A diagram and speed curve integrated generation method for passenger and freight train co-line operation

Abstract

The application relates to the technical field of train operation scheduling, in particular to a diagram and speed curve integrated generation method for passenger and freight train co-line operation; the diagram and speed curve of the passenger and freight train are optimized, the waiting and letting time of the train in the way is maximally reduced, resource allocation is optimized, operation cost is saved, the utilization rate of the whole line is improved, safe operation of the passenger and freight train in the co-line mode can be ensured, and the utilization rate of the whole line is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of train operation scheduling, and in particular to a method for integrating the generation of an operation diagram and a speed curve for co-linear operation of passenger and freight trains. Background Art

[0002] As a vital mode of transportation, railways carry an increasingly heavy load of passenger and freight transport, placing increasing demands on operational efficiency, safety, and service quality. Especially on routes where passenger and freight trains co-exist, properly managing the interactions between different types of trains and optimizing the allocation of time and space resources has become a key issue urgently needed for efficient railway operations.

[0003] The train schedule is a core tool for railway transport organization, used to plan the operation status of trains along the line within a specific time period, including train arrival and departure times, interval operation time, stop time, and passing arrangements. However, facing the complexity of passenger and freight trains running on the same line, it is necessary to take into account the differences in the characteristics of various train types, the rational allocation of line resources, and the flexible response to emergencies. The speed curve depicts the changes in train speed over time and position during operation. It is an important basis for ensuring train arrival on time, safe operation, and energy conservation and consumption reduction. When passenger and freight trains run on the same line, the speed curve must not only comply with the line speed limit and train performance requirements, but also consider the speed changes caused by operations such as passing and overtaking between different train types. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a method for integrating the generation of operation diagrams and speed curves for passenger and freight trains running on the same line. By constructing a mixed block system constraint and combining other safety constraints during the train operation process, an integrated generation model of operation diagrams and speed curves for passenger and freight trains running on the same line is established. At the same time, considering the train operation diagram optimization at the macro level and the train reference speed curve at the micro level, a trade-off is made between train travel time and energy consumption, thereby improving the operating efficiency of passenger and freight trains running on the same line and reducing energy consumption.

[0005] In order to solve the above technical problems, the technical solution provided by the present invention is:

[0006] The method for integrating the operation diagram and speed curve for co-linear operation of passenger and freight trains comprises the following steps:

[0007] S1: Establish an integrated model of the operation diagram and speed curve for passenger and freight trains running on the same line, and set the decision variables used in the model, including Q i,s Indicates the stop time of train i at station s; binary variable Indicates whether a certain curve in the speed curve candidate set is selected. If train i selects the kth curve in the interval [s, s+1], then otherwise Binary variables Indicates the order in which trains i and j enter the interval [s, s+1] in the upward direction. If train i enters the interval [s, s+1] first, then otherwise Binary variable τ i,j,s Indicates the order in which trains i and j enter the interval [s, s+1] in the downlink direction. If train i enters the interval [s, s+1] first, then τ i,j,s =1, otherwise τ i,j,s =0;

[0008] In the above formula, i, j are the train indices, s is the station and the index of the interval [s, s+1], O is the set of upgoing trains, and I is the set of downgoing trains;

[0009] S2: Set the constraints during the train operation according to the assumptions in step S1 and the decision variables in step S2;

[0010] Including train safety interval constraints:

[0011]

[0012]

[0013] In the above formula, is the minimum time interval between two consecutive trains i and j departing from the same station, is the minimum time interval between two consecutive trains i and j arriving at the same station, J is a positive constant, and N is the number of stations; formulas (1)-(4) are the safety interval formulas that trains in the upward direction should meet, and formulas (5)-(8) are the safety interval constraints that trains in the downward direction should meet. This constraint condition ensures the safety interval between two adjacent trains in the same direction;

[0014] Including train stop time constraints:

[0015]

[0016] In the above formula, Q i,s is the stopping time of train i at station s, is the minimum stopping time of train i at station s;

[0017] Including station arrival and departure line quantity constraints:

[0018]

[0019] In the above formula, λi,s,t is a 0-1 variable, indicating whether train i stops at station s at time t. If train i stops at station s at time t, then λ i,s,t =1, otherwise there is λ i,s,t =0, U s is the number of arrival and departure lines at station s;

[0020] Include speed curve selection constraints:

[0021]

[0022] In the above formula, A variable between 0 and 1, indicating whether a certain curve in the speed curve candidate set is selected. If train i selects the kth curve in the interval [s, s+1], then otherwise

[0023] Including mixed occlusion system constraints:

[0024] According to the different types of front and rear trains, train tracking operation is divided into four situations, namely passenger train tracking passenger train operation, passenger train tracking freight train operation, freight train tracking freight train operation and freight train tracking passenger train operation;

[0025] When the passenger train is following the passenger train, it shall comply with the operation constraints under the moving block system;

[0026] When the bus is tracking the truck, the braking end point of the bus is the starting point of the block section where the truck is located, and the bus follows the operation constraints under the moving block.

[0027] When a truck is following the vehicle ahead, it must follow the operating constraints under fixed block traffic.

[0028] S3: Setting the objective function of the model;

[0029] S4: define the model constructed in step S2, step S2, and step S3 as the original problem;

[0030] S4.1: Construct the main problem based on the original problem;

[0031] S4.2: Generate an initial feasible solution to the main problem;

[0032] S4.3: Solve the main problem to obtain the dual variables of the constructed subproblem;

[0033] S4.4: Construct a subproblem based on the dual variables obtained in step S4.2, solve the subproblem to obtain the "columns" of rows, and add them to the main problem;

[0034] S4.5: Repeat steps S4.3 and S4.4, that is, continue to solve the main problem to obtain new dual variables, and construct new subproblems to continue solving until no better new columns can be found, and output the optimal solution.

[0035] Compared with the existing technology, this solution has the following significant advantages:

[0036] This plan optimizes the operation diagram and speed curve of passenger and freight trains, minimizes the waiting and passing time of trains on the way, optimizes resource allocation, saves operating costs, and improves the overall utilization of the line. It can not only ensure the safe operation of passenger and freight trains on the same line, but also improve the overall utilization of the line. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0038] Figure 1 Schematic diagram of the line structure and block partition for the simplified operation scenario in this method;

[0039] Figure 2 This is a schematic diagram of the basic principle of moving block;

[0040] Figure 3 Schematic diagram of the basic principle of quasi-moving block;

[0041] Figure 4 This is a schematic diagram of the basic principle of fixed occlusion;

[0042] Figure 5 Schematic diagram of the steps of this method;

[0043] Figure 6 Schematic diagram of block division of railway line in the embodiment;

[0044] Figure 7 The train operation diagram obtained by using a commercial solver in the embodiment;

[0045] FIG8( a ) and FIG8 ( b ) are train reference speed curves obtained by a commercial solver in an embodiment;

[0046] Figure 9 A train operation diagram generated by the method in the embodiment;

[0047] Figure 10 and Figure 11 Schematic diagram of a train reference speed curve generated by the method in an embodiment. DETAILED DESCRIPTION

[0048] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention and are not used to limit the present invention.

[0049] The method for integrating the generation of an operation diagram and a speed curve for co-linear operation of passenger and freight trains according to the present invention comprises the following steps:

[0050] S1: Establish an integrated model of the operation diagram and speed curve for passenger and freight trains running on the same line, and set the decision variables used in the model, including Q i,s Indicates the stop time of train i at station s; binary variable Indicates whether a certain curve in the speed curve candidate set is selected. If train i selects the kth curve in the interval [s, s+1], then otherwise Binary variables Indicates the order in which trains i and j enter the interval [s, s+1] in the upward direction. If train i enters the interval [s, s+1] first, then otherwise Binary variable τ i,j,s Indicates the order in which trains i and j enter the interval [s, s+1] in the downlink direction. If train i enters the interval [s, s+1] first, then τ i,j,s =1, otherwise τ i,j,s =0;

[0051] In the above formula, i, j are the train indices, s is the station and the index of the interval [s, s+1], O is the set of upgoing trains, and I is the set of downgoing trains;

[0052] S2: Set the constraints during the train operation according to the assumptions in step S1 and the decision variables in step S2;

[0053] Including train safety interval constraints:

[0054]

[0055] In the above formula, is the minimum time interval between two consecutive trains i and j departing from the same station, is the minimum time interval between two consecutive trains i and j arriving at the same station, J is a positive constant, and N is the number of stations; formulas (1)-(4) are the safety interval formulas that trains in the upward direction should meet, and formulas (5)-(8) are the safety interval constraints that trains in the downward direction should meet. This constraint condition ensures the safety interval between two adjacent trains in the same direction;

[0056] Including train stop time constraints:

[0057]

[0058] In the above formula, Q i,s is the stopping time of train i at station s, is the minimum stopping time of train i at station s;

[0059] Including station arrival and departure line quantity constraints:

[0060]

[0061] In the above formula, λ i,s,t is a 0-1 variable, indicating whether train i stops at station s at time t. If train i stops at station s at time t, then λ i,s,t =1, otherwise there is λ i,s,t =0, U s is the number of arrival and departure lines at station s;

[0062] Include speed curve selection constraints:

[0063]

[0064] In the above formula, A variable between 0 and 1, indicating whether a certain curve in the speed curve candidate set is selected. If train i selects the kth curve in the interval [s, s+1], then otherwise This constraint stipulates that each train can choose one and only one speed profile.

[0065] like Figure 1 As shown, Figure 1 This is a schematic diagram of the line structure and block partitions for the simplified operating scenario in this plan.

[0066] Including mixed occlusion system constraints:

[0067] According to the different types of front and rear trains, train tracking operation is divided into four situations, namely passenger train tracking passenger train operation, passenger train tracking freight train operation, freight train tracking freight train operation and freight train tracking passenger train operation;

[0068] When the passenger train is following the passenger train, it follows the operating constraints under the moving block. The basic principle is as follows: Figure 2 As shown;

[0069] When the bus is tracking the truck, the exact location of the truck is unknown. At this time, the braking end point of the bus is the starting point of the block section where the truck is located. The bus follows the operating constraints under the moving block. The basic principle of quasi-moving block is as follows: Figure 3 As shown;

[0070] When a truck is following the vehicle ahead, it follows the operating constraints under fixed block. The basic principle of fixed block is as follows: Figure 4 shown.

[0071] Specifically, the process of constructing the hybrid blocking system constraint condition is as follows:

[0072] First, for two trains i and j running in a tracking manner, the speed of the following train can be expressed as:

[0073]

[0074] Similarly, the position of the following vehicle can be expressed as:

[0075]

[0076] When a passenger train is tracking a passenger train, the interval between the two trains can be expressed as:

[0077]

[0078] The braking distance of the following vehicle from the current speed to 0 is:

[0079]

[0080] The length of the preceding vehicle can be expressed as:

[0081]

[0082] Therefore, the interval between the two passenger trains running in the track should meet the constraints:

[0083]

[0084] Constraint (20) ensures the safe interval when the rear passenger train tracks the front passenger train. Since this scheme assumes that the train's running speed curve in the interval is given, the train's position and speed at a certain moment can be calculated based on the known train speed curve. When the time is determined, all the items in (20) are constants, thereby judging whether the speed curve selected by the train at that moment can meet the safe tracking interval constraint;

[0085] When a passenger train is following a freight train, it can only know the block section where the freight train is located but cannot know its specific location. Therefore, the passenger train behind needs to use the starting point of the block section where the freight train is located and add a certain safety protection distance as the braking end point. The block section number of the train is calculated as follows:

[0086]

[0087] In the above formula, is the rounding symbol;

[0088] The train interval in this tracking operation scenario should meet the constraints:

[0089]

[0090] When a truck is following a truck, the truck behind it must follow fixed block constraints. Since the line is divided into several block sections, speed control is required based on the block sections in which the preceding and following trucks are located. The number of free block sections ahead of the following truck is calculated using the following formula:

[0091]

[0092] When there are at least two free block sections ahead of the following vehicle, that is, When , the speed constraint that the rear truck needs to meet is:

[0093] V H (t)≤V lmax (25)

[0094] When there is an idle block section in front of the following vehicle, that is, When , the speed constraint that the rear truck needs to meet is:

[0095]

[0096] When there is no free block section in front of the following vehicle, When , the speed constraint that the rear truck needs to meet is:

[0097]

[0098] When the rear vehicle and the front vehicle are in the same block section, that is, When (actually not allowed), the speed constraint that the rear truck needs to meet is:

[0099] V H (t)=0(28)

[0100] When a truck follows a bus, the situation is similar to that of a truck following a truck. The number of free block sections in front of the following vehicle is calculated as follows:

[0101]

[0102] When there are at least two free block sections ahead of the following vehicle, that is, When , the speed constraint that the rear truck needs to meet is:

[0103] V h (t)≤V lmax (31)

[0104] When there is an idle block section in front of the following vehicle, that is, When , the speed constraint that the rear truck needs to meet is:

[0105]

[0106] When there is no free block section in front of the following vehicle, When , the speed constraint that the rear truck needs to meet is:

[0107]

[0108] When the rear vehicle and the front vehicle are in the same block section, that is, When (actually not allowed), the speed constraint that the rear truck needs to meet is:

[0109] V h (t) = V R =0(34)

[0110] In the above formula, L b is the length of the occlusion partition, is the number of free block sections ahead of the following vehicle, V lmax is the line speed limit value, is the length of the front vehicle, is the length of train i, For the distance between the front and rear vehicles, is the braking distance of the rear vehicle, is the braking acceleration of the rear vehicle, b i,t is the block section number where train i is located at time t, x SG is the safety protection distance, n is the number of speed curves in the speed curve alternative set for each train in each section, is the speed of train i at time t when it is in the kth speed curve in the speed curve alternative set in the interval [s, s+1], is the position of train i at time t when it is in the kth speed curve in the speed curve alternative set in the interval [s, s+1], V H (t) is the speed of the following vehicle at time t, x H (t) is the position of the following vehicle at time t, is a 0-1 train type indicator variable. When train i is a freight train, When train i is a passenger train,

[0111] S3: Setting the objective function of the model;

[0112] Specifically include:

[0113]

[0114] In the above formula, ζ i,j,s The value rules are:

[0115]

[0116] In the above formula, is the departure time of train i at station s, r i,s is the running time of train i in the interval [s, s+1], N m is the number of times passenger and freight trains pass each other, ω i,j A variable between 0 and 1, indicating whether the two trains traveling in opposite directions are of the same type: if the trains i and j traveling in opposite directions are of different types, then ω i,j =1, otherwise we have ω i,j =0, the number of times passenger and freight trains meet can be calculated by formula (35), which is the expression of the first objective function in the model;

[0117]

[0118]

[0119] In the above formula, is the departure time of train i at station s, r i,s is the running time of train i in the interval [s, s+1], Equation (37) represents the travel time of the train in the upward direction, Equation (38) represents the travel time of the train in the downward direction, and Equation (39) represents the total travel time of the train, which is the expression of the second objective function in the model;

[0120]

[0121] In the above formula, is the average energy consumption per unit mass corresponding to the k-th speed curve in the speed curve alternative set of train i in the interval [s, s+1], M i is the mass of train i; Equation (40) represents the energy consumption per unit mass of the train in the interval [s, s+1], Equation (41) represents the energy consumption of the train in the interval [s, s+1], and Equation (42) represents the total energy consumption of all trains, which is the expression of the third objective function in the model;

[0122] By introducing weight coefficients α1, α2, and α3, the above three objective functions are transformed into the traditional single objective function form, and the objective function of the model is obtained as follows:

[0123]

[0124] According to steps S1-S4, the model is represented as:

[0125]

[0126] In the model, a trade-off is made between train travel time and energy consumption, thereby improving the operating efficiency of passenger and freight trains and reducing energy consumption.

[0127] Based on the above solution, the model solving algorithm involved in step S4 is briefly described as follows:

[0128] Because the proposed model is a 0-1 mixed integer programming model, commercial solvers consume significant computational time when the problem is large, making it impossible to obtain a solution within an acceptable timeframe. Therefore, this proposal devised a column-generated, integrated generation algorithm for passenger and freight train schedules and speed curves, aiming to quickly and accurately identify a feasible solution. Through continuous iteration, the column generation algorithm gradually constructs an increasingly precise relaxation of the original optimization problem, ultimately obtaining an optimal solution or a near-optimal solution. This process avoids the computational overhead associated with enumerating all possible decision variables.

[0129] S4: define the model constructed in step S2, step S2, and step S3 as the original problem;

[0130] S4.1: Construct the master problem based on the original problem. Define the model described by Equation (40) as the original problem. According to the principle of column generation, the original problem is constructed as a model based on set partitioning, namely the master problem.

[0131] Define R as the set of all possible line operation plans, and R′ as the set of all feasible line operation plans. r is a feasible line operation plan, cost c r The calculation formula is:

[0132]

[0133] In the above formula, is the stop time of train i in section s in line operation plan r, is a binary variable, indicating whether the kth alternative speed curve of train i in section s in line operation plan r is selected. is the interval running time corresponding to the kth speed curve of train i in section s in the line operation plan r, is the energy consumption per unit mass corresponding to the kth speed curve of section s in the line operation plan r, M i is the mass of train i, c t 、c e are the equivalent costs per unit time and per unit energy consumption respectively;

[0134] Definition ξ r is a binary variable. When the line operation plan r is selected, ξ r= 1, in order to construct the linear relaxation master problem, let ξ r Relax as a continuous variable, define is a binary variable. When the operation plan for train i in the line operation plan r is o,

[0135] Then the master problem can be relaxed linearly:

[0136]

[0137] ξ r ≥0,r∈R′(49)

[0138] The objective function (46) minimizes the total cost of the selected line operation plan. Constraint (47) indicates that each train must and can only choose one train operation plan. Since different trains can choose the same operation plan, constraint (48) ensures that only one feasible line plan can be selected. Constraint (49) determines the value range of the above variables. The binary variables obtained by solving the main problem are added to the sub-problem to generate a new feasible plan. The dual variables β are defined for constraints (47) and (48). i ,χ;

[0139] S4.2: Specific generation scheme of the initial solution. In the main problem model, r is defined as a feasible line operation scheme to generate a feasible solution for the algorithm;

[0140] Specifically,

[0141] S4.2.1: All trains depart from their scheduled departure stations. Passenger trains stop at all intermediate stations, and freight trains do not stop at any intermediate stations. Passenger trains use the speed curve with the longest running time, and freight trains use the speed curve with the shortest running time. The stop times are generated according to the above principles. Speed ​​curve selection

[0142] S4.2.2: Generated according to step S4.2.1 Check whether the constraints (1) to (8) are violated. If so, adjust the train's stop time and the train's arrival and departure intervals at each station until Satisfying constraints (1) to (8), define the newly generated stop time and speed curve selection variables as

[0143] S4.2.3: Generated according to step S4.2.2 Check whether the mixed block system constraint is violated. If so, adjust the train's stop time and speed curve selection to adjust the train tracking interval. If the speed curve selection of two trains does not meet the mixed block system constraint, change the speed curve selection of the following train to a speed curve with a smaller running time in the corresponding section. If it still does not meet the constraint, repeat this step. If all speed curves do not meet the constraint, delay the departure time of the following train until To meet the mixed block system constraints, define the newly generated stop time and speed curve selection variables as

[0144] S4.2.4: Inspection Do the constraints (9) to (11) meet? If not, adjust the stop time and speed curve selection until all constraints are met. Take Q0 and σ0 as the initial solutions of the algorithm.

[0145] S4.3: Solve the master problem constructed in step S4.1 and obtain the dual variable β i ,χ;

[0146] S4.4: Construct a subproblem based on the dual variables obtained in step S4.3. Consider the line as a combination of multiple sections. Solving the optimal line operation plan can be transformed into solving the optimal line operation plan in each section separately. The subproblem is symbolized by PP. s Indicates that the model PP s The optimal line operation plan corresponding to the solution section s:

[0147]

[0148]

[0149] The objective function (50) minimizes the additional cost of the new line operation plan. This means that the cost of the new line operation plan obtained by solving the subproblem has increased, that is, no new line operation plan can continue to reduce the cost; if there is This means that the cost of the new line operation plan obtained by solving the subproblem has decreased, that is, there is a new line operation plan that can continue to reduce the cost. Constraints (51) to (61) are similar to constraints (1) to (10). The cost of the line operation plan of the subproblem is calculated by formula (62).

[0150] The subproblem PP s The new solution obtained after solving is added to the main problem as a new column to solve it again, and it is solved repeatedly until the sub-problem PP is solved. s If the cost reductions of the solutions obtained are all negative, it means that the solution to the current main problem is the optimal solution. Stop the calculation and output the results.

[0151] S4.5: Repeat steps S4.3 and S4.4, that is, continue to solve the main problem to obtain new dual variables, and construct new subproblems to continue solving until no better new columns can be found, and output the optimal solution.

[0152] The overall steps of the above method are as follows Figure 5 shown.

[0153] The following is combined with the preferred embodiment and Figures 6-10 Further explanation of this plan is given.

[0154] In the embodiment, we take the Jiaoji Railway (also known as the Jiaoji Line) in Shandong Province as the research object, and select 7 stations, namely Qingdao, Qingdao North, Gaomi, Weifang, Qingzhou, Zibo, and Jinan. As for the running direction of the train, Qingdao to Jinan is the upward direction, and Jinan to Qingdao is the downward direction, as shown in the schematic diagram. Figure 6 shown.

[0155] First, we selected 34 EMU passenger trains from the actual timetable, 17 each in the uplink and downlink directions. The lengths of each section were set based on actual Jiaoji Railway data. Secondly, due to the lack of actual freight train timetable data for the Jiaoji Railway, to address this issue, we added six freight trains to the existing EMU passenger train timetable, assigning each of these six freight trains a specific expected departure time from their originating station.

[0156] On this basis, the passenger train speed curve alternative set consists of four speed curves, including two traction-cruise-brake mode curves and two traction-cruise-coast-brake mode curves. The energy consumption and interval running time corresponding to different passenger train speed curves are shown in Table 1, among which Mode 1 and Mode 2 are speed curves in the traction-cruise-brake mode, and Mode 3 and Mode 4 are speed curves in the traction-cruise-coast-brake mode.

[0157] Since freight trains can stop at intermediate stations, the speed curve candidate set needs to include speed curves for when the train does not stop. Table 2 shows the dynamic parameters of freight trains in different modes. Modes 1 and 2 are the traction-cruise-brake mode curves when stopping at a station, Modes 3 and 4 are the traction-cruise-coasting and braking mode curves when stopping at a station, and Mode 5 is the speed curve for when the train does not stop at a station.

[0158] In addition, the Jiaoji Line is 393 km long, and the length of each block section is L b =1000m, there are 393 block sections in total. The specific block sections are divided as follows Figure 6 The train length is set to Safety protection distance xSG =50. The weight values ​​in the objective function (43) are set as α1 = 0.5, α2 = 0.3, and α3 = 0.2. The time, energy consumption, and number of crossings cost in the solution algorithm of the passenger and freight train operation diagram and speed curve integrated generation model designed based on column generation are set as c t =20 yuan / min, c e =1 yuan / kWh, c m =4000 yuan / time.

[0159]

[0160]

[0161] Table 1 Passenger car interval running time and unit mass energy consumption under different modes

[0162]

[0163]

[0164] Table 2. Truck interval operation time and unit mass energy consumption under different modes

[0165] In the above embodiments, the commercial solver and the model solving algorithm designed in this solution are used to solve the problem, respectively, to illustrate the effectiveness of the method designed in this solution.

[0166] Commercial solver: The train operation diagram under this method is as follows Figure 7 As shown in Figure 8(a) and Figure 8(b), the speed curves of G1074 and 10006 trains are shown respectively. Figure 7 As shown in Figure 8, this method can shorten the waiting time of some trains at the station, but it selects a more conservative operation strategy when tracking the preceding train in the section, that is, it selects a speed curve with a lower average speed to ensure a safe interval when tracking the preceding train.

[0167] Algorithm performance: In order to test the performance of the designed algorithm for solving the integrated generation model of passenger and freight train operation diagram and speed curve based on train generation, the designed algorithm is used to solve the integrated generation model. The algorithm stops after 862 seconds of calculation time. The obtained train operation diagram is as follows Figure 9 shown. Figure 10 、 Figure 11 The speed curves of train No. D6024 and No. 10006 are given respectively. Figure 9 、 Figure 10It can be seen that when D6024 train was tracking No. 10004 in the Weifang-Qingzhou section and the Qingzhou-Zibo section, it did not extend the stop time too much. Instead, it departed from the station after meeting the minimum stop time and selected a speed curve with a longer running time within the section, that is, a more conservative section operation strategy, to ensure a safe tracking interval with No. 10004 train.

[0168] In addition, the results of the proposed algorithm for solving the integrated generation model of passenger and freight train timetables and speed curves based on train generation were compared with those obtained by a commercial solver. The various metrics are shown in Table 3. As shown in Table 3, compared with the commercial solver, the solution obtained by the proposed algorithm reduced the total travel time by 4.4%, while increasing the total energy consumption by only 0.6%, while significantly reducing the computational time. This result demonstrates that the proposed algorithm for solving the integrated generation model of passenger and freight train timetables and speed curves based on train generation can generate feasible train timetables and reference speed curves within a reasonable timeframe, demonstrating that the proposed algorithm for solving the integrated generation model of passenger and freight train timetables and speed curves based on train generation is suitable and effective for solving the studied problem.

[0169]

[0170] Table 3 Comparison of calculation results.

Claims

1. A method for generating an integrated operation diagram and speed curve for passenger and freight trains running on the same line, characterized in that: The method comprises the following steps: S1: Establish an integrated model of the operation diagram and speed curve for passenger and freight trains running on the same line, and set the decision variables used in the model, including Q i,s Indicates the stop time of train i at station s; binary variable Indicates whether a certain curve in the speed curve candidate set is selected. If train i selects the kth curve in the interval [s, s+1], then otherwise Binary variables Indicates the order in which trains i and j enter the interval [s, s+1] in the upward direction. If train i enters the interval [s, s+1] first, then otherwise Binary variable τ i,j,s Indicates the order in which trains i and j enter the interval [s, s+1] in the downlink direction. If train i enters the interval [s, s+1] first, then τ i,j,s =1, otherwise τ i,j,s =0; In the above formula, i, j are the train indices, s is the station and the index of the interval [s, s+1], O is the set of upgoing trains, and I is the set of downgoing trains; S2: Set the constraints during the train operation according to the assumptions in step S1 and the decision variables in step S2; Including train safety interval constraints: In the above formula, is the minimum time interval between two consecutive trains i and j departing from the same station, is the minimum time interval between two consecutive trains i and j arriving at the same station, J is a positive constant, and N is the number of stations; formulas (1)-(4) are the safety interval formulas that trains in the upward direction should meet, and formulas (5)-(8) are the safety interval constraints that trains in the downward direction should meet. This constraint condition ensures the safety interval between two adjacent trains in the same direction; Including train stop time constraints: In the above formula, Q i,s is the stopping time of train i at station s, is the minimum stopping time of train i at station s; Including station arrival and departure line quantity constraints: In the above formula, λ i,s,t is a 0-1 variable, indicating whether train i stops at station s at time t. If train i stops at station s at time t, then λ i,s,t =1, otherwise there is λ i,s,t =0, U s is the number of arrival and departure lines at station s; Include speed curve selection constraints: In the above formula, A variable between 0 and 1, indicating whether a certain curve in the speed curve candidate set is selected. If train i selects the kth curve in the interval [s, s+1], then otherwise Including mixed occlusion system constraints: According to the different types of front and rear trains, train tracking operation is divided into four situations, namely passenger train tracking passenger train operation, passenger train tracking freight train operation, freight train tracking freight train operation and freight train tracking passenger train operation; When the passenger train is following the passenger train, it shall comply with the operation constraints under the moving block system; When the bus is tracking the truck, the braking end point of the bus is the starting point of the block section where the truck is located, and the bus follows the operation constraints under the moving block. When a truck is following the vehicle ahead, it must follow the operating constraints under fixed block traffic. S3: Setting the objective function of the model; S4: define the model constructed in step S2, step S2, and step S3 as the original problem; S4.1: Construct the main problem based on the original problem; S4.2: Generate an initial feasible solution to the main problem; S4.3: Solve the main problem to obtain the dual variables of the constructed subproblem; S4.4: Construct a subproblem based on the dual variables obtained in step S4.2, solve the subproblem to obtain the "columns" of the rows, and add them to the main problem; S4.5: Repeat steps S4.3 and S4.4, that is, continue to solve the main problem to obtain new dual variables, and construct new subproblems to continue solving until no better new columns can be found, and output the optimal solution.

2. The method for generating an integrated operation diagram and speed curve for passenger and freight trains running on the same line according to claim 1, characterized in that: In step S2, the process of constructing the hybrid blocking system constraint condition is as follows: First, for two trains i and j running in a tracking manner, the speed of the following train can be expressed as: Similarly, the position of the following vehicle can be expressed as: When a passenger train is tracking a passenger train, the interval between the two trains can be expressed as: The braking distance of the following vehicle from the current speed to 0 is: The length of the preceding vehicle can be expressed as: Therefore, the interval between the two passenger trains running in the track should meet the constraints: Constraint (20) ensures the safe interval when the rear passenger train tracks the front passenger train. The position and speed of the train at a certain moment can be calculated by the known train speed curve. When the time is determined, all the items in (20) are constants, thereby judging whether the speed curve selected by the train at that moment can meet the safe tracking interval constraint; When a passenger train is following a freight train, it can only know the block section where the freight train is located but cannot know its specific location. Therefore, the passenger train behind needs to use the starting point of the block section where the freight train is located and add a certain safety protection distance as the braking end point. The block section number of the train is calculated as follows: In the above formula, is the rounding symbol; The train interval in this tracking operation scenario should meet the constraints: When a truck is following a truck, the truck behind it must follow fixed block constraints. Since the line is divided into several block sections, speed control is required based on the block sections in which the preceding and following trucks are located. The number of free block sections ahead of the following truck is calculated using the following formula: When there are at least two free block sections ahead of the following vehicle, that is, When , the speed constraint that the rear truck needs to meet is: V H (t)≤V lmax (25) When there is an idle block section in front of the following vehicle, that is, When , the speed constraint that the rear truck needs to meet is: When there is no free block section in front of the following vehicle, When , the speed constraint that the rear truck needs to meet is: When the rear vehicle and the front vehicle are in the same block section, that is, When , the speed constraint that the rear truck needs to meet is: V H (t)=0(28) When a truck follows a bus, the situation is similar to that of a truck following a truck. The number of free block sections in front of the following vehicle is calculated as follows: When there are at least two free block sections ahead of the following vehicle, that is, When , the speed constraint that the rear truck needs to meet is: V h (t)≤V lmax (31) When there is an idle block section in front of the following vehicle, that is, When , the speed constraint that the rear truck needs to meet is: When there is no free block section in front of the following vehicle, When , the speed constraint that the rear truck needs to meet is: When the rear vehicle and the front vehicle are in the same block section, that is, When , the speed constraint that the rear truck needs to meet is: V h (t)=V R =0(34) In the above formula, L b is the length of the occlusion partition, is the number of free block sections ahead of the following vehicle, V lmax is the line speed limit value, is the length of the front vehicle, is the length of train i, For the distance between the front and rear vehicles, is the braking distance of the rear vehicle, is the braking acceleration of the rear vehicle, b i,t is the block section number where train i is located at time t, x SG is the safety protection distance, n is the number of speed curves in the speed curve alternative set for each train in each section, is the speed of train i at time t when it is in the kth speed curve in the speed curve alternative set in the interval [s, s+1], is the position of train i at time t when it is in the kth speed curve in the speed curve alternative set in the interval [s, s+1], V H (t) is the speed of the following vehicle at time t, x H (t) is the position of the following vehicle at time t, is a 0-1 train type indicator variable. When train i is a freight train, When train i is a passenger train, 3. The method for generating an integrated operation diagram and speed curve for passenger and freight trains running on the same line according to claim 2, characterized in that: The objective function set in step S3 is: In the above formula, ζ i,j,s The value rules are: In the above formula, is the departure time of train i at station s, r i,s is the running time of train i in the interval [s, s+1], N m is the number of times passenger and freight trains pass each other, ω i,j A variable between 0 and 1, indicating whether the two trains traveling in opposite directions are of the same type: if the trains i and j traveling in opposite directions are of different types, then ω i,j =1, otherwise we have ω i,j =0, the number of times passenger and freight trains meet can be calculated by formula (35), which is the expression of the first objective function in the model; In the above formula, is the departure time of train i at station s, r i,s is the running time of train i in the interval [s, s+1], Equation (37) represents the travel time of the train in the upward direction, Equation (38) represents the travel time of the train in the downward direction, and Equation (39) represents the total travel time of the train, which is the expression of the second objective function in the model; In the above formula, is the average energy consumption per unit mass corresponding to the k-th speed curve in the speed curve alternative set of train i in the interval [s, s+1], M i is the mass of train i; Equation (40) represents the energy consumption per unit mass of the train in the interval [s, s+1], Equation (41) represents the energy consumption of the train in the interval [s, s+1], and Equation (42) represents the total energy consumption of all trains, which is the expression of the third objective function in the model; By introducing weight coefficients α1, α2, and α3, the above three objective functions are transformed into the traditional single objective function form, and the objective function of the model is obtained as follows: According to steps S1-S4, the model is represented as: In the model, a trade-off is made between train travel time and energy consumption, thereby improving the operating efficiency of passenger and freight trains and reducing energy consumption.

4. The method for integrating the operation diagram and speed curve for co-linear operation of passenger and freight trains according to claim 3 is characterized in that: Step S4.1 includes defining the model described by equation (40) as the original problem, and constructing the original problem into a model based on set partitioning, i.e., the main problem, according to the principle of column generation; Define R as the set of all possible line operation plans, and R′ as the set of all feasible line operation plans. r is a feasible line operation plan, cost c r The calculation formula is: In the above formula, is the stop time of train i in section s in line operation plan r, is a binary variable, indicating whether the kth alternative speed curve of train i in section s in line operation plan r is selected. is the interval running time corresponding to the kth speed curve of train i in section s in the line operation plan r, is the energy consumption per unit mass corresponding to the kth speed curve of section s in the line operation plan r, M i is the mass of train i, c t 、c e are the equivalent costs per unit time and per unit energy consumption respectively; Definition ξ r is a binary variable. When the line operation plan r is selected, ξ r =1, and ξ r Relax as a continuous variable, define is a binary variable. When the operation plan for train i in the line operation plan r is o, Then the master problem can be relaxed linearly: x r ≥0,r∈R′(49) The objective function (46) minimizes the total cost of the selected line operation plan. Constraint (47) indicates that each train must and can only choose one train operation plan. Since different trains can choose the same operation plan, constraint (48) ensures that only one feasible line plan can be selected. Constraint (49) determines the value range of the above variables. The binary variables obtained by solving the main problem are added to the sub-problem to generate a new feasible plan. The dual variables β are defined for constraints (47) and (48). i ,χ; S4.2: Specific generation scheme of the initial solution. In the main problem model, r is defined as a feasible line operation scheme to generate a feasible solution for the algorithm; S4.3: Solve the master problem constructed in step S4.1 and obtain the dual variable β i ,χ; S4.4: Construct a subproblem based on the dual variables obtained in step S4.

3. Consider the line as a combination of multiple sections. Solving the optimal line operation plan can be transformed into solving the optimal line operation plan in each section separately. The subproblem is symbolized by PP. s Indicates that the model PP s The optimal line operation plan corresponding to the solution section s: The objective function (50) minimizes the additional cost of the new line operation plan. If minF s pp > 0, it means that the cost of the new line operation plan obtained by solving the subproblem has increased, that is, no new line operation plan can continue to reduce the cost; if there is a minF s pp <0, it means that the cost of the new line operation plan obtained by solving the subproblem has decreased, that is, there is a new line operation plan that can continue to reduce the cost; The subproblem PP s The new solution obtained after solving is added to the main problem as a new column to solve it again, and it is solved repeatedly until the sub-problem PP is solved. s If the cost reductions of the solutions obtained are all negative, it means that the solution to the current main problem is the optimal solution. Stop the calculation and output the results. S4.5: Repeat steps S4.2 and S4.3 until no better new column can be found when solving the subproblem, and output the current optimal solution.

5. The method for generating an integrated operation diagram and speed curve for co-linear operation of passenger and freight trains according to claim 4, characterized in that: The step S4.2 includes: S4.2.1: All trains depart from their scheduled departure stations. Passenger trains stop at all intermediate stations, and freight trains do not stop at any intermediate stations. Passenger trains use the speed curve with the longest running time, and freight trains use the speed curve with the shortest running time. The stop times are generated according to the above principles. Speed ​​curve selection S4.2.2: Generated according to step S4.2.1 Check whether the constraints (1) to (8) are violated. If so, adjust the train's stop time and the train's arrival and departure intervals at each station until Satisfying constraints (1) to (8), define the newly generated stop time and speed curve selection variables as S4.2.3: Generated according to step S4.2.2 Check whether the mixed block system constraint is violated. If so, adjust the train's stop time and speed curve selection to adjust the train tracking interval. If the speed curve selection of two trains does not meet the mixed block system constraint, change the speed curve selection of the following train to a speed curve with a smaller running time in the corresponding section. If it still does not meet the constraint, repeat this step. If all speed curves do not meet the constraint, delay the departure time of the following train until To meet the mixed block system constraints, define the newly generated stop time and speed curve selection variables as S4.2.4: Inspection Do the constraints (9) to (11) meet? If not, adjust the stop time and speed curve selection until all constraints are met. Take Q0 and σ0 as the initial solutions of the algorithm.

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