A method for compiling vehicle bottom utilization plan for cross-line operation of urban rail transit

Abstract

The present invention discloses a method for compiling a plan for the use of a train bed for cross-line operation of urban rail transit. According to the train schedule and other related information, a train bed connection network is constructed under the constraints of the operation such as the entry and exit and return of the train bed; a network flow integer linear programming model is constructed with the goal of minimizing the number of vehicles in use and the number of kilometers of vehicles in operation, and an initial set of train number chains is generated; considering the balance target of the use of the train bed, a set partitioning model based on the train number chain is constructed, and the train number chain executed by each train bed is determined by solving; a pricing sub-problem is designed based on the column generation algorithm idea, a new train number chain is generated, and a neighborhood train number chain is generated based on the neighborhood search; the set partitioning model based on the train number chain is solved again, and an iterative cycle is performed. The present invention aims to efficiently compile a train bed use plan for cross-line operation, ensuring that the number of kilometers of vehicles in operation and the number of vehicles in use are minimized while improving the balance of the use of the train bed.

Description

Technical Field

[0001] The present invention relates to the technical field of urban rail transit transportation organization, and in particular to a method for compiling a vehicle bottom utilization plan for cross-line operation of urban rail transit. Background Art

[0002] With the rapid development of urban rail transit in my country, cross-line operation has become a key development direction at this stage. Through the compatible unification of interconnection line transformation and power supply system, communication signal and dispatching command system, trains can cross-line from one line to another. Cross-line operation integrates multiple lines in the network to achieve operational unification or coordination. Cities such as Beijing and Chongqing in my country have realized cross-line operation between multiple lines. Under cross-line operation, the vehicle bottom (EMU) is no longer used independently on a single line, but can run between different lines and different routes. Reasonable arrangement of vehicle bottom use under cross-line operation is of great significance to improving vehicle bottom utilization efficiency and saving operation costs.

[0003] The urban rail transit train floor utilization plan stipulates the designated train numbers and their order for each floor, and is the basis for the preparation of train operation plans. The train floor utilization plan affects both the floor utilization cost and the balance of floor utilization. In terms of floor utilization cost: different floor utilization plans will affect the number of trains and connections that the floor can handle, which will lead to differences in the floor mileage and the number of vehicles in use when the floor is empty, affecting the floor utilization cost. In terms of floor utilization balance: the train floor utilization plan determines the number and order of trains that each floor can handle. At the same time, the cross-line routes and large and small routes of the trains that the floor can handle affect the length of the train chain, resulting in a certain difference in the total mileage of the train. Therefore, the preparation of the train floor plan needs to reduce the number of vehicles in use and the floor mileage, and improve the balance of floor utilization.

[0004] The preparation of train undercarriage plans under cross-line operation conditions is different from the preparation of traditional single-line undercarriage utilization plans. Due to the existence of cross-line crossings, the undercarriage types and yard sizes of different lines are different, and there are many combination types. How to consider the large and small crossings of the line and the cross-line crossings to comprehensively design the undercarriage utilization plan and select a reasonable and efficient undercarriage utilization combination plan is the key and difficulty to improve the efficiency of the cross-line operation network; on the other hand, in order to solve the problem of undercarriage duplication on multiple lines in cross-line operation, it is necessary to consider the differences in undercarriage types of different lines in detail to make it more consistent with the actual operation situation. Summary of the invention

[0005] The present invention is intended to provide a method for compiling a vehicle bottom utilization plan for cross-line operation of urban rail transit to solve the problems raised in the above-mentioned background technology.

[0006] To achieve the above object, the present invention provides the following technical solution: a method for compiling a vehicle bottom utilization plan for cross-line operation of urban rail transit, comprising the following steps:

[0007] Step 1: For the use of multiple vehicle types on multiple routes in cross-line operation, based on information including but not limited to train schedules, and under operational constraints including but not limited to vehicle entry, exit and return, a vehicle connection network for multiple vehicle types is constructed;

[0008] Step 2: With the goal of minimizing the number of vehicles in use and the number of kilometers traveled, an integer linear programming model of multi-commodity network flow is constructed, and a linear programming solver is used to solve the multi-commodity network flow model to generate an initial set of train number chains;

[0009] Step 3: Considering the balanced use of vehicle bottoms, a set segmentation model based on the train number chain is constructed, and a linear programming solver is used to determine the train number chain executed by each vehicle bottom, and the dual solution of the model is obtained;

[0010] Step 4: Design the pricing sub-problem based on the column generation algorithm, use the linear programming solver to solve the pricing sub-problem, and generate a new train chain;

[0011] Step 5: Design the neighborhood structure of the train number chain and search for and generate the neighborhood solution of the new train number chain;

[0012] Step 6: Return to step 3 and iterate until enough train chains are listed.

[0013] Preferably, the method can be applied to large intersections of the line, small intersections of the line and cross-line intersections.

[0014] Preferably, the vehicle bottom utilization plan of the present method is prepared by constructing a multi-commodity network flow model with the connection network arc flow of each vehicle bottom as the decision variable, and the linear programming solver is used to directly solve and generate an initial vehicle chain set, so as to reduce the number and cost of vehicle bottom utilization and improve vehicle bottom utilization.

[0015] Preferably, the vehicle bottom operation balance target is achieved by a column generation algorithm, comprising the following steps:

[0016] 1) The linear programming solver directly solves the multi-commodity network flow model considering the number of vehicles and the number of kilometers traveled to obtain the initial train chain set;

[0017] 2) Considering the goal of vehicle utilization balance, a set partitioning model based on train number chains is constructed as the main problem of the column generation algorithm; a pricing sub-problem is designed to solve and generate a train number chain with the minimum number of generated tests, and then added to the train number chain set;

[0018] 3) Use neighborhood search to increase the size of the train chain to accelerate the train generation algorithm and improve the efficiency of compiling the vehicle utilization plan.

[0019] The principle and beneficial effects of this technical solution:

[0020] Considering the shared use of vehicle bottoms in cross-line operations, a multi-commodity network flow integer linear programming model based on a connection network was constructed by describing in detail the operational restrictions such as vehicle bottom entry and exit, turnaround, and multiple entry and exit sections. A column generation algorithm embedded in neighborhood search was designed to efficiently solve the optimal vehicle bottom utilization plan.

[0021] According to the operation of the vehicle bottom operation, the connection between trains and the connection between the depot and the train are regarded as the connection network arc, and the connection network of the vehicle bottom operation is constructed. The flow of the connection network arc of each vehicle bottom is taken as the decision variable, and the flow balance constraints of each vehicle bottom in the train and the depot are considered. This can ensure that the balance of vehicle bottom operation is improved while the number of vehicles in use and the number of kilometers traveled are minimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flow chart of a method for compiling a vehicle bottom utilization plan for cross-line operation of urban rail transit according to the present invention;

[0023] Figure 2 This is a schematic diagram of the vehicle bottom same station continuous turnaround and turnaround before the station according to the present invention;

[0024] Figure 3 It is a schematic diagram of the present invention of turning back after connecting the same station under the vehicle to the turning back station;

[0025] Figure 4 This is a schematic diagram of the vehicle bottom entry and exit of the present invention;

[0026] Figure 5 This is a schematic diagram of the vehicle bottom entry and exit connection of the present invention;

[0027] Figure 6 This is a schematic diagram of the urban rail transit connection network of the present invention;

[0028] Figure 7 It is a schematic diagram of the urban rail transit yard connection network diagram of the present invention. DETAILED DESCRIPTION

[0029] The present invention is further described in detail below with reference to the accompanying drawings and embodiments:

[0030] Step 1: For the use of multiple vehicle types on multiple routes in cross-line operation, based on information including but not limited to train schedules, and under operational constraints including but not limited to vehicle entry, exit and return, a vehicle connection network for multiple vehicle types is constructed. The specific steps are as follows:

[0031] First, for multiple lines under cross-line operation, according to the determined train schedule, the train number is represented as n∈N. The train number n has four attributes: departure time d n, arrival time a n , starting station n and the terminal e n .

[0032] Secondly, denote the depot as d∈D and the station connected to the depot as s d , each vehicle bottom type in the parking lot is represented by k∈K, and the parking lot corresponding to vehicle bottom k is denoted by d k .

[0033] Then, consider a train as a node and a depot as two nodes: exit and entry. Take the connections between trains and the connections between depots and trains as arcs to construct a connection network G = (V, E). V is a node set, E is an arc set, including the exit arc set E start , Entry arc set E end And the set of connection arcs (return connection arcs and entry and exit connection arcs).

[0034] Exit arc (d - ,n) indicates that the vehicle starts from parking lot d and takes up the task of vehicle number n; the entry arc (n,d + ) indicates that the car returns to the yard node d after completing the execution of train node n; the connection arc (n,m) connects the train nodes n and m, indicating that the car executes train node m after completing the execution of train node n, including the return connection arc and the entry and exit connection arc.

[0035] The construction of the reversing connection arc takes into account the reversing operation constraints. The train executes train number n at station s and then continues to execute train number m. The operation time of the reversing station must meet the minimum operation time requirement, and it is not allowed to stay too long. According to the running order, the ordered set of trains departing from station s is defined as The ordered set of trains arriving at station s is like Figure 2 , 3 As shown, for train and The return connection before and after the station should meet the constraint conditions: τ min ≤d m -a n ≤τ max , where τ min is the minimum return operation time, τ max The maximum allowed return operation time.

[0036] The construction of exit arc and entry arc takes into account the entry and exit operation constraints. Two cases are considered. The first case is: the yard d is connected to the starting station of train number n, and the bottom of the car directly exits the yard to perform the train task. Since the bottom of the car usually exits at the beginning of the operation and before the morning and evening peaks, and the bottom of the car does not exit after the morning and evening peaks or at the end of the operation, if the train number n is executed by the bottom of the car in the yard, the construction of the exit arc must meet the exit time constraint, which is expressed as a n ∈T start , where T start The allowed exit time range is set according to the actual operation situation. Figure 4 As shown in the figure, the yard d is not connected to the starting station of train number n, and the bottom of the train needs to leave the yard and go to station s d The train will run empty to the starting station (and turn back) before it can start to connect with the next train. At this time, the empty run at the exit needs to consider the interval between the main line trains. The empty run can only be inserted when the interval between the two trains is large enough. If the train n is executed by the bottom of the car in the yard, the empty run must have a feasible arrival time a to meet the constraints: At the same time, since the train needs to turn around after completing the empty trip, the turnaround constraint should be met: τ min ≤d n -a≤τ max , a m+u ≥d n , a≥d n-u .

[0037] The entry and exit arcs take into account the parking time constraints. Figure 5 As shown, the train numbers n and m of the entry and exit connection arc must meet the following conditions: the train bottom can return to the yard after executing train number n, and train number m can be executed by the train bottom leaving the yard. At the same time, the time the train bottom stays in the yard from the morning peak to the evening peak should be longer. The entry and exit connection must meet the following conditions: d m -a n ≥κ, κ is the minimum entry and exit interval time.

[0038] Finally, in order to solve the multi-model problem under cross-line operation, a vehicle bottom connection network is constructed. The set of trips that can be executed by the vehicle bottom k of different models is defined as N k , construct the subnetwork G of vehicle bottom k k =(V k ,E k ).like Figure 5 As shown, the node set of the sub-network That is, it includes the nodes of the vehicle bottom k that can execute the train and its parking lot d k The exit and entry nodes of the arc segment set E k It includes the connection arcs between sub-network nodes, that is, E k ={(i,j)∈E|i∈V k,j∈V k}.

[0039] Step 2: With the goal of minimizing the number of vehicles in use and the number of kilometers traveled, considering the vehicle utilization constraints of cross-line operations, an integer linear programming model of multi-commodity network flow is constructed, and a linear programming solver is used to solve the multi-commodity network flow model to generate an initial set of train chain. The specific steps are as follows:

[0040] First, the model decision variables are established based on the flow of each vehicle bottom k in the connected network arc, with a value of 0 or 1, indicating whether the vehicle bottom k performs the task corresponding to the arc. The model considers two optimization objectives, including the minimum number of vehicles in use and the minimum number of kilometers traveled.

[0041] The model related parameters and decision variables are shown in Table 1.

[0042] Table 1 Model related parameters and decision variables

[0043]

[0044]

[0045] The network flow model is established as follows:

[0046]

[0047] The objective function (1) of the model is to minimize the number of vehicles in use and the number of kilometers traveled under the vehicle. Since the vehicle resources are generally tight in actual operation, the vehicle utilization plan should give priority to minimizing the number of vehicles in use, and secondly, minimize the number of kilometers traveled from the perspective of reducing empty trains.

[0048] Constraint (2) means that each train number n has one and only one train bottom to execute;

[0049] Constraint (3) is the flow balance constraint of each car bottom at the train node, which means that after the car bottom completes the train, it must execute the next train or return to the yard;

[0050] Constraint (4) is the flow balance constraint of each car bottom at its parking lot node, which means that the car bottom originating from and returning to the parking lot are the same;

[0051] Constraint (5) indicates that the number of vehicles used for vehicle type k does not exceed its available vehicle base.

[0052] Constraint (6) represents the decision variable The value range is 0-1 variable.

[0053] Step 3: Considering the balanced use of vehicle bottoms, a set segmentation model based on the train chain is constructed. The linear programming solver is used to obtain the train chain executed by each vehicle bottom and the model dual solution. The specific steps are as follows:

[0054] First, based on the network flow model, a set segmentation model based on the train chain is constructed. The basic feasible solution of the network flow model is defined as That is, it represents the train number chain of vehicle bottom k. Represents the train number chain p k Considering the balanced use of the vehicle base, the train number chain p k The number of kilometers driven without a car is recorded as The difference between the running vehicle mileage and the preset average vehicle mileage can be calculated as

[0055] Given a train chain set The original network flow model can be transformed into a set partitioning model, which can be used to decide the train chain selection for each car bottom. The decision variable y p k Indicates whether the vehicle k executes the vehicle chain p.

[0056]

[0057] The objective function (7) of the set segmentation model is consistent with the original network flow model, indicating that the number of vehicles in use and the number of kilometers traveled by the vehicle bottom are minimized, while considering the balance of vehicle bottom use;

[0058] Constraint (8) indicates that each train number n has one and only one train bottom execution;

[0059] Constraint (9) indicates that the number of vehicles used for vehicle type k does not exceed its available vehicle base.

[0060] Constraint (10) represents the decision variable y p k The value range of .

[0061] Then, a linear programming solver is used to solve the problem.

[0062] Step 4: Design the pricing sub-problem based on the column generation algorithm, use the linear programming solver to solve the pricing sub-problem, and generate a new train chain. Specifically include:

[0063] First, based on the idea of ​​column generation algorithm, establish the pricing sub-problem. Let α n and β k is the dual variable (shadow price) of constraints (8) and (9).

[0064]

[0065] Objective function (11) is to minimize the number of tests in the simplex method in the column generation algorithm; constraint (12) ensures that only one train chain is generated; constraints (15-16) are used to calculate the operating vehicle mileage and average vehicle mileage of vehicle base k deviation.

[0066] Then, a linear programming solver is used to find the optimal solution Add to collection Since the difference between different models in the same parking lot is the different executable train numbers, the train number chain p of model k k After generation, if another vehicle type k′ in the same parking lot can also execute the train chain, it will be copied to p k′ Add to the train chain collection, that is

[0067] Step 5: Design the neighborhood structure of the train number chain and search for domain solutions to generate new train number chains.

[0068] In the early stage of the column generation algorithm, the convergence efficiency is usually low due to the small size of the pole set. The present invention uses neighborhood search to increase the size of the train chain to accelerate the column generation algorithm. The train chain exchange operation is adopted for neighborhood design. For two train chains of the same model, it is detected whether there are exchangeable fragments. If there is a connectable arc between the two nodes of the two train chains, there is a replaceable fragment, which can be used as the neighborhood solution of the train chain.

[0069] First, for the initial solution train chain set For each vehicle type k, for any two vehicle number chains p k and p k′ , if p k and p k′ If there are exchangeable segments, perform the exchange operation, generate a new train chain, and add it to the collection

[0070] Then, if Figure 6 As shown, the optimal solution p for the pricing subproblem is k That is, from Select the train number chain k′ , if p k and p k′ If there is an exchangeable fragment, perform the exchange operation and add it to the set

[0071] Step 6: Return to step 3 to iterate and solve until enough train chains are listed.

[0072] According to the objective function value of the pricing sub-problem, determine whether to terminate the algorithm. If the solution is close to 0, terminate the step; if not, return to step three.

[0073] The technical solution of the present invention is aimed at multiple lines operating across the line, taking into account the shared use of car bottoms under multiple lines and multiple models, and effectively optimizing the preparation of train car bottom use plans. By describing in detail the operation restrictions such as car bottom entry and exit, turnaround, and multiple entry and exit sections, a connection network is constructed, and it is ensured that the connection network has no infeasible connection arcs to reduce the network scale; with the goal of minimizing the number of vehicles used and the number of kilometers traveled, the network flow integer linear programming model is solved to generate the initial set of train number chains; considering the balance target of car bottom use, a set partitioning model based on the train number chain is constructed to determine the train number chain executed by each car bottom; based on the column generation algorithm, a pricing sub-problem is designed to generate a new train number chain, and its neighborhood train number chain is generated based on the neighborhood search; the set partitioning model based on the train number chain is solved again, and an iterative cycle is performed.

[0074] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not limitations on the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made on the basis of the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the protection scope of the present invention.

[0075] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical solutions or characteristics in the solution is not described in detail here. For those skilled in the art, without departing from the technical solution of the present invention, several modifications and improvements can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for compiling a vehicle bottom utilization plan for cross-line operation of urban rail transit, characterized in that: The following steps are involved: Step 1: For the use of multiple vehicle types on multiple routes in cross-line operation, based on information including but not limited to train schedules, and under operational constraints including but not limited to vehicle entry, exit and return, a vehicle connection network for multiple vehicle types is constructed; Step 2: With the goal of minimizing the number of vehicles in use and the number of kilometers traveled, an integer linear programming model of multi-commodity network flow is constructed, and a linear programming solver is used to solve the multi-commodity network flow model to generate an initial set of train number chains; Step 3: Considering the balanced use of vehicle bottoms, a set segmentation model based on the train number chain is constructed, and a linear programming solver is used to determine the train number chain executed by each vehicle bottom, and the dual solution of the model is obtained; Step 4: Design the pricing sub-problem based on the column generation algorithm, use the linear programming solver to solve the pricing sub-problem, and generate a new train chain; Step 5: Design the neighborhood structure of the train number chain and search for and generate the neighborhood solution of the new train number chain; Step 6: Return to step 3 and iterate until enough train chains are listed.

2. The method for compiling a vehicle bottom utilization plan for cross-line operation of urban rail transit according to claim 1, characterized in that: This method can be applied to large intersections, small intersections and cross-line intersections.

3. The method for compiling a vehicle bottom utilization plan for cross-line operation of urban rail transit according to claim 1, characterized in that: The vehicle bottom utilization plan of this method is compiled by constructing a multi-commodity network flow model with the connection network arc flow of each vehicle bottom as the decision variable, and the linear programming solver is used to directly solve and generate the initial vehicle chain set, which is used to reduce the number and cost of vehicle bottom utilization and improve the utilization rate of vehicle bottom.

4. The method for compiling a vehicle bottom utilization plan for cross-line operation of urban rail transit according to claim 1, characterized in that: The column generation algorithm is used to achieve the vehicle bottom utilization balance goal, including the following steps: 1) The linear programming solver directly solves the multi-commodity network flow model considering the number of vehicles and the number of kilometers traveled to obtain the initial train chain set; 2) Considering the goal of vehicle utilization balance, a set partitioning model based on train number chains is constructed as the main problem of the column generation algorithm; a pricing sub-problem is designed to solve and generate a train number chain with the minimum number of generated tests, and then added to the train number chain set; 3) Use neighborhood search to increase the size of the train chain to accelerate the train generation algorithm and improve the efficiency of compiling the vehicle utilization plan.

Images