Urban rail train scheduling optimization method based on flexible marshalling strategy

Abstract

The invention is suitable for the technical field of rail transit, and provides an urban rail train scheduling optimization method based on a flexible marshalling strategy, which comprises the following steps: generating a passenger waiting time linearization calculation method according to a passenger arrival curve, and introducing constraint conditions in combination with the passenger waiting time linearization calculation method to obtain a passenger arrival curve; according to a passenger waiting time linearization calculation method after constraint conditions are introduced, a vehicle turnover scheme and timetable comprehensive optimization model based on a marshalling strategy is constructed, finally, a branch strategy based on priorities is determined, an effective cutting plane is introduced, a two-stage branch cutting algorithm is designed, a global optimal solution of the comprehensive optimization model is solved, and the optimal solution of the vehicle turnover scheme and timetable comprehensive optimization model is obtained. Therefore, the optimal running scheme, the timetable and the turnover scheme of the train are obtained. Therefore, waiting time of passengers and subway operation cost can be reduced, and train transport capacity utilization rate is improved.

Description

Technical Field

[0001] The present application belongs to the field of rail transit technology, and in particular relates to an urban rail train scheduling optimization method based on a flexible marshaling strategy. Background Art

[0002] With the rapid expansion of urban rail transit networks, the construction scale of urban lines has shown a sharp upward trend. As the main mode of transportation connecting the city center and the surrounding remote suburbs, urban lines have exposed many problems while playing an important role as a transportation hub. Among them, the low utilization rate of line capacity caused by the uneven distribution of passenger flow has become a problem that needs to be solved urgently. Summary of the invention

[0003] The embodiment of the present application provides an urban rail train scheduling optimization method based on a flexible marshaling strategy, which can solve the current problem of low line capacity utilization caused by uneven passenger flow distribution.

[0004] In the first aspect, an embodiment of the present application provides an urban rail train scheduling optimization method based on a flexible marshaling strategy, including: S1, generating a linear calculation method for passenger waiting time based on a passenger arrival curve; S2, introducing constraints in combination with the linear calculation method for passenger waiting time in S1; S3, constructing a comprehensive optimization model of vehicle turnover plan and timetable based on a marshaling strategy according to the linear calculation method for passenger waiting time after introducing the constraints in S2; S4, determining a priority-based branch strategy, introducing an effective cutting plane, and designing a two-stage branch cutting algorithm to obtain the global optimal solution of the comprehensive optimization model in S3, so as to obtain the most superior train operation plan, timetable, and turnover plan.

[0005] In a possible implementation of the first aspect, the method for generating a linear calculation method for passenger waiting time according to a passenger arrival curve includes:

[0006] Step S1-1: discretize the area under the passenger arrival curve into multiple rectangles according to preset equal time intervals, determine the height of each rectangle as the passenger arrival demand at each preset time interval, construct a passenger waiting curve according to the passenger arrival demand at each preset time interval, and then generate a linear calculation method for passenger waiting time according to the passenger waiting curve:

[0007]

[0008] t p =P * t,ori,des ·Δt

[0009] Among them, t p is the passenger waiting time, Δt is the preset time interval, P * t,ori,desrepresents the number of waiting passengers whose starting and ending points are ori station and des station within time t, P t,ori,des represents the number of passengers arriving at ori and des within time t. Indicates whether the up service train s arrives at ori station at time t-1. If it arrives, then The value of is 1. If it has not arrived, The value of is 0. ψ s,ori,t-1 Indicates whether the down service train s arrives at ori station at time t-1. If it arrives, then ψ s,ori,t-1 The value of is 1. If it has not arrived, ψ s,ori,t-1 The value of is 0, t, s are the time and the index of the service train respectively, ori, des are the index of the starting and ending points, are the set of up service trains, the set of down service trains, the set of time, and the set of stations respectively, and η is the number of stations.

[0010] Optionally, in another possible implementation of the first aspect, the linear calculation method for passenger waiting time in combination with S1 introduces constraints, including:

[0011] Step S2-1: Introduce the constraint conditions into the linear calculation method of passenger waiting time in S1, specifically:

[0012]

[0013] Among them, h min ,h max is the minimum and maximum value of the departure interval, n represents the nth station, a s,n is the time when service train s arrives at the nth station, d s,n is the time when service train s leaves the nth station, t safe is the minimum safe time interval, are the sets of uplink / downlink service express trains, r min ,r max They represent the minimum and maximum number of carriages in the flexible marshaling strategy, R s represents the number of carriages used by service train s, M represents the original number of carriages in the upper / lower garage, R s represents the number of carriages used by the down service train s, represents the number of carriages used by the up-service train s, ζ in, s , Respectively indicate whether the down train service s / up train service s enters the garage. If it enters the garage, then ζin, s , The values ​​of are 1, if you do not enter the garage, then ζ in, s , The values ​​of are 0, ζ out, s , Respectively indicate whether the down train service s / up train service s leaves the garage. If so, then ζ out, s , The values ​​of are 1, if there is no exit from the garage, then ζ out, s , The values ​​are 0, O s,n represents the number of people on board the service train s after it leaves the nth station, C is the maximum capacity of each carriage, Indicates whether the up service train and the down service train are connected. If so, The value of is 1. If it is not connected, The value of t is 0, turn ,t run ,t re They represent the turnaround time, the time to leave the garage, and the time to disassemble and reassemble. s ,η+1 represents the time when the down service train leaves the η+1th station, Indicates the time when the up service train arrives at the ηth station.

[0014] Optionally, in another possible implementation of the first aspect, the linear calculation method for passenger waiting time after introducing constraints in S2 is used to construct a comprehensive optimization model of vehicle turnover plan and timetable based on the grouping strategy, including:

[0015] Step S3-1: Based on the linear calculation method of passenger waiting time after introducing constraints in step S2-1, a vehicle turnover plan and timetable comprehensive optimization model based on the marshaling strategy is constructed, specifically:

[0016]

[0017] minZ=σ1·Z time +σ2·(Z fix +Z move )

[0018] Among them, P * t,n,n' represents the number of waiting passengers whose starting and ending points are the nth station and the n'th station within time t, Z time ,Z fix ,Zmove are time cost, fixed cost, and operation cost respectively, n' represents the n'th station, c fix ,c move are fixed cost coefficient and operating cost coefficient respectively, in,s Is the service train s entering the depot? If so, then ζ in,s The value of is 1. If there is no storage, then ζ in,s The value of is 0, out,s Is the service train s leaving the garage? If it enters the garage, then ζ out,s The value of is 1. If there is no storage, then ζ out,s The value of is 0, Z is the objective function, and σ1, σ2 are the weight coefficients corresponding to the target.

[0019] Optionally, in another possible implementation of the first aspect, the priority-based branch strategy is determined, and an effective cutting plane is introduced, and a two-stage branch-cut algorithm is designed to obtain the global optimal solution of the comprehensive optimization model in S3 to obtain the most superior train operation plan, timetable, and turnaround plan, including:

[0020] Step S4-1: Determine a priority-based branch strategy according to the constraints in S2, wherein the priority-based branch strategy is to convert the binary variable ( ζ out,s ,ζ in,s ) is set to have a higher branch priority than the integer variable (R s ,a s,n ,d s,n ) priority, important variables has higher priority than secondary variables ( ψ s,n,t ,ζ out,s ,ζ in,s ), the priority-based branch strategy is as follows:

[0021]

[0022] in, ψ s,n,t They respectively indicate whether the up service train s arrives at the nth station at time t and whether the down service train s arrives at the nth station at time t. Indicates whether the down service train and the up service train are connected. If so, The value of is 1. If it is not connected, The value of is 0;

[0023] Step S4-2: Construct a valid inequality and introduce a valid cutting plane. The specific valid inequality is:

[0024]

[0025] in, s1 represents the down service train s1, represents the up service train s1, s2 represents the downlink service train s2, represents the up service train s2, Indicates down service train s1 and up service trains Whether it is connected, if it is connected, then The value of is 1. If it is not connected, The value of is 0. Indicates an up service train With down service train s2 Whether it is connected, if it is connected, then The value of is 1. If it is not connected, The value of is 0. Indicates an up service train With down service train s Whether it is connected, if it is connected, then The value of is 1. If it is not connected, The value of is 0. Indicates down service train s With up service train Whether it is connected, if it is connected, then The value of is 1. If it is not connected, The value of is 0, and M is a positive integer greater than a preset threshold;

[0026] Step S4-3: The two-stage branch-cut algorithm obtains the global optimal solution of the comprehensive optimization model in S3, and obtains the most superior train operation plan, timetable, and turnaround plan based on the global optimal solution. The specific process is as follows:

[0027] Step S4-31: Determine the crossing plan and initialize the optimal solution set X of the comprehensive optimization model in step S2 G and the optimal solution set X G The corresponding optimal value Z G , let the number of iterations G = 0;

[0028] Step S4-32: traverse the feasible express passing stations in the station set, if there is a feasible express passing station, go to step S4-33, if all feasible express passing stations have been traversed, go to step S4-39;

[0029] Step S4-33: Determine the optimal scheduling solution. According to the feasible express train passing stations in step S4-32, construct the sub-problems of the comprehensive optimization model in step S3, and initialize the optimal node n0 and node set Q of the sub-problem. θ ;

[0030] Step S4-34: A branch strategy based on the priority of step S4-1 is used to select the node set Q in step S4-33. θ Select a discard node from the set Q and remove it from the set Q θ Remove the node from the list and use the simplex method to find the optimal solution to the problem corresponding to the discarded node;

[0031] Step S4-35: introducing the effective cutting plane of step S4-2, and using the simplex method to solve the integer solution of the problem corresponding to the discarded node;

[0032] Step S4-36: Update the upper and lower bounds of the discarded node according to the integer solution of step S4-35. If the lower bound of the discarded node exceeds the upper bound of the root node, pruning is performed, indicating that the discarded node is not the optimal node, and return to step S4-34. If the lower bound of the discarded node is less than or equal to the upper bound of the root node, the discarded node is determined as the new optimal node, and go to step S4-37;

[0033] Step S4-37: Create a new child node according to the priority branching strategy of step S4-1, and add the new child node to the node set Q θ And return to step S4-34;

[0034] Step S4-38: If the node set Q θ All nodes in the above are removed, and the optimal solution to the subproblem in step S4-33 is determined to be X G , and return to step S4-32;

[0035] Step S4-39: Compare the optimal values ​​Z corresponding to each iteration number G G The size of , selects the minimum optimal value and the optimal solution set corresponding to the minimum optimal value as the global optimal solution, terminates the algorithm and outputs the global optimal solution, and determines the most superior train operation plan, timetable and turnaround plan based on the global optimal solution.

[0036] In the technical solution of this application, a linear calculation method for passenger waiting time is generated according to the passenger arrival curve, and then combined with the linear calculation method for passenger waiting time, constraints are introduced. According to the linear calculation method for passenger waiting time after the constraints are introduced, a vehicle turnover plan and timetable comprehensive optimization model based on the grouping strategy is constructed, and finally a branch strategy based on priority is determined, and an effective cutting plane is introduced to design a two-stage branch cutting algorithm to obtain the global optimal solution of the comprehensive optimization model, so as to obtain the most superior train operation plan, timetable, and turnover plan. This can reduce passenger waiting time and subway operating costs, and improve train capacity utilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0038] Figure 1 It is a flow chart of a method for optimizing urban rail train scheduling based on a flexible marshaling strategy provided by an embodiment of the present application;

[0039] Figure 2 (a) is a schematic diagram of a passenger arrival curve provided in an embodiment of the present application;

[0040] Figure 2 (b) is a schematic diagram of a passenger waiting curve provided in an embodiment of the present application. DETAILED DESCRIPTION

[0041] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present application. However, it should be clear to those skilled in the art that the present application may also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present application.

[0042] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, wholes, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or combinations thereof.

[0043] It should also be understood that the term “and / or” used in the specification and appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0044] As used in the specification and appended claims of this application, the term "if" can be interpreted as "when" or "uponce" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "uponce it is determined" or "in response to determining" or "uponce [described condition or event] is detected" or "in response to detecting [described condition or event]", depending on the context.

[0045] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0046] References to "one embodiment" or "some embodiments" etc. described in the specification of this application mean that one or more embodiments of the present application include specific features, structures or characteristics described in conjunction with the embodiment. Therefore, the statements "in one embodiment", "in some embodiments", "in some other embodiments", "in some other embodiments", etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways. The terms "including", "comprising", "having" and their variations all mean "including but not limited to", unless otherwise specifically emphasized in other ways.

[0047] The urban rail train scheduling optimization method based on flexible marshaling strategy provided by the present application is described in detail below with reference to the accompanying drawings.

[0048] Figure 1 A flow chart of a method for optimizing urban rail train scheduling based on a flexible marshaling strategy provided in an embodiment of the present application is shown.

[0049] like Figure 1 As shown, the urban rail train scheduling optimization method based on the flexible marshaling strategy includes the following steps:

[0050] S1. Generate a linear calculation method for passenger waiting time based on the passenger arrival curve;

[0051] S2, combining the linear calculation method of passenger waiting time in S1, and introducing constraints;

[0052] S3, based on the linear calculation method of passenger waiting time after introducing constraints in S2, a comprehensive optimization model of vehicle turnover plan and timetable based on marshaling strategy is constructed;

[0053] S4. Determine the priority-based branching strategy, introduce the effective cutting plane, and design a two-stage branch-cutting algorithm to obtain the global optimal solution of the comprehensive optimization model in S3 to obtain the most superior train operation plan, timetable, and turnaround plan.

[0054] Furthermore, in a possible implementation of the embodiment of the present application, the above step S1 may include:

[0055] Step S1-1: discretize the area under the passenger arrival curve into multiple rectangles according to preset equal time intervals, determine the height of each rectangle as the passenger arrival demand at each preset time interval, construct a passenger waiting curve according to the passenger arrival demand at each preset time interval, and then generate a linear calculation method for passenger waiting time according to the passenger waiting curve:

[0056]

[0057] t p =P * t,ori,des ·Δt

[0058] Among them, t p is the passenger waiting time, Δt is the preset time interval, P * t,ori,des represents the number of waiting passengers whose starting and ending points are ori station and des station within time t, P t,ori,des represents the number of passengers arriving at ori and des within time t. Indicates whether the up service train s arrives at ori station at time t-1. If it arrives, then The value of is 1. If it has not arrived, The value of is 0. ψ s,ori,t-1 Indicates whether the down service train s arrives at ori station at time t-1. If it arrives, then ψ s,ori,t-1 The value of is 1. If it has not arrived, ψ s,ori,t-1 The value of is 0, t, s are the time and the index of the service train respectively, ori, des are the index of the starting and ending points, are the set of up service trains, the set of down service trains, the set of time, and the set of stations respectively, and η is the number of stations.

[0059] In one embodiment of the present application, Figure 2 In the passenger arrival curve diagram shown in (a), the area under the passenger arrival curve is discretized into multiple rectangles according to preset equal time intervals, wherein the height of each rectangle is determined as the passenger arrival demand at each preset time interval. Figure 2(b) Schematic diagram of the passenger waiting curve shown.

[0060] Furthermore, in a possible implementation of the embodiment of the present application, the above step S2 may include:

[0061] Step S2-1: Introduce the constraint conditions into the linear calculation method of passenger waiting time in S1, specifically:

[0062]

[0063] Among them, h min ,h max is the minimum and maximum value of the departure interval, n represents the nth station, a s,n is the time when service train s arrives at the nth station, d s,n is the time when service train s leaves the nth station, t safe is the minimum safe time interval, are the sets of uplink / downlink service express trains, r min ,r max They represent the minimum and maximum number of carriages in the flexible marshaling strategy, R s represents the number of carriages used by service train s, M Respectively represent the original number of carriages in the up / down garage, R s represents the number of carriages used by the down service train s, represents the number of carriages used by the up-service train s, ζ in, s , Respectively indicate whether the down train service s / up train service s enters the garage. If it enters the garage, then ζ in, s , The values ​​of are 1, if you do not enter the garage, then ζ in, s , The values ​​of are 0, ζ out, s , Respectively indicate whether the down train service s / up train service s leaves the garage. If so, then ζ out, s , The values ​​of are 1, if there is no exit from the garage, then ζ out, s , The values ​​are 0, O s,n represents the number of people on board the service train s after it leaves the nth station, C is the maximum capacity of each carriage, Indicates whether the up service train and the down service train are connected. If so, The value of is 1. If it is not connected, The value of t is 0, turn ,t run ,t re They represent the turnaround time, the time to leave the garage, and the time to disassemble and reassemble. s ,η+1 represents the time when the down service train leaves the η+1th station, Indicates the time when the up service train arrives at the ηth station.

[0064] Furthermore, in a possible implementation of the embodiment of the present application, the above step S3 may include:

[0065] Step S3-1: Based on the linear calculation method of passenger waiting time after introducing constraints in step S2-1, a vehicle turnover plan and timetable comprehensive optimization model based on the marshaling strategy is constructed, specifically:

[0066]

[0067] minZ=σ1·Z time +σ2·(Z fix +Z move )

[0068] Among them, P * t,n,n' represents the number of waiting passengers whose starting and ending points are the nth station and the n'th station within time t, Z time ,Z fix ,Z move are time cost, fixed cost, and operation cost respectively, n' represents the n'th station, c fix ,c move are fixed cost coefficient and operating cost coefficient respectively, in,s Is the service train s entering the depot? If so, then ζ in,s The value of is 1. If there is no storage, then ζ in,s The value of is 0, out,s Is the service train s leaving the garage? If it enters the garage, then ζ out,s The value of is 1. If there is no storage, then ζ out,s The value of is 0, Z is the objective function, and σ1, σ2 are the weight coefficients corresponding to the target.

[0069] Furthermore, in a possible implementation of the embodiment of the present application, the above step S4 may include:

[0070] Step S4-1: Determine a priority-based branch strategy according to the constraints in S2, wherein the priority-based branch strategy is to convert the binary variable ( ζ out,s ,ζ in,s ) is set to have a higher branch priority than the integer variable (R s ,a s,n ,d s,n ) priority, important variables has priority over secondary variables ( ψ s,n,t ,ζ out,s ,ζ in,s ), the priority-based branch strategy is as follows:

[0071]

[0072] in, ψ s,n,t They respectively indicate whether the up service train s arrives at the nth station at time t and whether the down service train s arrives at the nth station at time t. Indicates whether the down service train and the up service train are connected. If so, The value of is 1. If it is not connected, The value of is 0;

[0073] Step S4-2: Construct a valid inequality and introduce a valid cutting plane. The specific valid inequality is:

[0074]

[0075] in, s1 represents the down service train s1, represents the up service train s1, s2 represents the downlink service train s2, represents the up service train s2, Indicates down service train s1 and up service trains Whether it is connected, if it is connected, then The value of is 1. If it is not connected, The value of is 0. Indicates an up service train With down service train s2 Whether it is connected, if it is connected, then The value of is 1. If it is not connected, The value of is 0. Indicates an up service train Whether it connects with the downlink service train s, if so, The value of is 1. If it is not connected, The value of is 0. represents the down service train s and the up service train Whether it is connected, if it is connected, then The value of is 1. If it is not connected, The value of is 0, and M is a positive integer greater than a preset threshold;

[0076] Step S4-3: The two-stage branch-cut algorithm obtains the global optimal solution of the comprehensive optimization model in S3, and obtains the most superior train operation plan, timetable, and turnaround plan based on the global optimal solution. The specific process is as follows:

[0077] Step S4-31: Determine the crossing plan and initialize the optimal solution set X of the comprehensive optimization model in step S2 G and the optimal solution set X G The corresponding optimal value Z G , let the number of iterations G = 0;

[0078] Step S4-32: traverse the feasible express passing stations in the station set, if there is a feasible express passing station, go to step S4-33, if all feasible express passing stations have been traversed, go to step S4-39;

[0079] Step S4-33: Determine the optimal scheduling solution. According to the feasible express train passing stations in step S4-32, construct the sub-problems of the comprehensive optimization model in step S3, and initialize the optimal node n0 and node set Q of the sub-problem. θ ;

[0080] Step S4-34: A branch strategy based on the priority of step S4-1 is used to select the node set Q in step S4-33. θ Select a discard node from the set Q and remove it from the set Q θ Remove the node from the list and use the simplex method to find the optimal solution to the problem corresponding to the discarded node;

[0081] Step S4-35: introducing the effective cutting plane of step S4-2, and using the simplex method to solve the integer solution of the problem corresponding to the discarded node;

[0082] Step S4-36: Update the upper and lower bounds of the discarded node according to the integer solution of step S4-35. If the lower bound of the discarded node exceeds the upper bound of the root node, pruning is performed, indicating that the discarded node is not the optimal node, and return to step S4-34. If the lower bound of the discarded node is less than or equal to the upper bound of the root node, the discarded node is determined as the new optimal node, and go to step S4-37;

[0083] Step S4-37: Create a new child node according to the priority branching strategy of step S4-1, and add the new child node to the node set Q θ And return to step S4-34;

[0084] Step S4-38: If the node set Q θ All nodes in the above are removed, and the optimal solution to the subproblem in step S4-33 is determined to be X G , and return to step S4-32;

[0085] Step S4-39: Compare the optimal values ​​Z corresponding to each iteration number G G The size of , selects the minimum optimal value and the optimal solution set corresponding to the minimum optimal value as the global optimal solution, terminates the algorithm and outputs the global optimal solution, and determines the most superior train operation plan, timetable and turnaround plan based on the global optimal solution.

[0086] The urban rail train dispatch optimization method based on flexible grouping strategy provided by the present application first generates a linear calculation method for passenger waiting time according to the passenger arrival curve, and then introduces constraints in combination with the linear calculation method for passenger waiting time. According to the linear calculation method for passenger waiting time after the constraints are introduced, a vehicle turnover plan and timetable comprehensive optimization model based on the grouping strategy is constructed. Finally, a branch strategy based on priority is determined, and an effective cutting plane is introduced to design a two-stage branch cutting algorithm to obtain the global optimal solution of the comprehensive optimization model, so as to obtain the most superior train operation plan, timetable, and turnover plan. This can reduce passenger waiting time and subway operating costs, and improve train capacity utilization.

[0087] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0088] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0089] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for optimizing urban rail train scheduling based on a flexible marshaling strategy, characterized in that: The method comprises: S1. Generate a linear calculation method for passenger waiting time based on the passenger arrival curve; S2, combining the linear calculation method of passenger waiting time in S1, introducing constraint conditions; S3, constructing a comprehensive optimization model of vehicle turnover plan and timetable based on the marshaling strategy according to the linear calculation method of the passenger waiting time after the constraint condition is introduced in S2; S4. Determine a priority-based branching strategy, introduce an effective cutting plane, and design a two-stage branch-cutting algorithm to obtain the global optimal solution of the comprehensive optimization model described in S3 to obtain the most superior train operation plan, timetable, and turnaround plan.

2. The urban rail train scheduling optimization method based on flexible marshaling strategy according to claim 1 is characterized in that: The method for generating a linear calculation method for passenger waiting time according to the passenger arrival curve includes: Step S1-1: discretize the area under the passenger arrival curve into multiple rectangles according to preset equal time intervals, determine the height of each rectangle as the passenger arrival demand for each preset time interval, construct a passenger waiting curve according to the passenger arrival demand for each preset time interval, and then generate a linear calculation method for passenger waiting time according to the passenger waiting curve: t p =P * t,ori,des ·Δt Among them, t p is the passenger waiting time, Δt is the preset time interval, P * t,ori,des represents the number of waiting passengers whose starting and ending points are ori station and des station within time t, P t,ori,des represents the number of passengers arriving at ori and des within time t. Indicates whether the up service train s arrives at ori station at time t-1. If it arrives, then The value of is 1. If it has not arrived, The value of is 0, ψ s,ori,t-1 Indicates whether the down service train s arrives at ori station at time t-1. If it arrives, then ψ s,ori,t-1 The value of is 1. If it has not arrived, ψ s,ori,t-1 The value of is 0, t, s are the time and the index of the service train respectively, ori, des are the index of the starting and ending points, are the set of up service trains, the set of down service trains, the set of time, and the set of stations respectively, and η is the number of stations.

3. The urban rail train scheduling optimization method based on flexible marshaling strategy according to claim 1 is characterized in that: The linear calculation method for passenger waiting time combined with S1 introduces constraints, including: Step S2-1: Introducing the constraint condition into the linear calculation method of the passenger waiting time in S1, specifically: Among them, h min ,h max is the minimum and maximum value of the departure interval, n represents the nth station, a s,n is the time when service train s arrives at the nth station, d s,n is the time when service train s leaves the nth station, t safe is the minimum safe time interval, are the sets of uplink / downlink service express trains, r min ,r max They represent the minimum and maximum number of carriages in the flexible marshaling strategy, R s represents the number of carriages used by service train s, M represents the original number of carriages in the upper / lower garage, R s represents the number of carriages used by the down service train s, represents the number of carriages used by the up-service train s, ζ in,s , Respectively indicate whether the down train service s / up train service s enters the garage. If it enters the garage, then ζ in,s , The values ​​of are 1, if you do not enter the garage, then ζ in,s , The values ​​of are 0, ζ out,s , Respectively indicate whether the down train service s / up train service s leaves the garage. If so, then ζ out,s , The values ​​of are 1, if there is no exit from the garage, then ζ out,s , The values ​​are 0, O s,n represents the number of people on board the service train s after it leaves the nth station, C is the maximum capacity of each carriage, Indicates whether the up service train and the down service train are connected. If so, The value of is 1. If it is not connected, The value of t is 0, turn ,t run ,t re They represent the turnaround time, the time to leave the garage, and the time to disassemble and reassemble. s,η+1 represents the time when the down service train leaves the η+1th station, Indicates the time when the up service train arrives at the ηth station.

4. The urban rail train scheduling optimization method based on flexible marshaling strategy according to claim 3 is characterized in that: The linear calculation method for passenger waiting time after introducing the constraint condition in S2 is used to construct a vehicle turnover plan and timetable comprehensive optimization model based on the grouping strategy, including: Step S3-1: According to the linear calculation method of the passenger waiting time after the constraint conditions are introduced in step S2-1, the vehicle turnover plan and timetable comprehensive optimization model based on the grouping strategy is constructed, specifically: min Z=σ1 Z time +σ2 (Z fix +Z move ) Among them, P * t,n,n' represents the number of waiting passengers whose starting and ending points are the nth station and the n'th station within time t, Z time ,Z fix ,Z move are time cost, fixed cost, and operation cost respectively, n' represents the n'th station, c fix ,c move are fixed cost coefficient and operating cost coefficient respectively, in,s Is the service train s entering the depot? If so, then ζ in,s The value of is 1. If there is no storage, then ζ in,s The value of is 0, out,s Is the service train s leaving the garage? If it enters the garage, then ζ out,s The value of is 1. If there is no storage, then ζ out,s The value of is 0, Z is the objective function, and σ1, σ2 are the weight coefficients corresponding to the target.

5. The urban rail train scheduling optimization method based on flexible marshaling strategy according to claim 4 is characterized in that: The priority-based branch strategy is determined, and an effective cutting plane is introduced to design a two-stage branch cutting algorithm to obtain the global optimal solution of the comprehensive optimization model described in S3, so as to obtain the most superior train operation plan, timetable, and turnaround plan, including: Step S4-1: Determine the priority-based branching strategy according to the constraint condition in S2, wherein the priority-based branching strategy is to convert the binary variable The branch priority of the integer variable (R s ,a s,n ,d s,n ) priority, important variables has higher priority than secondary variables The priority-based branching strategy is specifically: in, ψ s,n,t They respectively indicate whether the up service train s arrives at the nth station at time t and whether the down service train s arrives at the nth station at time t. Indicates whether the down service train and the up service train are connected. If so, The value of is 1. If it is not connected, The value of is 0; Step S4-2: construct a valid inequality and introduce the valid cutting plane, the valid inequality is specifically: Among them, s 1 represents the down service train s1, represents the up service train s1, s2 represents the downlink service train s2, represents the up service train s2, Indicates downlink service train s 1 and up service trains Whether it is connected, if it is connected, then The value of is 1. If it is not connected, The value of is 0. Indicates up service train With down service train s2 Whether it is connected, if it is connected, then The value of is 1. If it is not connected, The value of is 0. Indicates up service train Whether it connects with the downlink service train s, if so, The value of is 1. If it is not connected, The value of is 0. represents the down service train s and the up service train Whether it is connected, if it is connected, then The value of is 1. If it is not connected, The value of is 0, and M is a positive integer greater than a preset threshold; Step S4-3: A two-stage branch-and-cut algorithm is used to obtain the global optimal solution of the comprehensive optimization model in S3, and the most superior train operation plan, the timetable, and the turnaround plan are obtained according to the global optimal solution. The specific process is as follows: Step S4-31: Determine the crossing plan and initialize the optimal solution set X of the comprehensive optimization model in step S2 G and the optimal solution set X G The corresponding optimal value Z G , let the number of iterations G = 0; Step S4-32: traverse the feasible express passing stations in the station set, if there are the feasible express passing stations, go to step S4-33, if all the feasible express passing stations have been traversed, go to step S4-39; Step S4-33: Determine the optimal scheduling solution, construct the sub-problem of the comprehensive optimization model in step S3 according to the feasible express train passing stations described in step S4-32, and initialize the optimal node n0 and node set Q of the sub-problem θ ; Step S4-34: Branching strategy based on the priority of step S4-1 from the node set Q in step S4-33 θ Select a discard node from the set Q and remove the discard node from the set Q θ Remove the node from the list, and use the simplex method to find the optimal solution to the problem of discarding the node; Step S4-35: introducing the effective cutting plane of step S4-2, and using the simplex method to solve the integer solution of the problem corresponding to the discarded node; Step S4-36: Update the upper and lower bounds of the discarded node according to the integer solution of step S4-35. If the lower bound of the discarded node exceeds the upper bound of the root node, pruning is performed, indicating that the discarded node is not the optimal node, and return to step S4-34. If the lower bound of the discarded node is less than or equal to the upper bound of the root node, the discarded node is determined as the new optimal node, and go to step S4-37. Step S4-37: Create a new child node according to the priority branch strategy of step S4-1, and add the new child node to the node set Q θ And return to step S4-34; Step S4-38: If the node set Q θ All nodes in the above are removed, and the optimal solution to the subproblem in step S4-33 is determined to be X G , and return to step S4-32; Step S4-39: Compare the optimal values ​​Z corresponding to the iteration times G G The size of , selects the minimum optimal value and the optimal solution set corresponding to the minimum optimal value as the global optimal solution, terminates the algorithm and outputs the global optimal solution, and determines the most superior train operation plan, the timetable and the turnaround plan according to the global optimal solution.

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