CN112541265B - High-speed rail running chart modeling method combining period and non-period of stop adjustment - Google Patents
High-speed rail running chart modeling method combining period and non-period of stop adjustment Download PDFInfo
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Abstract
The invention belongs to the field of programming and optimizing of high-speed railway train running diagrams, and particularly relates to a method for modeling a high-speed railway running diagram by combining a period and a non-period in consideration of stop adjustment. Taking a running scheme combining periodic and non-periodic and station and line information as input data; establishing an objective function by taking the minimum train travel time as a target, setting interval running time constraint, stop time constraint, overrun frequency constraint, train safety interval time constraint, starting time domain constraint, skylight constraint and periodicity constraint, and obtaining a fixed stop period and non-period combined high-speed rail running diagram optimization model; and obtaining the periodic and non-periodic combined high-speed train running diagram optimization model considering stop adjustment on the basis of the periodic and non-periodic combined high-speed train running diagram optimization model under the fixed stop. The passenger service quality is improved, and the competition of the passenger market is improved, so that the aims of improving the capacity of a busy trunk line and improving the efficiency of passenger transportation are fulfilled.
Description
Technical Field
The invention belongs to the field of programming and optimizing of high-speed railway train running diagrams, and particularly relates to a method for modeling a high-speed railway running diagram by combining a period and a non-period in consideration of stop adjustment.
Background
In the prior art, a lot of researches are developed for compiling and optimizing the running diagrams of the high-speed railway trains, and in the aspect of optimizing the running diagrams, periodic train running diagrams are adopted for foreign trains, and aperiodic train running diagrams are adopted for domestic trains. In the prior art, the related theoretical research of the periodic and non-periodic combined operation chart is less, the periodic and non-periodic combination is realized by adopting a periodic chart wire drawing technology, and the operation chart optimization is carried out according to experience by adopting a manual adjustment mode in a practical level.
The periodical operation chart has the characteristics of high regularity, convenience in transfer and high service level. However, the periodical operation chart is difficult to completely adapt to the complex requirements of high-speed rail large-scale networking operation. Therefore, a 'periodic and non-periodic' train operation diagram is adopted, and a non-periodic line is used for compensating the defect of a periodic train, so that the flexibility is increased. Aiming at the combination of period and non-period, the current high-speed railway train running chart optimizing method mainly faces the following problems:
1) The lack of systematic carding research generally aims at researching a train operation diagram of cycle and non-cycle, most of the research is concentrated on the problem of drawing and adding wires to the train operation diagram of cycle, and the problem that a plug wire train cannot be inserted or the periodicity of the cycle train is damaged easily; the primary optimization method of periodic lines and non-periodic lines is rarely comprehensively considered, and the method for compiling a train running chart by combing the periodic lines and the non-periodic lines by a system is also not provided;
2) The running map capacity planning is poor. In the process of working out the running chart, certain capacity bottleneck sections are likely to have the condition of capacity limitation, so that all trains in the train running scheme cannot be planned, and the model is free from solution. In this case, the train operation scheme may need to be adjusted, and the adjustment of the train operation scheme generally includes the following methods: adjusting stop, adjusting start and stop, adjusting frequency, adjusting grouping, etc. In the actual adjustment work, the main effects on the operability of the operation diagram and the operation of the high-speed rail need to be comprehensively considered, and a proper method is selected to optimize the capacity utilization.
Disclosure of Invention
Aiming at the technical problems, the invention provides a modeling method for a periodic and non-periodic combined high-speed rail running chart considering stop adjustment, which establishes a model of an adjustable stop aiming at the periodic and non-periodic combined train running chart, improves the service quality of passenger transportation and improves the market competition of the passenger transportation, thereby achieving the purposes of improving the capacity of a busy trunk line and improving the efficiency of passenger transportation.
The invention is realized by the following technical scheme:
a method of modeling a periodic and aperiodic combined high-speed rail operating map with consideration of stop adjustment, the method comprising:
taking a running scheme combining periodic and non-periodic and station and line information as input data; establishing an objective function by taking the minimum train travel time as a target, setting interval running time constraint, stop time constraint, overrun frequency constraint, train safety interval time constraint, starting time domain constraint, skylight constraint and periodicity constraint, and obtaining a fixed stop period and non-period combined high-speed rail running diagram optimization model;
on the basis of the fixed stop period and non-period combined high-speed rail running diagram optimization model, a train stop scheme is set as a variable, and only the condition that the train stop is only allowed to be increased is considered; and modifying interval running time constraint, stop time constraint and train safety interval time constraint, and simultaneously increasing stop frequency constraint of the same train and stop frequency constraint of the whole running scheme to obtain a periodic and non-periodic combined high-speed train running diagram optimization model considering stop adjustment.
Further, the objective function is built by taking the minimum train travel time as a target, specifically:
wherein i is a train mark, i epsilon L; l is the train set, l=l 1 ∪L 2 ，L 1 As a set of non-periodic trains,L 2 for periodic train sets, +.> Indicating the arrival time of train i at the terminating station,/->The departure time of train i at the origin is indicated.
Further, in the fixed stop period and non-period combined high-speed rail running diagram optimization model, the decision variable is the arrival time a of the train i at the station s is And the departure time d of the train i at the station s is ；
In the fixed stop period and non-period combined high-speed rail running chart optimization model, the set interval running time constraint, stop time constraint, overrun frequency constraint, train safety interval time constraint, starting time domain constraint, skylight constraint and periodicity constraint are specifically as follows:
interval run time constraint:
a is+1 -d is ≥r is +β is x is +γ is+1 x is+1 (i∈L,s∈S i )；
wherein a is is+1 The arrival time of the train i at the station s+1 is represented; d, d is The departure time of the train i at the station s is the departure time of the train i; r is (r) is Representing the pure running time of train i in the (s, s+1) interval; beta is Representing the additional time division of the start of the train i at the s station; x is x is For a stop scheme in the running scheme, stopping a train i at an s station to obtain 1, otherwise, obtaining 0; x is x is+1 For the stop scheme in the running scheme, the train i stops at the s+1 station to obtain 1, and otherwise, to obtain 0; gamma ray is Indicating the additional time division of stopping the train i at the s station; gamma ray is+1 Indicating the additional time division of stopping the train i at the s+1 station; s is S i Representing a station set through which the train i passes;s is a station mark, S epsilon S, S is a station set;
stop time constraint:
d is -a is ≥w is x is (i∈L,s∈S i )
d is -a is ≤(w is +Δw is )*x is (i∈L,s∈S i )；
wherein a is is Indicating the arrival time of the train i at the station s; w (w) is The stop time of the train i at the s station is represented; Δw is Indicating the stop time redundancy of the train i at the s station;
and (5) constraint of the number of times of crossing:
d is -a is ≤w is +y is *M(i∈L,s∈S i )
wherein M represents a constant; y is is A variable representing 0-1, representing whether the train i is overtraveled at the station s, can be overtraveled to take 1, otherwise, takes 0; y is Y i Representing the total number of stations where the train i can be most travelled;
train safety interval time constraint:
wherein: d, d js Indicating departure time of the train j at the station s; d, d js -d is Representing departure time intervals of the trains j and i at the s station; m is an auxiliary variable, which is a constant;representing the front-back relation of the 0-1 variable and the train i, j in the (s, s+1) interval, wherein the train i takes 1 before the train j, and otherwise takes 0; o (O) s ji Representing the front-back relation of 0-1 variable and trains j and i in the (s, s+1) interval, wherein the train j takes 1 before the train i, and otherwise takes 0; x is x js Indicating whether the train j stops at the station s, if the train j stops at the station s, indicating that the train j stops at the station s, and if the train j stops at the station s, indicating that the train j passes through the station without stopping at the station s, wherein the train j is 0; similarly, x js+1 A stop scheme of the train j at the station s+1 is shown; a, a js+1 And a is+1 The arrival times of the train j and the train i at the station s+1 are respectively represented; a, a js+1 -a is+1 Representing the arrival time intervals of train j and train i at s+1 stations; i. j are train marks, i, j epsilon L; ES (ES) ij Representing a station set through which the train i and the train j jointly pass; h s The safety interval parameters of the s stations are respectively represented by F, T and D, and the s stations arrive and pass through; the safety interval comprises 7 safety intervals of TT, TD, DT, DD, TF, FT and FF; FF (FF) s 、FT s 、TF s 、TT s Respectively representing a sending safety interval, a sending safety interval and a sending safety interval of the station s; DD (DD) s+1 DT s+1 、TD s+1 、TT s+1 The arrival safety interval, the arrival safety interval and the arrival safety interval of the station s+1 are respectively represented.
Originating time domain constraints:
in the method, in the process of the invention,indicating that train i is at its originating station sf i Lower limit of departure time domain of station, sf i Here, the originating station of train i is specified; />The upper limit of the departure time domain of the train i at the station s station is represented; />Indicating departure time of the train i at the origin station;
skylight constraint:
wherein END represents the skylight END time; START represents a sunroof START time;indicating departure time of the train i at the origin station; />Indicating that train i is at its terminating station ds i Is the arrival time of (a); this bar code indicates that the train must not travel during the skylight service time.
Cycle constraint:
in the method, in the process of the invention,indicating the time when the train i located in the first cycle arrives at station s; />Indicating the time when the train i located in the first cycle starts from station s; i.e l The trains i, i representing the first cycle l ∈L 2 The method comprises the steps of carrying out a first treatment on the surface of the l represents the cycle order, and represents the first cycle; t (T) i Represents the cycle length of the cycle train i, i epsilon L 2 ；ΔT i Represents the cycle length of the cycle train i, i epsilon L 2 。
Further, the interval running time constraint, the stop time constraint and the train safety interval time constraint are modified, specifically:
the modified interval runtime constraint is:
a is+1 -d is ≥r is +β is p is +γ is p is (i∈L,s∈S i )；
a is+1 -d is ≤r is +Δr is +β is p is +γ is p is (i∈L,s∈S i )；
wherein: p is p is A variable of 0-1, indicating whether the train i stops at station s, and if x is =1, then p is Must take 1, i.e.L 1 Otherwise p is Possibly taking 1 or 0; x is x is For a stop scheme in the running scheme, stopping a train i at an s station to obtain 1, otherwise, obtaining 0; Δr is Representing the operation of train i in the (s, s+1) intervalInter-redundancy;
the modified stop time constraint is:
d is -a is ≥w is p is (i∈L,s∈S i )；
d is -a is ≤(Δw is +w is )*p is (i∈L,s∈S i )；
the modified train safety interval time constraint is as follows:
wherein p is js Indicating whether the train j stops at the station s, if so, taking a value of 1, otherwise, taking a value of 0; p is p js+1 Indicating whether the train j stops at the station s+1, if so, taking a value of 1, otherwise, taking a value of 0;
P is indicating whether the train i stops at the station s, if so, taking a value of 1, otherwise, taking a value of 0; p (P) is+1 Indicating whether the train i stops at the station s+1, if so, taking a value of 1, otherwise, taking a value of 0; p (P) is And P is+1 Represented are 0-1 decision variables, and x mentioned above is And x is+1 Different, x is x is+1 The parameters represented, which are 0 or 1, are determined from the initial stop schedule, and are herein embodying the adjustability of the train stop schedule.
Z ijs+1 Is an auxiliary variable added to linearize the model,only when the train i and the train j are parked at the station s+1 at the same time, the value is 1, otherwise, the value is 0.
Further, the stop frequency constraint of the same train and the stop frequency constraint of the whole running scheme are increased, and the method specifically comprises the following steps:
the added stop times constraint of the same train is as follows:
the number of stops of the increased overall start-up scheme is constrained to be:
wherein p is is Representing a 0-1 variable, whether the train i stops at station s, and if x is =1, then p is Necessarily 1, i ε L 1 Otherwise, 1 or 0 may be taken; x is x is For a stop scheme in the running scheme, stopping a train i at an s station to obtain 1, otherwise, obtaining 0;
Ω i representing the maximum stop upper limit of the train i;
p represents the total newly added stop limit for all trains.
The beneficial technical effects of the invention are as follows:
1) The method comprises a certain proportion of periodic running scheme lines: the periodic operation of the train can realize the regular utilization of the transport capacity resources. The method provided by the invention can flexibly lay periodic trains, is beneficial to optimizing the regularity of running diagrams, meets the diversity of passenger flow demands, fully utilizes transportation resources and realizes the quality improvement and efficiency improvement of transportation organizations.
2) Train running diagram stop adjustment is designed based on actual application: according to practical application, the adjustment of the model constructed by the method of the invention is mainly concentrated on the addition of stop stations in stop station adjustment, on one hand, the newly added stop stations can possibly improve the 'local' homogeneity of the train stop stations or the 'local' elasticity of the running lines, so that the section passing capacity utilization is improved; on the other hand, the increase of stop stations can also improve the OD service frequency of passenger flows.
3) Reasonable selection of stop and override: the balanced stop is an important measure for guaranteeing the service frequency of the station, is also a key measure for attracting passenger flow, and can fully utilize reasonable override distribution.
Drawings
FIG. 1 is a flow chart of a method for modeling a periodic and aperiodic combined high-speed rail operation map with consideration of stop adjustment in accordance with an embodiment of the present invention.
FIG. 2 is a flowchart of the overall algorithm idea in an embodiment of the invention;
FIG. 3 is a schematic flow chart of a scrolling algorithm in an embodiment of the invention;
fig. 4 is a schematic flow chart of an iterative algorithm in an embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
On the contrary, the invention is intended to cover any alternatives, modifications, equivalents, and variations as may be included within the spirit and scope of the invention as defined by the appended claims. Further, in the following detailed description of the present invention, certain specific details are set forth in order to provide a better understanding of the present invention. The present invention will be fully understood by those skilled in the art without the details described herein.
The invention provides a modeling method of a periodic and non-periodic combined high-speed rail running chart considering stop adjustment, as shown in fig. 1, the method comprises the following steps:
taking a running scheme combining periodic and non-periodic and station and line information as input data; establishing an objective function by taking the minimum train travel time as a target, setting interval running time constraint, stop time constraint, overrun frequency constraint, train safety interval time constraint, starting time domain constraint, skylight constraint and periodicity constraint, and obtaining a fixed stop period and non-period combined high-speed rail running diagram optimization model;
on the basis of the fixed stop period and non-period combined high-speed rail running diagram optimization model, a train stop scheme is set as a variable, and only the condition that the train stop is only allowed to be increased is considered; and modifying interval running time constraint, stop time constraint and train safety interval time constraint, and simultaneously increasing stop frequency constraint of the same train and stop frequency constraint of the whole running scheme to obtain a periodic and non-periodic combined high-speed train running diagram optimization model considering stop adjustment.
In this embodiment, the objective function is that all train travel time is minimum, and the train travel time is obtained by subtracting the starting station departure time from the final arrival time of each train; the objective function established with the minimum train travel time as the target is as follows:
wherein i is a train mark, i epsilon L; l is the train set, l=l 1 ∪L 2 ，L 1 As a set of non-periodic trains,L 2 for periodic train sets, +.> Indicating the arrival time of train i at the terminating station,/->The departure time of train i at the origin is indicated.
Specifically, in the fixed stop period and non-period combined high-speed rail running chart optimization model: the set is defined as follows:
the relevant parameters are defined as follows:
in the fixed stop period and non-period combined high-speed rail running chart optimization model, the set interval running time constraint, stop time constraint, overrun frequency constraint, train safety interval time constraint, starting time domain constraint, skylight constraint and periodicity constraint are specifically as follows:
interval run time constraint:
the interval running time constraint refers to the running time of a train from a previous station to a next station, and generally comprises three parts of interval pure running time, start-stop additional time division and interval running redundancy. Determining the running speed of the train according to the mileage of the section when the section runs purely; the speed of the train when arriving at the station is gradually reduced to zero, the speed is increased from zero to the running speed when departing from the station, and the running time of the section which is more expensive than the running time of the train when not stopping and passing through the stations at the two ends of the section is respectively called as a parking additional time division and a starting additional time division. The interval operation redundancy is used for increasing the elasticity of the operation diagram and meeting the robustness of the operation diagram.
a is+1 -d is ≥r is +β is x is +γ is+1 x is+1 (i∈L,s∈S i )；
Stop time constraint:
stop time refers to the residence time of a train at a station. The stop time is required to be redundant in addition to the necessary passenger landing time and station technical operation time. On the one hand, some redundancy needs to be added for robustness of the running map; on the other hand, an overrun of a train in a station increases the extra stop time to avoid the train.
d is -a is ≥w is x is (i∈L,s∈S i )
d is -a is ≤(w is +Δw is )*x is (i∈L,s∈S i )；
And (5) constraint of the number of times of crossing:
d is -a is ≤w is +y is *M(i∈L,s∈S i )
train safety interval time constraint:
in this embodiment, the train safety interval time is an important factor that must be considered for train operation diagram construction. The train safety interval comprises a station safety interval and an interval tracking interval, and generally, the interval safety interval is often converted into the station safety interval constraint in the process of researching and paving an actual running chart, and the safety interval is constrained so as to ensure the safety time between trains.
In this embodiment, the originating time domain constraint is an important influencing factor for running map formulation, which plays a key role in train sequencing. In general, the wider the origin time domain, the greater the sequence adjustability of the train lines, and thus the greater the flexibility of the overall graph formulation. The starting time domain has a rough range for the departure time of the train according to the rule of the passenger flow, on the other hand, the schemes in the running scheme are numerous, the accessibility of each passenger flow OD in each time period is ensured as much as possible, certain constraint is also needed for the starting time of the running line, the time domain of the train is considered, the time domain of each station is not strictly constrained for increasing the value range, and the starting station time is only constrained:
time constraint of the originating station:
in this embodiment, in addition to the originating time domain constraint, skylights are also non-negligible factors. All trains must be operated within an operating period. The skylight of the high-speed railway line mainly adopts a rectangular or segmented rectangular skylight, and trains cannot be operated in the skylight time, so that all trains are ensured to be operated in an operation period:
skylight constraint:
cycle constraint:
the improvement made on the basis of the fixed stop model is as follows: the train stopping scheme is set as a variable, only the condition that the train stopping is only allowed to be increased is considered, and the newly added variables and parameters are as follows
Station related constraints that need to be modified include in particular: the interval running time constraint, the stop time constraint and the train safety interval time constraint are modified, and the method specifically comprises the following steps:
the modified interval runtime constraint is:
a is+1 -d is ≥r is +β is p is +γ is p is (i∈L,s∈S i )；
a is+1 -d is ≤r is +Δr is +β is p is +γ is p is (i∈L,s∈S i )；
the modified stop time constraint is:
d is -a is ≥w is p is (i∈L,s∈S i )；
d is -a is ≤(Δw is +w is )*p is (i∈L,s∈S i )；
the modified train safety interval time constraint is as follows:
in this embodiment, the stop frequency constraint of the same train and the stop frequency constraint of the whole running scheme are added, specifically:
the added stop times constraint of the same train is as follows:
the number of stops of the increased overall start-up scheme is constrained to be:
wherein p is is Representing a 0-1 variable, whether the train i stops at station s, and if x is =1, then p is Necessarily 1, i ε L 1 Otherwise, 1 or 0 may be taken; x is x is For a stop scheme in the running scheme, stopping a train i at an s station to obtain 1, otherwise, obtaining 0;
Ω i representing the maximum stop upper limit of the train i;
p represents the total newly added stop upper limit of all trains;
and obtaining the optimization model of the periodic and non-periodic combined high-speed train running chart considering stop adjustment by adding variables and modifying related constraints.
In this embodiment, the method aims at train travel time, and regularly reduces the solving scale according to a method of "sectional rolling and step-by-step optimization" for a strategy of borrowing and referring to the development of the periodic chart.
In the solving process, the time consistency of each period of the periodic train is ensured, so that the periodicity of the periodic train can be ensured; for an aperiodic train, the departure time domain of the aperiodic train needs to be reasonably distributed in each solving time and then solved. Thus, to complete the solution of the entire model, the calculation is started from the first solution period (combination of cycles), and only the trains within that period are solved at a time. For the next time period, solving by adopting a mode of fixedly adding periodic trains and freely adding non-periodic trains, and adopting an iteration strategy method to perform conflict fluffing and capacity utilization in the time period, and continuously rolling forwards and iterating fluffing capacity until all trains are paved; reasonable train planning is solved by performing cyclical redundancy iterations on periodic trains and stop changes on non-periodic trains. As shown in fig. 2.
After preprocessing the running scheme, all the originating domains of the trains fall into corresponding time periods, only accurate solving is needed in each time period, and the connection between the time periods can be untwined by adopting a rolling paving strategy. As shown in fig. 3: according to the time intervals divided in advance, two or more time intervals are selected each time to be solved together, for the solving result, only the trains in one time interval are reserved each time, and for the trains which span two or more time intervals, the trains are re-paved together with the trains in the next time interval. And rolling and paving in sequence until all trains are paved.
Although the solution scale is reduced by adopting the rolling paving method, the following problems are inevitably encountered:
1) The strong coupling of periodic trains results in wasted capacity
2) The interval capacity is too tight, resulting in unplanned trains
In order to solve the 2 problems, stepwise iteration can be adopted to find the proper redundancy time so as to solve the problem of capability waste of the periodic train; a reasonable train planning is found by adjusting a train stop model. A specific iterative flow is shown in fig. 4. According to the strict period, solving a fixed stop period and non-period combined high-speed rail running chart optimization model, and if the model has a solution, directly outputting; otherwise, the stop adjustment change is considered, the variable stop period and non-period combined train operation diagram model is solved, if the model has a solution, the model is directly output, otherwise, the adjustment period allowable fluctuation range is considered, and the solution is iterated.
Claims (2)
1. A method for modeling a periodic versus aperiodic combined high-speed rail operating map with consideration of stop adjustment, the method comprising:
taking a running scheme combining periodic and non-periodic and station and line information as input data; establishing an objective function by taking the minimum train travel time as a target, setting interval running time constraint, stop time constraint, overrun frequency constraint, train safety interval time constraint, starting time domain constraint, skylight constraint and periodicity constraint, and obtaining a fixed stop period and non-period combined high-speed rail running diagram optimization model;
on the basis of the fixed stop period and non-period combined high-speed rail running diagram optimization model, a train stop scheme is set as a variable, and only the condition that the train stop is only allowed to be increased is considered; modifying interval running time constraint, stop time constraint and train safety interval time constraint, and simultaneously increasing stop frequency constraint of the same train and stop frequency constraint of an overall running scheme to obtain a periodic and non-periodic combined high-speed train running diagram optimization model considering stop adjustment;
the method comprises the steps of establishing an objective function by taking the minimum train travel time as a target, wherein the objective function is specifically as follows:
wherein i is a train mark, i epsilon L; l is the train set, l=l 1 ∪L 2 ，L 1 As a set of non-periodic trains,L 2 for periodic train sets, +.> Indicating the arrival time of train i at the terminating station,/->Indicating departure time of the train i at the origin station;
in the fixed stop period and non-period combined high-speed rail running diagram optimization model, the decision variable is the arrival time a of the train i at the station s is And the departure time d of the train i at the station s is ；
In the fixed stop period and non-period combined high-speed rail running chart optimization model, the set interval running time constraint, stop time constraint, overrun frequency constraint, train safety interval time constraint, starting time domain constraint, skylight constraint and periodicity constraint are specifically as follows:
interval run time constraint:
a is+1 -d is ≥r is +β is x is +γ is+1 x is+1 (i∈L,s∈S i )；
wherein a is is+1 The arrival time of the train i at the station s+1 is represented; d, d is The departure time of the train i at the station s is the departure time of the train i; r is (r) is Representing the pure running time of train i in the (s, s+1) interval; beta is Representing the additional time division of the start of the train i at the s station; x is x is For a stop scheme in the running scheme, stopping a train i at an s station to obtain 1, otherwise, obtaining 0; x is x is+1 For the stop scheme in the running scheme, the train i stops at the s+1 station to obtain 1, and otherwise, to obtain 0; gamma ray is Indicating the additional time division of stopping the train i at the s station; gamma ray is+1 Indicating the additional time division of stopping the train i at the s+1 station; s is S i Representing a station set through which the train i passes; s is a station mark, S epsilon S, S is a station set;
stop time constraint:
d is -a is ≥w is x is (i∈L,s∈S i )
d is -a is ≤(w is +Δw is )*x is (i∈L,s∈S i )；
wherein a is is Indicating the arrival time of the train i at the station s; w (w) is The stop time of the train i at the s station is represented; Δw is Indicating the stop time redundancy of the train i at the s station;
and (5) constraint of the number of times of crossing:
d is -a is ≤w is +y is *M(i∈L,s∈S i )
wherein M represents a constant; y is is A variable representing 0-1, representing whether the train i is overtraveled at the station s, can be overtraveled to take 1, otherwise, takes 0; y is Y i Representing the total number of stations where the train i can be most travelled;
train safety interval time constraint:
wherein: d, d js Indicating departure time of the train j at the station s; d, d js -d is Representing departure time intervals of the trains j and i at the s station; m is an auxiliary variable, which is a constant;representing the front-back relation of the 0-1 variable and the train i, j in the (s, s+1) interval, wherein the train i takes 1 before the train j, and otherwise takes 0; o (O) s ji Representing the front-back relation of 0-1 variable and trains j and i in the (s, s+1) interval, wherein the train j takes 1 before the train i, and otherwise takes 0; x is x js Indicating whether the train j stops at the station s, if the train j stops at the station s, indicating that the train j stops at the station s, and if the train j stops at the station s, indicating that the train j passes through the station without stopping at the station s, wherein the train j is 0; x is x js+1 The stop scheme of the train j at the station s+1 is shown, if the scheme is 1, the stop is shown, and if the scheme is 0, the passing of the stop is shown; a, a js+1 And a is+1 The arrival times of the train j and the train i at the station s+1 are respectively represented; a, a js+1 -a is+1 Representing a trainj and the arrival time interval of train i at s+1 stations; i. j are train marks, i, j epsilon L; ES (ES) ij Representing a station set through which the train i and the train j jointly pass; h s The safety interval parameters of the s stations are respectively represented by F, T and D, and the s stations arrive and pass through; the safety interval comprises 7 safety intervals of TT, TD, DT, DD, TF, FT and FF s 、FT s 、TF s 、TT s Respectively representing a sending safety interval, a sending safety interval and a sending safety interval of the station s; DD (DD) s+1 DT s+1 、TD s+1 、TT s+1 Respectively representing the arrival safety interval, the arrival safety interval and the arrival safety interval of the station s+1;
originating time domain constraints:
in the method, in the process of the invention,indicating that train i is at its originating station sf i Lower limit of departure time domain; sf (sf) i In particular to an originating station of the train i;the upper limit of the departure time domain of the train i at the station s station is represented; />Indicating departure time of the train i at the origin station;
skylight constraint:
wherein END represents the skylight END time; START represents a sunroof START time;indicating that train i is at its originating station sf i Is set up in advance; />Representing the arrival time of train i at its final destination dsi; skylight constraint means that the train must not travel within skylight maintenance time;
cycle constraint:
in the method, in the process of the invention,indicating the time when the train i located in the first cycle arrives at station s; />Indicating the time when the train i located in the first cycle starts from station s; i.e l The trains i, i representing the first cycle l ∈L 2 The method comprises the steps of carrying out a first treatment on the surface of the l represents the cycle order, and represents the first cycle; t (T) i Represents the cycle length of the cycle train i, i epsilon L 2 ；ΔT i Represents the cycle length of the cycle train i, i epsilon L 2 ；
The stop frequency constraint of the same train and the stop frequency constraint of the whole running scheme are increased, and the method specifically comprises the following steps:
the added stop times constraint of the same train is as follows:
the number of stops of the increased overall start-up scheme is constrained to be:
wherein p is is Representing a 0-1 variable, whether the train i stops at station s, and if x is =1, then p is Necessarily 1, i ε L 1 Otherwise p is Taking 1 or 0; x is x is For a stop scheme in the running scheme, stopping a train i at an s station to obtain 1, otherwise, obtaining 0;
Ω i representing the maximum stop upper limit of the train i;
p represents the total newly added stop limit for all trains.
2. The method for modeling a periodic and aperiodic combined high-speed rail running map with consideration of stop adjustment according to claim 1, wherein the interval running time constraint, the stop time constraint and the train safety interval time constraint are modified, specifically:
the modified interval runtime constraint is:
a is+1 -d is ≥r is +β is p is +γ is p is (i∈L,s∈S i )；
a is+1 -d is ≤r is +Δr is +β is p is +γ is p is (i∈L,s∈S i )；
wherein: p is p is A variable of 0-1, indicating whether the train i stops at station s, and if x is =1, then p is Must take 1, i.e.L 1 Otherwise p is Taking 1 or 0; x is x is For a stop scheme in the running scheme, stopping a train i at an s station to obtain 1, otherwise, obtaining 0; Δr is Representing the run-time redundancy of train i in the (s, s+1) interval;
the modified stop time constraint is:
d is -a is ≥w is p is (i∈L,s∈S i )；
d is -a is ≤(Δw is +w is )*p is (i∈L,s∈S i )；
the modified train safety interval time constraint is as follows:
wherein p is js Indicating whether the train j stops at the station s, if so, taking a value of 1, otherwise, taking a value of 0; p is p js+1 Indicating whether the train j stops at the station s+1, if so, taking a value of 1, otherwise, taking a value of 0;
P is indicating that train i is at station sIf the station is stopped, the value is 1, otherwise, the value is 0; p (P) is+1 Indicating whether the train i stops at the station s+1, if so, taking a value of 1, otherwise, taking a value of 0; z is Z ijs+1 The auxiliary variable added for model linearization processing is a value of 1 only when the train i and the train j stop at the station s+1 at the same time, and is otherwise 0.
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