Metro connection bus operation organization method under normal state current limiting

Abstract

The present application relates to a kind of normal flow limiting under subway connection bus operation organization method.It is according to flow limiting station and the maximum running distance of connection bus screening research area range, and with historical passenger flow data, passenger OD distribution and the maximum running distance of connection bus, screening correction each flow limiting station OD.On this basis, it proposes two-stage optimization method of subway connection bus.The first stage is with the maximum running distance of bus, flow limiting passenger main OD station convergence etc.as constraint, determines all candidate routes meeting constraint using dynamic programming method idea;Second stage is with candidate bus route as input, considers bus total quantity, subway and bus section full load rate, bus minimum / maximum frequency of departure etc.constrains, establishes with the maximum number of passengers on connection bus as optimization target connection bus route selection and frequency optimization model.Original model is converted into mixed integer linear programming model by linearization means, and accurate solution is carried out using commercial software.The present application can support researcher to prepare normal flow limiting under subway connection bus operation organization scheme, expands traditional subway single line connection bus optimization method, can utilize connection bus to balance subway local line network passenger flow distribution, reduces the passenger waiting time outside flow limiting station;Through two-stage optimization method and linearization processing means, while guaranteeing the result optimality, it greatly improves solving efficiency, can satisfy the work demand of field management personnel.

Description

Technical Field

[0001] This invention relates to the field of traffic operation organization technology, and in particular to a method for organizing subway shuttle bus operations under normalized traffic control. Background Technology

[0002] With the rapid advancement of urbanization in my country, the demand for urban public transportation has experienced explosive growth. As a crucial backbone of urban public transportation, the subway has become a key focus of public transportation development in major Chinese cities. By the end of 2022, 41 cities in mainland my country had opened subway lines, with nearly 20 of them having entered the stage of networked subway operation. The rapid increase in subway passenger flow has placed higher demands on subway operation and management departments. Especially during morning and evening rush hours, the huge demand from commuters floods the subway system in a short period, exceeding the system's transport capacity and potentially leading to operational risks.

[0003] To address this, subway operation and management departments in various cities primarily adopt routine passenger flow control measures to reduce peak-hour passenger demand and thus ensure operational safety. Routine passenger flow control measures refer to the use of fixed time periods and intensity of flow control, taking into account the relatively stable spatial and temporal distribution of commuter travel, to restrict passenger flow exceeding the subway's capacity outside the stations. For example, in 2018, Beijing Subway implemented routine passenger flow control measures at 96 stations during morning and evening peak hours. While these measures ensure the operational safety of the subway system, they significantly increase the waiting time for passengers outside stations, reducing the system's operational service level.

[0004] As a flexible transportation mode with medium to low capacity, shuttle buses can effectively connect various subway stations. Under the background of normalized passenger flow control in the subway, transporting passengers subject to flow control outside the station to their destination station (short-distance origin-destination passenger flow) or other non-flow control stations along the route (medium to long-distance origin-destination passenger flow) via shuttle buses can effectively reduce passenger waiting time outside the station and the overall travel time. Determining the subway shuttle bus operation organization plan involves the following two key technical challenges. First, due to the limitation on the maximum operating distance of shuttle buses, it is impossible to perform global optimization of the entire subway network. Therefore, how to determine the local research area based on the flow control stations, and thus divide the subway network into multiple areas for optimization according to the "divide and conquer" approach. Second, within each research area, it is necessary to consider practical constraints such as the maximum service distance of buses, the full load rate of bus and subway sections, and the total number of buses to determine the optimal operating route and departure frequency of shuttle buses. Due to the complexity of the constraints and the large solution space of bus operating routes, how to design an efficient optimization method is another key aspect of this problem.

[0005] In summary, this invention aims to propose an optimization method for the operation of subway-connecting buses under normalized passenger flow control, comprising a two-stage optimization method: determining the research area and optimizing the subway-connecting bus service. The latter employs a phased optimization approach to pre-generate a candidate set of connecting bus routes, significantly improving the problem-solving efficiency without sacrificing optimality. This invention can assist researchers in developing subway-connecting bus operation organization plans. Summary of the Invention

[0006] This invention provides a method for organizing the operation of subway-connecting buses under normalized passenger flow control. It selects a local subway network as the research object based on the subway stations under flow control and the maximum service radius of connecting buses, considering the main origin-destination (OD) points of passengers at the controlled stations, and establishes a two-stage optimization method for subway-connecting buses. The first stage uses dynamic programming to determine all candidate routes that meet the constraints, such as the longest bus travel distance and the connection between the main OD stations of passengers under flow control. The second stage uses the candidate bus routes as input, considering constraints such as the total number of buses and the full load rate of subway and bus sections, to establish a connecting bus route selection and frequency optimization model with the optimization objective of maximizing the number of passengers taking connecting buses. Using this method, the optimal operating routes and frequencies of connecting buses under subway flow control conditions can be determined, reducing the delay time for passengers waiting outside controlled stations, balancing the full load rate of subway sections, and improving passenger service levels. The specific steps of this invention are described below:

[0007] Step 1: Determine the scope of the study area. Select any station within the subway network that has passenger flow control measures. p The preliminary research scope V is selected based on the maximum service radius R of the connecting buses, consisting of several subway stations with and without passenger flow restrictions, where the sets of stations with and without passenger flow restrictions are V and V, respectively. p and V c Select the set of stations with flow restriction V p For any station within the area, the research scope is redefined based on the service radius R, and then applied to V. p Repeat this step for the remaining stations, taking the union of the initial research scope and the research scope corresponding to each flow-limited station during the search process as the new preliminary research scope V', and updating V'. p and V' c For the set of stations with flow restriction V' p Repeat the above steps for all stations within the study area until the study scope no longer increases; the output is then used as the final study scope. The specific implementation is as follows:

[0008] (1) Select any flow-limiting station v p The preliminary study area V is selected based on the maximum service radius R of the connecting bus, where V = V p ∪V c V p and V c These are the groups of stations with and without passenger flow restrictions. k1 and k2 represent the number of stations with and without flow restriction, respectively;

[0009] (2) Initialize the parameters, let k = 1;

[0010] (3) Determine if k is equal to k1. If it is, jump to (4); otherwise, select V. p Inner station The research scope V was selected based on the maximum service radius R of the connecting bus. k , k = k + 1, and repeat (3);

[0011] (4) Determine the new preliminary research scope V', where V' = V∪V1∪V2∪...∪V k1 Update V' p and V' c ,

[0012] (5) Determine if V' is equal to V. If it is, jump to (6); otherwise, let V = V'. p =V' p V c =V' c , k1 = k1', k2 = k2', and jump to (2);

[0013] (6) Output the final research scope V', where the sets of flow-restricted and unrestricted stations are V' and V', respectively. p and V' c ,Finish.

[0014] Step 2: Station Passenger Flow Origin-Destination Screening and Processing. Take the set V' of stations within the research scope that are subject to flow control. p For any station within the area, OD passenger flow is sorted based on historical passenger flow data, and the connecting bus passenger capacity C is considered. b With minimum departure frequency f min Product C b ·f minTo meet the standard, OD pairs with passenger flow below this standard are removed to avoid wasting connecting bus capacity. Subsequently, since the study area determined in step one may be smaller than the original metro network, the destination stations for some passengers at restricted stations may be outside the study area and cannot be directly reached by connecting buses, requiring short-distance transfers. Therefore, it is necessary to determine transfer stations to replace the original point D. The shortest-time path scheme for OD pairs can be determined based on historical data, with the last non-restricted station within the study area passed through in the scheme as the corrected point D. On the other hand, although the ODs of some passengers at restricted stations are within the study area, their shortest distance may still exceed the longest service distance constraint of connecting buses. Therefore, the non-restricted station with the longest connecting bus distance passed through in the shortest-time path scheme should also be used as the corrected point D. For V' p Repeat this step for the remaining stations until all flow-limited stations have been processed, resulting in a set K of corrected OD pairs for each flow-limited station, where K = {1, 2, ..., k3}, and k3 represents the number of OD pairs.

[0015] Step 3: Determine the set of candidate bus routes. Based on the adjusted OD pairs for each restricted station, construct an undirected graph network G = (V”, A, W). Here, V” is the set of stations whose OD pairs have been adjusted; A is the set of edges between stations in V”, A = {a ij |a ij =(v” i ,v” j )},a ij For from station v” i to v” j The edges; W is the set of edge weight coefficients, W = {w ij |w ij =w(a ij )},w ij For edge a ij The length of the route is determined. Starting from point O of any OD pair, the shortest path is found to reach point D based on historical data. Based on the longest service distance constraint for buses and the existence of other feasible points D, it is determined whether adjacent stations are connected. This method is repeated to extend the bus route until all adjacent stations are infeasible. The stations traversed from point O to the current station form a candidate bus route. This method is repeated for the remaining OD pairs (excluding OD pairs contained in the candidate bus routes) to obtain a set of candidate bus routes. The specific implementation is as follows:

[0016] (1) Construct an undirected graph network G = (V”, A, W), where V” is the set of OD stations after the flow restriction is corrected; A is the set of edges between stations in V”, A = {a ij |a ij =(v” i ,v”j )},a ij For from station v” i to v” j The edges; W is the set of edge weight coefficients, W = {w ij |w ij =w(a ij )},w ij For edge a ij Length;

[0017] (2) Parameter initialization: Let k = 1, and set the candidate connecting bus routes. The set of OD pairs included in the candidate shuttle bus routes

[0018] (3) Determine if k is equal to k3. If it is, jump to (6). Otherwise, select the OD pair k within K. Determine if k belongs to ζ. If it does, then k = k + 1 and loop (3). Otherwise, read its OD stations respectively. and And the stations that the shortest path route passes through in G, according to the OD, will be recorded in the candidate connecting bus route l. k The cumulative running distance of bus routes Record the current OD pair k to ζ;

[0019] (4) Calculate in V” adjacent station v” j Cumulative running distance d = d + w ij Determine if the current d is less than or equal to the longest service distance l of the connecting bus. max If the condition is not met, the search for this OD pair k ends, k = k + 1, and jumps to (5). Otherwise, continue to determine whether there are other OD pairs, i.e., point O is located at l. k Inside, point D is v” j If so, then v” j Record to candidate shuttle bus routes k Record the sequence number of the satisfied OD pair into ζ, and use v” j If the station is the current station, loop (4); if not, then v” j Record to l k and with v” j The station is the current station, and the cycle repeats (4);

[0020] (5) Due to l k There may be some stations that do not belong to any OD pair, i.e., the last case in (4), v” j Recorded to l k However, v” j The adjacent stations do not meet the constraints, so l needs to be deleted.k This part of the station. Based on the OD pairs contained in ζ, delete the current l. k The station in the middle does not belong to any OD pair;

[0021] (6) End the search and output all candidate connecting bus routes. k This is the set of candidate bus routes.

[0022] Step 4: Establish a connecting bus optimization model. Using the set of candidate bus routes as input, and considering constraints such as the total number of buses, the occupancy rate of subway and bus sections, establish a connecting bus route selection and frequency optimization model with the goal of maximizing the number of passengers taking connecting buses.

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[0033] Equation (1) is the objective function, which is to maximize the number of passengers taking the connecting bus. Let M represent the number of passengers (persons / hour) taking bus route l from OD pair k. Equations (2) to (9) are the model-related constraints. Equation (2) indicates that passengers are allowed to board only when candidate bus route l is finally selected and the route passes through passenger OD pair k. M represents a maximum positive number, such as 10000; otherwise... The value is 0; x l The variable is 0 or 1, and is set to 1 when the candidate bus route l is finally selected, otherwise it is set to 0. and All parameters are 0 or 1. A value of 1 is used when the up / down direction of bus route l passes through OD pair k, and 0 otherwise. Equation (3) indicates that for any OD pair k, the cumulative number of passengers choosing different bus routes must be less than or equal to the number of ODs with limited flow outside the station. kLet represent the number of passengers restricted outside the station for OD at k, in persons / hour. Equations (4) and (5) represent the cross-section g in the up and down directions of any bus route l, where the cross-section's load factor must meet safety constraints. The parameter is 0 or 1; it is set to 1 when OD passes through section g of bus route l, and 0 otherwise. b This indicates the passenger capacity of public transport, in passengers per vehicle; f l Let f represent the departure frequency of route l, in vehicles / hour. Equation (6) indicates that for any bus route l, its departure frequency must meet upper and lower limits to satisfy regulations such as passenger service level. min and f max Here, t represents the minimum and maximum departure frequencies, respectively, in vehicles / hour. Equation (7) indicates that the cumulative number of buses required for each bus route must meet the maximum number of available buses requirement. The required number of buses for each route is obtained by dividing the turnaround time by the departure interval (the reciprocal of the departure frequency) and then rounding up. l The total turnaround time for route l is represented in hours, including travel time in both directions, stop time, and turnaround time between origin and destination. represents the rounding function; n represents the total number of buses. For example, if the turnaround time is 0.5 hours and the departure frequency is 30 buses / hour, then 15 buses are needed, and buses 16 to 30 can be connected by buses 1 to 15. Equation (8) indicates that after the operation of connecting buses, each subway section still needs to meet the maximum section load factor constraint to ensure operational safety. Q e This indicates the passenger flow at subway section e before the opening of connecting bus service, in people / hour. The parameter is 0 or 1. It is set to 1 when OD passes through the subway section e before the shuttle bus service is launched, and 0 otherwise. The parameter is 0 or 1. It is set to 1 when OD passes through the subway section e after the shuttle bus service starts, and 0 otherwise. e Let N represent the maximum transport capacity of section e of the subway, in people / hour. Equations (9) and (10) are both constraints on the values ​​of model variables, where N represents a natural number.

[0034] Step 5: Model linearization. Linearization is performed on equations (4) to (7) in Step 4 to transform the established mixed integer nonlinear programming (MINLP) model into a mixed integer linear programming (MILP) model. Finally, the model consists of equations (1)-(3) and (8)-(20).

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[0045] Where, λ l and ψ l Let x be a newly defined natural number. l ·f l as well as ε represents a very small positive number, such as 0.001.

[0046] Step Six: Determine the model solution method. By using a commercial linear programming solver (such as CPLEX, GUROBI, etc.) to program the established MILP model, the optimal connecting bus routes and departure frequencies under normalized subway passenger flow control can be determined, reducing the waiting time of passengers outside the restricted stations and improving passenger service levels.

[0047] The beneficial effects of this invention are that it proposes a two-stage optimization model for the operation of connecting buses under normalized passenger flow control conditions on metro networks. By generating candidate routes for connecting buses and implementing a comprehensive optimization model for route selection and frequency, it avoids the large-scale nonlinear optimization model (MINLP) problem caused by direct co-optimization in both stages. Furthermore, by employing dynamic programming and linearization methods for the two stages respectively, it significantly improves solution efficiency while ensuring optimal results. Simultaneously, this invention extends the traditional optimization method for connecting buses on a single metro line, utilizing connecting buses to balance passenger flow distribution within the local metro network and reduce passenger waiting times outside stations at flow-controlled stations. In summary, this invention can provide technical support for metro operating companies and bus operating enterprises in scheduling connecting bus operation plans. Attached Figure Description

[0048] Figure 1 Overall framework diagram of subway-connecting bus operation organization method

[0049] Figure 2 Schematic diagram of the method for determining the research scope of subway-connecting bus

[0050] Figure 3 Schematic diagram of passenger origin-destination (OD) processing at stations with flow control measures

[0051] Figure 4 A schematic diagram of the method for generating candidate bus routes.

[0052] Figure 5 The research scope of subway-connecting buses is as follows:

[0053] Figure 6 To study the distribution of passenger demand under flow restriction after OD processing in the example.

[0054] Figure 7 The set of candidate bus routes obtained using the method described in this paper in the research example.

[0055] Figure 8 To illustrate the final bus routes and departure frequencies obtained using the method described in this paper in the research example.

[0056] Figure 9 To study the data examples, we need to compare the number of users limited to each station using the method in this paper with the method before optimization. Detailed Implementation

[0057] The specific implementation steps of the present invention will be further described below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of protection of the claimed application, but merely represents selected embodiments of the present application. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without inventive effort are within the scope of protection of the present application. The present invention will be further described below with reference to the accompanying drawings.

[0058] In this embodiment, the proposed method for organizing subway-connecting bus operations under normalized passenger flow control is based on a simplified virtual subway network and a partial subway network of a city. The simplified virtual subway network more clearly and specifically demonstrates the key technical details of the invention, while the partial subway network of a city fully illustrates the implementation process and final optimization effect, verifying the rationality of the invention. (Appendix) Figure 1 The overall framework of this invention is mainly divided into four parts: defining the research scope, passenger flow origin-destination (OD) processing, determining candidate bus routes, and model optimization. The first three parts correspond to steps one, two, and three of the invention, respectively, while the fourth part corresponds to steps four through six. The specific steps of this embodiment are as follows:

[0059] Step 1: Using a subway station with regular passenger flow restrictions as the center, and the maximum service radius R of connecting buses as the radius, a preliminary study area is selected. This area consists of several non-restricted and restricted stations. The restricted stations within this area are then used as centers, and the area is extended using the maximum service radius R of connecting buses until the study area no longer changes, thus determining the final study area. Following this method, using... Figure 2 The following explanation uses the subway network shown as an example. Figure 2 The red boxes S1, S3, and S8 represent stations with passenger flow restrictions, while the rest are non-restricted stations. First, station S1 (with restrictions) is selected as the center, and a circle is drawn with the maximum service radius R of the connecting buses, as shown by the blue dashed line in the diagram. Within the blue dashed box, it is observed whether other stations with restrictions exist. If so, that station is selected, and the circle is drawn again with the maximum service radius R of the connecting buses, and so on. If no such stations exist, the search ends, and all stations within the blue dashed lines constitute the final research area. Three searches were performed, each centered on S1, S8, and S3. Ultimately, no new stations with restrictions were found, thus defining the research area, as shown by the black dashed box in the diagram.

[0060] Step Two: For all stations with flow restrictions within the study area, sort the OD (Original Departure) passenger flow of each station based on historical passenger flow data. Then, using the product of the connecting bus passenger capacity and the minimum departure frequency as the standard, eliminate OD pairs at each station whose OD passenger flow is less than this standard to avoid wasting connecting bus capacity resources. Subsequently, adjust the D point of each station's OD passenger flow based on whether the D point in the OD pair is located within the study area and whether the shortest distance of the OD pair is less than the longest service distance of the connecting bus, so that the processed OD passenger flow meets the above constraints. Figure 3 Each of the three flow-limited stations has three origin-destination (OD) passenger flows. The OD passenger flow from S1 to S5 is excluded due to its small number of passengers. Subsequently, the ODs from S1 to S15, S3 to S15, S8 to S10, and S8 to S5 are all modified because passenger point D is outside the study area. The last non-flow-limited station within the study area along the shortest path is used as the modified point D, resulting in the processed ODs. Meanwhile, the ODs from S1 to S6 and S3 to S6 are truncated because their length exceeds the maximum service distance for connecting buses; the destination station is modified to S7. Finally, the set of processed OD pairs within the study area is obtained.

[0061] Step 3: Using the corrected OD pair set for each restricted station as input, construct an undirected graph network containing all stations at points O and D, as well as the routes between each station. Then, sequentially select OD pairs, determine the shortest path to point D based on historical data, identify initial candidate connecting bus routes, and continue searching for stations around point D to extend bus routes to connect as many OD pairs as possible, until the maximum service distance constraint for buses is exceeded. The stations along the route from point O to the current station constitute the final candidate bus routes. Repeat this method for the remaining OD pairs (excluding OD pairs contained in candidate bus routes) to obtain the candidate bus route set.

[0062] Following the above method, Figure 3 The processed ODs shown generate a set of candidate bus routes for passenger flow. First, based on... Figure 3 The processed OD information shown is used to construct... Figure 4 The undirected graph network shown (S1, S3, S4, S7, S8, S12, S13, S14) retains only the stations involved in the origin-destination (OD) pairs, eliminating other intermediate stations to reduce network complexity. Then, OD pairs S1 to S14 are selected, and candidate connecting bus route 1 is generated based on the shortest path, i.e., starting from S1, passing through S8 and S7 to reach S14. The length of this bus route is calculated, and it is determined whether it satisfies the longest service distance l for connecting buses. max The constraints are used to record this route in the candidate feeder bus route set. Then, it is determined whether there are other OD pairs whose OD stations are all located within a candidate feeder bus route. Figure 3 Since both OD pairs S1 to S7 and S8 to S14 are located within route 1, these two OD pairs are removed.

[0063] Select the next OD pair S8 to S13 to generate candidate connecting bus route 2, which starts from S8, passes through S3 and S4, and arrives at S13. Route 2 eliminates the OD pairs S8 to S4 and S3 to S13. Repeat the above method to generate candidate connecting bus route 3, which starts from S3, passes through S8, and arrives at S7, and candidate connecting bus route 4, which starts from S3, passes through S4, and arrives at S12. This completes the search for all OD pairs, ultimately generating... Figure 4 The four candidate shuttle bus routes are shown.

[0064] Step 4: Using the candidate bus route set as input, and considering constraints such as the total number of buses, the full load rate of subway and bus sections, and the minimum / maximum bus departure frequency, establish a bus route selection and frequency optimization model with the optimization objective of maximizing the number of passengers taking connecting buses. Subsequently, through linearization, the original model is transformed into a linear programming model, and a commercial linear programming solver (such as CPLEX, GUROBI, etc.) is used to solve the established linear programming model to determine the optimal connecting bus routes and departure frequencies for each restricted station.

[0065] Following steps four through six, a partial section of a city's subway network was selected to verify the rationality of this method. First, the research area determined in step one was defined as follows: Figure 5 As shown; following step two, the processed OD passenger flow is as follows Figure 6 As shown; following step three, the final 16 candidate bus routes are generated, as follows: Figure 7 As shown.

[0066] Subsequently, based on Figures 5 to 7 Based on the relevant case data, the model was programmed and solved according to the model shown in step five. This invention uses Matlab software to call the Yalmip language for model programming and Cplex software for model solving. The software can find the optimal solution with a gap value of 0% within 5 seconds. The solution results are as follows... Figure 8 and 9 As shown. Figure 8 This demonstrates the final selection and departure frequencies of each candidate connecting bus route. With a total of 25 buses (n in constraint 7), this model ultimately selects 11 routes: 1, 2, 3, 5, 8, 10, 12, 13, 14, 15, and 16. The departure frequencies of each route vary depending on passenger demand, as detailed below. Figure 8 As shown, the operation of the shuttle bus service allows passengers subject to flow control measures outside the station to take the shuttle bus directly to their destination station or to a nearby subway station to continue their subway journey, significantly reducing the number of passengers subject to flow control measures outside the station. Figure 9 It can be seen that the present invention can reduce the number of people restricted outside the station from 4,849 to 193, a reduction of up to 96%, which greatly alleviates the passenger congestion outside the station caused by the normalized flow restriction of the subway during peak hours, and verifies the effectiveness of the present invention.

[0067] The embodiments described above are merely illustrative of the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications and substitutions should be covered within the scope of the claims of the present invention. Technical aspects, shapes, and structures not described in detail in this invention are all well-known technologies.

Claims

1. A method for optimizing the operation of subway connecting buses under normalized passenger flow control, characterized in that, Includes the following steps: S1. The research area is selected with the subway station with flow restriction as the center and the maximum operating distance of connecting buses as the radius. S2. For the study area, the OD of each restricted station is screened and corrected based on historical passenger flow data, passenger OD distribution and maximum operating distance of connecting buses. S3. Based on the corrected OD, use dynamic programming to determine the set of all candidate routes that satisfy the maximum operating distance constraint of connecting buses. S4. Using the set of candidate bus routes as input, establish a model for selecting connecting bus routes and optimizing their frequency. S4 includes: Establish a model for selecting and optimizing the frequency of connecting bus routes. The optimization objective is to maximize the number of passengers taking connecting buses. Considerations include allowing passengers to board only when the connecting bus route is finally selected, the cumulative number of connecting bus passengers must be less than or equal to the number of ODs outside the station, the upper limit of the full load rate of the bus up and down sections, the upper and lower limits of the bus departure frequency, the upper limit of the total number of buses, the upper limit of the full load rate of the subway section, and the range constraints of variable values. Including the following formulas: ； ； ； ； ； ； ； ； ； ； in, Indicates OD pair k Bus routes l Passenger count, people / hour; and All parameters are 0 or 1, when the bus route l The upward / downward direction passes through the OD pair k The value is 1 if the condition is met, otherwise it is 0. The parameter is 0 or 1. When OD is... k Bus routes l cross section The value is 1 if the condition is met, otherwise it is 0. The variables are 0 and 1, when the candidate bus routes l If it is the final selection, set it to 1; otherwise, set it to 0. This indicates the passenger capacity of public transportation, in passengers per vehicle. Indicate route l Departure frequency, vehicles / hour; Indicate route l The total turnaround time, including travel time in both directions, stop time, and turnaround time between origin and destination, in hours; This represents the floor function; Indicates the total number of buses; This indicates the section of the subway before the opening of connecting bus service. e Passenger flow, people / hour; The parameters are 0 and 1. Before the shuttle bus service was launched, the OD pair was... k Passing through the subway section The value is 1 if the condition is met, otherwise it is 0. The parameters are 0 and 1. When the shuttle bus service is launched, the OD (Original Department) is... k Passing through the subway section The value is 1 if the condition is met, otherwise it is 0. Indicates subway cross-section Maximum transport capacity of the section, people / hour; S5. Model linearization process: The established mixed integer nonlinear programming model is transformed into a mixed integer linear programming model. S6. Use a commercial linear programming solver to solve the established mixed-integer linear programming model accurately.

2. The method for optimizing the operation of subway shuttle buses under normalized passenger flow restriction as described in claim 1, characterized in that, S1 includes the following steps: S11. Select any subway station with passenger flow restrictions, and use the maximum operating distance of connecting buses as the service radius. Screening the preliminary research scope It consists of several subway stations with and without passenger flow restrictions; S12. Scope of Preliminary Research Repeat step S11 for the remaining stations within the restricted flow area, taking the initial research scope. and the research scope corresponding to each flow-limited station during the search process. Union ( (as a new preliminary research scope) ; S14. New Research Scope Repeat steps S11 to S13 for the restricted stations within the area until the research scope no longer increases, thus obtaining the final research scope.

3. The method for optimizing the operation of subway shuttle buses under normalized passenger flow restriction as described in claim 1, characterized in that, S2 includes the following steps: S21. Based on historical passenger flow data, sort the OD passenger flow of each subway station with passenger flow restrictions. S22, with connecting bus passenger capacity With minimum departure frequency product As a standard, OD pairs with OD passenger flow below this standard are removed; S23. Determine the shortest path solution for each OD pair based on historical data; S24. Take the last non-limited station within the research range passed through in the scheme as the corrected point D. Check whether the distance of the corrected OD pair meets the constraint of the maximum operating distance of the connecting bus. If it does not meet the constraint, take the non-limited station with the longest distance of the connecting bus passed through in the shortest time route scheme as the corrected point D again. S25. Obtain the set of OD pairs after correction for each flow-limited station.

4. The method for optimizing the operation of subway shuttle buses under normalized passenger flow restriction as described in claim 1, characterized in that, S3 includes the following steps: S31. Based on the modified OD pair set of each flow-limited station, construct an undirected graph network. ; The set consisting of the OD stations after the correction of each flow restriction station; for The set of edges formed by the stations in the middle, , For from the station to The edge; Let be the set of edge weight coefficients. , For the edge Length; S32. For any OD pair, determine the shortest path solution based on historical data, and determine whether it connects to adjacent stations based on the maximum bus travel distance constraint and whether there are other feasible D points. Repeat this method to extend the bus route until all adjacent stations are infeasible solutions. The stations passed from point O to the current station form a candidate bus route. S33. For the remaining OD pairs, i.e., the OD pairs contained in the candidate bus routes, repeat step S32 until the search of all OD pairs is completed, and the candidate bus route set will be obtained.

5. The method for optimizing the operation of subway shuttle buses under normalized passenger flow control as described in claim 1, characterized in that, S5 includes the following steps: By introducing 0,1 variables, real variables, minimal positive numbers, and maximal positive numbers, the nonlinear constraints in the original model are transformed into multiple equivalent linear constraints, thereby transforming the original mixed-integer nonlinear programming model into a mixed-integer linear programming model.

6. The method for optimizing the operation of subway shuttle buses under normalized passenger flow restriction as described in claim 1, characterized in that, S6 includes the following steps: Based on the established mixed-integer linear programming model and the specific parameters of the case, the data is input into a commercial solver, such as CPLEX or GUROBI, for fast and accurate solution.

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