A method for compiling a multi-period train operation plan for urban rail transit

Abstract

The present invention provides a method for compiling a multi-period train operation plan for urban rail transit, including: obtaining line data, passenger flow data and basic train operation data; constructing a train operation route alternative set; dividing the operation time into operation sub-periods according to the passenger flow fluctuation law; constructing a train service network according to the train operation route alternative set, constructing a passenger flow allocation model based on the optimal travel strategy, and realizing the rapid allocation of passenger flow in each period; constructing a vehicle bottom connection network according to the train operation route of each period; considering the effective turnover connection relationship of the vehicle bottom between time periods and the train operation constraint conditions, establishing a double-layer programming model for compiling a multi-period train operation plan for the whole day; designing a solution algorithm suitable for the double-layer programming model based on the sensitivity analysis method. The method provided by the present invention is helpful to improve the quality of the operation plan compilation, reduce the difficulty of laying out the later train operation diagram, and avoid the problems of poor coordination between time periods, low vehicle bottom utilization efficiency, and difficulty in entering and exiting the vehicle bottom caused by the existing single-period plan compilation.

Description

Technical Field

[0001] The present invention relates to the technical field of urban rail transit transportation organization, and in particular to a method for compiling a full-day multi-period train operation plan for urban rail transit. Background Art

[0002] The train operation plan occupies the primary position in the train operation plan. The reasonable preparation of the train operation plan is of great significance to improving the matching level of supply and demand and improving the quality of passenger service. The passenger flow of urban rail transit is characterized by uneven temporal and spatial distribution. The passenger flow and flow direction vary greatly during the morning and evening peaks, sub-peaks, flat peaks, and low peaks. It is necessary to formulate a train operation plan that matches it according to the passenger flow distribution law. In practice, the train operation plan is mainly formulated through manual experience. According to the passenger flow fluctuation law, trains are added / reduced in different operating periods, train routes are adjusted, and train departure intervals are adjusted, so as to splice the full-day train operation plan, resulting in problems such as low plan quality, poor connection between time periods, difficulty in connecting undercarriage, and difficulty in compiling the later train operation diagram.

[0003] At present, the theory and methods for the preparation of train operation plans in the field of railway operation organization are relatively mature, but their scope of application is based on days, and different operating days show repetitive patterns, which does not involve the connection between time periods within a day. The existing theories and methods for the preparation of urban rail transit train operation plans focus on a single time period, and lack consideration of the coordinated connection relationship of train operation plans for multiple time periods throughout the day. When the preparation scope is expanded from a single time period to multiple time periods throughout the day, it is necessary to focus on the effective connection relationship between the car bottoms of the time periods, and at the same time, the scale of model parameters and the difficulty of solving are greatly increased.

[0004] In some existing technologies, He Deqiang et al. have established an optimization model for the preparation of large and small route operation plans to address the passenger congestion problem during the morning peak hours of urban rail transit lines. Luo Yongji et al. have compiled multi-route train operation diagrams and train line connection plans for each time period in the order of peak hours first and flat hours later, and generated entry and exit plans for all trains throughout the day by considering the entry and exit constraints. Sun Yan et al. have studied the train operation plan problem for multiple circular sections on the line, established an optimization model for the daily train operation plan with the maximum train occupancy rate and the least number of sections, and designed a two-stage solution method for time segment optimization and train number optimization. Deng Lianbo et al. have analyzed the optimization problem of urban rail transit train operation plans under elastic demand, and determined the train formation length, train operation pair number and train operation time period. Wang Shuwen et al. used the ordered sample optimal segmentation method to divide the operating time period and proposed an optimization model for the running interval and the number of operation pairs.

[0005] In general, there is still a lack of integrated and coordinated compilation technology for urban rail transit's full-day, multi-period train operation plans, resulting in low quality in the compilation of existing operation plans, which has a serious impact on passenger service quality and operation organization efficiency. Summary of the invention

[0006] An embodiment of the present invention provides a method for compiling a multi-period train operation plan for urban rail transit, which is used to solve the problems existing in the prior art.

[0007] In order to achieve the above object, the present invention adopts the following technical scheme.

[0008] A method for compiling a multi-period train operation plan for urban rail transit, comprising:

[0009] S1 obtains line data, passenger flow data and basic train operation data;

[0010] S2 builds a train feasible route set based on the basic data of train operation, and screens the routes in the train feasible route set to form a train operation route candidate set;

[0011] S3 divides the whole day into multiple operating sub-periods based on the passenger flow fluctuation law by calculating the time imbalance index, direction imbalance index and section imbalance index of passenger flow;

[0012] S4 constructs a train service network based on the train operation route candidate set obtained in step S2, and uses the train service network as the underlying network to construct a passenger flow allocation model according to the optimal travel strategy; by solving the passenger flow allocation model, the passenger flow of each operating sub-period can be quickly allocated;

[0013] S5 constructs a train bottom connection network based on the train running route candidate set obtained in step S2;

[0014] S6 is based on the undercarriage connection network and passenger flow distribution model, with the dual optimization goals of minimizing enterprise operating costs and passenger travel costs, taking into account the constraints including undercarriage turnover connection relationship and train operation constraints, and constructing a two-level planning model for the preparation of full-day multi-period train operation plans;

[0015] S7 designs a double-level programming model solving algorithm for the preparation of train operation plans based on the sensitivity analysis method. By solving the double-level programming model for the preparation of the full-day multi-period train operation plan, the full-day multi-period train operation plan is obtained.

[0016] Preferably, step S4 comprises:

[0017] S4.1 constructs a train service network through a directed graph, including:

[0018] Set the attribute value of arc length and the attribute value of service frequency for each arc; define G'=(N,A) as the train service network, where N is the node set, n is the node index, A is the arc set, a is the arc index, c is the arc index, a is the length of arc a, f a is the train service frequency corresponding to arc a;

[0019] By c a Take the train interval running time, f a =+∞, construct the train operation arc;

[0020] By c a =0,f a Construct passenger boarding arcs for the train service frequencies corresponding to the associated routes;

[0021] By c a =0,f a =+∞, construct the passenger getting off arc;

[0022] By c a Take the transfer travel time, f a =+∞, construct a transfer arc;

[0023] S4.2 Based on the train service network, the passenger flow allocation model PL is established by taking the minimization of network flow cost (equivalent to minimizing passenger travel cost) as the goal, and considering the node inflow and outflow balance constraints, the constraint relationship between arc flow and service frequency, and node cost.

[0024]

[0025] The constraints include:

[0026] Node inflow and outflow balance constraints

[0027]

[0028] When the starting and ending points are the same, the arc current is zero

[0029]

[0030] Constraints between arc flow, service frequency, and node cost

[0031]

[0032] Correspondence between arc frequency and train crossing frequency

[0033]

[0034] Arc flow non-negative constraint

[0035]

[0036] In equations (1) to (6), m represents the direction of train movement, A m represents the set of arcs in direction m, N m represents the node set in direction m, s and n represent the node index, T represents the time period set, t and h represent the time period index, and R represents the intersection set. represents the flow to station (node) s in arc a during time period t, It represents the waiting time for passengers from station n to station s during time period t. represents the outflow arc set of node n', The inflow arc set of node n', represents the train running frequency corresponding to route r in time period t, represents the train running frequency corresponding to time period t arc a, is the passenger flow from node n' to node s' during time period t, R m represents the set of alternative train routes in direction m, △t is the unit time length, is the set of arcs on boarding in direction m, χ ra It is a 0-1 variable, which is 1 when the train route r contains arc a, and 0 otherwise.

[0037] Preferably, step S5 comprises:

[0038] S5.1 Set V = V R ∪V D represents the node set, W represents the arc set, and the formula

[0039] G=(V,W)(7)

[0040] Establish a car bottom transfer network to describe the car bottom transfer process between train routes and between routes and yards;

[0041] S5.2 Set the time period t∈T, the intersection node f(l,t)∈V R represents the train running frequency of route l∈R, and the yard node y(p,t)∈V D It represents the change in the number of vehicle bottoms in the parking lot p∈D; the arc set W represents the turnover connection relationship of the vehicle bottoms, connecting the node (l, t') and the node (k, h').

[0042] Preferably, step S6 comprises:

[0043] S6.1 Select the operation cost minimization and passenger travel cost minimization and pass the formula

[0044] and

[0045]

[0046] Establish the objective function; where c is the unit train kilometer cost, yuan / km; L r is the vehicle bottom turnover distance of intersection r, is the number of trains running on route r in time period t;

[0047] S6.2 pass-through

[0048]

[0049] Establish passenger service constraints; where S is the station set, α ri is a 0-1 variable, α ri =1 means that route r covers station i, otherwise α ri =0; m indicates the direction, m=0 indicates the uplink direction, m=1 indicates the downlink direction;

[0050] Set C as the train passenger capacity, limit the train load factor to no more than σ, and use the passenger flow OD matrix to calculate the formula

[0051]

[0052] Calculate the passenger flow in each time period In the formula, E is the interval set, β re is a 0-1 variable, β re =1 means that the path r covers the interval e, otherwise β re =0;

[0053] Pass-through

[0054]

[0055] Establish the maximum number of train crossings N passing through the station l Constraint; In the formula, is a 0-1 variable, Indicates that the train route r is opened, otherwise

[0056] Pass-through

[0057] and

[0058]

[0059] Establish train operation constraints; where S' is the set of turnaround stations, is the maximum reentry capacity of reentry station i, N max is the maximum passing capacity of the interval, Describe the relationship between route r and station i. When , it means that the train of route r turns back at station i;

[0060] Assume △t as the unit time length, Q as the number of equipped vehicles, and use the formula

[0061]

[0062] Calculate the required number of vehicle bottoms; where T rrepresents the vehicle turnover time corresponding to the intersection r;

[0063] Pass-through

[0064]

[0065] Establishing coupling constraint representation and the mutual relationships between them;

[0066] S6.3 pass-through

[0067]

[0068] Establish the vehicle bottom connection relationship constraint; where, h and t represent the time period number, k and p represent the node number in the vehicle bottom connection network, represents the number of vehicles transferred from node k in period h to node p in period t, represents the number of vehicles transferred from node p in period t to node k in period h, M is an infinite positive number, λ k,p Represents the connection relationship of the node, when λ k,p =1 indicates that node k in the vehicle bottom connection network can connect to node p, ρ k,p represents the connection time between node k and node p, It indicates the number of trains running on route l in time period t;

[0069] S6.4 pass-through

[0070]

[0071]

[0072] Establish parking lot related constraints; where, represents the number of changes in the number of vehicle bases at the end of time period t and time period h, respectively. p' is the deviation of the number of vehicle bases in stock allowed by the depot. T' represents the last time period within the planning range. is the number of vehicles stored in depot d during the initial period; N d is the storage capacity of depot d, η k,p is the idle driving distance between the intersection node k and the parking lot node p, and Π is the maximum value of the total idle driving distance.

[0073] Preferably, step S7 comprises:

[0074] S7.1 constructs an integer programming model P0 based on the objective function of sub-step S6.1 and the constraints of sub-steps S6.2 to S6.4, solves the integer programming model P0 by Gurobi, and obtains an initial multi-period operation plan;

[0075] S7.2 pass-through

[0076]

[0077] Solve the lower model and obtain the descending direction of the objective function (9) In the formula, represents the boarding arc corresponding to the intersection r∈R in the direction m={0,1}, and is the original optimal solution and the dual optimal solution of the lower model;

[0078] S7.3 pass-through

[0079]

[0080] Calculate the projection f of the descending direction on the upper model * ;

[0081] Pass-through

[0082]

[0083] Establish capacity and volume matching constraints; where χ r,a is a 0-1 parameter, χ r,a =1 means that path r covers arc a in the service network,

[0084] is the set of running arcs in direction m, It represents the total flow of arc a in time period t obtained by summing the arcs according to the end point s;

[0085] S7.4 pass-through

[0086]

[0087] The top-level problem is transformed; where z 1,nom ,z 2,nom is the optimal objective function value of enterprise operating cost z1 and passenger travel cost z2 under a single optimization objective, and γ is the weight coefficient;

[0088] By solving the formula

[0089]

[0090] Calculate the optimal step size ρ * ;

[0091] S7.5 If the objective function values ​​are the same for two consecutive iterations, the calculation is terminated and the train operation plan is output.

[0092] It can be seen from the technical solutions provided by the above-mentioned embodiments of the present invention that the present invention provides a method for compiling a full-day multi-period train operation plan for urban rail transit, including the following steps: obtaining line data, passenger flow data and basic train operation data; constructing a train operation route alternative set based on the line data and basic train operation data; dividing the operation time into operation sub-periods according to the passenger flow fluctuation law; constructing a train service network based on the train operation route alternative set, and constructing a passenger flow allocation model based on the optimal travel strategy to achieve rapid allocation of passenger flow in each time period; constructing a vehicle bottom connection network based on the train operation route alternative set; taking minimization of enterprise operating costs and passenger travel costs as the optimization goal, considering the effective vehicle bottom turnover connection relationship between time periods, train operation constraints and other constraints, and establishing a two-level planning model for compiling a full-day multi-period train operation plan; designing a solution algorithm suitable for the two-level planning model for operation plan compilation based on the sensitivity analysis method. The method provided by the present invention has the following advantages:

[0093] (1) The present invention takes into account the connection relationship between the vehicle bottoms when constructing the operation plan, which helps to reduce the difficulty of drawing the train operation diagram in the later stage, improve the efficiency of train operation organization, and avoid practical problems such as poor coordination between time periods and difficulty in train entering and exiting the vehicle depot, which are easily caused by the preparation of existing single-time period plans.

[0094] (2) The present invention constructs the multi-period operation plan compilation problem into a two-layer planning model. The upper-layer model realizes the integrated and coordinated compilation of multi-period operation plans while ensuring the effective connection of the vehicle bottom; the lower-layer model realizes the rapid allocation of passenger flow, thereby forming an interactive process between the upper and lower-layer models, effectively describing the complex coupling relationship between passenger flow and vehicle flow, thereby accurately matching passenger flow demand and improving the quality of operation plan compilation.

[0095] (3) The present invention designs an algorithm based on sensitivity analysis to solve the two-level planning model for operation plan preparation, which can improve the solution efficiency of the model, meet the actual problem of full-day operation plan preparation for medium and long lines, and provide support for the preparation of urban rail transit train operation plans.

[0096] Additional aspects and advantages of the present invention will be given in part in the following description, which will become obvious from the following description, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0098] Figure 1A processing flow chart of a method for compiling a multi-period train operation plan for urban rail transit provided by the present invention;

[0099] Figure 2 A train service network diagram of a method for compiling a multi-period train operation plan for urban rail transit provided by the present invention;

[0100] Figure 3 A simplified schematic diagram of a vehicle bottom turnaround connection network for a method for compiling a multi-period train operation plan for urban rail transit provided by the present invention;

[0101] Figure 4 A schematic diagram of a vehicle bottom turnaround connection network for a method for compiling a multi-period train operation plan for urban rail transit provided by the present invention;

[0102] Figure 5 The overall framework diagram of the model of a method for compiling a multi-period train operation plan for urban rail transit provided by the present invention;

[0103] Figure 6 The present invention provides an algorithm solution flow chart for a method for compiling a multi-period train operation plan for urban rail transit throughout the day. DETAILED DESCRIPTION

[0104] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0105] Those skilled in the art will appreciate that, unless otherwise stated, the singular forms "a", "an", "said" and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof.

[0106] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0107] To facilitate understanding of the embodiments of the present invention, several specific embodiments will be further explained below with reference to the accompanying drawings, and each embodiment does not constitute a limitation on the embodiments of the present invention.

[0108] The present invention provides a method for compiling a multi-period train operation plan for urban rail transit, which is used to solve the following technical problems existing in the prior art:

[0109] 1) The existing single-period operation plan compilation method is difficult to meet the actual needs of the full-day train operation plan compilation, resulting in a series of practical problems such as low plan quality, poor connection between time periods, difficulty in drawing operation diagrams, long distances for empty trains to return or leave the section, and serious waste of transportation capacity. The full-day operation plan obtained by splicing the traditional single-period independent compilation cannot consider the connection problem between time period plans, especially during the transition period between peak and flat peak. Once the connection between plans is not smooth, it will lead to difficulties in connecting the train bottom, and even the problem of "no trains available" will occur for lines with tight train bottoms.

[0110] 2) There is still a lack of collaborative compilation methods for urban rail transit multi-period operation plans throughout the day. When the compilation scope is expanded from a single period to multiple periods throughout the day, the influencing factors, model complexity, solution scale and difficulty are greatly increased. In addition, the connection relationship between time periods must be considered, which is essentially the effective connection of vehicle bottom turnover. For example, a large number of trains are put into operation during peak hours and return to the section after the peak, resulting in frequent vehicle bottom in and out of the depot; if the vehicle bottom connection problem is not considered when compiling the operation plan, it will bring challenges to the operation organization work.

[0111] In view of the above limitations, the method provided by the present invention is conducive to improving the quality of train operation plan preparation, reducing the number of car bottoms used, improving traffic organization efficiency, and reducing transportation costs.

[0112] See also Figure 1 The present invention provides a method for compiling a multi-period train operation plan for urban rail transit, comprising the following steps:

[0113] S1 obtains line data, passenger flow data and basic train operation data;

[0114] S2 builds a train feasible route set based on the basic data of train operation, and screens the routes in the train feasible route set to form a train operation route candidate set;

[0115] S3 divides the operation time into multiple operation sub-periods based on the passenger flow fluctuation law by calculating the time imbalance index, direction imbalance index and section imbalance index of the passenger flow;

[0116] S4 constructs a train service network based on the train operation route candidate set obtained in step S2, takes this as the underlying network, and constructs a passenger flow allocation model according to the optimal travel strategy; by solving the passenger flow allocation model, the passenger flow of each operating sub-period can be quickly allocated;

[0117] S5 constructs a train bottom connection network based on the train running route candidate set obtained in step S2;

[0118] S6 is based on the underlying network, the undercarriage connection network and the train service network, with the dual optimization goals of minimizing the enterprise operating cost and the passenger travel cost, and considering the constraints such as the undercarriage effective turnover connection relationship and train operation, to build a two-layer planning model for the preparation of the full-day multi-period train operation plan;

[0119] S7 designs a suitable algorithm for solving the bi-level programming model based on the sensitivity analysis method. By solving the full-day multi-period train operation plan, a bi-level programming model is compiled to obtain the full-day multi-period train operation plan.

[0120] An embodiment of the present invention provides a method for compiling a full-day multi-period train operation plan for urban rail transit. The upper layer of the method takes the minimization of enterprise operating costs and passenger travel time as the goal, and considers constraints such as passenger flow demand, service frequency, number of vehicles in use, undercarriage connection, yard capacity and empty driving distance; the lower layer is a passenger flow distribution model, which is used to calculate the passenger travel expenses and passenger flow distribution status under the upper layer optimization plan, and feed it back to the upper layer, so as to establish an interactive process between the upper and lower layer models.

[0121] In the embodiments provided by the present invention, the definitions of some terms and parameters are as follows:

[0122] An embodiment of the present invention provides a method for compiling a full-day multi-period train operation plan for urban rail transit. The upper layer of the method takes the minimization of enterprise operating costs and passenger travel time as the goal, and considers constraints such as passenger flow demand, service frequency, number of vehicles in use, undercarriage connection, yard capacity and empty driving distance; the lower layer is a passenger flow distribution model, which is used to calculate the passenger travel expenses and passenger flow distribution status under the upper layer optimization plan, and feed it back to the upper layer, so as to establish an interactive process between the upper and lower layer models.

[0123] The vehicle bottom turnover in the present invention refers to the transfer and connection of vehicle bottoms between different time periods, that is, the vehicle bottom executing route l in time period i continues to time period j and executes the task of route k in this time period. The difference between the vehicle bottom turnover in the present invention and the traditional vehicle bottom utilization plan is that the vehicle bottom turnover is the quantitative relationship between vehicle bottoms in time periods, and only needs to meet the requirements of the number of vehicle bottoms required for each route in any time period, rather than uniquely corresponding to a specific vehicle bottom.

[0124] Define the variables and symbols of the model in the embodiment of the present invention: define the variables, sets and parameters of the model design:

[0125] a.Variable

[0126]

[0127] b. Collection

[0128]

[0129] In the preferred embodiment provided by the present invention, the specific execution process of each step is as follows:

[0130] S1, obtain line data, passenger flow data and basic train operation data;

[0131] Specifically, the acquired line data includes: ordinary stations, turnaround stations, yards, the relationship between stations and sections, the maximum throughput capacity of sections, the turnaround capacity of turnaround stations, and the vehicle storage capacity of yards; the passenger flow data includes: the passenger flow OD matrix of each operating sub-period; the basic train operation data includes: the train's section running time, stop time and turnaround time, unit vehicle-kilometer cost, maximum vehicle base and train capacity.

[0132] S2, based on the basic data of train operation, construct feasible train routes; through manual screening, eliminate the routes with no practical value from the feasible routes to form a train route candidate set.

[0133] The basic principles for running train routes: the wiring layout of the intermediate turnaround station determines the direction of the train's turnaround at the station. When the train turns around at the intermediate station, the wiring layout of the intermediate station must be considered to exclude routes that cannot turn around; to avoid frequent train turns that increase the difficulty of transport organization and waste of transport capacity, the length of the train route should not be too short; to reduce the difficulty of transport organization, angled routes are generally not considered in actual transport organization work. Based on the basic principles, the steps for generating the train route candidate set in the present invention are:

[0134] 1) Combine all turnaround stations to determine the starting and ending points of the train operation route; 2) According to the wiring layout of the turnaround station, eliminate the routes that cannot turn around, the routes that are too short and the routes with corners, and determine the actual feasible routes; 3) Determine the coverage relationship between each route and the station and section in the feasible routes; 4) Obtain the turnaround distance and turnaround time of each route to generate a set of train operation route alternatives.

[0135] S3, according to the passenger flow fluctuation law, the operation time is divided into operation sub-periods; according to the passenger flow fluctuation law, the time imbalance index, direction imbalance index, and section imbalance index of the passenger flow are calculated, and the operation time is divided into several operation sub-periods according to the imbalance index.

[0136] S4, constructing a train service network based on the train operation route alternative set, and building a passenger flow allocation model based on the optimal travel strategy to achieve rapid allocation of passenger flow in each sub-time period;

[0137] S4.1, construct the train service network. Use a directed graph to describe the train service network, and set two attribute values ​​for each arc: arc length (depicted in time) and service frequency. Define G' = (N, A) as the train service network, where N is the node set and n is the node index; A is the arc set and a is the arc index; c a is the length of arc a; f a is the corresponding service frequency on arc a.

[0138] S4.2, such as Figure 2 As shown in the figure, based on the physical network, stations and sections are virtualized according to the operation plan, and virtual arcs are established to depict the passenger boarding and alighting, section travel and transfer process, so as to describe the travel strategy of passengers under complex train operation routes. The train service network mainly includes passenger boarding and alighting nodes, train virtual stop nodes, section operation arcs, boarding and alighting arcs and travel arcs (marked with corresponding graphics and line types in the figure).

[0139] Train running arc: c a Take the train interval running time, f a =+∞;

[0140] Passenger boarding arc: c a =0,f a The train service frequency corresponding to the associated route;

[0141] Passenger alighting arc: c a =0,f a =+∞;

[0142] Transfer arc: c a Take the transfer travel time, f a =+∞.

[0143] S4.3, based on the train service network, describe the passenger travel selection process, take the minimization of network flow cost (minimization of passenger travel cost) as the goal, consider the node inflow and outflow balance constraints, arc flow and service frequency, and the constraint relationship between node costs, and establish the passenger flow allocation model PL.

[0144]

[0145] Furthermore, the constraints of the passenger flow distribution model PL include: (1) node inflow and outflow balance constraint; (2) arc flow is zero when the starting and ending points are the same; (3) constraint relationship between arc flow and service frequency and node cost; (4) correspondence between arc frequency and train crossing frequency; (5) arc flow non-negative constraint. The specific constraint expressions are as follows:

[0146]

[0147]

[0148] In the formula is the passenger flow from node n to the station in time period t, is the set of boarding arcs in direction m. In equations (1) to (6), m represents the direction of train operation, A m represents the set of arcs in direction m, N m represents the node set in direction m, s and n represent the node index, represents the flow to station (node) s in arc a during time period t, It represents the waiting time for passengers from station n to station s during time period t. represents the outflow arc set of node n, The set of inflow arcs of node n, represents the train running frequency corresponding to route r in time period t, represents the train running frequency corresponding to time period t arc a, is the passenger flow from node n' to node s' during time period t, R m represents the set of alternative train routes in direction m, △t is the unit time length, is the set of arcs on boarding in direction m, χ ra It is a 0-1 variable, which is 1 when the train intersection r contains arc a, otherwise it is 0

[0149] S5 builds a train connection network based on the train running route alternative set;

[0150] Establish a car bottom turnover connection network. Car bottom connection must meet certain conditions. The car bottom connection can only be made when the arrival station of the current running route is the starting station of the subsequent running route. Figure 3 For example, the train of route R1 arrives at station S4 and then takes over route R3 to perform its transportation task. Given the route and analysis period, the above position relationship can be simplified by expressing the validity of the arc. Figure 3 The network structure of the turnover network G = (V, W) is established to represent the transfer relationship between train crossings and between crossings and yards during the analysis period, such as Figure 4 shown.

[0151] Furthermore, let V = V R ∪V D represents the node set, and W represents the arc set. In the time period t∈T, the intersection node f(l,t)∈V R represents the running frequency of train route l∈R, and the yard node y(p,t)∈V Drepresents the change in the number of car bottoms in the parking lot p∈D; the arc set W represents the turnover connection relationship of the car bottom, connecting the node (l, t') and the node (k, h'). The transfer of the car bottom can be represented by the process of the car bottom starting from the parking lot node, passing through one or more intersection nodes, and finally returning to the parking lot node. Since the car bottom will go on / off the line during the peak-peak transition period in reality, it is unreasonable to set up the parking lot only at the beginning and end time periods. Therefore, this embodiment includes a parking lot node in each time period.

[0152] S6, taking the minimization of enterprise operating costs and passenger travel costs as the dual optimization goals, considering the effective turnover connection relationship between the vehicle bottoms between time periods and the constraints on train operation, a two-level planning model for the preparation of the full-day multi-time period train operation plan is established. The specific steps include:

[0153] S6.1, select the operating cost as the objective function, which is the product of the frequency of the selected train route and the vehicle-kilometers during the entire period; secondly, considering that passengers want to reach their destination in the shortest time, minimize the travel time of all passengers as another objective function. The calculation formula of the objective function is:

[0154]

[0155] Where c is the unit train kilometer cost, RMB / km; L r is the vehicle bottom turnover distance of intersection r, is the number of trains running on route r during time period t.

[0156] S6.2, passenger service constraints. To avoid passengers waiting for too long on the platform, trains must maintain a minimum service frequency. According to the "Urban Rail Transit Operation Management Specifications", the longest departure interval should not exceed 10 minutes. For each station on the line, the interval between trains arriving at the station is limited to no more than 10 minutes.

[0157]

[0158] Where α ri is a 0-1 variable, α ri =1 means that route r covers station i, otherwise α ri =0, △t is the length of the operating sub-period.

[0159] The passenger flow in each time interval can be directly calculated using the passenger flow OD matrix Define C as the passenger capacity of the train, and limit the train load factor to no more than σ

[0160]

[0161] Where β re is a 0-1 variable, β re =1 means that the path r covers the interval e, otherwise βre =0.

[0162] When there are too many types of trains, it is easy for passengers to get on the wrong train. In order to improve the convenience of passengers' travel and reduce the difficulty of organizing passenger flow on the platform, the maximum number of train crossings N passing through the station is set. l Restrict

[0163]

[0164] S6.3, train operation constraints. Define S' as the set of turnaround stations, is the maximum reentry capacity of reentry station i, N max is the maximum passing capacity of the interval, Describe the relationship between route r and station i (assuming it is a turnaround station). When , it means that the train of route r turns back at station i. This association can be quickly established when determining the candidate route set. and interval capacity N max Constraints

[0165]

[0166] According to the vehicle bottom turnover time T r , the number of departure pairs can be used to estimate the required number of cars. Define △t as the time period length, Q as the number of cars to be equipped. To ensure the smooth operation of the train, the number of cars in use should not exceed the number of cars to be equipped.

[0167]

[0168] Calculate the required number of vehicle bottoms. In the formula, T r It represents the vehicle turnover time corresponding to the route r.

[0169] If the train route r is selected, its running frequency should not exceed the maximum capacity, and the coupling constraint is proposed to express and The relationship between

[0170]

[0171] S6.4, vehicle bottom turnover constraint. The vehicle bottom connection must meet both time and space requirements. Only when the corresponding vehicle bottom of the intersection meets the connection time requirement ρ k,l Only when the terminal station of the route is the same as the starting station of the connecting route, the corresponding vehicle bottom of the route can be connected; the vehicle bottom connection relationship in this embodiment can be expressed as

[0172]

[0173] Where λ k,lRepresents the connection relationship of the node, when λ k,l When =1, node k can connect to node l.

[0174] In the car-bottom turnover network, the frequency of the intersection node l is the sum of the car-bottoms that arrive at its departure station before the start of time period t. This condition ensures that there are sufficient car-bottom resources for train intersections with a specific frequency. Since the station does not have parking capacity, the flow entering the intersection node l is equal to the flow leaving the intersection node. The above constraints are

[0175]

[0176] In the formula, h and t represent the time period numbers, k and p represent the node numbers in the vehicle bottom connection network, represents the number of vehicles transferred from node k in period h to node p in period t, represents the number of vehicles transferred from node p in period t to node k in period h, M is an infinite positive number, λ k,p Represents the connection relationship of the node, when λ k,p =1 indicates that node k in the vehicle bottom connection network can connect to node p, ρ k,p represents the connection time between node k and node p, It indicates the number of trains running on route l in time period t.

[0177] S6.5, parking lot related constraints. Generally, it is necessary to ensure that the number of available parking spaces in each parking lot at the beginning of a cycle (operation sub-period) is not much different from that in the previous cycle. To ensure that there are enough parking spaces in the next cycle, the deviation of the number of parking spaces in each parking lot at the end of the analysis period should be limited as follows:

[0178]

[0179] Where p is the allowable deviation of the number of inventory vehicles in the vehicle depot, and T′ represents the last period within the planning range.

[0180] The number of cars in stock at any time is equal to the number of cars at the beginning Subtract the number of car bottoms that have driven out and add the number of car bottoms that have returned. In order to further improve the availability of resources, it is necessary to consider the number of car bottoms and the parking lot inventory capacity N d The inventory of each yard is non-negative in any period of time. If the yard storage line is full, the train cannot enter.

[0181]

[0182] Furthermore, when entering or leaving the yard, the vehicle bottom needs to run empty between the yard and the starting / ending station of the route it is responsible for. In order to formulate a practical and feasible multi-period operation plan, it is necessary to coordinate the empty running of the vehicle bottom in and out of the yard throughout the day. For this purpose, the total empty running distance is considered, which can be expressed as

[0183]

[0184] In formulas (21) to (25), represents the number of changes in the number of vehicle bases at the end of time period t and time period h, respectively, p' is the deviation of the number of vehicle bases in stock allowed by the vehicle depot, T ′ Indicates the last time period within the planning range. is the number of vehicles stored in depot d during the initial period; N d is the storage capacity of depot d, η k,p is the idle driving distance between the intersection node k and the parking lot node p, and Π is the maximum value of the total idle driving distance.

[0185] This embodiment implements the preparation of multi-period operation plans through the above steps, and takes into account the transfer of vehicle bottoms between different time periods. The operation plan determines the type of transportation products, which in turn affects the passenger flow distribution state, and the passenger flow state in turn affects the operation plan. In order to obtain the passenger flow of each route under the multi-period operation plan, the passenger flow distribution model based on the optimal travel strategy described in step 3 is embedded. The overall framework of the two-layer model is as follows: Figure 5 shown.

[0186] S7, design a solution algorithm for the bi-level programming model for train operation plan preparation based on sensitivity analysis;

[0187] In order to solve the problem of solving the two-level planning, an algorithm based on sensitivity analysis is designed. Step 7 of this embodiment includes the following sub-steps: first, a basic model is established based on the enterprise operating cost and the constraints described in step 6, and the model is solved to obtain an initial solution; according to the optimal strategy of the lower-level problem, the descent direction and optimal step length of the current multi-period operation plan are derived, and the operation plan is updated; it is gradually updated through multiple iterations until the solution converges, such as Figure 6 shown.

[0188] S7.1, initialization, generate the initial multi-period operation plan f0. Taking the minimum enterprise operating cost as the goal, that is, the objective function z1 of step 6.1, construct the integer programming model P0 with the constraints described in steps 6.2 to 6.5, call Gurobi for solution, and obtain the initial multi-period operation plan.

[0189] S7.2, use the labeling method to solve the lower model and obtain the descending direction. For a given f, use μ to represent the dual variable of the constraint relationship between arc flow and service frequency and node cost. For any f, let and is the original optimal solution and the dual optimal solution of the lower model. The descending direction of z2 can be calculated

[0190]

[0191] In the formula Represents the boarding arc corresponding to the intersection r∈R in the direction m={0,1}.

[0192] S7.3, find the projection f of the descending direction on the upper model * For any f, the descending direction can be projected onto the effective constraints of the upper layer. The model P1 is constructed to find its projection. Its objective function is as follows:

[0193]

[0194] In addition to the constraints described in steps 6.2 to 6.5, add capacity and volume matching constraints. Refine it from the "interval" level to the "intersection" level, and sum the arcs according to the end point s to obtain the total flow of arc a in time period t Limit it to less than the arc capacity

[0195]

[0196] Where χ r,a is a 0-1 parameter, χ r,a =1 means that path r covers arc a in the service network; is the set of running arcs in direction m.

[0197] S7.4, calculate the optimal step size ρ * , update the multi-period operation plan. The upper problem has two objectives, and the linear weighted method is used to transform it into:

[0198]

[0199] Where z 1,nom ,z 2,nom It is the optimal objective function value of enterprise operating cost z1 and passenger travel cost z2 under single objective, and γ is the weight coefficient.

[0200] Use discrete values ​​between [0,1] to evaluate ρ, consider all the constraints, and let f * The optimal solution of P1 is constructed by the following formula as the objective function:

[0201]

[0202] For each discrete value, solve the model PM to obtain the optimal step size ρ * .

[0203] S7.5, termination judgment. The number of iterations is preset. If the objective function value is the same for two consecutive iterations, the solution converges to the optimal value and the algorithm ends. The full-day multi-period train operation plan is obtained through the calculation results. The plan is used to arrange the train operation in multiple periods throughout the day.

[0204] In summary, the present invention provides a method for compiling a full-day multi-period train operation plan for urban rail transit, comprising the following steps: obtaining line data, passenger flow data and basic train operation data; constructing a train operation route alternative set based on the line data and basic train operation data; dividing the operation time into operation sub-periods according to the passenger flow fluctuation law; constructing a train service network based on the train operation route alternative set, and constructing a passenger flow allocation model based on the optimal travel strategy to achieve rapid allocation of passenger flow in each time period; constructing a vehicle bottom connection network based on the train operation route alternative set; taking minimizing enterprise operating costs and passenger travel costs as the dual optimization goals, considering the effective turnover connection relationship of the vehicle bottom and the train operation constraints, and establishing a two-level planning model for compiling a full-day multi-period train operation plan; designing a solution algorithm suitable for the two-level planning model for operation plan compilation based on the sensitivity analysis method. The method provided by the present invention has the following advantages:

[0205] (1) The present invention takes into account the connection relationship between the vehicle bottoms when constructing the operation plan, which helps to reduce the difficulty of drawing the train operation diagram, improve the efficiency of train operation organization, and avoid practical problems such as poor coordination between time periods and difficulty in trains entering and exiting the vehicle depot that are easily caused by the preparation of existing single-time period plans.

[0206] (2) The present invention constructs the multi-period operation plan compilation problem into a two-layer planning model. The upper-layer model realizes the integrated compilation of multi-period operation plans while ensuring the effective connection of the vehicle bottom; the lower-layer model realizes the rapid allocation of passenger flow, thereby forming an interactive process between the upper and lower-layer models, effectively describing the complex coupling relationship between passenger flow and vehicle flow, thereby accurately matching passenger flow demand and improving the quality of operation plan compilation.

[0207] (3) The present invention designs an algorithm based on sensitivity analysis to solve the two-level planning model for operation plan preparation, which can improve the solution efficiency of the model, meet the actual problem of full-day operation plan preparation for medium and long lines, and provide support for the preparation of urban rail transit train operation plans.

[0208] Those skilled in the art can understand that the accompanying drawings are only schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0209] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for compiling a multi-period train operation plan for urban rail transit, characterized in that: include: S1 obtains line data, passenger flow data and basic train operation data; S2 builds a train feasible route set based on the basic data of train operation, and screens the routes in the train feasible route set to form a train operation route candidate set; S3 divides the whole day into multiple operating sub-periods based on the passenger flow fluctuation law by calculating the time imbalance index, direction imbalance index and section imbalance index of passenger flow; S4 constructs a train service network based on the train running route candidate set obtained in step S2, and uses the train service network as the underlying network to construct a passenger flow allocation model according to the optimal travel strategy; By solving the passenger flow allocation model, the passenger flow of each operating sub-period can be quickly allocated; specifically, it includes: S4.1 constructs a train service network through a directed graph, including: Set the attribute value of arc length and the attribute value of service frequency for each arc; define G'=(N,A) as the train service network, where N is the node set, n is the node index, A is the arc set, a is the arc index, c is the arc index, a is the length of arc a, f a is the train service frequency corresponding to arc a; By c a Take the train interval running time, f a =+∞, construct the train operation arc; By c a =0,f a Construct passenger boarding arcs for the train service frequencies corresponding to the associated routes; By c a =0,f a =+∞, construct the passenger getting off arc; By c a Take the transfer travel time, f a =+∞, construct a transfer arc; S4.2 Based on the train service network, the passenger flow allocation model PL is established by taking the network flow cost minimization as the goal and considering the node inflow and outflow balance constraints, the constraint relationship between arc flow and service frequency and node cost. The constraints include: Node inflow and outflow balance constraints When the starting and ending points are the same, the arc current is zero Constraints between arc flow, service frequency, and node cost Correspondence between arc frequency and train crossing frequency Arc flow non-negative constraint In equations (1) to (6), m represents the direction of train movement, A m represents the set of arcs in direction m, N m represents the node set in direction m, s and n represent the node index, T represents the time period set, t and h represent the time period index, and R represents the intersection set. represents the flow to station s in arc a during time period t, It represents the waiting time for passengers from station n to station s during time period t. represents the outflow arc set of node n', The inflow arc set of node n', represents the train running frequency corresponding to route r in time period t, represents the train running frequency corresponding to time period t arc a, is the passenger flow from node n' to node s' during time period t, R m represents the set of alternative train routes in direction m, △t is the unit time length, is the set of arcs on boarding in direction m, χ ra is a 0-1 variable, which is 1 when the train intersection r contains arc a, otherwise it is 0; S5 builds a train connection network based on the train running route candidate set obtained in step S2; specifically includes: S5.1 Set V = V R ∪V D represents the node set, W represents the arc set, and the formula G=(V,W)(7) Establish a car bottom transfer network to describe the car bottom transfer process between train routes and between routes and yards; S5.2 Set the time period t∈T, the intersection node f(l,t)∈V R represents the train running frequency of route l∈R, and the yard node y(p,t)∈V D represents the change in the number of car bottoms in the parking lot p∈D; the arc set W represents the turnover connection relationship of the car bottom, connecting the node (l, t') and the node (k, h'); S6 is based on the undercarriage connection network and passenger flow distribution model, with the dual optimization goals of minimizing enterprise operating costs and passenger travel costs. It considers the constraints of undercarriage turnover connection relationship and train operation constraints, and builds a two-level planning model for the preparation of full-day multi-period train operation plans; specifically, it includes: S6.1 Select the operation cost minimization and passenger travel cost minimization and pass the formula Establish the objective function; where c is the unit train kilometer cost, yuan / km; L r is the vehicle bottom turnover distance of intersection r, is the number of trains running on route r in time period t; S6.2 pass-through Establish passenger service constraints; where S is the station set, α ri is a 0-1 variable, α ri =1 means that route r covers station i, otherwise α ri =0; m indicates the direction, m=0 indicates the uplink direction, m=1 indicates the downlink direction; Set C as the train passenger capacity, limit the train load factor to no more than σ, and use the passenger flow OD matrix to calculate the formula Calculate the passenger flow in each time period In the formula, E is the interval set, β re is a 0-1 variable, β re =1 means that the path r covers the interval e, otherwise β re =0; Pass-through Establish the maximum number of train crossings N passing through the station l Constraint; In the formula, is a 0-1 variable, Indicates that the train route r is opened, otherwise Pass-through Establish train operation constraints; where S' is the set of turnaround stations, is the maximum reentry capacity of reentry station i, N max is the maximum passing capacity of the interval, Describe the relationship between route r and station i. When φ ri =1 indicates that the train on route r turns back at station i; Assume △t as the unit time length, Q as the number of equipped vehicles, and use the formula Calculate the required number of vehicle bottoms; where T r represents the vehicle turnover time corresponding to the intersection r; Pass-through Establishing coupled constraint representation and the mutual relationships between them; S6.3 pass-through Establish the vehicle bottom connection relationship constraint; where h and t represent the time period number, k and p represent the node number in the vehicle bottom connection network, represents the number of vehicles transferred from node k in period h to node p in period t, represents the number of vehicles transferred from node p in period t to node k in period h, M is an infinite positive number, λ k,p Represents the connection relationship of the node, when λ k,p =1 indicates that node k in the vehicle bottom connection network can connect to node p, ρ k,p represents the connection time between node k and node p, f l t It indicates the number of trains running on route l in time period t; S6.4 pass-through Establish parking lot related constraints; where, represents the number of changes in the number of vehicle bases at the end of time period t and time period h, respectively. p' is the deviation of the number of vehicle bases in stock allowed by the depot. T' represents the last time period within the planning range. is the number of vehicles stored in depot d during the initial period; N d is the storage capacity of depot d, η k,p is the idle driving distance between the intersection node k and the parking lot node p, Π is the maximum value of the total idle driving distance; S7 designs a double-level programming model solving algorithm for the preparation of train operation plans based on the sensitivity analysis method. By solving the double-level programming model for the preparation of the full-day multi-period train operation plan, the full-day multi-period train operation plan is obtained.

2. The method according to claim 1, characterized in that Step S7 includes: S7.1 constructs an integer programming model P0 based on the objective function of sub-step S6.1 and the constraints of sub-steps S6.2 to S6.4, solves the integer programming model P0 by Gurobi, and obtains an initial multi-period operation plan; S7.2 pass-through Solve the lower model and obtain the descending direction of the objective function (9) In the formula, represents the boarding arc corresponding to the intersection r∈R in the direction m={0,1}, and is the original optimal solution and the dual optimal solution of the lower model; S7.3 pass-through Calculate the projection f of the descending direction on the upper model * ; Pass-through and Establish capacity and volume matching constraints; where χ r,a is a 0-1 parameter, χ r,a =1 means that path r covers arc a in the service network, is the set of running arcs in direction m, It represents the total flow of arc a in time period t obtained by summing the arcs according to the end point s; S7.4 pass-through The top-level problem is transformed; where z 1,nom ,z 2,nom is the optimal objective function value of enterprise operating cost z1 and passenger travel cost z2 under a single optimization objective, and γ is the weight coefficient; By solving the formula Calculate the optimal step size ρ * ; S7.5 If the objective function values ​​are the same for two consecutive iterations, the calculation is terminated and the train operation plan is output.

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