CN114148382B - Train running chart compiling 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

Train running chart compiling method for virtual formation

Technical Field

The invention relates to the technical field of urban rail transit train dispatching, in particular to a train running chart compiling method for virtual formation.

Background

Urban subways become an important solution for relieving urban traffic pressure because of the characteristics of higher reliability, lower pollution, greater transportation capacity and better energy efficiency. However, with the acceleration of the urban process, the passenger flow of the urban subway increases sharply, and in the running process of the subway train, the travel demand at the peak time can cause the passenger aggregation in the subway, so that the potential safety hazard of the subway is easily caused, the riding comfort of the passenger is easily reduced, however, huge time, manpower, material resources and financial resources are required to be consumed for expanding the station, and technical difficulties can be encountered.

The subway system faces the problem of large passenger flow in the peak period. The prior method for relieving the pressure mainly comprises the steps of increasing the number of trains and reducing the departure interval, but too many trains can cause the blockage of the trains in a turning-back section, and meanwhile, the balanced stop time of the trains can cause the waste of the transport capacity in the section with smaller passenger flow.

Disclosure of Invention

The embodiment of the invention provides a train operation diagram compiling method for virtual formation, which is used for effectively relieving the passenger flow pressure in the peak period.

In order to achieve the above purpose, the present invention adopts the following technical scheme.

A train running chart compiling method facing virtual formation comprises the following steps:

establishing a train virtual formation of rail transit;

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 of the rail transit.

Preferably, the virtual train formation for establishing the rail transit comprises:

beta for train formation index _m,m' The representation is:

setting the arrival time and departure time of the train m' to meet the following constraints:

wherein r is _m,k Representing the run time of train m between k-1 and k stations, t _m,k For stopping time of train m at k stations, N is a very large number, s _m,k For the headway distance between the trains m and m-1 at station k, s _m',k For the headway distance between the trains m 'and m' -1 at station k, s _m,1 For the headway between station 1 trains m and m-1,for maximum turnaround time at station 1, < > for>Is the minimum turnaround time at station 1;

setting the number of vehicles which can be called to be in line with the total number of trains, and restricting (4) as follows:

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

θ _m,m' for judging whether the departure time of the train service m' is reasonable or not, setting the following constraint (5):

preferably, the building a train operation model according to the virtual train formation includes:

let s be _m,k Is the locomotive distance between m and m-1 of the train, t _m,k For the stop time of the train m at the k stations, the dynamic change of the train headway is as follows:

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

wherein s is _1,k After opening for k stations, the time of arrival of the first vehicle;

in train systems, the waiting number of passengers is dynamically changed, using pd _m,k The representation is:

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

wherein a is _m,k After m-1 times of trains arrive at the station, m timesPassenger arrival rate of the train at the front k stops; c _m,k A control strategy for restricting passengers from entering the train m at the k station; pi (pi) _m,k Is the number of passengers entering train m at k stops; po (po) _m,k Is the number of passengers leaving train m at k stops; pd (pd) _m,k After the train m starts from the k station, the waiting number of passengers at the k station; pd (pd) _m-1,k After the train m-1 starts from the k stations, the waiting number of passengers at the k stations;

p number of passengers in k trains m _m,k The representation is:

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

wherein p is _m,k-1 Is the number of passengers in the k-1 train m;

the number po of passengers leaving the train m at station k _m,k Can be expressed by the following formula:

po _m,k ＝l _m,k p _m,k-1 (9)

wherein l _m,k The proportion of passengers of train m getting off at station k;

passenger number pi of entering train m at k stops _m,k 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)

wherein p is _max Is the maximum number of passengers that can be accommodated by a train.

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

constraint (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 )}

constraint (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 )}

wherein: p is p _m,0 ＝0；pd _0,k ＝0；c _0,0 ＝0

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

wherein lambda is ₁ ，λ ₂ ，λ ₃ For preset weight, J is an objective function value, and is determined according to actual requirements of train formation plan, passenger waiting time and train residence time, T ₁ Number of virtual formation for same train, T ₂ Representing passenger waiting time, T ₃ Indicating the stop time of the train.

Preferably, the setting considers the constraint condition of total number of trains capable of being scheduled, including:

and restraining 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 )}

setting the arrival time of the train m and the departure time of the train m' to meet the following constraints:

setting the number of the vehicles capable of being called to be in accordance with the inventory number:

preferably, said solving said train operation model based on said constraint condition outputs a train operation diagram of rail transit, comprising:

set property 1:

f (x). Ltoreq.0 is equivalent to κ=1

Wherein:

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

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 is _m,k ＝a-min{a,b}

p _m,k ＝p _max -b+min{a,b}

Let f=b-a and

then min { a, b } = a+ (b-a) κ = a+fκ

pd _m,k ＝-fκ

p _m,k ＝p _max -f+fκ

From the property (1) is obtained:

according to property 1, the constraint (5) is transformed into the following form:

the new variable z=κf (x) was introduced and property 2 was set as follows:

wherein: f (f) _max Is the maximum value of f (x), f _min Minimum value of f (x)

Converting constraints (11), (12) into the following form according to said properties 1 and 2:

let z=fκ, obtainable:

introduction of a New variable kappa ₃ ＝κ ₁ κ ₂ Property 3 was set as follows:

according to said property 3:

let lambda get _m,m' ＝β _m,m' θ _m,m'

Converting constraint (4) into the following form:

introducing new constraints (16) is:

all constraint conditions in the objective function of the train operation model are converted into linearity through the transformation, and a train collaborative optimization model is obtained, wherein the objective function of the train collaborative optimization model is as follows:

the constraint conditions are as follows:

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≤f _max κ

z≥f _min κ

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

wherein m is the train number, k is the platform number, lambda ₁ ，λ ₂ ，λ ₃ For preset weight, J is an objective function value, and is determined according to actual requirements of train formation plan, passenger waiting time and train residence time, T ₁ Number of virtual formation for same train, T ₂ Representing passenger waiting time, T ₃ The stop time of the train is indicated,and->Is a normalization factor;

β _m,m' is a binary variable if the trains m and m' are virtually queued and m<m' is beta _m,m' =1, otherwise β _m,m' ＝0；T ₂ Representing passenger waiting time, a _m,k After m-1 times of train arrives at the station, the arrival rate s of passengers at k stations before m times of train arrives at the station _m,k For the distance between the trains m and m-1, m-1 is the train preceding the train m, T ₃ Indicating the stop time of the train，t _m,k Stop time of the train m at the k stations;

and solving the train collaborative optimization model, and outputting a train operation diagram.

According to the technical scheme provided by the embodiment of the invention, the train operation plan is combined with the virtual formation plan to generate the virtual formation-oriented high-efficiency unbalanced train operation diagram, so that the peak passenger flow pressure can be effectively relieved, and the flexibility of train dispatching is improved.

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

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

Fig. 1 is a process flow diagram of a train operation diagram compiling method for virtual formation provided by an embodiment of the invention;

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

fig. 3 is a schematic diagram of a change curve of a train stop time generated under one embodiment of the present invention.

Detailed Description

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 refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary only for explaining the present invention and are not to be construed as limiting the present invention.

As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless expressly stated otherwise, as understood by those skilled in the art. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude 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 an element is referred to as 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. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. The term "and/or" as used herein includes any and all combinations of one or more of the associated listed items.

It will be understood by those skilled 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 will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

For the purpose of facilitating an understanding of the embodiments of the invention, reference will now be made to the drawings of several specific embodiments illustrated in the drawings and in no way should be taken to limit the embodiments of the invention.

According to the embodiment of the invention, a collaborative optimization model for balancing the utilization rate of the train, the residence time of passengers and the stop time of the train is established by combining a virtual formation technology, and is converted into a mixed integer linear programming model, and an unbalanced train operation diagram is compiled.

The invention aims to combine a virtual train formation technology, and provides a virtual train formation-oriented train operation diagram formation method, which comprises the following processing steps:

and step S10, establishing a train virtual formation.

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

TABLE 1

Beta for train formation index _m,m' The representation is:

constraint conditions:

the arrival time of train m' and departure time of train m should meet the following constraints:

wherein r is _m,k Representing the run time of train m between k-1 and k stations, t _m,k For stopping time of train m at k stations, N is a very large number, s _m,k For the headway distance between the trains m and m-1 at station k, s _m',k For the headway distance between the trains m 'and m' -1 at station k, s _m,1 For the headway between station 1 trains m and m-1,for maximum turnaround time at station 1, < > for>Is the minimum turnaround time at station 1.

The number of vehicles which can be called accords with the total number of trains, and the constraint (4) is as follows:

wherein N is _train The number M is the total number of trains originally running on the line.

θ _m,m' Judging index for judging whether departure time of train service m' is reasonable

And step S20, building a train operation model according to the train virtual formation.

Let s be _m,k Is the locomotive distance between m and m-1 of the train, t _m,k For stopping time of train m at k stations, the dynamic change of train head time distance is as follows

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

Wherein s is _1,k Time of arrival of first vehicle after opening for k station

In train systems, the waiting number of passengers is dynamically changed, using pd _m,k Representation of

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

Wherein a is _m,k After m-1 times of trains arrive at the station, the arrival rate of passengers at k stations before m times of trains arrive at the station; c _m,k A control strategy for restricting passengers from entering the train m at the k station; pi (pi) _m,k Is the number of passengers entering train m at k stops; po (po) _m,k Is the number of passengers leaving train m at k stops; pd (pd) _m,k After the train m starts from the k station, the waiting number of passengers at the k station; pd (pd) _m-1,k After the train m-1 starts from the k stops, the waiting number of passengers at the k stops is calculated.

P number of passengers in k trains m _m,k Representation of

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

Wherein p is _m,k-1 Is the number of passengers in train m at k-1.

The number po of passengers leaving the train m at station k _m,k Can be expressed by the following formula:

po _m,k ＝l _m,k p _m,k-1 , (9)

wherein l _m,k The proportion of passengers of train m getting off at station k.

Passenger number pi of entering train m at k stops _m,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)

wherein p is _max Is the maximum number of passengers that can be accommodated by a train.

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

constraint (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 )}

constraint (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 )}

wherein: p is p _m,0 ＝0；pd _0,k ＝0；c _0,0 ＝0

In our daily lives, the residence time of the train is fixed, but the traffic will vary greatly due to peak traffic. Therefore, the embodiment of the invention provides a virtual formation oriented unbalanced train operation diagram, and train residence time and operation time in different time periods are adjusted. In this case, the energy consumption of the train is reduced, the waiting time of passengers is reduced, the train is more flexibly called, and the benefits of both parties are ensured by proper virtual formation.

Therefore, the embodiment of the invention proposes the following linear objective function of the unbalanced train operation model as follows:

wherein lambda is ₁ ，λ ₂ ，λ ₃ And J is an objective function value for the preset weight, and is determined according to the actual requirements of the train formation plan, the passenger waiting time and the train residence time. T (T) ₁ Number of virtual formation for same train, T ₂ Representing passenger waiting time, T ₃ Indicating the stop time of the train. Of the three indexes, the first item is the normalized virtual train formation number, and the change item can reflect the train utilization rate; the second term is normalized passenger total waiting time; the third term is normalized total train stop time. Is a normalization factor. The multi-objective optimization problem is presented for the three items, and a linear weighting method is adopted for processing. 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 minimal. In addition, the optimization target comprises the headway, so that the compiled train schedule is unbalanced, is more flexible relative to the periodic schedule, and meets the requirements of actual passengers.

And step S30, setting constraint conditions of constraint conditions such as total number of trains which can be scheduled and the like by considering the time of entering and exiting the train.

And restraining 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 departure time of train m' should meet the following constraints:

the number of vehicles that can be called up corresponds to the stock:

and step S40, solving the train cooperative model based on the constraint conditions, and outputting a train operation diagram.

The objective function of the train operation model proposed in the embodiment of the present invention is linear, and the constraint condition includes a nonlinear equation, which needs to be converted into linearity, and includes the following properties 1:

f (x). Ltoreq.0 is equivalent to κ=1

Wherein:

according to property 1:

converting the constraints (11), (12) 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 is _m,k ＝a-min{a,b}

p _m,k ＝p _max -b+min{a,b}

Let f=b-a and

then min { a, b } = a+ (b-a) κ = a+fκ

pd _m,k ＝-fκ

Thus p is _m,k ＝p _max -f+fκ

The application properties (1) can be obtained by:

according to property 1:

converting constraint (5) into the following form:

introduction of the new variable z=κf (x)

Wherein: f (f) _max Is the maximum value of f (x), f _min Minimum value of f (x)

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

let z=fκ, obtainable:

introduction of a New variable kappa ₃ ＝κ ₁ κ ₂

According to property 3:

let lambda get _m,m' ＝β _m,m' θ _m,m'

Converting constraint (4) into the following form:

introducing new constraints as

Therefore, through the above transformation, all constraint conditions in the train operation model are converted into linearity, and a train collaborative optimization model is obtained, and the objective function of the train collaborative optimization model is as follows:

the constraint conditions are as follows:

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≤f _max κ

z≥f _min κ

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

and solving the train collaborative optimization model, and compiling a train operation diagram, wherein the train operation diagram comprises information such as the stop time of the train, the formation index and the like. In practical application, a CPLEX solver can be used for solving the objective function of the train collaborative optimization model.

In order to verify the effectiveness of the train collaborative optimization model provided by the embodiment of the invention, numerical experiments are carried out by using the data of Beijing also zhuang line. Beijing also bang line is a commute line, and has 14 stations. The upward direction is from the Song's village to the secondary canal, the downward direction is from the secondary canal to the Song's village, and the station is connected with the Song Guzhuang station. In the operation process of a subway system in one day, passenger flow is large in the morning and evening and in the peak time, a platform is easy to block, accidents occur, therefore, the increase of the number of trains is beneficial to the increase of driving safety, and the balanced stop time of the trains can cause the waste of transport capacity and increase of waiting time of passengers. Therefore, a new unbalanced train operation diagram is compiled by combining virtual formation, train operation and stop time are reasonably arranged, and flexibility of train scheduling is improved.

The invention adopts 14 vehicles to simulate, wherein, the initial values of some data adopted are shown in the following table 2:

table 2:

the invention numbers the train number and the station names respectively, and totally researches the running conditions of 14 trains at 14 stations. The passenger flow data statistics of the Beijing subway AFC (Automatic Fare Collection) automatic ticket checking system according to Beijing also zhuang line are available. The AFC automatic ticket checking system is one computerized automatic ticket selling, automatic ticket checking and automatic charging network system. The AFC data can collect a number of traffic data including time and place of arrival and arrival. Passenger waiting arrival rate beta of train _i,j And a passenger getting-off rate lambda _i,j The following are provided:

station number	a m,k	l m,k	Station 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	21	0.80	1.24
8	1.32	0.80	22	0.70	1.00
						9	1.00	0.60	23	0.65	1.00
10	0.90	0.70	24	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

And under the condition that the parameters are set, setting the departure time of the train to be 6.00, and solving the collaborative optimization model to obtain decision variables such as the stop time of the train, the formation index and the like. Thereby obtaining a train operation diagram. By optimizing the train schedule, the waiting number of stations is greatly reduced, and the waiting time of passengers is also greatly reduced. On the other hand, the flexibility of train scheduling is increased, and the problem of train tension scheduling is also relieved.

Fig. 2 is an optimized train operation chart provided by the embodiment of the invention, which respectively shows operation plans of 14 trains, and train schedules show 6:00-8:30, train operation. After the train starts from 6:00, the train arrives at the station 1 after a period of time, and enters the station 2 after the station 1 stays for a period of time, but because passengers are fewer at the moment, the train stay time is shorter, and passengers are obviously increased at about 7 points, and enter an early peak, it is obvious that one train is difficult to meet the requirements of large passengers, so that virtual formation is adopted, and the train continues to travel on a line together with 13 trains after the 1-train completes a traveling plan. Similarly, 2 cars and 14 cars are queued and the same train plan is executed. And after the early peak, the passenger quantity is reduced, the train is not queued any more, and the scheduled driving and planning are still carried out.

Fig. 3 is a schematic diagram of a change curve of a train stop time provided by an embodiment of the present invention, and it can be seen from fig. 3 that the change of the passenger capacity with time also changes the stop time obviously, but is within 1 minute. The optimized train schedule greatly increases the utilization rate of the train and reduces unnecessary stop time. Meanwhile, the stop time of different stations is different, and compared with the balanced stop time, the energy consumption of the train is reduced. Therefore, the train collaborative optimization model is significant, and the optimized train operation diagram has certain reference value.

In summary, the embodiment of the invention provides a collaborative optimization model combining virtual formation, and combines a train operation plan and a virtual formation plan to generate a virtual formation-oriented high-efficiency unbalanced train operation diagram. The passenger flow pressure in the peak period can be effectively relieved, the waste of the transportation capacity is reduced, and the flexibility of train dispatching is improved.

The method of the embodiment of the invention adopts a reasonable virtual formation plan to compile a new train running chart so as to be capable of performing treatment in advance under the condition of meeting peak passenger flow.

Those of ordinary skill in the art will appreciate that: the drawing is a schematic diagram of one embodiment and the modules or flows in the drawing are not necessarily required to practice the invention.

From the above description of embodiments, it will be apparent to those skilled in the art that the present invention may be implemented in software plus a necessary general hardware platform. Based on such understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a storage medium, such as a ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the embodiments or some parts of the embodiments of the present invention.

In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, the description is relatively simple, with reference to the description of method embodiments in part. The apparatus and system embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.

The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in 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 train running chart compiling method facing virtual formation is characterized by comprising the following steps:

establishing a train virtual formation of rail transit;

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;

solving the train operation model based on the constraint condition, and outputting a train operation diagram of rail transit;

the virtual formation of the train for establishing the rail transit comprises the following steps:

beta for train formation index _m,m' The representation is:

setting the arrival time and departure time of the train m' to meet the following constraints:

wherein r is _m,k Representing the run time of train m between k-1 and k stations, t _m,k For stopping time of train m at k stations, N is greater than 1, s _m,k For the headway distance between the trains m and m-1 at station k, s _m',k For the headway distance between the trains m 'and m' -1 at station k, s _m,1 For the headway between station 1 trains m and m-1,for maximum turnaround time at station 1, < > for>Is the minimum turnaround time at station 1;

setting the number of vehicles which can be called to be in line with the total number of trains, and restricting (4) as follows:

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

θ _m,m' for judging whether the departure time of the train service m' is reasonable or not, setting the following constraint (5):

the building of the train operation model according to the train virtual formation comprises the following steps:

let s be _m,k Is the locomotive distance between m and m-1 of the train, t _m,k For the stop time of the train m at the k stations, the dynamic change of the train headway is as follows:

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

wherein s is _1,k After opening for k stations, the time of arrival of the first vehicle;

in train systems, the waiting number of passengers is dynamically changed, using pd _m,k The representation is:

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

wherein a is _m,k After m-1 times of trains arrive at the station, the arrival rate of passengers at k stations before m times of trains arrive at the station; c _m,k A control strategy for restricting passengers from entering the train m at the k station; pi (pi) _m,k Is the number of passengers entering train m at k stops; po (po) _m,k Is the number of passengers leaving train m at k stops; pd (pd) _m,k After the train m starts from the k station, the waiting number of passengers at the k station; pd (pd) _m-1,k After the train m-1 starts from the k stations, the waiting number of passengers at the k stations;

p number of passengers in k trains m _m,k The representation is:

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

wherein p is _m,k-1 Is the number of passengers in the k-1 train m;

the number po of passengers leaving the train m at station k _m,k Can be expressed by the following formula:

po _m,k ＝l _m,k p _m,k-1 (9)

wherein l _m,k The proportion of passengers of train m getting off at station k;

passenger number pi of entering train m at k stops _m,k 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)

wherein p is _max A maximum number of passengers that can be accommodated for a train;

set according to formulas (6) - (10):

constraint (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 )}

constraint (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 )}

wherein: p is p _m,0 ＝0；pd _0,k ＝0；c _0,0 ＝0

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

wherein lambda is ₁ ，λ ₂ ，λ ₃ For preset weight, J is an objective function value, and is determined according to actual requirements of train formation plan, passenger waiting time and train residence time, T ₁ Number of virtual formation for same train, T ₂ Representing passenger waiting time, T ₃ Indicating the stop time of the train;

the setting considers the constraint condition of the total number of trains which can be scheduled by taking the time of entering and exiting the train into consideration, and comprises the following steps:

and restraining 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 )}

setting the arrival time of the train m and the departure time of the train m' to meet the following constraints:

setting the number of the vehicles capable of being called to be in accordance with the inventory number:

the method solves the train operation model based on the constraint condition, outputs a train operation diagram of rail transit, and comprises the following steps:

set property 1:

f (x). Ltoreq.0 is equivalent to κ=1

Wherein:

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

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 is _m,k ＝a-min{a,b}

p _m,k ＝p _max -b+min{a,b}

Let f=b-a and

then min { a, b } = a+ (b-a) κ = a+fκ

pd _m,k ＝-fκ

p _m,k ＝p _max -f+fκ

From the property (1) is obtained:

according to property 1, the constraint (5) is transformed into the following form:

the new variable z=κf (x) was introduced and property 2 was set as follows:

wherein: f (f) _max Is the maximum value of f (x), f _min Minimum value of f (x)

Converting constraints (11), (12) into the following form according to said properties 1 and 2:

let z=fκ, obtainable:

introduction of a New variable kappa ₃ ＝κ ₁ κ ₂ Property 3 was set as follows:

according to said property 3:

let lambda get _m,m' ＝β _m,m' θ _m,m'

Converting constraint (4) into the following form:

introducing new constraints (16) is:

all constraint conditions in the objective function of the train operation model are converted into linearity through the transformation, and a train collaborative optimization model is obtained, wherein the objective function of the train collaborative optimization model is as follows:

the constraint conditions are as follows:

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≤f _max κ

z≥f _min κ

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

wherein m is the train number, k is the platform number, lambda ₁ ，λ ₂ ，λ ₃ For preset weight, J is an objective function value, and is determined according to actual requirements of train formation plan, passenger waiting time and train residence time, T ₁ Number of virtual formation for same train, T ₂ Representing passenger waiting time, T ₃ The stop time of the train is indicated,andis a normalization factor;

β _m,m' is a binary variable if the trains m and m' are virtually queued and m<m' is beta _m,m' =1, otherwise β _m,m' ＝0；T ₂ Representing passenger waiting time, a _m,k After m-1 times of train arrives at the station, the arrival rate s of passengers at k stations before m times of train arrives at the station _m,k For the headway between the trains m and m-1, m-1 is the front of train mA train T ₃ Indicating the stop time of the train, t _m,k Stop time of the train m at the k stations;

and solving the train collaborative optimization model, and outputting a train operation diagram.