A train operation plan compiling method for Y-shaped metro line in flexible marshalling mode

Abstract

The application discloses a kind of Y type subway line train operation plan compilation methods under flexible marshalling mode, including construction integrated optimization model and solving algorithm, the establishment method of the optimization model includes defining decision variable, formulating constraint condition, and establishing target function.The application provides a kind of Y type subway line train operation plan compilation methods under flexible marshalling mode, by using the model and algorithm of the present application, under the condition of known passenger flow demand, the train timetable prepared can make the waiting time of passenger in system shorter, improve passenger service quality;Under the premise of guaranteeing passenger service quality, it can make the train consist used in system within specified time range less, save the fixed cost of car bottom;The model and algorithm established have strong development space, can adapt to other types of subway line train operation plan optimization.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of railway transport organization, and particularly relates to a train operation plan compilation method for Y-shaped metro lines under a flexible marshalling mode. BACKGROUND

[0002] In a city rail transit system, in order to reduce the operation complexity, the metro lines are usually in a linear structure, and the metro trains running in the lines are usually in a fixed marshalling. However, this operation mode has two major shortcomings: one is that some passengers need to change several times to complete their travel demand; the other is that the operator can only change the supply of train seats by adjusting the train departure time interval, and it is difficult to realize the accurate matching of supply and demand under the premise of ensuring the quality of passenger service. SUMMARY

[0003] The main purpose of the present application is to provide a train operation plan compilation method for Y-shaped metro lines under a flexible marshalling mode to overcome the shortcomings in the prior art.

[0004] To achieve the above-mentioned purposes, the technical scheme adopted by the present application comprises:

[0005] The present application provides a train operation plan compilation method for Y-shaped metro lines under a flexible marshalling mode, which comprises constructing an integrated optimization model and a solving algorithm. The method for constructing the optimization model comprises defining decision variables, formulating constraint conditions, and establishing an objective function. The solving algorithm method comprises first establishing a framework according to an adaptive large neighborhood search algorithm, then designing an algorithm according to the established framework to obtain the value of the objective function. Wherein,

[0006] The formula of the objective function is

[0007]

[0008] In the formula, α and β are weight coefficients of the total waiting time of passengers and the total number of car use, respectively,

[0009] If passenger p boards the car serving path r in the i-th train, then variable z p，i，r = 1; if passenger p does not board the car serving path r in the i-th train, then variable z p，i，r = 0; variable o i，s is the number of cars provided by the vehicle depot near station s in train i;

[0010] t p is the arrival time of passenger p, is the departure time of the i-th train from the departure station o pThe time of departure, P is the set of all passengers, I is the set of all trains, R is the set of all paths, the last station of the main / secondary branch line and the first station of the trunk line can be turned back, and the three stations are defined as turn-back stations, S ts is the set of turn-back stations.

[0011] Further, the decision variables include whether the train i is recombined / disassembled at the connecting station, whether the train i is operated by the recombined train when running on the trunk line, the departure time of the train i at the station s, the arrival time of the train i at the station s, the number of the train i in which the train i' is turned back at the station s, the number of the train i directly entering the nearby vehicle depot, the number of the train i provided by the nearby vehicle depot, and whether the passenger p boards the train i serving the path r.

[0012] Further, the parameters in the framework include the scores and weights of the destruction operator / repair operator.

[0013] Further, the solving process in the framework is divided into an asynchronous layer and a global layer. In the asynchronous layer, each thread is assigned an iteration task, and in each iteration, the destruction operator and the repair operator are executed in sequence on the current solution to obtain a new solution. When all tasks in the asynchronous layer are completed, the generated new solution forms a solution pool, and the solution pool is returned to the global layer. In the global layer, each solution in the solution pool is compared with the known optimal solution and the current solution, and then the solution and the parameters of the algorithm are updated according to the quality of the solution and the adaptive rule.

[0014] Further, the algorithm design includes formulating the feasibility proposition, generating the initial solution, operator design, passenger flow allocation, adaptive strategy, and algorithm termination condition.

[0015] Further, the feasibility proposition includes converting the train running time throughout the journey to τ tr , the minimum train bottom turn-back time to τ turn , T s is the start time of the considered time range, T e is the end time of the considered time range, then only the down train departing in the down side line time range [T s , T e -2τ tr -τ turn ] and the up train departing in the up side line time range [T s +τ tr +τ turn , T e -τ tr ] can be selected as the conversion train.

[0016] Further, the feasibility proposition includes the minimum number of train sets passing through the line l is

[0017]

[0018] where Count{x} is the counting function; Max{x} is the maximum function; Ceil{x} is the floor function; S l is the set of stations for a line l; L is the set of main line, main branch line and sub-branch line; Cap represents the seat capacity of a train set; represents the set of passengers passing through interval s, |S l represents the set S l The number of elements contained in the set.

[0019] Further, the feasibility proposition includes the latest train in the time range [T s , T e -2τ tr -τ turn ] on the down side track must satisfy

[0020]

[0021] where, is the minimum number of train sets passing through the sub-branch line in the down direction, calculated by the above feasibility proposition; is the total number of trains in the down direction; h min is the minimum headway time.

[0022] Further, the feasibility proposition includes the earliest train in the time range [T s +τ tr +τ turn , T e -τ tr ] on the up side track must satisfy

[0023]

[0024] where, is the minimum number of train sets passing through the sub-branch line in the up direction, calculated by the above feasibility proposition; is the total number of trains in the up direction.

[0025] Further, the passenger flow allocation includes using a simulation-based method to allocate passenger flow to corresponding train sets according to the first-come-first-served principle after the train operation timetable is determined.

[0026] Further, the termination condition of the algorithm includes:

[0027] the number of iterations or the calculation time reaches the preset maximum value; or

[0028] The time to search for the next better solution reaches a preset maximum value.

[0029] Compared with the prior art, the advantages of the present application include:

[0030] The present application provides a train operation plan compilation method for Y-type metro line in flexible marshalling mode. Through the model and algorithm of the present application, under the condition of known passenger flow demand, the train timetable compiled can make the waiting time of passengers in the system shorter, and improve the passenger service quality. Under the premise of ensuring the passenger service quality, the system can use fewer train sets within the specified time range, saving the fixed cost of train bottom. The objective function and algorithm established have strong expansion space, and can adapt to the train operation plan optimization of other types of metro lines (network). BRIEF DESCRIPTION OF DRAWINGS

[0031] Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The accompanying drawings are included to provide a description of the preferred embodiments and are not intended to limit the scope of the application. Furthermore, the same reference numerals are intended to denote the same components throughout the accompanying drawings. In the drawings:

[0032] Figure 1 is a schematic diagram of a Y-type metro line in an exemplary embodiment of the present application;

[0033] Figure 2 is a schematic diagram of reconnection / disconnection of train sets at a connection station in an exemplary embodiment of the present application;

[0034] Figure 3 is a schematic diagram of arrival of train sets at a turnaround station in an exemplary embodiment of the present application;

[0035] Figure 4 is a schematic diagram of departure of train sets from a turnaround station in an exemplary embodiment of the present application;

[0036] Figure 5 is a solution framework of the algorithm in an exemplary embodiment of the present application;

[0037] Figure 6 is a pseudo code of passenger flow distribution process in an exemplary embodiment of the present application;

[0038] Figure 7 is a line diagram of Guangzhou Metro Line 14 in an exemplary embodiment of the present application;

[0039] Figure 8a is a schematic diagram of passenger flow under peak passenger flow in an exemplary embodiment of the present application;

[0040] Figure 8bis a passenger flow schematic diagram under uniform passenger flow in an exemplary embodiment of the present application;

[0041] Figure 8c is a passenger flow schematic diagram under extreme passenger flow in an exemplary embodiment of the present application;

[0042] Figure 9a is an operation strategy under peak passenger flow in an exemplary embodiment of the present application;

[0043] Figure 9b is an operation strategy under uniform passenger flow in an exemplary embodiment of the present application;

[0044] Figure 9c is an operation strategy under extreme passenger flow in an exemplary embodiment of the present application. DETAILED DESCRIPTION

[0045] The present application will be further described in conjunction with specific embodiments, and the embodiments provided below are only for the purpose of illustrating the present application, and are not intended to limit the scope of the present application. The embodiments provided below can serve as a guide for further improvement by those of ordinary skill in the art, and do not in any way constitute a limitation on the present application.

[0046] One aspect of an embodiment of the present application provides a train operation plan compilation method for a Y-type metro line under a flexible marshalling mode, comprising constructing an integrated optimization model and a solution algorithm, the method for constructing the optimization model comprising defining decision variables, formulating constraint conditions, and establishing an objective function; wherein,

[0047] The formula of the objective function is

[0048]

[0049] In the formula, α and β are weight coefficients of total passenger waiting time and total number of car sets respectively,

[0050] If passenger p boards a car set serving path r in the i-th train, then variable z p，i，r = 1; if passenger p does not board a car set serving path r in the i-th train, then variable z p，i，r = 0; variable o i，s is the number of car sets provided by a vehicle depot near station s in train i;

[0051] t p is the arrival time of passenger p, is the departure time of the i-th train from the origin station o p of passenger p, S ts is a set of turnaround stations, P is a set of all passengers, I is a set of all trains, and R is a set of all paths.

[0052] The decision variables include whether the train i is to be recombined / disassembled at the junction station, whether the train i is to be operated by the recombined train when running on the main line, the departure time of the train i at the station s, the arrival time of the train i at the station s, the number of the train i in which the train i' is turned back at the station s, the number of the train i directly entering the nearby depot of the station s, the number of the train i provided by the nearby depot of the station s, and whether the passenger p boards the train i serving the path r.

[0053] The application provides a train operation plan compiling method for a Y-type subway line in a flexible marshalling mode.

[0054] The technical solutions of the application are described in detail below with reference to the drawings.

[0055] 1, Application scenario

[0056] Y-type subway line: Figure 1 A Y-type subway line composed of a main line, a main branch line and a secondary branch line is given. The set of the three parts of the line is denoted as L, and the set of all stations is denoted as S, wherein the set of stations of a line l is denoted as The first station of the main / secondary branch line and the last station of the main line correspond to the same station in practice, which is defined as a junction station, and the set is denoted as S js The last station of the main / secondary branch line and the first station of the main line can be turned back, and the three stations are defined as turn-back stations, and the set is denoted as S ts A depot is usually set near the turn-back station to provide train sets for the train operation plan. In addition, the direction from the main line to the branch line is defined as the down direction, and vice versa. Correspondingly, the set of down trains is denoted as The set of up trains is denoted as The set of all trains is denoted as I.

[0057] Flexible marshalling technology: The flexible marshalling technology can change the marshalling form of the train through rapid recombination / disassembly, so as to effectively cope with the spatial passenger flow imbalance phenomenon. Figure 2 The marshalling change of the train in the journey is shown, wherein the recombination / disassembly operation can only be performed at the junction station. Figure 3 The marshalling change of the train in the journey is shown, wherein the recombination / disassembly operation can only be performed at the junction station. Figure 4 The marshalling change of the train at the turn-back station is shown, whereinFigure 3 This means that when a train arrives at the turnaround station, its trainset can partially return to the depot and partially turn around. Figure 4 This explains that when a train departs from a turnaround station, its trainset can come partly from the depot and partly from the trainsets arriving in the opposite direction.

[0058] Passenger demand: within the time range T = [T s T e The passenger flow demand within the system is known, and the set of all passengers in the system is represented by P. Each passenger p is described by three attributes: origin station o. p Arrival station d p and the time t to enter the system p Because passenger tickets in the subway system are not tied to train seats, passengers on the same route are always served on a first-come, first-served basis.

[0059] The key technology of this model lies in combining flexible train formation technology with Y-shaped metro lines to integrate and optimize train timetables and train turnaround plans. Given the number of trains required and passenger demand within the operating time range of a Y-shaped metro line, the model determines the train timetable, train formation, and train turnaround plan to balance service quality and cost, with the goal of reducing passenger waiting time and the number of train sets used.

[0060] 2. Define decision variables

[0061] x i If train i is reconnected / disconnected at the connecting station, then x i =1; otherwise, x i =0.

[0062] y i If train i is operated by a coupled trainset on the main line, then y i =1; otherwise, y i =0.

[0063] The departure time of train i at station s.

[0064] The arrival time of train i at station s.

[0065] c i，i′，s : The number of trains in train i whose train i′ turns back at station s.

[0066] e i，s The number of trains in train i that directly enter the depot near station s.

[0067] o i，s The number of trains in train i supplied by the depot near station s.

[0068] z i，p，r If passenger p boards the train set of service path r in the i-th train, then z i，p，r = 1; otherwise, z i，p，r = 0.

[0069] 3. Formulate constraints

[0070] The following part of constraints is only shown in the down direction, and similar derivation can be done for the up direction.

[0071]

[0072]

[0073]

[0074]

[0075] Formulas (1)-(5) are train operation related constraints. Formula (1) guarantees that the departure interval time of two consecutive trains at the same station is not less than h min , which is usually given by the comprehensive consideration of line grade and train set type, etc. Formulas (2)-(4) derive the arrival and departure time of each train at each station according to the stop time and the interval running time, where denotes the running time of the train in the interval [s, s+1], denotes the stop time of the train at station s, τ cd denotes the time required for the train to be reconnected / disconnected in transit. Formula (5) indicates that the departure time of the train at the junction station is the same.

[0076] Formulas (6)-(8) are train marshalling related constraints, and a set of auxiliary variables μ i，s，r denotes the number of train sets that can serve path r for train i at station s. Formula (6) indicates that the transfer train always provides a set of train sets that pass through the station on the secondary path, where the parameter η s，2 = 1 indicates that station s is on the secondary path, and vice versa. Formula (7) indicates that the number of train sets provided by each train for the main path is equal to the total number of train sets when it runs on the main line minus the number of train sets on the secondary path, and the parameter η s，1 is similar to η s，2 , which takes the value of 1 when station s is on the main path, and vice versa. Formula (8) stipulates that the transfer train is always reconnected marshalling when it runs on the main line.

[0077] Equations (9)-(14) are the constraints related to the train consist circulation plan. Equations (9) and (10) indicate that the consist of a departure train is always turned back at the opposite station or provided by the yard, where parameter ξ s =1 means that the turnaround station s is equipped with a yard, and vice versa. Equations (11) and (12) indicate that the consist of a terminal train will always be turned back at the station to perform the opposite train or return to the yard. A set of train turnaround condition auxiliary variables ρ i，i′，s is introduced, where ρ i，i′，s =1 means that the consist of train i can be turned back immediately at station s and then perform train i'. Equation (13) indicates that the minimum turnaround time τ turn must be satisfied between the two trains whose consists are turned back. Equation (14) indicates that the actual number of turns of a consist can only be positive between two trains whose turnaround conditions are satisfied, where M is a sufficiently large positive number.

[0078] Equations (15)-(26) are the constraints related to the passenger flow assignment. In this part, auxiliary variables v pi are introduced, where v pi =1 means that passenger p satisfies the boarding condition of train i in the time dimension, and vice versa. Equations (15) and (16) indicate that a passenger satisfies the boarding condition of a train when the passenger arrives at the station before the train departs from the station, and vice versa, where t p represents the arrival time of passenger p at station s, and t r represents the set of passengers departing from station s. Equation (17) indicates that a passenger can only board a consist of a train when the passenger satisfies the boarding condition, and vice versa. Equation (18) indicates that a passenger can only board a unique consist. Equation (19) specifies that a main path passenger and a secondary path passenger can only choose a consist that matches their own travel path, where P r represents the set of non-trunk passengers whose travel paths match consist path r. Equations (20) and (21) indicate the first-come-first-served principle in the time dimension, where equation (20) indicates that a first-arriving trunk passenger always has priority to board, and equation (21) indicates that a first-arriving main path or secondary path passenger always has priority to board over passengers whose paths match their own, where P t′ represents the set of passengers arriving at time t', Equations (22) and (23) represent the first-come-first-served principle of passengers in the spatial dimension, and parameter Cap represents the seat capacity of a trainset. Equation (22) represents that a priority-arriving trunk passenger will board if there is a spare seat in any trainset of the train arriving at the station, and equation (23) represents that a priority-arriving passenger matching a path will board if there is a spare seat in the trainset of the path of the train arriving at the station. Equation (24) is a trainset capacity constraint, which stipulates that the number of passengers on each trainset cannot exceed the trainset capacity in any section along the way.

[0079] Equations (25) and (26) are two sets of additional constraints, wherein equation (25) stipulates that the turnaround direction of a train at a turnaround station is related to the actual running direction of the train, and equation (26) limits passengers to only being able to board a train running in the same direction as the direction of their travel path.

[0080] 4. Constructing the objective function

[0081] The present application aims to ensure passenger service quality and save the input cost of trainsets. Therefore, the objective function is composed of two parts, which are minimizing the total waiting time of passengers and minimizing the total number of trainsets used. The dual objectives are processed by the linear weight method, and the objective function is as shown in equation (27)

[0082]

[0083] Wherein α and β represent the weights of the two parts of the objective function, respectively.

[0084] The solving method provided by the present application is a self-adaptive large neighborhood search algorithm, which mainly includes two parts. The first part improves the classical framework of the self-adaptive large neighborhood search algorithm by introducing an asynchronous computing mechanism, and the second part designs the corresponding algorithm for the problem to be solved.

[0085] (1) Algorithm framework

[0086] The solving framework of the algorithm is as shown in Figure 5 According to the classical framework of the self-adaptive large neighborhood search algorithm, the parameters set in the present algorithm include the scores (θ d / θ r ) and weights of the destruction operator / repair operator. Furthermore, a simulated annealing mechanism is introduced to avoid the solution from getting trapped in local optima, by introducing two parameters: temperature (tem) and probability (prob). Unlike classic frameworks, this framework divides the solution process into an asynchronous layer and a global layer. In the asynchronous layer, each defined thread is assigned an iterative task. In each iteration, the destruction operator and the repair operator are executed sequentially on the current solution to obtain a new solution. When all tasks in the asynchronous layer are completed, the generated new solutions form a solution pool and are returned to the global layer. In the global layer, each solution in the solution pool is compared with the known optimal solution and the current solution, and then the algorithm's solution and parameters are updated according to the quality of the solution and adaptive rules.

[0087] (2) Algorithm Design

[0088] ① Feasibility proposition

[0089] To ensure the feasibility of the solution, the following feasibility proposition is formulated.

[0090] Proposition 1: Let τ be the total travel time of the changing train. tr The minimum time for the undercarriage to turn around is τ. turn T s T is the start time of the considered time range. e For the end time of the considered time range, then only in the downlink lateral time range [T] s T e -2τ tr -τ turn The departure of the downline train and the time range on the upline siding [T] s +τ tr +τ turn T e -τ tr The departing train can be selected as a transfer train.

[0091] Proposition 2: The minimum number of train sets required to pass through line l is

[0092]

[0093] Where Count{x} is the counting function; Max{x} is the maximum value function; Ceil{x} is the floor function; S l L is the set of stations on a line l; L is the set of three parts of a line: main line, main branch line, and secondary branch line; Cap represents the seating capacity of a train set. Let P represent the set of passengers passing through interval s, |S l | represents set S l The number of elements contained in a species.

[0094] Proposition 3: Downward lateral line time range [T] s Te -2τ tr -τ turn the latest train in the range of [T must satisfy

[0095] where, is the minimum number of train sets passing through the branch line in the down direction, which is calculated by Proposition 2; is the total number of trains in the down direction; h min is the minimum headway time.

[0096] Proposition 4: the time range of the up side line [T s +τ tr +τ turn , T e -τ tr the earliest train in the range of [T must satisfy

[0097] where, is the minimum number of train sets passing through the branch line in the up direction, which is calculated by Proposition 2; is the total number of trains in the up direction.

[0098] ② Initial solution generation

[0099] Before introducing the initial solution generation step, first introduce Lemma 1 to illustrate the feasibility of the generated initial solution in formulating the car bottom turnover plan.

[0100] Lemma 1: If the total number of trains departing in the down / up side line time range is and the headway time between up / down trains is where

[0101]

[0102]

[0103] then a feasible solution containing N for the converted train can always be generated, where

[0104] Proof: It is specified that the stopping time of the train at the turnaround station is zero, that is, the arrival time of the train at the turnaround station is equal to the departure time. In this case, we discuss two cases:

[0105] Case 1: If then Let represent the i-th train

[0106] Subtracting the two equations gives:

[0107]

[0108] Case 2: If then there is Let denote the arrival or departure time of the i-th column train in the reverse order at the station , then there is

[0109]

[0110] Subtracting the two equations, we get

[0111]

[0112] In summary, when selecting N for the conversion train (if ) or N for the conversion train (if ) in the reverse order, the train bottom turnaround time is always not less than the minimum turnaround time, i.e. the train bottom turnaround plan is always feasible. Therefore, Lemma 1 is proved.

[0113] Therefore, the steps of generating the initial solution are summarized as follows:

[0114] Step 1: According to Proposition 3 and Proposition 4, randomly select two trains as and

[0115] Step 2: All down / up trains departing within the down / up siding time range depart at uniform intervals;

[0116] Step 3: All trains are operated by reconsistencing when running on the main line;

[0117] Step 4: Select the conversion train according to Lemma 1.

[0118] ③ Operator design

[0119] Exploring other solutions in the neighborhood of the current solution by destroying and repairing operators is the basic idea of the adaptive large neighborhood search algorithm.

[0120] The core task of the algorithm designed in the present invention is to explore a reasonable timetable and train bottom turnaround plan, and the corresponding operator design is as follows.

[0121] Destroying operator 1: randomly change and

[0122] The operation procedure of this operator is the same as the steps of generating the initial solution.

[0123] Destroy operator 2: Randomly change the number of conversion trains.

[0124] In this operator, a train is randomly selected. If the selected train is a conversion train, it and the train in the current solution that has a car connection with it at the sidings are changed to be ordinary trains. If the selected train is an ordinary train, an opposite ordinary train that satisfies the car connection condition with the selected train at the sidings is selected, and the two trains are changed to be conversion trains.

[0125] Destroy operator 3: Randomly change the consist of an ordinary train.

[0126] In this operator, an ordinary train is randomly selected, and if its consist is a heavy consist, it is changed to be a single consist; otherwise, it is changed to be a heavy consist.

[0127] Destroy operator 4: Randomly shift the arrival / departure time of a train.

[0128] In this operator, a train is randomly selected, and its running line is shifted forward or backward. Note that after the shift, the minimum headway requirement with the trains before and after it needs to be satisfied, and the car connection condition in the current solution cannot be violated.

[0129] Repair operator 1: Reduce the maximum turnaround time of a car at the sidings.

[0130] If the turnaround time of a consist is too long, the turnover efficiency of the consist will decrease, and thus the number of consis used will increase. In this operator, the pair of trains with the longest turnover time at the station is first determined, and then a new car connection is generated by adjusting other ordinary trains to be conversion trains and replacing one of the trains in the current train pair, so that the turnover time of the cars is shorter.

[0131] Repair operator 2: Increase the number of conversion train pairs.

[0132] If the number of conversion trains is too small, the waiting time of passengers on the secondary path will be too long, and even some passengers may be stranded. To address this problem, a pair of ordinary trains is adjusted to be conversion trains, and a car connection is generated between them.

[0133] Repair operator 3: Reduce the maximum headway.

[0134] If the headway is too large, it will affect the waiting time of passengers and the turnover efficiency of consis. In this operator, for the two train pairs that run with the largest headway, their running lines are randomly shifted in opposite directions. Similar to the destroy operator 4, after the shift, the minimum headway requirement with the trains before and after it needs to be satisfied, and the car connection condition in the current solution cannot be violated.

[0135] ④ Passenger flow allocation ​

[0136] In subway system, since the tickets are not bound to seats, the passengers usually follow the first-come-first-served principle when getting on the train. In the present application, when the train operation timetable is determined, the passenger flow is allocated to the corresponding train set according to the first-come-first-served principle by using a simulation-based method. The detailed allocation process is shown in Figure 6 .

[0137] ⑤Adaptive strategy

[0138] In the present application, the standard adaptive strategy is used to select the corresponding operator in each iteration. Specifically, it can be divided into two parts: score and weight update. Next, a set of destruction operators is described, and the repair operators are similar.

[0139] Score: In an iteration, if a set of new solutions is obtained by disturbing the current solution by destruction operator k and any repair operator, then its score in this iteration process is The value is as follows:

[0140]

[0141] Wherein, score1≥score2≥score3≥score4.

[0142] Weight update: After the score of the operator is determined, the weight of the destruction operator k is updated as follows:

[0143]

[0144] Wherein, λ∈[0, 1].

[0145] In the present application, the corresponding destruction operator and repair operator are selected according to the weight of the operator in each iteration by designing a roulette mechanism, and the probability of selecting the destruction operator k is:

[0146]

[0147] Wherein, |O d | represents the total number of destruction operators.

[0148] ⑥Algorithm termination

[0149] In the present application, the algorithm termination conditions are as follows:

[0150] 1) The number of iterations or the calculation time reaches the preset maximum value;

[0151] 2) The time to search for the next better solution reaches the preset maximum value.

[0152] The algorithm terminates when one of the two criteria is met. Criterion 1) limits the maximum number of iterations and time of the algorithm, which is the most basic stopping condition and is widely used in heuristic algorithms. Criterion 2) limits the time to search for a better solution. When the algorithm terminates due to criterion 2), it means that the quality of the known optimal solution is already good enough that it is not possible to search for a higher quality solution in a short time.

[0153] 3. Example verification

[0154] To make the invention clearer, the following further illustrates the invention with examples and drawings. First, a small-scale numerical example is designed to compare the solution results of the algorithm designed in the invention and the commercial optimization software GUROBI, in order to verify the efficiency and effectiveness of the invention. Then the invention is applied to various passenger flow scenarios to verify the universality of the invention.

[0155] (1) Numerical case

[0156] Suppose a Y-shaped subway line, with the main line, main branch line and secondary branch line each consisting of three stations. Except for the secondary branch line, the turnaround stations on other lines are equipped with vehicle depots. Consider a time range of 50 minutes, and discretize it by 1 minute intervals. The stop time, reconnection / disassembly time at the connecting station are all set to 1 minute. The minimum train safety interval time and the minimum turnaround time of the train are both set to 2 minutes. Each train can accommodate a maximum of 50 passengers. The objective function weights α and β are taken as 1 and 20 respectively.

[0157] In this case, 15 instances are generated by changing the number of trains and passengers to test the performance of the ALNS algorithm and GUROBI. Considering that when commercial solvers solve mathematical programming problems, most of the computation time is spent on proving that the upper bound obtained at an earlier time is the optimal solution, therefore, in this case, the maximum solving time of GUROBI is set to 3 hours, and the upper bound obtained is taken as the optimal solution. When using the ALNS algorithm, the maximum number of iterations is set to 1000, the maximum solving time is set to 10 minutes, and the maximum time to search for a better solution is set to 3 minutes.

[0158] Table 1 Comparison of results of two solving methods

[0159]

[0160]

[0161] The comparison results are shown in Table 1. Among them, OBJ#1 represents the optimal result of GUROBI with a solving time of not less than 10 minutes, OBJ#2 represents the optimal result of GUROBI with a solving time of not less than 3 hours, and CPU#2 represents the time consumed by GUROBI to obtain OBJ#2. OBJ and CPU are the optimal result and the actual solving time of the ALNS algorithm when the maximum solving time is set to 10 minutes. Gap represents the percentage of the difference between OBJ and OBJ#2.

[0162] It can be seen from the comparison that when the calculation time of GUROBI is set to 10 minutes, the optimal solution can only be obtained in the case of fewer trains and passengers. With the gradual increase of the number of trains and passengers, even in some instances, it is impossible to obtain a feasible solution. However, after setting the calculation time to 3 hours, GUROBI can obtain better solutions. However, as the scale increases, the calculation time increases significantly. In contrast, the ALNS algorithm has a smaller increase in calculation time.

[0163] In terms of solution quality, the ALNS algorithm also performs well. Specifically, when the time limit of GUROBI is 10 minutes, the solution of ALNS is better than that of GUROBI in most cases, marked with * in Table 1. When the time limit of GUROBI is 3 hours, the solution of ALNS is still better than that of GUROBI in some cases, marked with □ in Table 1. The last column (Gap) shows that although the solution of ALNS is worse than that of GUROBI with a solving time limit of 3 hours in some instances, the relative difference between them is less than 3%. Considering the shorter calculation time, the ALNS designed in this paper is obviously superior to GUROBI.

[0164] (2) Actual case

[0165] In the actual case, Guangzhou Metro Line 14 is taken as the research object, and the line structure is shown in Figure 7 Three passenger flow scenarios are selected as shown in Figures 8a-8c , which are peak passenger flow, uniform passenger flow, and extreme passenger flow. Among them, the peak passenger flow represents that the passenger flow intensity of each section varies with time, with higher intensity at peak time and lower intensity at off-peak time; the uniform passenger flow represents that the passenger flow intensity of each section does not change with time, and passengers arrive uniformly with the same intensity; the extreme passenger flow is based on the peak passenger flow, with reduced passenger flow intensity on the secondary branch line and increased passenger flow intensity on the main branch line. The time range is selected from 7 am to 11 am, and the discretization processing is performed with a unit time of 30 seconds.

[0166] In addition, in this case, the parameters are set as follows: the stopping time of the train at all intermediate stations is 30 seconds; the marshalling / demarshalling time of the train at the connecting station τ cd30 seconds; minimum headway time h min 2 minutes; minimum turnaround time of train set at turnaround station τ turn 2 minutes; capacity of single train set is 900 passengers. In addition, set α = 1, β = 10000, tem = 3 and prob = 0.005.

[0167] The solution results are shown in Table 2 and Figures 9a-9c Table 2 shows the objective value (OBJ), total waiting time of passengers (TWT), number of train sets needed (#TU) and solving time (CPU) in each scenario, Figures 9a-9c Table 3 shows the detailed train schedules in each scenario.

[0168] Table 2 Solution results comparison in three scenarios

[0169]

[0170] By comparing the uniform passenger flow scenario and the peak passenger flow scenario, it can be seen that when passengers arrive at the station uniformly in the time dimension, the total waiting time of passengers in the system is less, but more train sets are needed to complete the schedule. By comparing the extreme passenger flow scenario and the peak passenger flow scenario, it can be seen that the number of train sets does not change, and the change of the total waiting time of passengers can be ignored because the difference is less than 0.2%. From the objective values of the three scenarios, all the objective function values are close, which shows that the algorithm designed in the present application can cope with different passenger flow demands and formulate corresponding high-quality schedules.

[0171] Figures 9a-9c Table 3 shows the detailed train schedules in each scenario.

[0172] (1) The change trend of train interval time is different in different scenarios. For example: in the peak passenger flow scenario, the interval time between down trains is greater in the early stage than in the later stage, while the interval time between up trains shows the opposite trend.

[0173] (2) In the early or late stage of the time range, more trains are executed by single marshalling because each train can only serve the main path.

[0174] (3) The turnaround time of most train sets at the turnaround station is short, indicating that the utilization efficiency of the flexible marshalling mode train set is high.

[0175] In summary, the model and algorithm disclosed by the application have good applicability in compiling operation plans of Y-type metro lines in flexible marshalling modes. Firstly, the application considers both operation cost and passenger service quality, and can effectively reduce the input cost of used train sets under the condition of ensuring passenger service quality. Secondly, the self-adaptive large neighborhood search algorithm designed by the application can quickly obtain high-quality solutions, ensuring the feasibility of the application in actual application cases.

[0176] The above merely describes some embodiments of the present application, and it should be noted that, for those skilled in the art, other modifications and improvements can be made without departing from the inventive concept of the present application, and these all fall within the protection scope of the present application.

Claims

1. A train operation planning method for Y-shaped metro line in flexible marshalling mode, characterized in that: This includes constructing an integrated optimization model and a solution algorithm. The method for establishing the optimization model includes defining decision variables, formulating constraints, and establishing an objective function. The decision variables include whether train i is coupled / disassembled at the connecting station, whether train i is operated by coupled trainsets on the main line, the departure time of train i at station s, the arrival time of train i at station s, and the composition of train i's trainset. The number of train sets turning back at station s, the number of train sets of train i directly entering the depot near station s, the number of train sets of train i supplied by the depot near station s, and whether passenger p boarded a train set of train i serving path r; the solution algorithm includes first establishing a framework based on an adaptive large neighborhood search algorithm, and then designing the algorithm based on the established framework to obtain the objective function value; wherein, The formula of the objective function is ， In the formula, α , β are the weight coefficients of the total passenger waiting time and the total number of train sets used, respectively. If the passenger boards the train set serving the route , the variable ; if the passenger does not board the train set serving the route , the variable ; the variable is the number of train sets provided by the marshalling yard near the station ; for the passenger to arrive at the station, for the train to depart from the station of the passenger, p o p for the train to depart, for the train to assemble at the turnaround station, P for the set of all passengers, I for the set of all trains, R for the set of all paths;​ The algorithm design includes formulating a feasibility proposition, generating an initial solution, designing operators, passenger flow allocation, adaptive strategy and algorithm termination condition. The feasibility proposition includes that the converted train running time is , the minimum time for train bottom turnaround is , is the start time of the considered time range, is the end time of the considered time range, only the down train starting from the down sidings time range and the up train starting from the up sidings time range can be selected as the converted train; The feasibility proposition includes a minimum number of train consists passing through the route is where, is a counting function; is a maximum function; is a rounding up function; the set of all stations is denoted by where the set of stations of a line is denoted by ; ; is the set of trunk line, main branch line and secondary branch line; Cap represents the seat capacity of a train set; represents the set of passengers passing through section s ; represents the set S l the number of elements contained in the set The feasibility proposition includes the latest train within the down side line time range must be met​ wherein, is the minimum number of train sets passing through the secondary branch in the down direction, is the total number of train services in the down direction; is the minimum headway time; The feasibility proposition includes the earliest train in the up side line time range must be satisfied​ wherein, is the minimum number of train sets passing through the secondary branch in the up direction, is the total number of train services in the up direction.

2. The train operation planning method for Y-shaped metro lines in flexible marshalling mode according to claim 1, characterized in that: The parameters in the algorithm framework include scores and weights of the destruction operator / repair operator.

3. The method for train operation scheduling of Y-type metro line in flexible marshalling mode according to claim 1, characterized in that: The solving process in the algorithm framework is divided into an asynchronous layer and a global layer, In the asynchronous layer, an iteration task is allocated to each thread defined, in each iteration, the destruction operator and the repair operator are executed in turn on the current solution to obtain a new solution, when all tasks in the asynchronous layer are completed, the new solutions form a solution pool, and the solution pool is returned to the global layer; in the global layer, each solution in the solution pool is compared with the known optimal solution and the current solution, and then the solution and the parameters of the algorithm are updated according to the quality of the solution and the adaptive rule.

4. The method for train operation planning of Y-type metro line in flexible marshalling mode according to claim 1, characterized in that: The passenger flow allocation includes, after the train operation timetable is determined, allocating the passenger flow to the corresponding train set according to the first-come-first-served principle by using a simulation-based method.

5. The method for train operation planning of Y-type metro line in flexible marshalling mode according to claim 1, characterized in that, The termination conditions of the algorithm include: The iteration number or the calculation time reaches a preset maximum value; or The time for searching for a better solution reaches a preset maximum value.

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