A method for optimizing passenger and freight train diagram considering interval forbidden meeting condition

Abstract

The present application relates to a kind of passenger and freight car co-line diagram optimization method considering section forbidden meeting condition, through preset default condition simplifying actual train operation scene;Preset constant;Set decision variable;Establish the constraint condition of train operation;Based on objective function, establish 0-1 mixed integer programming model;Generate an initial solution of model, the initial solution is as current global optimal solution;Based on variable neighborhood search algorithm VNS, 0-1 mixed integer programming model is solved, after multiple iterations, the current global optimal solution obtained by last iteration search is output, that is, the optimized passenger and freight car co-line diagram.The present application, in combination with the train operation organization characteristics of passenger and freight car co-line railway and relevant provisions, improves the train operation efficiency of passenger and freight car co-line railway, fully plays the transport capacity of line, has important practical significance for the research and development of passenger and freight car co-line railway;Can improve the operation efficiency of line train under the premise of ensuring that passenger and freight car do not meet in section.

Description

Technical Field

[0001] This invention relates to the field of train operation scheduling technology, specifically a method for optimizing passenger and freight train schedules on shared lines, taking into account the prohibition of passing conditions between trains. The prohibition of passing conditions refers to conditions under which passing between trains is forbidden. Background Technology

[0002] To meet regional economic development needs and enhance the competitiveness of railways in freight transport, the development of passenger-freight co-operation railways is a new trend. Passenger-freight co-operation railways refer to railway transport systems that operate both passenger and freight trains, as well as other necessary technical work vehicles. Existing 200km / h railway transport systems are generally existing upgraded trunk lines or newly built lines, not dedicated passenger lines, nor do they have corresponding parallel lines. Therefore, some railway lines also need to vigorously develop passenger-freight co-operation models.

[0003] Train timetables (or timetables for short) are the foundation of railway traffic organization, and their compilation and optimization are classic problems in the field of railway transportation organization. Currently, research on timetable optimization is relatively mature both domestically and internationally, with experts and scholars from various countries optimizing timetables by establishing optimization models with different objectives and constraints.

[0004] Currently, there is a lack of research on how to optimize the timetable of passenger and freight railways (hereinafter referred to as passenger and freight railway timetable) to meet the needs of developing railways with both passenger and freight lines, and there is no feasible solution yet.

[0005] The information disclosed in this background section is intended only to enhance the understanding of the general background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the present invention aims to provide an optimization method for passenger and freight train operation schedules on shared lines that considers the condition of no-passing between sections. Combining the train operation characteristics of shared passenger and freight railways with relevant regulations, this method improves the train operation efficiency of shared passenger and freight railways and fully utilizes the line's transport capacity. This has significant practical implications for the research and development of shared passenger and freight railways. It can improve the train operation efficiency of the line while ensuring that passenger and freight trains do not meet within sections.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for optimizing passenger and freight train operating schedules on co-line routes, considering the condition of no-passing between sections, is characterized by the following steps:

[0009] Simplify actual train operation scenarios by presetting default conditions;

[0010] Based on the simplified train operation scenario, preset constants are defined;

[0011] Based on the simplified train operation scenario, decision variables are set;

[0012] Establish constraints for train operation;

[0013] A 0-1 mixed integer programming model is established by linearly adding the total train travel time to the total delay time at the train's originating station as the objective function.

[0014] Generate an initial solution to the 0-1 mixed integer programming model, and use this initial solution as the current global optimal solution;

[0015] The 0-1 mixed integer programming model is solved based on the Variable Neighborhood Search (VNS) algorithm. After multiple iterations, the current global optimal solution obtained from the last iteration is output, which is the optimized passenger and freight car co-line operation diagram.

[0016] Based on the above technical solution, the default conditions specifically include:

[0017] Treat the train speed as a constant;

[0018] Trains are permitted to stop and / or overtake within stations, but are prohibited from stopping and / or overtaking within any section.

[0019] All intermediate stations are equipped with parking lines to allow freight cars to wait and pass.

[0020] All trains depart from their originating station no earlier than the expected departure time of the corresponding originating station.

[0021] The length of the train is negligible;

[0022] The time accuracy is 1 minute.

[0023] Based on the above technical solution, the preset constant specifically includes:

[0024] The number of stations is the total number of stations in the timetable, and the value of the number of stations is m;

[0025] Station number index s;

[0026] Station capacity R s This represents the total number of trains that can stop at a station at the same time.

[0027] Interval length l s , which is the distance in kilometers between two adjacent stations;

[0028] The number of trains is the total number of trains in the timetable, and the value of the number of trains is n.

[0029] Train number index i;

[0030] Train operating speed is the average number of kilometers a train travels per hour within a given section of track. It is specifically divided into passenger train operating speed (s). p and truck running speed s f ;

[0031] Expected departure time from originating station This refers to the time when the train departs from its originating station.

[0032] Minimum time interval between arrivals The time interval between two trains arriving at the same station;

[0033] Minimum departure interval The time interval between two trains leaving the same station;

[0034] Minimum stopping time ω at intermediate stations i,s This refers to the time the train stops at intermediate stations.

[0035] Based on the above technical solution, the setting of decision variables specifically includes:

[0036] Train arrival time a i,s The time when train i arrives at station s;

[0037] Train departure time d i,s The time when train i leaves station s;

[0038] The order in which two trains enter the same section; specifically including:

[0039] α i,j,s The order in which two trains traveling in the same direction enter the same section: when train i in the direction of travel enters section [s, s+1] before train j in the direction of travel, then α i,j,s =1; otherwise α i,j,s =0; where i,j∈O,s∈{1,2,...,m-1};

[0040] β i,j,s β is the order in which two trains in the down direction enter the same section. If train i in the down direction enters section [s, s+1] before train j in the down direction, then β i,j,s =1; otherwise β i,j,s =0; where i,j∈I,s∈{1,2,…,m-1};

[0041] γ i,j,s γ is the order in which two trains, one going up and one going down, enter the same section. If train i going up enters section [s, s+1] before train j going down, then γ...i,j,s =1; otherwise γ i,j,s =0; where i∈O, j∈I, s∈{1,2,…,m-1};

[0042] Where i,j are train number indices, s is station number index, [s,s+1] represents the interval between station s and station s+1, O is the set of trains in the up direction, and I is the set of trains in the down direction.

[0043] Based on the above technical solution, the specific constraints for establishing train operation include:

[0044] Train safety interval constraints are conditions that ensure the safe interval between two adjacent trains in the same direction; specifically, they include the interval constraints that trains in the up direction must meet and the interval constraints that trains in the down direction must meet.

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] Passenger and freight trains are prohibited from meeting within the section. This constraint ensures that two trains traveling in opposite directions will not meet within the section if they are of different types.

[0054] a i,s+1 ≤d j,s+1 +N·[(1-λ i,j )+(1-γ i,j,s )],i∈O,j∈I,s∈{1,2,...,m-1},(27)

[0055] a j,s ≤d i,s +N·[(1-λ i,j )+(1-γ j,i,s )],i∈O,j∈I,s∈{1,2,...,m-1},(28)

[0056] Intermediate station stop time constraint: This constraint ensures that when the train stops at the designated station, there is a certain amount of time to carry out the corresponding passenger or freight business.

[0057]

[0058] Origin station departure time constraint, which stipulates that a train cannot depart from its origin station earlier than its expected departure time.

[0059]

[0060]

[0061] Station capacity constraint, which stipulates that the number of trains stopping at the same station at the same time cannot exceed the maximum number of trains that the station can accommodate;

[0062]

[0063] Inter-section travel time constraint, which specifies the travel time for passenger cars and freight cars in each section;

[0064]

[0065]

[0066] Based on the above technical solution, the objective function is to linearly add the total train travel time to the total delay time at the train's originating station. The specific steps are as follows:

[0067] Let train travel time refer to the time interval between a train's departure from the originating station and its arrival at the destination station. The total train travel time T1 refers to the sum of the travel times of all trains, which is composed of the linear weighted sum of the total travel times of passenger cars and freight cars.

[0068] Let the train originating station delay time be the difference between the actual departure time of the train at the originating station and the expected departure time of the train at the originating station, and let the total train originating station delay time T2 be the sum of the train originating station delay times of all trains.

[0069] The objective function is:

[0070]

[0071] The final expression of the 0-1 mixed integer programming model is:

[0072]

[0073] The 0-1 mixed integer programming model aims to minimize the sum of the total train travel time and the total delay at the train's originating station.

[0074] Based on the above technical solution, the generation of an initial solution to the 0-1 mixed integer programming model adopts the following principles:

[0075] Principle 1: After all passenger buses have arrived at the terminal station, freight buses will depart from the originating station.

[0076] Principle 2: Passenger trains shall depart from their originating station at the expected departure time, and the stop time shall be equal to the minimum stop time at intermediate stations.

[0077] Principle 3: Freight trucks shall not stop at intermediate stations;

[0078] Based on the above principles, the solution of the 0-1 mixed integer programming model is generated as the initial solution S0.

[0079] Based on the above technical solution, when solving the 0-1 mixed integer programming model, data is first generated according to the actual train operation scenario and input into the 0-1 mixed integer programming model, and then solved using the Variable Neighborhood Search (VNS) algorithm; the specific steps are as follows:

[0080] Preset the maximum number of iterations;

[0081] First, the search process for the current global optimum is initiated by performing a perturbation process and a variable neighborhood descent process on the current global optimum. The iteration count is updated after each search is completed.

[0082] Then, determine whether the number of iterations equals the maximum number of iterations;

[0083] If equal to: terminate the search process for the current global optimal solution and output the current global optimal solution obtained from the last iteration search;

[0084] If it is less than: take the global optimal solution obtained in this iteration as the new current global optimal solution, and restart the search process for the current global optimal solution.

[0085] Based on the above technical solution, the Variable Neighborhood Search (VNS) algorithm is as follows:

[0086] The initial solution S0, and the neighborhood structure N used for the perturbation process and the variable neighborhood descent process. p (p = 1, 2, ..., P), N l (l = 1, 2, ... L) are input into the algorithm;

[0087] By performing a perturbation process to expand the search space of the current solution, the possibility of the algorithm getting trapped in local optima is reduced, enabling the algorithm to find a better solution; the perturbation process generates a neighborhood solution S′ of the current solution S from the p-th neighborhood structure of the current solution S;

[0088] The process searches for local optima in several designed neighborhood structures by performing a variable neighborhood descent process. The variable neighborhood descent process adopts the following principle: whenever a better solution than the current solution appears, the process resumes the search in the first neighborhood structure and selects the best solution among all the better solutions found as the new local optimum.

[0089] The specific process for performing the variable neighborhood descent is as follows:

[0090] Input the current solution S and the neighborhood structure N used for the variable neighborhood descent process. l (l=1,2,…L); Let the local optimal solution S′ be equal to the input current solution S; Starting from the first neighborhood structure, search for the current solution S in the neighborhood structure N. l The best neighborhood solution S″ is, i.e. If the objective function value of the optimal neighborhood solution S″ is less than the objective function value of the current solution S, then let the current solution S equal the optimal neighborhood solution S″, and let l = 1, and re-search the neighborhood structure N of the current solution S. l Find the optimal neighborhood solution S″; if the objective function value of the optimal neighborhood solution S″ is greater than the objective function value of the current solution S, then let l = l + 1, and re-search for the neighborhood structure N of the current solution S. l Find the best neighborhood solution S″ and repeat the above process until l > L. If the objective function value of the current solution S is less than the local optimum S′, then set the local optimum S′ equal to the current solution S and output the local optimum S′. The variable neighborhood descent process ends.

[0091] Let the global optimal solution S be equal to the initial solution S0, and let the number of iterations y be equal to 0;

[0092] First, a perturbation process is performed to generate a neighborhood solution S′ of the global optimum from the p-th neighborhood structure of the global optimum; then, a variable neighborhood descent process is performed on the neighborhood solution S′ to search for a local optimum, and S′ is set to be equal to the local optimum.

[0093] If the objective function value of S′ is less than the objective function value of the global optimal solution S, then let the global optimal solution S equal S′, the iteration number y equal 0, and start the perturbation process again from the first neighborhood structure, i.e., p equals 1.

[0094] If the objective function value of S′ is greater than or equal to the objective function value of the global optimal solution S, then let p equal p+1, and continue to generate a neighborhood solution S′ of the global optimal solution from the p-th neighborhood of the global optimal solution S, and so on.

[0095] One iteration is defined as executing all the neighborhood structures designed in the perturbation process once, that is, when p > P, it is a complete iteration;

[0096] When the number of iterations y exceeds the pre-defined maximum number of iterations MAX iter When the time is reached, the search process terminates and the global optimal solution S is output.

[0097] Based on the above technical solution, the neighborhood structure design of the disturbance process is as follows:

[0098] Changing the departure time of the train originating station: The first neighborhood structure of the disturbance process is mainly related to the departure time of the originating station; keeping the train type unchanged, randomly select two trains in the same direction, advance the departure time of the originating station of one train, and postpone the departure time of the originating station of the other train by the same amount of time.

[0099] Changing the stopping time of trains at intermediate stations: The second neighborhood structure of the disturbance process is mainly related to the stopping time of trains at intermediate stations; keeping the train type unchanged, randomly select two trains in the same direction, reduce the stopping time of one train at a certain intermediate station by a given time, and increase the stopping time of the other train at that station by the same time.

[0100] The neighborhood structure design for the variable neighborhood descent process is as follows:

[0101] Changing the departure time of a train originating station: The first neighborhood structure in the variable neighborhood descent process is to change the departure time of a train originating station; randomly select a train and advance or delay its departure time from the originating station by a given time.

[0102] Changing the stop time of a train at an intermediate station: The second neighborhood structure of the variable neighborhood descent process is to change the stop time of a train at an intermediate station; randomly select a train and decrease or increase its stop time at a certain intermediate station by a given time.

[0103] The method for optimizing passenger and freight train operating schedules considering no-passing conditions in sections, as described in this invention, has the following beneficial effects:

[0104] This invention optimizes the train operation schedule of passenger and freight railways based on the train operation characteristics of such railways and the regulations of China State Railway Group prohibiting passenger and freight trains from meeting in sections, thereby improving the overall operating efficiency of the line.

[0105] This invention is a timetable optimization method considering the condition of no-passenger-freight section. Using this invention can not only ensure the safe operation of passenger and freight trains when they share the same line, but also improve the overall utilization rate of the line.

[0106] The timetable optimization method described in this invention, combined with the train operation characteristics and relevant regulations of passenger and freight railways, improves the train operation efficiency of passenger and freight railways and makes full use of the line's transportation capacity. It has important practical significance for the research and development of passenger and freight railways. Simulation results show that the timetable optimization method described in this invention can improve the train operation efficiency of the line while ensuring that passenger and freight trains do not meet within the section. Attached Figure Description

[0107] The present invention includes the following figures:

[0108] The accompanying drawings are provided to better understand the invention and are not intended to unduly limit the scope of the invention. Wherein:

[0109] Figure 1 The flowchart of an optimization method for passenger and freight car co-line operation schedule considering the no-passing condition in the section, as described in this invention.

[0110] Figure 2 Schematic diagram of the default train operation scenario.

[0111] Figure 3 A flowchart of the variable neighborhood descent process.

[0112] Figure 4 A flowchart of the variable neighborhood search algorithm.

[0113] Figure 5 A schematic diagram of the railway line studied in the examples of this invention.

[0114] Figure 6 The train operation diagram of scenario 1 in the example of the present invention.

[0115] Figure 7 The train operation diagram in scenario 2 of the present invention.

[0116] Figure 8 The train operation diagram in scenario 3 of the present invention. Detailed Implementation

[0117] The present invention will be further described in detail below with reference to the accompanying drawings. This detailed description is an illustration in conjunction with exemplary embodiments of the invention, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the invention. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0118] This invention provides a method for optimizing passenger and freight train operating schedules that considers no-passing conditions in sections, such as... Figure 1 As shown, it includes the following steps:

[0119] Simplify actual train operation scenarios by presetting default conditions;

[0120] Based on the simplified train operation scenario, preset constants are defined;

[0121] Based on the simplified train operation scenario, decision variables are set;

[0122] Based on the characteristics of train operation on railways with both passenger and freight traffic and relevant regulations, constraints on train operation are established.

[0123] A 0-1 mixed integer programming model is established by linearly adding the total train travel time to the total delay time at the train's originating station as the objective function.

[0124] Generate an initial solution to the 0-1 mixed integer programming model, and use this initial solution as the current global optimal solution;

[0125] The 0-1 mixed integer programming model is solved using the Variable Neighborhood Search (VNS) algorithm. After multiple iterations, the current global optimal solution obtained from the last iteration is output, which is the optimized passenger and freight car co-line operation diagram.

[0126] Based on the above technical solution, the default conditions specifically include:

[0127] The train speed is considered constant, that is, the acceleration and deceleration process of the train is not considered.

[0128] Trains are permitted to stop and / or overtake within stations, but are prohibited from stopping and / or overtaking within any section.

[0129] All intermediate stations are equipped with stop lines for freight cars to wait and pass; intermediate stations refer to stations other than the originating station and the terminal station.

[0130] All trains shall depart from their originating station no earlier than the expected departure time of the corresponding originating station, in order to ensure the necessary time for preparation of departure operations at the originating station.

[0131] The length of the train is negligible;

[0132] The time accuracy is 1 minute.

[0133] Based on the above technical solution, the preset constant specifically includes:

[0134] The number of stations is the total number of stations in the timetable, and its value is m; for example... Figure 2 In the train operation scenario shown, the starting station and the destination station in the upward direction are station 1 and station m, respectively, and the starting station and the destination station in the downward direction are station m and station 1, respectively.

[0135] Station number index s;

[0136] Station capacity R s This represents the total number of trains that can stop at a station at the same time.

[0137] Interval length l s , where is the distance in kilometers between two adjacent stations; the interval refers to the operating area between two adjacent stations, denoted by [s, s+1], and the number of intervals is the total number of stations minus one;

[0138] The number of trains is the total number of trains in the timetable, and the value of the number of trains is n.

[0139] Train number index i, i∈O∪I and i∈P∪F, O is the set of all trains in the up direction, I is the set of all trains in the down direction, P is the set of all passenger cars, F is the set of all freight cars, and the number of trains contained in O∪I and P∪F is equal to n.

[0140] Train operating speed is the average number of kilometers a train travels per hour within a given section of track. It is specifically divided into passenger train operating speed (s). p and truck running speed s f ;

[0141] Expected departure time from originating station This refers to the time when the train departs from its originating station. While ensuring safe train operation, the train should, as far as possible, depart from its originating station at the expected departure time.

[0142] Minimum time interval between arrivals The time interval between two trains arriving at the same station;

[0143] Minimum departure interval The time interval between two trains leaving the same station;

[0144] Minimum stopping time ω at intermediate stations i,s , is the stopping time of the train at intermediate stations; and is the shortest time for the train to perform necessary operations at intermediate stations, including passenger boarding and alighting, and loading and unloading of goods.

[0145] Based on the above technical solution, the setting of decision variables specifically includes:

[0146] Train arrival time a i,s The time when train i arrives at station s;

[0147] Train departure time d i,s The time when train i leaves station s;

[0148] The order in which two trains enter the same section; both trains are running on the track, for example: both can be going up, both can be going down, or one can be going up and the other down; specifically including:

[0149] α i,j,s The order in which two trains traveling in the same direction enter the same section: when train i in the direction of travel enters section [s, s+1] before train j in the direction of travel, then α i,j,s =1; otherwise α i,j,s =0; where i,j∈O,s∈{1,2,...,m-1};

[0150] β i,j,s β is the order in which two trains in the down direction enter the same section. If train i in the down direction enters section [s, s+1] before train j in the down direction, then β i,j,s =1; otherwise β i,j,s =0; where i,j∈I,s∈{1,2,...,m-1};

[0151] γ i,j,s γ is the order in which two trains, one going up and one going down, enter the same section. If train i going up enters section [s, s+1] before train j going down, then γ... i,j,s =1; otherwise γ i,j,s =0; where i∈O, j∈I, s∈{1,2,...,m-1};

[0152] Where i,j are train number indices, s is station number index, [s,s+1] represents the interval between station s and station s+1, O is the set of trains in the up direction, and I is the set of trains in the down direction.

[0153] Based on the above technical solution, the specific constraints for establishing train operation include:

[0154] Train safety separation constraint: This constraint ensures the safe separation between two adjacent trains in the same direction, as detailed below:

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] Formulas (1)-(4) represent the interval constraints that trains in the up direction must meet, and formulas (5)-(8) represent the interval constraints that trains in the down direction must meet; where: d i,s Let d be the train departure time of train i leaving station s. j,s , d i,s+1 d j,s+1 With d i,s Similarly; a i,s Let a be the train arrival time of train i at station s. i,s+1 a j,s a j,s+1 With a i,s Similarly; The minimum time interval between two trains departing from the same station; α is the minimum time interval between the arrivals of two trains at the same station. i,j,s α j,i,s Indicates the order in which two trains traveling in the upward direction enter the same section; β i,j,s β j,i,s This indicates the order in which two trains in the downward direction enter the same section; N is a sufficiently large positive number, meaning that regardless of the decision variable α... i,j,s α j,i,s β i,j,s β j,i,s The value of N is 0 or 1, and the value of N must make equations (1)-(8) always true;

[0164] The constraint prohibiting passenger and freight trains from meeting within a section ensures that two trains traveling in opposite directions will not meet within the section if they are of different types (i.e., one is a passenger train and the other is a freight train), as detailed below:

[0165] a i,s+1 ≤d j,s+1 +N·[(1-λ i,j )+(1-γ i,j,s )],i∈O,j∈I,s∈{1,2,...,m-1},(45)

[0166] a j,s ≤d i,s +N·[(1-λ i,j )+(1-γ j,i,s )],i∈O,j∈I,s∈{1,2,...,m-1},(46)

[0167] Where: a i,s+1 Let a be the arrival time of train i at station s+1. j,s With a i,s+1 Similarly; d j,s+1 Let d be the train departure time of train j leaving station s+1. i,s With d j,s+1 Similarly; λ i,j λ is a 0-1 variable used to determine whether train i in the up direction and train j in the down direction are different types of trains. That is, if train i and train j are different types of trains, then λ... i,j =1; otherwise λ i,j =0; γ i,j,s γ j,i,s N, representing the order in which two trains, one going up and one going down, enter the same section, is a sufficiently large positive number. "Sufficiently large" means that regardless of the variable λ... i,j γ i,j,s γ j,i,s The value of N is 0 or 1, and the value of N must make equations (9)-(10) always true;

[0168] Intermediate station stop time constraints: This constraint ensures that when the train stops at the designated station, there is sufficient time for corresponding passenger or freight operations, such as passenger boarding and alighting, and cargo loading and unloading, as detailed below:

[0169]

[0170] Where: d i,s Let a be the train departure time of train i from station s; i,s ω represents the arrival time of train i at station s; i,s ω is the minimum stopping time for train i at intermediate stations in station s. When station s is not a pre-planned stop for train i, ω i,s =0;

[0171] The departure time constraint at the originating station stipulates that a train cannot depart from its originating station earlier than its expected departure time, as detailed below:

[0172]

[0173]

[0174] Where: d i,1 This refers to the departure time of train i in the upward direction from its originating station, i.e., station 1; d i,m This refers to the departure time of train i in the down direction from its originating station, i.e., station m. The expected departure time of train i from its originating station;

[0175] Station capacity constraint: This constraint stipulates that the number of trains stopping at the same station at the same time cannot exceed the maximum number of trains that the station can accommodate, as detailed below:

[0176]

[0177] Where: x i,s,t x is a 0-1 variable used to determine whether train i stops at station s at time t. That is, if train i stops at station s at time t, then x... i,s,t =1; otherwise x i,s,t =0; R s Let be the station capacity of station s; T be the time range for all train operations;

[0178] The interval travel time constraint specifies the travel time for passenger cars and freight cars in each interval, as follows:

[0179]

[0180]

[0181] Where: a i,s+1 Let a be the arrival time of train i at station s+1. i,s With a i,s+1 Similarly; d i,s Let d be the train departure time of train i leaving station s. i,s+1 With d i,s Similarly; s p s f These are the operating speeds of passenger cars and freight cars, respectively; s Let be the length of the interval [s, s+1]. This is a 0-1 variable used to determine the type of train i, i.e., when i∈P. When i∈F

[0182] Based on the above technical solution, the objective function is to linearly add the total train travel time to the total delay time at the train's originating station. The specific steps are as follows:

[0183] Let train travel time refer to the time interval between a train's departure from the originating station and its arrival at the destination station. The total train travel time T1 refers to the sum of the travel times of all trains, which is composed of the linear weighted sum of the total travel times of passenger cars and freight cars.

[0184] T i travel =a i,m -d i,1 ,i∈O∩P,(53)

[0185] T i travel =a i,1 -d i,m ,i∈I∩P,(54)

[0186]

[0187]

[0188]

[0189] Wherein: T i travel This represents the travel time of bus i, which is the difference between the time bus i arrives at the destination station and the time bus i departs from the origin station. Let represent the travel time of truck j, that is, the difference between the time truck j arrives at the destination station and the time truck j departs from the origin station; a i,m d represents the arrival time of passenger train i in the upward direction to its final destination station m. i,1 This refers to the departure time of passenger train i in the upward direction from its originating station, i.e., station 1; a i,1 d represents the arrival time of passenger train i in the down direction at its final destination, station 1. i,m a is the departure time of passenger train i in the down direction from its originating station m. j,m d represents the arrival time of freight train i in the upward direction at its destination station m. j,1 This refers to the departure time of freight train i in the upward direction from its originating station, i.e., station 1; a j,1 Let d be the arrival time of freight car i in the down direction at its destination station, i.e., station 1. j,m Let θ1 and θ2 be the train departure times of freight car i in the down direction from its originating station m; θ1 and θ2 are the weights of the total travel time of passenger cars and the total travel time of freight cars; Formula (21) represents the total travel time of trains, which is composed of the linear weighted sum of the total travel time of passenger cars and the total travel time of freight cars.

[0190] Let the train originating station delay time be the difference between the actual departure time of the train at the originating station and the expected departure time of the train at the originating station, and let the total train originating station delay time T2 be the sum of the train originating station delay times of all trains.

[0191]

[0192]

[0193]

[0194] Where: k is the train sequence number index. d represents the delay time of train k at the originating station, that is, the difference between the actual time the train departs from the originating station and the expected departure time from the originating station. k,1 This refers to the departure time of train k in the upward direction from its originating station, i.e., station 1; d k,m This represents the departure time of train k in the down direction from its originating station, i.e., station m. Let k be the expected departure time from the originating station of train k; Formula (24) represents the total delay time at the originating station of train k.

[0195] The objective function is:

[0196]

[0197] The final expression of the 0-1 mixed integer programming model is:

[0198]

[0199] The 0-1 mixed integer programming model shown in Formula (26) aims to minimize the sum of the total train travel time and the total delay at the train's originating station, that is, to allow the train to depart from the originating station as close as possible to the expected departure time at the originating station while reaching the destination as quickly as possible.

[0200] Based on the above technical solution, the generation of an initial solution to the 0-1 mixed integer programming model adopts the following principles:

[0201] Principle 1: After all passenger buses have arrived at the terminal station, freight buses will depart from the originating station.

[0202] Principle 2: Passenger trains shall depart from their originating station at the expected departure time, and the stop time shall be equal to the minimum stop time at intermediate stations.

[0203] Principle 3: Freight trucks shall not stop at intermediate stations;

[0204] Based on the above principles, the solution of the 0-1 mixed integer programming model is generated as the initial solution S0.

[0205] In this invention, for the sake of simplicity, the principle is that all passenger cars arrive at the terminal station before freight cars depart from the originating station, and passenger cars depart from the originating station according to their expected departure time, with the stop time equal to the minimum stop time at intermediate stations, and freight cars do not stop at intermediate stations. The solution generated by the above principle is taken as the initial solution S0 of the problem.

[0206] Based on the above technical solution, when solving the 0-1 mixed integer programming model, data is first generated according to the actual train operation scenario and input into the 0-1 mixed integer programming model, and then solved using the Variable Neighborhood Search (VNS) algorithm; the specific steps are as follows:

[0207] Preset the maximum number of iterations;

[0208] First, the search process for the current global optimum is initiated by performing a perturbation process and a variable neighborhood descent process on the current global optimum. The iteration count is updated after each search is completed.

[0209] Then, determine whether the number of iterations equals the maximum number of iterations;

[0210] If equal to: terminate the search process for the current global optimal solution and output the current global optimal solution obtained from the last iteration search;

[0211] If it is less than: take the global optimal solution obtained in this iteration as the new current global optimal solution, and restart the search process for the current global optimal solution.

[0212] The variable neighborhood search algorithm is a metaheuristic algorithm based on local search, suitable for solving combinatorial optimization problems. The basic idea is to systematically change the neighborhood structure set of the current solution during the search process to expand the search range, then find a local optimum through a local search algorithm, and then repeat the above process based on this local optimum. After multiple iterations, convergence is finally achieved.

[0213] In this invention, since the proposed model is a 0-1 mixed integer programming model, when the problem size is large, using commercial solvers will consume a lot of computation time and cannot obtain the solution to the problem in an acceptable time. Therefore, this invention designs an efficient variable neighborhood search algorithm, VNS, which aims to find feasible solutions quickly and accurately.

[0214] Based on the above technical solution, the Variable Neighborhood Search (VNS) algorithm is as follows:

[0215] The initial solution S0, and the neighborhood structure N used for the shaking process and the Variable Neighborhood Descent (VND) process are...p (p = 1, 2, ..., P), N l (l = 1, 2, ... L) are input into the algorithm;

[0216] By performing a perturbation process to expand the search space of the current solution, the possibility of the algorithm getting trapped in local optima is reduced, enabling the algorithm to find a better solution; the perturbation process generates a neighborhood solution S′ of the current solution S from the p-th neighborhood structure of the current solution S;

[0217] The neighborhood structure design for the shaking process is as follows:

[0218] Change the departure time of the train's originating station: The first neighborhood structure of the disturbance process is mainly related to the departure time of the originating station; keep the train type unchanged, randomly select two trains in the same direction, advance the departure time of the originating station of one train, and postpone the departure time of the originating station of the other train by the same time; for example, the departure time of the originating station of train i is 10:35 and the departure time of the originating station of train j is 13:50. In the search process of the neighborhood structure, the above two trains are selected, and the departure time of train i is required to be 5 minutes earlier. Then the departure times of the originating stations of these two trains after the change are 10:30 and 13:55 respectively; due to the existence of constraints (12)-(13), the departure time of the originating station of the changed train cannot be earlier than the expected departure time of its originating station. Therefore, when the departure time of the originating station of the changed train does not meet the constraints (12)-(13), two trains are randomly selected again, and the above process is repeated until the conditions are met.

[0219] Changing the stopping time of trains at intermediate stations: The second neighborhood structure of the disturbance process is mainly related to the stopping time of trains at intermediate stations; keeping the train type unchanged, randomly select two trains in the same direction, reduce the stopping time of one train at a certain intermediate station by a given time, and increase the stopping time of the other train at that station by the same time; for example, the stopping time of train i at station 3 (the number of stations is greater than 3) is 8 minutes, and the stopping time of train j at that station is 5 minutes. In the search process of this neighborhood structure, the above two trains are selected, and it is required that the stopping time of train i at that station be reduced by 3 minutes. Then the stopping times of these two trains at that station after the change are 5 minutes and 8 minutes, respectively; where, due to the existence of constraint (11), the stopping time of the train at the intermediate station after the change cannot be less than the minimum stopping time of the intermediate station. Therefore, when the stopping time of the train at the intermediate station after the change does not meet the constraint (11), two trains are randomly selected again, and the above process is repeated until the condition is met.

[0220] The variable neighborhood descent process searches for local optima in several designed neighborhood structures. This process follows the principle that whenever a better solution appears, the search resumes in the first neighborhood structure, and the best solution among all found better solutions is selected as the new local optimum. The specific steps of the variable neighborhood descent process are as follows: input the current solution S and the neighborhood structure N used for the process. l (l = 1, 2, ..., L); Let the local optimal solution S′ be equal to the input current solution S; Starting from the first neighborhood structure (l = 1), search for the current solution S in the neighborhood structure N. l The best neighborhood solution S″ is, i.e. If the objective function value of the optimal neighborhood solution S″ is less than the objective function value of the current solution S, then let the current solution S equal the optimal neighborhood solution S″, and let l = 1, and re-search the neighborhood structure N of the current solution S. l Find the optimal neighborhood solution S″; if the objective function value of the optimal neighborhood solution S″ is greater than the objective function value of the current solution S, then let l = l + 1, and re-search for the neighborhood structure N of the current solution S. l Find the best neighborhood solution S″ and repeat the above process until l > L. At this point, if the objective function value of the current solution S is less than the local optimum S′, then set the local optimum S′ equal to the current solution S and output the local optimum S′. The variable neighborhood descent process ends. The flowchart of the above variable neighborhood descent process is as follows: Figure 3 As shown.

[0221] The neighborhood structure design for the variable neighborhood descent process (VND) is as follows:

[0222] Changing the departure time of the train's originating station: The first neighborhood structure in the variable neighborhood descent process is to change the departure time of the train's originating station; randomly select a train and advance or delay its departure time from the originating station by a given time; for example, if the departure time of a train's originating station is 9:00, during the search process of this neighborhood structure, the train is selected and its departure time is required to be delayed by 5 minutes, then the departure time of the train becomes 9:05; where, due to the existence of constraints (12)-(13), the departure time of the changed train's originating station cannot be earlier than the expected departure time of its originating station, so when the departure time of the changed train's originating station does not meet the constraints (12)-(13), a train is randomly reselected and the above process is repeated until the conditions are met;

[0223] Changing the intermediate station stopping time of the train: The second neighborhood structure of the variable neighborhood descent process is to change the intermediate station stopping time of the train; randomly select a train and reduce or increase its stopping time at a certain intermediate station by a given time; for example, a train has a stopping time of 7 minutes at station 3 (the number of stations is greater than 3). In the search process of this neighborhood structure, the train is selected and it is required that its stopping time at this station be reduced by 2 minutes. Then the stopping time of the train at station 3 becomes 5 minutes; where, due to the existence of constraint (11), the changed intermediate station stopping time of the train cannot be less than the minimum stopping time of the intermediate station. Therefore, when the changed intermediate station stopping time of the train does not meet the constraint (11), a train is randomly reselected and the above process is repeated until the condition is met.

[0224] Let the global optimal solution S be equal to the initial solution S0, and let the number of iterations y be equal to 0;

[0225] First, a perturbation process is performed to generate a neighborhood solution S′ of the global optimum from the p-th neighborhood structure of the global optimum; then, a variable neighborhood descent process is performed on the neighborhood solution S′ to search for a local optimum, and S′ is set to be equal to the local optimum.

[0226] If the objective function value of S′ is less than the objective function value of the global optimal solution S, then let the global optimal solution S equal S′, the iteration number y equal 0, and start the perturbation process again from the first neighborhood structure, i.e., p equals 1.

[0227] If the objective function value of S′ is greater than or equal to the objective function value of the global optimal solution S, then let p equal p+1, and continue to generate a neighborhood solution S′ of the global optimal solution from the p-th neighborhood of the global optimal solution S, and so on.

[0228] One iteration is defined as executing all the neighborhood structures designed in the perturbation process once, that is, when p > P, it is a complete iteration;

[0229] When the number of iterations y exceeds the pre-defined maximum number of iterations MAX iter When the time is reached, the search process terminates and the global optimal solution S is output.

[0230] The overall flowchart of the variable neighborhood search algorithm is as follows: Figure 4 As shown.

[0231] To more clearly illustrate the present invention, the following description, in conjunction with preferred embodiments and appendices, provides further details. Figure 5-8 The present invention will be further described below. Those skilled in the art should understand that the specific description below is illustrative and not restrictive, and should not be construed as limiting the scope of protection of the present invention.

[0232] In this case study, we use the Jiaoji Railway (also known as the Jiaoji Line) located in Shandong Province, China, as our research object. We select seven stations with frequent train stops and high passenger demand: Qingdao, Qingdao North, Gaomi, Weifang, Qingzhou, Zibo, and Jinan. Regarding the train's direction of travel, according to relevant regulations, Qingdao to Jinan is the up-traffic direction, and Jinan to Qingdao is the down-traffic direction, as shown in the diagram below. Figure 5 As shown.

[0233] First, we selected 14 high-speed passenger trains from the actual timetable, with 7 trains in each direction. The length of each section was set according to the actual Jiaoji Railway data. Second, due to the lack of actual freight train timetable data on the Jiaoji Railway, to solve this problem, we allocated 6 freight trains to the existing timetable based on the original high-speed passenger train timetable, that is, we artificially assigned an expected departure time to a starting station for these 6 freight trains.

[0234] Based on this, we set up a total of 20 trains in the experiment, with 10 trains in each direction (up and down), including 7 passenger trains and 3 freight trains. The arrival and departure intervals were both set to 5 minutes. Passenger trains stopped at all intermediate stations to allow passengers to board and alight, with a minimum stop time of 3 minutes at intermediate stations; freight trains could stop at intermediate stations without stopping, meaning the minimum stop time at intermediate stations was set to 0 minutes. The passenger train speed was set to 200 km / h, and the freight train speed was set to 80 km / h. The interval travel time was derived by dividing the interval length by the train speed. For ease of description, all generated interval travel times were set to integers. It should be noted that since we assume the train speed is constant in each interval, the interval travel time will differ from the actual situation. The interval lengths and the train travel times in each interval are shown in Table 1.

[0235] Table 1. Train travel distances and travel times for each section

[0236]

[0237] In this example, we designed three scenarios to illustrate the effectiveness of the method involved in this invention.

[0238] Scenario 1: No constraint prohibiting passing between passenger and freight vehicles is set, but other constraints in the 0-1 mixed-integer programming model still apply. The train operation diagram for this scenario is as follows: Figure 6 As shown.

[0239] Figure 6The two different line types represent passenger trains and freight trains respectively. The train numbers of passenger trains are all the actual train numbers in the actual timetable. The train numbers of the added freight trains are given as F101, F102, F103, F104, F105, and F106. Among them, freight trains F102, F104, and F106 are trains in the upward direction, and freight trains F101, F103, and F105 are trains in the downward direction (the same applies below).

[0240] As can be seen, after allocating the six freight trains to the existing timetable, passenger and freight trains meet in multiple sections (not all are marked). For example, freight train F104, traveling in the uphill direction, departs from Qingdao Station and meets the D6965 and D6015 EMU trains in the opposite direction in the Gaomi-Weifang section, then meets the D8181 EMU train in the opposite direction in the Weifang-Qingzhou section. After stopping at Qingzhou Station, it meets the G6991 EMU train in the opposite direction in the Qingzhou-Zibo section, and finally stops at Zibo Station before continuing to its final destination, Jinan Station.

[0241] Apart from freight train F104, which encountered a meeting with a high-speed train within the section, the other five freight trains also experienced the same situation. This means that assigning a specific originating station and expected departure time to freight trains based on the existing timetable and requiring them to operate at a predetermined speed is not feasible, because passenger trains have a very high probability of meeting freight trains within the section.

[0242] Scenario 2: Given the following conditions: when a passenger train and a freight train are about to meet in a section, the passenger train must have priority to pass, while the freight train must wait in the station to give way. Under these conditions, the train timetable is as follows: Figure 7 As shown.

[0243] As can be seen, once the passenger train priority passage condition is set, passenger trains and freight trains will no longer meet within the section. Let's take freight train F104 as an example. After departing from Qingdao Station, freight train F104 stops at Gaomi Station and then proceeds directly to its final destination, Jinan Station. During its operation, freight train F104 only meets freight train F101 in the opposite direction within the Gaomi-Weifang section, and freight trains F103 and F105 in the opposite direction within the Weifang-Qingzhou section. It does not meet with any other trains within the section.

[0244] Scenario 3: The priority passage condition for passenger trains is no longer set; the 0-1 mixed integer programming model established in this invention is directly applied, where the weights for the total travel time of passenger trains and freight trains are α1 = 0.9 and α2 = 0.1, respectively. The optimal train schedule obtained in this scenario is as follows: Figure 8 As shown.

[0245] Table 2 Comparison of experimental results under different scenarios

[0246]

[0247] As can be seen, after applying the 0-1 mixed-integer programming model proposed in this invention, passenger trains and freight trains did not meet in any section. Let's take freight train F104 as an example. After departing from Qingdao Station, freight train F104 stopped at Gaomi Station and then proceeded directly to its final destination, Jinan Station. During its operation, freight train F104 only met with freight trains F103 and F101 in the Gaomi-Weifang section, and with freight train F105 in the Weifang-Qingzhou section. It did not meet with any other trains within any section. However, unlike scenario 2, freight train F106 waited for a considerable amount of time at Qingdao North Station, and freight train F103 also waited for a relatively long time at Zibo Station. In scenario 3, after optimization using the 0-1 mixed-integer programming model, we can see that the waiting time of freight trains F106 and F103 at intermediate stations has been significantly reduced. To make a more intuitive comparison of the experimental results, we have listed the evaluation indicators of train operation in Table 2.

[0248] A comparison of scenarios 2 and 3 shows that, using the 0-1 mixed-integer programming model proposed in this invention, compared to the scenario where passenger cars have unconditional priority, the total travel time for passenger cars only increases by 3 minutes, which is within an acceptable range. However, the total travel time for freight cars decreases by 164 minutes, with an average reduction of 27 minutes per freight car. This analysis demonstrates that the 0-1 mixed-integer programming model proposed in this invention can reduce the total travel time of all trains by 161 minutes while ensuring that passenger cars and freight cars do not meet within the interval.

[0249] Through the above discussion, it is easy to see that the method proposed in this invention can reduce the total travel time of trains and improve the line operation efficiency while satisfying the condition that passenger and freight trains are prohibited from meeting each other in the section, thus verifying the effectiveness of the proposed timetable optimization method.

[0250] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0251] Obviously, the above examples of the present invention are merely illustrative of the present invention and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for optimizing a passenger and freight train co-line diagram considering the interval forbidden meeting condition, characterized in that, Includes the following steps: Simplify actual train operation scenarios by presetting default conditions; Based on the simplified train operation scenario, preset constants are defined; Based on the simplified train operation scenario, decision variables are set; Establish constraints for train operation; A 0-1 mixed integer programming model is established by linearly adding the total train travel time to the total delay time at the train's originating station as the objective function. Generate an initial solution to the 0-1 mixed integer programming model, and use this initial solution as the current global optimal solution; The 0-1 mixed integer programming model is solved based on the variable neighborhood search algorithm (VNS). After multiple iterations, the current global optimal solution obtained from the last iteration is output, which is the optimized passenger and freight car co-line operation diagram. The specific constraints for establishing train operation include: Train safety interval constraints are conditions that ensure the safe interval between two adjacent trains in the same direction; specifically, they include the interval constraints that trains in the up direction must meet and the interval constraints that trains in the down direction must meet. Passenger and freight trains are prohibited from meeting within the section. This constraint ensures that two trains traveling in opposite directions will not meet within the section if they are of different types. Intermediate station stop time constraint: This constraint ensures that when the train stops at the designated station, there is a certain amount of time to carry out the corresponding passenger or freight business. Origin station departure time constraint, which stipulates that a train cannot depart from its origin station earlier than its expected departure time. Station capacity constraint, which stipulates that the number of trains stopping at the same station at the same time cannot exceed the maximum number of trains that the station can accommodate; Inter-section travel time constraint, which specifies the travel time for passenger cars and freight cars in each section.

2. The method for optimizing the operating schedule of passenger and freight vehicles on the same line, considering the no-passing condition in sections, as described in claim 1, is characterized in that... The default conditions specifically include: Treat the train speed as a constant; Trains are permitted to stop and / or overtake within stations, but are prohibited from stopping and / or overtaking within any section. All intermediate stations are equipped with parking lines to allow freight cars to wait and pass. All trains depart from their originating station no earlier than the expected departure time of the corresponding originating station. The length of the train is negligible; The time accuracy is 1 minute.

3. The method for optimizing the operating schedule of passenger and freight vehicles on the same line, considering the no-passing condition in sections, as described in claim 1, is characterized in that... The preset constants specifically include: The number of stations is the total number of stations in the timetable, and the value of the number of stations is [value missing]. ; Station number index ; Station capacity This represents the total number of trains that can stop at a station at the same time. Interval length , which is the distance in kilometers between two adjacent stations; The number of trains is the total number of trains in the timetable, and the value of the number of trains is [value missing]. ; Train number index ; Train operating speed is the average number of kilometers a train travels per hour within a given section of track. It is specifically divided into passenger train operating speed. and truck speed ; Expected departure time from originating station This refers to the time when the train departs from its originating station. Minimum time interval between arrivals , which is the time interval between the arrival of two trains at the same station; Minimum departure interval This is the time interval between two trains leaving the same station. Minimum stop time at intermediate stations This refers to the time the train stops at intermediate stations.

4. The method for optimizing the operating schedule of passenger and freight vehicles on the same line, considering the no-passing condition in sections, as described in claim 3, is characterized in that... The setting of decision variables specifically includes: Train arrival time ,train Arrival at the station Time; Train departure time ,train Leaving the station Time; The order in which two trains enter the same section; specifically including: The order in which two trains traveling in the upward direction enter the same section. Trains traveling in the upward direction Previously entered the range At that time, ;otherwise ;in, ; The order in which two trains in the down direction enter the same section, and the order in which trains in the down direction enter the same section. Trains in the downward direction Previously entered the range At that time, ;otherwise ;in, ; The order in which two trains, one going up and one going down, enter the same section. When the train going up... Trains in the downward direction Previously entered the range At that time, ;otherwise ;in, ; in: For train number index, For station number index, Indicates station With the station The interval between For the collection of trains traveling in the upward direction, This is a collection of trains traveling in the downward direction.

5. The method for optimizing the operating schedule of passenger and freight vehicles on the same line, considering the no-passing condition in sections, as described in claim 1, is characterized in that... The specific constraints for establishing train operation include: The train safety interval constraints are as follows: ; ; ; ; ; ; ; ; Passenger and freight vehicles are prohibited from meeting within the designated area, specifically as follows: ; ; The time constraints for stopping at intermediate stations are as follows: ; The departure time constraints at the originating station are as follows: ; ; The station capacity constraints are as follows: ; The time constraints for inter-regional travel are as follows: ; 。 6. The method for optimizing the operating schedule of passenger and freight vehicles on the same line, considering the no-passing condition in sections, as described in claim 5, is characterized in that... The objective function is to linearly add the total train travel time to the total delay time at the train's originating station, and the specific steps are as follows: Let train travel time refer to the time interval between the train's departure from the originating station and its arrival at the destination station. The total train travel time... It refers to the sum of the travel times of all trains, which is composed of the linear weighted sum of the total travel times of passenger trains and the total travel times of freight trains; Let the train's originating station delay time be the difference between the actual departure time of the train at the originating station and the expected departure time of the train at the originating station, and let the total train originating station delay time be... This refers to the sum of delay times at the originating stations of all trains; The objective function is: ; The final expression of the 0-1 mixed integer programming model is: ; The 0-1 mixed integer programming model aims to minimize the sum of the total train travel time and the total delay at the train's originating station.

7. The method for optimizing the operating schedule of passenger and freight vehicles on the same line, considering the no-passing condition in sections, as described in claim 1, is characterized in that... The generation of an initial solution to the 0-1 mixed integer programming model adopts the following principles: Principle 1: After all passenger buses have arrived at the terminal station, freight buses will depart from the originating station. Principle 2: Passenger trains shall depart from their originating station at the expected departure time, and the stop time shall be equal to the minimum stop time at intermediate stations. Principle 3: Freight trucks shall not stop at intermediate stations; Based on the above principles, a solution to the 0-1 mixed integer programming model is generated as the initial solution. .

8. The method for optimizing the operating schedule of passenger and freight vehicles on the same line, considering the no-passing condition in sections, as described in claim 7, is characterized in that... When solving the 0-1 mixed-integer programming model, data is first generated based on the actual train operation scenario and input into the 0-1 mixed-integer programming model. Then, the solution is obtained based on the Variable Neighborhood Search (VNS) algorithm. The specific steps are as follows: Preset the maximum number of iterations; First, the search process for the current global optimum is initiated by performing a perturbation process and a variable neighborhood descent process on the current global optimum. The iteration count is updated after each search is completed. Then, determine whether the number of iterations equals the maximum number of iterations; If equal to: terminate the search process for the current global optimal solution and output the current global optimal solution obtained from the last iteration search; If it is less than: take the global optimal solution obtained in this iteration as the new current global optimal solution, and restart the search process for the current global optimal solution.

9. The method for optimizing the operating schedule of passenger and freight vehicles on the same line, considering the no-passing condition in sections, as described in claim 8, is characterized in that... The Variable Neighborhood Search (VNS) algorithm is as follows: The initial solution And neighborhood structures used for perturbation processes and variable neighborhood descent processes. Input into the algorithm; By performing a perturbation process to expand the search space of the current solution, the possibility of the algorithm getting trapped in local optima is reduced, enabling the algorithm to find a better solution; the perturbation process expands the search space of the current solution. The The current solution is generated in each neighborhood structure. A neighborhood solution ; The process searches for local optima in several designed neighborhood structures by performing a variable neighborhood descent process. The variable neighborhood descent process adopts the following principle: whenever a better solution than the current solution appears, the process resumes the search in the first neighborhood structure and selects the best solution among all the better solutions found as the new local optimum. The specific process for performing the variable neighborhood descent is as follows: Enter the current solution and neighborhood structure for variable neighborhood descent process Let the local optimal solution Equal to the current solution input ; Starting from the first neighborhood structure, search for the current solution. In neighborhood structure The best neighborhood solution ,Right now If the optimal neighborhood solution The objective function value is less than the current solution If the objective function value is 0, then let the current solution be 0. Equal to the optimal neighborhood solution and order Re-search the current solution In neighborhood structure The best neighborhood solution If the optimal neighborhood solution The objective function value is greater than the current solution If the objective function value is , then let Re-search the current solution In neighborhood structure The best neighborhood solution Repeat the above process until... If the current solution is The objective function value is less than the local optimum. Then let the local optimal solution equal to the current solution Output the local optimum solution. The neighborhood descent process ends; Let the global optimal solution equal to the initial solution Meanwhile, let the number of iterations Equal to 0; First, perform the perturbation process, starting from the global optimal solution. The A neighborhood solution that generates the global optimal solution in a neighborhood structure. ; in this neighborhood solution Based on this, a variable neighborhood descent process is performed to search for a local optimum, letting It equals the local optimum; like The objective function value is less than the global optimal solution. If the objective function value is such that the global optimal solution is obtained, then... equal Number of iterations It equals 0, and starts from the first neighborhood structure, i.e. The perturbation process will be re-executed when the value is 1. like The objective function value is greater than or equal to the global optimal solution. If the objective function value is , then let equal Continue from the globally optimal solution The A neighborhood solution that generates the global optimal solution from among the neighborhoods. The process continues in the same manner. One iteration is defined as performing all the neighborhood structures designed in the perturbation process once, that is, when This constitutes one complete iteration; When the number of iterations Exceeding the pre-defined maximum number of iterations When the time is right, terminate the search process and output the global optimal solution. .

10. The method for optimizing the operating schedule of passenger and freight vehicles on the same line, considering the no-passing condition in sections, as described in claim 9, is characterized in that... The neighborhood structure design for the disturbance process is as follows: Changing the departure time of the train originating station: The first neighborhood structure of the disturbance process is mainly related to the departure time of the originating station; keeping the train type unchanged, randomly select two trains in the same direction, advance the departure time of the originating station of one train, and postpone the departure time of the originating station of the other train by the same amount of time. Changing the stopping time of trains at intermediate stations: The second neighborhood structure of the disturbance process is mainly related to the stopping time of trains at intermediate stations; keeping the train type unchanged, randomly select two trains in the same direction, reduce the stopping time of one train at a certain intermediate station by a given time, and increase the stopping time of the other train at that station by the same time. The neighborhood structure design for the variable neighborhood descent process is as follows: Changing the departure time of a train originating station: The first neighborhood structure in the variable neighborhood descent process is to change the departure time of a train originating station; randomly select a train and advance or delay its departure time from the originating station by a given time. Changing the stop time of a train at an intermediate station: The second neighborhood structure of the variable neighborhood descent process is to change the stop time of a train at an intermediate station; randomly select a train and decrease or increase its stop time at a certain intermediate station by a given time.

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