Method for determining reasonable path set of combined transport of highway and railway based on fuzzy conversion

Abstract

The application provides a reasonable path set determination method for combined transport based on fuzzy conversion, which comprises the following steps: an ideal point solution set satisfying a multi-objective function is obtained in a Q-dimensional target space, and a limited geometric distance of a combined transport node network is calculated according to a fuzzy membership function; compared with a traditional hard constraint contradiction without solution, the method can make the calculation and iteration process easier, improve the solving efficiency, save the operation time, greatly improve the convergence speed, save the iteration time, and is very suitable for solving the multi-objective reasonable path set problem of the combined transport.

Description

Technical Field

[0001] The present invention belongs to the technical field of road-rail intermodal transport, and in particular relates to a method for determining a reasonable path set for road-rail intermodal transport based on fuzzy conversion. Background Art

[0002] Combined road-rail transport combines the flexibility of road transport for short- and medium-haul freight collection and distribution with the high capacity, economy, and reliability of rail transport for long-haul transport. It is the most representative form of intermodal transport and has become a vital component of the intermodal transport system. Route optimization is key to the efficient operation of intermodal transport systems. However, a large amount of shared information exists between route selections. Considering only a single route can lead to congestion caused by traffic overload or wasteful resource utilization due to low system utilization. A reasonable path set provides a reference for simplifying the abstract road-rail transport network and freight flow distribution. Currently, a reasonable path is defined as the set of all possible paths that travelers can choose between a given OD pair based on their travel needs.

[0003] Currently, the determination of reasonable path sets primarily targets urban road traffic networks. Based on the principle of rational decision-making behavior by travelers and maximizing individual utility, the shortest path is selected as the reasonable path set. However, for intermodal transport networks, reasonable paths are directly related to key factors such as freight transportation time, cost, and service satisfaction. Current methods for determining the shortest path on urban roads fail to effectively reflect the changes in routes associated with intermodal transport, nor do they consider the specific characteristics of freight transportation processes and transshipment costs at transshipment nodes. Consequently, they fail to meet the demand for a reasonable path set that comprehensively considers multiple factors in intermodal transport. Summary of the Invention

[0004] Purpose of the invention: In order to solve the above problems, the present invention proposes a method for determining a reasonable path set for road-rail intermodal transport based on fuzzy theory. Compared with the traditional hard constraint unsolvable contradiction, this method can make the calculation and iteration process easier, improve the solution efficiency, and save computing time; this method can also greatly improve the convergence speed, save iteration time, and is very suitable for solving the problem of a reasonable path set for multi-objective road-rail intermodal transport.

[0005] Technical solution: To solve the above technical problems, the present invention proposes a method for determining a reasonable set of road-rail transport paths based on fuzzy theory. The method comprises the following steps:

[0006] Step 1: Collect road and rail network data, establish connectivity information for each node and section in the transport network under different transport modes based on the road-rail intermodal transport network data, and connect the transport networks of different transport modes based on the connectivity information to obtain the road-rail intermodal transport network;

[0007] Step 2: initialize the combined transport network; determine the OD pairs, input the starting point set and the ending point set, input the coordinate positions of all nodes in the combined transport network, let the initial reasonable path set be empty, and backup the original road network data;

[0008] Step 3: determine the optimization target of the combined transport reasonable path, establish the transportation cost set and the transportation time set of all OD road sections in the combined transport, and the transfer cost set and the transfer time set of each node; establish the N-dimensional target space of the reasonable path set;

[0009] Step 4: determine the optimal solution and the worst solution of the single-target path planning in the target space based on the ideal point method;

[0010] Step 5: normalize the ideal point and the target value;

[0011] Step 6: map the feasible solution to the target space vector in the target space, calculate the fuzzy membership function based on the space mapping point using the Euclidean norm calculation model, and determine the shortest distance of the road section;

[0012] Step 7: search the combined transport reasonable path based on fuzzy bound, including initializing the path set, judging the combined transport node transfer, judging whether the maximum transfer number is exceeded, judging whether the number of paths exceeds the reasonable path number, judging whether the current node search is completed, and performing the next node search after completion;

[0013] Step 8: establish the combined transport reasonable path set that meets the multi-factor optimization target;

[0014] Step 9: terminate the search of the current origin-destination point, select a new origin-destination point, repeat the search process of step 7, and terminate the algorithm after traversing all origin-destination points.

[0015] Further, in step 1, the transportation network and the connection information of each node and road section established according to the combined transport data, specifically includes: considering a combined transport network G(V,A,K), wherein V is the node set, A is the set of transportation lines and sections, and K is the set of transportation modes from node i to node j, i,j∈V, let M represent the set of all OD pairs in the combined transport network, the starting node set is represented by O, the ending point set is represented by D, v o is the starting node, v o ∈O; v D is the ending node, v D ∈D, x ij is the unit quantity from node i to node j, x kk' is the unit transfer quantity from transportation mode k to k', which is a triangular fuzzy number, k,k'∈K, Trans max is the maximum allowed transfer number of multimodal transport, n p is the number of reasonable paths in the combined transport.

[0016] Further, in step 3, the reasonable path optimization target of combined transport is determined, and the N-dimensional target space of the reasonable path set is established, which specifically includes:

[0017] Suppose that the transport path of combined transport is determined by Q targets, the qth target function can be expressed as:

[0018]

[0019]

[0020]

[0021] The constraint conditions are as follows:

[0022]

[0023]

[0024]

[0025]

[0026] Further, in step 4, the optimal solution and the worst solution of single-target path planning in the target space are solved based on the ideal point method, which specifically includes:

[0027] Step 4.1: Hierarchical solution of ideal points satisfying multi-targets. Suppose that the transport path of combined transport is determined by Q targets, the target function is shown in formulas (1)-(3), under the qth target function q∈Q, there is a shortest path satisfying the optimal solution The target value is Then is the coordinate value of the ideal point in the coordinate vector space of the qth target, and the ideal points of each target are sequentially solved in layers, and a Q-dimensional space is established with Q targets as vectors, which is the ideal point of the shortest path satisfying the multi-target path optimization of combined transport in the Q-dimensional space;

[0028] Step 4.2: Optimal solution and worst solution of single-target path planning in the target space. Each road section a m , a m ∈A, the target value of the qth target function on the road section a m is z qi , for the qth target, there must be a path satisfying the minimum target value and a path satisfying the maximum target value

[0029] Further, the normalization processing of the target value in step 5 is as follows:

[0030] Calculate all paths a in the road network of the combined transport of highway and railway m The target value z corresponding to each target qm Determine the value interval corresponding to the qth target The target value and ideal point on each path in the transport line set A are normalized, and the target value is mapped to the value interval [0, 1];

[0031]

[0032] That is, the normalized target vector is (z' 1m , z' 2m , …, z' Qm ), and the target value of the ideal point of the shortest path after normalization is (0, 0, …, 0).

[0033] Further, in step 5, the fuzzy membership function determination method specifically includes: based on the mapping node in the Q-dimensional space, w m is the road segment a in the combined transport network of highway and railway m The weight value of each target influencing factor, m∈M, M represents the set of all OD pairs in the combined transport network of highway and railway, and the fuzzy membership function μ m is the distance between the actual node and the ideal point:

[0034]

[0035] Further, in step 7, the fuzzy limit search reasonable path of the combined transport of highway and railway is as follows:

[0036] Step 7.1: initialization, let v i =v1, v1∈O; a m =a1, a1∈A, reasonable path set Trans=0;

[0037] Step 7.2: check the search node, if the current node is the end point, i.e. v i =v D , go to step 8, otherwise go to step 7.3;

[0038] Step 7.3: use Dijkstra algorithm to solve the shortest path of each target

[0039] Step 7.4: if the shortest path of each single target is the same path, i.e. , then the path is the optimal solution of the multi-objective problem, and is also the shortest path of the combined transport of highway and railway, if Add the path to the path set R, Trans++, and go to step 7.2; otherwise, go to step 7.5;

[0040] Step 7.5: Calculate the starting point v o To the end v D All paths a in the path set A between m The corresponding target value z under each objective function qm , determine the value range For the target value z of each path qm Normalize the target value with the ideal point; calculate the Euclidean distance d between the target value and the ideal point qm , if d qm ≤1, go to step 7.6; if d qm >1, delete the path, Trans++, and go to step 7.2;

[0041] Step 7.6 determines whether the search of all nodes is completed, and the nodes that have been searched are marked as 1, and the nodes that have not been searched are marked as 0. i =v D , and v D When the mark is 1, go to step 8.

[0042] Furthermore, in step 8, a reasonable road-rail transport route is a route that meets the following conditions:

[0043] Step 8.1: Determine whether the number of transfers in the path exceeds the maximum number of transfers. If not, max , that is, Trans≤Trans max , go to step 9, otherwise go to step 8.2;

[0044] Step 8.2: Determine the number of paths in the reasonable path set. If the number of paths is less than n p , then go to step 8.3; otherwise, delete the longest path until the number of paths is n p ;

[0045] Step 8.3: Determine whether the current path is a non-repeated driving path, that is, any identical road section or node is passed only once, and there is no circuitous path between the starting and ending points. If so, add the path to the reasonable path set R; otherwise, go to step 9. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly introduced below. Obviously, the drawings in the following description only relate to some embodiments of the present invention, but are not intended to limit the present invention.

[0047] Figure 1 is a flow chart of the method of the present invention;

[0048] Figure 2 Flow chart for reasonable path search of combined transport of highway and railway for the present application;

[0049] Figure 3 Simple road network of combined transport of highway and railway for the present application used for verification method;

[0050] Figure 4 Schematic diagram of iteration convergence of method operation for the present application. DETAILED DESCRIPTION

[0051] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions of the embodiments of the present application will be described clearly and completely below with reference to the drawings of the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments of the present application.

[0052] Unless otherwise defined, the technical terms or scientific terms used herein should be understood as the usual meanings understood by those skilled in the art to which the present application belongs.

[0053] As shown in Figure 1 The present application proposes a method for determining a reasonable path set of combined transport of highway and railway based on fuzzy theory, which comprises the following steps:

[0054] Step 1: Collect road network data of highway transport and railway transport, establish the connection information of each node and each road section in the transport network under different transport modes according to the combined transport road network data, and obtain the combined transport network by connecting the transport networks of different transport modes according to the connection information;

[0055] Step 2: Initialize the combined transport network; determine the OD pair, input the starting point set and the ending point set, input the coordinate positions of all nodes in the combined transport network, let the initial reasonable path set be an empty set, and backup the original road network data;

[0056] Step 3: Determine the optimization target of the reasonable path of combined transport of highway and railway, establish the transport cost set and the transport time set of all OD road sections in the combined transport, and establish the transfer cost set and the transfer time set of each node; establish the N-dimensional target space of the reasonable path set;

[0057] Step 4: Determine the optimal solution and the worst solution of the single-target path planning in the target space based on the ideal point method;

[0058] Step 5: Normalize the ideal point and the target value;

[0059] Step 6: Map the feasible solution to the target space vector in the target space, determine the shortest distance of the road section by using the Euclidean norm calculation model to calculate the fuzzy membership function based on the space mapping point;

[0060] Step 7: Reasonable path of combined transport is searched based on fuzzy bound search, including initialization of path set, judgment of combined transport node transfer, judgment of whether the maximum transfer number is exceeded, judgment of whether the number of paths exceeds the reasonable path number, judgment of whether the current node search is completed, and next node search is performed after completion;

[0061] Step 8: Reasonable path set of combined transport meeting multi-factor optimization target is established;

[0062] Step 9: The search of the current origin-destination point is terminated, the origin-destination point is selected again, and the search process of step 7 is repeated, and the algorithm is terminated after traversing all origin-destination points.

[0063] In step 1, the transport network and the connection information of each node and section are established according to the combined transport data, which specifically includes: considering a combined transport network G(V,A,K), wherein V is the node set, A is the set of transport lines and sections, and K is the set of transport modes from node i to node j, i,j∈V, let M represent the set of all OD pairs in the combined transport network, the set of starting nodes is represented by O, the set of terminal points is represented by D, v o is the starting node, v o ∈O; v D is the terminal point, v D ∈D, x ij is the unit quantity from node i to node j, x kk' is the unit transfer quantity from transport mode k to k', which is a triangular fuzzy number, k,k'∈K, Trans max is the maximum allowed transfer number of multimodal transport, n p is the number of reasonable paths in combined transport.

[0064] In step 3, the optimization target of reasonable path of combined transport is determined, and the N-dimensional target space of reasonable path set is established, which specifically includes:

[0065] Assuming that the transport path of combined transport is determined by Q targets, the qth target function can be expressed as:

[0066]

[0067]

[0068]

[0069] The constraint conditions are as follows:

[0070]

[0071]

[0072]

[0073]

[0074] In step 4, the optimal solution and the worst solution of single-objective path planning in the target space are solved based on the ideal point method, and specifically include:

[0075] Step 4.1: Hierarchical solution of ideal points satisfying multi-objectives, assuming that the transportation path of the combined transport is determined by Q objectives, and the objective function is shown in formulas (1)-(3), under the qth objective function q e Q, there is a shortest path satisfying the optimal solution The target value is Then That is, the coordinate value of the ideal point in the coordinate vector space of the qth objective, the ideal points of each objective are sequentially solved in layers, and a Q-dimensional space is established with Q objectives as the vector, That is, the ideal point of the shortest path satisfying the multi-objective optimization of the combined transport path in the Q-dimensional space;

[0076] Step 4.2: Optimal solution and worst solution of single-objective path planning in the target space, traversing each road section a m , a m e A, the target value of the qth objective function on the road section a m is z qi For the qth objective, there must be a path satisfying the minimum target value and a path satisfying the maximum target value

[0077] In step 5, the normalization of the target value is as follows:

[0078] Calculate the target value z m corresponding to each objective of all paths a qm in the combined transport road network, determine the value interval of the qth objective For the target value and ideal point on each path in the transportation line set A, the normalization processing is performed, and the target value is mapped to the value interval [0, 1];

[0079]

[0080] That is, the normalized target vector is (z' 1m , z' 2m , …, z' Qm ), and the target value of the ideal point of the shortest path after normalization processing is (0, 0, …, 0).

[0081] The step 5, the fuzzy membership function determination method specifically includes: based on the mapping node in the Q-dimensional space, w m For the road section a m The weight value of each target influence factor, m∈M, M represents the set of all OD pairs in the intermodal network, and the fuzzy membership function μ is calculated using the Euclidean norm m As the distance between the actual node and the ideal point:

[0082]

[0083] In the step 7, the fuzzy limit search intermodal reasonable path is as follows:

[0084] Step 7.1: initialization, let v i =v1, v1∈O; a m =a1, a1∈A, the reasonable path set Trans=0;

[0085] Step 7.2: check the search node, if the current node is the end point, i.e. v i =v D , step 8 is converted, otherwise step 7.3 is converted;

[0086] Step 7.3: the shortest path of each target is solved by using Dijkstra algorithm

[0087] Step 7.4: if the shortest path of single target is the same path, i.e. Then the path is the optimal solution of the multi-objective problem, and is also the shortest path of intermodal transportation, if The path is added to the path set R, Trans++, step 7.2 is converted; otherwise, step 7.5 is converted;

[0088] Step 7.5: calculate the path set A between the starting point v o and the end point v D All the path a m Corresponding target value z qm Under each objective function, determine the value interval The target value z qm And the ideal point of each path are normalized; the Euclidean distance d qm Between the target value and the ideal point is calculated, if d qm ≤1, step 7.6 is converted; if d qm >1, delete the path, Trans++, step 7.2 is converted;

[0089] Step 7.6: judging whether the search of all nodes is completed, marking the searched nodes as 1 and the unsearched nodes as 0, when v i = v D , and v D is marked as 1, go to Step 8.

[0090] In Step 8, the reasonable path of the combined transport is a path satisfying the following conditions:

[0091] Step 8.1: judging whether the number of transshipment of the path exceeds the maximum number of transshipment, if not, go to Step 9, otherwise go to Step 8.2. max , i.e. Trans≤Trans max , go to Step 9, otherwise go to Step 8.2;

[0092] Step 8.2: judging the number of paths in the reasonable path set, if the number of paths is less than n p , go to Step 8.3; otherwise, delete the longest path until the number of paths is n p ;

[0093] Step 8.3: judging whether the current path is a non-repeated driving path, i.e. any same road section or node is only passed through once, and there is no detour path between the origin and the destination, if yes, add the path to the reasonable path set R, otherwise, go to Step 9.

[0094] The performance of the reasonable path determination method of the combined transport based on the fuzzy theory is tested by a simple combined transport network, and the effectiveness of the present application is verified. The test network selects an 8-node network containing 2 types of road sections, i.e. highway and railway, and the coordinate information of the network nodes, the transportation cost of the road sections, and the transshipment time information of the nodes are shown in Table 1. The search this time is to find 2 reasonable paths of the combined transport and the number of transshipments does not exceed 5, and the reasonable path set is 2. The transportation path between the origin 0 and the destination is selected based on three objectives: objective 1 is the minimum transportation cost, objective 2 is the shortest transshipment time, and objective 3 is the lowest carbon emission. Figure 3

[0095] 1) solving the shortest path of each objective under single objective

[0096] The shortest path of objective 1 is the path with the objective value of 110;

[0097] The shortest path of objective 2 is the path with the objective value of 4;

[0098] The shortest path of objective 3 is the path with the objective value of 5.8;

[0099] According to the shortest path of each objective, the ideal point is (110, 4, 5.8)

[0100] ​2) Determine the path set R, and calculate the target value of each path in the set R, as shown in Table 1.

[0101] Table 1 Target value corresponding to each path target

[0102]

[0103] Therefore, the value interval of the three targets is respectively: X1 = [110, 310], X2 = [4, 14], X3 = [5.8, 10.9].

[0104] 3) Normalization processing. Taking the path OAED as an example, the processed value is:

[0105]

[0106]

[0107]

[0108] 4) Calculate the distance between the target value and the ideal point. Taking OADE as an example, the calculation result is d1 = 0.31, and the minimum distance can be obtained by the same method:

[0109] The path distance of O-A-B-F-E-D is 0.71

[0110] The path distance of O-B-F-G-D is 0.42

[0111] The path distance of O-B-F-G-D is 0.42

[0112] The path distance of O-C-G-D is 0.71

[0113] 5) According to step 8, the reasonable path set is O-B-F-E-D and O-B-F-G-D.

[0114] In summary, the reasonable path set determination method for combined transport based on fuzzy theory has good performance in solving the reasonable path of combined transport.

Claims

1. A method for determining a reasonable set of paths for combined transport of passengers and freight based on fuzzy theory, characterized in that, The method comprises the following steps: Step 1: Collecting road network data of highway transportation and railway transportation, establishing the connection information of each node and each road section in the transportation network under different transportation modes according to the road network data of combined transportation, and connecting the transportation networks of different transportation modes to obtain the combined transportation network; Step 2: Initializing the combined transportation network; determining the OD pair, inputting the starting point set and the ending point set, inputting the coordinate positions of all nodes in the combined transportation network, setting the initial reasonable path set as an empty set, and backing up the original road network data; Step 3: Determining the optimization target of the combined transportation reasonable path, establishing the transportation cost set and the transportation time set of all OD road sections in the combined transportation, and establishing the transfer cost set and the transfer time set of each node; and establishing the N-dimensional target space of the reasonable path set; Step 4: Determining the optimal solution and the worst solution of the single-target path planning in the target space based on the ideal point method; Step 5: Normalizing the ideal point and the target value; Step 6: Mapping the feasible solution to the target space vector in the target space, calculating the fuzzy membership function based on the space mapping point by using the Euclidean norm calculation model, and determining the shortest distance of the road section; Step 7: Searching the combined transportation reasonable path based on the fuzzy bound, including initializing the path set, judging the node transfer of the combined transportation, judging whether the maximum transfer number is exceeded, judging whether the number of paths exceeds the reasonable path number, judging whether the current node search is completed, and performing the next node search after the completion; Step 8: Establishing the combined transportation reasonable path set satisfying the multi-factor optimization target; Step 9: Terminating the search of the current starting and ending point, selecting the starting and ending point again, repeating the search process of step 7, and terminating the algorithm after traversing all starting and ending points; In step 1, the transport network and the connection information of each node and section are established according to the combined transport data, specifically including: considering a combined transport network G(V,A,K), wherein V is the node set, A is the transport line and section set, and K is the transport mode set from node i to node j, i,j∈V, let M represent the set of all OD pairs in the combined transport network, the starting node set is represented by O, the ending node set is represented by D, v o is the starting node, v o ∈O; v D is the ending node, v D ∈D, x ij is the unit quantity from node i to node j, x kk' is the unit transfer quantity from transport mode k to k', which is a triangular fuzzy number, k,k'∈K, Trans max is the maximum allowed transfer number of multimodal transport, n p is the reasonable path number in combined transport; In step 7, the steps of searching the combined transportation reasonable path based on the fuzzy bound are as follows: Step 7.1: Initialization, let v i = v1, v1 e O; a m = a1, a1 e A, set of reasonable paths Trans = 0; Step 7.2: Check the search node, if the current node is the end point, i.e. v i = v D , go to step 8, otherwise go to step 7.3; Step 7.3: Solve the shortest path for each target by using Dijkstra algorithm Step 7.4: If the shortest paths of all the single objectives are the same, i.e. then the path is the optimal solution of the multi-objective problem and the shortest path of the combined transport, if the path is added to the path set R, Trans++, and the process goes back to Step 7.2; otherwise, the process goes to Step 7.5; where Q is the number of objectives. Step 7.5: Calculate the starting point v o To the end v D All paths a in the path set A between m The corresponding target value z under each objective function qm , determine the value range For the target value z of each path qm Normalize the target value with the ideal point; calculate the Euclidean distance d between the target value and the ideal point qm , if d qm ≤1, go to step 7.6; if d qm >1, delete the path, Trans++, go to step 7.2; where, is the minimum target value of the qth target, is the maximum target value of the qth target; Step 7.6 Determine if all nodes have been searched. Mark the nodes that have been searched with a 1 and the nodes that have not been searched with a 0. When v i = v D and v D is marked with a 1, go to Step 8.

2. The method for determining a reasonable set of paths for combined transport of passengers and freight based on fuzzy theory according to claim 1, characterized in that, In step 3, the optimization target of the combined transportation reasonable path is determined, and the N-dimensional target space of the reasonable path set is established, which specifically includes: Assuming that the transportation path of the combined transportation is determined by Q targets, the qth target function can be expressed as: The constraint conditions are as follows:

3. The method of claim 2, wherein the method further comprises: In step 4, the optimal solution and the worst solution of the single-target path planning in the target space are solved based on the ideal point method, which specifically includes: Step 4.1 Hierarchical solution of ideal points satisfying multi-objective, assuming that the transport path of the combined transport of highway and railway is determined by Q objectives, and the objective functions are shown in formulas (1)-(3), under the qth objective function q∈Q, there is a shortest path that satisfies the optimal solution The target value is Then That is, the coordinate value of the ideal point in the coordinate vector space of the qth objective, the ideal points of each objective are solved in turn, and a Q-dimensional space is established with Q objectives as vectors, That is, the ideal point of the shortest path satisfying the multi-objective optimization of the combined transport of highway and railway in the Q-dimensional space; Step 4.2 The optimal solution and the worst solution of the single-objective path planning in the target space, traversing each section a of the road-rail transport network m , a m ∈A, the qth objective function on section a m The target value on is z qi , for the qth target, there must be a minimum target value Path and meet the maximum target value Path 4. The method of claim 3, wherein the method further comprises: In step 5, the normalization of the target value is as follows: Calculate all paths a in the combined road-rail network m The corresponding target value z under each target qm Determine the value interval corresponding to the qth target The target values and ideal points on each path in the transport line set A are normalized, and the target values are mapped to the value interval [0, 1]; The target vector after normalization is (z 1m ,z 2m ,…,z Qm ), and the target value of the ideal point of the shortest path after normalization is (0, 0, …, 0).

5. The method of claim 4, wherein the method further comprises: The step 5 specifically comprises: determining the fuzzy membership function based on the mapping nodes in the Q-dimensional space, w m For the road section a m The weight value of each target influencing factor, m∈M, M represents the set of all OD pairs in the combined transport network, and the fuzzy membership function μ is calculated using the Euclidean norm m As the distance between the actual node and the ideal point:

6. The method of claim 5, wherein the method further comprises: In step 8, the combined transportation reasonable path is a path satisfying the following conditions: Step 8.1, judge whether the number of transits of the path exceeds the maximum number of transits, if not, go to Step 8.2, otherwise go to Step 9. max i.e. Trans≤Trans max max, go to Step 9, otherwise go to Step 8.

2. Step 8.2, judge the path number of the reasonable path set, if the path number is less than n p then turn to step 8.3; Otherwise, delete the longest path until the number of paths is n p ; Step 8.3, judging whether the current path is a non-repeated driving path, i.e. any same road section or node is only passed through once, and there is no detour path between the starting point and the ending point, if the condition is met, the path is added to the reasonable path set R, otherwise, step 9 is performed.

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