogs in front with a random reference individual, and the speed update of the tail sled dog is additionally influenced by the sled dogs in the same group. Obstacle avoidance refers to the avoidance strategies that the sled dog team adopts when encountering obstacles; for example, when the random number... When the obstacle avoidance mechanism is triggered, The value is 0.7, and the sled dog positions are updated based on the globally optimal and worst individual positions. Disorientation refers to the random exploration strategy adopted by the sled dog team when it loses its way; for example, when a random number... The disorientation mechanism is triggered at certain times, in which The value is set to 0.9, and a standard normally distributed random number is introduced to expand the search range. The training mechanism refers to a mechanism for reinforcing sled dogs that did not participate in the core search task; for example, for sled dogs not selected to perform the core search task, superior individuals in the population are used as benchmarks, and differentiated position update terms are constructed based on individual learning abilities. The retirement mechanism refers to a population renewal mechanism that simulates sled dogs retiring due to attrition and being replaced by new individuals; for example, individuals with low fitness rankings are retired, and new individuals are replaced by randomly swapping individuals at specific positions in the population.

[0049] The iterative update of the population's individual positions refers to the process of continuously updating the position vectors of individuals within the sled dog population through multiple iterations. For example, in each iteration, dynamic selection, movement mechanisms, obstacle avoidance, disorientation mitigation, training mechanisms, and retirement mechanisms are executed sequentially to update the positions of 30 individuals in the population. The iteration termination condition refers to the criteria for stopping the iteration of the sled dog optimization algorithm; for example, iteration stops when the maximum number of iterations (80) is reached.

[0050] The optimal decision vector refers to the position of the individual in the population with the best fitness value at the end of the iteration. For example, the optimal decision vector output at the end of the iteration is 14 hidden layer neurons, 0.98 truncated quantiles, and 0 year feature switch variables.

[0051] S500. Configure the number of neurons in the hidden layer of the multilayer perceptron model, the truncated quantile, and the on / off variables of the year feature according to the optimal decision vector. Retrain the configured multilayer perceptron model using the training set and the validation set through the backpropagation algorithm to obtain a trained multilayer perceptron model. Use the trained multilayer perceptron model to predict the input feature data of the city to be predicted to obtain the predicted value of computing power scale at the logarithmic scale. Perform an exponential transformation on the predicted value of computing power scale at the logarithmic scale to obtain the predicted result of computing power scale at the original scale.

[0052] The well-trained multilayer perceptron model refers to the multilayer perceptron model that has been retrained based on the optimal decision vector configuration. For example, the number of hidden layer neurons is set to 14, the truncation quantile is set to 0.98, and the year feature switch variable is set to 0 based on the optimal decision vector. The model is then retrained using the training set and validation set through the backpropagation algorithm to obtain the well-trained multilayer perceptron model.

[0053] The city to be predicted refers to the target city for which computing power scale prediction is needed; for example, city G is used as the city to be predicted, and city G is not involved in the construction of the training set and validation set. The input feature data refers to the urban development status data and policy data of the city to be predicted after logarithmic transformation; for example, the city's GDP, secondary industry growth value, tertiary industry growth value, number of internet users, and policy data in 2024 are collected for city G, and after logarithmic transformation, they constitute the input feature data.

[0054] Here, "original scale" refers to the scale of the original data obtained after exponential transformation; for example, the predicted computing power scale under the original scale is 424 AI companies. "Computing power scale prediction result" refers to the final output predicted city computing power scale; for example, the predicted computing power scale for city G in 2024 is 424 AI companies.

[0055] The technical solution of this embodiment constructs an MLP parameter optimization architecture driven by the sled dog optimization algorithm. It encodes the number of hidden layer neurons, truncation quantiles, and year feature switch variables into decision vectors. It designs a multi-objective fitness function that integrates training set error, validation set error, generalization gap penalty, model complexity penalty, and stability penalty. It simulates the dynamic selection, movement, obstacle avoidance, disorientation, training, and retirement behaviors of the sled dog population for iterative optimization. It solves the problems of traditional grid search and random search easily getting trapped in local optima and the reliance on human experience for key MLP parameter configuration. At the same time, it overcomes the defects of insufficient fitting of statistical models and overfitting of conventional neural networks in small sample scenarios, and realizes the improvement of the prediction accuracy of urban computing power scale and the enhancement of model generalization performance.

[0056] In one alternative approach, the hidden layer employs a hyperbolic tangent sigmoid function as the activation function; both the training set error term and the validation set error term are root mean square errors on a logarithmic scale, and the expression for the root mean square error is: ;in, This serves as the identifier for the training or validation set. For set The number of samples in Let be the decision vector. For parameters The multilayer perceptron model described below applies to samples The log-scale prediction output, For the sample The output data at the logarithmic scale.

[0057] The hyperbolic tangent sigmoid function refers to a function that maps the input to an interval. The nonlinear activation function is expressed as follows: For example, the hidden layer neurons perform a nonlinear transformation on the intermediate value of the weighted sum of the inputs using a hyperbolic tangent sigmoid function to obtain the hidden layer output features. An activation function is a mapping function that introduces nonlinearity to enable the neural network to fit complex functions; for example, the hidden layer might use a hyperbolic tangent sigmoid function as its activation function, while the output layer might use a linear function.

[0058] Among the above optional methods, it is further clarified that the hidden layer adopts the hyperbolic tangent sigmoid function as the activation function, and the error terms of the training set and the validation set are standardized to be root mean square errors under logarithmic scale, which makes the error measurement in the model training process more uniform, improves the accuracy of data fitting after logarithmic transformation, and provides a reliable evaluation benchmark for subsequent parameter optimization.

[0059] In one alternative approach, the expression for the generalization gap penalty term is: ;in, Weighting for the difference penalty For the verification set error term, The training set error term, The allowed generalization gap threshold.

[0060] The expression for the model complexity penalty term is: ,in This is the complexity penalty coefficient. These are the parameters of the multilayer perceptron model. This is the threshold for the maximum allowed number of parameters.

[0061] The expression for the stability penalty term is: ;in, To stabilize the penalty weight, It is a function of standard deviation. For the first The validation set error is obtained by randomly initializing the training data. This represents the number of repetitions for training.

[0062] Among the above-mentioned optional methods, specific mathematical expressions for the generalization gap penalty term, model complexity penalty term, and stability penalty term are further constructed. By balancing the model's fitting ability and generalization performance through multi-dimensional penalty constraints, the risk of overfitting is avoided, while enhancing the stability of the model training process and making the optimization results more robust and reliable.

[0063] In one alternative approach, the constraint on the number of neurons is: ; The number of neurons in the hidden layer. This represents the minimum number of neurons. This represents the maximum number of neurons.

[0064] The constraint condition of the quantile is: ; The quantile point of the truncation. The minimum value at the quantile. This represents the maximum value of the quantile.

[0065] In the above-mentioned optional methods, further constraints are set on the number of neurons and quantiles to define reasonable search boundaries for key parameters in the decision vector, prevent extreme parameter configurations during the optimization process, ensure the rationality of the MLP model structure, and improve the search efficiency and solution quality of the sled dog optimization algorithm.

[0066] In one alternative approach, the sled dog population is initialized using a random generation method, wherein the expression for random generation is: ;in, The lower boundary of the search space, The upper boundary of the search space, For interval Random numbers generated internally.

[0067] Among the above optional methods, it is further specified that the sled dog population is initialized by random generation, so that the individuals in the population are evenly distributed in the search space, which enhances the diversity of the initial population, lays a good foundation for subsequent iterative optimization, and helps the algorithm to quickly locate the potential optimal solution region.

[0068] In one alternative approach, the dynamic selection involves the number of sled dogs participating in the core search task. The expression is: ;in, This refers to the total number of sled dog populations. For the range of values ​​in random variables, For the range of values ​​in A random variable.

[0069] In the above optional approach, a formula for calculating the number of sled dogs participating in the core search task in dynamic selection is further defined, and random variables are introduced to realize the dynamic adjustment of the number of core individuals, balancing global exploration and local development capabilities, so that the algorithm can adaptively respond to the optimization needs at different stages.

[0070] In one alternative approach, the marching mechanism includes: speed update at the head of the queue, speed update in the middle of the queue, and speed update at the tail of the queue.

[0071] The expression for updating the speed of the queue head is: ,in , For the first The speed of a sled dog For inertial weights, and As a learning factor, and For interval Internally generated random numbers, For the first The best historical position for a sled dog. The reference position is randomly selected from multiple optimal positions. For the first The location of the sled dog.

[0072] The expression for the velocity update in the queue is: ,in , Individuals generated randomly. For interval Integers within.

[0073] The expression for updating the tail velocity is: ,in , The value can be 0 or 1. For interval Internally generated random numbers, Indicates the position of the other sled dogs in the same group.

[0074] Among the above-mentioned optional approaches, the speed update strategies for the sled dogs at the front, middle, and rear of the procession are further refined. By simulating the cooperative behavior of a real sled dog group through differentiated movement rules, the search direction is guided by the collective intelligence information, thereby accelerating the convergence speed and improving the global optimality of the solution.

[0075] In another embodiment of the urban computing power scale prediction method based on sled dog optimized MLP of the present invention, the following steps are specifically included: S1. Data acquisition and processing for the computing power scale prediction model.

[0076] S11. Data Collection: Acquire data on urban computing power scale, urban development status, and policy data. The number of urban AI enterprises is used as a proxy variable for computing power scale. Urban development status data includes urban GDP, urban secondary industry growth rate, urban tertiary industry growth rate, and the number of urban internet users. Policy data is quantified using a dummy variable method, with the year the national "Eastern Data, Western Computing" policy was launched as the dividing line; values ​​after the policy launch are 1, and values ​​before the launch are 0. In this embodiment, data from 30 cities between 2013 and 2023 are selected, where the number of urban AI enterprises, urban GDP, urban secondary industry growth rate, urban tertiary industry growth rate, and the number of urban internet users are all derived from publicly available statistical data.

[0077] S12. Data Processing: Perform logarithmic transformation on the collected data, using... The formula processes the original data to obtain the input feature data and the output data on a logarithmic scale. Logarithmic transformation can correct the skewed distribution of the data and compress the dynamic range of the variables, making the transformed data more consistent with the sensitivity interval of the activation function of the multilayer perceptron model. (This is relevant to the analysis of urban GDP.) Logarithmic transformation yields For the growth value of the city's secondary industry Logarithmic transformation yields The growth value of the city's tertiary industry Logarithmic transformation yields For the number of urban internet users Logarithmic transformation yields The number of urban artificial intelligence enterprises Logarithmic transformation yields The output data in the training set is processed according to the truncated quantiles. Truncation is performed to retain only data below the quantile for training, thus avoiding interference from outliers in model training.

[0078] like Figure 2 As shown in the schematic diagram of the neural network operating framework, the input layer receives input feature data after logarithmic transformation. This input feature data includes the logarithmic transformation values ​​of the city's GDP, the secondary industry growth rate, the tertiary industry growth rate, the number of internet users, and policy data. The input layer passes the data to the hidden layer, which extracts deep-level features through weighted summation and nonlinear transformation. The output layer performs a weighted summation on the features output from the hidden layer and outputs a predicted value of computing power scale on a logarithmic scale.

[0079] S2. Construction of a multilayer perceptron model for neural networks.

[0080] A multilayer perceptron model is constructed, consisting of an input layer, hidden layers, and an output layer. The input layer receives the input feature data. The hidden layer, employing a single hidden layer structure, performs weighted summation and nonlinear transformation on the input feature data to obtain the hidden layer output features. The output layer has one node, which performs weighted summation on the hidden layer output features to output the predicted computing power scale at a logarithmic scale. The hidden layer uses a hyperbolic tangent sigmoid function as the activation function, with the function expression as follows: This function maps the input to a range. It can effectively introduce nonlinear factors.

[0081] The forward propagation process of the multilayer perceptron model is as follows: Layer The outputs of each neuron satisfy the following relationship: in, For the first Layer The output of each neuron For the first The activation function of the layer, For the first The number of neurons in a layer. For the first Layer The output of each neuron For the first Layer The first neuron and the second Layer The connection weights of each neuron For the first Layer Bias of each neuron.

[0082] The training and validation sets are divided based on the input feature data and the output data on a logarithmic scale. In this embodiment, data from 24 cities between 2013 and 2023 are used as the training set, totaling 264 samples; data from 3 cities between 2013 and 2023 are used as the validation set, totaling 33 samples; and data from the remaining 3 cities are used as the test set. The multilayer perceptron model is trained using the backpropagation algorithm, employing a Bayesian regularized backpropagation algorithm with 400 iterations and a minimum gradient threshold of [value missing]. .

[0083] S3, Sled Dog Optimization Objective and Constraints.

[0084] Define decision vectors The decision vector contains the number of neurons in the hidden layer. 1. Crop points of the output data in the training set And a switch variable for whether to include year features. Number of neurons in the hidden layer Used to control network capacity and fitting ability, truncation quantiles Switching variables are used to reduce the dominant influence of extreme samples on training. Used to determine whether the input feature dimension includes the year feature.

[0085] Construct the overall objective function The overall objective function consists of a training set error term, a validation set error term, a generalization gap penalty term, a model complexity penalty term, and a stability penalty term. The expression for the overall objective function is: in, The final objective function value is the quantity that the sled dog optimization algorithm aims to minimize; To verify the error weight, a value of 0.85 is used in this embodiment; To validate the error term in the set; The training set error weight is set to 0.15 in this embodiment; For the training set error term; This is a generalization gap penalty term used to suppress overfitting; This is a model complexity penalty term used to limit network capacity; The stability penalty term is used to reduce performance fluctuations caused by random initialization. The above five sub-terms form a synergistic constraint during the optimization process: the weighted combination of the training set error term and the validation set error term ensures that the model fits the training data while also considering generalization ability; the generalization gap penalty term applies a penalty when the difference between the two exceeds a threshold to prevent overfitting; the model complexity penalty term applies a secondary penalty when the number of network parameters exceeds a set upper limit to limit the model capacity; and the stability penalty term measures the robustness of the hyperparameter combination through the standard deviation of multiple repeated training iterations. Through these multi-dimensional constraints, the sled dog optimization algorithm is guided to select a hyperparameter combination in the search space that combines low error, low generalization gap, low complexity, and high stability.

[0086] Both the training set error term and the validation set error term are root mean square errors on a logarithmic scale, expressed as: in, This serves as the identifier for the training or validation set. For set The number of samples in Let be the decision vector. For parameters The multilayer perceptron model for samples The log-scale prediction output, For the sample Output data on a logarithmic scale.

[0087] The expression for the generalization gap penalty term is: in, The penalty weight for the gap is set to 1.5 in this embodiment; To validate the error term in the set; For the training set error term; The allowable generalization gap threshold is set to 0.06 in this embodiment.

[0088] The expression for the input feature dimension is: in, The final input feature dimension, with the constant 5 indicating that there are 5 independent variables. This is an indicator function; it takes the value 1 when the year feature is included, and 0 otherwise. This is a switch variable for whether to include the year feature.

[0089] The parameter expression for a single hidden layer multilayer perceptron model is as follows: in, This refers to the total number of network parameters, including weights and biases. For the input feature dimension, This represents the number of neurons in the hidden layer.

[0090] The expression for the model complexity penalty term is: in, The value is the complexity penalty coefficient, which is set to a value of in this embodiment. ; These are the parameters of the multilayer perceptron model; The maximum allowed parameter threshold is set to 180 in this embodiment.

[0091] The expression for the stability penalty term is: in, To ensure a stable penalty weight, a value of 0.4 is used in this embodiment; It is a function of standard deviation; For the first Error of the validation set obtained from random initialization training; The number of repetitions is 3 in this embodiment.

[0092] Set constraints on the number of neurons and the quantiles. The constraint on the number of neurons is as follows: ,and ,in The number of neurons in the hidden layer. For a set of integers, This represents the minimum number of neurons; in this embodiment, it is set to 4. This represents the maximum number of neurons; in this embodiment, it is set to 20. The constraint condition for the quantiles is... ,in For the truncated quantile, The minimum quantile value is 0.95 in this embodiment. The maximum value of the quantile is 0.995 in this embodiment.

[0093] S4. Collaborative optimization strategy based on sled dog algorithm.

[0094] The sled dog optimization algorithm is used to optimize the decision vector under the constraints of the number of neurons and quantiles. The overall objective function is used as the fitness function. The position of individuals in the population is updated iteratively by simulating the initialization, dynamic selection, movement mechanism, obstacle avoidance, disorientation, training mechanism and retirement mechanism of the sled dog population. The optimal decision vector is output when the iteration termination condition is met.

[0095] like Figure 3 As shown, the execution flow of the sled dog optimization algorithm is as follows: After starting, population initialization is performed to generate an initial sled dog population. The current iteration number is then determined. Is it less than the maximum number of iterations? If not, the algorithm terminates and outputs the optimal solution. If yes, proceed to the iterative process: update the values ​​of all parameters, sort the individuals according to the elimination mechanism, and select the most suitable sled dog. (Judgment) If the condition is met, the sled dog training mechanism is executed; otherwise, the sled dog positions are updated according to the sled dog training mechanism. Then, the sled dog speed and position are updated according to the sled dog movement mechanism, and the troop moves normally. Check if the condition is met. If so, update the sled dog's position according to the sled dog obstacle avoidance mechanism; otherwise, keep the sled dog's position unchanged. and Check if this condition is true; if so, the sled dog's position remains unchanged. Determine... Check if the condition is met. If so, update the sled dog's position according to the sled dog disorientation mechanism; otherwise, leave the sled dog's position unchanged. Perform disorientation processing, iterating a certain number of times. Increment by 1, then return to the loop.

[0096] Population initialization uses a random generation method; the sled dog population can be represented as: OK Column matrix: in, The lower boundary of the search space, The upper boundary of the search space, This represents the total number of sled dogs; in this example, the value is 30. The dimension of the population is 3 in this embodiment. For interval Random numbers generated internally.

[0097] In the dynamic selection of sled dogs, the number of sled dogs participating in the core search task. The expression is: in, This refers to the total number of sled dog populations. For the range of values ​​in random variables, For the range of values ​​in A random variable.

[0098] In the sled dog movement mechanism, the expression for updating the speed of the lead sled dog is: in, For the first The speed of a sled dog The inertial weight decreases linearly from 1.0 to 0 with the number of iterations. and As a learning factor, and For interval Internally generated random numbers, For the first The best historical position for a sled dog. The reference position is randomly selected from multiple optimal positions. For the first The location of the sled dog.

[0099] The expression for updating the speed of the sled dogs in the team is: in, Individuals generated randomly. For interval Integers within.

[0100] The expression for updating the speed of the sled dogs at the rear of the column is: , in, The value can be 0 or 1. For interval Internally generated random numbers, Indicates the position of the other sled dogs in the same group.

[0101] Learning factor and The expressions are as follows: in, This represents the current iteration number. The maximum number of iterations is set to 80 in this embodiment. The recursive formula is , The initial value is set to 0.1. The formula for updating the sled dog's position is: .

[0102] In the obstacle avoidance mechanism, the expression for updating the sled dog's position is: in, To take the value of integers, The individual with the worst fitness value, , They are respectively Random numbers generated within the interval and Calculate according to the following formula: In the disorientation mechanism, the expression for updating the sled dog's position is: in, Individuals generated randomly. , For interval Internally generated random numbers, Let be a random variable that follows a standard normal distribution, with the probability density function being... To address the choice between obstacle avoidance and disorientation behaviors, parameters are introduced. and In this embodiment , :like Sled dogs perform obstacle avoidance maneuvers; if The sled dog is determined to be lost; if The team is moving normally and requires no additional operation. Belongs to the interval Random numbers.

[0103] In the sled dog training mechanism, the position update expression for sled dogs that have not met the standards is: in, , , and For interval Internally generated random numbers, The formula for calculating the learning ability of sled dogs is as follows: , Indicates the first Fitness value for a sled dog.

[0104] The gap between sled dogs , , Determined by the following formula: in, To select the best individuals randomly from those performing the sled-pulling task. Individuals who were not selected to perform the sled-pulling task.

[0105] Position update term during training , , Determined by the following formula: In the sled dog retirement mechanism, individuals in the population are ranked from best to worst based on their fitness values. Dogs ranked lower have a higher probability of retirement, while those ranked higher have a lower probability. A random replacement mechanism simulates the retirement process. In the boundary control strategy, when an individual's value in a certain dimension exceeds the upper search limit or falls below the lower search limit, a new value is randomly generated within the search space for replacement. The mathematical expression is: .

[0106] In this embodiment, the population size is set to 30, the maximum number of iterations is set to 80, the number of historical best solutions retained is 4, and the population update step size is limited to [missing value]. Random probability thresholds that trigger different update strategies , During the iteration process, the optimal fitness value of each iteration is recorded to form a convergence curve.

[0107] like Figure 4As shown in the convergence curve of the sled dog optimization algorithm, the horizontal axis represents the number of iterations, and the vertical axis represents the objective function value. From Figure 4 As can be seen, the objective function value starts from the initial value of 1.058, decreases to 0.998 after 10 iterations, stabilizes at 0.998 after 20 iterations, decreases to 0.994 after 30 iterations, and then remains stable at 0.994 during the 40 to 80 iterations, indicating that the sled dog optimization algorithm has good convergence performance.

[0108] After the iteration terminates, the final global optimal fitness value and the corresponding optimal individual position are output. This optimal position is the optimal decision vector for the hyperparameter optimization problem. In this embodiment, the optimal decision vector has 14 hidden layer neurons, a truncated quantile of 0.98, and a year feature switch variable of 0.

[0109] S5. Model Prediction and Result Evaluation.

[0110] The number of neurons in the hidden layer, the truncated quantile, and the on / off variable for the year feature are configured in the multilayer perceptron model according to the optimal decision vector. In this embodiment, the number of neurons in the hidden layer is set to 14, the truncated quantile is set to 0.98, and the on / off variable for the year feature is set to 0. The configured multilayer perceptron model is retrained using the backpropagation algorithm on the training and validation sets to obtain the trained multilayer perceptron model.

[0111] The trained multilayer perceptron model is used to predict the input feature data of the city to be predicted, and the predicted value of computing power scale on a logarithmic scale is obtained. This predicted value differs from the predicted computing power scale at the original scale. The relationship between them is satisfied An exponential transformation is applied to the predicted computing power scale on a logarithmic scale. The exponential transformation formula is as follows: This yields the original-scale prediction results of computing power.

[0112] like Figure 5 As shown in the graph comparing the true and predicted values ​​on the logarithmic scale in the test set, the horizontal axis represents the sample number in the test set, and the vertical axis represents the true and predicted values ​​on the logarithmic scale. Figure 5 The solid line represents the actual value curve, and the dashed line represents the predicted value curve. From Figure 5 As can be seen, the true and predicted values ​​are highly consistent on the log scale, and the predicted value curve accurately follows the trend of the true value curve, indicating that the well-trained multilayer perceptron model has high prediction accuracy. In the final optimized training results, the goodness of fit of the training set is 0.9962, the goodness of fit of the validation set is 0.9950, and the goodness of fit of the test set is 0.8613.

[0113] The optimization results of this embodiment verify the effectiveness of the proposed method: the goodness of fit on the training set reaches 0.9962, and the goodness of fit on the validation set reaches 0.9950, indicating that the optimized MLP model has excellent fitting performance on both training and validation data; the goodness of fit on the test set is 0.8613, indicating that the model still maintains good predictive ability on test data that was not used in training, demonstrating significant generalization performance. Compared with traditional methods that use only a single error term as the optimization objective, this embodiment effectively suppresses the risk of overfitting while ensuring fitting accuracy by introducing generalization gap penalties, model complexity penalties, and stability penalties, thereby improving the reliability of the model in practical applications.

[0114] Figure 6 This diagram illustrates a structural schematic of an embodiment of a city computing power scale prediction system 200 based on sled dog optimized MLP provided by the present invention. Figure 6 As shown, the urban computing power scale prediction system 200 based on sled dog optimized MLP includes: The processing module 201 is used to acquire urban computing power scale data, urban development status data and policy data, and to perform logarithmic transformation on the urban computing power scale data and the urban development status data to obtain input feature data and output data under logarithmic scale. Module 202 is used to construct a multilayer perceptron model comprising an input layer, a hidden layer, and an output layer. It divides the input feature data and the output data at the logarithmic scale into training, validation, and test sets, and trains the multilayer perceptron model using a backpropagation algorithm. The input layer receives the input feature data, the hidden layer performs weighted summation and nonlinear transformation on the input feature data to obtain hidden layer output features, and the output layer performs weighted summation on the hidden layer output features to output a predicted computing power scale at the logarithmic scale. The setting module 203 is used to set a decision vector, which includes the number of neurons in the hidden layer, the quantiles for truncating the output data in the training set, and a switch variable for whether to add year features; construct a total objective function, which includes a training set error term, a validation set error term, a generalization gap penalty term, a model complexity penalty term, and a stability penalty term; and set constraints on the number of neurons and the quantiles. The iteration module 204 is used to optimize the decision vector under the constraints of the number of neurons and the quantiles using the sled dog optimization algorithm. The overall objective function is used as the fitness function. The position of the individuals in the population is updated iteratively by simulating the initialization, dynamic selection, movement mechanism, obstacle avoidance, disorientation, training mechanism and retirement mechanism of the sled dog population. The optimal decision vector is output when the iteration termination condition is met. The prediction module 205 is used to configure the number of neurons in the hidden layer of the multilayer perceptron model, the truncated quantile, and the on / off variables of the year feature according to the optimal decision vector. It retrains the configured multilayer perceptron model using the training set and the validation set through the backpropagation algorithm to obtain a trained multilayer perceptron model. It then uses the trained multilayer perceptron model to predict the input feature data of the city to be predicted to obtain a predicted value of computing power scale at a logarithmic scale. Finally, it performs an exponential transformation on the predicted value of computing power scale at a logarithmic scale to obtain the predicted result of computing power scale at the original scale.

[0115] In one alternative approach, the hidden layer employs a hyperbolic tangent sigmoid function as the activation function; both the training set error term and the validation set error term are root mean square errors on a logarithmic scale, and the expression for the root mean square error is: ;in, This serves as the identifier for the training or validation set. For set The number of samples in Let be the decision vector. For parameters The multilayer perceptron model described below applies to samples The log-scale prediction output, For the sample The output data at the logarithmic scale.

[0116] In one alternative approach, the expression for the generalization gap penalty term is: ;in, Weighting for the difference penalty For the verification set error term, The training set error term, The allowed generalization gap threshold; The expression for the model complexity penalty term is: ,in This is the complexity penalty coefficient. These are the parameters of the multilayer perceptron model. The maximum allowed number of parameters is the threshold. The expression for the stability penalty term is: ;in, To stabilize the penalty weight, It is a function of standard deviation. For the first The validation set error is obtained by randomly initializing the training data. This represents the number of repetitions for training.

[0117] In one alternative approach, the constraint on the number of neurons is: ; The number of neurons in the hidden layer. This represents the minimum number of neurons. This represents the maximum number of neurons. The constraint condition of the quantile is: ; The quantile point of the truncation. The minimum value at the quantile. This represents the maximum value of the quantile.

[0118] In one alternative approach, the sled dog population is initialized using a random generation method, wherein the expression for random generation is: ;in, The lower boundary of the search space, The upper boundary of the search space, For interval Random numbers generated internally.

[0119] In one alternative approach, the dynamic selection involves the number of sled dogs participating in the core search task. The expression is: ;in, This refers to the total number of sled dog populations. For the range of values ​​in random variables, For the range of values ​​in A random variable.

[0120] In one alternative approach, the marching mechanism includes: speed update at the head of the queue, speed update in the middle of the queue, and speed update at the tail of the queue; The expression for updating the speed of the queue head is: ,in , For the first The speed of a sled dog For inertial weights, and As a learning factor, and For interval Internally generated random numbers, For the first The best historical position for a sled dog. The reference position is randomly selected from multiple optimal positions. For the first The location of the sled dogs; The expression for the velocity update in the queue is: ,in , Individuals generated randomly. For interval Integers within; The expression for updating the tail velocity is: ,in , The value can be 0 or 1. For interval Internally generated random numbers, Indicates the position of the other sled dogs in the same group.

[0121] It should be noted that the beneficial effects of the urban computing power scale prediction system 200 based on sled dog optimized MLP provided in the above embodiments are the same as those of the urban computing power scale prediction method based on sled dog optimized MLP, and will not be repeated here. Furthermore, the system provided in the above embodiments is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the system can be divided into different functional modules according to the actual situation to complete all or part of the functions described above. In addition, the system and method embodiments provided in the above embodiments belong to the same concept, and their specific implementation process is detailed in the method embodiments, and will not be repeated here.

[0122] The urban computing power scale prediction system 200 based on sled dog optimized MLP of the present invention can be a computer program (including program code) running on a computer device. For example, the urban computing power scale prediction system 200 based on sled dog optimized MLP of the present invention is an application software that can be used to execute the corresponding steps in the urban computing power scale prediction method based on sled dog optimized MLP of the present invention.

[0123] In some embodiments, the urban computing power scale prediction system 200 based on sled dog optimized MLP of the present invention can be implemented in a combination of hardware and software. As an example, the urban computing power scale prediction system 200 based on sled dog optimized MLP of the present invention can be a processor in the form of a hardware decoding processor, which is programmed to execute the urban computing power scale prediction method based on sled dog optimized MLP of the present invention. For example, the processor in the form of a hardware decoding processor can adopt one or more application specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components.

[0124] The modules described in the embodiments of this invention can be implemented in software or hardware. The names of the modules are not, in some cases, limiting the scope of the module itself.

[0125] An electronic device according to an embodiment of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements any of the above-mentioned urban computing power scale prediction methods based on sled dog optimized MLP. That is, an electronic device according to an embodiment of the present invention may include, but is not limited to: a processor and a memory; the memory is used to store the computer program; the processor is used to execute the urban computing power scale prediction method based on sled dog optimized MLP shown in any embodiment of the present invention by calling the computer program.

[0126] In one alternative embodiment, an electronic device is provided, such as Figure 7 As shown, Figure 7 The illustrated electronic device 4000 includes a processor 4001 and a memory 4003. The processor 4001 and the memory 4003 are connected, for example, via a bus 4002. Optionally, the electronic device 4000 may further include a transceiver 4004, which can be used for data interaction between the electronic device and other electronic devices, such as sending and / or receiving data. It should be noted that in practical applications, the transceiver 4004 is not limited to one type, and the structure of the electronic device 4000 does not constitute a limitation on the embodiments of the present invention.

[0127] Processor 4001 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this invention. Processor 4001 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0128] Bus 4002 may include a path for transmitting information between the aforementioned components. Bus 4002 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 4002 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 7 The bus 4002 is represented by only one thick line, but this does not mean that there is only one bus or one type of bus.

[0129] The memory 4003 may be ROM (Read Only Memory) or other types of static storage devices capable of storing static information and instructions, RAM (Random Access Memory) or other types of dynamic storage devices capable of storing information and instructions, or EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto.

[0130] The memory 4003 stores application code (computer program) for executing the present invention, and its execution is controlled by the processor 4001. The processor 4001 executes the application code stored in the memory 4003 to implement the content shown in the foregoing method embodiments.

[0131] Among them, electronic devices can also be terminal devices. A terminal device can be any terminal device that can install applications and access web pages through applications, including at least one of smartphones, tablets, laptops, desktop computers, smart speakers, smartwatches, smart TVs, and smart in-vehicle devices.

[0132] It should be noted that, Figure 7 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0133] An embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements any of the above-mentioned methods for predicting the scale of urban computing power based on sled dog-optimized MLP.

[0134] Alternatively, the computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a compact disc read-only memory (CD-ROM), magnetic tape, a floppy disk, and an optical data storage device, etc.

[0135] In an exemplary embodiment, a computer program product or computer program is also provided, which includes computer instructions stored in a computer-readable storage medium. A processor of an electronic device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the electronic device to perform the aforementioned urban computing power scale prediction method based on sled dog optimized MLP.

[0136] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0137] It should be understood that the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0138] The computer-readable storage medium provided in this invention can be, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0139] The aforementioned computer-readable storage medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the method shown in the above embodiments.

[0140] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of disclosure in this invention is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-disclosed concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this invention.

[0141] It should be noted that the terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and represent a limitation on a specific order or sequence. Where appropriate, the order of use for similar objects can be interchanged so that the embodiments of this application described herein can be implemented in an order other than that shown or described.

[0142] Those skilled in the art will recognize that this invention can be implemented as a system, method, or computer program product. Therefore, this invention can be specifically implemented in the following forms: it can be entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," or "system." Furthermore, in some embodiments, this invention can also be implemented as a computer program product contained in one or more computer-readable media, which includes computer-readable program code.

[0143] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for predicting the scale of urban computing power based on sled dog-optimized MLP, characterized in that, include: Acquire urban computing power scale data, urban development status data, and policy data, and perform logarithmic transformation on the urban computing power scale data and the urban development status data to obtain input feature data and output data under logarithmic scale; A multilayer perceptron model comprising an input layer, a hidden layer, and an output layer is constructed. Training, validation, and test sets are divided based on the input feature data and the output data at the logarithmic scale. The multilayer perceptron model is trained using the backpropagation algorithm. The input layer receives the input feature data; the hidden layer performs weighted summation and nonlinear transformation on the input feature data to obtain the hidden layer output features; and the output layer performs weighted summation on the hidden layer output features to output a predicted value of computing power scale at the logarithmic scale. Define a decision vector, which includes the number of neurons in the hidden layer, the quantiles for truncating the output data in the training set, and a switch variable for whether to add year features; construct a total objective function, which includes a training set error term, a validation set error term, a generalization gap penalty term, a model complexity penalty term, and a stability penalty term; set constraints on the number of neurons and the quantiles. The sled dog optimization algorithm is used to optimize the decision vector under the constraints of the number of neurons and the quantile. The total objective function is used as the fitness function. The position of the individuals in the population is updated iteratively by simulating the initialization, dynamic selection, movement mechanism, obstacle avoidance, disorientation, training mechanism and retirement mechanism of the sled dog population. The optimal decision vector is output when the iteration termination condition is met. Based on the optimal decision vector, configure the number of neurons in the hidden layer of the multilayer perceptron model, the truncated quantile, and the on / off variables of the year feature. Retrain the configured multilayer perceptron model using the training set and the validation set through the backpropagation algorithm to obtain a trained multilayer perceptron model. Use the trained multilayer perceptron model to predict the input feature data of the city to be predicted to obtain the predicted value of computing power scale at the logarithmic scale. Perform an exponential transformation on the predicted value of computing power scale at the logarithmic scale to obtain the predicted result of computing power scale at the original scale.

2. The method for predicting urban computing power scale based on sled dog-optimized MLP according to claim 1, characterized in that, The hidden layer uses a hyperbolic tangent sigmoid function as the activation function; both the training set error term and the validation set error term are root mean square errors on a logarithmic scale, and the expression for the root mean square error is: ;in, This serves as the identifier for the training or validation set. For set The number of samples in Let be the decision vector. For parameters The multilayer perceptron model described below is used for samples Log-scale prediction output, For the sample The output data at the logarithmic scale.

3. The method for predicting urban computing power scale based on sled dog-optimized MLP according to claim 2, characterized in that, The expression for the generalization gap penalty term is: ;in, Weighting for the difference penalty For the verification set error term, The training set error term, The allowed generalization gap threshold; The expression for the model complexity penalty term is: ,in This is the complexity penalty coefficient. These are the parameters of the multilayer perceptron model. The maximum allowed number of parameters is the threshold. The expression for the stability penalty term is: ;in, To stabilize the penalty weight, It is a function of standard deviation. For the first The validation set error is obtained by randomly initializing the training data. This represents the number of repetitions for training.

4. The method for predicting urban computing power scale based on sled dog-optimized MLP according to claim 1, characterized in that, The constraint on the number of neurons is as follows: ; The number of neurons in the hidden layer. This represents the minimum number of neurons. This represents the maximum number of neurons. The constraint condition of the quantile is: ; The quantile point of the truncation. The minimum value at the quantile. This represents the maximum value of the quantile.

5. The method for predicting urban computing power scale based on sled dog-optimized MLP according to claim 1, characterized in that, The sled dog population is initialized using a random generation method, and the expression for random generation is: ;in, The lower boundary of the search space, The upper boundary of the search space, For interval Random numbers generated internally.

6. The method for predicting urban computing power scale based on sled dog-optimized MLP according to claim 5, characterized in that, In the dynamic selection, the number of sled dogs participating in the core search task The expression is: ;in, This refers to the total number of sled dog populations. For the range of values ​​in random variables, For the range of values ​​in A random variable.

7. The method for predicting urban computing power scale based on sled dog-optimized MLP according to claim 6, characterized in that, The movement mechanism includes: speed update at the head of the column, speed update in the middle of the column, and speed update at the tail of the column; The expression for updating the speed of the queue head is: ,in , For the first The speed of a sled dog For inertial weights, and As a learning factor, and For interval Internally generated random numbers, For the first The best historical position for a sled dog. The reference position is randomly selected from multiple optimal positions. For the first The location of the sled dogs; The expression for the velocity update in the queue is: ,in , Individuals generated randomly. For interval Integers within; The expression for updating the tail velocity is: ,in , The value can be 0 or 1. For interval Internally generated random numbers, Indicates the position of the other sled dogs in the same group.

8. A city computing power scale prediction system based on sled dog optimized MLP, characterized in that, include: The processing module is used to acquire urban computing power scale data, urban development status data, and policy data, and to perform logarithmic transformation on the urban computing power scale data and the urban development status data to obtain input feature data and output data under logarithmic scale. A construction module is used to construct a multilayer perceptron model comprising an input layer, a hidden layer, and an output layer. Based on the input feature data and the output data at the logarithmic scale, a training set, a validation set, and a test set are divided. The multilayer perceptron model is trained using a backpropagation algorithm. The input layer receives the input feature data; the hidden layer performs weighted summation and nonlinear transformation on the input feature data to obtain the hidden layer output features; and the output layer performs weighted summation on the hidden layer output features to output a predicted value of computing power scale at the logarithmic scale. A setting module is used to set a decision vector, which includes the number of neurons in the hidden layer, the quantiles for truncating the output data in the training set, and a switch variable for whether to add year features; constructing a total objective function, which includes a training set error term, a validation set error term, a generalization gap penalty term, a model complexity penalty term, and a stability penalty term; and setting constraints on the number of neurons and the quantiles. The iterative module is used to optimize the decision vector under the constraints of the number of neurons and the quantiles using the sled dog optimization algorithm. The overall objective function is used as the fitness function. The position of the individuals in the population is updated iteratively by simulating the initialization, dynamic selection, movement mechanism, obstacle avoidance, disorientation, training mechanism and retirement mechanism of the sled dog population. The optimal decision vector is output when the iteration termination condition is met. The prediction module is used to configure the number of neurons in the hidden layer of the multilayer perceptron model, the truncated quantile, and the on / off variables of the year feature according to the optimal decision vector. It then retrains the configured multilayer perceptron model using the training set and the validation set through a backpropagation algorithm to obtain a trained multilayer perceptron model. The trained multilayer perceptron model is then used to predict the input feature data of the city to be predicted to obtain a predicted value of computing power scale at a logarithmic scale. Finally, the predicted value of computing power scale at the logarithmic scale is subjected to an exponential transformation to obtain the predicted result of computing power scale at the original scale.

9. An electronic device, characterized in that, The electronic device includes a processor coupled to a memory, the memory storing at least one computer program, which is loaded and executed by the processor to enable the electronic device to implement the urban computing power scale prediction method based on sled dog optimized MLP as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one computer program, which, when executed by a processor, implements the urban computing power scale prediction method based on sled dog optimized MLP as described in any one of claims 1 to 7.

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