CN111932034B - Regional multi-system rail transit train running scheme compiling method and system - Google Patents

Regional multi-system rail transit train running scheme compiling method and system Download PDF

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CN111932034B
CN111932034B CN202010998691.4A CN202010998691A CN111932034B CN 111932034 B CN111932034 B CN 111932034B CN 202010998691 A CN202010998691 A CN 202010998691A CN 111932034 B CN111932034 B CN 111932034B
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王莹
刘岭
刘军
张波
李擎
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Abstract

The invention discloses a regional multi-system rail transit train running scheme compiling method and a system thereof, wherein the running scheme compiling method comprises the steps of constructing an objective function taking a passenger congestion coefficient and train running cost as double targets; determining decision variables and one or more of the following constraints: passenger travel demand constraint, regional multi-system rail transit overload rate constraint, train running frequency range constraint, interval capacity constraint, station capacity constraint and parameter variable constraint. The passenger crowding coefficient and the train running cost are jointly used as double targets of a running method programming model to optimize, so that the difference characteristics of regional multi-system rail transit transportation are accurately reflected, and the running scheme of the regional multi-system rail transit is more refined.

Description

Regional multi-system rail transit train running scheme compiling method and system
Technical Field
The invention belongs to the field of tracks, and particularly relates to a regional multi-system track traffic train running scheme compiling method and a system thereof.
Background
In recent years, urban rail transit operation mileage and traffic are in a high-speed development stage, and the existing rail transit operation method is mainly composed of operation method composing based on a mathematical method, operation method composing based on an alternative set and operation method composing of a side stop scheme.
Yu-HernChang establishes a multi-objective linear programming model optimized by a train running method, an objective function is to minimize railway operation cost and total passenger time loss, and a fuzzy mathematical programming method is adopted for solving. The indexes that the model can solve include an optimal train operation method set (comprising stop schemes), train operation frequency, the number of motor train units capable of meeting passenger demand, and the number of passengers between stations in each scheme (see Yu-Hern Chang, chung-Hsing Yeh, ching-Cheng Screen. A multiobjective model for passenger train services planning: application to a high-speed rail line. Transport science.2000.34 (2). 91-106). The Chi-Kang LEE focuses more on the autonomous selection of passengers for transportation services, and the author establishes a double-layer planning model for train operation method design and also applies the double-layer planning model to a high-speed railway system (see Chi-Kang LEE, wen-jin HSIEH.A Demand Oriented Service planning.process [ A ]. The World Congress On Railway research.2001.55-89.). Shi Feng the method for starting passenger trains related to passenger lines is researched, the dual benefits of railway enterprises and passengers are considered in the research, a model is constructed to optimize the method for starting the passenger trains (see Shi Feng, deng Lianbo, rixinhua, fang Qi. The method for starting passenger trains related to passenger lines is researched [ J ]. Railway school report, 2004, (02), 16-20); the method comprises the steps of (1) constructing a train operation method evaluation index system (Deng Lianbo, shi Feng) by the aid of a passenger train operation method evaluation index system [ J ] China railway science, 2006, (03), 106-110.) and designing a double-layer planning model and algorithm of a passenger train operation method, wherein an upper-layer planning is a train operation method optimization model, and a mixed integer linear planning model is constructed for minimizing the cost of transportation enterprises or maximizing profits by the aid of an objective function; the objective function of lower-level planning is that the travel time of the passenger is the shortest or the cost is the most economical, and the assignment of passengers to the service network according to the utility function is described as a nonlinear programming problem (see Shi Feng, deng Lianbo, huo Liang. Two-level planning model and algorithm for passenger train departure method [ J ]. Chinese railway science, 2007, (03), 110-116).
The foreign railway network has smaller scale, and most of trains adopt a high-frequency and periodical operation mode. The most typical method in the research of the foreign railway running method is a train running method alternative set generation method, and the method generates an alternative set of the running method according to the shortest path information and aiming at a research line, and selects the optimal running method through a certain research target and constraint. Scholl and Schobel studied the optimization of train departure methods with the shortest travel time and the smallest passenger transfer (see Scholl S. Customer-oriented line planning. PHD thesis. University of Kaiserlauern.2005, 23-56, sch. Bel A, scholl S. Line Planning with Minimal Traveling Time [ J ]. 2005, and Schobel A., scholl S. Line planning with minimal transfers. In 5th Workshop on Algorithmic methods and Models for Optimization of Railways, number 06901 in DagStuhl Seminar Proceedings, 2006.).
Aiming at the starting method establishment of the side stop scheme, qi X and Xiong J provide a train starting method optimization method based on a stop plan under the condition of a passenger special line, and factors such as a train starting station/finishing station, a path, a train grade, the number of started trains, a stop plan and the like are considered in a model. The difference between the operating revenue and the operating cost is an objective function (see Xin Q, jian x, optimization method of passenger train plan based on stop schedule plan for passenger dedicated line [ C ]. International Conference on Uncertainty Reasoning & Knowledge Engineering, 2012.). Yang L, qi J, li S, gao Y built a multi-objective mixed integer linear programming model. The model aims to minimize the total residence time and total delay between the actual departure times and the predicted departure times of all trains on the high-speed rail corridor (see Yang L, qi J, li S, et al Collaborative optimization for train scheduling and train stop planning on high-speed railway [ J ], omega, 2016, 64:57-76.). Luo Q, hou Y, li W, zhang XF proposed an integer programming model of the train stop plan. A genetic algorithm is used to solve a model that targets the minimum total travel time of the passenger (see Luo Q, hou Y, li W, et al Stop plan of express and local train for regional rail transit line [ J ]. Journal of Advanced Transportation, 2018: 1-11.).
The existing running method in the aspect of rail transit mainly aims at running cost and running cost, partial related researches consider the comfort level of the passengers in the running cost, and most of the running cost is calculated by using punishment coefficients as a part of the running cost. The existing running method can be only well suitable for single-system track traffic running method programming, but the integrated running method for multi-system track traffic programming in the area lacks differential description. Meanwhile, the most important crowding degree for expressing comfort is different in different travel processes in the area, and the perception of passengers on crowding in a plurality of travel links cannot be represented by a single punishment coefficient.
Therefore, how to provide a method for implementing the congestion factor has become an urgent technical problem to be solved.
Disclosure of Invention
Aiming at the problems, the invention discloses a regional multi-system rail transit train operation scheme compiling method and a system thereof, wherein the operation scheme compiling method takes passenger comfort and operation benefit into consideration, optimizes the operation scheme and has universality.
The invention aims to provide a regional multi-system rail transit train operation scheme compiling method, which comprises the following steps of,
Constructing an objective function which takes the passenger congestion coefficient and the train running cost as double targets;
determining decision variables and one or more of the following constraints:
passenger travel demand constraint, regional multi-system rail transit overload rate constraint, train running frequency range constraint, interval capacity constraint, station capacity constraint and parameter variable constraint.
Further, the method for programming the running scheme further comprises the step of inputting the regional track traffic networking alternative set and the section passenger flow volume as basic data, wherein the method comprises the steps of,
constructing a train set, an interval set and a station set of the regional multi-system track traffic based on the regional track traffic networking alternative set, wherein,
the train set is represented by Q, the element L represents the first train in the train set, L is E Q, and L elements are in the train set;
the interval set is represented by E, the element i represents one interval, i epsilon E, and M elements in the interval set are all contained;
the station set is denoted by S, the element j denotes a station, j epsilon S, and N elements are in the station set.
Further, the constructing the objective function with the passenger congestion factor and the train running cost as the double targets comprises the objective function with the minimum passenger congestion factor and the objective function with the minimum train running cost as the targets.
Further, the running scheme compiling method also comprises the steps of,
dividing regional multi-system track traffic into class 1 track traffic, class 2 track traffic and class 3 track traffic;
based on regional multi-system track traffic division, calculating the congestion coefficient of any type of track traffic in regional multi-system track traffic in section i and the congestion coefficient of station j in regional multi-system track traffic;
and acquiring an objective function with the minimum passenger congestion coefficient as a target based on the calculated congestion coefficient of any type of the regional multi-system track traffic in the section i and the congestion coefficient of the station j in the regional multi-system track traffic.
Further, the congestion coefficients of the class 1 track traffic and the class 2 track traffic in the zone i in the multi-system track traffic of the calculated area comprise,
acquiring the average effective area of the train and the average passenger carrying number of the train in the interval i;
based on the average effective area of the trains and the average passenger carrying number of the trains in the interval i, calculating the passenger average occupied area of the interval i;
and acquiring congestion coefficients of the class 1 track traffic and the class 2 track traffic in the section i based on the passenger average occupied area of the section i.
Further, the congestion coefficient of the class 3 track traffic in the regional multi-system track traffic in the section i is calculated to comprise,
Acquiring the passenger flow in a section i and the passenger capacity which can be provided by all trains in the section i;
acquiring the average full rate of all trains in the section i based on the passenger flow in the section i and the passenger capacity which can be provided by all trains in the section i;
and (3) averaging the average full load rates of all trains in the section i to obtain the congestion coefficient of the class 3 track traffic in the section i.
Further, calculating the congestion factor of the station j in the regional multi-system track traffic comprises,
acquiring a difference value of the passenger flow volume of the section of the adjacent section of the station j and a passenger flow coefficient exchanged by the station j;
obtaining the product of the difference value of the section passenger flow volume of the adjacent section of the station j and the coefficient of the passenger flow volume exchanged by the station j, and averaging the product to each train passing through the station j to obtain the average passenger flow volume exchanged by the train at the station j;
acquiring the effective area of a station j platform;
obtaining the ratio of the effective area of station j platform to the average exchange passenger flow of the train at station j to obtain the passenger average occupied area of station j platform
And acquiring the congestion coefficient of the station j in the regional multi-system rail transit based on the passenger average occupied area of the station j station.
Further, the objective function targeting the minimum passenger congestion factor is:
（3）
Wherein M is the total number of sections in the regional multi-system track traffic, N is the total number of stations in the regional multi-system track traffic, i represents a section, j represents a station,congestion factor indicating interval i, +.>Section passenger flow volume of section i +.>Representing the average running time of the train in section i, < > and>congestion factor indicating station j, < > j>Representing the average exchange traffic per train in station j,/>Representing the average stop time of the train at the station j;
the objective function with the minimum train running cost as the objective is as follows:
（2）
wherein l represents a first train in regional multi-system rail transit,represents the frequency of the start of train l, +.>Indicating the running cost of the train l.
Further, the congestion factor of section iThe method meets the following conditions:
（4）
wherein,representing congestion coefficient of kth type track traffic in regional multi-system track traffic in section i,/>Is 0,1 variable, ">Indicating that section i belongs to the kth class of rail traffic, < > and>the section i does not belong to the k-th type of track traffic, and k is 1, 2 and 3.
Further, the congestion coefficients of the class 1 track traffic and the class 2 track traffic in the section i satisfy:
（5）
wherein,the passenger flow passenger average occupied area of the section i is represented by m 2 Person/person->， />A parameter representing a linear function of the interval congestion coefficient; and passenger flow passenger average occupied area of interval i +.>The ratio of the average effective area of the train to the average passenger load of the train in interval i:
（6）
wherein,represents the average effective area of the train in section i, the unit is m 2 ；/>Mean passenger number of trains in section i is represented, and the following are satisfied:
（7）
wherein L represents the number of elements in the train set,represents the frequency of the start of train l, +.>Is a variable of 0 and 1,indicating that the train l operation section includes section i, < >>Indicating that the train i operation section does not include section i,/or->The section passenger flow volume of the section i is represented;
the congestion coefficient of the type 3 track traffic in the section i satisfies:
（8）
wherein,representing the average full load rate of all trains in the section i; and the average full rate of all trains in section i +.>Ratio of passenger volume in section i to passenger volume that all trains in section i can offer:
（9）
wherein L represents the number of elements in the train set,represents the frequency of the start of train l, +.>Is a variable of 0 and 1,indicating that the train l operation section includes section i, < >>Indicating that the train i operation section does not include section i,/or->Represents a permanent person of the train l;
the congestion coefficient of the station j in the regional multi-system rail transit meets the following conditions:
（10）
Wherein,representing passenger average occupied area, m of station platform j 2 Person/person->，/>Parameters representing a linear function of a station congestion coefficient; and passenger's area occupied by station platform j ∈>The ratio of the effective area of station j to the average exchange passenger flow of the train at station j:
（11）
wherein,the effective area of the platform of the station j is expressed as m 2 ；/>The average exchange passenger flow quantity of the train at the station j is represented, wherein the average exchange passenger flow quantity of the train at the station j is obtained by multiplying the passenger flow quantity difference value of the section passenger flow of the adjacent section of the station j by the exchange passenger flow coefficient of the station j and averaging the passenger flow quantity of the train at the station j to each train passing through the station, and the average exchange passenger flow quantity of the train at the station j meets the following conditions:
（12）
wherein,representing the exchange passenger flow coefficient of station j, M is the number of elements in the interval set, L is the number of elements in the train set, and +.>Section passenger flow volume of section i +.>Represents the 0,1 variable, ">Starting station indicating section i is j, +.>The start station representing section i is not j,/>represents the 0,1 variable, ">The terminal station representing section i is j,the terminal station representing section i is not j, < > or->Represents the 0,1 variable, ">Indicating that station j is included in the running path of train l>Indicating that station j is not included in the running path of train l >Indicating the frequency of operation of train l.
Further, the passenger travel demand constraint is:
（13）
wherein,represents the frequency of the start of train l, +.>0, 1 variable, ">Indicating that the train l operation section includes section i, < >>Indicating that the train i operation section does not include section i,/or->Represents the driver of train l, +.>Indicating the maximum overload rate allowed for train l, < >>The section passenger flow volume in section i is shown.
Further, the regional multi-system rail transit overload rate constraint is as follows:
（14）
wherein,indicating the rail traffic to which the train belongs, +.>。
Further, the train operation frequency range constraint is as follows:
（15）
wherein,represents the frequency of the start of train l, +.>Representing the minimum frequency of operation of train i capable of operating,/->Indicating that the train l can start runningIs set to the maximum line frequency of (a).
Further, the interval capability constraint is:
（16）
wherein,represents the frequency of the start of train l, +.>0, 1 variable, ">Indicating that the train l operation section includes section i, < >>Indicating that the train i operation section does not include section i,/or->Represents the driver of train l, +.>Indicating the maximum overload rate allowed for train l, < >>Section passenger flow volume of section i +.>Representing the maximum transport capacity of interval i.
Further, the station capability constraint is:
（17）
Wherein,represents the frequency of the start of train l, +.>Is 0,1 variable, ">Indicating that station j is included in the running path of train l>Indicating that station j is not included in the running path of train l>Indicating the maximum transport capacity of station j.
Further, the parameter variable constraint is:
（18）
wherein N is the total number of stations in the regional multi-system rail transit.
Further, the decision variable is the running frequency of the class I trainWherein, the method comprises the steps of, wherein,
the value range of (2) is the whole natural number, < >>And if not, the first train is started in the research period, otherwise, the first train is started in the research period.
Further, the running scheme compiling method also comprises the steps of,
for the objective function with minimum passenger crowding coefficient and the minimum train running costSolving the objective function of (2) to obtain the corresponding expected value、/>；
Optimizing an objective function construction, and acquiring a double-objective mathematical model of comprehensive running cost and congestion coefficient based on an objective function with minimum passenger congestion coefficient and an objective function with minimum train running cost:
（19）
where p is the p-th priority, q is the q-th objective function,priority factor representing the p-th priority, < - > Weight coefficients representing positive and negative bias variables of different objective functions in the same priority, +.>、/>Respectively, an objective function with the minimum passenger congestion coefficient as an objective function and an objective function with the minimum train running cost as an objective function are respectively compared with corresponding expected values to obtain an objective excess value and an objective deficiency value;
assigning a priority factor and a weight coefficient to the double-target mathematical model, and optimizing the double-target mathematical model as follows:
（20）
wherein,objective function and expectation value targeted at minimum passenger congestion factor>A comparative target deficiency value;is the objective function and the expected value aiming at the minimum train running cost>A comparative target deficiency value;
constructing an optimization objective setThe optimized target set meets the objective function with the minimum passenger congestion coefficient as the objective function and the objective function with the minimum train running cost as the objective function respectively:
（21）
（22）
wherein,objective function and expectation value targeted at minimum passenger congestion factor>The target of the phase comparison exceeds the value;is the objective function and the expected value aiming at the minimum train running cost>The target of the phase comparison exceeds the value; />、/>The running cost and the crowding coefficient after the optimization of the double-target mathematical model are respectively;
Taking formulas (4) - (18) and (20) - (22) as constraints of the optimized double-target mathematical model, and adopting Global valve in Lingo to calculate the optimal solution of the optimized double-target mathematical model.
Further, the opening compilation system comprises,
the construction module is used for constructing an objective function taking the passenger congestion coefficient and the train running cost as double targets;
a determining module for determining decision variables and one or more of the following constraints:
passenger travel demand constraint, regional multi-system rail transit overload rate constraint, train running frequency range constraint, interval capacity constraint, station capacity constraint and parameter variable constraint.
The regional multi-system rail transit train running scheme compiling method comprehensively considers the interests of passengers and operators, optimizes the passenger congestion coefficient and the train running cost together as the double targets of the running method compiling model, accurately reflects the difference characteristics of regional multi-system rail transit transportation, and enables the running scheme of regional multi-system rail transit to be more refined.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are 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 shows a schematic flow diagram of a regional multi-system rail transit train operation scheme compiling method in an embodiment of the invention;
FIG. 2 is a graph showing a relationship between passenger occupancy area and passenger congestion factor in accordance with an embodiment of the invention;
FIG. 3 shows a close proximity zone passenger flow difference in an embodiment of the inventionIs an analytical schematic of (a);
fig. 4 shows a schematic circuit diagram of regional multi-system rail transit formed by a Chongqing subway 5 wire south section, a Chongqing subway Jiang Tiaoxian and a Chongqing high-speed rail section in the embodiment of the invention;
fig. 5 shows a schematic diagram of a regional multi-system rail transit train operation scheme compiling system according to an embodiment of the invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the embodiment of the invention discloses a method for compiling a regional multi-system rail transit train running scheme, which comprises the following steps: firstly, constructing an objective function which takes the passenger congestion coefficient and the train running cost as double targets; then, decision variables and one or more of the following constraints are determined: passenger travel demand constraint, regional multi-system rail transit overload rate constraint, train running frequency range constraint, interval capacity constraint, station capacity constraint and parameter variable constraint. And the congestion coefficient is quantified according to the differences of different rail traffic systems in the section, the congestion degree of the passengers and the rail traffic system characteristics, the congestion coefficient of the passengers is taken as a main factor influencing the rail traffic service level, the differential characteristics of the regional multi-system rail traffic are accurately mastered, the interests of passengers and operators are comprehensively considered, the congestion coefficient of the passengers and the running cost of the trains are jointly taken as the double targets of the running method programming model to optimize, the differential characteristics of the regional multi-system rail traffic transportation are accurately reflected, and the running scheme of the regional multi-system rail traffic is more refined.
In this embodiment, the method for compiling a running scheme further includes inputting the regional track traffic networking candidate set and the section passenger flow volume as basic data. Specifically, in the embodiment of the present invention, the elements of the alternative set include: train origin-destination, train path, train speed class, train consist, etc. And constructing a train set, an interval set and a station set of the regional multi-system rail transit based on the regional rail transit networked alternative set. Specifically, each element in the train set represents a class 1 train, each class of trains includes a train path (originating, terminating, and all intermediate stations), all sections in which the trains run, and the transit time at each station and the running time at each section, and the train set can be represented by Q, where element L represents a class i train L e Q in the train set, and there are L elements in the set. The interval set is represented by E, wherein the element i represents one interval, i epsilon E, and M elements in the set are shared; the station set is denoted by S, the element j denotes a station, j e S, and there are N elements in the set. Preferably, one section in the section set has one type of track traffic corresponding to it, and the station in the station set has only one type of track traffic corresponding to it.
In this embodiment, the objective function for constructing the double objective of the passenger congestion factor and the train running cost includes an objective function for constructing the minimum passenger congestion factor and an objective function for constructing the minimum train running cost.
In this embodiment, the method for compiling a running scheme further includes obtaining an objective function with a minimum passenger congestion coefficient as a target, specifically, first, dividing regional multi-system rail traffic into a 1 st type rail traffic, a 2 nd type rail traffic and a 3 rd type rail traffic; the multi-system rail transit in the area comprises subways, light rails, tramcars, urban (suburban) railways, inter-urban railways, high-speed railways, common-speed railways and the like, and can be divided into 3 types according to the transportation organization characteristics, specifically, as shown in table 1:
table 1 classification and specification of rail transit of each system
The class 1 rail transit provides high-frequency transportation service, the running speed of a train is lower, the general speed per hour is not higher than 100km/h (kilometer/hour), passengers select the class of rail transit to go out without guiding by taking a train schedule, and the class mainly comprises rail transit systems such as subways, light rails, trams and the like, and the trains are allowed to overtake, and even exceed 20% in part of urban partial sections according to actual operation experience.
The class 2 rail transit mainly comprises urban (suburban) railways and general speed railways, the running frequency of the train is higher, the design speed is lower than 200km/h, passengers travel according to a train schedule, the train is allowed to have a part of overman condition, and the overman condition can be strictly controlled according to ticketing links.
The 3 rd type of rail transit mainly refers to inter-city railways and high-speed railways, the running frequency of trains is high, the speed per hour of the trains can reach more than 200km/h, passengers are strictly arranged to travel according to a train schedule, and overuse is generally not allowed.
Then, based on the regional multi-system track traffic division, calculating the congestion coefficient of any type of track traffic in the regional multi-system track traffic in the section i and the congestion coefficient of the station j in the regional multi-system track traffic; the passenger congestion coefficient comprises an interval congestion coefficient and a station congestion coefficient, and congestion perception of different types of rail transit in the traveling process of the passenger is different to a certain extent. Specifically, overguard is allowed for trains in the class 1 track traffic and the class 2 track traffic, the congestion perception of passengers in the train has a strong correlation with the density of the passenger flow, and the congestion perception is reflected by the density of the passenger flow, so that the classification threshold of no congestion and congestion in the train is 3.6 people/m 2 The classification threshold for congestion and very congestion was 6.2 people/m 2 Further, the classification threshold is converted into a passenger average occupied area threshold, wherein 1/3.6= 0.278,1/6.2=0.161, so that the thresholds of the passenger average occupied areas of no congestion and very congestion in the vehicle are respectively 0.278m 2 Human and 0.161m 2 The congestion factor can then be set as a piecewise function according to the passenger average occupancy area, as shown in fig. 2, the passenger congestion factor satisfies: the occupied area of passenger per capita is more than or equal to 0.278m 2 When per person, the passenger crowding coefficient is 0, and the passenger average occupied area is less than or equal to 0.161m 2 When the congestion coefficient is 1, the occupied area of the passenger is between the two, and the linear relation expression is adopted, so that the congestion coefficients of the class 1 track traffic and the class 2 track traffic in the interval i are satisfied:
(5)
wherein,the passenger average occupied area of the section i is expressed in m 2 Person/person->，/>A parameter representing a linear function of the interval congestion factor. Note that 1 (2) represents k=1 or k=2.
Further specifically, passenger flow passenger average occupied area of section iThe ratio of the average effective area of the train to the average passenger load of the train in interval i:
(6)
Wherein,represents the average effective area of the train in section i, the unit is m 2 ；/>The average passenger carrying number of the trains in the section i is shown, and the average passenger carrying number of the trains in the section i is +.>The method meets the following conditions:
(7)
wherein L represents the number of elements in the train set,represents the frequency of the start of train l, +.>Is a variable of 0 and 1,indicating that the train l operation section includes section i, < >>Indicating that the train i operation section does not include section i,/or->The section passenger flow volume in section i is shown.
In this embodiment, the train in the class 3 track traffic is not allowed to overrun, which means that passengers have seats, the congestion coefficient of the traveling of the passengers is obviously lower than that of the class 1 and class 2 track traffic, the range of the congestion coefficient of the class 3 track traffic is defined as 0-0.5, that is, in the embodiment of the invention, the maximum congestion coefficient of the class 3 track traffic is set as 0.5, the minimum congestion coefficient is set as 0, and the congestion coefficient is in direct proportion to the average full load rate of the train, then the congestion coefficient of the class 3 track traffic in the interval i satisfies:
(8)
wherein,the average full rate of all trains in section i is indicated. Average full rate of all trains in section i +.>Ratio of passenger volume in section i to passenger volume that all trains in section i can offer:
(9)
Wherein L represents the number of elements in the train set,represents the frequency of the start of train l, +.>Is a variable of 0 and 1,indicating that the train l operation section includes section i, < >>Indicating that the train i operation section does not include section i,/or->Indicating the permanent of train l.
In this embodiment, since the station is most significantly crowded with stations, the congestion perception of passengers at stations of different systems is basically similar, and the passenger average occupied area reflects the service level, so that the congestion coefficients are all represented by the passenger average occupied area of the stations. The congestion coefficient of the station can be set as a piecewise function according to the average occupation area of the station, the congestion coefficient corresponding to the average occupation area of the station passenger at the level E of the service level is defined as 1, the congestion coefficient corresponding to the average occupation area of the station passenger at the level A of the service level is defined as 0, namely the average occupation area of the station passenger is larger than or equal to 3.247m 2 When per person, the crowding coefficient is 0, and the average occupied area of platform passengers is less than or equal to 0.464m 2 When the crowding coefficient is 1, the crowding coefficient is expressed by adopting a linear relation between the crowding coefficient and the crowding coefficient, so that the crowding coefficient of the station j in the regional multi-system rail transit meets the following conditions:
(10)
wherein,representing passenger average occupied area of station platform j, with unit being m 2 Person/person->，/>Parameters representing a linear function of the station congestion factor.
Further specifically, the passenger average occupied area of the station platform jThe ratio of the effective area of station j to the average exchange passenger flow of the train at station j:
(11)
wherein,the effective area of the platform of the station j is expressed as m 2 ；/>Representing the average number of exchanges of trains at station j. The average exchanging passenger flow of the train at the station j is that the passenger flow difference value of the section passenger flow of the adjacent section of the station j is multiplied by the exchanging passenger flow coefficient of the station j and then is averaged to each train passing through the station, so that the average exchanging passenger flow of the train at the station j meets the following conditions:
(12)
wherein,representing the exchange passenger flow coefficient of station j, M is the number of elements in the interval set, L is the number of elements in the train set, and +.>Section passenger flow volume of section i +.>Represents the 0,1 variable, ">Starting station indicating section i is j, +.>The origin station representing section i is not j, < > or->Represents the 0,1 variable, ">The terminal station representing section i is j,the terminal station representing section i is not j, < > or->Represents the 0,1 variable, ">Indicating that station j is included in the running path of train l>Indicating that station j is not included in the running path of train l>Indicating the frequency of operation of train l.
In the present embodiment, as shown in fig. 3, the passenger flow volume exchanged at station j in a certain period of timeWhen (I)>Passenger flow difference from the immediate vicinity>In connection with, wherein->Expressed as:
（1）
wherein M is the number of elements in the interval set, L is the number of elements in the train set,section passenger flow volume of section i +.>Represents the 0,1 variable, ">Starting station indicating section i is j, +.>The origin station representing section i is not j, < > or->Represents the 0,1 variable, ">The terminal station representing interval i is j, +.>The end station representing section i is not j.
Then, based on the calculated congestion coefficient of any one of the regional multi-system rail transit in the section i and the congestion coefficient of the station j in the regional multi-system rail transit, an objective function which aims at the minimum of the passenger congestion coefficient is obtained, specifically, the objective function which aims at the minimum of the passenger congestion coefficient is as follows:
(3)
wherein M is the total number of sections in the regional multi-system track traffic, N is the total number of stations in the regional multi-system track traffic, i represents a section, j represents a station,congestion factor indicating interval i, +.>Section passenger flow volume of section i +.>Representing the average running time of the train in section i, < > and >Congestion factor indicating station j, < > j>Representing the average exchange traffic per train in station j,/>Indicating the average stop time of the train at station j.
Finally, the minimized passenger congestion factor can be obtained based on an objective function that minimizes the passenger congestion factor.
In this embodiment, the process of minimizing the congestion coefficient of the regional multi-system track traffic passenger further includes obtaining the congestion coefficient of the section i in the regional multi-system track based on the congestion coefficient of any type of track traffic in the section i in the regional multi-system trackThe method meets the following conditions:
(4)
wherein,representing congestion coefficient of kth type track traffic in regional multi-system track traffic, and +.>Is 0,1 variable, ">Indicating that section i belongs to the kth class of rail traffic, < > and>the section i does not belong to the k-th type of track traffic, and k is 1, 2 and 3.
The congestion coefficients of the sections i are respectively acquired aiming at different types of track traffic, the difference of congestion perception of the track traffic of different types in the traveling process of passengers is comprehensively considered, and finally the congestion coefficients of any section in the regional multi-system track traffic are acquired, so that the calculation of the regional multi-system track traffic congestion coefficients is more universal.
In this embodiment, when the section congestion factor and the station congestion factor are calculated, the passenger flow of the section is evenly distributed to each train, instead of accurately matching the passenger flow of the section to each train.
In this embodiment, the objective function with minimum train running cost as the objective is:
(2)
wherein l represents a first train in regional multi-system rail transit,indicating the frequency of train operation,/->Indicating the running cost of the train l.
In this embodiment, the decision variable is the running frequency of the class i trainWherein->The value range of (2) is the whole natural number, < >>And if not, the first train is started in the research period, otherwise, the first train is started in the research period.
In this embodiment, the passenger travel demand constraint is:
(13)
wherein,represents the frequency of the start of train l, +.>0, 1 variable, ">Indicating that the train l operation section includes section i, < >>Indicating that the train i operation section does not include section i,/or->Represents the driver of train l, +.>Indicating the maximum overload rate allowed for train l, < >>The section passenger flow volume in section i is shown. />
The maximum overload rate allowed by the train l is introduced into the passenger travel demand constraint, so that the fact that the rail transit of various different systems exists in the area is fully considered, and each type of rail transit train has larger difference in the aspects of overtime and overtime proportion, so that the running scheme programming method is more in line with the characteristics of the multi-system rail transit of the area, and the accuracy is higher.
The regional multi-system rail transit overload rate constraint is as follows:
(14)
wherein,indicating the rail traffic to which the train belongs, +.>。
The train running frequency range constraint is as follows:
(15)
wherein,represents the frequency of the start of train l, +.>Representing the minimum frequency of operation of train i capable of operating,/->The maximum operating frequency at which the train l can be operated is indicated.
The interval capability constraint is:
(16)
wherein,represents the frequency of the start of train l, +.>0,1 variable, ">Indicating that the train l operation section includes section i, < >>Indicating that the train i operation section does not include section i,/or->Represents the driver of train l, +.>Indicating the maximum overload rate allowed for train l, < >>Section passenger flow volume of section i +.>Representing the maximum transport capacity of interval i.
The station capability constraint is as follows:
(17)
wherein,represents the frequency of the start of train l, +.>Is 0,1 variable, ">Indicating that station j is included in the running path of train l>Indicating that station j is not included in the running path of train l>Indicating the maximum transport capacity of station j.
The parameter variable constraint is as follows:
(18)
wherein,the running frequency of the train l is represented, and N is the total number of stations (namely the number of elements in a station set) in the regional multi-system rail transit>Is 0,1 variable, " >Indicating that section i belongs to the kth class of rail traffic, < > and>indicating that section i does not belong to the kth class of rail traffic, < > or->Represents the 0,1 variable, ">Starting station indicating section i is j, +.>The origin station representing section i is not j, < > or->0,1 variable, ">Indicating that the train l operation section includes section i, < >>Indicating that the train i operation section does not include section i,/or->Represents the 0,1 variable, ">The running path of the train l includes a station j,indicating that station j is not included in the running path of train l>Represents the 0,1 variable, ">The terminal station representing interval i is j, +.>The end station representing section i is not j. />
The regional multi-system rail transit train running scheme programming method is an objective function taking the passenger congestion coefficient and the train running cost as double targets, namely a double-target planning model, so that the running scheme programming method further comprises the step of solving the objective function taking the passenger congestion coefficient and the train running cost as the double targets based on the target planning method, and specifically comprises the following steps of:
for the objective function with minimum passenger crowding coefficient and the minimum train running costSolving the objective function of the target to obtain corresponding expected values 、/>. Firstly, carrying out optimization solution on a single objective function to obtain an expected value, namely obtaining an optimal target value of each objective function in the running scheme programming method under the single objective function.
Optimizing an objective function construction, and acquiring a double-objective mathematical model of comprehensive running cost and congestion coefficient based on an objective function with minimum passenger congestion coefficient and an objective function with minimum train running cost:
（19）
where p is the p-th priority, q is the q-th objective function,priority factor representing the p-th priority, < ->、/>Weight coefficient representing positive and negative bias variables of different objective functions in the same priority, +.>、/>Respectively, an objective function with the minimum passenger congestion coefficient as an objective function and an objective function with the minimum train running cost as an objective function are respectively compared with corresponding expected values to obtain an objective excess value and an objective deficiency value;
assigning a priority factor and a weight coefficient to the double-target mathematical model, and optimizing the double-target mathematical model as follows:
（20）
wherein,objective function and expectation value targeted at minimum passenger congestion factor>A comparative target deficiency value;is the objective function and the expected value aiming at the minimum train running cost >A comparative target deficiency value; because running cost and congestion coefficient are very important in regional multi-system rail transit operation, in the embodiment of the invention, the priority factor is taken as 1, and the ≡n is adopted as the priority factor>、/>1 is also taken.
Constructing an optimization objective setThe optimized target set meets the objective function with the minimum passenger congestion coefficient as the objective function and the objective function with the minimum train running cost as the objective function respectively:
（21）
（22）
wherein,objective function and expectation value targeted at minimum passenger congestion factor>The target of the phase comparison exceeds the value;is the objective function and the expected value aiming at the minimum train running cost>The target of the phase comparison exceeds the value; />、/>The running cost and the crowding coefficient after the optimization of the double-target mathematical model are respectively;
taking the formulas (4) - (18) and (20) - (22) as constraints of the optimized double-target mathematical model, and adopting a Global server in the Lingo to obtain an optimal solution of the optimized double-target mathematical model.
Adopting Global Sever in Lingo to calculate the optimal solution of the model; the solution obtained at this time is the optimal solution for comprehensively considering the running cost and congestion coefficient of the running scheme and guiding the actual running scheme. Preferably, the solution is appropriately added、/>Is a constraint on the range of values.
For example, as shown in fig. 4, a regional multi-system rail traffic network is exemplified by Chongqing subway 5 wire south section, jiang Tiaoxian and Chongqing section of Chongqing high-speed rail.
Specifically, the Chongqing subway No. 5 south section is class 1 track traffic, the total length is 11.2km (kilometers), jiang Tiaoxian is class 2 track traffic, the total length is 28.22km, the Yukun high-speed rail Chongqing section is class 3 track traffic, the total length is 100km, wherein an area multi-system track traffic network formed by the three sections has 18 stations and 30 sections (up and down, respectively), and Chongqing western stations and jump station are multi-system transfer stations.
The area multi-system rail transit network is correspondingly provided with 20 trains, wherein 8 trains are stopped at a station, and 12 trains are stopped at a large station. The passenger flow rate in the model adopts the section passenger flow rate data of peak hours predicted at the initial stage of each line, namely the section passenger flow rate of each section of the peak hours.
Based on the selected road network, the model data is structured, and a running scheme is obtained by adopting a Global Solver of the Lingo according to the lowest running cost, the lowest congestion coefficient and the double-target optimal solution, wherein the Lingo is a Solver, and the optimal solution can be obtained by converting the model expression into the language of the Lingo one by one and selecting the Global Solver in the Lingo. Further, the dual-objective planning can iterate within 2s to obtain a globally optimal solution. At this time, the minimum value of the running cost is 2133.6 and the minimum value of the congestion factor is 1384.1, but when one target is controlled to be minimum, the number of parties opposing the control is greatly increased. After the double-objective optimization is adopted, the cost and the congestion coefficient are both increased, but the cost fluctuation is controlled within 25%, and the congestion coefficient fluctuation is controlled within 35%.
When the cost is the minimum, the 13% interval full rate exceeds 1, and the 40% interval full rate is more than or equal to 0.7. And when the minimum congestion coefficient is taken as a target, the obtained trains are close to the maximum departure frequency, and the full load rate of most sections is lower than 0.5. After the double-objective optimization is adopted, the interval full load rate of 13% of peak hours is between 0.7 and 1, and the interval full load rate of more than half is lower than 0.5.
After the train running cost and the congestion coefficient are comprehensively optimized, 85 trains of trains are jointly run in peak hours, the average running distance of the trains is reduced to 33.3km, the running frequency is improved, and the speed of the turnover of the trains is increased.
As shown in fig. 5, the embodiment of the invention also introduces a regional multi-system rail transit train running scheme compiling system, which can execute the regional multi-system rail transit train running scheme compiling, specifically, the running scheme compiling system comprises a construction module and a determination module, wherein the construction module is used for constructing an objective function taking a passenger congestion coefficient and train running cost as double targets; the determination module is used for determining decision variables and one or more of the following constraints: passenger travel demand constraint, regional multi-system rail transit overload rate constraint, train running frequency range constraint, interval capacity constraint, station capacity constraint and parameter variable constraint. The specific content, decision variables and one or more constraint conditions of the objective function are consistent with those in the above-mentioned open programming, and will not be described in detail herein.
The regional multi-system rail transit train running scheme is compiled by comprehensively considering benefits of passengers and operators, and the passenger congestion coefficient and the train running cost are jointly used as double targets of a running method compiling model to optimize, so that the differential characteristics of regional multi-system rail transit transportation are accurately reflected, and the regional multi-system rail transit running scheme is more refined.
Although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (17)

1. A regional multi-system rail transit train operation scheme programming method is characterized in that the operation scheme programming method comprises the steps of,
constructing an objective function taking the passenger congestion coefficient and the train running cost as double targets, wherein the objective function comprises an objective function taking the minimum passenger congestion coefficient as a target and an objective function taking the minimum train running cost as a target, and the objective function taking the minimum passenger congestion coefficient as a target is as follows:
（1）
Wherein M is the total number of sections in the regional multi-system track traffic, N is the total number of stations in the regional multi-system track traffic,
i represents a section, j represents a station,congestion factor indicating interval i, +.>Section passenger flow volume of section i +.>Representing the average running time of the train in section i, < > and>congestion factor indicating station j, < > j>Representing the average exchange traffic per train in station j,/>Representing the average stop time of the train at the station j;
the objective function with the minimum train running cost as the objective is as follows:
（2）
wherein,Lthe number of elements in the train set is represented,representing +.f. in regional multisystem rail transit>Train-like, or->Indicating +.>Is>Indicating +.>Running cost of (2);
determining decision variables and one or more of the following constraints:
passenger travel demand constraint, regional multi-system rail transit overload rate constraint, train running frequency range constraint, interval capacity constraint, station capacity constraint and parameter variable constraint.
2. The method for programming regional multi-system rail transit train operation scheme according to claim 1, further comprising inputting a regional rail transit networked candidate set and section passenger flow volume as basic data, wherein the method comprises,
Constructing a train set, an interval set and a station set of the regional multi-system track traffic based on the regional track traffic networking alternative set, wherein,
the train set is represented by Q, the elementsRepresenting the%>Train-like, or->E, Q, L elements in the train set;
the interval set is represented by E, the element i represents one interval, i epsilon E, and M elements in the interval set are all contained;
the station set is denoted by S, the element j denotes a station, j epsilon S, and N elements are in the station set.
3. The method for programming the regional multi-system rail transit train operation scheme according to claim 2, wherein the operation scheme programming method further comprises the steps of,
dividing regional multi-system track traffic into class 1 track traffic, class 2 track traffic and class 3 track traffic;
based on regional multi-system track traffic division, calculating the congestion coefficient of any type of track traffic in regional multi-system track traffic in section i and the congestion coefficient of station j in regional multi-system track traffic;
and acquiring an objective function with the minimum passenger congestion coefficient as a target based on the calculated congestion coefficient of any type of the regional multi-system track traffic in the section i and the congestion coefficient of the station j in the regional multi-system track traffic.
4. The method for programming a regional multi-system rail transit train operation scheme according to claim 3, wherein calculating congestion coefficients of class 1 and class 2 rail transit in the regional multi-system rail transit in section i comprises,
acquiring the average effective area of the train and the average passenger carrying number of the train in the interval i;
based on the average effective area of the trains and the average passenger carrying number of the trains in the interval i, calculating the passenger average occupied area of the interval i;
and acquiring congestion coefficients of the class 1 track traffic and the class 2 track traffic in the section i based on the passenger average occupied area of the section i.
5. The method for programming a regional multi-system rail transit train operation scheme according to claim 4, wherein calculating the congestion factor of the class 3 rail transit in the regional multi-system rail transit in the section i comprises,
acquiring the passenger flow in a section i and the passenger capacity which can be provided by all trains in the section i;
acquiring the average full rate of all trains in the section i based on the passenger flow in the section i and the passenger capacity which can be provided by all trains in the section i;
and (3) averaging the average full load rates of all trains in the section i to obtain the congestion coefficient of the class 3 track traffic in the section i.
6. The method for programming a regional multi-system rail transit train operation scheme of claim 5, wherein calculating the congestion factor of the station j in the regional multi-system rail transit comprises,
acquiring a difference value of the passenger flow volume of the section of the adjacent section of the station j and a passenger flow coefficient exchanged by the station j;
obtaining the product of the difference value of the section passenger flow volume of the adjacent section of the station j and the coefficient of the passenger flow volume exchanged by the station j, and averaging the product to each train passing through the station j to obtain the average passenger flow volume exchanged by the train at the station j;
acquiring the effective area of a station j platform;
the ratio of the effective area of the station j platform to the average exchange passenger flow of the train at the station j is obtained, and the passenger average occupied area of the station j platform is obtained;
and acquiring the congestion coefficient of the station j in the regional multi-system rail transit based on the passenger average occupied area of the station j station.
7. The regional multi-system rail transit train operation scheme programming method as claimed in claim 6, wherein the region
Congestion factor of mThe method meets the following conditions:
（3）
wherein,representing congestion coefficient of kth type track traffic in regional multi-system track traffic in section i,/>Is set to be 0, the number of the components is set to be 0,
the variable number 1 is used to determine,indicating that section i belongs to the kth class of rail traffic, < > and >The section i does not belong to the k-th type of track traffic, and k is 1, 2 and 3.
8. The method for programming a regional multi-system rail transit train operation scheme according to claim 7, wherein,
the congestion coefficients of the class 1 track traffic and the class 2 track traffic in the section i satisfy:
（4）
wherein,the passenger flow passenger average occupied area of the section i is represented by m 2 Person/person->， />Linear function representing interval crowding coefficientParameters of (2); and passenger flow passenger average occupied area of interval i +.>The ratio of the average effective area of the train to the average passenger load of the train in interval i:
（5）
wherein,represents the average effective area of the train in section i, the unit is m 2 ；/>Representing average load of trains in section i
The number of passengers, and satisfies:
（6）
wherein L represents the number of elements in the train set,indicating +.>Is>0, 1 variable, ">Indicating that the train l operation section includes section i, < >>Indicating +.>The operating interval does not include interval i->The section passenger flow volume of the section i is represented;
the congestion coefficient of the type 3 track traffic in the section i satisfies:
（7）
wherein,representing the average full load rate of all trains in the section i; and the average full rate of all trains in section i +.>Is that
Ratio of passenger volume in section i to passenger volume that all trains in section i can offer:
（8）
Wherein L represents the number of elements in the train set,indicating +.>Is>0, 1 variable, ">Indicating that the train l operation section includes section i, < >>Indicating +.>The operating interval does not include interval i->Representing a trainIs a member of the order;
the congestion coefficient of the station j in the regional multi-system rail transit meets the following conditions:
（9）
wherein,representing passenger average occupied area, m of station platform j 2 Person/person->，/>Congestion coefficient line for representing station
Parameters of the sexual function; and passenger average occupied area of station platform jIs the effective area of station j platform and station j
Ratio of average exchange traffic of trains:
（10）
wherein,the effective area of the platform of the station j is expressed as m 2 ；/>Mean switch passenger representing train at station j
The average exchange passenger flow of the train at the station j is obtained by multiplying the passenger flow difference value of the section passenger flow of the adjacent section of the station j by the exchange of the station j
The passenger flow coefficient is averaged to each train passing through the station, and the average exchange passenger flow of the train of station j meets the following conditions:
（11）
wherein,representing the passenger flow coefficient of station j exchange passenger flow, M is the number of elements in the interval set, L is the number of elements in the train set, and +.>Section passenger flow volume of section i +. >Represents the 0,1 variable, ">Starting station indicating section i is j, +.>The origin station representing section i is not j, < > or->Represents the 0,1 variable, ">The terminal station representing interval i is j, +.>The terminal station representing section i is not j, < > or->Represents the 0,1 variable, ">Indicating +.>The running path of (a) comprises station j, & lt + & gt>Indicating that station j is not included in the running path of train l>Indicating +.>Is a frequency of opening of the display.
9. The regional multi-system rail transit train operation scheme programming method according to any one of claims 1-8, wherein the passenger travel demand constraint is:
（12）
wherein,indicating +.>Is>0,1 variable, ">Indicating +.>The operation interval comprises interval i, ">Indicating +.>The operating interval does not include interval i->Indicating +.>Is (are) staffed by (are)>Indicating +.>Maximum overload rate allowed, +_>The section passenger flow volume in section i is shown.
10. The regional multi-system rail transit train operation scheme programming method of claim 9, wherein the regional multi-system rail transit overload rate constraint is:
（13）
wherein,indicating the rail traffic to which the train belongs, +.>。
11. The regional multi-system rail transit train operation scheme programming method of claim 10, wherein the train operation frequency range constraint is:
（14）
Wherein,indicating +.>Is>Indicating +.>Minimum frequency of opening that can be opened, < ->Indicating +.>Maximum line frequency at which lines can be opened.
12. The regional multi-system rail transit train operation scheme programming method of claim 11, wherein the interval capacity constraint is:
（15）
wherein,indicating +.>Is>0,1 variable, ">Indicating +.>The operation interval comprises interval i, ">Indicating +.>The operating interval does not include interval i->Indicating +.>Is (are) staffed by (are)>Indicating +.>Maximum overload rate allowed, +_>Section passenger flow volume of section i +.>Representing the maximum transport capacity of interval i.
13. The regional multi-system rail transit train operation scheme programming method of claim 12, wherein the station capability constraint is:
（16）
wherein,indicating +.>Is>Is 0,1 variable, ">Indicating +.>The running path of (a) comprises station j, & lt + & gt>Indicating +.>Station j, -is not included in the travel path of (a)>Indicating the maximum transport capacity of station j.
14. The regional multi-system rail transit train operation scheme programming method of claim 13, wherein the parameter variable constraints are:
（17）
Wherein N is the total number of stations in the regional multi-system track traffic,is 0,1 variable, ">Representation intervaliBelonging to the firstkRail-like traffic->Representation intervaliNot of the first kindkRail-like traffic->Represents the 0,1 variable, ">Representation intervaliThe starting station isj，/>Representation intervaliThe starting station is notj，/>0,1 variable, ">Indicating +.>The operation section includes a sectioni，/>Indicating +.>The operation interval does not include an intervali，/>Represents the values of the 0,1 variables,indicating +.>Including stations in the path of travel of (a)j，/>Indicating +.>Station is not included in the path of travel of (a)j，Represents the 0,1 variable, ">Representation intervaliStation at the end of (a)j，/>Representation intervaliIs not at the end ofj。
15. The regional multi-system rail transit train operation scheme programming method of claim 14, wherein the decision variable is an operation frequency of a class i trainWherein, the method comprises the steps of, wherein,
the value range of (2) is the whole natural number, < >>When the first train is not running, otherwise, the first train is representedClass trains are launched within the study period.
16. The method for programming regional multi-system rail transit train operation scheme according to claim 15, further comprising,
respectively solving an objective function with the minimum passenger congestion coefficient as a target and an objective function with the minimum train running cost as a target to obtain corresponding expected values 、/>；
Optimizing an objective function construction, and acquiring a double-objective mathematical model of comprehensive running cost and congestion coefficient based on an objective function with minimum passenger congestion coefficient and an objective function with minimum train running cost:
（18）
where p is the p-th priority, q is the q-th objective function,priority factor representing the p-th priority, < ->、Weight coefficient representing positive and negative bias variables of different objective functions in the same priority, +.>、/>Respectively, an objective function with the minimum passenger congestion coefficient as an objective function and an objective function with the minimum train running cost as an objective function are respectively compared with corresponding expected values to obtain an objective excess value and an objective deficiency value;
assigning a priority factor and a weight coefficient to the double-target mathematical model, and optimizing the double-target mathematical model as follows:
（19）
wherein,objective function and expectation value targeted at minimum passenger congestion factor>A comparative target deficiency value; />Is the objective function and the expected value aiming at the minimum train running cost>A comparative target deficiency value;
constructing an optimization objective setThe optimized target set meets the objective function with the minimum passenger congestion coefficient as the objective function and the objective function with the minimum train running cost as the objective function respectively:
（20）
（21）
Wherein,objective function and expectation value targeted at minimum passenger congestion factor>The target of the phase comparison exceeds the value; />Is the objective function and the expected value aiming at the minimum train running cost>The target of the phase comparison exceeds the value; />、/>The running cost and the crowding coefficient after the optimization of the double-target mathematical model are respectively;
taking formulas (3) - (11), (12) - (17), (19) - (21) as constraints of the optimized double-target mathematical model, and adopting Global valve in Lingo to calculate the optimal solution of the optimized double-target mathematical model.
17. The regional multi-system rail transit train operation scheme programming system is characterized in that the operation programming system can execute the regional multi-system rail transit train operation scheme programming method of any one of 1-16, comprising,
the construction module is used for constructing an objective function taking the passenger congestion coefficient and the train running cost as double targets;
a determining module for determining decision variables and one or more of the following constraints:
passenger travel demand constraint, regional multi-system rail transit overload rate constraint, train running frequency range constraint, interval capacity constraint, station capacity constraint and parameter variable constraint.
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