A method for coordinating optimization of subway train schedule and passenger flow OD

Abstract

The application discloses a kind of subway train timetable and passenger flow OD collaborative optimization method, comprising: obtaining the expected arrival time period and origin-destination point of all passengers, obtain the minimum train interval, train capacity, line station and length;Construct subway train timetable and the collaborative optimization model of passenger flow OD, this is a mixed integer programming model, constraint conditions include departure interval constraint, delay passenger quantity constraint and passenger service constraint;Design adaptive branch and bound algorithm, calculate the above collaborative optimization model, output train departure scheme, the successful boarding time period and origin-destination point of all passengers.The application can reduce congestion and passenger delay time effectively while optimizing cost, improve the travel efficiency and experience of passengers.On this basis, based on the customization improvement of branch and bound algorithm on the basis of the theoretical characteristics of collaborative optimization model, can provide certain reference for solving large-scale subway network calculation efficiency problem.

Description

Technical Field

[0001] This invention relates to the technical field of subway operation management and control, and in particular to a method for collaborative optimization of subway train timetables and passenger flow origin-destination (OD) systems. Background Technology

[0002] Most current subway train timetables are designed based on historical passenger flow distribution data, with the goal of passively meeting passenger flow demand. However, they pay little attention to how to further and rationally utilize real-time passenger flow OD data to proactively guide passenger flow demand.

[0003] Currently, most measures to limit the total number of passengers entering stations are implemented for ease of implementation, but they give little consideration to passenger experience and fail to address the fine-grained control of passenger flow origin-destination (OD). Furthermore, the lack of integration with train timetables prevents the optimization of operating costs while reducing passenger waiting times, thus hindering the maximization of system benefits. Existing research on optimizing train timetables and passenger flow OD control at different stations on rail lines primarily focuses on controlling the total number of people entering the station. Even the few studies on precise OD control neglect the impact of collaborative optimization of different ODs at different stations on the overall queue length and train operating costs of the rail line.

[0004] The optimization model of large-scale train timetables is a recognized NP-hard problem. Currently, the academic community generally considers algorithm design to be the most important and challenging aspect of the train timetable problem. Designing effective and reliable solution algorithms is of significant theoretical and practical importance for the practical application of optimization models. Due to the obvious discrete characteristics of the train timetable optimization problem, existing research on solution algorithms mainly focuses on three categories: customized or improved classical algorithms, optimization solver-based algorithms based on model modifications, and intelligent algorithms. Existing research has yielded many customized improvements to classical algorithms tailored to the characteristics of the models they have built, but these are all based on the specific features of their own models and have poor applicability to different optimization models. Algorithms relying on solvers often cannot guarantee computational efficiency in large-scale cases. Therefore, constructing new optimization models requires considering both the characteristics of the model itself and the computational scale requirements in order to design efficient and high-quality solution algorithms. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings and deficiencies of existing technologies and propose a method for collaborative optimization of subway train timetables and passenger flow origin-destination (OD) systems. For subway lines and stations with high passenger flow during peak hours, this method proactively controls the number of passengers entering the station and their arrival time in different OD directions from the perspective of optimizing passenger delay time and train operating costs. This is then jointly optimized with the subway train timetable. This approach can effectively reduce congestion and passenger delay time while optimizing costs, improving passenger travel efficiency and experience. It facilitates refined passenger flow management in subway operations, thereby enhancing the service quality and competitiveness of the subway system. Based on this, the branch-and-bound algorithm is customized and improved according to the theoretical characteristics of the collaborative optimization model, exploring effective ways to improve algorithm efficiency. This provides a reference for solving computational efficiency problems in large-scale subway networks and helps to promote the application of research results in practical large-scale train timetable problems.

[0006] To achieve the above objectives, the technical solution provided by this invention is: a method for collaborative optimization of subway train timetables and passenger flow origin-destination (OD) data, comprising the following steps:

[0007] S1. Obtain the expected arrival time and origin / destination of all passengers, with origin at O ​​and destination at D. Obtain the minimum train departure interval, train capacity, line stations, and length.

[0008] S2. Construct a collaborative optimization model for subway train timetables and passenger flow origin-destination (OD). This is a mixed integer programming model with constraints including departure interval constraints, delayed passenger number constraints, and passenger service constraints.

[0009] S3. Design an adaptive branch and bound algorithm to calculate the above collaborative optimization model and output the train departure plan, the successful boarding time period for all passengers, and the origin and destination points.

[0010] Furthermore, step S2 includes the following steps:

[0011] S21. Based on existing research and the characteristics of the subway, the following hypothesis is made:

[0012] The train stays at all stations for the same amount of time, maintains the same speed, and takes the same amount of time to pass two stations that are equidistant from each other. Based on this, the time at each station is shifted so that the arrival and departure times of a train are the same at all stations.

[0013] Given the known OD (Original Departure) volume, passengers with the same OD volume will board on a first-come, first-served basis.

[0014] The operating cost of each train trip is fixed and consistent.

[0015] During operating hours, there is a sufficient number of train carriages.

[0016] S22. One type of decision variable is the 0-1 decision variable x for train departure. js Another type is integer decision variables. and q uvj This refers to the number of passengers who are expected to arrive before time j but have not yet been assigned a successfully booked boarding time slot and are experiencing delays in the queue.

[0017] x js : 0-1 decision variable for train departure; equal to 1 indicates that the train departs from station s at time j; equal to 0 indicates that departure is not considered;

[0018] The number of passengers whose origin and destination points pass through station s before time j but have not yet been allocated a successfully booked boarding time slot.

[0019] q uvj This indicates the number of passengers (ODs) whose origin and destination are stations u and v, and who are expected to arrive before time j, but have not yet been assigned a time slot for their successfully booked boarding.

[0020] S23. Formulate constraints based on the decision variables. Each constraint includes departure interval constraints, delayed passenger number constraints, and passenger service constraints, mathematically expressed as follows:

[0021] The departure interval between two adjacent trains shall not be less than the minimum departure interval. j Its constraint expression is as follows:

[0022]

[0023] The train stops at every station and departs at the same time at all stations. Its constraint expression is as follows:

[0024]

[0025] At the initial moment, the number of delayed passengers at all stations is zero, and the constraint expression is as follows:

[0026]

[0027] At the initial moment, the number of delayed passengers (ODs) for all types of passengers is zero, and the constraint expression is as follows:

[0028]

[0029] If the train does not depart at time j, the number of passengers at the delayed section of station s is the sum of the number of passengers expected to arrive at and pass through station s during the time period [j-1,j]. If the train departs at time j, the number of passengers at the delayed section of station s is not less than the difference between the number of passengers at the delayed section of station s at time j-1 and the sum of the number of passengers expected to arrive at and pass through station s during the time period [j-1,j], minus the train's carriage capacity. The constraint expression is as follows:

[0030]

[0031] For passengers with origin and destination points u and v, the number of delays at time j is no greater than the sum of the number of delays at time j-1 and the number of expected arrivals (ODs) of passengers with origin and destination points u and v within the time period [j-1,j]. The constraint expression is as follows:

[0032]

[0033] The number of delayed passengers at station s at time j-1 is equal to the sum of the number of delayed passengers originating from and departing at station s, and its constraint expression is as follows:

[0034]

[0035] In the final operational moments The number of delays for passengers with destinations u and v is zero, and all passengers board the train. The constraint expression is as follows:

[0036]

[0037] The decision variables are constrained within different numerical ranges. The train departure variable is a 0-1 variable, while the station section delay queue number and passenger OD delay number are integers greater than or equal to zero. The constraint expressions are as follows:

[0038]

[0039]

[0040]

[0041] In the formula: A set representing station serial numbers;

[0042] s,u,v represent the station numbers.

[0043] Let S represent the set of upstream stations and the set of downstream stations of station S;

[0044] j represents the time point number within the operating time range.

[0045] j' represents a set of time points; j' represents the operating time range [j- j The time point number within [+1,J];

[0046] x j'1 This represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from the first station at time j'; a value of 0 indicates that departure is not considered.

[0047] x j1 The variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from the first station at time j; a value of 0 indicates that departure is not considered.

[0048] q 0s This indicates the number of passengers whose origin and destination points pass through station s before time 0 but have not yet been allocated a successfully booked boarding time slot.

[0049] q uv0 This indicates the number of passengers whose origin and destination are stations u and v, and who are expected to arrive before time 0, but have not yet been assigned a time slot for their successfully booked boarding.

[0050] This represents the number of passengers whose origin and destination points pass through station s before time j-1 but have not yet been allocated a successfully booked boarding time slot.

[0051] This indicates the desired arrival time at the upstream station within the reserved time period [j-1,j]. And you need to go to the station. The number of passenger cross-sections;

[0052] q uv,j- 1 indicates the number of passengers whose origin and destination are stations u and v, and who are expected to arrive before time j-1, but have not yet been assigned a time slot for their successfully booked boarding.

[0053] a uvj This represents the number of passengers who are expected to arrive at station u and station v within the reserved time period [j-1,j].

[0054] c represents the maximum number of passengers the train can accommodate;

[0055] S24. The objective function that minimizes the total delay time cost for passengers and the train departure cost is obtained as follows:

[0056]

[0057] w represents the time cost incurred by a single passenger for delaying a scheduled time period;

[0058] δ represents the duration of a time interval for a scheduled period.

[0059] Furthermore, the specific details of the branch and bound algorithm are as follows:

[0060] a. Theoretical property 1, theoretical property 2 and theoretical property 3 are proposed for subsequent solution;

[0061] Theoretical property 1: at time 1 If a feasible solution exists The solution is obtained if the following conditions are met. The optimal solution at time j1:

[0062] That is, train J1 departs at time J1;

[0063] That is, before the departure of train J1, the number of passengers delayed at each station shall not exceed the train's capacity.

[0064] That is, after train J1 departs, the number of delayed passengers at each station is zero;

[0065] For feasible solutions The variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from station s at time j1; a value of 0 indicates that departure is not considered.

[0066] This represents the number of passengers whose origin and destination points pass through station s before time j1 but have not yet been allocated a successfully booked boarding time slot.

[0067] This indicates the number of passengers (ODs) whose origin and destination are stations u and v, and who are expected to arrive before time j1, but have not yet been assigned a time slot for their successfully booked boarding.

[0068] Theoretical property 2: A feasible solution for the collaborative optimization model Time j1 and j2 are two adjacent train departure times, that is The feasible solution O is the optimal solution in the time range [j1,j2] if the following conditions are met:

[0069] The sum of delayed passenger origin-destination (OD) values ​​at all stations at time j1 is minimized, i.e.

[0070] When train J2 departs, the number of passengers delayed at all stations will not exceed the train's carriage capacity.

[0071]

[0072] Theoretical property 3: There are two feasible solutions in the time range [0,j1]. and If two solutions satisfy the following conditions, then the solution... Superior

[0073] untie The time elapsed from the last departure to time j1 is no less than [time value missing]. From the last departure to the time The elapsed time, i.e.

[0074] untie At time j1, the passenger OD (Original Delay) volume for each type of delay at all stations is no greater than [amount missing]. Right now

[0075]

[0076] untie Total cost incurred from time 0 to time j1 Comparison Total cost incurred from time 0 to time j1 Small, that is

[0077] In the formula: The variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from station s at time j1; a value of 0 indicates that departure is not considered.

[0078] The variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from station s at time j2; a value of 0 indicates that departure is not considered.

[0079] This indicates the number of passengers (ODs) whose origin and destination are stations u and v, and who are expected to arrive before time j1, but have not yet been assigned a time slot for their successfully booked boarding.

[0080] This represents the minimum sum of the number of delayed passengers at all stations at time j1;

[0081] This represents the number of passengers whose origin and destination points pass through station s before time j1 but have not yet been allocated a successfully booked boarding time slot.

[0082] For feasible solutions The variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from station s at time j; a value of 0 indicates that departure is not considered. This represents the number of passengers whose origin and destination points pass through station s before time j, but who have not yet been assigned a successfully booked boarding time slot. This represents the number of passengers whose origin and destination are stations u and v, respectively, and who are expected to arrive before time j but have not yet been assigned a time slot for their successfully booked boarding. Here, j∈[0,j1].

[0083] Solution The number of time intervals elapsed from the last departure to time j1;

[0084] Solution From the last departure to the time The number of time intervals that have elapsed;

[0085] b. Algorithm 1 and Algorithm 2 are proposed for subsequent solutions. Algorithm 1 is used to calculate the minimum sum of the number of delayed passengers at all stations and the corresponding delayed passenger OD scheme. Algorithm 2 is used to calculate the delayed passenger OD scheme with the minimum delay time cost.

[0086] The specific steps of Algorithm 1 are as follows:

[0087] For departure times at stations with oversaturation Assume the set of passengers whose reservations were successful when the train departs is OD. Delayed passenger OD set According to constraints The station section corresponding to the OD of passengers who have successfully booked their trains is as follows: The corresponding station cross-section for delayed passenger origin-destination (OD) is: According to the conservation of the sum of the origin-destination (OD) of passengers who successfully booked and the OD of delayed passengers, we have:

[0088]

[0089] In the formula: Indicates that the origin and destination are station u and station v, at time... The number of passengers whose arrival time was previously expected and who were delayed due to their successfully booked boarding time slots;

[0090] Indicates that the origin and destination are station u and station v, at time... The number of passengers whose arrival time was previously expected but has been delayed due to unallocated boarding time slots;

[0091] Indicates that the origin and destination are station u and station v, at time... The number of passengers whose arrival time was previously expected but has been delayed due to unallocated boarding time slots;

[0092] Indicates the time slot during the reservation period The number of vehicles expected to arrive at stations u and v from which they originate;

[0093] At the beginning of the algorithm, let

[0094] Step 11: Calculate the set of oversaturated stations Suppose there are k oversaturated stations, os={s1,s2,...,s k};

[0095] In the formula: s1, s2, ..., s k Indicates an oversaturated station;

[0096] Indicates at time The number of passengers whose origin and destination points are connected to station S and who were previously expected to arrive and were assigned to a successfully booked boarding time slot.

[0097] Step 12: Determine if there is an OD that passes through station k. If so, select the OD that passes through the fewest stations and set its origin and destination as o and d, respectively. Then proceed to Step 13; otherwise, set k = k-1 and re-execute Step 12.

[0098] In the formula: Indicates that the origin and destination are station o and station d, at time The number of passengers whose arrival time was previously expected and who were delayed due to their successfully booked boarding time slots;

[0099] Step 13: Update

[0100]

[0101]

[0102]

[0103]

[0104] In the formula: s i s represents an oversaturated station i ∈os;

[0105] Step 14: Determine if it is full If satisfied, then calculate. Output time The minimum value of the sum of delayed passengers at all stations q j And the corresponding delayed passenger OD set is End the algorithm, otherwise return to Step 11;

[0106] In the formula: Indicates at time The number of passengers whose origin and destination points pass through station S and who were expected to arrive but have not yet been assigned a successfully booked boarding time slot.

[0107] The specific steps of Algorithm 2 are as follows:

[0108] Step 21: Initialize j', let...

[0109] In the formula: This indicates the number of passengers whose origin and destination are stations u and v, and who are expected to arrive before time j1-1, but have not yet been assigned a time slot for their successfully booked boarding.

[0110] This represents the number of passengers whose origin and destination points pass through station s before time j1-1 but have not yet been allocated a successfully booked boarding time slot.

[0111] Step 22: If j' > j2, proceed to Step 23; otherwise, calculate.

[0112] In the formula: q uvj' This indicates the number of passengers (ODs) whose origin and destination are stations u and v, and who are expected to arrive before time j', but have not yet been assigned a time slot for their successfully booked boarding.

[0113] This represents the number of passengers whose origin and destination points pass through station s before time j', but who have not yet been assigned a successfully booked boarding time slot.

[0114] This represents the minimum number of passengers delayed at station s at time j'.

[0115]

[0116]

[0117]

[0118] Set j' = j' + 1, and re-execute Step 22;

[0119] In the formula: This represents the number of passengers who are expected to arrive at stations u and v within the reserved time period [j'-1,j'].

[0120] x j's This indicates a given train departure plan; 1 indicates the train departs from station s at time j'; 0 indicates no departure.

[0121] x j's The variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from station s at time j'; a value of 0 indicates that departure is not considered.

[0122] This indicates the desired arrival time at the upstream station within the reserved time period [j'-1,j']. And you need to go to the station. The number of passenger cross-sections;

[0123] This represents the minimum number of passengers delayed at station s at time j'-1.

[0124] Step 23: If Output For the time period [j1, j2], the minimum delay time cost given the departure plan is:

[0125]

[0126] The algorithm ends, and the passenger OD scheme is output.

[0127] if The current minimum delay time cost z is:

[0128]

[0129] Proceed to Step 24;

[0130] Step 24: Calculate j1”, j2”:

[0131]

[0132]

[0133] In the formula: j”1 represents the time point number within the operating time range [j1,j2];

[0134] j”2 represents the time point number within the operating time range [j”1,j2];

[0135] This represents the number of passengers whose origin and destination points pass through station s before time j”-1, who are expected to arrive but have not yet been assigned a successfully booked boarding time slot.

[0136] If j”2 does not exist, then let j”2 = j2; replace delayed passenger ODs passing through oversaturated station sections and other station sections with fewer passenger ODs passing through other station sections to reduce the impact of other sections, compare the total cost changes of the two, and update the delayed passenger OD scheme with the minimum cost. Set j1 = j”2, re-execute Step 24 until j”1 no longer exists, and output the result. For the time period [j1,j2], the minimum delay time cost under a given train departure plan is:

[0137]

[0138] Algorithm ends;

[0139] c. To facilitate the description of the search tree constructed by the customized branch and bound algorithm, the following variables are defined: let l represent the depth of the tree, at the root node l = 0, and the set of all nodes with depth l is... The set has N nodes. l The nth node of a tree of depth l is represented as (l, n), and each node contains the following information: the index of the parent node p. ln Train departure index x ln Time index j ln Delayed passenger OD volume Station delays in passenger volume Minimum number of passengers delayed at the station Total cumulative cost c ln The time interval h after train departure ln The upper and lower bounds of the node are and b ln The upper and lower bounds of the global boundary are respectively and B ;

[0140] In the formula: Indicates that the origin and destination are station u and station v, and at time j ln The number of passengers whose arrival time was previously expected but has been delayed due to unallocated boarding time slots;

[0141] Indicates at time j ln The number of passengers whose origin and destination points pass through station S and who were expected to arrive but have not yet been assigned a successfully booked boarding time slot.

[0142] Indicates at time jln The minimum number of passengers delayed at station s;

[0143] The constructed search tree employs a depth-first search strategy, and all nodes are stored in a local selection pool set. and global selection pool set In two different pools, Includes all child nodes of the current parent node. It includes all unpruned nodes; in addition, l0, n0, l1, and n1 are the tree depth of the parent node, the node number of the parent node, the depth of the child node, and the node number of the child node, respectively.

[0144] Furthermore, the specific steps of the branch and bound algorithm are as follows:

[0145] Step 1: Initialization settings: The algorithm starts at the root node (0,0), and the parent node index is p. 00 =1, root node train departure index x 00 =0, the time interval h after the train departs from the root node 00 = j , root node time index j 00 =0, Passenger volume at the root node station delay section Root node delays passenger OD volume Minimum number of passengers delayed at the root node station The cumulative total cost of the root node c 00 =0, lower bound of the root node b 00 =0, upper bound of the root node In addition, set l0 = 0, n0 = 0, B =0;

[0146] In the formula: q uv0 This indicates the number of passengers whose origin and destination are stations u and v, and who are expected to arrive before time 0, but have not yet been assigned a time slot for their successfully booked boarding.

[0147] This indicates the number of passengers whose origin and destination points pass through station s before time 0 but have not yet been allocated a successfully booked boarding time slot.

[0148] This represents the minimum number of passengers delayed at station s at time 0.

[0149] Step 2: Create and update child nodes: The tree depth of the child nodes is calculated as l1 = l0 + 1, based on the index of the time interval after train departure in the parent node (l0, n0). Create child nodes based on constraints (1) and (2). And update other information for the child nodes: child node train departure index. Time interval after train departure from sub-node Child node time index Child node delays passenger OD volume Passenger volume at sub-node stations Minimum number of passengers delayed at sub-node stations Cumulative total cost of child nodes Child node lower bound Upper bound of child nodes The calculation method is as follows:

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156] In the formula: Indicates the time index of the parent node;

[0157] Indicates the time index of the child node;

[0158] Indicates that the origin and destination are station u and station v, at time... The number of passengers whose arrival time was previously expected but has been delayed due to unallocated boarding time slots;

[0159] Indicates the time slot during the reservation period The number of passengers expected to arrive at stations u and v;

[0160] Indicates the time slot during the reservation period Internal expectation to reach the upstream station And you need to go to the station. The number of passenger cross-sections;

[0161] Indicates at time The minimum number of passengers delayed at station s;

[0162] Indicates at time The minimum number of passengers delayed at station s;

[0163] This represents the cumulative total cost of the parent node;

[0164] The lower bound of node (l1, n1) is in This is the sum of the train departure cost and delay time cost incurred from the root node to the current child node (l1, n1). This represents the future departure cost incurred by nodes after the child node (l1, n1). This represents the future delay time cost incurred by nodes after the child node (l1, n1);

[0165] To facilitate the calculation of the lower bound of the child node (l1, n1), according to the inequality... Calculation Convert to separate calculation and in: It is the theoretical minimum departure cost required to ensure that all passengers in the child node (l1,n1) can successfully make a reservation. The minimum delay time cost for all passengers following the child node (l1,n1) under the condition of operating with the minimum departure interval is calculated by Algorithm 2;

[0166] In the formula: Indicates at time The number of passengers whose origin and destination points pass through station S and who were expected to arrive but have not yet been assigned a successfully booked boarding time slot.

[0167] Indicates the time slot during the reservation period Internal expectation to reach the upstream station And you need to go to the station. The number of passenger cross-sections;

[0168] Upper Realm The calculation method is as follows: Starting from the current node, under the condition of satisfying constraints (1), (2) and the minimum departure interval, the minimum delay time cost and train departure cost of all subsequent passengers of the child node (l1,n1);

[0169] Subsequently, the nodes (l1, n1) that can generate feasible solutions are added to the local selection pool set. middle;

[0170] Step 3: Node Search Strategy: Select a new parent node for branching and update the global upper and lower bounds. Use a depth-first strategy in the node exploration strategy, provided that the node's time index j is within the range of the node being explored. lnThe final moment J has been reached, i.e., j ln =J, or the local selection pool set Empty, that is Under the depth-first strategy, if the branch can no longer branch, the node ends the branch and selects from the global selection pool set. Select lower bound b ln The smallest node is selected as the next new parent node for branching; if the above conditions are not met, the node with the smallest lower bound from the local selection pool is selected as the next parent node.

[0171]

[0172] After selecting the next parent node, the local selection pool set will be... All unexplored nodes are added to the global selection pool set. Set up local selection pool Clear, thus Add the node to the local selection pool set while waiting for the next branch. In the middle, update the global selection pool set. Local selection pool set and global upper and lower bounds and B ;

[0173]

[0174] In the formula: Indicates the upper bound of the node;

[0175] Step 4: Return to Step 2 based on the newly selected parent node (l0, n0); the algorithm ends if the difference between the global upper and lower bounds reaches the given convergence value or the algorithm runtime reaches the limit.

[0176] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0177] 1. This invention designs a method for collaboratively optimizing train timetables and passenger flow origin-destination (OD) to effectively reduce congestion and passenger delays while optimizing costs, thereby improving passenger travel efficiency and experience, and ultimately enhancing the service quality and competitiveness of the subway system.

[0178] 2. This invention combines the theoretical characteristics of the subway timetable and passenger flow OD control collaborative optimization model to explore effective ways to improve algorithm efficiency. It can provide a certain reference for solving the computational efficiency problem of large-scale subway networks and help to promote the application of research results in practical large-scale train timetable problems.

[0179] In summary, this invention can effectively solve the problems of platform congestion and long waiting time for passengers during peak hours by utilizing accurate spatiotemporal distribution information of all passengers. Attached Figure Description

[0180] Figure 1 This is a flowchart illustrating the design process of subway train timetables and passenger flow OD collaborative optimization schemes during peak hours.

[0181] Figure 2 This is a flowchart illustrating the construction process of a collaborative optimization model for subway train timetables and passenger flow origin-destination (OD) during peak hours.

[0182] Figure 3 This is a flowchart of a customized branch and bound algorithm. Detailed Implementation

[0183] The present invention will be further described below with reference to specific embodiments.

[0184] like Figure 1 As shown in the figure, this embodiment provides a method for collaborative optimization of subway train timetables and passenger flow origin-destination (OD) data. The steps are as follows:

[0185] S1. Obtain the expected arrival time and origin / destination of all passengers, with origin at O ​​and destination at D. Obtain the minimum train departure interval, train capacity, line stations, and length.

[0186] S2. Construct a collaborative optimization model for subway train timetables and passenger flow origin-destination (OD) patterns. This is a mixed-integer programming model with constraints including departure interval constraints, delayed passenger number constraints, and passenger service constraints. Figure 2 As shown, it includes the following steps:

[0187] S21. Based on existing research and the characteristics of the subway, the following hypothesis is made:

[0188] The train stays at all stations for the same amount of time, maintains the same speed, and takes the same amount of time to pass two stations that are equidistant from each other. Based on this, the time at each station is shifted so that the arrival and departure times of a train are the same at all stations.

[0189] Given the known OD (Original Departure) volume, passengers with the same OD volume will board on a first-come, first-served basis.

[0190] The operating cost of each train trip is fixed and consistent.

[0191] During operating hours, there is a sufficient number of train carriages.

[0192] S22. One type of decision variable is the 0-1 decision variable x for train departure. js Another type is integer decision variables. and q uvjThis refers to the number of passengers who are expected to arrive before time j but have not yet been assigned a successfully booked boarding time slot and are experiencing delays in the queue.

[0193] x js : 0-1 decision variable for train departure; equal to 1 indicates that the train departs from station s at time j; equal to 0 indicates that departure is not considered;

[0194] The number of passengers whose origin and destination points pass through station s before time j but have not yet been allocated a successfully booked boarding time slot.

[0195] q uvj This indicates the number of passengers (ODs) whose origin and destination are stations u and v, and who are expected to arrive before time j, but have not yet been assigned a time slot for their successfully booked boarding.

[0196] S23. Formulate constraints based on the decision variables. Each constraint includes departure interval constraints, delayed passenger number constraints, and passenger service constraints, mathematically expressed as follows:

[0197] The departure interval between two adjacent trains shall not be less than the minimum departure interval. j Its constraint expression is as follows:

[0198]

[0199] The train stops at every station and departs at the same time at all stations. Its constraint expression is as follows:

[0200]

[0201] At the initial moment, the number of delayed passengers at all stations is zero, and the constraint expression is as follows:

[0202]

[0203] At the initial moment, the number of delayed passengers (ODs) for all types of passengers is zero, and the constraint expression is as follows:

[0204]

[0205] If the train does not depart at time j, the number of passengers at the delayed section of station s is the sum of the number of passengers expected to arrive at and pass through station s during the time period [j-1,j]. If the train departs at time j, the number of passengers at the delayed section of station s is not less than the difference between the number of passengers at the delayed section of station s at time j-1 and the sum of the number of passengers expected to arrive at and pass through station s during the time period [j-1,j], minus the train's carriage capacity. The constraint expression is as follows:

[0206]

[0207] For passengers with origin and destination points u and v, the number of delays at time j is no greater than the sum of the number of delays at time j-1 and the number of expected arrivals (ODs) of passengers with origin and destination points u and v within the time period [j-1,j]. The constraint expression is as follows:

[0208]

[0209] The number of delayed passengers at station s at time j-1 is equal to the sum of the number of delayed passengers originating from and departing at station s, and its constraint expression is as follows:

[0210]

[0211] In the final operational moments The number of delays for passengers with destinations u and v is zero, and all passengers board the train. The constraint expression is as follows:

[0212]

[0213] The decision variables are constrained within different numerical ranges. The train departure variable is a 0-1 variable, while the station section delay queue number and passenger OD delay number are integers greater than or equal to zero. The constraint expressions are as follows:

[0214]

[0215]

[0216]

[0217] In the formula: A set representing station serial numbers;

[0218] s,u,v represent the station numbers.

[0219] Let S represent the set of upstream stations and the set of downstream stations of station S;

[0220] j represents the time point number within the operating time range.

[0221] j' represents a set of time points; j' represents the operating time range [j- j The time point number within [+1,J];

[0222] x j'1 This represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from the first station at time j'; a value of 0 indicates that departure is not considered.

[0223] x j1 The variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from the first station at time j; a value of 0 indicates that departure is not considered.

[0224] q 0s This indicates the number of passengers whose origin and destination points pass through station s before time 0 but have not yet been allocated a successfully booked boarding time slot.

[0225] q uv0 This indicates the number of passengers whose origin and destination are stations u and v, and who are expected to arrive before time 0, but have not yet been assigned a time slot for their successfully booked boarding.

[0226] This represents the number of passengers whose origin and destination points pass through station s before time j-1 but have not yet been allocated a successfully booked boarding time slot.

[0227] This indicates the desired arrival time at the upstream station within the reserved time period [j-1,j]. And you need to go to the station. The number of passenger cross-sections;

[0228] q uv,j- 1 indicates the number of passengers whose origin and destination are stations u and v, and who are expected to arrive before time j-1, but have not yet been assigned a time slot for their successfully booked boarding.

[0229] a uvj This represents the number of passengers who are expected to arrive at station u and station v within the reserved time period [j-1,j].

[0230] c represents the maximum number of passengers the train can accommodate;

[0231] S24. The objective function that minimizes the total delay time cost for passengers and the train departure cost is obtained as follows:

[0232]

[0233] w represents the time cost incurred by a single passenger for delaying a scheduled time period;

[0234] δ represents the duration of a time interval for a scheduled period.

[0235] S3. Design an adaptive branch and bound algorithm to calculate the above collaborative optimization model and output the train departure plan, the successful boarding time periods for all passengers, and the origin and destination points. For example... Figure 3 As shown, the specific details of the branch and bound algorithm are as follows:

[0236] a. Theoretical property 1, theoretical property 2 and theoretical property 3 are proposed for subsequent solution;

[0237] Theoretical property 1: at time 1 If a feasible solution exists The solution is obtained if the following conditions are met. The optimal solution at time j1:

[0238] That is, train J1 departs at time J1;

[0239] That is, before the departure of train J1, the number of passengers delayed at each station shall not exceed the train's capacity.

[0240] That is, after train J1 departs, the number of delayed passengers at each station is zero;

[0241] For feasible solutions The variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from station s at time j1; a value of 0 indicates that departure is not considered.

[0242] This represents the number of passengers whose origin and destination points pass through station s before time j1 but have not yet been allocated a successfully booked boarding time slot.

[0243] This indicates the number of passengers (ODs) whose origin and destination are stations u and v, and who are expected to arrive before time j1, but have not yet been assigned a time slot for their successfully booked boarding.

[0244] Theoretical property 2: A feasible solution for the collaborative optimization model Time j1 and j2 are two adjacent train departure times, that is The feasible solution O is the optimal solution in the time range [j1,j2] if the following conditions are met:

[0245] The sum of delayed passenger origin-destination (OD) values ​​at all stations at time j1 is minimized, i.e.

[0246] When train J2 departs, the number of passengers delayed at all stations will not exceed the train's carriage capacity.

[0247]

[0248] Theoretical property 3: There are two feasible solutions in the time range [0,j1]. and If two solutions satisfy the following conditions, then the solution... Superior

[0249] untie The time elapsed from the last departure to time j1 is no less than [time value missing]. From the last departure to the time The elapsed time, i.e.

[0250] untie At time j1, the passenger OD (Original Delay) volume for each type of delay at all stations is no greater than [amount missing]. Right now

[0251] untie Total cost incurred from time 0 to time j1 Comparison Total cost incurred from time 0 to time j1 Small, that is

[0252] In the formula: x j1s The variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from station s at time j1; a value of 0 indicates that departure is not considered.

[0253] xj2s represents a 0-1 decision variable for train departure; 1 indicates that the train departs from station s at time j2; 0 indicates that departure is not considered.

[0254] q uvj1 This indicates the number of passengers (ODs) whose origin and destination are stations u and v, and who are expected to arrive before time j1, but have not yet been assigned a time slot for their successfully booked boarding.

[0255] This represents the minimum sum of the number of delayed passengers at all stations at time j1;

[0256] This represents the number of passengers whose origin and destination points pass through station s before time j1 but have not yet been allocated a successfully booked boarding time slot.

[0257] For feasible solutions The variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from station s at time j; a value of 0 indicates that departure is not considered. This represents the number of passengers whose origin and destination points pass through station s before time j, but who have not yet been assigned a successfully booked boarding time slot. This represents the number of passengers whose origin and destination are stations u and v, respectively, and who are expected to arrive before time j but have not yet been assigned a time slot for their successfully booked boarding. Here, j∈[0,j1].

[0258] Solution The number of time intervals elapsed from the last departure to time j1;

[0259] Solution From the last departure to the time The number of time intervals that have elapsed;

[0260] b. Algorithm 1 and Algorithm 2 are proposed for subsequent solutions. Algorithm 1 is used to calculate the minimum sum of the number of delayed passengers at all stations and the corresponding delayed passenger OD scheme. Algorithm 2 is used to calculate the delayed passenger OD scheme with the minimum delay time cost.

[0261] The specific steps of Algorithm 1 are as follows:

[0262] For departure times at stations with oversaturation Assume the set of passengers whose reservations were successful when the train departs is OD. Delayed passenger OD set According to constraints The station section corresponding to the OD of passengers who have successfully booked their trains is as follows: The corresponding station cross-section for delayed passenger origin-destination (OD) is: According to the conservation of the sum of the origin-destination (OD) of passengers who successfully booked and the OD of delayed passengers, we have:

[0263]

[0264] In the formula: Indicates that the origin and destination are station u and station v, at time... The number of passengers whose arrival time was previously expected and who were delayed due to their successfully booked boarding time slots;

[0265] Indicates that the origin and destination are station u and station v, at time... The number of passengers whose arrival time was previously expected but has been delayed due to unallocated boarding time slots;

[0266] Indicates that the origin and destination are station u and station v, at time... The number of passengers whose arrival time was previously expected but has been delayed due to unallocated boarding time slots;

[0267] Indicates the time slot during the reservation period The number of vehicles expected to arrive at stations u and v from which they originate;

[0268] At the beginning of the algorithm, let

[0269] Step 11: Calculate the set of oversaturated stations Suppose there are k oversaturated stations, os={s1,s2,...,s k};

[0270] In the formula: s1, s2, ..., s k Indicates an oversaturated station;

[0271] Indicates at time The number of passengers whose origin and destination points are connected to station S and who were previously expected to arrive and were assigned to a successfully booked boarding time slot.

[0272] Step 12: Determine if there is an OD that passes through station k. If so, select the OD that passes through the fewest stations and set its origin and destination as o and d, respectively. Then proceed to Step 13; otherwise, set k = k-1 and re-execute Step 12.

[0273] In the formula: Indicates that the origin and destination are station o and station d, at time The number of passengers whose arrival time was previously expected and who were delayed due to their successfully booked boarding time slots;

[0274] Step 13: Update

[0275]

[0276]

[0277]

[0278]

[0279] In the formula: s i s represents an oversaturated station i ∈os;

[0280] Step 14: Determine if it is full If satisfied, then calculate. Output time The minimum value of the sum of delayed passengers at all stations q j And the corresponding delayed passenger OD set is End the algorithm, otherwise return to Step 11;

[0281] In the formula: Indicates at time The number of passengers whose origin and destination points pass through station S and who were expected to arrive but have not yet been assigned a successfully booked boarding time slot.

[0282] The specific steps of Algorithm 2 are as follows:

[0283] Step 21: Initialize j', let...

[0284] In the formula: This indicates the number of passengers whose origin and destination are stations u and v, and who are expected to arrive before time j1-1, but have not yet been assigned a time slot for their successfully booked boarding.

[0285] This represents the number of passengers whose origin and destination points pass through station s before time j1-1 but have not yet been allocated a successfully booked boarding time slot.

[0286] Step 22: If j' > j2, proceed to Step 23; otherwise, calculate.

[0287] In the formula: q uvj' This indicates the number of passengers (ODs) whose origin and destination are stations u and v, and who are expected to arrive before time j', but have not yet been assigned a time slot for their successfully booked boarding.

[0288] This represents the number of passengers whose origin and destination points pass through station s before time j', but who have not yet been assigned a successfully booked boarding time slot.

[0289] This represents the minimum number of passengers delayed at station s at time j'.

[0290]

[0291]

[0292]

[0293] Set j' = j' + 1, and re-execute Step 22;

[0294] In the formula: a uvj' This represents the number of passengers who are expected to arrive at stations u and v within the reserved time period [j'-1,j'].

[0295] x j's This indicates a given train departure plan; 1 indicates the train departs from station s at time j'; 0 indicates no departure.

[0296] x j'sThe variable represents a 0-1 decision variable for train departure; a value of 1 indicates that the train departs from station s at time j'; a value of 0 indicates that departure is not considered.

[0297] This indicates the desired arrival time at the upstream station within the reserved time period [j'-1,j']. And you need to go to the station. The number of passenger cross-sections;

[0298] This represents the minimum number of passengers delayed at station s at time j'-1.

[0299] Step 23: If Output For the time period [j1, j2], the minimum delay time cost given the departure plan is:

[0300]

[0301] The algorithm ends, and the passenger OD scheme is output.

[0302] if The current minimum delay time cost z is:

[0303]

[0304] Proceed to Step 24;

[0305] Step 24: Calculate j”1, j”2:

[0306]

[0307]

[0308] In the formula: j”1 represents the time point number within the operating time range [j1,j2];

[0309] j”2 represents the time point number within the operating time range [j”1,j2];

[0310] This represents the number of passengers whose origin and destination points pass through station s before time j”-1, who are expected to arrive but have not yet been assigned a successfully booked boarding time slot.

[0311] If j”2 does not exist, then let j”2 = j2; replace delayed passenger ODs passing through oversaturated station sections and other station sections with fewer passenger ODs passing through other station sections to reduce the impact of other sections, compare the total cost changes of the two, and update the delayed passenger OD scheme with the minimum cost. Set j1 = j”2, re-execute Step 24 until j”1 no longer exists, and output the result. For the time period [j1,j2], the minimum delay time cost under a given train departure plan is:

[0312]

[0313] Algorithm ends;

[0314] c. To facilitate the description of the search tree constructed by the customized branch and bound algorithm, the following variables are defined: let l represent the depth of the tree, at the root node l = 0, and the set of all nodes with depth l is... The set has N nodes. l The nth node of a tree of depth l is represented as (l, n), and each node contains the following information: the index of the parent node p. ln Train departure index x ln Time index j ln Delayed passenger OD volume Station delays in passenger volume Minimum number of passengers delayed at the station Total cumulative cost c ln The time interval h after train departure ln The upper and lower bounds of the node are and b ln The upper and lower bounds of the global boundary are respectively and B ;

[0315] In the formula: Indicates that the origin and destination are station u and station v, and at time j ln The number of passengers whose arrival time was previously expected but has been delayed due to unallocated boarding time slots;

[0316] Indicates at time j ln The number of passengers whose origin and destination points pass through station S and who were expected to arrive but have not yet been assigned a successfully booked boarding time slot.

[0317] Indicates at time j ln The minimum number of passengers delayed at station s;

[0318] The constructed search tree employs a depth-first search strategy, and all nodes are stored in a local selection pool set. and global selection pool set In two different pools, Includes all child nodes of the current parent node. It includes all unpruned nodes; in addition, l0, n0, l1, and n1 are the tree depth of the parent node, the node number of the parent node, the depth of the child node, and the node number of the child node, respectively.

[0319] Specifically, the steps of the customized branch and bound algorithm are as follows:

[0320] Step 1: Initialization settings: The algorithm starts at the root node (0,0), and the parent node index is p. 00 =1, root node train departure index x 00 =0, the time interval h after the train departs from the root node 00 = j , root node time index j 00 =0, Passenger volume at the root node station delay section Root node delays passenger OD volume Minimum number of passengers delayed at the root node station The cumulative total cost of the root node c 00 =0, lower bound of the root node b 00 =0, upper bound of the root node In addition, set l0 = 0, n0 = 0, B =0;

[0321] In the formula: q uv0 This indicates the number of passengers whose origin and destination are stations u and v, and who are expected to arrive before time 0, but have not yet been assigned a time slot for their successfully booked boarding.

[0322] This indicates the number of passengers whose origin and destination points pass through station s before time 0 but have not yet been allocated a successfully booked boarding time slot.

[0323] This represents the minimum number of passengers delayed at station s at time 0.

[0324] Step 2: Create and update child nodes: The tree depth of the child nodes is calculated as l1 = l0 + 1, based on the index of the time interval after train departure in the parent node (l0, n0). Create child nodes based on constraints (1) and (2). And update other information for the child nodes: child node train departure index. Time interval after train departure from sub-node Child node time index Child node delays passenger OD volume Passenger volume at sub-node stations Minimum number of passengers delayed at sub-node stations Cumulative total cost of child nodes Child node lower bound Upper bound of child nodes The calculation method is as follows:

[0325]

[0326]

[0327]

[0328]

[0329]

[0330]

[0331] In the formula: Indicates the time index of the parent node;

[0332] Indicates the time index of the child node;

[0333] Indicates that the origin and destination are station u and station v, at time... The number of passengers whose arrival time was previously expected but has been delayed due to unallocated boarding time slots;

[0334] Indicates the time slot during the reservation period The number of passengers expected to arrive at stations u and v;

[0335] Indicates the time slot during the reservation period Internal expectation to reach the upstream station And you need to go to the station. The number of passenger cross-sections;

[0336] Indicates at time The minimum number of passengers delayed at station s;

[0337] Indicates at time The minimum number of passengers delayed at station s;

[0338] This represents the cumulative total cost of the parent node;

[0339] The lower bound of node (l1, n1) is in This is the sum of the train departure cost and delay time cost incurred from the root node to the current child node (l1, n1). This represents the future departure cost incurred by nodes after the child node (l1, n1). This represents the future delay time cost incurred by nodes after the child node (l1, n1);

[0340] To facilitate the calculation of the lower bound of the child node (l1, n1), according to the inequality... Calculation Convert to separate calculation and in: It is the theoretical minimum departure cost required to ensure that all passengers in the child node (l1,n1) can successfully make a reservation. The minimum delay time cost for all passengers following the child node (l1,n1) under the condition of operating with the minimum departure interval is calculated by Algorithm 2;

[0341] In the formula: Indicates at time The number of passengers whose origin and destination points pass through station S and who were expected to arrive but have not yet been assigned a successfully booked boarding time slot.

[0342] Indicates the time slot during the reservation period Internal expectation to reach the upstream station And you need to go to the station. The number of passenger cross-sections;

[0343] Upper Realm The calculation method is as follows: Starting from the current node, under the condition of satisfying constraints (1), (2) and the minimum departure interval, the minimum delay time cost and train departure cost of all subsequent passengers of the child node (l1,n1);

[0344] Subsequently, the nodes (l1, n1) that can generate feasible solutions are added to the local selection pool set. middle;

[0345] Step 3: Node Search Strategy: Select a new parent node for branching and update the global upper and lower bounds. Use a depth-first strategy in the node exploration strategy, provided that the node's time index j is within the range of the node being explored. ln The final moment J has been reached, i.e., j ln =J, or the local selection pool set Empty, that is Under the depth-first strategy, if the branch can no longer branch, the node ends the branch and selects from the global selection pool set. Select lower bound b lnThe smallest node is selected as the next new parent node for branching; if the above conditions are not met, the node with the smallest lower bound from the local selection pool is selected as the next parent node.

[0346]

[0347] After selecting the next parent node, the local selection pool set will be... All unexplored nodes are added to the global selection pool set. Set up local selection pool Clear, thus Add the node to the local selection pool set while waiting for the next branch. In the middle, update the global selection pool set. Local selection pool set and global upper and lower bounds and B ;

[0348]

[0349] In the formula: Indicates the upper bound of the node;

[0350] Step 4: Return to Step 2 based on the newly selected parent node (l0, n0); the algorithm ends if the difference between the global upper and lower bounds reaches the given convergence value or the algorithm runtime reaches the limit.

[0351] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Therefore, any changes made in accordance with the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for coordinated optimization of metro train timetable and passenger flow OD, characterized in that, Comprising the following steps: S1, obtaining the expected arrival time period and origin-destination point of all passengers, the origin point is O and the destination point is D, obtaining the minimum train departure interval, train capacity, line station and length; S2, constructing a subway train timetable and passenger flow OD collaborative optimization model, the collaborative optimization model is a mixed integer programming model, the constraint conditions include departure interval constraint, delayed passenger quantity constraint and passenger service constraint, comprising the following steps: S21, making assumptions based on existing research and the characteristics of the subway, as follows: The train stays at all stations for the same length of time, the train maintains the same speed while running, and it takes the same time to travel through two stations with the same distance; based on this, the station time is offset to make the arrival and departure time of a train at all stations the same; The passenger flow OD quantity is known, and the same passenger flow OD passengers adopt the principle of first come first served; The cost of each train operation is fixed and consistent; The number of train bottoms is sufficient within the operating time; S22, the decision variable is a 0-1 decision variable x of train departure js , another is an integer decision variable and q uvj , is the passenger delay queuing quantity expected to arrive before time j but not assigned to the reservation successful boarding time period. x js : 0-1 decision variable of train departure; equal to 1 indicates that the train departs from station s at time j; equal to 0 indicates that departure is not considered; the number of passengers at the origin and destination of the passenger who is expected to arrive before time j but has not been assigned to a successful reservation boarding time period yet, passing through the station s; q uvj OD number of passengers whose origin and destination are station u and station v, who are expected to arrive at station v before time j, but have not been assigned to the reservation successful boarding time period delay yet; S23, formulating constraint conditions according to the decision variables, each constraint condition includes a departure interval constraint, a delayed passenger quantity constraint and a passenger service constraint, which are mathematically expressed as follows: The interval between two adjacent trains is not less than the minimum interval The constraint expression is as follows: The train stops at each station, and the departure time at all stations is the same, and its constraint expression is as follows: At the initial time, the delayed passenger quantity of all stations is zero, and its constraint expression is as follows: At the initial time, the OD quantity of each type of delayed passenger is zero, and its constraint expression is as follows: If the train does not depart at time j, the delayed section passenger quantity of station s is the sum of the delayed section passenger quantities that are expected to arrive in the time period [j-1, j] and pass through station s; if the train departs at time j, the delayed section passenger quantity of station s is not less than the difference between the delayed section passenger quantity of station s at time j-1 and the sum of the delayed section passenger quantities that are expected to arrive in the time period [j-1, j] and pass through station s minus the train compartment capacity, and its constraint expression is as follows: The number of delayed passengers with origin-destination point u and v at time j is not greater than the number of delayed passengers at time j-1 and the sum of the passenger OD quantities that are expected to arrive in the time period [j-1, j] and have origin-destination point u and v, and its constraint expression is as follows: The delayed section passenger quantity of station s at time j-1 is equal to the sum of the delayed passenger OD quantities that pass through station s, and its constraint expression is as follows: At the last operation moment The number of delays for passengers OD u and v is zero, and all passengers are on board. The constraint expression is as follows: The decision variable is constrained in different numerical ranges, the train departure variable is a 0-1 variable, the section delayed queue quantity of the station and the delayed quantity of the passenger OD are integers greater than or equal to zero, and its constraint expression is as follows: In the formulae: denotes a set of station numbers; s, u, v represent the sequence number of the station, representing an upstream set of stations and a downstream set of stations of the station s; j denotes the time point sequence number within the operating time range, set of time points; j' denotes the operating time range time point index within the operating time range x j'1 Xi,j' represents the train departure 0-1 decision variable; equal to 1 indicates that the train departs at the first station at time j'; equal to 0 indicates that departure is not considered; x j1 0-1 decision variable representing the departure of a train; equal to 1 if the train departs at the first station at time j; equal to 0 if the departure is not considered; q 0s the number of passengers expected to arrive at the station s before time 0 but not yet assigned to a successful boarding time interval; q uv0 OD number of passengers whose origin and destination are stations u and v, who are expected to arrive at station u before time 0, but have not been assigned a reservation success boarding time period delay; the number of passengers expected to arrive at the station s before time j-1 but not yet assigned to a successful boarding time interval of the reservation; represents the number of passengers expected to arrive at the upstream station during the reservation period [j-1, j] and who want to go to the station ; q uv,j-1 OD number of passengers whose origin and destination are stations u and v, and who are expected to arrive at station v before time j-1, but have not been assigned to a reservation success boarding time period delay; a uvj represents the number of passengers expected to arrive in the reservation period [j-1, j] and having station u and station v as the origin and destination points; c represents the maximum number of passengers that the train can accommodate; S24, obtaining the objective function of minimizing the total delayed time cost of passengers and the train departure cost as follows: w represents the time cost generated by a single passenger delaying a reservation time period; δ represents the time interval length of a reservation time period; S3, designing an adaptive branch and bound algorithm to calculate the above collaborative optimization model, and outputting the train departure scheme, the successful boarding time period and origin-destination point of all passengers.

2. The method for coordinated optimization of metro train timetable and passenger flow OD according to claim 1, characterized in that, The specific case of the branch and bound algorithm is as follows: a. Theoretical characteristics 1, 2 and 3 are proposed for subsequent solving; Theoretical property 1 : At time If there is a feasible solution Satisfying the following condition, the solution Is the optimal solution at time j1 : i.e. at time j1 the train departs; That is, the number of passengers delayed at each station does not exceed the train capacity at the section before the train departs at time j1. That is, the number of delayed passengers OD at each station is zero after the train departs at time j1. For feasible solution 0-1 decision variable representing the departure of a train; equal to 1 indicates that a train departs from station s at time j1; equal to 0 indicates that departure is not considered; the number of passengers expected to arrive at the station s before the time j1 but not yet assigned to a successful boarding time interval of the reservation; ODj1uv represents the number of passengers with the origin and destination of station u and station v, who are expected to arrive at station v before time j1, but have not been assigned to the reservation successful boarding time period delay. Theoretical property 2: For a feasible solution of the collaborative optimization model The time instants j1 and j2 are two adjacent train departure times, i.e. When the following condition is satisfied, the feasible solution O is an optimal solution in the time range [j1, j2]: The sum of the passenger OD amounts at all stations at time j1 is minimized, i.e. At the time j2 when the train departs, the sectional passenger quantity of all stations delayed does not exceed the train compartment capacity, that is Theory property 3: In the time range [0, j1], there are two feasible solutions and If both solutions satisfy the following condition, the solution is better than Solution The time elapsed from the last departure to time j1 is not less than The time elapsed from the last departure to time j1, i.e. Solution At time j1, the OD volume of each type of delay at each station is not greater than That is Solution Total cost incurred from time 0 to time j1 Solution Total cost incurred from time 0 to time j1 Solution In the formula: Xi,j1represents the 0-1 decision variable of train departure; equal to 1 indicates that the train departs from station s at time j1; equal to 0 indicates that the departure is not considered; 0-1 decision variable representing the departure of a train; equal to 1 if a train departs from station s at time j2; equal to 0 if departure is not considered; ODj1uv represents the number of passengers whose origin and destination are stations u and v, who are expected to arrive at station v before time j1, but have not been assigned to a reservation success boarding time period yet. denotes the minimum value of the sum of the number of delayed passengers at all stations at time j1; the number of passengers expected to arrive at the station s before the time j1 but not yet assigned to a successful boarding time interval of the reservation; 0-1 decision variable representing train departure; equal to 1 indicates that train departs from station s at time j; equal to 0 indicates no departure is considered; 0-1 decision variable representing train departure; equal to 1 indicates that train departs from station s at time j; equal to 0 indicates no departure is considered; denotes the number of passengers of OD pair (u, v) who are expected to arrive at station s before time j but have not been assigned to a reserved boarding time interval yet; denotes the number of passengers of OD pair (u, v) who are expected to arrive at station s before time j but have not been assigned to a reserved boarding time interval yet; representation solution the number of time intervals elapsed from the last departure to time j1; representation solution from the last departure to the time number of elapsed time intervals; b. Algorithms 1 and 2 are proposed for subsequent solving, Algorithm 1 is used to calculate the minimum sum of delayed passenger quantity of all stations and the corresponding delayed passenger OD scheme, and Algorithm 2 is used to calculate the delayed passenger OD scheme with the minimum delay time cost; The specific steps of Algorithm 1 are as follows: Departure time for the case of over-saturated station Let OD set of passengers who successfully get on the train at departure time be OD set of delayed passengers is According to the constraint Station section corresponding to OD of passengers who successfully get on the train is Station section corresponding to OD of delayed passengers is According to the conservation of the sum of OD of passengers who successfully get on the train and OD of delayed passengers, we have: In the formula: denotes the origin and destination points are stations u and v, and the OD number of passengers expected to arrive at station v before time t+T and assigned to the reservation success boarding time period delay. denotes the number of passengers OD whose expected arrival time is before time but whose OD has not been assigned to a reservation success boarding time period yet. denotes the number of passengers OD whose expected arrival time is before time but whose OD number has not been assigned to the reservation success boarding time period delay. representing the number of passengers expected to arrive in the reservation time period and having station u and station v as the origin and destination points, respectively; representing the number of passengers expected to arrive in the reservation time period and having station u and station v as the origin and destination points, respectively; At the beginning of the algorithm, let Step 11: Calculate the set of oversaturated stations Let k be the number of oversaturated stations, os = {s1, s2,..., sk} be the set of oversaturated stations, and os_size be the size of the set of oversaturated stations. k} wherein: s1, s2,..., s k over-saturated stations; represents the number of passengers expected to arrive at time the number of passenger origin-destination pairs passing through the section of the station s that are expected to arrive before time t and are assigned to the reservation success boarding time period; Step 12: judge whether there is OD passing k stations, if yes, select OD passing the least stations from them and set the origin and destination as o and d, and go to Step 13, otherwise let k=k-1 and re-execute Step 12. Step 13: judge whether k=0, if yes, go to Step 14, otherwise let k=k-1 and re-execute Step 12. Step 14: judge whether the number of ODs is less than 2, if yes, go to Step 15, otherwise let In the formula: represents the number of passengers OD expected to arrive at the station before the time and assigned to the reservation success boarding time period delay, with the starting and ending points being stations o and d. Step 13: Update where: s i represents a supersaturated station, s i ∈os; Step 14: judge whether If yes, calculate Output time The minimum value of the sum of the number of delayed passengers at all stations And the corresponding delayed passenger OD set is End the algorithm, otherwise go back to Step 11; In the formula: represents the number of passengers who are expected to arrive at the time before the scheduled arrival time but have not been assigned to the successful reservation boarding time period, and the number of passengers who pass through the station s at the delay section of the passenger origin-destination point. The specific steps of Algorithm 2 are as follows: Step 21: Initialize j', let j' = 0 In the formula: represents the number of passengers OD who are expected to arrive at station before time j1-1, but have not been assigned to the reservation successful boarding time period delay with the starting and ending points being stations u and v; the number of passengers expected to arrive at the station s before time j1-1 but not yet assigned to a successful boarding time interval; Step 22: If j' > j2, go to Step 23, otherwise compute In the formula: q uvj' represents the number of passengers OD who are expected to arrive at station before time j', but have not been assigned to the reservation successful boarding time period delay, with the starting and ending points being stations u and v. the number of passengers expected to pass through station s at the delay section before time j' but not yet assigned to a successful pick-up time slot of the reservation; denotes the minimum value of the cross-sectional number of passengers delayed at station s at time j'; Let j'=j'+1, re-execute Step 22; wherein: a uvj' represents the number of passengers expected to arrive in the reservation period [j'-l, j'] and having the origin station u and the destination station v; x j's 1 if the train departs from station s at time j'; 0 if the train does not depart; x j's 0-1 decision variable representing the departure of a train; equal to 1 indicates that a train departs at time j' from station s; equal to 0 indicates that no departure is considered; represents the number of passengers expected to arrive at the upstream station during the reservation period [j'-l, j'] and who want to go to the station ; Minj'1(s) represents the minimum value of the cross-sectional passenger number at station s at time j'-1; Step 23: If Output The minimum delay time cost under the given departure plan in the time period [j1, j2] is: algorithm ends, output passenger OD solution If The current minimum delay time cost z is: Go to Step 24; Step 24: Calculate j1", j"2: In the formula: j"1 represents the time point sequence number in the operation time range [j1, j2]; j"2 represents the time point sequence number in the operation time range [j1", j2]; the number of passengers expected to arrive at the station s before time j" - 1 but not yet assigned to a successful boarding time interval of the reservation; If j"2 does not exist, let j"2 = j2; replace the OD of the delayed passengers passing through the oversaturated station section and the OD of the passengers passing through other station sections with the OD of the passengers passing through other station sections, reduce the influence of other sections, compare the total cost changes of the two, and update the delayed passenger OD scheme at the minimum cost Let j1 = j"2, re-execute Step 24 until j"1 does not exist, and output In the time period [j1, j2], the minimum delay time cost under the given train departure scheme is: The algorithm ends; c. Branch and bound algorithm constructs a search tree, define the following variables: use l to represent the depth of the tree, at the root node, l = 0, all the node set of tree depth l is The number of nodes in this set is N l The nth node of tree depth l is expressed as (l, n), each node contains the following information: parent node index p ln , train departure index x ln , time index j ln , delayed passenger OD volume Station delay section passenger volume The minimum value of the station delay section passenger volume Cumulative total cost c ln , time interval h after train departure ln , the upper and lower bounds of the node are and b ln , and the global upper and lower bounds are and B ; In the formula: denotes the start and end points of the station u and the station v at time j ln The number of passengers OD who are expected to arrive at the station before time j but have not been assigned to the reservation successful boarding time period delay. represents the number of passengers who are expected to arrive at time j ln the number of passengers whose origin-destination pair is not assigned to a successful boarding time period before time j but is expected to arrive at time j denotes the time instant j ln the minimum of the cross-sectional passenger number of the station s delayed; The constructed search tree adopts a depth-first search strategy, and all nodes are stored in a local selection pool set and a global selection pool set In the two different pool sets, all child nodes of the current parent node are included, all unpruned nodes are included; in addition, l0, n0, l1, and n1 are the tree depth where the parent node is located, the node number of the parent node, the depth where the child node is located, and the node number of the child node, respectively.

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