Multi-constraint route recommendation method for air-rail intermodal transport network

Abstract

A multi-constraint route recommendation method for an air-rail transport network comprises the following steps: 1) constructing an air-rail transport network model; 2) using a prediction model to predict the user acceptance rate of the currently feasible routes between the starting point and the destination; and 3) prioritizing the route recommendations with reference to the user acceptance rate of the feasible routes. In step 1), the air-rail transport network model is composed of an upper aviation network layer and a lower high-speed rail network layer, and the two layers are connected by an intra-city transfer system. In step 2), the prediction model is as follows: using air-rail transport route screening conditions to filter out route data in the air-rail transport network model; combining the time cost, economic cost, and user acceptance rate of each route under different departure times into a triplet data set; constructing a linear regression equation as an air-rail transport route prediction model; importing the triplet data set into the linear regression equation, calculating the unknown parameters in the linear regression equation, and obtaining the air-rail transport route prediction model.

Description

Technical Field

[0001] The present invention is an application technology of computer technology in transportation network, specifically a multi-constraint path recommendation method for air-rail transport network. Background Art

[0002] Air-rail intermodal transport refers to a combined transport mode that combines air transport and rail transport. It combines high-speed rail and civil aviation, two modes of transport that meet the needs of efficient travel. It can quickly build a three-dimensional, efficient, comprehensive transportation system and form a three-dimensional transportation pattern that combines air and land. Therefore, it has strong practical significance. As one of the various transportation solutions [1], air-rail intermodal transport involves issues such as the construction of a transportation system network model, the optimization of transportation routes, and the establishment of a criterion for determining the quality of a route based on the time cost and economic cost of the route [2].

[0003] Current research on air-rail transport route recommendation is mainly divided into network model construction, path screening and recommendation. Network model construction is the basic problem of air-rail transport. In terms of network model construction, many studies have been devoted to optimizing logistics transportation efficiency and resource allocation. In the complex air-rail transport network, different types of nodes are involved, including airport nodes, railway station nodes and nodes of the urban transfer system sub-network. The traditional single-plane network topology cannot fully describe this large and complex network problem. Therefore, it is necessary to introduce a super network [3] model to construct the air-rail transport network architecture. Wang R et al. proposed a hub-and-spoke network model based on the mode networks of both sides in highway-rail intermodal transport [4]. They used time and economic cost as the evaluation indicators of network efficiency and focused on land freight transport. Dai Fuqing et al. designed a double-layer air-rail transport super network [5]. They used the urban traffic network to connect the upper and lower aviation networks and railway networks. On this basis, they established a traffic flow distribution model to study the relationship between air-rail transport and traffic flow distribution and existing supply capacity.

[0004] In terms of route screening and recommendation, the main body of existing research content is mainly focused on freight transportation, and time cost and economic cost have become the main criteria for judging the quality of routes in the research. However, in air-rail intermodal transport, which mainly transports people over long distances, time and economic cost alone are not enough to fully reflect the actual situation of the route. The influence of subjective factors as criteria for judging the quality of routes still needs further research. Jing X et al. applied the idea of ​​genetic algorithm to the route optimization problem in freight intermodal transport and proposed a hybrid genetic algorithm [6]. They established a mathematical model for intermodal transport and solved the optimal route in intermodal transport, focusing on calculating the recommended route for a single objective function. Wang R et al., based on the analysis of the characteristics of the intermodal transport model, used the weighted sum method [7] to give an equivalent single-objective MILP formula for the time and economic cost of routing and obtained a high-quality solution under the MA method.

[0005] In the prior art, Chinese patent application CN113869991A, “A method for recommending an air-rail transport combination,” also discusses different air-rail transport route recommendation methods. Summary of the Invention

[0006] Different from the existing technology and solving the problems existing in the existing technology, the present invention proposes a multi-constraint path recommendation method for air-rail intermodal transport network, which includes the following steps:

[0007] 1) Construct a double-layered super network model as the air-rail intermodal transport network model;

[0008] 2) In the air-rail intermodal transport network model, the air-rail intermodal transport route prediction model is used to predict the user acceptance rate of the current feasible path between the origin and the destination;

[0009] 3) Prioritize the recommended paths based on the user acceptance rate of feasible paths for new users to choose from;

[0010] In step 1), the air-rail transport network model consists of an upper aviation network layer and a lower high-speed rail network layer, and the two layers are connected by an intra-city transfer system;

[0011] In the upper aviation network layer, each node represents an airport, each edge represents a flight route between two airports, and the edge weight represents the time cost and economic cost of the flight;

[0012] In the lower high-speed rail network layer, each node represents a train station, each edge represents the railway line between two train stations, and the edge weight represents the time cost and economic cost of the train;

[0013] In the same city, the edge between the corresponding nodes of the airport and the railway station represents the transfer system subnetwork within the corresponding city, and the edge weight represents the time cost and economic cost of the transfer;

[0014] In air-rail transport, users need to pass through multiple cities on the way from the starting point to the destination. Any two adjacent cities have at least one of the following modes of transport: air or rail. Each mode has different time and economic costs. In addition, if you switch from one mode of transport to another within the same city, you will need to pay transfer fees and transfer time. Each transfer process only occurs within the city, and different cities have different transfer fees and transfer time. The number of transfers cannot exceed two.

[0015] In step 2), the design method of the air-rail intermodal transport route prediction model is as follows:

[0016] First, define the user acceptance rate: it represents the acceptance ratio of the same path by the historical user group. The higher the acceptance ratio, the better the path.

[0017] Then, the air-rail transport path screening conditions are used to filter out the path data in the air-rail transport network model; the time cost, economic cost and user acceptance rate of each path under different departure times are combined into a triple data set;

[0018] Then, a linear regression equation is constructed as the air-rail intermodal transport route prediction model based on the time cost, economic cost and user acceptance rate of the historical routes in the dataset;

[0019] Finally, the constructed triplet dataset is imported into the linear regression equation, the unknown parameters in the linear regression equation are calculated, the mathematical relationship between user acceptance rate and time cost and economic cost is determined, and the air-rail intermodal transport route prediction model is obtained;

[0020] In step 3), when a new user searches for a path, the user acceptance rate of the feasible path is predicted using a linear regression equation. After the user acceptance rates of the feasible paths are sorted, multiple paths are recommended to the new user. After the new user makes a choice, the actual acceptance rate of the path is recorded and stored in the dataset, thereby achieving iterative updates of the dataset. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a schematic diagram of the air-rail intermodal transport network model;

[0022] Figure 2 It is a virtual route diagram of the air-rail intermodal transport network model;

[0023] Figure 3(a) shows the probability density of acceptance rate of economic-oriented user dataset;

[0024] Figure 3(b) is a scatter plot of the acceptance rate of the economic-oriented user dataset;

[0025] Figure 4(a) shows the probability density of acceptance rate of the time-oriented user dataset;

[0026] Figure 4(b) is a scatter plot of the acceptance rate of the time-oriented user dataset;

[0027] Figure 5(a) shows the probability density of acceptance rate of the comprehensive-oriented user dataset;

[0028] Figure 5(b) is a scatter plot of the acceptance rate of the comprehensive-oriented user dataset;

[0029] Figure 6(a) shows the gradient descent fitting surface under the first set of hyperparameters in the model performance verification;

[0030] Figure 6(b) shows the cost function fitting curve under the first set of hyperparameters in the model performance verification;

[0031] Figure 7(a) shows the gradient descent fitting surface under the second set of hyperparameters in the model performance verification;

[0032] Figure 7(b) shows the cost function fitting curve under the second set of hyperparameters in the model performance verification;

[0033] Figure 8(a) shows the gradient descent fitting surface under the third set of hyperparameters in the model performance verification;

[0034] Figure 8(b) shows the cost function fitting curve under the third set of hyperparameters in the model performance verification;

[0035] Figure 9(a) is a scatter plot of the depression path dataset;

[0036] Figure 9(b) is a scatter plot of the depression path predicted by the model. DETAILED DESCRIPTION

[0037] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0038] 1. Overview of the Program

[0039] The present invention proposes a user acceptance rate prediction model, which introduces the user's subjective factors in air-rail intermodal transport, quantifies the functional relationship between historical user acceptance rate and time cost and economic cost, and predicts the user acceptance rate of the current feasible path. On this basis, the path recommendation priority is sorted.

[0040] In this specific embodiment:

[0041] First, we constructed an air-rail intermodal hypernetwork model using aviation data (provided by China Eastern Airlines) and high-speed rail data. After determining the starting and ending nodes, we filtered out the path information with attribute data such as time, price, and historical user acceptance rate to form a data set.

[0042] Then, a prediction model is built;

[0043] Finally, combined with an open-source user shopping behavior dataset, we study the objective relationship between user acceptance rate and other attributes and find the optimal solution of the model to help air-rail intermodal transport service providers establish the optimal evaluation criteria for screening and recommending feasible paths.

[0044] 2 System Model

[0045] 2.1 Air-Rail Network Model

[0046] This paper adopts a double-layered hypernetwork model to describe the air-rail intermodal transport route recommendation problem. The model consists of an upper aviation network layer and a lower high-speed rail network layer, and the two layers are connected by an intra-city transfer system. Figure 1 In the upper aviation network layer, each node represents an airport, each edge represents a flight route between two airports, and the edge weight represents the time and economic cost of the flight. In the lower high-speed rail network layer, each node represents a train station, each edge represents a railway route between two train stations, and the edge weight represents the time and economic cost of the train. The vertical aviation network nodes and railway network nodes are two nodes in the same city. In the intra-city transfer system, each edge represents a sub-network composed of intra-city transfer transportation between two transfer points. In this study, the intra-city transfer sub-network is simplified to an edge connecting the airport node and the train station node in the same city, and the edge weight represents the time and economic cost of the transfer.

[0047] In this hypernetwork model, a priority queue is used to store the nodes that have been visited and sort them in ascending order according to the path length. Each time, the node with the smallest path length is taken from the queue for expansion until the specified number of paths is reached or the queue is empty. In the calculation, the upper limit of the number of jumps on the path is set to avoid repeated calculations and infinite loops. In the hypernetwork model, a feasible path diagram from the starting point to the end point is selected, as shown in the figure below. Figure 2 shown.

[0048] 2.2 Routing Metrics

[0049] The route recommendation problem for air-rail intermodal transport is modeled as a linear programming problem. The following metrics need to be considered in the model.

[0050] (1) Number of transfers / transfers

[0051] In air-rail transport, the mode of travel is a combination of airplanes and high-speed trains. To ensure the passengers' travel experience, the number of transfers between different vehicles is limited to two or less. k,k Indicates whether a transfer occurs at the node. If a transfer occurs at node k, the value is 1, otherwise it is 0.

[0052] (2) Time cost

[0053] The time cost is divided into two parts: the travel time cost between nodes and the transfer time cost within the super node. represents the time cost between railway nodes i and j, T represents the time cost between aviation nodes i and j; k represents the transfer time cost within city k.

[0054] (3) Economic costs

[0055] The economic cost is divided into two parts: the economic cost of the distance between nodes (such as the cost of train tickets and plane tickets) and the economic cost of transfers within the city (such as the cost of online car-hailing, subway, bus, etc. within the city). represents the economic cost between railway nodes i and j, represents the economic cost between aviation nodes i and j; the transfer time cost within super node k is represented by C k express.

[0056] (4) Depression parameters

[0057] In the aviation part of air-rail transport, some sections have low occupancy rates and low user acceptance rates, but the gap between the travel time cost and economic cost and the optimal section is within a specific acceptable range. In order to increase the economic benefits of this section, the airline will set a discount rate d for this section.

[0058] 2.3 Routing Constraints

[0059] Air-rail transport is a solution led by airlines or railway departments, which organically combines aviation and rail transportation to provide air-rail transport services for long-distance travelers, thereby making full use of transportation resources and improving users' travel experience. In the process of air-rail transport, to reach the destination from the starting point, the user needs to pass through N cities on the way, and there is at least one of the two modes of transportation, aviation or rail, between any two adjacent cities. Each mode has different time and economic costs, and if you change from one mode of transportation to another in the same city, you will need to pay transfer fees and transfer time. Each transfer process only occurs within the city, and different cities have different transfer fees and transfer times. The number of transfers shall not exceed two times. For example Figure 2 In the air-rail transport case from Harbin to Shenzhen, a feasible path from the starting point to the end point is represented by W = V HEB V PEK V NKG V NJH V SH V SZ , where the user only had one intra-city transfer in Nanjing, X NKG,NJH The value of is set to 1, the economic cost incurred in this process is F1, and the time cost is F2.

[0060]

[0061] The air-rail transport route screening needs to meet the following four conditions:

[0062] Condition 1: Each transfer occurs only within a city node, and each city node has at most one transfer;

[0063] Condition 2: In a specific route, only one mode of transportation and one route can be selected between two adjacent node cities;

[0064] Condition 3: The total time consumed by the whole process does not exceed T;

[0065] The total economic cost of the entire process under condition 4 does not exceed C.

[0066] The filtering conditions are abstracted into the following formula:

[0067] (1) Indicates that only one route can be chosen between two adjacent nodes

[0068]

[0069] (2) Indicates that there are at most two transfers during the entire journey

[0070]

[0071] (3) The total time of the entire path must not exceed the time limit T

[0072]

[0073] (4) The total cost of the entire journey must not exceed the cost limit C

[0074]

[0075] 3. Design

[0076] In air-rail intermodal transport, the concept of user acceptance rate α is introduced to represent the historical acceptance rate of a route by a user group, which is used to determine the quality of a route. Using the four filtering criteria above, a dataset of route data filtered from the air-rail intermodal transport graph model is constructed. For each route, the time cost, economic cost, and historical user acceptance rate for different departure times form a triplet dataset.

[0077] A linear regression mathematical model is constructed based on the time cost, economic cost, and user acceptance rate of historical routes in the dataset. The constructed triplet dataset is imported to calculate the unknown parameters in the linear regression equation, and the mathematical relationship between user acceptance rate and time and economic cost is determined. When users subsequently search for routes, the linear regression formula is used to predict the user acceptance rate of feasible routes. After sorting the acceptance rates of feasible routes, multiple routes are recommended to users. After the user makes a selection, the actual acceptance rate of the route is recorded and stored in the dataset, thereby achieving iterative updates of the dataset. The user acceptance rate prediction model for air-rail intermodal routes is expressed as follows:

[0078]

[0079] By quantifying the relationship between user acceptance rate and time cost, economic cost, and the depression parameter, the model determines two unknown parameters, which are used to predict routes with unknown user acceptance rates. This allows for route ranking and recommending ten routes with the highest acceptance rates to specific users. Furthermore, air-rail intermodal service providers can use this model to determine the rationality of the depression parameter to optimize transportation resource allocation.

[0080] 3.1 Prediction Error Metrics

[0081] In the mathematical model of air-rail transport discussed in this invention, the factors affecting the user acceptance rate α include time cost, economic cost and depression parameter d. Therefore, mathematical model (7) belongs to the multivariate linear regression model [9]. In the given mathematical model (7), this invention uses the least squares method to solve the optimal solution of the two unknown parameters so that the error between the model's predicted value and the true value is minimized, that is, the following loss function is minimized:

[0082]

[0083] The optimal solution is obtained by solving the partial derivative of the loss function (8) and setting it equal to 0. That is, solving the following system of equations:

[0084]

[0085] Substituting mathematical model (7) into (9), we get:

[0086]

[0087] Next, we bring the two partial derivatives into the gradient descent formula and get:

[0088]

[0089] Update model parameters:

[0090]

[0091] Where d is the depression parameter, h is the learning rate, and t is the number of iterations. In the algorithm, the dataset is substituted into the above formula to find the optimal solution for the two unknown parameters.

[0092] After solving the model parameters, the test set data is imported into the model and the MSE value of the model is calculated to evaluate the model error.

[0093] 3.2 Model parameter calculation

[0094] Based on the routing constraints in Section 2.3, feasible paths were screened. A triplet dataset consisting of route time cost, economic cost, and user acceptance rate was constructed. The dataset was then divided into three categories based on user profiles. The first category consisted of economically oriented users, who prioritized economic cost over time, with time cost having a minimal impact on their choices. The second category consisted of time-oriented users, who prioritized time and preferred less time-consuming routes, with economic cost having a minimal impact on their choices. The third category consisted of comprehensive-oriented users, for whom time and economic costs had almost equal influence. By training on a dataset of user purchasing habits and using user acceptance rates as a reference, the values ​​of the two parameters were fixed to optimize the model for optimal route recommendation in an air-rail intermodal system. To prevent the influence of the depression parameter on the model parameters, the value of the depression parameter d was set to 1 by default before the algorithm was run.

[0095] (1) Analysis of model parameters for economically oriented users

[0096] Figure 3(a) shows the probability density of the economic-oriented dataset. Substituting the route data of the dataset into the least squares algorithm, we can obtain the values ​​of parameters w1 and w2 in the economic-oriented mathematical model as [0.00247, 0.08130]. ​​Substituting these two parameters into the mathematical model (7), the mean square error (MSE) of the model is calculated using the test set data and is 0.0033.

[0097] In the scatter plot model Figure 3(b) above, the z-axis represents user acceptance rate, and the x- and y-axes represent economic cost and time cost, respectively. In the scatter plot, the hollow black dots represent the actual model generated from the consumption data of users in the economically oriented dataset, while the solid black dots represent the user acceptance rate predicted by the model based on the time and economic cost data in this user data type. The scatter plot model shows that user acceptance rates, which are influenced by subjective factors when purchasing tickets, exhibit significant dispersion and uncontrollability. However, overall, the acceptance rate for economically oriented users is concentrated between 0.45 and 0.65. The model's predicted results generally fall within the 0.50-0.60 range, which is highly representative when compared to the actual acceptance rate of this type of user.

[0098] (2) Analysis of model parameters for time-oriented user models

[0099] Substituting the route data of the dataset into the least squares algorithm, it can be concluded that in the economic-oriented mathematical model, the values ​​of parameters w1 and w2 are [0.00188, 0.11051]. Substituting the two parameters into the mathematical model (7), the mean square error (MSE) of the model is calculated using the test data and is 0.0032.

[0100] Referring to Figures 4(a) and 4(b), the probability density plot and scatter plot for this user type's data set show that this type of user's consumption trend clearly favors the lowest time cost. Overall, user acceptance rates range from 0.45 to 0.65, while the acceptance rate predicted by the model based on the calculated parameters is concentrated around 0.55. Based on this result, when this type of user purchases a ticket for this route, the acceptance rate calculated using this mathematical model can determine whether a particular air-rail intermodal route can be pushed to a specific user.

[0101] (3) Analysis of comprehensive oriented user model parameter results

[0102] Substituting the above dataset into the least squares algorithm, we can find that in the comprehensive-oriented data model, the values ​​of parameters w1 and w2 are [0.00171, 0.12154]. Substituting the two parameters into the mathematical model (1), the mean square error (MSE) of the model is calculated using the test set data and is 0.0031.

[0103] Referring to Figures 5(a) and 5(b), based on the probability density plot and scatter plot for this dataset, we can see that the consumption trends of comprehensive-oriented users follow an elliptical, uniform distribution on the model. There is no clear trend between time cost and economic cost, and there is no significant dispersion compared to the single-factor-oriented three-point model. Overall, user acceptance rates are concentrated between 0.45 and 0.65, while the acceptance rate predicted by the model based on the calculated parameters is concentrated in the range of 0.55 to 0.60.

[0104] 4 Performance Evaluation and Result Visualization

[0105] 4.1 Model Performance Verification

[0106] Based on the above prediction model parameter solution, the gradient descent method is used to verify the accuracy of the model

[10] . Taking the comprehensive oriented model as an example, three different sets of initial parameters are set

[11] . The model parameters are fitted by substituting the test set data into the gradient descent method, and the mean and variance are calculated to evaluate the differences between the three groups of experiments.

[0107] (1) The first set of hyperparameter settings: step size 0.0000001, number of iterations 2000, initial model parameter w [0.0017, 0.125]. This set of initial parameters directly adopts the unknown parameter values ​​calculated from the comprehensive guided data set above.

[0108] The fitting results show that the parameter w is [0.00168, 0.12149] and the mean-variance error (MSE) of the model is 0.00309. See Figure 6(a) and Figure 6(b).

[0109] (2) The second set of hyperparameter settings: step size is 0.0000001, number of iterations is 2000, and the initial model parameter w is [0.002, 0.13].

[0110] The fitting results show that the parameter w is [0.00158, 0.12999] and the mean-variance error (MSE) of the model is 0.00317. See Figure 7(a) and Figure 7(b).

[0111] (3) The third set of hyperparameter settings: step size is 0.0000001, number of iterations is 2000, and the initial model parameter w is [0.01, 0.01].

[0112] The fitting results show that the parameter w is [0.00328, 0.00999] and the model mean variance MSE is 0.009994. Refer to Figure 8(a) and Figure 8(b).

[0113] Table 1 Comparison of results of multiple parameter models

[0114]

[0115] As shown in Table 1, after further fitting based on the parameters calculated by the least squares method

[12] , the solved model parameters did not change significantly, and the mean variance of the optimized model only decreased within a limited range. When the initial parameters in the hyperparameter setting deviate from the original parameters, the convergence speed and fitting parameters change significantly, and the mean variance increases exponentially, and the model error increases significantly

[13] . Experiments show that in the air-rail intermodal transport route prediction model, the model parameters calculated by the least squares method have significant reliability and accuracy.

[0116] 4.2 Impact of depression parameters on the model

[0117] In the mathematical prediction model (7) for user acceptance rate, a depression parameter d is introduced. To avoid the influence of the depression parameter, the default value of d is set to 1 when analyzing the results of three different types of user model parameters. In the transportation system, there are some railway shuttles or routes with low occupancy rates, but the gap between the time cost and economic cost and the optimal route is within an acceptable range. These are called depression paths. In the data statistics, air-rail intermodal routes with user acceptance rates below 0.477 are classified as depression paths, and the impact of the depression parameters of these routes on user acceptance is discussed.

[0118] To avoid the impact of time or economic costs on the depression parameters, a comprehensive-oriented dataset was used for comparison. In the comprehensive-oriented user model scatter plot, all square scatter points representing the model's predicted acceptance rate and circular scatter points with user acceptance rates below 0.477 in the dataset were selected, as shown in Figure 9(a).

[0119] Based on the impact of the discount rate on the user acceptance rate in the user consumption behavior dataset, the depression parameter is set to 0.95 in the prediction model (7). As shown in Figure 9(b), the triangle scatter plot is the acceptance rate model of users in the dataset after the corresponding depression parameter is affected, and the cross scatter plot is the model predicted after the depression parameter is substituted into the prediction model. It can be seen that under the influence of the depression parameter, the user acceptance rate increases and is distributed above and below the results predicted by the model. Therefore, it can be proved that the setting of the depression parameter has a certain drainage effect on the depression path. At the same time, the prediction model can also correctly reflect the impact of the depression parameter on the user acceptance rate.

[0120] 5. Summary

[0121] This invention establishes an air-rail intermodal route prediction model that considers different consumer types by studying the relationship between user acceptance rate and time cost, economic cost, and the "depression" parameter. The mathematical prediction model scatter plots for economically, time-, and comprehensive-oriented users, as well as the corresponding model mean-variance, demonstrate that the calculated model can accurately predict different types of user satisfaction with routes. Furthermore, validated by the gradient descent method, the least squares model demonstrates strong reliability and convergence. When purchasing tickets, accurate personalized recommendations can be made based on user satisfaction with routes. This demonstrates that incorporating time, economic factors, and user acceptance rate into the mathematical model can effectively predict the most acceptable route for users, improving the accuracy of air-rail intermodal route recommendations. Furthermore, the invention further discusses the ubiquitous "depression" route conditions in transportation systems. By incorporating the depression parameter into the prediction model, it can be observed that the model accurately predicts the impact of the depression parameter on user acceptance rate, thereby helping air-rail intermodal product providers make relatively accurate adjustments to depression routes to increase economic returns.

[0122] References

[0123] [1]Jing

[0124] [2]Xu J, Zhang J, Guo J.Modeling and empirical analysis of regionalhub-and-spoke road-rail combined transport network based on uncertain cost-time-demand[J]. Journal of Intelligent&Fuzzy Systems, 2020, 39(5):7293-7313.

[0125] [3]

[0126] [4]Wang R, Yang K, Yang L, et al.Modeling and optimization of a road–rail intermodal transport system under uncertain information[J]. EngineeringApplications of Artificial Intelligence, 2018,72:423-436.

[0127] [5] Dai Fuqing, Pang Bizhao, Yuan Jie, et al. Air-rail combined traffic flow distribution model based on super network [J]. Journal of Wuhan University of Technology: Transportation Science and Engineering, 2017, 41(5): 770-775.

[0128] [6]Jing X,Liu Y,Cao W.A hybrid genetic algorithm for routeoptimization in multimodal transport[C] / / 2012Fifth International Symposium onComputational Intelligence and Design.IEEE,2012,1:261-264.

[0129] [7]Wang R,Yang K,Yang L,et al.Modeling and optimization of a road–rail intermodal transport system under uncertain information[J].EngineeringApplications of Artificial Intelligence,2018,72:423-436.

[0130] [8]Mehmood T,Liland K H,Snipen L,et al.A review of variable selectionmethods in partial least squares regression[J].Chemometrics and intelligentlaboratory systems,2012,118:62-69.

[0131] [9]Gavin H P.The Levenberg-Marquardt algorithm for nonlinear leastsquares curve-fitting problems[J].Department of Civil and EnvironmentalEngineering,Duke University,2019,19.

[0132]

[10] Fehrman B,Gess B,Jentzen A.Convergence rates for the stochasticgradient descent method for non-convex objective functions[J].The Journal ofMachine Learning Research,2020,21(1):5354-5401.

[0133]

[11] Maclaurin D,Duvenaud D,Adams R.Gradient-based hyperparameteroptimization through reversible learning[C] / / International conference onmachine learning.PMLR,2015:2113-2122.

[0134]

[12] Haji S H,Abdulazeez AM.Comparison of optimization techniquesbased on gradient descent algorithm:A review[J].PalArch's Journal ofArchaeology of Egypt / Egyptology,2021,18(4):2715-2743.

[0135]

[13] Mandt S,Hoffman M D,Blei D M.Stochastic gradient descent asapproximate bayesian inference[J].arXiv preprint arXiv:1704.04289,2017.

Claims

1. A multi-constraint path recommendation method for air-rail intermodal transport network, characterized by the following steps: include: 1) Construct a double-layered super network model as the air-rail intermodal transport network model; 2) In the air-rail intermodal transport network model, the air-rail intermodal transport route prediction model is used to predict the user acceptance rate of the current feasible path between the origin and the destination; 3) Prioritize the recommended paths based on the user acceptance rate of feasible paths for new users to choose from; In step 1), the air-rail transport network model consists of an upper aviation network layer and a lower high-speed rail network layer, and the two layers are connected by an intra-city transfer system; In the upper aviation network layer, each node represents an airport, each edge represents a flight route between two airports, and the edge weight represents the time cost and economic cost of the flight; In the lower high-speed rail network layer, each node represents a train station, each edge represents the railway line between two train stations, and the edge weight represents the time cost and economic cost of the train; In the same city, the edge between the corresponding nodes of the airport and the railway station represents the transfer system subnetwork within the corresponding city, and the edge weight represents the time cost and economic cost of the transfer; In air-rail transport, users need to pass through multiple cities on the way from the starting point to the destination. Any two adjacent cities have at least one of the following modes of transport: air or rail. Each mode has different time and economic costs. In addition, if you switch from one mode of transport to another within the same city, you will need to pay transfer fees and transfer time. Each transfer process only occurs within the city, and different cities have different transfer fees and transfer time. The number of transfers cannot exceed two. In step 2), the design method of the air-rail intermodal transport route prediction model is as follows: First, define the user acceptance rate: it represents the acceptance ratio of the same path by the historical user group. The higher the acceptance ratio, the better the path. Then, the air-rail transport path screening conditions are used to filter out the path data in the air-rail transport network model; the time cost, economic cost and user acceptance rate of each path under different departure times are combined into a triple data set; Then, a linear regression equation is constructed as the air-rail intermodal transport route prediction model based on the time cost, economic cost and user acceptance rate of the historical routes in the dataset; Finally, the constructed triplet dataset is imported into the linear regression equation, the unknown parameters in the linear regression equation are calculated, the mathematical relationship between user acceptance rate and time cost and economic cost is determined, and the air-rail intermodal transport route prediction model is obtained; There are four screening conditions for the air-rail transport route, which are: Condition 1: Each transfer occurs only within a city node, and each city node has at most one transfer; Condition 2: In a specific route, only one mode of transportation and one route can be selected between two adjacent node cities; Condition 3 is that the total duration of the entire path does not exceed the set value; Condition 4 is that the total economic cost of the entire route does not exceed the set value; In step 3), when a new user searches for a path, the user acceptance rate of feasible paths is predicted using a linear regression equation. After ranking the user acceptance rates of the feasible paths, multiple paths are recommended to the new user. After the new user makes a choice, the actual acceptance rate of the path is recorded and stored in the dataset, thereby achieving iterative updates of the dataset. The metrics used in the air-rail intermodal route prediction model include: (1) Number of transfers / transfers In the air-rail intermodal network model, travel is a combination of airplanes and high-speed rail, and the number of transfers between different vehicles is limited to two or less; k,k Indicates whether a transfer occurs at the node. If a transfer occurs at node k, X k,k is 1, otherwise X k,k is 0; (2) Time cost Time cost includes the travel time cost between nodes and the transfer time cost within the super node; represents the time cost between railway nodes i and j, represents the time cost between aviation nodes i and j; T k represents the transfer time cost within city k; (3) Economic costs The economic cost includes the distance economic cost between nodes and the transfer economic cost within the city; represents the economic cost between railway nodes i and j, represents the economic cost between aviation nodes i and j; the transfer time cost within super node k is represented by C k express; (4) Depression parameters The airline sets a discount rate d for some routes. The occupancy rate of these routes is low, and the user acceptance rate is low. However, the difference between the travel time cost and the economic cost and the optimal route is within a certain acceptable range. Nodes i and j are both city nodes; Air-rail transport route filtering conditions: Assume that the economic cost of the entire path is F1 and the time cost is F2. The screening conditions for air-rail transport routes are summarized as follows: (1) Indicates that only one route can be chosen between two adjacent nodes (2) Indicates that there are at most two transfers during the entire journey (3) The total time consumed by the entire path does not exceed the upper limit T (4) The total economic cost of the entire journey does not exceed the upper limit C N represents the number of city nodes.

2. The multi-constraint path recommendation method for air-rail transport network according to claim 1 is characterized by In step 2), the user acceptance rate prediction model of the air-rail intermodal transport route is expressed as follows: In formula (7), the factors that affect the user acceptance rate α include time cost, economic cost and depression parameter d; the model of formula (7) belongs to the multiple linear regression model; In the given model of formula (7), the least squares method is used to find the optimal solution of the two unknown parameters w1 and w2 so that the error between the model's predicted value and the true value is minimized, that is, the following loss function is minimized: The optimal solution is obtained by solving the partial derivative of the loss function (8) and setting it equal to 0, that is, solving the following system of equations: Substituting formula (7) into formula (9), we get: Next, we bring the two partial derivatives into the gradient descent method and get: Update parameters: Where d represents the depression parameter, h represents the learning rate, and t represents the number of iterations. Substitute the triplet data set into the formula to find the optimal solution for the two unknown parameters w1 and w2. After solving the model parameters, the test set data is imported into the model and the MSE value of the model is calculated to evaluate the model error.

3. The multi-constraint route recommendation method for air-rail intermodal transport networks according to claim 2 is characterized in that the triple data set is divided into three categories according to user profiles: The first category is economically oriented users, who are more concerned about economic costs, and time costs have little impact on their choices; The second category is time-oriented users. They are more concerned about time costs and tend to choose routes that take less time. Economic costs have less impact on them. The third category is comprehensive-oriented users, for whom time cost and economic cost have almost the same impact; By training on a dataset of user purchasing habits and using user acceptance rates as a reference, the values ​​of two parameters, w1 and w2, are solidified to optimize the model and recommend the optimal route for the air-rail intermodal transport system. To avoid the influence of depression parameters on parameters, the value of depression parameter d is set to 1 by default.

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