A passenger railway train timetable optimization method considering efficiency and fairness

Abstract

The application discloses a kind of efficiency and fairness considered passenger railway train timetable optimization method, it includes: step 1: construction passenger railway customized space-time network;Step 2: establish the train timetable model P1 based on passenger railway efficiency maximization;Step 3: establish the train timetable model P2 based on passenger railway fairness;Step 4: using column line generation algorithm to solve the train timetable model P1 for efficiency, obtain the train timetable scheme for efficiency;Step 5: the train timetable model P2 for fairness is applied to decomposition scheme, then solve using column line generation algorithm, obtain the train timetable scheme considering fairness.The present application is based on the train timetable model of maximum efficiency, constructs the train timetable model for fairness of train operator, and proposes to decompose model so that it can be solved using column line generation optimization algorithm, solves the technical problem that existing train timetable efficiency and fairness are difficult to balance.

Description

TECHNICAL FIELD

[0001] The present application relates to a passenger train timetable optimization method in the field of railway trains, and particularly relates to a passenger train timetable optimization method considering efficiency, a passenger train timetable optimization method considering fairness, and a passenger train timetable optimization method considering efficiency and fairness. BACKGROUND

[0002] Railways are capital-intensive infrastructure that require significant investment for construction and continuous maintenance and renovation during operation. Therefore, railways are usually invested and owned by the government or private sectors. To improve operational sustainability and maximize returns, railway line owners usually allow multiple train operators to provide diverse services for passengers using the railway infrastructure. For example, the Beijing-Shanghai high-speed railway line (referred to as the Beijing-Shanghai line) is owned by the Beijing-Shanghai High-Speed Railway Company Limited (referred to as the Beijing-Shanghai Company), and train services on this line are provided by four companies. Train operators: Beijing-Shanghai Company, China Railway Beijing Group Co., Ltd. (referred to as China Railway Beijing), China Railway Shanghai Group Co., Ltd. (referred to as China Railway Shanghai), and China Railway Jinan Group Co., Ltd. (referred to as China Railway Jinan). These operators share the railway infrastructure (such as track sections and platforms) to meet their service needs and pay for the use of infrastructure and facilities.

[0003] To coordinate operations between different operators, the line owner needs to develop an integrated train timetable to determine the resource allocation of trains and the time when trains occupy resources. Maximizing train operation efficiency is a key goal in developing a train timetable. System efficiency is usually quantified using resource utilization and service level (such as additional train waiting time and expected travel time) of trains. However, since train services on a railway line are provided by multiple train operators, another important goal of the train timetable is to maximize the operational fairness of train operators.

[0004] The fairness issue in the train timetable is mainly studied at the train level. Existing work attempts to balance the disadvantages between trains by assigning running priorities to different trains. Although this approach helps to avoid systematic discrimination against certain trains, it can lead to disproportionate allocation at the operator level, resulting in a biased service plan that is not favorable to one or more operators. SUMMARY

[0005] To address the technical problem that existing train timetables do not consider the fairness of train operators, this invention provides a passenger railway train timetable optimization method that considers fairness; to address the technical problem that existing train timetable models are complex and difficult to solve, this invention provides a method based on a column generation algorithm; to address the technical problem that existing train timetables are difficult to balance between efficiency and fairness, this invention provides a passenger railway train timetable optimization method that considers both efficiency and fairness.

[0006] The present invention is implemented using the following technical solution: a passenger railway train timetable optimization method considering efficiency, which includes: step 1: constructing a customized spatiotemporal network for passenger railways; step 2: establishing a train timetable model P1 based on maximizing passenger railway efficiency; step 4: solving the efficiency-oriented train timetable model P1 using a column generation algorithm to obtain an efficiency-oriented train timetable scheme.

[0007] This invention also provides a method for optimizing passenger railway train timetables that considers fairness, comprising: Step 1: constructing a customized spatiotemporal network for passenger railways; Step 3: establishing a train timetable model P2 based on passenger railway fairness; Step 5: applying a decomposition scheme to the fairness-oriented train timetable model P2, and then solving it using a column generation algorithm to obtain a fairness-considered train timetable scheme.

[0008] This invention also provides a method for optimizing passenger railway train timetables that considers efficiency and fairness, comprising: Step 1: constructing a customized spatiotemporal network for passenger railways; Step 2: establishing a train timetable model P1 based on maximizing passenger railway efficiency; Step 3: establishing a train timetable model P2 based on passenger railway fairness; Step 4: solving the efficiency-oriented train timetable model P1 using a column generation algorithm to obtain an efficiency-oriented train timetable scheme; Step 5: applying a decomposition scheme to the fairness-oriented train timetable model P2, and then solving it using a column generation algorithm to obtain a fairness-considered train timetable scheme.

[0009] As a further improvement to the above scheme, in step 1, the method for constructing the spatiotemporal network includes the following steps:

[0010] Step 1.1: Initialization;

[0011] Assume a passenger train runs on railway tracks, and there are n stations along the line, forming a station set S = {s1, s2, ..., sn}. n}, s i This represents the i-th station on the railway track where the passenger train runs, i = 1, 2, ..., n;

[0012] Step 1.2: Obtain the data of train lines, train operators, and trains, and thus construct a customized space-time network G = (V, A) for passenger railways, where V represents a set of all space-time nodes, and let where A represents a set of space-time arcs; represents a virtual start point, represents a virtual end point; T represents a set of time nodes, t ∈ T; represents the arrival node of a train at station s i at platform l at time t; represents the departure node of a train at station s i at platform l at time t; m i represents the number of platform tracks at station s i , m i ≥ 1; represents the track through which a train passes at station s i at time t, represents the departure of a train from station s i at time t.

[0013] Further, the set of space-time arcs A includes:

[0014] a start arc: when a train starts to serve from a start point, there will be a start arc For any train k, if o k = i and t = τ k , then otherwise, where o k represents the start point of train k, τ k represents the earliest possible running time of train k at the start station ; and represents the cost generated by train k passing through the start arc .

[0015] an end arc: when a train completes service at an end point, there will be an end arc For any train k, if d k = i and , then otherwise where d k represents the end point of train k, represents the latest allowed completion time of train k at the end station ; and represents the cost generated by train k passing through the end arc .

[0016] a virtual arc: if there is a virtual arc which indicates that the train mission is canceled, and the penalty cost is where, denotes the cancellation of virtual arc by train k, and k denotes the cancellation penalty of train k;

[0017] Residence Arc: A train can use a residence arc to stop at platform l in station s i For any train k, if o k ≤i≤d k , t≥ Table 1 k , and then otherwise, where t' denotes the time when the train ends the stop at the station; b ki denotes the minimum residence time required for train k to stop at s i ; denotes the cost generated by train k stopping at residence arc ; and c' k denotes the unit residence cost of train k on the track; b ki denotes the minimum residence time required for train k to stop at s i ;

[0018] Waiting Arc: Used to represent the case where a train continues to stop on a platform track after using up the specified minimum residence time, and the waiting arc For any train k, if o k ≤i≤d k , then otherwise, where, denotes the departure node of train k at platform l in station s i at time t+1; denotes the cost generated by train k experiencing waiting arc ;

[0019] Departure Arc: Used to represent the case where a train has finished stopping on a platform track and is ready to leave the current station, and the departure arc For any train k, if o k ≤i≤d k , and then otherwise, where, denotes the cost generated by train k experiencing departure arc ;

[0020] Running Arc: used to represent the situation that a train runs on the track between two adjacent stations, since there are four kinds of train activities at both ends of the track, there are four types of running arcs: represent stay & stay, stay & pass, pass & stay, pass & pass, respectively, for any train k, if o k ≤ i ≤ d k (s i ∈ S k ), then the running cost is c k (t'-t); otherwise, the running cost is +∞, where, denotes the time t+1 at station s i is the departure node of the train at the platform l.

[0021] Further, in step 2, the method for establishing the train timetable model P1 includes the following steps:

[0022] The objective function f of the train timetable model P1 based on efficiency maximization is defined by formula (1):

[0023]

[0024] The purpose of the objective function is to find the scheme with the minimum total train running cost, i.e., the most efficient train timetable, under the condition of meeting the constraints. In formula (1), P represents the set of all arcs connecting and , for any path p∈P, A p represents the set of arcs along the path, denotes the running cost generated by train k along path p, and the set P k denotes the set of feasible paths for train k; x p denotes whether the path is assigned to the train, if assigned, x p =1, otherwise, x p =0;

[0025] The constraints of the train timetable model based on efficiency maximization are established by formulas (2)-(5):

[0026]

[0027] Formula (2) ensures that each train can only be assigned one path in the space-time network; formula (3) covers all conflict constraints, such as headway constraints, overtaking constraints and passing capacity constraints, is the set of conflict arcs; formula (4) and formula (5) are variable type constraints.

[0028] As a further improvement of the above scheme, if step 4 exists, in step 4, the generation method of the efficiency-oriented train timetable scheme comprises the following steps:

[0029] Step 4.1: constructing a relaxed efficiency train timetable model RLMP1;

[0030] Step 4.1.1: constructing a subset P k of P Only contains two paths: the path corresponding to the ideal timetable of train k from the virtual starting point to the terminal point;

[0031] Step 4.1.2: constructing a subset P of P is constructed based on P in step 4.2, if the arcs in P violate the interval, overtaking or track capacity constraints, then update P

[0032] Step 4.1.3: bring P and P into the model P1 shown in right 2, to obtain a relaxed train timetable model; the objective function

[0033] Step 4.1.4: the relaxed constraint conditions are composed of equations (8)-(10):

[0034]

[0035] Step 4.2: initializing the parameters of the column generation algorithm;

[0036] Define and initialize the iteration number and iter, and are empty sets, and the dual variable vector corresponding to constraints (8) and (9) is λ, μ, represents the optimal objective function value of model P, represents the optimal objective function value of model RLMP1, and the objective function value interval is ε;

[0037] Step 4.3: for each train k∈K, generate a path p that satisfies by dynamic programming;

[0038] Step 4.4: add the newly generated path p to the set P Update the incompatible arc set P

[0039] Step 4.5: If no path can be found to reduce the objective function or ε is small enough, then output the most efficient train timetable scheme directly.

[0040] Further, in step 4.5, if a path can be found to reduce the objective function or ε is small enough, then return to step 4.3 to perform sequentially;

[0041]

[0042] As a further improvement of the above scheme, if step 3 exists, then in step 3, the method for establishing the train timetable model P2 includes the following steps:

[0043] The objective function d of the fair-based train timetable model P2 is defined by formula (6) r :

[0044]

[0045] v k represents the weight coefficient if train k is adjusted, and the constraint condition of the model is formula (2)-formula (5).

[0046] Further, in step 5, the method for generating a fair train timetable scheme includes the following steps:

[0047] Step 5.1: Construct a sub-model of the decomposed fair-based train timetable problem

[0048] Step 5.2: The objective function is The constraint is formula (13)-formula (16);

[0049]

[0050] The objective function is to minimize the loss caused by the timetable deviation of different train operators, represents the loss of the actual train timetable deviating from the ideal timetable, represents the penalty of train shift and extended service interval, satisfying the following formula, where a ki represents the ideal time required for train k to run from s i to s i+1 .

[0051]

[0052] represents the set of train operators whose timetables have been optimized, if one train in C accesses an arc in C, then π C = 1;

[0053] Step 5.3: initialize the parameters of the column-row generation algorithm;

[0054] Input data and initialize For each set constraint C, set C Initialize to 0, iteration

[0055] Step 5.4: if For the current set of non-optimized operators, find the operator r with the highest unfairness and generate an optimized running graph for it, update C And Step 5.5: output the train timetable fair to the operator.

[0056] Compared with the prior art, the present application has the following beneficial effects:

[0057] 1. The present application develops a column-row generation based method for the efficiency maximization train timetable problem, which combines platform allocation and stop decision, solving the technical problem that existing train timetables do not consider maximizing train operation efficiency

[0058] 2. The method based on the decomposition scheme is introduced for the fair train timetable problem, aiming to maximize the fairness between train operators, which can effectively generate a fair train timetable, solving the technical problem that existing train timetables do not consider the fairness between train operators.

[0059] 3. The present application is based on the efficiency maximization train timetable model, and constructs a train timetable model for the fairness of train operators, and proposes to decompose the model so that it can be solved by the optimization algorithm of column-row generation, solving the technical problem that the efficiency and fairness of existing train timetables are difficult to balance.

[0060] 4. The present application solves the problem of large-scale train timetable model difficult to solve by designing a new type of train timetable model P1 based on the efficiency maximization of passenger railway and a train timetable model P2 based on the fairness of passenger railway. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1 The flowchart of the passenger railway train timetable optimization method considering efficiency and fairness provided by the embodiments of the present application.

[0062] Figure 2 The customized space-time network diagram used in the passenger railway train timetable optimization method. Figure 1 The customized space-time network diagram used in the passenger railway train timetable optimization method. DETAILED DESCRIPTION

[0063] With reference to the accompanying drawings, the technical solutions in the embodiments of the present application will be clearly and completely described in order to make the technical solutions in the embodiments of the present application apparent to those skilled in the art. Obviously, the described embodiments are only a part but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts should fall into the scope of the present application.

[0064] The embodiment of the present application discloses a passenger railway train timetable optimization method considering efficiency and fairness, which is based on a train timetable model of maximum efficiency, constructs a train timetable model for fairness of train operators, and proposes to decompose the model so that it can be solved by the optimization algorithm generated by column and row, solving the technical problem that the existing train timetable efficiency and fairness are difficult to balance.

[0065] Please refer to Figure 1 which is the overall flowchart of the passenger railway train timetable optimization method, mainly including the following steps:

[0066] Step 1: constructing a customized space-time network under passenger railway;

[0067] Step 2: establishing a train timetable model P1 based on the maximum efficiency of passenger railway;

[0068] Step 3: establishing a train timetable model P2 based on the fairness of passenger railway;

[0069] Step 4: solving the train timetable model P1 for efficiency by using the column and row generation algorithm to obtain the train timetable scheme for efficiency;

[0070] Step 5: applying the decomposition scheme to the train timetable model P2 for fairness, and then solving it by using the column and row generation algorithm to obtain the train timetable scheme considering fairness.

[0071] Among them, step 1, step 2 and step 4 can form a main technical scheme of a passenger railway train timetable optimization method considering efficiency, and generate the train timetable scheme for efficiency; and step 1, step 3 and step 5 can form a main technical scheme of a passenger railway train timetable optimization method considering fairness, and generate the train timetable scheme considering fairness. Whether the train timetable scheme for efficiency or the train timetable scheme considering fairness is obtained, the customized space-time network under passenger railway is indispensable.

[0072] Next, each step will be described in detail.

[0073] Step 1: constructing a customized space-time network under passenger railway.

[0074] The construction method of the space-time network mainly includes two steps: (1) Step 1.1: initialization; and step 1.2: obtaining data of train lines, train operators and trains, so as to construct a customized space-time network G=(V,A) of passenger railway.

[0075] Step 1.1: initialization.

[0076] Please refer to Figure 2 , it is assumed that the passenger train runs on the rail, and there are n stations along the line, which constitute a station set S={s1,s2,…,sn}. n Let any station in the station set S be s, the departure station be s1, and the terminal station be sn. n s∈S;

[0077] Let g i represent the minimum arrival interval of the station s i .

[0078] Let h i represent the minimum departure interval of the station s i .

[0079] Let m i represent the number of platform tracks of the station s i , m i ≥1.

[0080] Let m′ i represent the number of passing tracks of the station s i , m′1=m′ n =0 and m′2=m′3=…=m′ n-1 =1.

[0081] Let R represent a set of train operators, and there are m operators constituting a set R={r1,r2,…,rm}. m

[0082] Let k represent a set of trains; K r represents that the train is operated by the operator r,

[0083] Let o k represent the starting point of the train k; d k represent the terminal station of the train k.

[0084] Let S k represent a set of stations that the train k can skip;

[0085] Let represent a set of stations that the train k must skip;

[0086] Let represent the latest time allowed for the train k to complete the operation at the terminal station . ​

[0087] Let τ k This indicates that train k is at the originating station. Earliest possible runtime;

[0088] Let a ki Indicates that train k starts from s i to s i+1 Time;

[0089] Let a′ k This indicates that train k has additional time for acceleration;

[0090] Let a″ k This indicates that train k has additional time to decelerate;

[0091] Let b ki This indicates that if train k stops at s i Minimum required stay time;

[0092] Let c k This represents the unit operating cost of train k on the track;

[0093] Let c′ k This represents the cost per unit stay of train k on the track;

[0094] Let π k This indicates the cancellation penalty for train k;

[0095] Let ∈ k This represents the shift change penalty cost for train k;

[0096] Let ε′ k This represents the unit penalty cost for train k to continue extending its service area.

[0097] Let T denote the set of time nodes, t∈T;

[0098] Step 1.2: Obtain data on train lines, train operators, and trains to construct a customized spatiotemporal network for passenger railways, G = (V, A).

[0099] Where V represents the set of all spatiotemporal nodes, let Among them, the station arrival node Indicates when the train is at station s at time t. i At platform l, the station departs from the node. Indicates when the train is at station s at time t. i At platform l, the station passes through nodes. Indicates the time t at station s i Track traversed, station departure node This indicates that the train departs from station s at time t. i Set off, Indicates a virtual starting point. Indicates a virtual endpoint.

[0100] Where A represents the set of all spatiotemporal arcs, including start arcs, end arcs, virtual arcs, stationary arcs, waiting arcs, departure arcs, and running arcs.

[0101] Start arc: A start arc exists when a train begins service from its origin. For any train k, if o k =i and t= Table 1 k ,but otherwise, Where ξ k (u,v) represents the cost incurred by train k traversing arc u→v. Here, u represents the start of the arc, and v represents the end of the arc. For example, in this case, u is... v means In the following text, for example u is... v means

[0102] Termination arc: A train will have a termination arc when it completes its service at the terminal. For any train k, if d k =iand but otherwise

[0103] Virtual arc: If there exists a virtual arc for train k. This indicates that the train mission has been cancelled, and the resulting penalty cost is...

[0104] Stop arc: A train can use a stop arc Indicates at station s i If the train stops at platform l, and for any train k, if o k ≤i≤d k ,t≥τ k ,and but otherwise,

[0105] Waiting arc: Used to indicate a situation where a train continues to remain on the track at a certain platform after the minimum prescribed dwell time has been used up; it is shaped like... For any train k, if o k ≤i≤d k , but otherwise,

[0106] Departure arc: used to represent the case that the train stays on the platform track and prepares to leave the current station, shaped like For any train k, if o k ≤i≤d k , and then otherwise,

[0107] Running arc: used to represent the case that the train runs on the track between two adjacent stations, since there are four kinds of train activities at both ends of the track, there are four types of running arcs, shaped like representing stay & stay, stay & pass, pass & stay, pass & pass, respectively, for any train k, if o k ≤i≤d k (s i ∈S k ), then the running cost is c k (t'-t); otherwise, the running cost is +∞.

[0108] Step 2: Establish a train timetable model P1 based on the maximum efficiency of passenger railway.

[0109] The establishment method of the train timetable model P1 mainly includes the following steps: step 2.1 and step 2.2.

[0110] Step 2.1, define the objective function f of the train timetable model P1 based on the maximum efficiency by using formula (1):

[0111]

[0112] The purpose of the objective function is to find the scheme with the minimum total train running cost, i.e. the maximum efficiency train timetable, under the condition of meeting the constraints. In formula (1), P represents the set of all arcs connecting and , for any path p∈P, A p represents the arc set along the path, represents the running cost generated by train k running along path p, and set P k represents the path set available to train k. x p represents whether the path is assigned to the train, if assigned, x p =1, otherwise, x p =0.

[0113] Step 2.2, establish the constraint conditions of the train timetable model based on the maximum efficiency by using formulas (2)-(5):

[0114]

[0115] Equation (2) ensures that each train can only be assigned one path in the spatiotemporal network; Equation (3) covers all conflict constraints, such as headway constraints, overtaking constraints, and capacity constraints. It is a set of conflict arcs; Equations (4) and (5) are variable type constraints.

[0116] Step 3: Establish a train timetable model P2 based on passenger railway fairness.

[0117] The method for establishing the train timetable model P2 mainly includes the following steps: Step 3.1 and Step 3.2.

[0118] Step 3.1, use equation (6) to define the objective function d for the fair train timetable model P2. r :

[0119]

[0120] The objective function is explained as follows: Train operators hope that trains can operate according to the ideal timetable, but due to various factors (such as scheduling adjustments), the actual service may deviate from the ideal timetable. Therefore, d r It is used to quantify the degree of loss caused by the deviation between actual train operation and ideal train operation plan by train operators. Equation (6)v k This represents the weighting coefficient if train k is adjusted.

[0121] Step 3.2, the constraints of the model are Equation (2) - Equation (5).

[0122] Step 4: Solve the efficiency-oriented train timetable model P1 using the column generation algorithm to obtain the efficiency-oriented train timetable scheme.

[0123] The method for generating efficiency-oriented train timetable schemes mainly includes the following steps: Steps 4.1 to 4.5.

[0124] Step 4.1: Construct the relaxed efficiency train timetable model RLMP1.

[0125] Step 4.1.1: Construct P k subset of It contains only two paths: the path from the virtual starting point to the destination and the path corresponding to the ideal timetable of train k.

[0126] Step 4.1.2: Construction subset of Based on step 4.2 To construct, if If the arc violates the spacing, overtaking, or track capacity constraints, then update.

[0127] Step 4.1.3: Substitute the above into the model P1 shown in claim 2 to obtain the relaxed train timetable model; the objective function

[0128] Step 4.1.4: the relaxed constraints are composed of equations (8)-(10):

[0129]

[0130] Step 4.2: initialize the parameters of the column generation algorithm;

[0131] Define and initialize the iteration number and iter, and to empty set, the dual variable vectors corresponding to constraints (8) and (9) are λ, μ, denote the optimal objective function value of model P, denote the optimal objective function value of model RLMP1, the objective function value gap ε.

[0132] Step 4.3: for each train k∈K, generate a path p that satisfies

[0133] Step 4.4: add the newly generated path p to the set update the incompatible arc set

[0134] Step 4.5: if no path can be found to reduce the objective function or ε is small enough, directly output the most efficient train timetable scheme; otherwise, return to step 4.3 for sequential execution.

[0135]

[0136] Step 5: apply the decomposition scheme to the fair-oriented train timetable model P2, and then solve it using the column generation algorithm to obtain the train timetable scheme considering fairness.

[0137] The generation method of the train timetable scheme considering fairness mainly includes the following steps: steps 5.1-5.5.

[0138] Step 5.1: construct the sub-model of the decomposed fair-based train timetable problem

[0139] Step 5.2: the objective function is the constraints are equations (13)-(16); ​​​

[0140]

[0141] Objective function is to minimize the loss caused by different train operator schedule deviation, denotes the loss of train actual running schedule deviating from ideal schedule, denotes the penalty of train crew change and extended service interval, satisfying the following formula, where a ki denotes the ideal time needed for train k to run from s i to s i+1 .

[0142]

[0143] denotes the set of train operators whose schedule has been optimized, if one train in C visits one arc in C, then π C = 1.

[0144] Step 5.3: initialize the parameters of column generation algorithm.

[0145] Input data and initialize to empty set, for each set constraint C, initialize π C to 0, iteration number

[0146] Step 5.4: if find the operator r with the highest unfairness for the current set of unoptimized operators, and generate optimized running graph for it, update π C and

[0147] Step 5.5: output train schedule fair to operators.

[0148] In order to demonstrate the feasibility of the present application, a detailed data example is carried out in the present embodiment.

[0149] Beijing-Shanghai line is 1302 kilometers long, and there are 23 train stations. These stations are divided into 7 main stations and 16 secondary stations, among which the main stations are the starting and destination stations of train service, and often have more platform tracks than the secondary stations. There are four train operators on Beijing-Shanghai line. According to the operation data in 2015, the total number of trains operated is 70, among which the proportion of trains owned by Beijing-Shanghai Company, Zhongche Beijing, Zhongche Jinan and Zhongche Shanghai four operators is 35 trains. Respectively, 35%, 20%, 15% and 30%. These trains are divided into two types, namely "G train" and "D train". The average running speed of G train and D train is 300 km / h and 250 km / h respectively.

[0150] We use one of the busiest high-speed railway lines in China: the Beijing-Shanghai high-speed railway, and the operational data we obtained generate test instances.

[0151] Table 1 Operational data

[0152] Station number Station name m i ]]> m' i ]]> Type Distance (km) 0 Beijing South 6 0 Main 0 1 Langfang 1 1 Secondary 59 2 Tianjin South 2 1 Main 131 3 Cangzhou West 1 1 Secondary 219 4 Dezhou East 2 1 Secondary 327 5 Jinan West 7 1 Main 419 6 Taian 1 1 Secondary 462 7 Qufu West 1 1 Secondary 533 8 Tengzhou East 1 1 Secondary 589 9 Zaozhuang 1 1 Secondary 625 10 Xuzhou East 6 1 Main 688 11 Suzhou East 1 1 Secondary 767 12 Bengbu South 4 1 Main 844 13 Dingyuan 1 1 Secondary 897 14 Chuzhou 1 1 Secondary 959 15 Nanjing South 5 1 Main 1018 16 Zhenjiang South 1 1 Secondary 1087 17 Danyang North 1 1 Secondary 1112 18 Changzhou North 1 1 Secondary 1144 19 Wuxi East 1 1 Secondary 1201 20 Suzhou North 1 1 Secondary 1227 21 Kunshan South 1 1 Secondary 1259 22 Shanghai Hongqiao 10 0 Main 1302

[0153] The length of the planning horizon T = 1080, and each time unit represents 1 minute.

[0154] The number of trains is set to |K| = 30, 40, 50, 60, 70. For each |K| value, 3 instances are randomly generated, for a total of 15 instances. In each instance, there are four train operators, and the railway line data (S, m i , m' i ) is generated according to the settings shown in Table 1.

[0155] For each station i, we set the arrival headway g i to 4 minutes, and the departure headway h i to 2 minutes.

[0156] In addition, we generate the set K r by assigning each train to the Beijing-Shanghai Company, CNR Beijing, CNR Jinan, and CNR Shanghai with probabilities of 35%, 20%, 15%, and 30%, respectively.

[0157] For each train k e K, we first assign it a start and end point (i.e., o k , d k ). These stations are randomly chosen from a predefined set of major stations, and the specific station pairs are {(0, 5), (0, 10), (0, 22), (10, 22), (12, 22), (15, 22)}.

[0158] After the start point o k and end point d k are determined for each train, the train can pass through some intermediate stations. The probability of each intermediate station appearing in the train's station set S k is 1 / 10.

[0159] If a certain intermediate station is not selected into S k , it has a certain probability of being assigned to another set , with a probability of 1 / 10 for major stations entering and a probability of 3 / 10 for minor stations entering .

[0160] The probability of assigning a G-type train is 1 / 7, while the probability of assigning a D-type train is 6 / 7.

[0161] a′ k Fixed to 2 minutes, a″ for D-type trains k Fixed to 2 minutes, a″ for G-type trains k Fixed to 3 minutes.

[0162] a ki Depends on the average speed of the train and the distance between adjacent stations.

[0163] b ki Is randomly generated, randomly chosen from 3, 4, 5 if it is a secondary station; if it is not a primary station in , randomly chosen from 6, 8, 10.

[0164] When solving P2 problem, v k is randomly chosen from 1, 2, 3.

[0165] Test results are shown in Table 2. Since the content of Table 2 is relatively large, in order to more clearly show the data of Table 2, Table 2 is divided into two tables of left and right content: Table 2-1 and Table 2-2. Therefore, when referring to Table 2, please also splice Table 2-1 and Table 2-2 in parallel.

[0166] Table 2-1 Test Results

[0167]

[0168] Table 2-2 Test Results

[0169]

[0170] From Table 2, we can see that the efficiency maximization model of P1, i.e., the minimum total operating cost, the fairness model of P2, i.e., the minimum loss of train operators, P1 and P2 are slightly in conflict. In order to achieve fairness between train operators, a certain operating cost is paid as a price, and the optimal fairness may lose some efficiency, and vice versa. From the lower bound of P1 and the total operating cost column, we see that the lower and upper bound values almost increase linearly with the increase of the number of trains. Although the optimality gap tends to increase slightly as the number of trains involved increases, the optimality gap of all test instances is less than 5%, which shows that the proposed train schedule generation method can generate a near-optimal solution for the efficiency maximization model under the actual problem and the upper bound generation time and the lower bound generation time are at an acceptable level (all instances are less than 70 seconds), showing admirable computing performance. We also observe from the operator loss value that there is no significant change between instances with different |K|. This shows that the average deviation between the allocated timetable and the ideal timetable is not very sensitive to the number of trains in the efficiency maximization solution.

[0171] The above embodiments only express several implementation manners of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be noted that for ordinary skilled persons in the art, without departing from the concept of the present application, several modifications and improvements can be made, which are within the scope of protection of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A method for optimizing passenger railway train timetables considering both efficiency and fairness, characterized in that, It includes: Step 1: Construct a customized spatiotemporal network for passenger railways; Step 2: Establish a train timetable model based on maximizing passenger railway efficiency P1: Using equation (1), we define the objective function f of the efficiency-maximizing train timetable model P1: The objective function aims to find the train timetable with the minimum total operating cost, i.e., the most efficient train timetable, while meeting the constraints; in equation (1), P represents the connection of virtual origins. and virtual endpoint For any path p∈P, A is the set of all arcs. p Represents the set of arcs along the path. Let P represent the operating cost incurred by train k traveling along path p. k x represents the set of feasible paths for train k; p Indicates whether the path is assigned to a train; if assigned, then x p =1, otherwise, x p =0; Using equations (2)-(5), the constraints for establishing a train timetable model based on efficiency maximization are: Equation (2) ensures that each train can only be assigned one path in the spatiotemporal network; Equation (3) covers all conflict constraints, such as headway constraints, overtaking constraints, and capacity constraints. It is a set of conflict arcs; Equations (4) and (5) are variable type constraints; Step 3: Establish a train timetable model based on passenger railway fairness P2: Using equation (6), we define the objective function d of the fair train timetable model P2. r : v k The weight coefficients of train k are adjusted, and the constraints of the model are Equations (2) to (5). Step 4: Solve the efficiency-oriented train timetable model P1 using a column-row generation algorithm to obtain the efficiency-oriented train timetable scheme: Step 4.1: Construct the relaxed efficiency train timetable model RLMP1; Step 4.1.1: Construct P k subset of It contains only two paths: the path from the virtual starting point to the destination and the path corresponding to the ideal timetable of train k; Step 4.1.2: Construction subset of Based on step 4.2 To construct, if If the arc violates the spacing, overtaking, or track capacity constraints, then update. Step 4.1.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation and Substituting into model P1, we obtain the relaxed train timetable model; objective function Step 4.1.4: The relaxed constraint conditions are constructed from equations (8) to (10): Step 4.2: Initialize the parameters of the column and row generation algorithm; Define and initialize the iteration count l and iter. and For an empty set, the dual variable vectors corresponding to constraints (8) and (9) are λ, μ. This represents the optimal objective function value of model P. Let ε represent the optimal objective function value of model RLMP1, and the interval between objective function values ​​be ε. Step 4.3: For each train k∈K, use dynamic programming to generate a set of trains that satisfy... The path p; Step 4.4: Add the newly generated path p to the set. Update incompatible arc set Step 4.5: If no path can be found to narrow down the objective function or ε is small enough, then directly output the train timetable scheme with the highest efficiency; Step 5: Apply the decomposition scheme to the fairness-oriented train timetable model P2, and then solve it using the column-row generation algorithm to obtain the fairness-considered train timetable scheme: Step 5.1: Construct the decomposed sub-model of the fairness-based train timetable problem Step 5.2: The objective function is The constraints are Equations (13) to (16); The objective function is to minimize the losses caused by timetable offsets between different train operators. This indicates the loss caused by the deviation of the actual train timetable from the ideal timetable. The penalty for train shift changes and extended service intervals is expressed by the following formula, where a ki Indicates that train k starts from s i Run to s i+1 The ideal time required; This represents the set of train operators whose timetables have been optimized. If a train in C visits an arc in C, then π C =1; Step 5.3: Initialize the parameters of the column and row generation algorithm; Input data and initialize Given an empty set, constrain C for each set, and set π... C Initialize to 0, iteration count l = 1; Step 5.4: If l≤|R|, for the current set of unoptimized operators, find the operator r with the highest unfairness, generate an optimized operation graph for it, and update π. C and l; Step 5.5: Output a train timetable that is fair to the train operators.

2. The method for optimizing passenger railway train timetables according to claim 1, characterized in that, In step 1, the method for constructing the spatiotemporal network includes the following steps: Step 1.1: Initialization; Assume a passenger train runs on railway tracks, and there are n stations along the line, forming a station set S = {s1, s2, ..., sn}. n }, s i This represents the i-th station on the railway track where the passenger train runs, i = 1, 2, ..., n; Step 1.2: Obtain data on train lines, train operators, and trains to construct a customized spatiotemporal network for passenger railways, G = (V, A), where V represents the set of all spatiotemporal nodes. Where A represents the set of spacetime arcs; Indicates a virtual starting point. The virtual endpoint is represented by T; T represents the set of time nodes, t∈T; Indicates time t at station s i At the arrival point of train l at platform l; Indicates time t at station s i At the departure point of train l at platform l; m i Station s i The number of platform tracks, m i ≥1; For each station, a node represents a point at station s where the train arrives at station s at time t. i The track that passed; Let be the station departure node, indicating that the train departs from station s at time t. i Set off.

3. The method for optimizing passenger railway train timetables considering efficiency and fairness according to claim 2, characterized in that, The set of spacetime arcs A includes: Start arc: A start arc exists when a train begins service from its origin. For any train k, if o k =i and t= τ k ,but otherwise, Among them, o k Indicates the starting point of train k. τ k This indicates that train k is at the originating station. Earliest possible runtime; This indicates that train k has passed through the starting arc. The costs incurred; Termination arc: A train will have a termination arc when it completes its service at the terminal. For any train k, if d k =iand but otherwise Where, d k Indicates the destination of train k. This indicates that train k is at the terminal station. The latest allowed time to complete the run; This indicates that train k has passed through the ending arc. The costs incurred; Virtual arc: If a virtual arc exists for train k. This indicates that the train mission has been cancelled, and the resulting penalty cost is... in, This indicates that train k cancels the virtual arc. The resulting costs, π k This indicates the cancellation penalty for train k; Stop arc: A train can use a stop arc Indicates at station s i If the train stops at platform l, and for any train k, if o k ≤i≤d k ,t≥ τ k ,and but otherwise, Where t′ represents the time when the train finishes its stop at the station; b ki This indicates that if train k stops at s i Minimum required stay time; This indicates that train k is stopped at the stopping arc. The resulting costs, c′ k b represents the unit cost of train k staying on the track; ki This indicates that if train k stops at s i Minimum required stay time; Waiting arc: Used to indicate the situation where a train continues to remain on the track at a certain station after the minimum prescribed dwell time has been used up. For any train k, if but otherwise, in, This indicates that at time t+1 at station s i At the departure point of the train at platform l; This indicates that train k is experiencing a waiting arc. The costs incurred; Departure arc: Used to indicate that the train has finished stopping on the platform tracks and is preparing to leave the current station. For any train k, if o k ≤i≤d k ,and but otherwise, in, This indicates that train k is experiencing the departure arc. The costs incurred; Running arc: Used to represent the movement of a train on the track between two adjacent stations. Since there are four types of train activity at both ends of the track, there are four types of running arcs: These represent stop & stop, stop & pass, pass & stop, and pass & pass, respectively. For any train k, if The operating cost is c. k (t ′ -t); otherwise, the operating cost is +∞, where, Representing time t ′ The train at station s i+1 The departure node at platform l.

4. The passenger railway train timetable optimization method according to claim 3, characterized in that, In step 4.5, if a path is found that can narrow down the objective function or ε is small enough, then return to step 4.3 and execute sequentially.

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