Bus turnover plan optimization method considering bus number task allocation fairness

Abstract

The invention discloses a bus turnover plan optimization method considering train number task distribution fairness, which comprises the following steps: step 1, constructing a turnover state space-time network capable of representing that buses execute train number tasks according to a given time table, including constructing a space-time node set and a space-time arc set in a space-time network diagram; step 2, based on the established space-time network, establishing a bus turnover plan network flow model with the goal of minimizing the number of buses executing the service task; 3, solving the mathematical model by using a Lagrange relaxation algorithm to obtain an initial public transport vehicle turnover plan scheme; and step 4, considering fairness, adjusting the obtained initial public transport vehicle turnover plan scheme, and finally obtaining an optimal public transport vehicle turnover plan scheme. According to the method, the fairness of bus number task allocation is considered, buses are used as few as possible, it is guaranteed that all bus number tasks are executed, the bus operation efficiency is improved, and the workload of bus service personnel is balanced.

Description

Technical Field

[0001] The invention belongs to the technical field of urban public transportation operation, and specifically is a bus turnover plan optimization method considering fairness in bus task allocation. Background Art

[0002] In the modern transportation system, public transportation uses green, low-carbon and environmentally friendly energy, which not only saves energy and reduces emissions, but also provides a large passenger volume and a comfortable, convenient and comfortable riding environment for residents. At this stage, major cities are accelerating the construction and improvement of urban transportation systems and improving the public transportation service system and level.

[0003] The rapid development of urban public transportation systems has also brought high operating expenses and complex vehicle turnover scheduling. Reasonable vehicle turnover planning can not only reduce the number of vehicles used and the operating expenses of the public transportation system, but also improve the travel efficiency of passengers. Traditional vehicle turnover planning often ignores the number of bus missions undertaken by buses, resulting in an imbalance in the number of bus missions assigned to buses. Some buses may be assigned more missions, while others may be assigned fewer missions. This problem may affect the performance and life of buses, leading to unreasonable use of bus transportation resources, and may also lead to unfair work distribution for bus drivers. Summary of the invention

[0004] The present invention aims to solve the deficiencies of the above-mentioned prior art and proposes a bus turnover plan optimization method taking into account the fairness of bus task allocation, so as to formulate a reasonable vehicle turnover plan under the condition of considering the fairness of bus task allocation, thereby improving the operating efficiency of the bus and reasonably and effectively allocating bus resources to better meet the travel needs of passengers.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0006] The bus turnover plan optimization method of the present invention considering the fairness of bus task allocation is characterized in that it includes the following steps:

[0007] Step 1: Set the starting station, terminal station, departure time set and arrival time set of the bus on a bus route;

[0008] Step 2: Given The bus operation schedule with multiple bus tasks is used to construct the spatiotemporal network of bus turnover status ,in, represents a collection of spatiotemporal nodes, represents a collection of spacetime arcs;

[0009] Step 3: Spatiotemporal network based on turnover state , establish a bus turnover planning model with the goal of minimizing the number of buses performing service tasks;

[0010] Step 4: Use the Lagrangian relaxation algorithm to solve the bus turnover plan model and obtain the initial bus turnover plan. ;

[0011] Step 5: Considering fairness, an insertion heuristic algorithm is used to Make adjustments to get the optimal bus turnover plan .

[0012] The bus turnover plan optimization method considering fairness of bus task allocation according to the present invention is also characterized in that step 1 comprises:

[0013] The two directions in which buses run on a bus route are recorded as the up direction and downlink direction , and constitute a set of driving directions ;

[0014] Let the starting station in the upward direction be , the terminal is recorded as , the starting station in the downlink direction is recorded as , the terminal is recorded as , and constitute a collection of stations ;

[0015] Let the bus set be ,and Any bus is denoted as ,make express The total number of buses in Indicates The set of bus tasks assigned to the buses; ; represents the set of bus schedule tasks in the bus timetable; express The total number of train missions;

[0016] Define the starting station and There is a virtual starting point upstream of , the terminal and There is a virtual endpoint downstream of ;

[0017] make Middle and upper direction All train missions are at the starting station The departure time set is recorded as ,make Any moment in ;

[0018] make Downward direction All train missions are at the starting station The departure time set is recorded as ,make Any moment in ;

[0019] make Middle and upper direction All train missions are at the terminal The arrival time set of ,but Always in the upward direction Starting point The train mission of the departure arrives at the terminal The time is ,and ,in, It is the running time between the starting station and the terminal station of a train task in a single running direction;

[0020] make Downward direction All train missions are at the terminal The arrival time set of ,but Always in the downward direction Starting point The train mission of the departure arrives at the terminal Moment ,and .

[0021] Furthermore, the set of spatiotemporal nodes in step 2 ,in, represents the set of spatiotemporal nodes of the parking lot, and , Represents the parking lot space-time node near the upward starting station or downward terminal station of a bus line, Represents the parking lot space-time node near the downbound starting station or upbound terminal station of a bus line; represents the set of spatiotemporal nodes of train missions, and , for Always in the upward direction Starting point The time and space nodes of the train mission for departure; for Always in the upward direction Terminal The time and space node of the arrived train mission; for Always in the downward direction Starting point The time and space nodes of the train mission for departure; for Always in the downward direction Terminal The time and space node of the arrived train mission; represents the set of spatial nodes during a single empty trip, and , for Always in the upward direction Starting point The time and space node of a single empty trip of the train, for Always in the downward direction Starting point The time and space nodes of a single empty trip of the vehicle; Any three space-time nodes in , and ;

[0022] Let spacetime arc set Any spacetime arc in , and include:

[0023] Start arc: bus in the upward direction From the virtual starting point Start running to the starting station The time and space nodes of the parking lot A starting arc of ;

[0024] The bus is in the down direction From the virtual starting point Start running to the starting station The time and space nodes of the parking lot A starting arc of ;

[0025] End arc: bus in the upward direction From the terminal The time and space nodes of the parking lot Run to the virtual end point The end arc of ;

[0026] The bus is in the down direction From the terminal The time and space nodes of the parking lot Run to the virtual end point The end arc of ;

[0027] Entering arc: Bus in the upward direction From the starting point Parking lot space-time nodes Start running to Always at the starting point The time and space nodes of the train mission An approaching arc is denoted by ;

[0028] The bus is in the down direction From the starting point Parking lot space-time nodes Start running to Always at the starting point The time and space nodes of the train mission An approaching arc is denoted by ;

[0029] Exit arc: Bus in the upward direction On Time from the terminal The time and space nodes of the train mission Run to the terminal Parking lot space-time nodes An outgoing arc of ;

[0030] The bus is in the down direction On Time from the terminal The time and space nodes of the train mission Run to the terminal Parking lot space-time nodes An outgoing arc of ;

[0031] Running arc: Bus in the upward direction On Time from the starting point The time and space nodes of the train mission Run to Time terminal The time and space nodes of the train mission A running arc of ;

[0032] The bus is in the down direction On Time from the starting point The time and space nodes of the train mission Run to Time terminal The time and space nodes of the train mission A running arc of ;

[0033] Conversion arc: bus in the up direction On Time from the terminal The time and space nodes of the train mission Run to Time of departure Single empty trip time and space node A conversion arc of ,and ;

[0034] The bus is in the down direction On Time from the downlink terminal The time and space nodes of the train mission Run to Time Upward Starting Station Single empty trip time and space node A conversion arc of ,and ,in, It is the transfer time between the terminal station in any direction and the starting station in the opposite direction;

[0035] Waiting arc: bus in the up direction On Always at the starting point The time and space nodes of the train mission Wait until There is a waiting arc at time , denoted as ,and , ;

[0036] The bus is in the down direction On Always at the starting point The time and space nodes of the train mission Wait until A waiting arc at time , denoted as , meet the time , ;

[0037] The bus is in the upward direction On At the terminal The time and space nodes of the train mission Wait until There is a waiting arc at time , denoted as , meet the time , ;

[0038] The bus is in the down direction On At the terminal The time and space nodes of the train mission Wait until A waiting arc at time , denoted as , meet the time , ;

[0039] Empty arc: The bus is in the down direction On Time from the starting point Single empty trip time and space node Run to Time terminal The time and space nodes of the train mission The empty arc of a train is recorded as ,and ;

[0040] The bus is in the upward direction On Time from the starting point Single empty trip time and space node Run to Time terminal The time and space nodes of the train trip The empty arc of a train is recorded as , meet the time ,in, It is the single empty running time between the starting station and the terminal station of a train task in a single running direction;

[0041] The bus starts from the virtual starting point Run to the virtual end point A non-working arc of .

[0042] Furthermore, the step 3 comprises:

[0043] Step 3.1: Use formula (1) to construct the objective function of the bus turnover planning model :

[0044] (1)

[0045] In formula (1), represents the set of start arcs of all buses; Indicates bus Whether it passes through any starting arc If it passes, then , otherwise, let ;

[0046] Step 3.2: Use equations (2) to (7) to construct the constraints of the bus turnover planning model:

[0047] (2)

[0048] (3)

[0049] (4)

[0050] (5)

[0051] (6)

[0052] (7)

[0053] In formula (2) to formula (7), Indicates bus Whether to pass from the virtual starting point All space-time arcs departing , if passed, then let , otherwise, let ,in, Represents a set of spacetime arcs From the virtual starting point All space-time arcs of departure; Indicates bus Whether to reach the virtual destination Arc , if passed, then let , otherwise, let , Represents a set of spacetime arcs Reach the virtual destination All space-time arcs of; Represents a set of spacetime arcs From any space-time node To the space-time node The space-time arc, Represents a set of spacetime arcs From the time and space node To the space-time node The space-time arc, Representing a spatiotemporal node The set of space-time nodes after deleting the virtual starting point and the virtual end point; Shows the bus passing through the space-time arc The unit battery capacity consumed, Indicates the maximum battery power of each bus when performing a mission; Indicates bus The set of running arcs of ;

[0054] Formula (8) is used to measure the fairness of the vehicle-to-vehicle tasks:

[0055] (8)

[0056] In formula (8), Indicates vehicle The number of train tasks, Represents the average number of missions for all vehicles.

[0057] Further, the step 4 comprises:

[0058] Step 4.1: Build the bus turnover planning model after Lagrangian relaxation;

[0059] Step 4.1.1: Use equation (9) to construct the objective function of the bus turnover planning model after Lagrangian relaxation :

[0060] (9)

[0061] In formula (9), Representing a spatiotemporal node The Lagrange multiplier of ;

[0062] Step 4.1.2: Use equations (2)-(5) and (7) to form the constraints of the bus turnover planning model after Lagrangian relaxation;

[0063] Step 4.2: Define the parameters in the Lagrangian relaxation algorithm and assign initial values;

[0064] Define and initialize the current number of iterations , define and initialize the optimal evaluation function gap=100%, the maximum number of iterations is , the step length is , let the relaxed upper bound be , and initialize , let the relaxed lower bound be , and initialize , No. The Lagrange multiplier of all time and space nodes of the iteration ,in, Indicates Iteration Node The Lagrange multiplier of The sub-gradient vector of the iteration , the error control value is ;

[0065] Step 4.3: According to The set of Lagrange multipliers of the space-time nodes of the iteration , the shortest path algorithm is used to solve the bus turnover planning model after Lagrangian relaxation, and the The bus turnover plan corresponding to the minimum number of buses required to complete all bus tasks is executed in the first iteration and used as the The relaxed lower bound at the iteration ,from and Select the larger value and assign it to ;

[0066] Step 4.4: Based on and The set of Lagrange multipliers of the space-time nodes of the iteration , the greedy algorithm is used to solve the bus turnover planning model after Lagrangian relaxation, and the The bus turnover plan corresponding to the maximum number of buses required to complete all bus tasks is executed in the first iteration and used as the The relaxed upper bound at the iteration ,from and Select the smaller value and assign it to ;

[0067] Step 4.5: Use formula (10) to Update to get The time and space nodes of the iteration Lagrange multipliers :

[0068] (10)

[0069] Step 4.6: If Established or If established, The relaxed lower bound at the iteration is used as the initial vehicle turnover plan Otherwise, Assign to Then, return to step 4.3 and continue iterating in sequence.

[0070] Furthermore, the greedy algorithm used in step 4.4 includes:

[0071] Step 4.4.1: Define the number of iterations as inter, and initialize inter=1; define the set of train tasks for the interth time as , and initialize , defines the Lagrange multiplier set of the space-time nodes at the inter iteration ,initialization = ;

[0072] Step 4.4.2: Set of Lagrange multipliers based on the space-time nodes of the inter-th iteration , use the shortest path algorithm to solve the Lagrangian relaxed bus turnover plan model for the interth time, obtain the shortest path of the interth iteration, and assign buses to execute according to the task sequence in the shortest path of the interth iteration, obtain the turnover plan for all buses under the interth iteration, and obtain the interth iteration from Delete the train tasks required for the shortest path of the inter iteration, so that the train task set of the inter+1 iteration ;

[0073] Step 4.4.3: Judgement Is it empty? If not, execute step 4.4.4. Otherwise, it means that all bus tasks have been assigned. The turnover plan of all buses under the inter iteration is used as the The relaxed upper bound at iterations;

[0074] Step 4.4.4: After assigning inter+1 to inter, return to step 4.4.2 and execute sequentially until Until it is empty.

[0075] Further, the step 5 comprises:

[0076] Step 5.0: Initialization ; Initialize the Iteration of vehicle turnover plan ;

[0077] Step 5.1: Judgement Are the number of bus tasks assigned to all buses in the same? If so, As the optimal solution for all vehicle turnover plans after considering fairness adjustments ; Otherwise, go to step 5.2;

[0078] Step 5.2: According to The size of the number of bus tasks assigned to each bus in the vehicle turnover plan is Sort all the vehicle turnover plans in descending order and get The vehicle turnover plan after descending sorting of iterations ;

[0079] Step 5.3: From The vehicle turnover plan with the largest number of assigned train tasks is selected as , then the vehicle turnover plan for all remaining buses is recorded as , and The vehicle turnover plan of any bus in is recorded as ;

[0080] Step 5.4: Judgement Is the number of train tasks in greater than The number of train tasks in, if so, then Any train mission insert and assign the train mission from Delete and update and , and with The remaining bus turnover plans together constitute the Iteration of vehicle turnover plan Then, execute step 5.5; otherwise, After selecting another bus turnover plan, return to step 5.4 and execute sequentially until Until the vehicle turnover plan for all public buses is completed;

[0081] Step 5.5: Assign to Then, return to step 5.1 and execute sequentially.

[0082] The electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the bus turnover plan optimization method, and the processor is configured to execute the program stored in the memory.

[0083] The present invention provides a computer-readable storage medium, and the computer-readable storage medium stores a computer program, which is characterized in that when the computer program is run by a processor, the steps of the bus turnover plan optimization method are executed.

[0084] Compared with the prior art, the present invention has the following beneficial effects:

[0085] 1. Aiming at the problem of cumbersome calculations and waste caused by uneven allocation of vehicle resources in the current bus turnover plan solution process, the present invention proposes a method of combining a time-space network diagram to characterize complex bus turnover plan tasks, innovatively proposes to consider the problem of bus operating power capacity limitation and the use of as few buses as possible to complete the task of the trip, and establishes a model based on the formulated time-space network diagram, and solves the model using the Lagrangian relaxation algorithm that combines the shortest path algorithm and the greedy algorithm, effectively improving the efficiency of the vehicle turnover plan. The present invention generates an initial vehicle turnover plan through the Lagrangian relaxation algorithm, while considering the fairness of the task allocation of the trip, overcoming the problem of uneven allocation ignored by the traditional bus turnover plan, thereby effectively improving the working efficiency of the bus and the rational allocation and utilization of bus resources.

[0086] 2. In the process of building the space-time network of the present invention, the space-time node set and space-time arc set defined in the space-time network diagram can correctly reflect the actual operating task status of the bus in the operating direction. The formulated space-time network can abstract the complex operating conditions of the bus on the route into space-time arcs with different meanings in the network, which is beneficial for characterizing the task status of different trains and for the subsequent modeling and analysis to solve the vehicle turnover plan.

[0087] 3. The present invention comprehensively considers the actual operation of buses in performing the mission on a route, flexibly adjusts the vehicle turnover plan, and by considering the constraints of the bus operating power capacity and the fairness of the mission allocation, it can generate a bus turnover plan that is both high-quality, efficient and fair. This can not only make more rational use of bus transport resources, but also promote the vigorous development of public transportation. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 It is the overall flow chart of the present invention;

[0089] Figure 2 A schematic diagram of a bus route of the present invention;

[0090] Figure 3 A schematic diagram of the space-time network constructed for the present invention;

[0091] Figure 4 It is a solution flow chart of the Lagrangian relaxation algorithm of the present invention. DETAILED DESCRIPTION

[0092] In this embodiment, Figure 1As shown, a bus turnover plan optimization method considering the fairness of bus task allocation is to first construct a customized space-time network diagram of the bus turnover plan according to the bus task plan of a given bus schedule, then build a model of the space-time network diagram, and then use the Lagrangian relaxation algorithm that combines the shortest path algorithm and the greedy algorithm to solve the model to obtain a high-quality initial bus turnover plan. On this basis, consider the fairness of bus task allocation and use the insertion heuristic algorithm to adjust and optimize the initial bus turnover plan, and finally obtain a high-quality bus turnover plan with fair allocation of bus tasks. Specifically, the method is carried out in the following steps:

[0093] Step 1: Record the two directions in which buses run on a bus route as the up direction and downlink direction , and constitute a set of driving directions ;

[0094] like Figure 2 As shown, let the starting station in the upward direction be , the terminal is recorded as , the starting station in the downlink direction is recorded as , the terminal is recorded as , and constitute a collection of stations ;

[0095] Let the bus set be ,and Any bus is denoted as ,make express The total number of buses in Indicates The set of bus tasks assigned to the buses; ; represents the set of bus schedule tasks in the bus timetable; express The total number of train missions.

[0096] Define the starting point and There is a virtual starting point upstream of , the terminal and There is a virtual endpoint downstream of ;

[0097] make Middle and upper direction All train missions are at the starting station The departure time set is recorded as ,make Any moment in ;

[0098] make Downward direction All train missions are at the starting station The departure time set is recorded as ,make Any moment in ;

[0099] make Middle and upper direction All train missions are at the terminal The arrival time set of ,but Always in the upward direction Starting point The train mission of the departure arrives at the terminal The time is ,and ,in, It is the running time between the starting station and the terminal station of a train task in a single running direction;

[0100] make Downward direction All train missions are at the terminal The arrival time set of ,but Always in the downward direction Starting point The train mission of the departure arrives at the terminal Moment ,and ;

[0101] In this embodiment, the spatiotemporal network of the bus turnover plan is as follows: Figure 3 As shown, the black circles represent different space-time nodes, the directed line segments connecting two nodes represent different space-time arcs, and the dotted boxes represent all the train trip space-time nodes and single empty trip space-time nodes in the two running directions.

[0102] Given The bus operation schedule with multiple bus tasks is used to construct the spatiotemporal network of bus turnover status ,in, represents a collection of spatiotemporal nodes, and ,in, represents the set of spatiotemporal nodes of the parking lot, and , Represents the parking lot space-time node near the upward starting station or downward terminal station of a bus line, Represents the parking lot space-time node near the downbound starting station or upbound terminal station of a bus line; represents the set of spatiotemporal nodes of train missions, and , for Always in the upward direction Starting point The time and space nodes of the train mission for departure; for Always in the upward direction Terminal The time and space node of the arrived train mission; for Always in the downward direction Starting point The time and space nodes of the train mission for departure; for Always in the downward direction Terminal The time and space node of the arrived train mission; represents the set of spatial nodes during a single empty trip, and , for Always in the upward direction Starting point The time and space node of a single empty trip of the train, for Always in the downward direction Starting point The time and space nodes of a single empty trip of the vehicle; Any three space-time nodes in , and .

[0103] Denote the set of spacetime arcs, let the spacetime arc set Any spacetime arc in , and include:

[0104] Start arc: bus in the upward direction From the virtual starting point Start running to the starting station The time and space nodes of the parking lot A starting arc of ;

[0105] The bus is in the down direction From the virtual starting point Start running to the starting station The time and space nodes of the parking lot A starting arc of ;

[0106] End arc: bus in the upward direction From the terminal The time and space nodes of the parking lot Run to the virtual end point The end arc of ;

[0107] The bus is in the down direction From the terminal The time and space nodes of the parking lot Run to the virtual end point The end arc of ;

[0108] Entering arc: Bus in the upward direction From the starting point Parking lot space-time nodes Start running to Always at the starting point The time and space nodes of the train mission An approaching arc is denoted by ;

[0109] The bus is in the down direction From the starting point Parking lot space-time nodes Start running to Always at the starting point The time and space nodes of the train mission An approaching arc is denoted by ;

[0110] Exit arc: Bus in the upward direction On Time from the terminal The time and space nodes of the train mission Run to the terminal Parking lot space-time nodes An outgoing arc of ;

[0111] The bus is in the down direction On Time from the terminal The time and space nodes of the train mission Run to the terminal Parking lot space-time nodes An outgoing arc of ;

[0112] Running arc: Bus in the upward direction On Time from the starting point The time and space nodes of the train mission Run to Time terminal The time and space nodes of the train mission A running arc of ;

[0113] The bus is in the down direction On Time from the starting point The time and space nodes of the train mission Run to Time terminal The time and space nodes of the train mission A running arc of ;

[0114] Conversion arc: bus in the up direction On Time from the terminal The time and space nodes of the train mission Run to Time of departure Single empty trip time and space node A conversion arc of ,and ;

[0115] The bus is in the down direction On Time from the downlink terminal The time and space nodes of the train mission Run to Time Upward Starting Station Single empty trip time and space node A conversion arc of ,and ,in, It is the transfer time between the terminal station in any direction and the starting station in the opposite direction.

[0116] Waiting arc: bus in the up direction On Always at the starting point The time and space nodes of the train mission Wait until There is a waiting arc at time , denoted as ,and , ;

[0117] The bus is in the down direction On Always at the starting point The time and space nodes of the train mission Wait until A waiting arc at time , denoted as , meet the time ;

[0118] The bus is in the upward direction On At the terminal The time and space nodes of the train mission Wait until There is a waiting arc at time , denoted as , meet the time ;

[0119] The bus is in the down direction On At the terminal The time and space nodes of the train mission Wait until A waiting arc at time , denoted as , meet the time ;

[0120] Empty arc: The bus is in the down direction On Time from the starting point Single empty trip time and space node Run to Time terminal The time and space nodes of the train mission The empty arc of a train is recorded as , meet the time ;

[0121] The bus is in the upward direction On Time from the starting point Single empty trip time and space node Run to Time terminal The time and space nodes of the train trip The empty arc of a train is recorded as , meet the time ,in, It is the single empty running time between the starting station and the terminal station of a train task in a single running direction;

[0122] The bus starts from the virtual starting point Run to the virtual end point A non-working arc of .

[0123] Step 2: Spatiotemporal network based on turnover state , establish a bus turnover planning model with the goal of minimizing the number of buses performing service tasks;

[0124] Using formula (1) to construct the objective function of the bus turnover planning model :

[0125] (1)

[0126] In formula (1), represents the set of start arcs of all buses; Indicates bus Whether it passes through any starting arc If it passes, then , otherwise, let ;

[0127] The constraints of the bus turnover planning model are constructed using equations (2) to (7):

[0128] (2)

[0129] (3)

[0130] (4)

[0131] (5)

[0132] (6)

[0133] (7)

[0134] In formula (2) to formula (7), Indicates bus Whether to pass from the virtual starting point All space-time arcs departing , if passed, then let , otherwise, let ,in, Represents a set of spacetime arcs From the virtual starting point All space-time arcs of departure; Indicates bus Whether to reach the virtual destination Arc , if passed, then let , otherwise 0, Represents a set of spacetime arcs Reach the virtual destination All space-time arcs of; Represents a set of spacetime arcs From any time and space node To the space-time node The space-time arc, Represents a set of spacetime arcs From the time and space node To the space-time node The space-time arc, Representing a spatiotemporal node The set of space-time nodes after deleting the virtual starting point and the virtual end point; Shows the bus passing through the space-time arc The unit battery capacity consumed, Indicates the maximum battery power of each bus when performing a mission; Indicates bus The set of running arcs.

[0135] Formula (8) is used to measure the fairness of the vehicle-to-vehicle tasks:

[0136] (8)

[0137] In formula (8), Indicates vehicle The number of train tasks, Represents the average number of missions for all vehicles.

[0138] Step 3: If Figure 4 As shown, the Lagrangian relaxation algorithm is used to solve the bus turnover plan model and obtain the initial bus turnover plan. , the specific steps are as follows:

[0139] Step 3.1: Build the bus turnover planning model after Lagrangian relaxation;

[0140] Step 3.1.1: Use equation (9) to construct the objective function of the bus turnover planning model after Lagrangian relaxation :

[0141] (9)

[0142] Step 3.1.2: Use equations (2) to (5) and (7) to form the constraints of the bus turnover planning model after Lagrangian relaxation.

[0143] Step 3.2: Define the parameters in the Lagrangian relaxation algorithm and assign initial values;

[0144] Define and initialize the current number of iterations , define and initialize the optimal evaluation function gap=100%, the maximum number of iterations is , the step length is , let the relaxed upper bound be , and initialize , let the relaxed lower bound be , and initialize , No. The Lagrange multiplier of all time and space nodes of the iteration ,in, Indicates Iteration Node The Lagrange multiplier of The sub-gradient vector of the iteration , the error control value is ;

[0145] Step 3.3: According to The set of Lagrange multipliers of the space-time nodes of the iteration , the shortest path algorithm is used to solve the bus turnover planning model after Lagrangian relaxation, and the The minimum number of buses required to complete all the bus tasks and the turnover plan of all vehicles are executed in the second iteration, and the turnover plan of all buses is used as the first The relaxed lower bound at the iteration ,from and Select the larger value and assign it to .

[0146] Step 3.4: Based on and The set of Lagrange multipliers of the space-time nodes of the iteration , the greedy algorithm is used to solve the bus turnover planning model after Lagrangian relaxation, and the The maximum number of buses required to complete all the bus tasks and the turnover plan of all vehicles are executed in the first iteration, and the turnover plan of all buses is used as the first The relaxed upper bound at the iteration ,from and Select the smaller value and assign it to ;

[0147] Step 3.5: Use formula (10) to Update to get The time and space nodes of the iteration Lagrange multipliers :

[0148] (10)

[0149] Step 3.6: If Established or If established, The relaxed lower bound at the iteration is used as the initial vehicle turnover plan Otherwise, Assign to Then, return to step 3.3 and continue iterating in sequence.

[0150] Step 4: Use the greedy algorithm to find the upper bound feasible solution of the Lagrangian relaxation algorithm. The specific steps are as follows:

[0151] Step 4.1: Define the number of iterations as inter, and initialize inter=1; define the set of train tasks for the interth time as , and initialize , defines the Lagrange multiplier set of the space-time nodes at the inter iteration ,initialization = ;

[0152] Step 4.2: Lagrange multiplier set based on the space-time node of the inter iteration , use the shortest path algorithm to solve the Lagrangian relaxed bus turnover plan model for the interth time, obtain the shortest path of the interth iteration, and assign buses to execute according to the task sequence in the shortest path of the interth iteration, obtain the turnover plan for all buses under the interth iteration, and obtain the interth iteration from Delete the train tasks required for the shortest path of the inter iteration, so that the train task set of the inter+1 iteration .

[0153] Step 4.3: Judgement Is it empty? If not, execute step 4.4. Otherwise, it means that all bus tasks have been assigned. The turnover plan of all buses under the inter iteration is used as the The relaxed upper bound at iterations;

[0154] Step 4.4: After assigning inter+1 to inter, return to step 4.2 and execute sequentially until Until it is empty.

[0155] Step 5: Considering fairness, an insertion heuristic algorithm is used to optimize the initial vehicle turnover plan. Adjustments are made to obtain the optimal vehicle turnover plan that takes fairness into account , the specific steps are as follows:

[0156] Step 5.0: Initialization ; Initialize the Iteration of vehicle turnover plan ;

[0157] Step 5.1: Judgement Are the number of bus tasks assigned to all buses in the same? If so, As the optimal solution for all vehicle turnover plans after considering fairness adjustments ; Otherwise, proceed to step 5.2.

[0158] Step 5.2: According to The size of the number of bus tasks assigned to each bus in the vehicle turnover plan is Sort all the vehicle turnover plans in descending order and get The vehicle turnover plan after descending sorting of iterations ;

[0159] Step 5.3: From The vehicle turnover plan with the largest number of assigned train tasks is selected as , then the vehicle turnover plan for all remaining buses is recorded as , and The vehicle turnover plan of any bus in is recorded as ;

[0160] Step 5.4: Judgement Is the number of train tasks in greater than The number of train tasks in, if so, then Any train mission insert and assign the train mission from Delete and update and , and with The remaining bus turnover plans together constitute the Iteration of vehicle turnover plan Then, execute step 5.5; otherwise, After selecting another bus turnover plan, return to step 5.4 and execute sequentially until Until the vehicle turnover plan for all public buses is completed;

[0161] Step 5.5: Assign to Then, return to step 5.1 and execute sequentially.

[0162] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0163] In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

Claims

1. A bus turnover plan optimization method considering the fairness of bus task allocation, characterized in that: The following steps are involved: Step 1: Set the starting station, terminal station, departure time set and arrival time set of the bus on a bus route; Step 2: Given The bus operation schedule with multiple bus tasks is used to construct the spatiotemporal network of bus turnover status ,in, represents a collection of spatiotemporal nodes, represents a collection of spacetime arcs; Step 3: Spatiotemporal network based on turnover state , establish a bus turnover planning model with the goal of minimizing the number of buses performing service tasks; Step 4: Use the Lagrangian relaxation algorithm to solve the bus turnover plan model and obtain the initial bus turnover plan. ; Step 5: Considering fairness, use the insertion heuristic algorithm to Make adjustments to get the optimal bus turnover plan .

2. A bus turnover plan optimization method considering fairness of bus task allocation according to claim 1, characterized in that: The step 1 comprises: The two directions in which buses run on a bus route are recorded as the up direction and downlink direction , and constitute a set of driving directions ; Let the starting station in the upward direction be , the terminal is recorded as , the starting station in the downlink direction is recorded as , the terminal is recorded as , and constitute a collection of stations ; Let the bus set be ,and Any bus is denoted as ,make express The total number of buses in Indicates The set of bus tasks assigned to the buses; ; represents the set of bus schedule tasks in the bus timetable; express The total number of train missions; Define the starting station and There is a virtual starting point upstream of , the terminal and There is a virtual endpoint downstream of ; make Middle and upper direction All train missions are at the starting station The departure time set is recorded as ,make Any moment in ; make Downward direction All train missions are at the starting station The departure time set is recorded as ,make Any moment in ; make Middle and upper direction All train missions are at the terminal The arrival time set of ,but Always in the upward direction Starting point The train mission of the departure arrives at the terminal The time is ,and ,in, It is the running time between the starting station and the terminal station of a train task in a single running direction; make Downward direction All train missions are at the terminal The arrival time set of ,but Always in the downward direction Starting point The train mission of the departure arrives at the terminal Moment ,and .

3. A bus turnover plan optimization method considering fairness of bus task allocation according to claim 2, characterized in that: The collection of spatiotemporal nodes in step 2 ,in, represents the set of spatiotemporal nodes of the parking lot, and , Represents the parking lot space-time node near the upward starting station or downward terminal station of a bus line, Represents the parking lot space-time node near the downbound starting station or upbound terminal station of a bus line; represents the set of spatiotemporal nodes of train missions, and , for Always in the upward direction Starting point The time and space nodes of the train mission for departure; for Always in the upward direction Terminal The time and space node of the arrived train mission; for Always in the downward direction Starting point The time and space nodes of the train mission for departure; for Always in the downward direction Terminal The time and space node of the arrived train mission; represents the set of spatial nodes during a single empty trip, and , for Always in the upward direction Starting point The time and space node of a single empty trip of the train, for Always in the downward direction Starting point The time and space nodes of a single empty trip of the vehicle; Any three space-time nodes in , and ; Let spacetime arc set Any spacetime arc in , and include: Start arc: bus in the upward direction From the virtual starting point Start running to the starting station The time and space nodes of the parking lot A starting arc of ; The bus is in the down direction From the virtual starting point Start running to the starting station The time and space nodes of the parking lot A starting arc of ; End arc: bus in the upward direction From the terminal The time and space nodes of the parking lot Run to the virtual end point The end arc of ; The bus is in the down direction From the terminal The time and space nodes of the parking lot Run to the virtual end point The end arc of ; Entering arc: Bus in the upward direction From the starting point Parking lot space-time nodes Start running to Always at the starting point The time and space nodes of the train mission An approaching arc is denoted by ; The bus is in the down direction From the starting point Parking lot space-time nodes Start running to Always at the starting point The time and space nodes of the train mission An approaching arc is denoted by ; Exit arc: Bus in the upward direction On Time from the terminal The time and space nodes of the train mission Run to the terminal Parking lot space-time nodes An outgoing arc of ; The bus is in the down direction On Time from the terminal The time and space nodes of the train mission Run to the terminal Parking lot space-time nodes An outgoing arc of ; Running arc: Bus in the upward direction On Time from the starting point The time and space nodes of the train mission Run to Time terminal The time and space nodes of the train mission A running arc of ; The bus is in the down direction On Time from the starting point The time and space nodes of the train mission Run to Time terminal The time and space nodes of the train mission A running arc of ; Conversion arc: bus in the up direction On Time from the terminal The time and space nodes of the train mission Run to Time of departure Single empty trip time and space node A conversion arc of ,and ; The bus is in the down direction On Time from the downlink terminal The time and space nodes of the train mission Run to Time Upward Starting Station Single empty trip time and space node A conversion arc of ,and ,in, It is the transfer time between the terminal station in any direction and the starting station in the opposite direction; Waiting arc: bus in the up direction On Always at the starting point The time and space nodes of the train mission Wait until There is a waiting arc at time , denoted as ,and , ; The bus is in the down direction On Always at the starting point The time and space nodes of the train mission Wait until A waiting arc at time , denoted as , meet the time , ; The bus is in the upward direction On At the terminal The time and space nodes of the train mission Wait until There is a waiting arc at time , denoted as , meet the time , ; The bus is in the down direction On At the terminal The time and space nodes of the train mission Wait until A waiting arc at time , denoted as , meet the time , ; Empty arc: The bus is in the down direction On Time from the starting point Single empty trip time and space node Run to Time terminal The time and space nodes of the train mission The empty arc of a train is recorded as ,and ; The bus is in the upward direction On Time from the starting point Single empty trip time and space node Run to Time terminal The time and space nodes of the train trip The empty arc of a train is recorded as , meet the time ,in, It is the single empty running time between the starting station and the terminal station of a train task in a single running direction; The bus starts from the virtual starting point Run to the virtual end point A non-working arc of .

4. A bus turnover plan optimization method considering fairness of bus task allocation according to claim 3, characterized in that: The step 3 comprises: Step 3.1: Use formula (1) to construct the objective function of the bus turnover planning model : (1) In formula (1), represents the set of start arcs of all buses; Indicates bus Whether it passes through any starting arc If it passes, then , otherwise, let ; Step 3.2: Use equations (2) to (7) to construct the constraints of the bus turnover planning model: (2) (3) (4) (5) (6) (7) In formula (2) to formula (7), Indicates bus Whether to pass from the virtual starting point All space-time arcs departing , if passed, then let , otherwise, let ,in, Represents a set of spacetime arcs From the virtual starting point All space-time arcs of departure; Indicates bus Whether to reach the virtual destination Arc , if passed, then let , otherwise, let , Represents a set of spacetime arcs Reach the virtual destination All space-time arcs of; Represents a set of spacetime arcs From any space-time node To the space-time node The space-time arc, Represents a set of spacetime arcs From the time and space node To the space-time node The space-time arc, Representing a spatiotemporal node The set of space-time nodes after deleting the virtual starting point and the virtual end point; Shows the bus passing through the space-time arc The unit battery capacity consumed, Indicates the maximum battery power of each bus when performing a mission; Indicates bus The set of running arcs of ; Formula (8) is used to measure the fairness of the vehicle-to-vehicle tasks: (8) In formula (8), Indicates vehicle The number of train tasks, Represents the average number of missions for all vehicles.

5. The bus turnover plan optimization method considering the fairness of bus task allocation according to claim 4 is characterized in that: The step 4 comprises: Step 4.1: Build the bus turnover planning model after Lagrangian relaxation; Step 4.1.1: Use equation (9) to construct the objective function of the bus turnover planning model after Lagrangian relaxation : (9) In formula (9), Representing a spatiotemporal node The Lagrange multiplier of ; Step 4.1.2: Use equations (2)-(5) and (7) to form the constraints of the bus turnover planning model after Lagrangian relaxation; Step 4.2: Define the parameters in the Lagrangian relaxation algorithm and assign initial values; Define and initialize the current number of iterations , define and initialize the optimal evaluation function gap=100%, the maximum number of iterations is , the step length is , let the relaxed upper bound be , and initialize , let the relaxed lower bound be , and initialize , No. The Lagrange multiplier of all time and space nodes of the iteration ,in, Indicates Iteration Node The Lagrange multiplier of The sub-gradient vector of the iteration , the error control value is ; Step 4.3: According to The set of Lagrange multipliers of the space-time nodes of the iteration , the shortest path algorithm is used to solve the bus turnover planning model after Lagrangian relaxation, and the first The bus turnover plan corresponding to the minimum number of buses required to complete all bus tasks is executed in the first iteration and used as the The relaxed lower bound at the iteration ,from and Select the larger value and assign it to ; Step 4.4: Based on and The set of Lagrange multipliers of the space-time nodes of the iteration , the greedy algorithm is used to solve the bus turnover planning model after Lagrangian relaxation, and the The bus turnover plan corresponding to the maximum number of buses required to complete all bus tasks is executed in the first iteration and used as the The relaxed upper bound at the iteration ,from and Select the smaller value and assign it to ; Step 4.5: Use formula (10) to Update to get The time and space nodes of the iteration Lagrange multipliers : (10) Step 4.6: If Established or If established, The relaxed lower bound at the iteration is used as the initial vehicle turnover plan Otherwise, Assign to Then, return to step 4.3 and continue iterating in sequence.

6. The bus turnover plan optimization method considering the fairness of bus task allocation according to claim 5 is characterized in that: The greedy algorithm used in step 4.4 includes: Step 4.4.1: Define the number of iterations as inter, and initialize inter=1; define the set of train tasks for the interth time as , and initialize , defines the Lagrange multiplier set of the space-time nodes at the inter iteration ,initialization = ; Step 4.4.2: Set of Lagrange multipliers based on the space-time nodes of the inter-th iteration , use the shortest path algorithm to solve the Lagrangian relaxed bus turnover plan model for the interth time, obtain the shortest path of the interth iteration, and assign buses to execute according to the task sequence in the shortest path of the interth iteration, obtain the turnover plan for all buses under the interth iteration, and obtain the interth iteration from Delete the train tasks required for the shortest path of the inter iteration, so that the train task set of the inter+1 iteration ; Step 4.4.3: Judgement Is it empty? If not, execute step 4.4.

4. Otherwise, it means that all bus tasks have been assigned. The turnover plan of all buses under the inter iteration is used as the The relaxed upper bound at iterations; Step 4.4.4: After assigning inter+1 to inter, return to step 4.4.2 and execute sequentially until Until it is empty.

7. The bus turnover plan optimization method considering the fairness of bus task allocation according to claim 6 is characterized in that: The step 5 comprises: Step 5.0: Initialization ; Initialize the Iteration of vehicle turnover plan ; Step 5.1: Judgement Are the number of bus tasks assigned to all buses in the same? If so, As the optimal solution for all vehicle turnover plans after considering fairness adjustments ; Otherwise, go to step 5.2; Step 5.2: According to The size of the number of bus tasks assigned to each bus in the vehicle turnover plan is Sort all the vehicle turnover plans in descending order and get The vehicle turnover plan after descending sorting of iterations ; Step 5.3: From The vehicle turnover plan with the largest number of assigned train tasks is selected as , then the vehicle turnover plan for all remaining buses is recorded as , and The vehicle turnover plan of any bus in is recorded as ; Step 5.4: Judgement Is the number of train tasks in greater than The number of train tasks in, if so, then Any train mission insert and assign the train mission from Delete and update and , and The remaining bus turnover plans together constitute the Iteration of vehicle turnover plan Then, execute step 5.5; otherwise, After selecting another bus turnover plan, return to step 5.4 and execute sequentially until Until the vehicle turnover plan for all public buses is completed; Step 5.5: Assign to Then, return to step 5.1 and execute sequentially.

8. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the bus turnover plan optimization method described in any one of claims 1-7, and the processor is configured to execute the program stored in the memory.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the bus turnover plan optimization method described in any one of claims 1 to 7 are executed.

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