Train operation method and device in fast-slow train and overline combined mode

Abstract

The invention provides a train operation method and device in a fast and slow train and overline combined mode, and the method comprises the steps: constructing a train operation network in the combined mode, screening an effective path in the train operation network, and calculating the probability that the effective path is selected through a prediction model; obtaining a pre-established operation model in a multi-target planning form; and inputting the statistical data of the probability and the effective path into the operation model, solving the operation model by using a multi-objective evolutionary algorithm, and outputting the departure frequency of each route on the train operation network. According to the method, in the fast and slow train and overline combined mode, a comprehensive multi-target nonlinear optimization model is established as an operation model, and the operation cost is reduced while the requirements of passengers are met; and the operation model is solved by using a multi-objective evolutionary algorithm with relatively high efficiency so as to quickly obtain a train operation result.

Description

Technical Field

[0001] The present invention relates to the technical field of train operation optimization, and particularly to a train operation method and device under a combination mode of express trains and cross-line trains. Background Art

[0002] The combination of the express train and cross-line train mode is a complex operation strategy, aiming to further improve the operation efficiency and service quality of the rail transit system by introducing express trains and cross-line operations simultaneously.

[0003] In related technologies, since the speeds of express trains and slow trains are different and express trains need to skip some stations, it is necessary to accurately and safely determine the departure frequency of trains. Although intelligent dispatching systems have been introduced in some urban rail transits, in the combination mode of express trains and cross-line trains, the existing dispatching algorithms still have limitations and cannot fully adapt to complex dynamic changes. Especially during peak periods, it may not be able to adjust the train departure interval or path in time, resulting in an increase in passenger waiting time.

[0004] Based on the analysis of the development status of this technical field, the existing technologies lack a solution to construct a comprehensive multi-objective planning model and use a multi-objective evolutionary algorithm to solve the departure frequency of each route. Summary of the Invention

[0005] The purpose of the present invention is to provide a train operation method and device under a combination mode of express trains and cross-line trains, aiming to solve the above problems in the existing technologies.

[0006] According to the first aspect of the embodiments of the present invention, a train operation method under a combination mode of express trains and cross-line trains is provided, including:

[0007] Construct a train operation network under the combination mode, screen effective paths in the train operation network, and use a prediction model to calculate the probability that the effective paths are selected;

[0008] Obtain a pre-established operation model in the form of multi-objective planning;

[0009] Input the probability and statistical data of the effective paths into the operation model, use a multi-objective evolutionary algorithm to solve the operation model, and output the departure frequency of each route on the train operation network.

[0010] According to the second aspect of the embodiments of the present invention, a train operation device under a combination mode of express trains and cross-line trains is provided, including:

[0011] A construction module, configured to construct a train operation network under the combination mode, screen effective paths in the train operation network, and use a prediction model to calculate the probability that the effective paths are selected;

[0012] A model acquisition module, configured to acquire a pre-established operation model in the form of multi-objective programming;

[0013] A solving module, configured to input the probability and statistical data of effective paths into the operation model, solve the operation model using a multi-objective evolutionary algorithm, and output the departure frequencies of each train route on the train operation network.

[0014] According to a third aspect of an embodiment of the present invention, there is provided an electronic device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, where when the computer program is executed by the processor, it implements the steps of the train operation method in the express and local train and cross-line combination mode provided in the first aspect of the present disclosure.

[0015] According to a fourth aspect of an embodiment of the present invention, there is provided a computer-readable storage medium, on which an implementation program for information transmission is stored, and when the program is executed by a processor, it implements the steps of the train operation method in the express and local train and cross-line combination mode provided in the first aspect of the present disclosure.

[0016] The technical solution provided by the embodiment of the present invention has the following beneficial effects: In the express and local train and cross-line combination mode, a comprehensive multi-objective non-linear optimization model is established as the operation model, which reduces the operation cost while meeting the passenger demand; and a highly efficient multi-objective evolutionary algorithm is used to solve the operation model to quickly obtain the train operation results.

[0017] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in one or more embodiments of the present specification or in the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments recorded in the present specification, and for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0019] Figure 1 is a flowchart of the train operation method in the express and local train and cross-line combination mode of the embodiment of the present invention;

[0020] Figure 2 is a schematic diagram of the express and local train and cross-line combination mode scenario of the embodiment of the present invention;

[0021] Figure 3 is a schematic diagram of the train operation network of the embodiment of the present invention;

[0022] Figure 4 is a schematic diagram of the train operation diagram within the express train cycle of the embodiment of the present invention;

[0023] Figure 5 It is a schematic diagram of the passing-related riding arc of the embodiment of the present invention;

[0024] Figure 6 It is a schematic diagram of the NSGA-II multi-objective evolutionary algorithm of the embodiment of the present invention;

[0025] Figure 7 It is a schematic diagram of the train operation device in the combined mode of express and slow trains and cross-line of the embodiment of the present invention;

[0026] Figure 8 It is a schematic diagram of the electronic device of the embodiment of the present invention. Detailed implementation manners

[0027] In order to enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the following will clearly and completely describe the technical solutions in one or more embodiments of this specification with reference to the accompanying drawings in one or more embodiments of this specification. Obviously, the described embodiments are only a part of the embodiments of this specification, rather than all the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of this document.

[0028] For the convenience of the following description, the parameters involved in the present invention are explained as shown in Table 1:

[0029] Table 1. Display of model parameters

[0030]

[0031]

[0032]

[0033] The model assumptions are as follows:

[0034] (1) It is assumed that the technical conditions such as lines, traction power supply, and signal control required for cross-line operation are met between the two cross-line operating lines. At the same time, if the formation of the cross-line train is inconsistent with that of the local train, the doors and platform screen doors can match each other in the co-line operation section.

[0035] (2) The line is equipped with a passing station, which can meet the wiring requirements for the express train to pass.

[0036] (3) All the trains on the two lines use the same vehicle type and the same vehicle configuration, so the operating speeds of the trains on each route are the same. The difference between the express train and the slow train lies in that there is no additional starting and stopping time and no stopping time at intermediate stations.

[0037] (4) The up and down trains on the same route run in pairs and have the same operating speed.

[0038] (5) Assume that passengers arrive evenly during the research period, and the complex situation of passengers taking reverse trains is not considered.

[0039] Method Embodiment

[0040] According to an embodiment of the present invention, there is provided a train operation method under the combination mode of express and local trains and cross-line operation. Figure 1 It is a flowchart of the train operation method under the combination mode of express and local trains and cross-line operation in the embodiment of the present invention, as Figure 1 shown. The train operation method under the combination mode of express and local trains and cross-line operation according to the embodiment of the present invention specifically includes:

[0041] In step S110, a train operation network under the combination mode is constructed, valid paths are screened in the train operation network, and a prediction model is used to calculate the probability of a valid path being selected, which specifically includes:

[0042] Construct a train operation network under the combination operation mode of express and local trains and cross-line operation. Based on the existing train operation network, a depth-first search algorithm is designed to solve all valid paths between any stations. On this basis, a prediction model is used to calculate the probability of each valid path being selected, and the path allocation of the network passengers is completed. The specific process is as follows:

[0043] 1. Obtain the stations of each route on the main line and the auxiliary line, and construct a train operation network with stations as nodes and the distances between stations as edges. Among them, the routes on the main line include long-haul local trains, short-haul local trains, and non-stop express trains, and the routes on the auxiliary line include short-haul local trains and long-haul local trains;

[0044] Figure 2 It is a schematic diagram of the scenario of the combination mode of express and local trains and cross-line operation in the embodiment of the present invention, as Figure 2 shown. The main line A and the auxiliary line B are connected to form a Y-shaped structure. The turn-back points of the short-haul routes on both lines are at the cross-line station (S t ). The section from the cross-line station to the airport line (S N1 ) is a co-line operation section, and the non-stop express train overtakes the local train at the overtaking station with train formation tracks, that is, the model is a fast-slow train mode with overtaking. The embodiment of the present invention is based on this typical combination mode structure. If other structural scenarios are adopted, this solution can also be easily updated;

[0045] Figure 3 It is a schematic diagram of the train operation network in the embodiment of the present invention, as Figure 3As shown in the figure, the physical network of urban rail transit can be represented by a weighted directed connection graph. The combined operation service network of express and local trains and cross-line trains is G = (N, E), where N and E represent the node set and arc set respectively. The node set N includes the line station node set N s and the node set N r of each train operation section, that is, N = N s ∪N r ; The arc set E includes waiting arcs, boarding arcs, alighting arcs and transfer arcs. The weight of the arc is the impedance of each arc segment, that is, the time (unit: min) spent by passengers passing through this arc segment on the travel path. The waiting arc is the waiting time of passengers at the station; The boarding arc is the time of passengers on the train, including the running time of the train section in the train operation section where the boarding arc is located and the stop time at the starting station of the section. That is, for the boarding arc e i in the section (S j ), S i,j , its weight is The alighting arc is the walking time for passengers to get off the train and leave the station or transfer to the transfer platform; Figure 3 In e1 - e 62 is the label of the arc segment of the service network. 2. Based on the train operation service network, design a depth - first algorithm to find all effective paths between any two stations. On this basis, use a prediction model to calculate the probability of each effective path being selected to complete the path assignment of passengers in the line network;

[0046] Under the condition of combined operation of express and local trains and cross - line trains in urban rail transit, the transfer relationship of passengers in the line network is more complex. There are many feasible paths between any OD pair of stations, but there are significant differences in the impedance and transfer times among all feasible paths. Therefore, in the actual travel process, passengers do not consider all possible paths, but only consider some relatively reasonable and beneficial paths for themselves. These paths are defined as effective paths;

[0047] Suppose the path k between the OD pair (r, s) of stations is called an effective path. The prior art often uses the threshold definition method. For example, generally speaking, passengers will not transfer from Route A to Route B during the travel process and then transfer back to Route A. In the operation service network, this means that the same route only appears once in one path; In addition, passengers will not choose a "round - trip" during the travel process, that is, the same node cannot appear more than twice in the same path. The threshold can be set to, for example, the maximum number of transfers N max = 3;

[0048] The above method cannot reflect the real - time change situation. Therefore, use one of the Dial algorithm, K - shortest path algorithm and depth - first search algorithm to screen the effective paths between stations. In the embodiment of the present invention, the depth - first search algorithm is used because this method will not miss any paths. The main process of the depth - first search algorithm is as follows:

[0049] (1) Initialize variables and generate an adjacency matrix;

[0050] (2) Use Dijkstra or Floyd algorithm to calculate the minimum generalized travel cost between OD pairs, obtain the path impedance threshold of effective paths, and set the root node r as the current node i;

[0051] (3) Starting from the current node i, traverse all nodes adjacent to node i. For example, for a certain adjacent node j, if the connected path starting from node i meets the definition conditions of an effective path, update node j as the current node and execute (4); otherwise, go to step (6);

[0052] (4) If node j is the end node, execute the next step; otherwise, return to (3);

[0053] (5) Store all effective paths and calculate the impedance of each effective path;

[0054] (6) Go back to the previous one. If reaching the root node, return to the step.

[0055] Obtain the riding time, waiting time, and transfer time of the effective path. Use formula 23 to obtain the riding time, use formula 24 to obtain the waiting time, and use formula 25 to obtain the transfer time:

[0056]

[0057] Among them, represents the running time of the train in section i on the k-th effective path; represents the stopping time of the train at station j on the k-th effective path; when the through express train overtakes the slow train at the overtaking station, the stopping time of the slow train at the running station will be extended accordingly, and the extended time can be calculated as

[0058]

[0059] Among them, represents the waiting time of the passenger on the k-th effective path between OD pairs rs; f i represents the departure frequency (trains / hour) of the route taken by this effective path; for public transportation with a short headway, the average waiting time of passengers is taken as half of the headway time;

[0060]

[0061] Among them, represents the transfer time of the k-th path between OD pairs rs; λ represents the transfer walking time penalty coefficient; t trDenote the transfer walking time of passengers at the cross-line station; x represents a 0-1 variable, which is 1 if transferring at the cross-line station and 0 otherwise;

[0062] Use the Logit prediction model of Formula 1 to calculate the probability that the effective path is selected:

[0063]

[0064] where, denotes the probability of the kth effective path from station r to station s, and θ represents the familiarity fixed value, denotes the generalized travel cost of the kth effective path from station r to station s. The generalized travel cost is the sum of the riding time, waiting time, and transfer time, that is

[0065] In step S120, obtain the pre-established operation model in the form of multi-objective programming, specifically including:

[0066] 1. Obtain the objective function for establishing the total enterprise operation cost;

[0067] The enterprise operation cost mainly includes fixed cost and variable cost. The fixed cost is the vehicle purchase cost and the cost of line and equipment transformation. Since the cost of line and equipment transformation cannot be quantified, it is not considered in this article; the variable cost mainly includes the train running distance cost and the stop cost;

[0068] Obtain the objective function of the total enterprise operation cost of the operation model established based on Formula 2,

[0069] minC1 = C g +C z +C t Formula 2;

[0070] Use Formulas 3 to 8 to represent the parameters in the total enterprise operation cost:

[0071]

[0072] where, C1 represents the total enterprise operation cost, C g represents the train fixed cost, C z represents the train running kilometer cost, C t represents the stop additional cost, ε 备 represents the spare vehicle ratio coefficient, ε 检 represents the maintenance vehicle ratio coefficient, β represents the purchase conversion cost per vehicle per unit time, R represents the set of train routes {r1, r2, r3, r4, r5}, and the set R represents the slow trains on the main line's large loop, small loop, and direct express trains, and the slow trains on the small loop and large loop of the auxiliary line in sequence, f(r s ) represents the train route rs The departure frequency of represents the route r s the train formation, represents the turnaround time of the train on route r s on, represents the time for the slow train's stop to be extended due to the express train overtaking, T represents the research duration, τ at represents the time interval from the station to the through section, τ td represents the time interval from the station to the departure, represents route r s of the train at station S i of the stop time, S m and S n represent two fixed overtaking stations on the main line, e j represents section j, E represents the set of all sections, represents route r s of the train in section e j of the running time, represents that if section e j is covered by route r s it is 1 otherwise 0, S i represents station i, S represents the set of all stations on the line, represents that if station S i is covered by route r s it is 1 otherwise 0, represents route r s the turnaround time at the two terminal turnaround stations, ω represents the running cost per unit kilometer of each train, represents route r s of the running distance, represents section e j of the length, represents route r s at the total turnaround distance at the two terminal turnaround stations, γ represents the single - stop cost of the train;

[0073] The fixed cost of the train is composed of the product of the converted cost per unit train, the number of in - service trains, and the research duration. The number of in - service trains includes the number of vehicles, spare vehicles, and maintenance vehicles. The number of spare vehicles and maintenance vehicles is usually the number of vehicle uses multiplied by the corresponding proportionality coefficients; Due to the express train overtaking the slow train, according to the analysis of the impact of fast and slow trains on the line capacity in Chapter 2, in order to minimize the deduction impact of operating express trains on the line capacity as much as possible, and considering the travel needs of long - distance passengers, the first two trains of the express train are fixed as slow trains on the large - scale route of this line and are overtaken by the express train;

[0074] The stop - related additional cost C in Formula 8 tDepending on the total number of stops of the train during the research period, since the through express train stops at all intermediate stations, only the local trains on the other 4 routes will generate additional stop additional costs. Figure 4 It is a schematic diagram of the train operation diagram within the express train cycle of the embodiment of the present invention, as Figure 4 shown, which shows the complete operation process of the express train.

[0075] 2. Obtain the objective function for establishing the cost in passenger travel;

[0076] Obtain the objective function of the total cost of passenger travel for the operation model established based on Formula 9, and use Formulas 10 to 11 to represent the parameters in the total cost of passenger travel:

[0077]

[0078] represents, K represents the set of effective paths between stations, Q ij represents the passenger flow from station i to j, represents the probability of choosing the kth effective path for travel between stations i-j, represents the total travel time of choosing the kth effective path for travel between stations i-j, represents the total in-vehicle time extended by the line network passengers due to the overtaking of the express train, represents the total amount of the travel paths of the line network passengers that include the riding arc e u of, represents the total amount of the travel paths of the line network passengers that include the riding arc e v of, e u and e v represent two special riding arcs that require additional extended stop time due to the overtaking of the express train. Due to the overtaking of the express train, the stop time of the overtaken local train at the overtaking station is extended during the express train diagramming cycle, which is reflected in the service network. Therefore, the values of the two riding arcs e u and e v need to add the extended stop time additionally, represents the total waiting time of choosing the kth effective path between stations i-j, represents the total in-vehicle time of choosing the kth effective path between stations i-j, represents 1 if the kth effective path between stations i-j transfers at the cross-line station and 0 otherwise, represents the transfer walking time of choosing the kth effective path between stations i-j;

[0079] The total travel cost of passengers includes the ticket purchase cost and travel time cost. Under the current fare rules of subway operation, the ticket purchase cost is usually only related to the starting station of the passenger's journey. At the same starting station, the fare is the same under different riding strategies of passengers. Therefore, the optimization model in the embodiments of the present invention does not consider the ticket purchase cost of passengers;

[0080] Regardless of the type of passenger, the travel time is equal to the sum of the weights of each arc in the travel path. However, due to the operation of direct express trains, the first two local trains with long turnbacks of the same line of the direct express train will be overtaken at the passing station, resulting in different stop times from the regular stop times, and the stop time will be extended. In the operation service network, the weight of the riding arc is equal to the sum of the corresponding interval running time and stop time. Therefore, there are two special riding arcs e u 、e v , Figure 5 is a schematic diagram of the riding arcs related to overtaking in the embodiments of the present invention, as Figure 5 shown; in order to calculate the total in-vehicle time extended by passengers in the line network due to the overtaking of express trains When making path selection for passengers, it is necessary to count the total quantity of all paths that contain the riding arcs e u 、e v ;

[0081] 3. Obtain the actual application constraints as the constraint conditions for the operation model;

[0082] Obtain the constraints including the departure frequency constraint of direct express trains, the line passing capacity constraint, the interval departure headway constraint, the upper and lower limits of the departure frequency of trains on each turnback, the load factor constraint, and the integer constraint of decision variables;

[0083] Use Formula 12 to describe the departure frequency constraint of direct express trains. Since the direct express trains of the same line only stop at S1 and S N1 to pick up and drop off passengers, the passenger flow of the audience is small. Assuming that passengers are generally familiar with the line network departure timetable and do not consider reverse riding of passengers, in order to avoid excessive waste of transport capacity caused by operating too many direct express trains and interference with overtaking of the remaining local trains, the departure frequency of direct express trains is limited within the following range:

[0084]

[0085] Among them, represents the ceiling function, Q 1,N1 represents the passenger flow from the starting station S1 to the terminal station S N1 ;

[0086] By focusing on the analysis of the deduction coefficient of the express train under combined operation and the loss of passing capacity under cross-line interference, the maximum passing capacity constraints of each line are obtained; according to the coverage scope of each train operation section in the model, it is divided into three areas: the non-collinear operation section of Line A, the collinear operation section of Line A, and Line B.

[0087] Use Equation 13 to describe the passing capacity constraint of the main line in the non-collinear operation area, and use Equations 14 to 15 to represent the parameters in Equation 13:

[0088]

[0089] Among them, represents the minimum headway in the main line, represents the express train deduction coefficient of the main line, represents the loss of passing capacity caused by cross-line interference, represents the travel time difference between the express train and the local train from the starting station S1 to the second passing station S n n, 越 represents the number of times the local train is overtaken by the express train during the extra occupancy time of the express train. It is assumed that the main line includes two fixed passing stations, and the trains of each operation section are closely arranged. Therefore, only two local trains are overtaken by the express train within one express train cycle. So n 越 takes the value of 2.

[0090] Under the combined operation of express trains and local trains and cross-line operation, some sections will be covered by multiple operation sections. To ensure operation safety and a certain level of train service, it is necessary to set the headway of each section, which is usually expressed as the ratio of the research period to the sum of the departure frequencies of each operation section;

[0091] Use Equation 16 to describe the passing capacity constraint of the main line in the collinear operation area, and use Equation 17 to represent the parameters in Equation 16:

[0092]

[0093] Among them, represents the express train deduction coefficient of the collinear section, represents the travel time of the local train from the cross-line station k to the terminal station N1, represents the travel time of the local train from the cross-line station k to the terminal station N1, represents the travel time of the local train from the cross-line station k to the passing station S n , represents the travel time of the express train from the cross-line station k to the passing station S n τ, aa represents the arrival interval time, τ td represents the through interval time, τ da represents the departure-arrival interval time;

[0094] Use formula 18 to describe the line capacity constraint of the auxiliary line:

[0095]

[0096] Among them, represents the minimum headway in the auxiliary line;

[0097] Use formula 19 to describe the headway constraint of the section:

[0098]

[0099] Among them, represents the lower limit of the headway on section e j and represents the upper limit of the headway on section e j .

[0100] Since the line capacity of each line in the urban rail transit network and the turning-back capacity of the turning-back stations at both ends of each train formation are limited, the upper limit of the train departure frequency of each train formation in the studied rail transit network should be restricted. On the other hand, if the train departure frequency of the train formation is too small, the waiting time of passengers will increase, resulting in an extension of the passenger travel time. In order to provide passengers with a better travel experience and better travel services, use formula 20 to describe the upper and lower limit constraints of the train departure frequency of each train formation:

[0101]

[0102] Among them, represents the lower limit of the departure frequency of each train formation, represents the lower limit of the departure frequency of each train formation.

[0103] The transport capacity that the urban rail transit network can provide should not only meet the passenger flow demand of each section, but also not be too large to cause waste of transport capacity. As an index to measure the operation state of transport capacity, the load factor is the ratio of passenger flow demand to train transport capacity. If the load factor is too high, the transport capacity is insufficient and the service level is poor; if the load factor is too low, the transport capacity is wasted; use formula 21 to describe the load factor constraint:

[0104]

[0105] Among them, η min represents the minimum section load factor, represents the section passenger flow of section e j , represents the number of passengers that the vehicles of line r s can carry, and η max represents the maximum section load factor.

[0106] The departure frequency of each train route should be a positive integer, and the integer constraint of the decision variable is described using Formula 22:

[0107]

[0108] where Z + represents a positive integer.

[0109] In step S130, the probability and the statistical data of the effective paths are input into the operation model, and the multi-objective evolutionary algorithm is used to solve the operation model, and the departure frequencies of each train route on the train operation network are output, specifically including:

[0110] Use the NSGA-II multi-objective evolutionary algorithm to solve the operation model to obtain the optimal departure frequencies of each train route on the train operation network:

[0111] Obtain the set of feasible solution individuals that meet the constraint conditions as the initial population, perform non-dominated sorting on the initial population, calculate the crowding distance between individuals in the same non-dominated layer, and select parent individuals from the initial population according to the results of non-dominated sorting and crowding distance;

[0112] Perform crossover and mutation operations on the parent individuals to generate new individuals, and select and combine the new individuals and the parent individuals as the initial population for the next round of iteration;

[0113] After the iteration ends, the output of the operation model is obtained.

[0114] Figure 6 is a schematic diagram of the NSGA-II multi-objective evolutionary algorithm of the embodiment of the present invention, as Figure 6 shown, which shows the specific solution process.

[0115] In summary, in view of the problems existing in the current situation, the train operation method in the fast and slow train and cross-line combination mode of the present invention establishes a comprehensive multi-objective non-linear optimization model as the operation model under the fast and slow train and cross-line combination mode, which reduces the operation cost while meeting the passenger demand; the operation model considers the total operation cost of the enterprise and the total travel cost of passengers to highlight that the most influential factors on the quality of the train operation plan are the enterprise operation and passenger travel; the constraint conditions include the departure frequency constraint of the direct express train, the line passing capacity constraint, the interval departure interval constraint, the upper and lower limit constraints of the departure frequencies of each train route, the load factor constraint, and the integer constraint of the decision variable, which can meet the requirements under the combination mode; and the more efficient multi-objective evolutionary algorithm NSGA-II is used to solve the operation model to quickly obtain the train operation results.

[0116] Device Embodiment

[0117] According to an embodiment of the present invention, there is provided a train operation device in a fast and slow train and cross-line combination mode, Figure 7It is a schematic diagram of a train operation device in the fast and slow train and cross-line combination mode of the embodiments of the present invention. As Figure 7 shown, the train operation device in the fast and slow train and cross-line combination mode according to the embodiments of the present invention specifically includes:

[0118] A construction module 70, configured to construct a train operation network in the combination mode, screen effective paths in the train operation network, and calculate the probability of an effective path being selected using a prediction model. Specifically, it is used for:

[0119] Obtain the stations of each train route on the main line and the auxiliary line, and construct a train operation network with stations as nodes and the distances between stations as edges. Among them, the train routes on the main line include slow trains on long-distance routes, slow trains on short-distance routes, and non-stop express trains, and the train routes on the auxiliary line include slow trains on short-distance routes and slow trains on long-distance routes.

[0120] Use one of the Dial algorithm, the K shortest path algorithm, and the depth-first search algorithm to screen the effective paths between stations.

[0121] Obtain the riding time, waiting time, and transfer time of the effective path; use the Logit prediction model of Formula 1 to calculate the probability of the effective path being selected:

[0122]

[0123] Among them, represents the probability of the kth effective path from station r to station s, θ represents the familiarity constant value, represents the generalized travel cost of the kth effective path from station r to station s, and the generalized travel cost is the sum of the riding time, waiting time, and transfer time.

[0124] A model acquisition module 72, configured to acquire a pre-established operation model in the form of multi-objective programming. Specifically, it is used for:

[0125] Obtain the objective function of the total enterprise operation cost of the operation model established based on Formula 2, and use Formulas 3 to 8 to represent the parameters in the total enterprise operation cost:

[0126] minC1 = C g + C z + C t Formula 2;

[0127]

[0128] Among them, C1 represents the total enterprise operation cost, C g represents the fixed cost of the train, C z represents the cost per running kilometer of the train, C t represents the additional cost for stops, ε 备 represents the standby vehicle ratio coefficient, ε检 represents the maintenance vehicle ratio coefficient, β represents the purchase conversion cost per vehicle per unit time, R represents the set of train operation routes {r1, r2, r3, r4, r5}, in which the slow trains on the main line's long-haul route, slow trains on the short-haul route, and direct express trains, slow trains on the short-haul route and long-haul route on the branch line are represented in sequence, f(r s ) represents the departure frequency of route r s . represents the train formation of route r s . represents the turnaround time of the train on route r s . represents the time extension of the slow train's stop due to the overtaking of the direct express train, T represents the research duration, τ at represents the time interval from the station to the through section, τ td represents the time interval from the station through section to departure, represents the stop time of the train on route r s at station S i . S m and S n represent two fixed overtaking stations on the main line, e j represents section j, E represents the set of all sections, represents the running time of the train on route r s in section e j . represents that if section e j is covered by route r s it is 1 otherwise 0, S i represents station i, S represents the set of all stations on the line, represents that if station S i is covered by route r s it is 1 otherwise 0, represents the turnaround time at the two terminal turnaround stations of route r s , ω represents the running cost per unit kilometer of each train, represents the running distance of route r s . represents the length of section e j . represents the total turnaround distance of route r s at the two terminal turnaround stations, γ represents the single-stop cost of the train;

[0129] Obtain the objective function of the total passenger travel cost of the operation model established based on Formula 9, and use Formulas 10 to 11 to represent the parameters in the total passenger travel cost:

[0130]

[0131] represents, K represents the set of effective paths between stations, Qij Indicates the passenger flow from station i to j. Indicates the probability of choosing the k-th effective path for travel between stations i - j. Indicates the total travel time of choosing the k-th effective path for travel between stations i - j. Indicates the total in-vehicle time extended for network passengers due to express train overtaking. Indicates the total quantity of all travel paths of network passengers that include the boarding arc e u of. Indicates the total quantity of all travel paths of network passengers that include the boarding arc e v of, e u and e v Indicates two special boarding arcs that require additional extended stop time due to express train overtaking. Indicates the total waiting time of choosing the k-th effective path between stations i - j. Indicates the total in-vehicle time of choosing the k-th effective path between stations i - j. Indicates whether the k-th effective path between stations i - j transfers at the cross-line station (1 if yes, 0 otherwise). Indicates the transfer walking time of choosing the k-th effective path between stations i - j.

[0132] Obtain the actual application constraints as the constraints for the operation model.

[0133] Obtain the constraints including the departure frequency constraint of direct express trains, the line passing capacity constraint, the interval departure headway constraint, the upper and lower limits of the departure frequency of trains on each route, the load factor constraint, and the integer constraint of decision variables.

[0134] Use Equation 12 to describe the departure frequency constraint of direct express trains:

[0135]

[0136] Where, Indicates the ceiling function, Q 1,N1 Indicates the passenger flow from the starting station S1 to the terminal station S N1 of.

[0137] Use Equation 13 to describe the line passing capacity constraint in the non-collinear operation area of the main line, and use Equations 14 to 15 to represent the parameters in Equation 13:

[0138]

[0139] Where, Indicates the minimum departure headway in the main line. Indicates the express train deduction coefficient of the main line. Indicates the loss of passing capacity caused by cross-line intersection interference. Indicates from the starting station S1 to the second passing station S n The travel time difference between the express and local trains, n 越 Indicates the number of times the local train is overtaken during the extra occupancy time of the express train, n 越 The value is 2;

[0140] Describes the line passing capacity constraint of the main line collinear operation area using formula 16, and represents the parameters in formula 16 using formula 17:

[0141]

[0142] Among them, Indicates the express train deduction coefficient of the collinear section, Indicates the travel time of the local train from the cross-line station k to the terminal station N1, Indicates the travel time of the local train from the cross-line station k to the terminal station N1, Indicates the travel time of the local train from the cross-line station k to the passing station S n of the travel time, Indicates the travel time of the express train from the cross-line station k to the passing station S n of the travel time, τ aa Indicates the arrival interval time, τ td Indicates the through interval time, τ da Indicates the arrival and departure interval time;

[0143] Describes the line passing capacity constraint of the auxiliary line using formula 18:

[0144]

[0145] Among them, Indicates the minimum departure interval in the auxiliary line;

[0146] Describes the interval departure interval constraint using formula 19:

[0147]

[0148] Among them, Indicates interval e j the lower limit of the departure interval on, Indicates interval e j the upper limit of the departure interval on;

[0149] Describes the upper and lower limit constraints of the train departure frequencies of each route using formula 20:

[0150]

[0151] Among them, Indicates the lower limit of the departure frequency of each route, Indicates the lower limit of the departure frequency of each route;

[0152] The full-load rate constraint is described using Equation 21:

[0153]

[0154] where η min represents the minimum cross-section full-load rate, represents the passenger flow of cross-section of section e j and represents the seating capacity of vehicles on line r s and η max represents the maximum cross-section full-load rate;

[0155] The integer constraint of the decision variable is described using Equation 22:

[0156]

[0157] where Z + represents a positive integer.

[0158] The solution module 74 is configured to input the statistical data of the probability and the effective paths into the operation model, solve the operation model using a multi-objective evolutionary algorithm, and output the departure frequencies of each train operation route on the train operation network, specifically for:

[0159] Existing technologies often use genetic algorithms, particle swarm optimization algorithms, simulated annealing algorithms, or ant colony algorithms. However, the particle swarm optimization algorithm is suitable for solving continuous optimization problems and dynamic optimization problems; the simulated annealing algorithm is suitable for solving continuous optimization problems and optimization problems with non-convex objective functions; the ant colony algorithm is suitable for solving optimization combination problems and path planning problems; therefore, the above algorithms are not suitable for solving the multi-objective problems of train operation in the combination mode of express and local trains and cross-line trains;

[0160] The NSGA-II algorithm is an improved genetic algorithm, also known as the non-dominated sorting genetic algorithm. It is optimized based on the traditional genetic algorithm, introducing non-dominated sorting of the population and calculation of the crowding distance. These improvements enable the algorithm to effectively maintain the diversity of the population and find the Pareto optimal solution set of the problem.

[0161] The basic idea of the NSGA-II algorithm is as follows: First, an initial population with N individuals is randomly generated. Then, non-dominated sorting is performed on these initial individuals, and they are divided into different non-dominated levels. Subsequently, for each individual in each non-dominated level, its crowding distance is calculated to ensure the diversity and convergence of the population. On this basis, according to the non-dominated relationship and crowding distance, appropriate individuals are selected to form a new parental population. Subsequently, crossover and mutation operations are performed on the parental population to generate a new offspring population. The parental and offspring populations are combined into a new total population. Finally, non-dominated sorting and crowding distance calculation are performed on the new total population to obtain the Pareto front, that is, the Pareto optimal solution set. If the stopping condition is met, the Pareto front is output; otherwise, the iteration continues.

[0162] On the one hand, the NSGA-II algorithm can directly solve the multi-objective optimization model. On the other hand, it shows better performance among similar algorithms. Use the NSGA-II multi-objective evolutionary algorithm to solve the operation model:

[0163] Obtain the set of feasible solution individuals that meet the constraint conditions as the initial population, perform non-dominated sorting on the initial population, and for each pair of individuals P i and P j , determine the dominance relationship between them by comparing their objective function values. If P i is not inferior to P j in all objective functions, and P i is superior to P j in a certain objective function, then P i dominates P j , and at the same time P j is dominated by P i . If P i and P j do not dominate each other, then there is no dominance relationship between them;

[0164] According to the dominance relationship, the individuals in the population are divided into different non-dominated levels; the individuals in the first level are not dominated by any other individuals, the individuals in the second level are dominated by the individuals in the first level, and so on;

[0165] Calculate the crowding distance between individuals in the same non-dominated level. The crowding distance calculation is used to evaluate the distribution density of individuals in the population. The crowding distance can be achieved by calculating the sum of the distances between adjacent individuals after normalizing the objective function values. In this way, the distribution density of individuals in the objective function space can be evaluated. The larger the distance, the sparser the distribution between individuals, and the smaller the distance, the denser the distribution between individuals. Select parental individuals from the initial population according to the results of non-dominated sorting and crowding distance;

[0166] Perform crossover and mutation operations on the parent individuals to generate new individuals, and select and combine the new individuals and the parent individuals as the initial population for the next iteration;

[0167] After the iteration ends, the output of the operation model is obtained.

[0168] In summary, in view of the existing problems, the train operation device in the combination mode of express and local trains and cross-line trains of the present invention establishes a comprehensive multi-objective non-linear optimization model as the operation model in the combination mode of express and local trains and cross-line trains, which reduces the operation cost while meeting the passenger demand; the operation model considers the total operation cost of the enterprise and the total travel cost of passengers to highlight that the most influential factors on the quality of the train operation plan are the enterprise operation and passenger travel; the constraint conditions include the departure frequency constraint of direct express trains, the line passing capacity constraint, the interval departure interval constraint, the upper and lower limits of the departure frequencies of trains on each route, the load factor constraint, and the integer constraint of decision variables, which can meet the demands in the combination mode; and the multi-objective evolutionary algorithm NSGA-II with high efficiency is used to solve the operation model to quickly obtain the train operation results.

[0169] Embodiment of electronic device

[0170] Figure 8 It is a schematic diagram of the electronic device according to the embodiment of the present invention. The electronic device 800 may include at least one processor 810 and a memory 820. The processor 810 may execute instructions stored in the memory 820. The processor 810 is communicatively connected to the memory 820 via a data bus. In addition to the memory 820, the processor 810 may also be communicatively connected to an input device 830, an output device 840, and a communication device 850 via the data bus.

[0171] The processor 810 may be any conventional processor, such as a commercially available CPU. The processor may also include, for example, a Graphic Process Unit (GPU), a Field Programmable Gate Array (FPGA), a System on Chip (SOC), an Application Specific Integrated Circuit (ASIC), or a combination thereof.

[0172] The memory 820 may be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic memory, flash memory, a magnetic disk, or an optical disk.

[0173] In an embodiment of the present disclosure, executable instructions are stored in the memory 820, and the processor 810 can read the executable instructions from the memory 820 and execute the instructions to implement all or part of the steps of the train operation method in any of the fast and slow train and cross-line combination modes in the above exemplary embodiments.

[0174] Embodiment of computer-readable storage medium

[0175] In addition to the above methods and apparatuses, an exemplary embodiment of the present disclosure may also be a computer program product or a computer-readable storage medium storing the computer program product. The computer program product includes computer program instructions that can be executed by a processor to implement all or part of the steps described in the train operation method in any of the fast and slow train and cross-line combination modes in the above exemplary embodiments.

[0176] The computer program product can be written in any combination of one or more programming languages for programming code to perform the operations of the embodiments of the present application. The programming languages include object-oriented programming languages such as Java, C++, etc., and also include conventional procedural programming languages such as the "C" language or similar programming languages and scripting languages (such as Python). The programming code can be executed entirely on the user computing device, partially on the user device, executed as an independent software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0177] The computer-readable storage medium can adopt any combination of one or more readable media. The readable media can be a readable signal medium or a readable storage medium. The readable storage medium can, for example, include but is not limited to electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or components, or any combination of the above. More specific examples of the readable storage medium include: static random access memory (SRAM) with one or more wire electrical connections, electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, a magnetic disk or an optical disk, or any suitable combination of the above.

[0178] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for train operation in a combination mode of express and local trains and overline trains, characterized in that Including: Construct a train operation network in a combined mode, screen effective paths in the train operation network, and use a prediction model to calculate the probability of an effective path being selected; Obtain a pre-established operation model in the form of multi-objective programming; Input the probability and statistical data of the effective path into the operation model, solve the operation model using a multi-objective evolutionary algorithm, and output the departure frequencies of each train route on the train operation network.

2. The method according to claim 1, characterized in that, The specific process of constructing the train operation network in the combined mode includes: Obtain the stations of each train route on the main line and the auxiliary line, and construct a train operation network with these stations as nodes and the distances between stations as edges. Among them, the train routes on the main line include long-haul slow trains, short-haul slow trains, and direct express trains, and the train routes on the auxiliary line include short-haul slow trains and long-haul slow trains.

3. The method according to claim 1, wherein The specific process of screening effective paths in the train operation network includes: screening effective paths between stations using one of the Dial algorithm, the K shortest path algorithm, and the depth-first search algorithm.

4. The method according to claim 1, characterized in that, The specific process of using the prediction model to calculate the probability of an effective path being selected includes: Obtain the riding time, waiting time, and transfer time of the effective path; use the Logit prediction model of Formula 1 to calculate the probability of the effective path being selected: Among them, represents the probability of the k-th effective path from site r to site s, and θ represents a fixed value of familiarity. represents the generalized travel cost of the k-th effective path from site r to site s, and the generalized travel cost is the sum of the riding time, the waiting time, and the transfer time.

5. The method according to claim 1, characterized in that The specific process of obtaining the pre-established operation model in the form of multi-objective programming includes: Obtain the objective function of the total enterprise operation cost of the operation model established based on Formula 2, and use Formulas 3 to 8 to represent the parameters in the total enterprise operation cost; minC1 = C g + C z + C t Formula 2; Among them, C1 represents the total operating cost of the enterprise, C g represents the fixed cost of the train, C z represents the cost per running kilometer of the train, C t represents the additional cost of stops, ε 备 represents the proportion coefficient of spare cars, ε 检 represents the proportion coefficient of inspection cars, β represents the purchase conversion cost per unit time of each car, R represents the set of routes {r1, r2, r3, r4, r5}, and in the set R, it represents the slow train on the main line's large loop, slow train on the small loop, and direct express train in sequence, the slow train on the small loop and large loop on the branch line, f(r s ) represents the departure frequency of route r s . represents the train formation of route r s . represents the turnover time of the train on route r s . represents the time extension of the slow train's stop due to the overtaking of the direct express train, T represents the research duration, τ at represents the interval time from the station to the through track, τ td represents the interval time from the through track to the departure, represents the stop time of the train on route r s at station S i . S m and S n represent two fixed overtaking stations on the main line, e j represents section j, E represents the set of all sections, represents the running time of the train on route r s in section e j . represents that if section e j is covered by route r s it is 1 otherwise 0, S i represents station i, S represents the set of all stations on the line, represents that if station S i is covered by route r s it is 1 otherwise 0, represents the turnaround time at the two terminal turnaround stations of route r s , ω represents the running cost per unit kilometer of each train, represents the running distance of route r s . represents the length of section e j . represents the total turnaround distance at the two terminal turnaround stations of route r s , γ represents the single-stop cost of the train; Obtain the objective function of the total passenger travel cost of the operation model established based on Formula 9, and use Formulas 10 to 11 to represent the parameters in the total passenger travel cost; Let \(K\) denote the set of valid paths between stations, and \(Q\) ij denotes the passenger flow from station \(i\) to station \(j\). denotes the probability of choosing the \(k\)-th valid path between stations \(i - j\) for travel. denotes the total travel time of choosing the \(k\)-th valid path between stations \(i - j\). denotes the total in-vehicle time extended for passengers in the network due to express train overtaking. denotes that among all travel paths of passengers in the network, it contains the boarding arc \(e\) u in total quantity. denotes that among all travel paths of passengers in the network, it contains the boarding arc \(e\) v in total quantity, \(e\) u and \(e\) v denotes two special boarding arcs that require additional extended stop times due to express train overtaking. denotes the total waiting time of choosing the \(k\)-th valid path between stations \(i j\). denotes the total in-vehicle time of choosing the \(k\)-th valid path between stations \(i - j\). denotes that the \(k\)-th valid path between stations \(i - j\) is 1 at the transfer station for transfer and 0 otherwise. denotes the transfer walking time of choosing the \(k\)-th valid path between stations \(i - j\). Obtain the actual application constraints as the constraint conditions of the operation model.

6. The method according to claim 5, characterized in that The specific process of obtaining the actual application constraints as the constraint conditions of the operation model includes: obtaining constraints including the departure frequency constraint of direct express trains, the line passing capacity constraint, the interval departure interval constraint, the upper and lower limits of the departure frequencies of trains on each route, the load factor constraint, and the integer constraint of decision variables; Use Formula 12 to describe the departure frequency constraint of direct express trains: Among them, represents the ceiling function, Q 1,N1 represents the passenger flow from the starting station S1 to the terminal station S N1 ; represents the transfer line r s the seating capacity of the vehicles on the line; Use Formula 13 to describe the line passing capacity constraint in the non-collinear operation area of the main line, and use Formulas 14 to 15 to represent the parameters in Formula 13; Among them, represents the minimum headway in the main line, represents the express train deduction coefficient of the main line, represents the capacity loss caused by cross-line intersection interference, represents from the starting station S1 to the second passing station S n The travel time difference between the express train and the slow train, n 越 represents the number of times the slow train is overtaken during the extra occupancy time of the express train, n 越 The value is 2; Use Formula 16 to describe the line passing capacity constraint in the collinear operation area of the main line, and use Formula 17 to represent the parameter in Formula 16; Among them, represents the deduction coefficient of the express train on the same line, represents the travel time of the slow train from the over-line station k to the terminal N1, represents the travel time of the slow train from the over-line station k to the terminal N1, represents the travel time of the slow train from the over-line station k to the passing station S n ; represents the travel time of the express train from the over-line station k to the passing station S n ; τ aa represents the arrival interval time; τ td represents the connection interval time; τ da represents the departure-arrival interval time; Use Formula 18 to describe the line passing capacity constraint of the auxiliary line: wherein, represents the minimum headway in the auxiliary line; Use Formula 19 to describe the interval departure interval constraint: Among them, represents the lower limit of the departure headway in section e j and represents the upper limit of the departure headway in section e j . Use Formula 20 to describe the upper and lower limits of the departure frequencies of trains on each route: Among them, represents the lower limit of the departure frequency of each line; represents the lower limit of the departure frequency of each line; Use Formula 21 to describe the load factor constraint: Among them, η min represents the full-load rate of the minimum cross-section, represents the passenger flow of the cross-section of section e j ; represents the number of passengers that can be carried by the vehicles on line r s ; η max represents the full-load rate of the maximum cross-section. Use Formula 22 to describe the integer constraint of decision variables: Among them, Z + represents a positive integer.

7. The method according to claim 1, characterized in that, The specific process of using the multi-objective evolutionary algorithm to solve the operation model includes: Use the NSGA-II multi-objective evolutionary algorithm to solve the operation model: Obtain a set of feasible solution individuals that meet the constraint conditions as the initial population, perform non-dominated sorting on the initial population, calculate the crowding distance between individuals in the same non-dominated layer, and select parent individuals from the initial population according to the results of the non-dominated sorting and the crowding distance. Perform crossover and mutation operations on the parental individuals to generate new individuals, and select and combine the new individuals and the parental individuals as the initial population for the next round of iteration; The output of the operation model is obtained after the iteration ends.

8. A train operation device under the combination mode of fast and slow trains and overpass lines, characterized in that It includes: A construction module for constructing a train operation network in a combined mode, screening valid paths in the train operation network, and calculating the probability of a valid path being selected using a prediction model; A model acquisition module for acquiring a pre-established operation model in the form of multi-objective programming; A solution module for inputting the probability and statistical data of valid paths into the operation model, solving the operation model using a multi-objective evolutionary algorithm, and outputting the departure frequencies of each train route on the train operation network.

9. An electronic device, characterized in that, It includes: A memory, a processor, and a computer program stored on the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of the train operation method in the express and local train and cross-line combination mode as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, An implementation program for information transmission is stored on the computer-readable storage medium. When the program is executed by the processor, it implements the steps of the train operation method in the express and local train and cross-line combination mode as described in any one of claims 1 to 7.

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