CN114148382B - A train operation chart compilation method for virtual formation - Google Patents

Abstract

The invention provides a train running chart compiling method for virtual formation. The method comprises the following steps: establishing a train virtual formation; establishing a train operation model according to the train virtual formation; setting constraint conditions considering the time of entering and exiting the train and the total number of trains which can be scheduled; and solving the train operation model based on the constraint condition, and outputting a train operation diagram. According to the invention, the train operation plan is combined with the virtual formation plan, and the high-efficiency unbalanced train operation diagram facing the virtual formation is output, so that the passenger flow pressure in the peak period can be effectively relieved, and the flexibility of train dispatching is improved.

Description

A method for preparing train operation charts for virtual formations

Technical field

The invention relates to the technical field of urban rail transit train dispatching, and in particular to a method for preparing train operation diagrams for virtual formations.

Background technique

Urban subways have become an important solution to alleviate urban traffic pressure due to their higher reliability, lower pollution, greater transport capacity and better energy efficiency. However, with the acceleration of urbanization, the passenger flow of urban subways has increased sharply. During the operation of subway trains, travel demand during peak hours will cause passengers to gather in the subway, which may easily lead to subway safety hazards and reduce passenger comfort. However, Expanding the station requires a huge amount of time, manpower, material and financial resources, and may encounter technical difficulties.

The subway system faces the problem of large passenger flow during peak hours. In the past, the main methods to alleviate the pressure were to increase the number of trains and shorten the departure interval. However, too many vehicles will cause trains to be blocked in the return section. At the same time, the balanced stop time of the train will lead to a waste of capacity in the direction of smaller passenger flow.

Contents of the invention

Embodiments of the present invention provide a train operation diagram compilation method for virtual formations to effectively alleviate the pressure of passenger flow during peak hours.

In order to achieve the above object, the present invention adopts the following technical solutions.

A method for preparing train operation charts for virtual formations, including:

Establish a virtual train formation for rail transit;

Establish a train operation model based on the virtual train formation;

Set constraints that take into account the entry and exit times of trains entering and exiting the station and the total number of trains that can be dispatched;

The train operation model is solved based on the constraints and a train operation diagram of the rail transit is output.

Preferably, the establishment of a virtual train formation for rail transit includes:

Express the train formation index as β _m,m' :

The arrival time and departure time of train m' are set to comply with the following constraints:

Among them, r _m,k represents the running time of train m between k-1 and k stations, t _m,k is the stopping time of train m at station k, N is a large number, s _m,k is The headway between train m and m-1 at station k, s _m',k is the headway between train m' and m'-1 at station k, s _m,1 is the headway between train m and m- at station 1 The head distance between 1, is the maximum turnaround time at station 1,/> is the minimum turnaround time at station 1;

The number of vehicles that can be set must match the total number of trains. Constraint (4) is as follows:

Among them, N _train is the number of trains originally running on the line, and M is the total number of trains;

θ _m,m' is the criterion for determining whether the departure time of train service m' is reasonable, and the following constraints (5) are set:

Preferably, establishing a train operation model based on the virtual train formation includes:

Assume that s _m,k is the headway between train m and m-1, t _m,k is the stopping time of train m at station k, and the dynamic change of train headway is as follows:

s _m,k+1 ＝s _m,k +t _m,k -t _m-1,k , (6)

Among them, s _1,k is the arrival time of the first vehicle after station k is opened;

In the train system, the number of waiting passengers changes dynamically, expressed by pd _m,k :

pd _m,k ＝pd _m-1,k +s _m,k a _m,k -c _m,k -pi _m,k , (7)

Where a _m,k is the passenger arrival rate at station k after train m-1 arrives and before train m arrives; c _m,k is the control strategy to restrict passengers from entering train m at station k; pi _m,k is The number of passengers entering train m at station k; po _m,k is the number of passengers leaving train m at station k; pd _m,k is the number of passengers waiting at station k after train m departs from station k; pd _{m-1, k} is the number of passengers waiting at station k after train m-1 departs from station k;

The number of passengers on train m at station k is represented by p _m,k :

p _m,k =p _m,k-1 +pi _m,k -po _m,k (8)

where p _m,k-1 is the number of passengers on train m at station k-1;

The number of passengers po _m,k who leave train m at station k can be expressed by the following formula:

po _m,k =l _m,k p _m,k-1 (9)

where l _m,k is the proportion of passengers of train m getting off at platform k;

The number of passengers pi _{m,k entering train m at station k} is expressed by the following formula:

pi _m,k =min{pd _m-1,k +s _m,k a _m,k -c _m,k ,(1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )} (10)

where p _max is the maximum number of passengers a train can accommodate.

Set according to formula (6)-(10):

Constraints (11):

pd _m,k ＝pd _m-1,k +s _m,k a _m,k -c _m,k -min{pd _m-1,k +s _m,k a _m,k -c _m,k ,( 1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )}

Constraints (12):

p _m,k =[1-l _m,k ]p _m,k-1 +min{pd _m-1,k +s _m,k a _m,k -c _m,k ,(1+β _{m,m '} )(p _max -[1-l _m,k ]p _m,k-1 )}

Among them: p _m,0 =0; pd _0,k =0; c _0,0 =0

The objective function of the train operation model established according to the virtual train formation in the embodiment of the present invention is as follows:

Among them, λ ₁ , λ ₂ , λ ₃ are preset weights, J is the objective function value, which is determined according to the actual requirements of the train formation plan, passenger waiting time, and train dwell time. T ₁ is the virtual formation of the same train. times, T ₂ represents the passenger waiting time, and T ₃ represents the train stopping time.

Preferably, the setting takes into account the entry and exit times of trains entering and exiting the station, and the constraints of the total number of trains that can be scheduled, including:

Constrain the train operation process:

s _m,k+1 =s _m,k +t _m,k -t _m-1,k

pd _m,k ＝pd _m-1,k +s _m,k a _m,k -c _m,k -min{pd _m-1,k +s _m,k a _m,k -c _m,k ,( 1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )}p _m,k =[1-l _m,k ]p _m,k-1 +min{ pd _m-1,k +s _m,k a _m,k -c _m,k ,(1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )}

The arrival time of train m and the departure time of train m' are set to comply with the following constraints:

Set the number of vehicles that can be called to match the inventory quantity:

Preferably, the method of solving the train operation model based on the constraints and outputting the train operation diagram of rail transit includes:

Set property 1:

f(x)≤0 is equivalent to κ=1

in:

According to the above property 1, constraints (11) and (12) are converted into the following form:

Let a＝pd _m-1,k +s _m,k a _m,k -c _m,k , b＝(1+β _m,m' )(p _max -[1-l _m,k ]p _{m, k-1} )

Then pd _m,k =a-min{a,b}

p _m,k =p _max -b+min{a,b}

Let f=ba and

Then min{a,b}=a+(b-a)κ=a+fκ

pd _m,k =-fκ

p _m,k =p _max -f+fκ

According to the property (1), we get:

According to property 1, the constraint (5) is converted into the following form:

Introduce a new variable z=κf(x) and set property 2 as follows:

Among them: f _max is the maximum value of f(x), f _min is the minimum value of f(x)

According to the properties 1 and 2, constraints (11) and (12) are converted into the following forms:

Let z=fκ, we can get:

Introduce a new variable κ ₃ =κ ₁ κ ₂ and set the following property 3:

According to the property 3:

Let λ _m,m' = β _m,m' θ _m,m'

Convert constraint (4) into the following form:

Introduce new constraints (16) as:

Through the above transformation, all constraints in the objective function of the train operation model are converted into linear, and the train collaborative optimization model is obtained. The objective function of the train collaborative optimization model is:

The constraints are:

s _m,k+1 =s _m,k +t _m,k -t _m-1,k

pd _m,k =-z

p _m,k =p _max -f+z

_z≤fmaxκ

_z≥fminκ

z≤f(x)-f _min (1-κ)

z≥f(x)-f _max (1-κ)

f(x)≤f _max (1-κ)

f(x)≥0.01+(f _min -0.01)κ

s _m,k+1 =s _m,k +t _m,k -t _m-1,k

-β _m,m' +λ _m,m' ≤0

-θ _m,m' +λ _m,m' ≤0

β _m,m' +θ _m,m' -λ _m,m' ≤1

Where m is the train number, k is the platform number, λ ₁ , λ ₂ , λ ₃ are preset weights, J is the objective function value, which is determined according to the actual requirements of the train formation plan, passenger waiting time and train dwell time, T ₁ is the number of virtual formations of the same train, T ₂ represents the passenger waiting time, T ₃ represents the train stop time, and/> is the normalization factor;

β _m,m' is a binary variable. If trains m and m' are in virtual formation and m<m', then β _m,m' =1, otherwise β _m,m' =0; T ₂ represents the passenger waiting time , a _m,k is the passenger arrival rate at station k after train m-1 arrives and before train m arrives, s _m,k is the headway between train m and m-1, m-1 is the train The train before m, T ₃ represents the stop time of train, t _m,k is the stop time of train m at station k;

Solve the train collaborative optimization model and output the train operation chart.

It can be seen from the technical solutions provided by the above embodiments of the present invention that the embodiments of the present invention combine the train operation plan with the virtual formation plan to generate a highly efficient non-balanced train operation diagram for virtual formations, which can effectively alleviate the passenger flow during peak hours. quantity pressure, increasing the flexibility of train dispatching.

Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will be obvious from the description, or may be learned by practice of the invention.

Description of the drawings

In order to explain the technical solutions of the embodiments of the present invention more clearly, the drawings needed to be used in the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. Those of ordinary skill in the art can also obtain other drawings based on these drawings without exerting creative efforts.

Figure 1 is a processing flow chart of a method for preparing a train operation chart for virtual formations provided by an embodiment of the present invention;

Figure 2 is an optimized train operation diagram provided by an embodiment of the present invention;

Figure 3 is a schematic diagram of the change curve of the train stop time generated in a case provided by the embodiment of the present invention.

Detailed ways

Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the drawings are exemplary and are only used to explain the present invention and cannot be construed as limitations of the present invention.

Those skilled in the art will understand that, unless expressly stated otherwise, the singular forms "a", "an", "the" and "the" used herein may also include the plural form. It should be further understood that the word "comprising" used in the description of the present invention refers to the presence of stated features, integers, steps, operations, elements and/or components, but does not exclude the presence or addition of one or more other features, Integers, steps, operations, elements, components and/or groups thereof. It will be understood that when we refer to an element being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Additionally, "connected" or "coupled" as used herein may include wireless connections or couplings. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.

It will be understood by one of ordinary skill in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It should also be understood that terms such as those defined in general dictionaries are to be understood to have meanings consistent with their meaning in the context of the prior art, and are not to be taken in an idealized or overly formal sense unless defined as herein. explain.

In order to facilitate understanding of the embodiments of the present invention, several specific embodiments will be further explained below with reference to the accompanying drawings, and each embodiment does not constitute a limitation to the embodiments of the present invention.

The embodiment of the present invention combines virtual formation technology to establish a collaborative optimization model that trades off train utilization, passenger dwell time, and train stop time, transforms it into a mixed integer linear programming model, and compiles non-equilibrium train operation picture.

The purpose of this invention is to combine the virtual train formation technology and propose a processing flow of a method for preparing train operation diagrams for virtual formations, as shown in Figure 1, including the following processing steps:

Step S10: Establish a virtual train formation.

The variables used in the present invention and their representative meanings are shown in Table 1:

Table 1

The train formation index is expressed by β _m,m' :

Restrictions:

The arrival time of train m' and the departure time of train m should comply with the following constraints:

Among them, r _m,k represents the running time of train m between k-1 and k stations, t _m,k is the stopping time of train m at station k, N is a large number, s _m,k is The headway between train m and m-1 at station k, s _m',k is the headway between train m' and m'-1 at station k, s _m,1 is the headway between train m and m- at station 1 The head distance between 1, is the maximum turnaround time at station 1,/> is the minimum turnaround time at station 1.

The number of vehicles that can be called must match the total number of trains, and constraint (4) is as follows:

Among them, N _train is the number of trains originally running on the line, and M is the total number of trains.

θ _m,m' is the criterion for determining whether the departure time of train service m' is reasonable.

Step S20: Establish a train operation model based on the above-mentioned virtual train formation.

Assume that s _m,k is the headway between train m and m-1, t _m,k is the stopping time of train m at station k, the dynamic change of train headway is as follows

s _m,k+1 ＝s _m,k +t _m,k -t _m-1,k , (6)

Among them, s _{1, k} is the arrival time of the first car after station k is opened.

In the train system, the number of waiting passengers changes dynamically, represented by pd _m,k

pd _m,k ＝pd _m-1,k +s _m,k a _m,k -c _m,k -pi _m,k , (7)

Where a _m,k is the passenger arrival rate at station k after train m-1 arrives and before train m arrives; c _m,k is the control strategy to restrict passengers from entering train m at station k; pi _m,k is The number of passengers entering train m at station k; po _m,k is the number of passengers leaving train m at station k; pd _m,k is the number of passengers waiting at station k after train m departs from station k; pd _{m-1, k} is the number of passengers waiting at station k after train m-1 departs from station k.

The number of passengers on train m at station k is represented by p _m,k

p _m,k =p _m,k-1 +pi _m,k -po _m,k . (8)

Where p _m,k-1 is the number of passengers on train m at station k-1.

The number of passengers po _m,k who leave train m at station k can be expressed by the following formula:

po _m,k =l _m,k p _m,k-1 , (9)

Among them, l _m,k is the proportion of passengers of train m getting off at platform k.

The number of passengers pi _{m,k entering train m at station k} can be expressed by the following formula:

pi _m,k =min{pd _m-1,k +s _m,k a _m,k -c _m,k ,(1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )} (10)

where p _max is the maximum number of passengers a train can accommodate.

Set according to formula (6)-(10):

Constraints (11):

pd _m,k ＝pd _m-1,k +s _m,k a _m,k -c _m,k -min{pd _m-1,k +s _m,k a _m,k -c _m,k ,( 1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )}

Constraints (12):

p _m,k =[1-l _m,k ]p _m,k-1 +min{pd _m-1,k +s _m,k a _m,k -c _m,k ,(1+β _{m,m '} )(p _max -[1-l _m,k ]p _m,k-1 )}

Among them: p _m,0 =0; pd _0,k =0; c _0,0 =0

In our daily lives, the dwell time of trains is fixed, but due to the passenger flow during peak hours, the passenger flow will vary greatly. Therefore, the embodiment of the present invention proposes a non-equilibrium train operation chart for virtual formations to adjust the train dwell time and operation time in different periods. In this case, the energy consumption of the train is reduced, the waiting time of passengers is reduced, the train call is more flexible, and the appropriate virtual formation protects the interests of both parties.

Therefore, the embodiment of the present invention proposes the linear objective function of the following non-equilibrium train operation model as follows:

Among them, λ ₁ , λ ₂ , and λ ₃ are preset weights, and J is the objective function value, which is determined according to the actual requirements of the train formation plan, passenger waiting time, and train dwell time. T ₁ is the number of virtual formations of the same train, T ₂ represents the passenger waiting time, and T ₃ represents the train stop time. Among these three indicators, the first is the normalized number of virtual trains, which can be changed to reflect the train utilization rate; the second is the normalized total passenger waiting time; the third is the normalized total train Stop time. is the normalization factor. A multi-objective optimization problem is proposed for the above three items and processed using linear weighting method. The objective function achieves a balance between train utilization and passenger comfort, so that train utilization is relatively optimal and passenger waiting time is relatively shortest. In addition, since the optimization goal includes headway, the compiled train timetable is non-equilibrium, which is more flexible and more in line with actual passenger needs than the periodic timetable.

Step S30: Set constraints that take into account the entry and exit times of trains entering and exiting the station, the total number of trains that can be scheduled, and other constraints.

Constrain the train operation process:

s _m,k+1 =s _m,k +t _m,k -t _m-1,k

pd _m,k ＝pd _m-1,k +s _m,k a _m,k -c _m,k -min{pd _m-1,k +s _m,k a _m,k -c _m,k ,( 1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )}p _m,k =[1-l _m,k ]p _m,k-1 +min{ pd _m-1,k +s _m,k a _m,k -c _m,k ,(1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )}

The arrival time of train m and the departure time of train m' should comply with the following constraints:

The number of vehicles that can be called must comply with the inventory:

Step S40: Solve the above-mentioned train coordination model based on the above-mentioned constraints and output the train operation diagram.

The objective function of the train operation model proposed in the embodiment of the present invention is linear, and the constraints include nonlinear equations. The nonlinear equations need to be converted into linear equations, which include the following properties 1:

f(x)≤0 is equivalent to κ=1

in:

According to property 1:

Convert constraints (11) and (12) into the following forms:

Let a＝pd _m-1,k +s _m,k a _m,k -c _m,k , b＝(1+β _m,m' )(p _max -[1-l _m,k ]p _{m, k-1} )

Then pd _m,k =a-min{a,b}

p _m,k =p _max -b+min{a,b}

Let f=ba and

Then min{a,b}=a+(b-a)κ=a+fκ

pd _m,k =-fκ

Therefore p _m,k =p _max -f+fκ

Using property (1), we can get:

According to property 1:

Convert constraint (5) into the following form:

Introduce new variable z=κf(x)

Among them: f _max is the maximum value of f(x), f _min is the minimum value of f(x)

According to properties 1 and 2, constraints (11) and (12) are converted into the following forms:

Let z=fκ, we can get:

Introducing a new variable κ ₃ = κ ₁ κ ₂

According to property 3:

Let λ _m,m' = β _m,m' θ _m,m'

Convert constraint (4) into the following form:

Introduce new constraints as

Therefore, through the above transformation, all the constraints in the above train operation model are converted into linear, and the train collaborative optimization model is obtained. The objective function of the train collaborative optimization model is as follows:

The constraints are:

s _m,k+1 =s _m,k +t _m,k -t _m-1,k

pd _m,k =-z

p _m,k =p _max -f+z

_z≤fmaxκ

_z≥fminκ

z≤f(x)-f _min (1-κ)

z≥f(x)-f _max (1-κ)

f(x)≤f _max (1-κ)

f(x)≥0.01+(f _min -0.01)κ

s _m,k+1 =s _m,k +t _m,k -t _m-1,k

-β _m,m' +λ _m,m' ≤0

-θ _m,m' +λ _m,m' ≤0

β _m,m' +θ _m,m' -λ _m,m' ≤1

The above-mentioned train collaborative optimization model is solved and a train operation diagram is prepared. The train operation diagram includes the train's stop time, formation index and other information. In practical applications, the CPLEX solver can be used to solve the objective function of the above train collaborative optimization model.

In order to verify the effectiveness of the train collaborative optimization model proposed in the above embodiment of the present invention, we used the data of Beijing Yizhuang Line to conduct numerical experiments. Beijing Yizhuang Line is a commuter line with a total of 14 stations. The upward direction is from Songjiazhuang to Ciqu, and the downward direction is from Ciqu to Songjiazhuang. The station is connected to Songjiazhuang Station. During the operation of the subway system throughout the day, the passenger flow is relatively large in the morning, evening and peak hours, which can easily lead to platform congestion and accidents. Therefore, increasing the number of train formations is conducive to increasing driving safety, while the balanced stop time of trains will cause a waste of transportation capacity. and increased waiting times for passengers. Therefore, a new unbalanced train operation diagram is compiled based on the virtual formation, which reasonably arranges train operation and stop time, and increases the flexibility of train dispatching.

This invention uses 14 vehicles for simulation, and some of the initial data values used are as shown in Table 2 below:

Table 2:

This invention numbers the train numbers and station names respectively, and studies the operation of 14 trains at 14 stations in total. It is based on passenger flow data statistics of the Beijing Metro AFC (Automatic Fare Collection) automatic fare collection system on the Beijing Yizhuang Line. AFC automatic ticket checking system is an automated network system controlled by computer for automatic ticket sales, automatic ticket checking and automatic charging. AFC data can collect many passenger flow data including entry and exit time and location. The passenger waiting arrival rate β _i,j and the passenger alighting rate λ _i,j of the train are as follows:

Platform serial number a _m,k l _m,k Platform serial number (return) a _m,k l _m,k 1 1.40 0.00 15 0.00 1.20 2 1.57 0.25 16 0.30 1.20 3 1.31 0.24 17 0.25 1.30 4 1.35 0.50 18 0.50 1.20 5 0.90 0.70 19 0.60 1.23 6 1.00 0.85 20 0.80 1.24 7 1.20 0.60 twenty one 0.80 1.24 8 1.32 0.80 twenty two 0.70 1.00 9 1.00 0.60 twenty three 0.65 1.00 10 0.90 0.70 twenty four 0.60 0.95 11 0.80 0.70 25 0.80 0.70 12 0.90 0.65 26 0.90 0.65 13 0.90 0.75 27 0.56 0.89 14 0.00 1.00 28 1.00 0.00

When the above parameters have been set, set the departure time of the train to 6.00, and solve the collaborative optimization model to obtain the train's stop time, formation index and other decision variables. This results in a train schedule. Through the optimization of the train timetable, the number of people waiting on the platform has been greatly reduced, and the waiting time of passengers has also been greatly reduced. On the other hand, the increased flexibility of train dispatching also alleviates the tight train dispatching problem.

Figure 2 is an optimized train operation diagram provided by an embodiment of the present invention, showing the operation plans of 14 vehicles respectively. The train timetable shows the operation status of the trains from 6:00 to 8:30. After the train departed at 6:00, it arrived at station 1 after a period of time. After staying at station 1 for a period of time, it entered station 2. However, because there were fewer passengers at that time, the train stayed for a shorter time. Around 7 o'clock, the number of passengers increased significantly. Entering the morning rush hour, it is obvious that one train can no longer meet the large passenger demand, so a virtual formation is adopted. After one train completes the trip plan, it continues to drive on the line together with 13 trains. In the same way, 2 cars and 14 cars form a formation and execute the same train plan. After the morning rush hour has passed and the number of passengers has decreased, the trains will no longer be in formation and will still carry out scheduled runs and plans.

Figure 3 is a schematic diagram of the change curve of a train's stop time provided by an embodiment of the present invention. From Figure 3, it can be seen that the changes over time, the number of passengers, and the stop time also change significantly, but they are all within 1 minute. . The optimized train timetable has greatly increased train utilization and reduced unnecessary stop times. At the same time, it can also be seen that the stopping time of different platforms is also different, which reduces the energy consumption of the train compared with the balanced stopping time. Therefore, the train collaborative optimization model is meaningful, and the optimized train operation chart also has certain reference value.

To sum up, the embodiment of the present invention proposes a collaborative optimization model that combines virtual formations, combines the train operation plan with the virtual formation plan, and generates an efficient non-equilibrium train operation chart for virtual formations. It can effectively alleviate the passenger flow pressure during peak hours, reduce the waste of transportation capacity, and increase the flexibility of train dispatching.

The method of the embodiment of the present invention prepares a new train operation chart based on a reasonable virtual formation plan, so that it can respond in advance when encountering peak passenger flow.

Those of ordinary skill in the art can understand that the accompanying drawing is only a schematic diagram of an embodiment, and the modules or processes in the accompanying drawing are not necessarily necessary for implementing the present invention.

From the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus a necessary general hardware platform. Based on this understanding, the technical solution of the present invention can be embodied in the form of a software product in essence or that contributes to the existing technology. The computer software product can be stored in a storage medium, such as ROM/RAM, disk , optical disk, etc., including a number of instructions to cause a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of the present invention.

Each embodiment in this specification is described in a progressive manner. The same and similar parts between the various embodiments can be referred to each other. Each embodiment focuses on its differences from other embodiments. In particular, the device or system embodiments are described simply because they are basically similar to the method embodiments. For relevant details, please refer to the partial description of the method embodiments. The device and system embodiments described above are only illustrative, in which the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, It can be located in one place, or it can be distributed over multiple network elements. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Persons of ordinary skill in the art can understand and implement the method without any creative effort.

The above are only preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person familiar with the technical field can easily think of changes or modifications within the technical scope disclosed in the present invention. All substitutions are within the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (1)

1. A method for preparing train operation charts for virtual formations, which is characterized by including: Establish a virtual train formation for rail transit; Establish a train operation model based on the virtual train formation; Set constraints that take into account the entry and exit times of trains entering and exiting the station and the total number of trains that can be dispatched; Solve the train operation model based on the constraints and output the train operation diagram of rail transit; The establishment of a virtual train formation for rail transit includes: Express the train formation index as β _m,m' : The arrival time and departure time of train m' are set to comply with the following constraints: Among them, r _m,k represents the running time of train m between station k-1 and k, t _m,k is the stopping time of train m at station k, N is greater than 1, and s _m,k is train m at station k. The head distance between train m' and m-1, s _m',k is the head distance between train m' and m'-1 at station k, s _m,1 is the head distance between train m and m-1 at station 1 Head distance, is the maximum turnaround time at station 1,/> is the minimum turnaround time at station 1; The number of vehicles that can be set must match the total number of trains. Constraint (4) is as follows: Among them, N _train is the number of trains originally running on the line, and M is the total number of trains; θ _m,m' is the criterion for determining whether the departure time of train service m' is reasonable, and the following constraints (5) are set: The establishment of a train operation model based on the virtual train formation includes: Assume that s _m,k is the headway between train m and m-1, t _m,k is the stopping time of train m at station k, and the dynamic change of train headway is as follows: s _m,k+1 ＝s _m,k +t _m,k -t _m-1,k ,(6) Among them, s _1,k is the arrival time of the first vehicle after station k is opened; In the train system, the number of waiting passengers changes dynamically, expressed by pd _m,k : pd _m,k ＝pd _m-1,k +s _m,k a _m,k -c _m,k -pi _m,k ,(7) Where a _m,k is the passenger arrival rate at station k after train m-1 arrives and before train m arrives; c _m,k is the control strategy to restrict passengers from entering train m at station k; pi _m,k is The number of passengers entering train m at station k; po _m,k is the number of passengers leaving train m at station k; pd _m,k is the number of passengers waiting at station k after train m departs from station k; pd _{m-1, k} is the number of passengers waiting at station k after train m-1 departs from station k; The number of passengers on train m at station k is represented by p _m,k : p _m,k =p _m,k-1 +pi _m,k -po _m,k (8) where p _m,k-1 is the number of passengers on train m at station k-1; The number of passengers po _m,k who leave train m at station k can be expressed by the following formula: po _m,k =l _m,k p _m,k-1 (9) where l _m,k is the proportion of passengers of train m getting off at platform k; The number of passengers pi _{m,k entering train m at station k} is expressed by the following formula: pi _m,k =min{pd _m-1,k +s _m,k a _m,k -c _m,k ,(1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )} (10) where p _max is the maximum number of passengers a train can accommodate; Set according to formula (6)-(10): Constraints (11): pd _m,k ＝pd _m-1,k +s _m,k a _m,k -c _m,k -min{pd _m-1,k +s _m,k a _m,k -c _m,k ,( 1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )} Constraints (12): p _m,k =[1-l _m,k ]p _m,k-1 +min{pd _m-1,k +s _m,k a _m,k -c _m,k ,(1+β _{m,m '} )(p _max -[1-l _m,k ]p _m,k-1 )} Among them: p _m,0 =0; pd _0,k =0; c _0,0 =0 The objective function of the train operation model established based on the virtual train formation is as follows: Among them, λ ₁ , λ ₂ , λ ₃ are preset weights, J is the objective function value, which is determined according to the actual requirements of the train formation plan, passenger waiting time, and train dwell time. T ₁ is the virtual formation of the same train. times, T ₂ represents the passenger waiting time, T ₃ represents the train stopping time; The settings described take into account the entry and exit times of trains entering and exiting the station, and the constraints of the total number of trains that can be dispatched, including: Constrain the train operation process: s _m,k+1 =s _m,k +t _m,k -t _m-1,k pd _m,k ＝pd _m-1,k +s _m,k a _m,k -c _m,k -min{pd _m-1,k +s _m,k a _m,k -c _m,k ,( 1+β _m,m' )(p _max -[1-l _m,k ]p _m,k-1 )} p _m,k =[1-l _m,k ]p _m,k-1 +min{pd _m-1,k +s _m,k a _m,k -c _m,k ,(1+β _{m,m '} )(p _max -[1-l _m,k ]p _m,k-1 )} The arrival time of train m and the departure time of train m' are set to comply with the following constraints: Set the number of vehicles that can be called to match the inventory quantity: The method of solving the train operation model based on the constraints and outputting the train operation diagram of the rail transit includes: Set property 1: f(x)≤0 is equivalent to κ=1 in: According to the above property 1, constraints (11) and (12) are converted into the following form: Let a＝pd _m-1,k +s _m,k a _m,k -c _m,k , b＝(1+β _m,m' )(p _max -[1-l _m,k ]p _{m, k-1} ) Then pd _m,k =a-min{a,b} p _m,k =p _max -b+min{a,b} Let f=ba and Then min{a,b}=a+(b-a)κ=a+fκ pd _m,k =-fκ p _m,k =p _max -f+fκ According to the property (1), we get: According to property 1, the constraint (5) is converted into the following form: Introduce a new variable z=κf(x) and set property 2 as follows: Among them: f _max is the maximum value of f(x), f _min is the minimum value of f(x) According to the properties 1 and 2, constraints (11) and (12) are converted into the following forms: Let z=fκ, we can get: Introduce a new variable κ ₃ =κ ₁ κ ₂ and set the following property 3: According to the property 3: Let λ _m,m' = β _m,m' θ _m,m' Convert constraint (4) into the following form: Introduce new constraints (16) as: Through the above transformation, all constraints in the objective function of the train operation model are converted into linear, and the train collaborative optimization model is obtained. The objective function of the train collaborative optimization model is: The constraints are: s _m,k+1 =s _m,k +t _m,k -t _m-1,k pd _m,k =-z p _m,k =p _max -f+z _{z≤fmaxκ z≥fminκ} z≤f(x)-f _min (1-κ) z≥f(x)-f _max (1-κ) f(x)≤f _max (1-κ) f(x)≥0.01+(f _min -0.01)κ s _m,k+1 =s _m,k +t _m,k -t _m-1,k -β _m,m' +λ _m,m' ≤0 -θ _m,m' +λ _m,m' ≤0 β _m,m' +θ _m,m' -λ _m,m' ≤1 Where m is the train number, k is the platform number, λ ₁ , λ ₂ , λ ₃ are preset weights, J is the objective function value, which is determined according to the actual requirements of the train formation plan, passenger waiting time and train dwell time. T ₁ is the number of virtual formations of the same train, T ₂ represents the passenger waiting time, T ₃ represents the train stop time, and is the normalization factor; β _m,m' is a binary variable. If trains m and m' are in virtual formation and m<m', then β _m,m' =1, otherwise β _m,m' =0; T ₂ represents the passenger waiting time , a _m,k is the passenger arrival rate at station k after train m-1 arrives and before train m arrives, s _m,k is the headway between train m and m-1, m-1 is the train The train before m, T ₃ represents the stop time of train, t _m,k is the stop time of train m at station k; Solve the train collaborative optimization model and output the train operation chart.