Passenger railway train timetable optimization method considering efficiency and fairness

Abstract

The invention discloses a passenger railway train timetable optimization method considering efficiency and fairness. The method comprises the following steps: step 1, constructing a customized space-time network under a passenger railway; step 2, establishing a train timetable model P1 based on passenger transport railway efficiency maximization; step 3, establishing a train timetable model P2 based on passenger railway fairness; 4, solving the efficiency-oriented train timetable model P1 by using a column-row generation algorithm to obtain an efficiency-oriented train timetable scheme; and 5, applying a decomposition scheme to the fairness-oriented train timetable model P2, and then solving by using a column-row generation algorithm to obtain a train timetable scheme considering fairness. According to the method, the train timetable model oriented to the fairness of the train operators is constructed based on the train timetable model with the maximum efficiency, and the model is decomposed, so that the train timetable model can be solved by using an optimization algorithm generated by columns and rows, and the technical problem that the efficiency and the fairness of an existing train timetable are difficult to balance is solved.

Description

Technical Field

[0001] The present invention relates to a passenger railway train timetable optimization method in the railway train field, and in particular to a passenger railway train timetable optimization method considering efficiency, a passenger railway train timetable optimization method considering fairness, and a passenger railway train timetable optimization method considering efficiency and fairness. Background Art

[0002] Railways are capital-intensive infrastructure that requires large investments for construction and constant maintenance and renovation during operation. Therefore, railways are usually invested and owned by the government or the private sector. In order to improve operational sustainability and maximize returns, railway line owners usually allow multiple train operators to provide diversified services to passengers using the railway infrastructure. For example, China's Beijing-Shanghai High-Speed ​​Railway Line (referred to as the Beijing-Shanghai Line) is owned by Beijing-Shanghai High-Speed ​​Railway Co., Ltd. (referred to as the Beijing-Shanghai Company), and train services on the line are provided by four companies. Train operators: Beijing-Shanghai Company, China Railway Beijing Group Co., Ltd. (referred to as CRRC Beijing), China Railway Shanghai Group Co., Ltd. (referred to as CRRC Shanghai), China Railway Jinan Group Co., Ltd. (referred to as China Railway Jinan) China Resources-Jinan). These operators share railway infrastructure (such as track sections and platforms) to meet their service needs and pay for the use of infrastructure and facilities.

[0003] In order to coordinate operations between different operators, line owners need to develop a comprehensive 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 train resource utilization and service level (e.g., additional train waiting time and expected travel time). However, since train services on a railway line are provided by multiple train operators, another important goal of the train timetable is to maximize operational fairness among train operators.

[0004] Fairness issues in train schedules have been mainly studied at the train level. Existing work attempts to balance the drawbacks between trains by assigning operating priorities to different trains. While this approach helps avoid systematic discrimination against certain trains, it can lead to disproportionate allocations at the operator level, resulting in biased service schedules that disadvantage one or more operators. Summary of the invention

[0005] In order to solve the technical problem that the existing train timetable does not take the fairness of train operators into consideration, the present invention provides a method for optimizing a passenger railway train timetable taking fairness into consideration; in order to solve the technical problem that the existing train timetable model is complex and difficult to solve, the present invention provides a method for solving it based on a column-row generation algorithm; in order to solve the technical problem that it is difficult to balance the efficiency and fairness of the existing train timetable, the present invention provides a method for optimizing a passenger railway train timetable taking efficiency and fairness into consideration.

[0006] The present invention is implemented by the following technical scheme: a method for optimizing a passenger railway train timetable taking efficiency into consideration, which comprises: step 1: constructing a customized space-time 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-row generation algorithm to obtain an efficiency-oriented train timetable solution.

[0007] The present invention also provides a method for optimizing a passenger railway train schedule taking fairness into consideration, which comprises: step 1: constructing a customized space-time network for passenger railways; step 3: establishing a train schedule model P2 based on fairness for passenger railways; step 5: applying a decomposition scheme to the fairness-oriented train schedule model P2, and then solving it using a column-row generation algorithm to obtain a train schedule scheme taking fairness into consideration.

[0008] The present invention also provides a passenger railway train schedule optimization method taking into account efficiency and fairness, which includes: step 1: constructing a customized space-time network for passenger railways; step 2: establishing a train schedule model P1 based on maximizing the efficiency of passenger railways; step 3: establishing a train schedule model P2 based on the fairness of passenger railways; step 4: using a column-row generation algorithm to solve the efficiency-oriented train schedule model P1 to obtain an efficiency-oriented train schedule plan; step 5: applying a decomposition plan to the fairness-oriented train schedule model P2, and then solving it with a column-row generation algorithm to obtain a train schedule plan that takes fairness into account.

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

[0010] Step 1.1: Initialization;

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

[0012] Step 1.2: Obtain data on train lines, train operators, and trains to build a customized space-time network for passenger railways G = (V, A), where V represents the set of all space-time nodes. Among them, A represents the set of space-time arcs; represents the virtual starting point, represents the virtual end point; T represents the time node set, t∈T; represents time t at station s i The arrival node of the train at platform l; represents time t at station s i The departure node of the train at platform l; m i Indicates stations i Number of platform tracks, m i ≥1; is a station passing node, indicating that the train is at station s at time t i Through the track, is the station departure node, indicating that the train leaves station s at time t i Set off.

[0013] Furthermore, the space-time arc set A includes:

[0014] Start arc: A train has a start arc when it starts service from the starting point. For any train k, if o k =i and t = τ k ,but otherwise, Among them, k represents the starting point of train k, τ k Indicates that train k is at the departure station Earliest possible running time; Indicates that train k passes the starting arc the costs incurred;

[0015] End arc: A train has an end arc when it completes service at the terminal. For any train k, if d k =iand but otherwise Among them, d k represents the destination of train k, Indicates that train k is at the terminal The latest time allowed for the run to complete; Indicates that train k passes the end arc the costs incurred;

[0016] Virtual arc: If there is a virtual arc for train k This indicates that the train mission is cancelled, and the penalty cost is in, Indicates that train k cancels the virtual arc The cost incurred, π k represents the cancellation penalty of train k;

[0017] Dwell arc: A train can use a dwell arc Indicates at the station i The platform l stops. For any train k, if o k ≤i≤d k ,t≥ τ k ,and but otherwise, Where t′ represents the time when the train stops at the station; b ki If train k stops at s i the minimum required stay time; Indicates that train k stays on the stop arc Costs incurred, c′ k represents the unit stop cost of train k on the track; b ki If train k stops at s i the minimum required stay time;

[0018] Waiting arc: It is used to indicate that a train continues to stay on a platform track after using up the prescribed minimum stay time. For any train k, if o k ≤i≤d k , but otherwise, in, Indicates that the train is at station s at time t+1 i At the departure node of station l; Indicates that train k is experiencing a waiting arc the costs incurred;

[0019] Departure arc: It is used to indicate that the train has finished staying on the platform track and is ready to leave the current station. For any train k, if o k ≤i≤d k ,and but otherwise, in, Indicates that train k is experiencing the departure arc the costs incurred;

[0020] Running arc: It is used to represent the situation where a train runs on a track between two adjacent stations. Since there are four types of train activities at both ends of the track, there are four types of running arcs: They represent stop & stop, stop & pass, pass & stop, pass & pass. For any train k, if o k ≤i≤d k (s i ∈S k ), The operating cost is c k (t′-t); otherwise, the operating cost is +∞, where Indicates time t+1 at station s i The departure node of the train at platform l.

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

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

[0023]

[0024] The objective function is to find the solution with the minimum total train operation cost under the condition of meeting the constraints, that is, the most efficient train schedule. and All arc sets of A, for any path p∈P, p represents the set of arcs along the path, represents the running cost of train k running along path p, and the set P k represents the set of feasible paths for train k; x p Indicates whether the path is assigned to a train. If so, x p =1, otherwise, x p =0;

[0025] The constraints of the train schedule model based on efficiency maximization are established using equations (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 conflicting constraints, such as headway constraints, overtaking constraints, and capacity constraints. is a set of conflict arcs; Equations (4) and (5) are variable type constraints.

[0028] As a further improvement of the above solution, if step 4 exists, then in step 4, the method for generating an efficiency-oriented train timetable solution includes the following steps:

[0029] Step 4.1: Construct the relaxed efficient train schedule model RLMP1;

[0030] Step 4.1.1: Build P k Subset of It contains only two paths: the path from the virtual starting point to the end point and the path corresponding to the ideal schedule of train k;

[0031] Step 4.1.2: Build Subset of Based on step 4.2 To construct, if If the arc in violates the interval, overtaking or track capacity constraints, update

[0032] Step 4.1.3: and Substitute into the model P1 shown in right 2 to obtain the relaxed train schedule model; the objective function

[0033] Step 4.1.4: The relaxed constraints are formed by equations (8) to (10):

[0034]

[0035] Step 4.2: Initialize the parameters of the column and row generation algorithm;

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

[0037] Step 4.3: For each train k∈K, use dynamic programming to generate a train that satisfies The path p;

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

[0039] Step 4.5: If no path is found to reduce the objective function or ε is small enough, directly output the most efficient train schedule solution.

[0040] Furthermore, in step 4.5, if a path is found to reduce the objective function or ε is small enough, then return to step 4.3 and execute sequentially;

[0041]

[0042] As a further improvement of the above solution, 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 train schedule model P2 is defined using equation (6): r :

[0044]

[0045] v k It represents the weight coefficient if train k is adjusted. The constraints of the model are formula (2)-formula (5).

[0046] Furthermore, in step 5, the method for generating a fair train schedule solution includes the following steps:

[0047] Step 5.1: Construct the decomposed sub-model of the fairness-based train schedule problem

[0048] Step 5.2: The objective function is The constraints are equation (13)-equation (16);

[0049]

[0050] The objective function is to minimize the loss caused by the deviation of the timetable of different train operators. It indicates the loss caused by the deviation of the actual train operation schedule from the ideal schedule. represents the penalty for train shift change and extended service interval, which satisfies the following formula, where a ki Indicates that train k starts from s i Run to s i+1 Ideal time needed.

[0051]

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

[0053] Step 5.3: Initialize the parameters of the column and row generation algorithm;

[0054] Input data and initialize is an empty set. For each set constraint C, set π C Initialized to 0, number of iterations

[0055] Step 5.4: If For the current unoptimized operator set, find the operator r with the highest unfairness, generate an optimized operation diagram for it, and update π C and Step 5.5: Output a train schedule that is fair to operators.

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

[0057] 1. This paper develops a method based on column-row generation for the problem of maximizing the efficiency of train timetables. This method combines platform allocation and stop decision making, solving the technical problem that the existing train timetable does not consider maximizing train operation efficiency.

[0058] 2. A decomposition-based approach is introduced to address the fair train timetable problem, which aims to maximize fairness among train operators. This approach can effectively generate a fair train timetable and solve the technical problem that the existing train timetable does not consider fairness among train operators.

[0059] 3. Based on the most efficient train timetable model, the present invention constructs a fair train timetable model for train operators, and proposes to decompose the model so that it can be solved by an optimization algorithm generated by columns and rows, thus solving the technical problem that it is difficult to balance the efficiency and fairness of the existing train timetable.

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

[0061] Figure 1 A flowchart of a method for optimizing a passenger railway train schedule taking into account efficiency and fairness provided in an embodiment of the present invention.

[0062] Figure 2 for Figure 1 Schematic diagram of the customized space-time network used in the passenger railway train schedule optimization method. DETAILED DESCRIPTION

[0063] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] The embodiment of the present invention discloses a passenger railway train schedule optimization method that takes efficiency and fairness into consideration. Based on the train schedule model with the highest efficiency, a fair train schedule model for train operators is constructed, and it is proposed to decompose the model so that it can be solved by an optimization algorithm generated by columns and rows, thereby solving the technical problem that it is difficult to balance the efficiency and fairness of the existing train schedule.

[0065] See also Figure 1 , which is an overall flow chart of the passenger railway train schedule optimization method, mainly comprising the following steps:

[0066] Step 1: Build a customized space-time network for passenger railways;

[0067] Step 2: Establish a train schedule model P1 based on maximizing passenger railway efficiency;

[0068] Step 3: Establish a train schedule model P2 based on passenger railway fairness;

[0069] Step 4: Solve the efficiency-oriented train timetable model P1 using the column-row generation algorithm to obtain the efficiency-oriented train timetable solution;

[0070] 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 a fairness-oriented train timetable solution.

[0071] Among them, step 1, step 2, and step 4 can form a main technical solution of a passenger railway train schedule optimization method considering efficiency, and generate a train schedule solution oriented to efficiency; and step 1, step 3, and step 5 can form a main technical solution of a passenger railway train schedule optimization method considering fairness, and generate a train schedule solution considering fairness. Whether it is a train schedule solution oriented to efficiency or a train schedule solution considering fairness, it is inseparable from the customized space-time network under the passenger railway of the present invention.

[0072] Next, each step is described in detail.

[0073] Step 1: Build a customized space-time network for passenger railways.

[0074] The method for constructing a space-time network mainly includes two steps: (1) Step 1.1: Initialization; Step 1.2: Obtain data on train lines, train operators, and trains to construct a customized space-time network G = (V, A) for passenger railways.

[0075] Step 1.1: Initialization.

[0076] Please combine Figure 2 , assuming that the passenger train runs on the rails, there are n stations along the line, forming a station set S = {s1, s2, ..., s n}, let any station in the station set S be denoted as s, the departure station be denoted as s1, and the destination station be denoted as s n , s∈S;

[0077] Let g i Indicates stations i The minimum arrival interval of

[0078] Let h i Indicates stations i The minimum departure interval;

[0079] Let m i Indicates stations i Number of platform tracks, m i ≥1;

[0080] Let m′ i Indicates stations i The number of passing tracks, m′1=m′ n = 0 and m′2 = m′3 = ... = m′ n-1 =1;

[0081] Let R represent the set of train operators. There are m operators in total, which constitute the set R = {r1, r2, …, r m};

[0082] Let k denote the set of trains; K r indicates that the train is operated by operator r,

[0083] Order o k represents the starting point of train k; d k represents the destination of train k;

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

[0085] make represents the set of stations that train k must skip;

[0086] make Indicates that train k is at the terminal The latest time allowed for the run to complete;

[0087] Let τ k Indicates that train k is at the departure station Earliest possible running time;

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

[0089] Let a′ k represents the extra time if train k accelerates;

[0090] Let a″ k represents the extra time for train k to decelerate if there is any;

[0091] Let b ki If train k stops at s i the minimum required stay time;

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

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

[0094] Let π k represents the cancellation penalty of train k;

[0095] Let ∈ k represents the shift penalty cost of train k;

[0096] Let ε′ k represents the unit penalty cost of train k continuing to extend the service interval.

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

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

[0099] Where V represents the set of all spatiotemporal nodes, Among them, the station arrival node Indicates that the train is at station s at time t i At platform l, the station leaves the node Indicates that the train is at station s at time t i At platform l, the station passes through the node Indicates that the train is at station s at time t i Passing tracks, station departure nodes It means that the train leaves station s at time t. i Set off, represents the virtual starting point, Indicates a virtual endpoint.

[0100] Among them, A represents the set of all space-time arcs, including start arc, end arc, virtual arc, stay arc, waiting arc, departure arc, and running arc.

[0101] Start arc: A train has a start arc when it starts service from the starting point. For any train k, if o k =i and t= τ k ,but otherwise, where ξ k (u,v) represents the cost of train k passing through arc u→v. Here u represents the start of the arc and v represents the end of the arc. For example, here, u is v is In the following, for example u is v is

[0102] End arc: A train has an end arc when it completes service at the terminal. For any train k, if d k =iand but otherwise

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

[0104] Dwell arc: A train can use a dwell arc Indicates at the station i The platform l stops. For any train k, if o k ≤i≤d k ,t≥τ k ,and but otherwise,

[0105] Waiting arc: It is used to indicate that a train continues to stay on a platform track after using up the prescribed minimum stay time. For any train k, if o k ≤i≤d k , but otherwise,

[0106] Departure arc: used to indicate that the train has finished staying on the platform track and is ready to leave the current station, as shown in For any train k, if o k ≤i≤d k ,and but otherwise,

[0107] Running arc: It is used to represent the situation where a train runs on a track between two adjacent stations. Since there are four types of train activities at both ends of the track, there are four types of running arcs, such as They represent stop & stop, stop & pass, pass & stop, pass & pass. For any train k, if o k ≤i≤d k (s i ∈S k ), The operating cost is c k (t′-t); otherwise, the operating cost is +∞.

[0108] Step 2: Establish a train schedule model P1 based on maximizing passenger railway efficiency.

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

[0110] Step 2.1, use formula (1) to define the objective function f of the train schedule model P1 based on efficiency maximization:

[0111]

[0112] The objective function is to find the solution with the minimum total train operation cost under the condition of meeting the constraints, that is, the most efficient train schedule. and All arc sets of A, for any path p∈P, p represents the set of arcs along the path, represents the running cost of train k running along path p, and the set P k represents the set of feasible paths for train k. p Indicates whether the path is assigned to a train. If so, x p =1, otherwise, x p =0.

[0113] Step 2.2, use equations (2)-(5) to establish the constraints of the train schedule model based on efficiency maximization:

[0114]

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

[0116] Step 3: Establish a train schedule model P2 based on fairness of passenger railways.

[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: Define the objective function d of the fair train schedule model P2 using equation (6): r :

[0119]

[0120] The objective function is explained as follows: the train operator hopes that the train can run according to the ideal schedule, but due to various factors (such as scheduling adjustments, etc.), the actual service of the train may deviate from the ideal schedule. Therefore, d r It is used to quantify the loss caused by the deviation between the actual train operation and the ideal train operation plan. k Represents the weight coefficient if train k is adjusted.

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

[0122] Step 4: Use the column-row generation algorithm to solve the efficiency-oriented train timetable model P1 and obtain the efficiency-oriented train timetable solution.

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

[0124] Step 4.1: Construct the relaxed efficient train schedule model RLMP1.

[0125] Step 4.1.1: Build P k Subset of It contains only two paths: the path from the virtual starting point to the end point and the path corresponding to the ideal schedule of train k.

[0126] Step 4.1.2: Build Subset of Based on step 4.2 To construct, if If the arc in violates the interval, overtaking or track capacity constraints, update

[0127] Step 4.1.3: and Substitute into the model P1 shown in right 2 to obtain the relaxed train schedule model; the objective function

[0128] Step 4.1.4: The relaxed constraints are formed by equations (8) to (10):

[0129]

[0130] Step 4.2: Initialize the parameters of the column and row generation algorithm;

[0131] Define and initialize the number of iterations and iter, and is an empty set, and the dual variable vectors corresponding to constraints (8) and (9) are 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 ε.

[0132] Step 4.3: For each train k∈K, use dynamic programming to generate a train that satisfies The path p.

[0133] Step 4.4: Add the newly generated path p to the set Update incompatible arc collection

[0134] Step 4.5: If no path is found to reduce the objective function or ε is small enough, directly output the most efficient train schedule plan; otherwise, return to step 4.3 and execute sequentially.

[0135]

[0136] 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 a fairness-oriented train timetable solution.

[0137] The method for generating a fair train schedule plan mainly includes the following steps: step 5.1 to step 5.5.

[0138] Step 5.1: Construct the decomposed sub-model of the fairness-based train schedule problem

[0139] Step 5.2: The objective function is The constraints are equation (13)-equation (16);

[0140]

[0141] The objective function is to minimize the loss caused by the deviation of the timetable of different train operators. It indicates the loss caused by the deviation of the actual train operation schedule from the ideal schedule. represents the penalty for train shift change and extended service interval, which satisfies the following formula, where a ki Indicates that train k starts from s i Run to s i+1 Ideal time needed.

[0142]

[0143] represents the set of train operators whose schedules have been optimized, if A train in visits an arc in C, then π C =1.

[0144] Step 5.3: Initialize the parameters of the column and row generation algorithm.

[0145] Input data and initialize is an empty set. For each set constraint C, set π C Initialized to 0, number of iterations

[0146] Step 5.4: If For the current unoptimized operator set, find the operator r with the highest unfairness, generate an optimized operation diagram for it, and update π C and

[0147] Step 5.5: Output a train schedule that is fair to operators.

[0148] In order to demonstrate the feasibility of the present invention, detailed data examples are given in this embodiment.

[0149] The Beijing-Shanghai Line is 1,302 kilometers long and has a total of 23 railway stations. These stations are divided into 7 major stations and 16 minor stations, of which the major stations are the departure and destination stations of the train services and often have more platform tracks than the minor stations. There are four train operators on the Beijing-Shanghai Line. According to the 2015 operating data, the total number of operating trains is 70, of which the proportion of trains owned by the four operators, Beijing-Shanghai Company, CRRC Beijing, CRRC Jinan, and CRRC Shanghai, is 35%. They are 35%, 20%, 15%, and 30% respectively. These trains are divided into two types, namely "G trains" and "D trains". The average running speeds of G-type trains and D-type trains are 300 km / h and 250 km / h respectively.

[0150] We generate test instances using operational data from one of China’s busiest high-speed railway lines: the Beijing-Shanghai High-Speed ​​Railway.

[0151] Table 1 Operational data

[0152] Station number Station Name <![CDATA[m i ]]> <![CDATA[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 Texas 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 is 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, with a total of 15 instances. In each instance, there are four train operators, and the railway line data (S, m i ,m′ i ).

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

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

[0157] For each train k∈K, we first assign it a starting point and a destination (i.e., o k ,d k ). These sites are randomly selected from a predefined set of primary sites, the specific site pairs are {(0,5),(0,10),(0,22),(10,22),(12,22),(15,22)}.

[0158] For each train, the starting point o is determined k and end point d k After that, the train may pass through some intermediate stations. Each intermediate station appears in the station set S of the train. k The probability of winning is 1 / 10.

[0159] If a stop is not selected in S k , then it has a certain probability of being assigned to another set The main site entry The probability is 1 / 10, the secondary site enters The probability is 3 / 10.

[0160] The probability of assignment to a G train is 1 / 7, while the probability of assignment to a D train is 6 / 7.

[0161] a′ k Fixed at 2 minutes, a″ for D-type trains k 2 minutes, G-type train a″ k For 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. If it is a secondary site, it is randomly selected from 3, 4, and 5; if it is not The main sites in the network are randomly selected from 6, 8, and 10.

[0164] When solving the P2 problem, v k Randomly select from 1, 2, 3.

[0165] The test results are shown in Table 2. Since Table 2 contains a lot of content, in order to more clearly display the data in Table 2, Table 2 is divided into two tables with left and right contents: Table 2-1 and Table 2-2. Therefore, when looking up 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] As can be seen from Table 2, the efficiency maximization model of P1 is the minimum total operating cost, and the fairness model of P2 is the minimum loss of train operators. P1 and P2 are slightly in conflict. In order to achieve fairness among train operators, a certain operating cost must be paid as a price. Achieving optimal fairness may lose some efficiency, and vice versa. From the lower bound and total operating cost columns of P1, we see that the lower and upper bound values ​​increase almost linearly with the number of trains. Although the optimality difference tends to increase slightly with the number of trains involved, the optimality gap of all test instances is less than 5%, which shows that the proposed column and row generation method is able to generate near-optimal solutions for the efficiency maximization model under practical problems and the generation upper and lower bound times are at acceptable levels (less than 70 seconds for all instances), showing admirable computational performance. We also observed from the operator loss value that there is no significant change between instances with different |K|. This shows that the average deviation between the assigned schedule and the ideal schedule is not very sensitive to the number of trains in the efficiency maximization solution.

[0171] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A passenger railway train schedule optimization method considering efficiency, characterized in that: It includes: Step 1: Build a customized space-time network for passenger railways; Step 2: Establish a train schedule model P1 based on maximizing passenger railway efficiency; Step 4: Use the column-row generation algorithm to solve the efficiency-oriented train timetable model P1 and obtain the efficiency-oriented train timetable solution.

2. A method for optimizing passenger railway train schedules taking fairness into consideration, characterized in that: It includes: Step 1: Build a customized space-time network for passenger railways; Step 3: Establish a train schedule model P2 based on passenger railway fairness; 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 a fairness-oriented train timetable solution.

3. A passenger railway train schedule optimization method considering efficiency and fairness, characterized in that: It includes: Step 1: Build a customized space-time network for passenger railways; Step 2: Establish a train schedule model P1 based on maximizing passenger railway efficiency; Step 3: Establish a train schedule model P2 based on passenger railway fairness; Step 4: Solve the efficiency-oriented train timetable model P1 using the column-row generation algorithm to obtain the efficiency-oriented train timetable solution; 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 a fairness-oriented train timetable solution.

4. The passenger railway train schedule optimization method according to claim 1, 2 or 3, characterized in that: In step 1, the method for constructing the spatiotemporal network includes the following steps: Step 1.1: Initialization; Assume that a passenger train runs on a railroad and there are n stations along the line, forming a station set S = {s1, s2, ..., s n },s i represents the i-th station where the passenger train runs on the track, i = 1, 2, ..., n; Step 1.2: Obtain data on train lines, train operators, and trains to build a customized space-time network for passenger railways G = (V, A), where V represents the set of all space-time nodes. Among them, A represents the set of space-time arcs; represents the virtual starting point, represents the virtual end point; T represents the time node set, t∈T; represents time t at station s i The arrival node of the train at platform l; represents time t at station s i The departure node of the train at platform l; m i Indicates stations i Number of platform tracks, m i ≥1; is a station passing node, indicating that the train is at station s at time t i Tracks passing by; is the station departure node, indicating that the train leaves station s at time t i Set off.

5. The passenger railway train schedule optimization method considering efficiency and fairness according to claim 4 is characterized in that: The space-time arc set A includes: Start arc: A train has a start arc when it starts service from the starting point. For any train k, if o k =i and t = τ k ,but otherwise, Among them, k represents the starting point of train k, τ k Indicates that train k is at the departure station Earliest possible running time; Indicates that train k passes the starting arc the costs incurred; End arc: A train has an end arc when it completes service at the terminal. For any train k, if d k =iand but otherwise Among them, d k represents the destination of train k, Indicates that train k is at the terminal The latest time allowed for the run to complete; Indicates that train k passes through the end arc the costs incurred; Virtual arc: If there is a virtual arc for train k This indicates that the train mission is cancelled, and the penalty cost is in, Indicates that train k cancels the virtual arc The cost incurred, π k represents the cancellation penalty of train k; Dwell arc: A train can use a dwell arc Indicates at the station i The platform l stops. For any train k, if o k ≤i≤d k ,t≥τ k ,and but otherwise, Among them, t ′ Indicates the time when the train stops at the station; b ki If train k stops at s i the minimum required stay time; Indicates that train k stays on the stop arc The costs incurred, c ′ k represents the unit stop cost of train k on the track; b ki If train k stops at s i the minimum required stay time; Waiting arc: It is used to indicate that a train continues to stay on a platform track after using up the prescribed minimum stay time. For any train k, if o k ≤i≤d k , but otherwise, in, Indicates time t+1 at station s i The departure node of the train at platform l; Indicates that train k is experiencing a waiting arc the costs incurred; Departure arc: It is used to indicate that the train has finished staying on the platform track and is ready to leave the current station. For any train k, if o k ≤i≤d k ,and but otherwise, in, Indicates that train k is experiencing the departure arc the costs incurred; Running arc: It is used to represent the situation where a train runs on a track between two adjacent stations. Since there are four types of train activities at both ends of the track, there are four types of running arcs: They represent stop & stop, stop & pass, pass & stop, pass & pass. For any train k, if o k ≤i≤d k (s i ∈S k ), The operating cost is c k (t′-t); otherwise, the operating cost is +∞, where Indicates that the train is at station s at time t′ i+1 At the departure node of station l.

6. The passenger railway train schedule optimization method according to claim 5, characterized in that: If step 2 exists, then in step 2, the method for establishing the train schedule model P1 includes the following steps: The objective function f of the train schedule model P1 based on efficiency maximization is defined using formula (1): The objective function is to find the solution with the minimum total train operation cost under the condition of meeting the constraints, that is, the most efficient train schedule. and All arc sets of A, for any path p∈P, p represents the set of arcs along the path, represents the running cost of train k running along path p, and the set P k represents the set of feasible paths for train k; x p Indicates whether the path is assigned to a train. If so, x p =1, otherwise, x p =0; The constraints of the train schedule model based on efficiency maximization are established using equations (2)-(5): Formula (2) ensures that each train can only be assigned one path in the space-time network; Formula (3) covers all conflicting constraints, such as headway constraints, overtaking constraints, and capacity constraints. is a set of conflict arcs; Equations (4) and (5) are variable type constraints.

7. The passenger railway train schedule optimization method according to claim 6, characterized in that: In step 4, the method for generating an efficiency-oriented train timetable solution includes the following steps: Step 4.1: Construct the relaxed efficient train schedule model RLMP1; Step 4.1.1: Build P k Subset of It contains only two paths: the path from the virtual starting point to the end point and the path corresponding to the ideal schedule of train k; Step 4.1.2: Build Subset of Based on step 4.2 To construct, if If the arc in violates the interval, overtaking or track capacity constraints, update Step 4.1.3: and Substitute into the model P1 shown in right 2 to obtain the relaxed train schedule model; the objective function Step 4.1.4: The relaxed constraints are formed by equations (8) to (10): Step 4.2: Initialize the parameters of the column and row generation algorithm; Define and initialize the number of iterations and iter, and is an empty set, and the dual variable vectors corresponding to constraints (8) and (9) are λ,μ, represents the optimal objective function value of model P, It represents the optimal objective function value of model RLMP1, and the objective function value interval ε; Step 4.3: For each train k∈K, use dynamic programming to generate a train that satisfies The path p; Step 4.4: Add the newly generated path p to the set Update incompatible arc collection Step 4.5: If no path is found to reduce the objective function or ε is small enough, directly output the most efficient train schedule solution.

8. The passenger railway train schedule optimization method according to claim 7, characterized in that: In step 4.5, if a path is found to reduce the objective function or ε is small enough, return to step 4.3 and execute sequentially; 9. The passenger railway train schedule optimization method according to claim 5, characterized in that: If step 3 exists, then in step 3, the method for establishing the train schedule model P2 includes the following steps: The objective function d of the fair train schedule model P2 is defined using equation (6): r : v k It represents the weight coefficient if train k is adjusted. The constraints of the model are formula (2)-formula (5).

10. The passenger railway train schedule optimization method according to claim 9, characterized in that: In step 5, the method for generating a fair train schedule solution includes the following steps: Step 5.1: Construct the decomposed sub-model of the fairness-based train schedule problem Step 5.2: The objective function is The constraints are equation (13)-equation (16); The objective function is to minimize the loss caused by the deviation of the timetable of different train operators. It indicates the loss caused by the deviation of the actual train operation schedule from the ideal schedule. represents the penalty for train shift change and extended service interval, which satisfies the following formula, where a ki Indicates that train k starts from s i Run to s i+1 Ideal time needed. represents the set of train operators whose schedules have been optimized, if A train in 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 is an empty set. For each set constraint C, set π C Initialized to 0, number of iterations Step 5.4: If For the current unoptimized operator set, find the operator r with the highest unfairness, generate an optimized operation diagram for it, and update π C and Step 5.5: Output a train schedule that is fair to train operators.

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