Modular bus dispatching optimization method for bus corridors

Abstract

The invention belongs to the field of bus dispatching optimization, and particularly relates to a modular bus dispatching optimization method for a bus corridor, in particular to a modular bus dispatching optimization method for the bus corridor. The objective of the invention is to solve the problems of low operation efficiency, long passenger transfer waiting time, long passenger in-bus time and high operation cost of a bus company of an existing bus system. The invention discloses a modularized bus scheduling optimization method for a bus corridor. The method comprises the following steps: 1, collecting basic information of bus stations, configuring modularized vehicles, configuring modularized bus shifts, and collecting passenger travel request data; 2, defining optimization variables; 3, judging a transfer strategy, and calculating the number of transferred passengers based on the transfer strategy; 4, splitting and combining the vehicle to complete passenger transfer, and updating shift information based on a passenger transfer result; 5, establishing a modularized bus scheduling optimization model; and 6, solving the modularized bus scheduling optimization model, and outputting an optimal scheduling scheme.

Description

Technical Field

[0001] The present invention belongs to the field of bus dispatching optimization, and particularly relates to a modular bus dispatching optimization method for a bus corridor. Background Art

[0002] The bus operation on the passenger flow corridor of the urban arterial road bears the daily travel needs of a large number of citizens, and is of great significance for reducing private car travel, alleviating urban traffic congestion, and promoting the sustainable development of the transportation system. However, the traditional arterial bus operation still faces many problems. On the one hand, the fixed bus vehicle capacity is difficult to effectively respond to the uneven passenger demands at each stop, and the fixed departure interval results in inevitable waste of transport capacity during the vehicle operation; on the other hand, passengers need to get off and wait during the transfer process, resulting in inconvenient travel and increased travel time.

[0003] As a new type of public transportation vehicle, the modular bus provides a new idea for solving the above problems. Each modular bus can be combined into a fleet or split during operation to adapt to the passenger flow differences at each section; at the same time, passengers can transfer between the modular buses within the fleet, overcoming the inconvenience that passengers need to get off and transfer in the traditional bus mode. The existing traditional bus dispatching methods are mainly based on fixed vehicle numbers and operation routes, and are difficult to cope with the dynamic changes of the passenger flow on the urban bus corridor. Especially when facing modular buses, the traditional methods cannot effectively coordinate the changes in the fleet form, do not consider the flexibility of fleet combination and splitting, and do not optimize the time and efficiency of the transfer link. Therefore, the traditional bus dispatching methods are not suitable for modular buses. In order to improve the operation efficiency of modular buses on the arterial passenger flow corridor, it is necessary to establish a new dispatching method to accurately coordinate the departure times of each modular bus, so as to reduce the waiting time of passengers during the transfer link and the travel uncertainty, and give full play to the flexibility advantages of modular buses. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems that the existing bus dispatching methods cannot effectively coordinate the changes in the fleet form, do not consider the flexibility of fleet combination and splitting, are not suitable for modular buses, resulting in low operation efficiency of the bus system, long waiting time for passengers to transfer, long time for passengers in the vehicle, and high operation cost of the bus company, and to propose a modular bus dispatching optimization method for a bus corridor.

[0005] The specific process of a modular bus dispatching optimization method for a bus corridor is as follows: Step 1, collect the basic information of bus stops, configure modular vehicles, configure modular bus schedules, and collect passenger travel request data; Step 2, define optimization variables; the specific process is as follows: Define a 0-1 variable Indicates a modular vehicle And the section On the th shift The relationship between, if the modular vehicle Participates in the execution of the shift , then , otherwise ; Define a 0-1 variable , if on section s the th shift Travels from station To station Within the section , then , otherwise equal to 0; where stations And Both belong to the set of stations in the section ; Define a 0-1 variable Indicates the relationship between a passenger travel request And a modular vehicle , if the passenger travel request Is served by the modular vehicle , then , otherwise ; Define a continuous variable Indicates the time when the th shift On section Arrives at the station Within the section ; Define a continuous variable Indicates the average running speed of the th shift On section Within the section , in m / s.

[0006] Step 3: Based on Steps 1 and 2, determine the transfer strategy and calculate the number of transfer passengers based on the transfer strategy; Step 4: Based on Step 3, split and combine the vehicles to complete passenger transfer, and update the shift information based on the passenger transfer result; Step 5: Based on Steps 1, 2, 3, and 4, establish an optimization model for modular bus vehicle scheduling; Step 6: Solve the optimization model for modular bus vehicle scheduling and output the optimal scheduling plan .

[0007] The beneficial effects of the present invention are as follows: Under the environment of the arterial passenger flow corridor, considering the operation characteristics of modular bus vehicles, the present invention proposes a new modular bus vehicle scheduling method, which focuses on solving the following key problems: Introduce the combination and separation mechanism of modular bus vehicles, enabling the fleet to dynamically adjust according to the unbalanced passenger flow demand, avoiding resource waste, and ensuring that the bus system can more accurately meet the travel needs of passengers; The present invention designs a precise transfer coordination strategy, which supports both in-vehicle transfer and alighting transfer for passengers, eliminating the inconvenience of having to alight and transfer in the traditional bus system. The proposed optimization scheme will improve the operation efficiency of the bus system, reduce the passenger transfer waiting time, and reduce the in-vehicle time of passengers; Combined with the dynamic changes of passenger flow at key stations, the present invention finely adjusts the distribution and scheduling of vehicle resources to ensure that the resources at each station can be accurately matched according to real-time needs, avoiding the inefficiency and mismatch caused by fixed resource allocation in the traditional method, and improving the overall operation efficiency of the bus system.

[0008] The optimization method proposed by the present invention considers the impacts of fleet form adjustment, in-vehicle transfer of passengers, and vehicle reallocation on the operation of modular bus vehicles. The generated scheduling scheme can reduce the operation cost of the bus company, reduce the travel cost of passengers, improve the operation efficiency of the bus system, and reduce the passenger transfer waiting time. At the same time, the invention also improves the service level of the bus system, provides strong support for the future intelligentization of bus scheduling, and promotes the sustainable development and digital transformation of the bus system. Brief Description of the Drawings

[0009] Figure 1 It is a flowchart of the present invention. Detailed Embodiment

[0010] Detailed Embodiment 1: The specific process of a modular bus scheduling optimization method for a bus corridor in this embodiment is as follows: Step 1: Collect the basic information of bus stops, configure modular vehicles (1 vehicle), configure modular bus schedules, and collect passenger travel request data; Step 2: Define optimization variables; the specific process is as follows: Define 0-1 variables indicating the relationship between modular vehicle and the th schedule on section . If modular vehicle participates in executing schedule , then , otherwise ; Define 0-1 variables , if the th shift on section travels from station to station , then , otherwise it is equal to 0; where stations and both belong to the set of stations on section ; Define a 0-1 variable to represent the relationship between the passenger travel request and the modular vehicle . If the passenger travel request is served by the modular vehicle , then , otherwise ; Define a continuous variable to represent the time when the th shift on section arrives at the station within section ; Define a continuous variable to represent the average running speed of the th shift on section within section , in m / s.

[0011] Step 3: Based on Steps 1 and 2, judge the transfer strategy and calculate the number of transfer passengers based on the transfer strategy; Step 4: Based on Step 3, split and combine the vehicles to complete passenger transfer, and update the shift information based on the passenger transfer result; Step 5: Based on Steps 1, 2, 3, and 4, establish an optimization model for modular bus vehicle scheduling; Step 6: Solve the optimization model for modular bus vehicle scheduling and output the optimal scheduling plan .

[0012] Specific Embodiment 2: The difference between this embodiment and Specific Embodiment 1 is that in Step 1, the basic information of bus stops is collected, modular vehicles (1 vehicle) are configured, modular bus shifts are configured, and passenger travel request data is collected; the specific process is as follows: Step 1.1: Collect the basic information of bus stops; the specific process is as follows: Divide the bus operations on the arterial passenger flow corridor into the upstream direction and the downstream direction, and each direction contains bus stops; The set of stations in the upward direction is denoted as , and the set of stations in the downward direction is denoted as ; All stations on the passenger flow corridor are denoted as the set ; Set the passenger flow threshold (there is 1 passenger flow threshold for each hour in 24 hours of a day), and set the stations with passenger flow greater than the passenger flow threshold among all stations as key stations; The key stations are used for splitting and combining modular bus fleets; Store the key stations on the passenger flow corridor into the key station set , ; Among them, represents the first key station in the key station set , represents the second key station in the key station set , represents the th key station in the key station set , represents the key station set; Taking the key stations as boundaries, adjacent key stations are divided into 1 section, and the passenger flow corridor is sectioned; Let represent the set of sections divided in the upward direction with the key stations as boundaries; Let represent the set of sections divided in the downward direction with the key stations as boundaries; Among them, and respectively represent the maximum values of the number of sections divided in the upward and downward directions of the passenger flow corridor with the key stations as boundaries; All sections on the passenger flow corridor are denoted as the set ; Step 1.2. Configure modular vehicles (1 vehicle); The specific process is as follows: Let represent the set of numbers of all modular vehicles participating in the scheduling during the operation period ; Among them, is the total number of modular vehicles configured on the passenger flow corridor, and the numbers increase sequentially starting from 1; To ensure the smooth operation, store vehicles at the key station before the start time of the operation; Each shift consists of one or more modular vehicles. Each section contains shifts with different departure times. Each shift is a process of traveling from one key station to an adjacent key station and picking up and dropping off passengers on the way to complete the operation task. Let the set represent all shifts on the bus corridor during the operation period ; Among them, represents the set of all shifts in section 1 based on the section division in step 1.1; represents the set of all shifts in section 2 based on the section division in step 1.1; represents the set of all shifts in section ; represents the set of all shifts in section based on the key station section division in step 1.1; The set is further represented as ; Among them, represents the first shift on section , represents the second shift on section , represents the th shift on section , represents the th shift on section ; represents the total number of shifts in section , section ; Step 1.4. Collect passenger travel request data; the specific process is as follows: Collect the set of passenger travel requests on the passenger flow corridor during the operation period in the past 30 working days; The information contained in a passenger travel request includes: the boarding station , the alighting station , the earliest expected start service time , the latest expected start service time and the number of passengers to be served ; ; For the convenience of judging the transfer strategy in step 3, the passenger travel requests are divided into three categories. Traverse each request in the set of passenger travel requests in the set , and determine the section where the boarding station is located and the section where the alighting station is located; If the section where the boarding station is located and the section where the alighting station are within the same section, that is , then the request is classified as a direct passenger within the section and no transfer is required; If the section where the boarding station is located and the section where the alighting station are in adjacent sections, that is , then the request is classified into the set of passengers with one transfer across sections and one transfer is required; If the section where the boarding station is located and the section where the alighting station are neither in the same section nor in adjacent sections, that is , then the request is classified into the set of passengers with transfers across sections , where the is greater than 1 and is a positive integer; Until all requests are classified.

[0013] Other steps and parameters are the same as those in the first specific implementation.

[0014] Specific implementation method three: The difference between this implementation method and the first or second specific implementation method is that in step 3, the transfer strategy is determined based on steps 1 and 2, and the number of transfer passengers is calculated based on the transfer strategy; the specific process is as follows: Step 3.1 The section is a section bounded by the key stations and , that is, the key stations and are respectively the starting station and the ending station of the section ; According to the formula Calculation section The th shift The number of passengers waiting for transfer at the end station : : In the formula, Represents the shift At the end station The set of cross-section one-time transfer passengers waiting for transfer; Represents the shift At the end station Cross-section waiting for transfer The set of th transfer passengers, where the Is greater than 1 and is a positive integer; Is a request in the set ; Is a request in the set ; Represents the number of passengers to be served included in the request , in units of people; , in units of people; Represents the number of passengers to be served included in the request , in units of people; , in units of people; Represents the th shift on the section The th shift At the end station The number of cross-section one-time transfer passengers waiting for transfer, in units of people; Represents the th shift on the section The th shift At the end station Cross-section waiting for transfer The number of th transfer passengers, in units of people; Step 3.2. Use the 0-1 variable To judge the transfer strategy adopted by the th shift on the section The th shift Adopted transfer strategy; If the th shift on the section The th shift Adopts the full-in-vehicle transfer strategy, then ; If the th shift on a section adopts the strategy of mainly transferring inside the vehicle and supplemented by transferring outside the vehicle, then ; According to Equation calculate the variable : In the formula, represents the unit modular vehicle capacity, with the unit of person / vehicle; represents the ceiling function, which is used to calculate the minimum number of modular vehicles required to carry passengers, with the unit of vehicle; represents the set of all modular vehicle numbers participating in the scheduling during the operation period , is the modular vehicle with the number in the set ; is a 0-1 variable, indicating the relationship between the modular vehicle and the th shift on the section. If the modular vehicle participates in the execution of the shift , then , otherwise ; represents the number of vehicles called for the shift , with the unit of vehicle; Step 3.3, When , according to Equation and calculate the number of passengers transferring outside the vehicle th shift at the end station and the number of passengers transferring inside the vehicle : When , according to Equation and calculate the number of passengers transferring outside the vehicle th shift At the end station Number of passengers getting off and transferring and number of in-vehicle transfer passengers : Wherein, represents the remainder function, used to calculate the number of passengers who fail to make a single modular vehicle reach the full-load state, with the unit of person; Identify and determine the shift through the set of passenger travel requests Set of numbers of in-vehicle transfer passengers and shift Set of numbers of passengers getting off and transferring ; ; According to the passenger travel request classification method in step 1.4, form the shift Set of numbers of in-vehicle transfer passengers who belong to cross-section one-time transfer passengers and shift In-vehicle transfer and belong to cross-section Set of numbers of passengers for the nth transfer ; The is greater than 1 and takes a positive integer; According to the passenger travel request classification method in step 1.4, form the shift Set of numbers of passengers getting off and transferring who belong to cross-section one-time transfer passengers and shift Passengers getting off and transferring and belonging to cross-section Set of numbers of passengers for the nth transfer ; The is greater than 1 and takes a positive integer.

[0015] Steps 3.1, 3.2, and 3.3 are carried out sequentially.

[0016] Other steps and parameters are the same as those in the first or second specific implementation manner.

[0017] Specific implementation manner four: The difference between this implementation manner and one of the first to third specific implementation manners is that in step 4, the vehicle is split and combined based on step 3 to complete passenger transfer, and the shift information is updated based on the passenger transfer result; The specific process is as follows: Step 4.1, When or , calculate the shift according to the in-vehicle transfer passengers who belong to cross-section one-time transfer passengers ​The convoy is at the end station The number of vehicles that need to be split is as follows: As shown: when or When the train is transferred within the train and it is a cross-section Transfer passengers , calculate shifts The convoy is at the end station The number of vehicles that need to be split is as follows: As shown: In the formula, Indicates that the passengers are transferring within the vehicle and are transferring across sections. , shift The convoy is at the end station The number of vehicles that need to be split, in units of vehicles; Indicates that the vehicle is used for transfer and it is a cross-section Transfer passengers , shift The convoy is at the end station The number of vehicles that need to be split, in units of vehicles; Represents the unit modular vehicle capacity, in units of persons / vehicle; For collection A request in For collection A request in Express request The number of passengers to be served included in , in persons; Express request The number of passengers to be served included in , in persons; and Representing shifts At the end site The number of passengers waiting for transfers in the train and the number of passengers transferring across sections The number of passengers transferring each time, in persons; represents the rounding function, which is used to calculate the minimum number of modular vehicles required to carry passengers, in units of vehicles; For passengers transferring within the train and transferring across sections and transfer within the vehicle and across sections transfer passengers The transfer process is divided into the following four cases: (1) If and , the in-vehicle transfer passengers and transfer to the new trips by splitting the trips at the end station and joining the fleets of the new trips and respectively; the new trips and are added on the basis of the existing trips on section . represents the total number of existing trips on section , in trips; the fleets of trip are split to form the new trips and , and the number of vehicles is and respectively; among them, represents the th trip on section ; represents the th trip on section ; (2) If and , the in-vehicle transfer passengers transfer to the new trip by splitting the trips at the end station and joining the fleet of the new trip ; the new trip is added on the basis of the existing trips on section . represents the total number of existing trips on section ; the number of vehicles formed by splitting the fleet of trip for the new trip is ; (3) If and , the in-vehicle transfer passengers transfer to the new trip by splitting the trips at the end station and joining the fleet of the new trip ; the new trip is added on the basis of the existing trips on section . represents the total number of existing trips on section ; the trips The vehicle fleet is split and new shifts are formed The number of vehicles is vehicles; (4) If and , there are no passengers who transfer inside the vehicle, and there is no need to generate new shifts for service transfer; Execute Step 4.2; Step 4.2: When , the passengers gather All the passengers in get off and transfer at the end station and enter Step 4.3; Step 4.3: When or , update the information of the new shifts carrying passengers who transfer inside the vehicle and , and execute Step 4.4; The specific process is as follows: (1) If and , calculate the number of split vehicles and according to Step 4.1; Select the first vehicles in ascending order of their numbers from the vehicle set of the forming shift for splitting and combine them into a new shift ; Select the first vehicles in ascending order of their numbers from the vehicle set of the forming shift for splitting and combine them into a new shift ; According to the set of transfer passenger numbers obtained in Step 3.3, assign the numbers of the passengers who transfer inside the vehicle and belong to the passengers with one-time cross-section transfer to the set of travel passenger numbers of the new shift , and assign the numbers of the passengers who transfer inside the vehicle and belong to the passengers with times cross-section transfer to the set of travel passenger numbers of the new shift ; ; ; Set the departure time of the new shift to be ; Set the departure time of the new shift to be ; Among them, represents the th shift arriving at the end station of the section at the moment; represents the end station of the section represents the total number of existing shifts on the section, in units of shifts; (2) If and , calculate the number of split vehicles according to Step 4.1; Select the first vehicles in ascending order of number from the vehicle set of the composed shift for splitting and combine them into a new shift ; According to the set of transfer passenger numbers obtained in Step 3.3, assign the numbers of the in-vehicle transfer passengers who belong to the cross-section th transfer passengers to the set of travel passenger numbers of the new shift ; ; Set the departure time of the new shift to be ; Among them, represents the th shift arriving at the end station of the section at the moment; represents the end station of the section represents the total number of existing shifts on the section, in units of shifts; (3) If and , calculate the number of split vehicles according to Step 4.1; Select the first vehicles in ascending order of number from the vehicle set of the composed shift for splitting and combine them into a new shift ; According to the set of transfer passenger numbers obtained in Step 3.3, assign the numbers of the in-vehicle transfer passengers who belong to the cross-section once transfer passengers to the new shift Set of passenger numbers for trips ; ; Set a new schedule Departure time The value of ; Among them, Represents the section On the th schedule Arrive at the section End station Time; Represents the end station of the section , Represents the section Total number of existing schedules on, unit: schedule; (4) If And , no new schedule is generated, no need to update schedule information; Step 4.4. When , update the information of the schedule carrying passengers getting off and transferring; The specific process is as follows: (1) If , , then record the section On the th schedule Arrive at the section End station Time , traverse the existing schedules on the section , record the departure time of the schedule , find the schedule that satisfies And satisfies the capacity constraint ; Among all eligible schedules, select The smallest schedule ; According to the set of passenger numbers for transfer obtained in Step 3.3, add the set of numbers of passengers getting off and transferring and belonging to one-time cross-section transfer passengers of the schedule To the set of passenger numbers for trips Of the schedule , ; Among them, ; Among them, Represents the section On the th schedule; ; Represents the section division based on Step 1.1, section The set of all shifts within (2) If , , then record the th shift on the arrival section at the end station at the moment , traverse the existing shifts on the , record the departure time of the shift , find the shift that satisfies and the capacity constraint ; among all eligible shifts, select the shift with the smallest ; according to the set of transfer passenger numbers obtained in step 3.3, add the set of the numbers of passengers who get off and transfer and belong to the cross-section th transfer passengers to the set of the travel passenger numbers of the shift , . .

[0018] Other steps and parameters are the same as those in any one of the specific implementation manners one to three.

[0019] Specific implementation manner five: The difference between this implementation manner and any one of the specific implementation manners one to four is that in step 5, a modular bus vehicle scheduling optimization model is established based on steps 1, 2, 3, and 4; The specific process is as follows: Step 5.1, construct the objective function according to equation : Among them, represents the modular bus operation cost, in yuan; represents the passenger travel cost, in yuan; represents the total cost, in yuan; Step 5.2, calculate the modular bus operation cost according to equations ~ ; the specific process is as follows: In the formula, represents the fixed cost of modular buses, in yuan; represents the energy consumption cost of modular buses, in yuan; represents the fixed cost per modular bus, in yuan / bus; is a binary variable. If the modular vehicle participates in operation, then , otherwise it is equal to 0; represents the unit average operation cost, in yuan / km; represents the station and the station the distance between them, in km; and respectively represent the starting station and the ending station of the section ; Step 5.3. Calculate the passenger travel cost according to Equation ~ ; The specific process is as follows: In the formula, represents the in-vehicle cost of passengers, in yuan; represents the waiting cost of passengers, in yuan; represents the penalty cost for passengers getting off and transferring, in yuan; represents the section the th shift arrives at the boarding request the time of the next stop ; represents the section the th shift arrives at the boarding request the time of the previous stop ; Indicates the section The th shift Arrival boarding request The alighting stop of; Indicates the section The th shift Arrival boarding request The alighting stop of; Indicates the request The earliest expected start service time; Function Used to calculate the waiting service time of a passenger travel request , in minutes; Is a passenger travel request, , Is the set of passenger travel requests; Indicates the section The th shift The number of alighting and transferring passengers at the end stop , in persons; The set of passenger travel requests Is divided into three categories: , , ; Indicates the set of direct passengers within the section; Indicates the set of one-time transfer passengers across sections; Indicates across sections times transfer passenger set; Indicates the in-vehicle cost per unit time of a passenger, in yuan / min; Indicates the waiting cost per unit time of a passenger, in yuan / min; Indicates the unit penalty cost for a passenger to alight and transfer, in yuan / person; 5.4. Set the constraint conditions; the specific process is as follows: The modular bus fleet is restricted not to exceed the maximum vehicle formation length : The section constraint The th shift The capacity is ensured so that the demand carried by the shift does not exceed the total carrying capacity of the actual vehicles: Wherein, represents the th shift arriving at the station with the number of passengers still on the vehicle, in units of people; Constraining the number of vehicles stored at the key station to be the same at the end of the operation as at the start: Wherein, represents the number of modular vehicles stored at the key station before the start of the operation period, in units of vehicles; represents the number of modular vehicles stored at the key station after the end of the operation period, in units of vehicles; Constraining the driving speed of the modular bus not to exceed the safe range: Wherein, and respectively represent the minimum and maximum operating speeds of the modular bus, in units of m / s; Constraining the modular bus to arrive at the key station before the end of the operation period: Wherein, represents the th shift arriving at the end station of the section at the moment; represents the end moment of the operation period; Constraining the bus to arrive at the passenger boarding station within the passenger's desired start service time window: Wherein, represents the earliest desired start service moment of the request ; represents the section The shift arrival request at the boarding station of; Indicates the request The latest expected start service time; Constrained vehicle The executed shift And the shift There is no time conflict between: Wherein, Indicates the section The shift Arrival section At the end station of; Indicates the section The shift Arrival section At the end station of; Section , , , ; Is a binary variable. If the modular vehicle Participates in the execution of the shift , then , otherwise .

[0020] Other steps and parameters are the same as those in the first to fourth specific embodiments.

[0021] Specific embodiment six: The difference between this embodiment and any one of the first to fifth specific embodiments is that in step 6, the modular bus vehicle scheduling optimization model is solved to output the optimal scheduling plan ; The specific process is as follows: The adaptive large neighborhood search algorithm is used to solve the model. By optimizing and iterating the initial solution, the vehicle number sequence, the service request sequence, and the departure time sequence of the operation shift are dynamically optimized. This algorithm needs to set the maximum number of iterations , the annealing temperature , the cooling rate And the reaction coefficient And other parameters.

[0022] Step 6.1. Construct the initial solution: Define the operation shift sequence of the first-layer coding , ; ; ; ; where represents the vehicle number sequence of all shifts on section 1, represents the vehicle number sequence of all shifts on section , represents the vehicle number sequence of all shifts on section ; represents the vehicle number of the first shift on section 1 , represents the vehicle number of the first shift on section 1 ; represents the vehicle number of the th shift on section 1 ; represents the vehicle number of the first shift on section ; represents the vehicle number of the first shift on section ; represents the vehicle number of the th shift on section ; represents the vehicle number of the th shift on section ; represents the vehicle number of the first shift on section ; represents the vehicle number of the first shift on section ; represents the vehicle number of the th shift on section ; represents the vehicle number of the th shift on section ; represents the vehicle number of the th shift on section Define the service request sequence of the second-layer coding ; ; ; ; Among them, represents the sequence of sets of travel requests for all shifts on section 1, represents section the sequence of sets of travel requests for all shifts on it, represents section the sequence of sets of travel requests for all shifts on it; represents the set of travel requests served by the first shift on section 1 ; represents the th shift on section 1 and the set of travel requests it serves; represents the th shift on section 1 and the set of travel requests it serves; represents section the set of travel requests served by the first shift on it ; represents section the th shift on it and the set of travel requests it serves; represents section the th shift on it and the set of travel requests it serves; represents section the set of travel requests served by the first shift on it ; represents section the th shift on it and the set of travel requests it serves; represents section the th shift on it and the set of travel requests it serves; Define the departure time sequence of the third - layer coding ; ; ; Among them, represents the departure time sequence of all shifts on section 1, represents section The departure time sequences of all shifts on represents the section The departure time sequences of all shifts on; represents the first shift on section 1 of the departure time, represents the th shift on section 1 of the departure time; represents the th shift on section 1 of the departure time; represents the section the first shift on of the departure time; represents the section on the th shift of the departure time; represents the section on the th shift of the departure time; represents the section the first shift on of the departure time; represents the section on the th shift of the departure time; represents the section on the th shift of the departure time; The specific process is as follows: Step 6.1.1. According to the passenger travel request , combined with each request boarding station and alighting station respectively located in the section and , count the passenger flow demand on each section, and calculate the modular vehicle quantity stored at the starting station of the section ; expressed as: ; In the formula, represents at the start time of operation , stored in the section The starting station The number of modular vehicles, in units of vehicles; Indicates the section The passenger flow demand on, in units of people; From the operation period The set of all modular vehicle numbers participating in the scheduling within Randomly select Vehicles and allocate them to the starting station of the section The starting station And add it to the set of vehicle numbers stored at the starting station before the operation The set of vehicle numbers Among them; During this process, ensure that each vehicle can only be allocated once; Step 6.1.2. Under the condition of satisfying the maximum shift formation length constraint Traverse the set of vehicle numbers stored at the starting station generated in Step 6.1.1 The set of vehicle numbers Randomly select 1 to Vehicles to form a set of vehicle numbers for the shift The set of vehicle numbers Until each vehicle is allocated to a shift; For each request If it satisfies And the shift Satisfies the capacity constraint Condition, then allocate the request To the set of service requests for the shift Among them, until each request finds the corresponding boarding shift; Under the condition of satisfying the speed constraint And the service request time window constraint Randomly determine the departure time Of the shift The departure time Until the departure time of each shift is determined; Indicates the request The boarding station Of the section where it is located; To meet the needs of transfer passengers, the set of vehicle numbers, the set of service requests, and the set of departure times for the shift formed will be updated in Step 6.1.3; Step 6.1.3. According to the formula in Step 3.1 Calculate the number of transfer passengers Of the shift at the end station The number of transfer passengers If , according to the shift in Step 3.2 , it is necessary to judge the transfer strategy. Then, according to Step 4, split and combine the vehicles to complete the passenger transfer, and update the set of vehicle numbers for the shift based on the passenger transfer result , service request set and departure time ; otherwise, skip the shift , continue to judge the next shift; until all shifts in the bus corridor during the operation period in the shift set have been inspected; Step 6.1.4. Combine the updated set of vehicle numbers for the component shifts , the updated shift service request set and the updated shift departure time set , find the shift with the latest departure time in the existing shift set , determine the shift to reach the end station time ; judge at the time the modular vehicle quantity stored at the key station ; if , no reallocation is required; if , reallocate the key station until the key station meets ; ; Repeat Step 6.1.4 until all key stations meet ; Among them, the process of reallocating the key station is as follows: 1). Traverse each key station in the key station set to find the key station that meets the condition, and randomly select in the set of vehicle numbers stored at the station vehicles and reallocate them to the key station that meets the condition ; and generate a new shift on the existing shift that includes the key station , determine the set of vehicle numbers that make up the new shift of the section of the new shift ; the departure time of the new shift is ​​, the set of service passenger requests is empty; 2), update the key stations after reallocation and the set of stored vehicle numbers , and the stored vehicle quantity , ; Judge at time the key station the stored modular vehicle quantity , if , no reallocation is required; if , then re-execute 1), 2) until the key station meets ; represents the number of modular vehicles stored at the key station before the start time of operation ; represents the number of modular vehicles stored at the key station before the start time of operation ; The set of vehicle numbers for the updated composition shifts, the updated set of shift service requests and the updated shift departure time together constitute the initial solution ; Step 6.2, design the destruction operator and repair operator; the specific process is as follows: Step 6.2.1, design five destruction operators to expand the neighborhood of the candidate solution, specifically including: (1) Random destruction operator ; the specific process is as follows: Randomly select 10% of the travel requests in the total demand and remove them from the current solution to obtain the destroyed solution and add the deleted requests to the list of requests to be served ; The total demand is the set of passenger travel requests on the passenger flow corridor during the operation period of the past 30 working days ; ; (2) Worst destruction operator ; the specific process is as follows: Define the insertion cost ; Among them, Represents the current solution of the travel cost Represents removing the travel request from the current solution and then the travel cost; Sorted in descending order of insertion cost, select the top 10% of the travel requests to be removed from the current solution to obtain the damaged solution and add the deleted requests to the list of requests to be served ; (3) Correlation destruction operator ; The specific process is as follows: Randomly select a travel request , and according to Equation find the travel request with the strongest correlation with the request , remove these two requests from the current solution , and repeat the above operation until the number of removed requests reaches 10% of the total demand and then stop to obtain the damaged solution and add the deleted requests to the list of requests to be served ; The total demand is the set of passenger travel requests on the passenger flow corridor during the operation period of the past 30 working days ; ; In the formula, represents the correlation between requests and , and the correlation between requests and is obtained based on time, request load, and distance (the first to the third items); and respectively represent the expected earliest start service times of requests and ; and respectively represent the expected latest start service times of requests and ; and respectively represent the number of passengers included in requests and , in units of people; ​​respectively represent the distances between the boarding stations of the two requests and the reference station 1, in km; and respectively represent the distances between the alighting stations of the two requests and the reference station 1, in km.

[0023] Indicates a parameter, and each item is weighted using the parameter respectively; (4)Modular vehicle destruction operator ; The specific process is as follows: Randomly select 10% of the total number of modular vehicles and remove them from the current solution . At the same time, since the shift capacity has changed, randomly select trip requests within the shift and remove them from the current solution until the capacity constraint is satisfied and then stop; Finally, obtain the destroyed solution and add the deleted requests to the list of requests to be served ; (5)Bus shift destruction operator ; The specific process is as follows: Sort in descending order according to the occupancy rate and remove the last 10% of the shifts to obtain the destroyed solution and add the trip requests served by the shifts to the list of requests to be served ; Step 6.2.2. For the destroyed solution and the list of requests to be served , two repair operators are designed to repair the destroyed solution to obtain a new solution , specifically including: (1)For the destroyed solution and the list of requests to be served , design a random repair operator to repair the destroyed solution to obtain a new solution , specifically including: Traverse each trip request in the list of requests to be served , and according to the request classification in step 1.4, randomly insert it into according to the category to which the request belongs, and update the operating shift sequence , the sequence of trip requests served by the shifts and the sequence of shift departure times ; ; until the list of requests to be served All travel requests are inserted, and a new solution is finally obtained. ; (2) For the solution after disruption and the list of requests to be served , design a greedy repair operator to repair the disrupted solution to obtain a new solution , specifically including: Traverse each travel request in the list of requests to be served , and according to the request classification in step 1.4, randomly insert it into ; Calculate the difference between the total cost after inserting the travel request and the total cost of the disrupted solution . Insert the travel request corresponding to the minimum difference into to update the operation shift sequence , the sequence of travel requests served by the shift and the departure time sequence of the shift ; until all travel requests in the list of requests to be served are inserted, and a new solution is finally obtained ; Step 6.3, generate operator pairs and initialize the weights of operator pairs; the specific process is as follows: For the disruption operator designed in step 6.2 and the repair operator , combine them pairwise to generate operator pairs ; Initially, the weight of each operator pair is 1, and the score is 0; Step 6.4, solve the modular bus vehicle scheduling optimization model based on steps 6.1, 6.2, and 6.3, and output the optimal scheduling plan ; The specific process is as follows: 6.4.1, let the iteration number ; 6.4.2, select the disruption and repair operators and generate a new solution; ; 6.4.3, update the current solution and the optimal solution; 6.4.4, update the scores of the operator pairs; ; 6.4.5, update the weights of the operator pairs; 6.4.3, update the current solution and the optimal solution; 6.4.4, update the scores of the operator pairs; 6.4.5, update the weights of the operator pairs; 6.4.6. Let the number of iterations , substitute the updated operator pair fraction and the updated operator pair weight into Step 6.4.2, and repeat Steps 6.4.2 to 6.4.6 until the maximum number of iterations is reached, then output the optimal scheduling plan .

[0024] which includes the set of vehicle numbers, the set of served requests, and the departure times for each operation shift in the scheduling plan.

[0025] Other steps and parameters are the same as those in Embodiments 1 to 5.

[0026] Embodiment 7: The difference between this embodiment and Embodiment 1 to 6 is that: in Step 6.4.2, a destruction and repair operator is selected and a new solution is generated; The specific process is as follows: Step 6.4.2.1. Select a destruction and repair operator: Based on the roulette wheel strategy, randomly select an operator pair according to the normalized weight of the operator ; The specific process is as follows: First, normalize the weight of the operator pair according to the formula : In the formula, represents the weight of the operator pair ; represents the sum of the weights of all operator pairs; represents the probability that the operator pair is selected, satisfying ; Among them, set the parameter to balance the relationship between the solution time and the timeliness of weight update.

[0027] Next, construct a cumulative probability interval for each operator pair according to the formula (each operator pair corresponds to 1 cumulative probability interval, for example ) (the cumulative probability interval range ): In the formula, initialize the cumulative probability to 0, represents the cumulative probability up to the operator pair ; Then, generate a random number uniformly distributed , and then, according to the cumulative probability interval into which the random number falls, select the corresponding operator pair ; Step 6.4.2.2, generate a new solution; the specific process is as follows: According to the operator pair selected in 6.4.2.1 , determine the selected destruction operator and repair operator , and perform operations on the current solution according to the destruction process and repair process in step 6.2 (selecting one of the five and one of the two), to obtain a new solution .

[0028] Other steps and parameters are the same as those in any one of the first to sixth specific embodiments.

[0029] Specific embodiment eight: The difference between this embodiment and any one of the first to seventh specific embodiments is that in step 6.4.3, update the current solution and the optimal solution; the specific process is as follows: Define to represent the current solution, the new solution, and the optimal solution respectively (the optimal solution is the comparison of the solutions between iterations, the current solution is the solution obtained in step 6.4.3 of the previous iteration, and the new solution is the solution obtained in step 6.4.2.2 of this iteration); If , then the value of the optimal solution is replaced by the value of the new solution ; If , then the value of the current solution is replaced by the value of the new solution ; If , then use the simulated annealing criterion to decide whether to accept the new solution; the specific process is as follows: Generate a random number , if , then the value of the current solution is replaced by the value of the new solution ; otherwise, the value of the current solution remains unchanged and the new solution is not accepted; Calculate the simulated annealing probability according to the formula : wherein, represents the annealing temperature; represents the objective function value of the new solution ; Represents the optimal solution of the objective function value; Represents the current solution of the objective function value.

[0030] Other steps and parameters are the same as those in the first to seventh specific embodiments.

[0031] Specific Embodiment Nine: The difference between this embodiment and any one of the first to eighth specific embodiments is that: the fraction of the update operator pair in step 6.4.4; the specific process is as follows: Design the score of the operator pair Update rule: If , the score of the operator pair increases by ; If , the score of the operator pair increases by ; If , if accepted by the simulated annealing criterion, the score of the operator pair increases by ; if not accepted by the simulated annealing criterion, the score of the operator pair remains unchanged.

[0032] Other steps and parameters are the same as those in the first to eighth specific embodiments.

[0033] Specific Embodiment Ten: The difference between this embodiment and any one of the first to ninth specific embodiments is that: the weight of the update operator pair in step 6.4.5; the specific process is as follows: Define Represents the weight of the operator pair at the th iteration, Represents the reaction coefficient, Represents the score of the operator pair , Represents the number of successful applications of the operator pair ; Update the weight according to Equation : .

[0034] Other steps and parameters are the same as those in the first to ninth specific embodiments.

[0035] The present invention can also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations should all fall within the protection scope of the appended claims of the present invention.

Claims

1. A modular bus scheduling optimization method for bus corridors, characterized in that: The specific process of the method is as follows: Step 1: Collect basic information of bus stops, configure modular vehicles, configure modular bus schedules, and collect passenger travel request data; Step 2: Define optimization variables; the specific process is as follows: Define 0-1 variable Indicates a modular vehicle And the section On the th shift The relationship between, if the modular vehicle Participates in the execution of the shift , then , otherwise ; Define a 0-1 variable , if the th shift on section s travels from station to station within section , then , otherwise equal to 0; where both stations and belong to the set of stations of section Define a 0-1 variable Indicates a passenger travel request With a modular vehicle The relationship between, if the passenger travel request Is provided by a modular vehicle Then Otherwise ; Define continuous variables Indicates the section On the th shift Arrival section Internal site Time; Define continuous variable Indicates the section The th shift The average running speed within the section in m / s; Step 3: Determine the transfer strategy based on Steps 1 and 2, and calculate the number of transfer passengers based on the transfer strategy; Step 4: Split and combine the vehicles based on Step 3 to complete passenger transfer, and update the schedule information based on the passenger transfer result; Step 5: Establish an optimization model for modular bus vehicle scheduling based on Steps 1, 2, 3, and 4; Step 6, solve the modular bus vehicle scheduling optimization model and output the optimal scheduling plan .

2. The modular bus scheduling optimization method for a bus corridor according to claim 1, characterized in that: In Step 1, collect basic information of bus stops, configure modular vehicles, configure modular bus schedules, and collect passenger travel request data; the specific process is as follows: Step 1.1: Collect basic information of bus stops; the specific process is as follows: Divide the bus operations on the arterial passenger flow corridor into the upward and downward directions, each direction containing bus stops; The set of stations in the upward direction is denoted as , and the set of stations in the downward direction is denoted as ; All stations on the passenger flow corridor are recorded as a set ; Set the passenger flow threshold, and set the stops with passenger flow greater than the passenger flow threshold among all stops as key stops; The key stops are used for splitting and combining the modular bus fleet; Store the key stations on the passenger flow corridor into the key station set , ; Among them, represents the first key site in the set of key sites , represents the second key site in the set of key sites , represents the -th key site in the set of key sites represents the set of key sites; Taking the key stops as boundaries, adjacent key stops are divided into 1 section, and the passenger flow corridor is sectioned; Let represent the set of sections divided in the upstream direction with the key site as the boundary; Let represent the set of sections divided in the downlink direction with key sites as boundaries; Among them, and respectively represent the maximum number of sections after the division of the upstream and downstream directions of the passenger flow corridor with the key stations as the boundaries; All sections on the passenger flow corridor are denoted as a set ; Step 1.

2. Configure modular vehicles; the specific process is as follows: Let represent the set of all modular vehicle numbers participating in scheduling within the operation period; Among them, is the total number of modular vehicles configured on the passenger flow corridor, and the numbers increase sequentially starting from 1; Operation start time Previously at key stations Store Vehicles of modular design Step 1.

3. Configure modular bus schedules; the specific process is as follows: Each schedule consists of one or more modular vehicles. Each section contains schedules with different departure times. Each schedule is a process of traveling from one key stop to the adjacent key stop and picking up and dropping off passengers on the way to complete the operation task; Let the set represent all the bus trips on the bus corridor during the operation period ; Among them, Denote the set of all shifts within section 1; Denote the set of all shifts within section 2; Indicates the section All shift sets within; Indicates the section All shift sets within; Set Further expressed as ; Among them, represents the first shift on section , represents the second shift on section , represents the -th shift on section ; represents the -th shift on section ; represents the total number of shifts within section , section ; Step 1.

4. Collect passenger travel request data; the specific process is as follows: Collect the set of passenger travel requests on the passenger flow corridor during the operation period in the past 30 working days ; ; A passenger travel request contains the following information: the boarding station , the alighting station , the earliest expected service start time , the latest expected service start time and the number of passengers to be served ; ； Traverse each request in the set of passenger travel requests in , and judge the request boarding station where the section is located and the alighting station where the section is located ; If the request boarding station section where it is located and the alighting station section where it is located are in the same section, that is , then the request is classified as a direct passenger within the section and no transfer is required; If the request boarding station the section where it is located and the alighting station the section where it is located are in adjacent sections, that is , then the request is classified as the set of passengers with one transfer across sections , and one transfer is required; If the request boarding station section where it is located and the alighting station section where it is located are not in the same section and not in adjacent sections, that is , then the request is classified as an inter - section transfer passenger set , where the is greater than 1 and is a positive integer; Until all requests are classified.

3. A modular bus scheduling optimization method for a bus corridor according to claim 2, characterized in that: In Step 3, determine the transfer strategy based on Steps 1 and 2, and calculate the number of transfer passengers based on the transfer strategy; the specific process is as follows: Step 3.1, Section is a section bounded by key stations and , that is, key stations and are the starting station and ending station of section respectively; according to formula calculate the number of passengers waiting for transfer at the ending station of the th shift on section : ​ In the formula, represents the shift at the end station set of cross-section one-time transfer passengers waiting for transfer; Indicates the shift At the end station Intersection section waiting for transfer The passengers of the -th transfer are gathered, where is greater than 1 and is a positive integer; Greater than 1 and taking positive integers; For a request in the set in the set For a request in the set in the set; Indicates the number of passengers to be served contained in the request, , in units of people; Indicates the number of passengers to be served contained in the request, , in units of people; Indicates a section The th shift At the end station The number of cross-section one-transfer passengers waiting for transfer, in units of people; Indicates a section On the th shift Waiting for transfer at the end station Number of cross-section transfer passengers waiting for transfer, in persons; ​ Step 3.2, Adopt 0-1 variables Judgment section On the th shift The transfer strategy adopted; If the section on the nth shift adopts a full in-vehicle transfer strategy, then ; If the section uses the strategy of mainly transferring inside the vehicle and supplemented by getting off and transferring for the th shift then ; According to the formula calculate the variable : In the formula, represents the unit modular vehicle capacity, with the unit of person / vehicle; Denotes the ceiling function; Indicates the operation period The set of all modular vehicle numbers participating in scheduling within is the set in which the number is of the modular vehicle; is a 0-1 variable representing a modular vehicle and the th shift on a section. If the modular vehicle participates in executing the shift , then , otherwise ; Indicates shift Number of vehicles called, in units of vehicles; Step 3.3, When is reached, calculate the number of passengers getting off and transferring at the end station and for the th shift on section and the number of in-vehicle transfer passengers : ​ When at that time, calculate according to formula and the number of passengers getting off and transferring at the end station the th shift at the end station and the number of in-vehicle transfer passengers : ​ In the formula, represents the remainder function; Through the set of passenger travel requests Identify and determine the shifts Set of in-vehicle transfer passenger numbers and shifts Set of alighting transfer passenger numbers ; According to the passenger travel request classification method in step 1.4, form shifts The set of numbers of passengers who transfer within the vehicle and belong to the cross-section one-time transfer passengers And shifts Transfer within the vehicle and belong to the cross-section The set of numbers of passengers for the [[number of transfers]]th transfer ; The is greater than 1 and is a positive integer; According to the classification method of passenger travel requests in Step 1.4, form a shift The set of numbers of passengers who get off and transfer and belong to cross-section one-time transfer passengers and the shift Get off and transfer and belong to cross-section The set of numbers of passengers for the th transfer Greater than 1 and taking positive integers.

4. The modular bus scheduling optimization method for a bus corridor according to claim 3, wherein: In Step 4, split and combine the vehicles based on Step 3 to complete passenger transfer, and update the schedule information based on the passenger transfer result; The specific process is as follows: Step 4.1, When or , calculate the number of vehicles to be split at the end station of the fleet for passengers who transfer within the vehicle and make a one-time transfer across sections as shown in Equation as follows: When or for in-vehicle transfer passengers who are cross-section secondary transfer passengers calculate the number of vehicles that need to be split at the end station for the fleet of shift as shown in Equation shown below:​ In the formula, Indicates the number of passengers who transfer within the vehicle and belong to the cross-section one-time transfer passengers , shift The number of vehicles that need to be split at the end station by the fleet , unit: vehicle; Indicating that it is for on-vehicle transfer and belongs to cross-section Transfer passengers for the second time , the schedule The number of vehicles that need to be split by the fleet at the end station , in units of vehicles; Represent the modular vehicle capacity per unit, with the unit of person / vehicle; For a request in the set in the set For a request in the set in the set; Indicates the number of passengers waiting to be served contained in the request, in persons; Indicates the number of passengers waiting to be served contained in the request, in units of people; and respectively represent the shift at the end station the number of cross-section one-time transfer passengers waiting for in-vehicle transfer and the number of cross-section transfer passengers for the number of transfers, in persons; Denotes the ceiling function; For passengers who transfer within the vehicle and belong to one-time cross-section transfer passengers and passengers who transfer within the vehicle and belong to cross-section transfer passengers The transfer process is divided into the following four situations: (1) If and , in-vehicle transfer passengers and transfer to the new trips by splitting the trips at the end stations and respectively; the new trips and are added on the basis of the existing trips on the section represents the total number of existing trips on the section in the unit of trips; after the vehicle fleets of the trips and are split, the number of vehicles and of the new trips Among them, represents the th shift on section represents the th shift on section (2) If and , in-vehicle transfer passengers transfer to the new shift through the fleet that splits shifts at the end station ; the new shift is added on the basis of the existing shifts on the section ; represents the total number of existing shifts on the section ; the number of vehicles formed by splitting the fleet of shift to form the new shift is ; the number of vehicles of the new shift is vehicles; (3) If and , in-vehicle transfer passengers transfer to the new shift through the fleet that splits the shift at the end station ; the new shift is added on the basis of the existing shift on the section ; represents the total number of existing shifts on the section ; the number of vehicles of the new shift formed after the fleet of the shift is split is ; The number of vehicles of the new shift is (4) If and there are no passengers transferring inside the vehicle, there is no need to generate new schedules for service transfer; Execute Step 4.2; Step 4.

2. When the passengers in have all alighted and transferred at the end station proceed to Step 4.3; Step 4.3, when or occurs, update the information of the new shift carrying passengers who transfer inside the vehicle and , and execute Step 4.4; the specific process is as follows: (1) If and , calculate the number of split vehicles and according to Step 4.1; Select the first vehicles in ascending order of number from the set of vehicles that make up the shift and split them to form a new shift ; Select the first vehicles in ascending order of number from the vehicle set that makes up the shift, and split and combine them into a new shift ; ; According to the set of transfer passenger numbers obtained in step 3.3, the numbers of in-vehicle transfer passengers who belong to one-time cross-section transfer passengers are assigned to the new shift of the set of travel passenger numbers , and the numbers of in-vehicle transfer passengers who belong to cross-section transfer passengers are assigned to the new shift of the set of travel passenger numbers ; ； ； Set a new shift The departure time The value is ; Set a new shift Departure time The value is ; Among them, represents the th shift arriving at the ending station of the section; represents the ending station of the section; represents the total number of existing shifts on the section, in units of shifts; (2) If and , calculate the number of split vehicles according to step 4.1 ; Select the first vehicles in ascending order of number from the vehicle set that makes up the shift, and split and combine them into a new shift ; ; According to the set of transfer passenger numbers obtained in step 3.3, assign the numbers of the transfer passengers who transfer within the vehicle and belong to cross-section transfer to the new shift of the set of travel passenger numbers ; ; Set a new shift departure time The value of ; Among them, represents the th shift arriving at the end station of section ; represents the moment; represents the end station of section ; represents the total number of existing shifts on section , in units of shifts; (3) If and , calculate the number of split vehicles according to step 4.1 ; Select the first vehicles in ascending order of numbers from the set of vehicles that make up the shift, and split and combine them into a new shift ; According to the set of transfer passenger numbers obtained in step 3.3, the numbers of in-vehicle transfer passengers who are one-time transfer passengers across sections are assigned to the new shift in the set of travel passenger numbers ; ; Set a new shift of the departure time The value is ; Among them, represents the th shift arriving at the end station of section ; represents the moment of arriving at the end station of section ; represents the end station of section ; represents the total number of existing shifts on section , in units of shifts. (4) If and , no new shift is generated and there is no need to update the shift information; Step 4.

4. When occurs, update the information of the passengers getting off and transferring to another vehicle for the shift; the specific process is as follows: (1) If , , then record the time at which the th shift on section arrives at the end station of section . Traverse the existing shifts on section and record the departure time of shift . Find the shift that satisfies and the capacity constraint . Among all the eligible shifts, select the shift with the smallest . According to the set of transfer passenger numbers obtained in step 3.3, add the set of the numbers of passengers who get off and transfer and belong to the once-transfer passengers across sections to the set of the travel passenger numbers of shift . . ; Among them, represents the th shift on the section; ; Indicates the section All shift sets within; (2) If , , then record the arrival time at the end station of the shift on section . Traverse the existing shifts on section , record the departure time of the shift , and find the shift that satisfies and the capacity constraint . Among all the eligible shifts, select the shift with the smallest . According to the set of transfer passenger numbers obtained in step 3.3, add the set of numbers of the passengers who get off and transfer and belong to the cross-section transfer passengers to the set of travel passenger numbers of the shift , and add it to the set of travel passenger numbers of the shift. .

5. The modular bus scheduling optimization method for a bus corridor according to claim 4, wherein: In Step 5, establish an optimization model for modular bus vehicle scheduling based on Steps 1, 2, 3, and 4; The specific process is as follows: Step 5.

1. According to Equation Construct the objective function: Among them, represents the modular bus operation cost, in yuan; represents the passenger travel cost, in yuan; represents the total cost, in yuan; Step 5.

2. Calculate the modular bus operation cost according to Equation ~ The specific process is as follows: In the formula, Represents the fixed cost of modular buses, in yuan; Represents the energy consumption cost of modular buses, in yuan; Indicates the fixed cost per modular bus, in yuan per bus; is a binary variable. If the modular vehicle participates in the operation, then , otherwise it is equal to 0; Indicates the unit average operating cost, in yuan / km; Indicates the site With the site The distance between them, in km; and represent the starting station and the ending station of the section respectively; Step 5.

3. Calculate the passenger travel cost according to Equation ~ The specific process is as follows: In the formula, Indicates the cost per passenger in the vehicle, in yuan; Indicates the waiting cost per passenger, in yuan; Indicates the penalty cost for passengers getting off and transferring, in yuan; Indicates a section On the th shift Arrival request for boarding Of the next stop At that time; Indicates a section On the th shift Arrival request for boarding Of the boarding station Time; Indicates a section On the th shift Arrival boarding request Of the alighting stop At the moment; Indicates a section On the th shift Request to arrive and board Of the next stop Time; Indicates the earliest expected start service time of the request ; Function used to calculate the waiting service time for passengers' travel requests , in minutes; is a passenger travel request, , is a set of passenger travel requests; Indicates the section The th shift At the end station The number of passengers getting off and transferring, in persons; Set of passenger travel requests It is divided into three categories: , , ; Denote the set of through passengers within the section; Denote the set of passengers with one transfer across sections; Denote the set of passengers with transfers across sections; It represents the cost per minute of the passenger in the vehicle, with the unit of yuan / min; It represents the waiting cost per minute of the passenger, with the unit of yuan / min; It represents the penalty cost per person for the passenger to get off and transfer, with the unit of yuan / person; 5.

4. Set constraint conditions; the specific process is as follows: Restrict the modular bus fleet to not exceed the maximum vehicle formation length : Constrained section on the th shift capacity to ensure that the demand carried by the shift does not exceed the total carrying capacity of the actual vehicles: In the formula, Indicates the section On the th shift Arrival station The number of passengers still in the vehicle when arriving at the station, in persons; Constrained critical sites The number of vehicles stored at the end of the operation is the same as at the start of the operation: In the formula, Indicates the number of modular vehicles stored at key stations before the start of the operation period The unit is vehicle; Indicates the number of modular vehicles stored at key stations after the end of the operation period The unit is vehicle; Restrict the driving speed of modular buses Do not exceed the safe range: In the formula, and represent the minimum and maximum operating speeds of the modular bus, respectively, with the unit of m / s; Constrained modular buses arrive at key stops before the end of the operating period: In the formula, Indicates the section On the th shift Arrival section End station of The moment of; Indicates the end time of the operation period; Constraining the bus to arrive at the passenger boarding station within the start service time window expected by the passengers : In the formula, Indicates the earliest expected start service time of the request ; Indicates the th shift on the section and the arrival time at the boarding station of the request; Indicates the latest expected start service time of the request ; Constrained vehicle Shift performed With the shift There is no time conflict: In the formula, Indicates a section On the th shift Arrival section End station of The moment of; Indicates the section The th shift Arrives at the section End station of The moment of; section , , , ; is a binary variable. If the modular vehicle participates in the execution of a shift , then , otherwise .

6. The modular bus scheduling optimization method for a bus corridor according to claim 5, characterized in that: In step 6, solve the modular bus vehicle scheduling optimization model and output the optimal scheduling plan ; The specific process is as follows: Step 6.

1. Construct an initial solution: Define the first-layer coded operation shift sequence , ; ； ； ； Among them, Represents the vehicle number sequence of all shifts on section 1, Represents the composition section The vehicle number sequence of all shifts on, Represents the composition section The vehicle number sequence of all shifts on; Indicates the vehicle number of the first shift on section 1 , Indicates the vehicle number of the first shift on section 1 ; Indicates the th shift on section 1; Indicates the vehicle number of the first shift on the constituent section ; Indicates the vehicle number of the th shift on the constituent section ; Indicates the vehicle number of the th shift on the constituent section ; ​​​ Indicates the vehicle number of the first shift on the constituent section ; Indicates the vehicle number of the -th shift on the constituent section ; Indicates the vehicle number of the -th shift on the constituent section ; Indicates the vehicle number of the -th shift on the constituent section ; Define the second-layer coding service request sequence ; ； ； ； Among them, A sequence of sets of travel requests for all scheduled services on section 1, denotes section A sequence of sets of travel requests for all scheduled services on denotes section A sequence of sets of travel requests for all scheduled services on; Indicates the first shift on section 1 Set of trip requests served Indicates the th shift Set of trip requests served; Indicates the th shift Set of trip requests served; Indicates a section The first shift on The set of trip requests served; Indicates a section The th shift The set of trip requests served; Indicates a section The th shift The set of trip requests served; Indicates the section The first shift on The set of trip requests served; Indicates the section The th shift The set of trip requests served; Indicates the section The th shift The set of trip requests served; Define the departure time sequence of the third-layer coding ; ； ； Among them, Represents the departure time sequence of all trips on section 1, Represents section The departure time sequence of all trips on, Represents section The departure time sequence of all trips on; Indicates the departure time of the first shift on section 1 , Indicates the th shift on section 1; Indicates the th shift on section 1; Indicates the section The departure time of the first shift on; Indicates the section on the th shift The departure time of; Indicates the section on the th shift The departure time of; Indicates the section The departure time of the first shift on; Indicates the section on the th shift The departure time of; Indicates the section on the th shift The departure time of; The specific process is as follows: Step 6.1.

1. According to the passenger travel request , combined with each request 's boarding station and alighting station respectively located in the section and , count the passenger flow demand on each section, and calculate and store the modular vehicle quantity at the starting station of the section ; expressed as: ; In the formula, Indicates the start time of operation , the number of modular vehicles stored at the starting station of the section ; the unit is vehicle ; Indicates the passenger flow demand on the section , in units of people; From the operation period Of all the modular vehicle number sets participating in the dispatching During, randomly select Vehicles and allocate them to the starting station of the section And add them to the vehicle number set stored at the station before the start of operation ; ; Among them; During this process, ensure that each vehicle can only be assigned once; Step 6.1.

2. Under the condition of satisfying the maximum shift formation length constraint , traverse the set of vehicle numbers stored at the starting station generated in Step 6.1.1 , and randomly select 1 to vehicles from it to form a set of vehicle numbers for the shift , until each vehicle is assigned to a shift; For each request If it satisfies and the shift meets the capacity constraint condition, then the request is assigned to the set of service requests of the shift until each request finds its corresponding boarding shift; Under the condition of meeting the speed constraint and the service request time window constraint randomly determine the departure time of each shift until the departure time of each shift is determined; Indicates the request boarding station in the section where it is located; Step 6.1.

3. Calculate the shift according to the formula in Step 3.1 calculate the shift at the end station the number of transfer passengers ; If , according to the shift in Step 3.2 , it is necessary to judge the transfer strategy. After that, the vehicle is split and combined according to Step 4 to complete the passenger transfer, and the set of vehicle numbers of the shift is updated based on the passenger transfer result , the service request set and the departure time ; otherwise, judge the next shift; until all shifts in the set of shifts on the bus corridor within the operation period are inspected ; Step 6.1.4, combine the set of vehicle numbers of the formed shifts updated in Step 6.1.3 , the updated set of shift service requests and the updated set of shift departure times , find the shift with the largest departure time in the existing set of shifts , determine the shift arrives at the end station at the time ; judge the number of modular vehicles stored at the critical station at the time . If , no reallocation is required; if , reallocate the critical station until the critical station meets ; ; Repeat step 6.1.4 until all critical sites are satisfied ; Among them, for the key sites The process of reallocation is as follows: 1) Traverse the key site collection For each key site, find Key sites of conditions , and at the site The stored vehicle number collection Random selection vehicles, reallocated to meet Key sites of conditions , and include key sites Section Create a new shift based on an existing shift , determine the composition of new shifts Vehicle number collection , new flights Departure time for , service passenger request set is empty; 2), Update the key sites after reallocation and the stored set of vehicle numbers , and the stored vehicle quantity , ; Judge at the moment Key site Stored modular vehicle quantity , if , no reallocation is required; if , then re - execute 1) and 2) until the key site meets ; Indicates the start time of operation Before at the key station Stores the number of modular vehicles; Indicates the start time of operation Before at key stations Stores the number of modular vehicles; Step 6.1.5, the set of vehicle numbers of the updated composition shifts in Step 6.1.4 , the set of updated shift service requests and the updated shift departure times together constitute the initial solution ; Step 6.2: Design a destruction operator and a repair operator; the specific process is as follows: Step 6.2.1: Design five destruction operators , specifically including: (1)Random destruction operator ; The specific process is as follows: Randomly select 10% of the total demand of the travel requests to be removed from the current solution to obtain a damaged solution and add the deleted requests to the list of requests to be served ; The total demand is the set of passenger travel requests on the passenger flow corridor during the operation period in the past 30 working days collected ; (2) Worst damage operator ; The specific process is as follows: Define the insertion cost ; Among them, represents the travel cost of the current solution , represents the travel cost after removing the travel request from the current solution . Select the top 10% of trip requests sorted in descending order of insertion cost and remove them from the current solution to obtain the damaged solution and add the deleted requests to the list of requests to be served ; (3) Correlation destruction operator ; The specific process is as follows: Randomly select a travel request , according to formula find the travel request with the strongest correlation with the request , remove these two requests from the current solution , repeat the above operation until the number of removed requests reaches 10% of the total demand and stop, obtaining the damaged solution and add the deleted requests to the list of requests to be served ; The total demand is the set of passenger travel requests on the passenger flow corridor during the operation period in the past 30 working days ; ​ In the formula, Indicates a request and the correlation between; and respectively represent the request and the earliest expected service start time; and respectively represent the request and the latest expected start service time; and respectively represent the number of passengers included in the request and , with the unit of person; and respectively represent the distances between the boarding stations of the two requests and the reference station 1, with the unit of km; and represent the distances between the alighting stops of two requests and the reference stop 1 respectively, in km; Indicates a parameter; (4)Modular vehicle destruction operator ; The specific process is as follows: Randomly select 10% of the total number of modular vehicles and remove them from the current solution Randomly select trip requests within the shift and remove them from the current solution until the capacity constraint is satisfied and then stop; finally, obtain the damaged solution and add the deleted requests to the list of requests to be served ; (5)Bus schedule disruption operator ; The specific process is as follows: Sort in descending order according to the passenger load factor, and remove the trips with the lowest 10% in the sorted list to obtain the disrupted solution And add the trip requests served by the trips to the list of requests to be served ; Step 6.2.

2. For the solution after destruction and the list of service requests to be processed , two repair operators are designed to repair the solution after destruction and obtain a new solution , specifically including: (1)For the solution after disruption and the list of service requests to be served , design a random repair operator to repair the solution after disruption to obtain a new solution , specifically including: Traverse the list of service requests to be processed for each travel request in it, and determine the request according to Step 1.4 for classification, and randomly insert it into to update the operation shift sequence , the sequence of travel requests served by the shift and the sequence of departure times of the shift ; Until all travel requests in the list of requests to be served are all inserted, and finally a new solution is obtained ; (2)For the solution after disruption and the list of service requests to be served , design a greedy repair operator to repair the solution after disruption to obtain a new solution , specifically including: Traverse the list of requests to be served for each travel request and, according to step 1.4, judge the request category and randomly insert it into accordingly; Calculate the total cost after inserting the inserted trip request of and the total cost of the solution after disruption ; take the difference between them, and insert the inserted trip request corresponding to the minimum difference value into to update the operating shift sequence , the sequence of trip requests served by the shift and the sequence of departure times of the shift ; ;​ Until all travel requests in the list of requests to be served are inserted, a new solution is finally obtained ;​ Step 6.3: Generate operator pairs and initialize the weights of the operator pairs; For the destruction operator designed in step 6.2 and the repair operator are combined pairwise to generate operator pairs ; Initially, the weight of each operator pair is 1 and the score is 0; Step 6.

4. Solve the modular bus vehicle scheduling optimization model based on Steps 6.1, 6.2, and 6.3, and output the optimal scheduling plan. The specific process is as follows: 6.4.

1. Set the number of iterations ; 6.4.

2. Select a destruction and repair operator and generate a new solution; 6.4.

3. Update the current solution and the optimal solution; 6.4.

4. Update the score of the operator pair; 6.4.

5. Update the weights of the operator pairs; 6.4.

6. Let the number of iterations , substitute the updated operator pair fraction and the updated operator pair weight into Step 6.4.2, and repeat Steps 6.4.2 to 6.4.6 until the maximum number of iterations is reached, and then output the optimal scheduling plan ; It includes the set of vehicle numbers, the set of requests served, and the departure times for each operation schedule in the scheduling plan.

7. A modular bus scheduling optimization method for a bus corridor according to claim 6, characterized in that: In Step 6.4.2, select a destruction and repair operator and generate a new solution; the specific process is as follows: Step 6.4.2.1, Select the destruction and repair operators: Based on the roulette wheel strategy, randomly select operator pairs according to the normalized weights of the operators ; The specific process is as follows: First, according to formula normalize the weights of the operator pair : In the formula, Represents the weights of the operator pair ; Represents the sum of the weights of all operator pairs; Indicates the operator pair The probability of being selected satisfies ; Among them, set parameters to balance the relationship between the solution time and the timeliness of weight update; Next, according to Equation construct a cumulative probability interval for each operator pair: In the formula, the initial cumulative probability is 0, denotes the cumulative probability up to the operator pair ; Then, a random number uniformly distributed is generated , and then according to the random number , the corresponding operator pair is selected according to the cumulative probability interval into which it falls ; Step 6.4.2.2: Generate a new solution; the specific process is as follows: The operator pair selected according to 6.4.2.1 , determine the selected disruption operator and the repair operator , operate on the current solution according to step 6.2 to obtain a new solution .

8. A modular bus scheduling optimization method for a bus corridor according to claim 7, characterized in that: Update the current solution and the optimal solution in step 6.4.3; The specific process is as follows: Definition respectively represent the current solution, the new solution and the optimal solution; If , then the value of the optimal solution is replaced by the value of the new solution ; If , then the value of the current solution is replaced by the value of the new solution ; If , the simulated annealing criterion is used to decide whether to accept the new solution; the specific process is as follows: Generate a random number If then replace the value of the current solution with the value of the new solution ; otherwise, the value of the current solution remains unchanged and the new solution is not accepted ; According to the formula calculate the simulated annealing probability : Among them, represents the annealing temperature; Denote the objective function value of the new solution ; Denote the objective function value of the optimal solution ; Denote the objective function value of the current solution .

9. The modular bus scheduling optimization method for a bus corridor according to claim 8, characterized in that: Update the scores of the operator pairs in step 6.4.4; The specific process is as follows: Design operator pair score Update rule: If , the operator pair score increases by ; If , the operator pair score increases by ; If , if accepted by the simulated annealing criterion, the operator pair score increases ; if not accepted by the simulated annealing criterion, the operator pair score remains unchanged.

10. A modular bus scheduling optimization method for bus corridors according to claim 9, characterized in that: Update the weights of the operator pairs in step 6.4.5; The specific process is as follows: Definition Denote the operator pair At the weight of the Denote the reaction coefficient Denote the operator pair score of Denote the operator pair number of successful applications; According to the formula Update the weight: 。

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