Timetable design and vehicle scheduling integration method for multi-line coordination of pure electric buses

Abstract

The invention discloses a multi-line collaborative timetable design and vehicle scheduling integration method for pure electric buses, and relates to a design method for scheduling of pure electric buses. The invention aims to solve the technical problems of poor coordination and high operation cost of the existing pure electric bus. The model established by the method is a mixed integer linear programming model, belongs to a minimum and maximum dual-objective optimization problem, and aims to find a satisfactory solution suitable for the problem. By considering the non-uniform departure time table, the nonlinear charging curve, the time-of-use electricity price and the charging facility limitation and focusing on the operation characteristics of the pure electric buses, the pure electric bus coordination time table and vehicle scheduling and scheduling integrated design method is provided, the optimal fleet and charging plan is established, the passenger transfer efficiency in multiple lines is improved, and the passenger transfer efficiency is improved. The risk of bunching is reduced, the regularity of the operation service of the pure electric bus line is improved, and the operation cost of an enterprise is reduced.

Description

Technical Field

[0001] The invention relates to a design method for scheduling pure electric public buses. Background Art

[0002] Due to the widespread use of carbon fuel vehicles, the total carbon dioxide emissions in the transportation sector account for about a quarter of the global carbon dioxide emissions, which is one of the main causes of climate change. Therefore, in order to reduce carbon pollution and protect the livable environment on which we depend, it is particularly urgent to develop new energy travel tools. In the context of global emission reduction and active promotion of new energy vehicles, electric buses have been proven to make significant contributions to the decarbonization of the transportation sector. Among them, pure electric bus systems are considered to be both economical and environmentally friendly means of transportation. Local governments in many countries have implemented a series of policies, such as policy subsidies, financial incentives, and tax exemptions, to promote the vigorous development and deployment of pure electric buses. The new energy of public transportation has become a development trend of urban buses. In view of its high efficiency, low pollution, low cost, and good mobility, many cities are building pure electric bus line networks. Therefore, the study of pure electric bus operation planning and scheduling has important practical significance for energy conservation and emission reduction and the realization of green transportation.

[0003] Transfer coordination and reduction of congestion at shared line sections are necessary in public transport networks to create a more efficient service network by allowing more flexible route planning and reducing total operating costs. Uncoordinated transfer connections and long transfer waiting times will greatly reduce the attractiveness of bus services, thereby frustrating and annoying existing bus passengers and losing a portion of potential new users. Therefore, reducing transfer waiting times can improve the passenger riding experience, thereby increasing the number of public transport passengers and competitiveness with private cars. Therefore, an important issue that public transport policy makers, service planners and operators need to consider is how to optimize the transfer coordination of routes to achieve good connections and transfer services. In addition, since different routes often converge at specific stations in the network, that is, bus route overlap and station overlap sections, it is necessary to reduce congestion at common stations on route overlap sections to improve service levels. Line coordination is considered to occur when the schedule avoids two buses from different routes arriving at the same station at the same time, or when it allows passengers to transfer efficiently and with sufficient time to transfer from one route to another.

[0004] The coordinated optimization of multi-line pure electric bus schedules needs further in-depth research. The uniqueness of the pure electric bus operation mode brings greater challenges to the realization of coordinated scheduling. The traffic nodes of the pure electric bus line network include not only coordinated stations, but also charging station locations, and consider issues such as charging pile scheduling and nonlinear charging curves. Figure 1As shown, the location of the charging station is determined to facilitate charging when the vehicle is low on power, and reasonable charging scheduling is carried out. Figure 2 This is a schematic diagram of the charging pile scheduling to ensure the charging scheduling and operation of the vehicle. The process first determines the time when the vehicle arrives at the charging station and the charging time required. According to the occupancy of each pile at the current moment, the vehicle charging time is inserted into the available time segment of each pile after the current moment to find the nearest available charging pile. Figure 3 It is a fitting diagram of the nonlinear charging curve and the piecewise function. The piecewise linear function is used to represent the changes in the battery state of charge and charging duration. The charge level at each segment point can be obtained through the piecewise linear function.

[0005] At present, there are few studies on the coordinated optimization of multi-line timetables for pure electric buses, vehicle charging scheduling, and charging pile scheduling at charging stations, which are limited in charging facilities, waiting for vehicles to charge, nonlinear charging behavior of vehicles, and time-of-use electricity prices during bus operation. Considering the operational characteristics of pure electric bus systems, it is necessary to solve large-scale and complex multi-line timetable coordination and vehicle charging scheduling problems. Based on the coordination of conventional bus timetables and combined with related research on pure electric bus charging scheduling, an integrated optimization model and efficient solution algorithm were established. In the model development, since the vehicle charging scheduling model and timetable coordination model based on pure electric bus trip connections both use vehicle departure time as the decision variable, the vehicle charging scheduling model based on vehicle trip connections is used to establish an integrated optimization model. Summary of the invention

[0006] The present invention aims to solve the technical problems of poor coordination and high operating cost of current pure electric buses, and provides a timetable design and vehicle scheduling integration method for multi-line coordinated pure electric buses.

[0007] The method for integrating timetable design and vehicle scheduling for multi-line coordinated pure electric bus of the present invention is carried out in the following steps:

[0008] Step 1: Build a pure electric bus route network and establish the attribute set of each traffic node in the network;

[0009] The attribute set of each traffic node includes a starting station, a terminal station, a coordinated station, a non-coordinated station and a charging station;

[0010] The charging station includes its location and the number of charging posts;

[0011] Collaborative stations include collaborative entry / transfer at the same platform and collaborative transfer at different platforms;

[0012] Coordinated entry / transfer at the same station: In bus planning, multiple bus lines are allowed to enter / transfer at the same station to avoid congestion caused by buses running in parallel at the station and reduce the waiting time for passengers who need to transfer;

[0013] Collaborative transfer between different platforms: To solve the transfer problem between bus lines, we optimize the departure time of each line and realize collaborative transfer between different lines to improve passengers' travel efficiency and satisfaction;

[0014] Step 2: Collect and establish the running status set of each line according to the operating period;

[0015] The train operation status set includes the number of up and down train departures, vehicle travel routes, departure frequency range, minimum and maximum departure intervals, initial departure schedule and arrival time of each line during operation;

[0016] Step 3: Collect the AVL data during the operation period within one month, calculate the inter-station travel time of adjacent stations, round it off to the nearest integer in minutes, and include it in the set of travel time of adjacent stations. Then, an integer set of the travel time of adjacent stations is obtained, and the average of the inter-station travel time is taken.

[0017] Step 4: Use the card and code swiping data on pure electric buses to collect the boarding passenger data at each station during the operation period of one month, and calculate the average passenger arrival rate at each station on each route;

[0018] Step 5: Focus on the operation characteristics of pure electric buses and build a pure electric bus coordinated timetable and vehicle dispatch optimization model;

[0019] 1. Vehicle motion equation part

[0020] The arrival and departure times of vehicles at each station are related to the travel time between stations and the stop time at the station. The arrival time of the pth train of line i at station b is The departure time of the vehicle at the previous stop b-1 Travel time between stations The departure time at station b is determined by Arrival time and the stop time at station b The vehicle’s stop time at a station includes the door opening and closing time t° and the passenger boarding and alighting time t up , where the time required for passengers to get on and off the bus depends on the maximum value of the passenger boarding time and the passenger getting off time; and denote the number of passengers getting on and off the p-th bus of line i at station b, respectively. α1 and α2 denote the average time required for each passenger to get on and off the bus, respectively. The time required for the bus to get on and off passengers at station b is the product of the number of passengers getting on and off and the time of getting on and off. Here, it is assumed that only one person can get on and off the bus at the same time.

[0021] Studies have shown that the time required for passengers to get off the bus is less than the time required to get on the bus. Therefore, the time required for passengers to get off the bus is ignored in the present invention. The formulas are as follows:

[0022]

[0023] b∈N i , N i is the set of bus stops on bus route i;

[0024] 2. Objective Function

[0025] 1) Maximize the number of timetable collaborations

[0026] For line i with collaborative station b, collaborative station b includes collaborative entry / transfer at the same platform b' and collaborative transfer at a different platform b"; define binary auxiliary variables represents the number of coordinated times of multi-line pure electric buses at coordinated station b, include and in It represents the coordination between line i and line j at the same station and the same direction at the coordinated station b', solving the problem of coordinated entry / transfer at the same station; represents the coordination between line i and line j at different platform coordinated transfer b”, solving the problem of different platform coordinated transfer; the pth train of line i is represented as train number i(p), is the main decision variable, representing the departure time of train number i(p). When the absolute difference between the time when train number i(p) arrives at the cooperative station b and train number j(q) is within the preset cooperative time window, In, a binary auxiliary variable representing the number of collaborations is 1, otherwise it is 0, which means as follows:

[0027]

[0028] represents the time when the pth train of line i arrives at the cooperative station b; represents the travel time of the p-th train of line i from the initial station to the coordinated station b, that is, the sum of the inter-station running time and the stop time at each station from the initial station to the coordinated station b;

[0029] Formula (7) below represents the number of coordinated transfers between routes i and j at the same station; Formula (8) represents the number of coordinated transfers between routes i and j at different stations; Formula (9) represents the goal of maximizing the total number of coordinated transfers between routes; f i represents the set showing the number of departures of route i; p is the number of trains of route i, q is the number of trains of route j; I represents the set of routes;

[0030]

[0031] 2) Minimize total operating costs

[0032] ① Establish a train chain: The vehicle charging scheduling gives a train schedule, each of which includes a departure station, departure time, arrival station, arrival time, charging location, and whether to charge; establish a multi-depot vehicle charging scheduling model based on train connection, with the departure time of the vehicle at the starting station as the decision variable; introduce binary auxiliary variables To measure the number of buses on bus line i 1 (p) and down train number i 2 (q) Whether they can be connected in series, i.e. whether the planned trip is carried out by the same vehicle, i 1 (p) represents the train number p of line i in the upward direction, i 2 (q) represents the train number q of line i in the down direction; the train number is integrated into the train number chain, and then the train number chain is executed by the vehicle; in order to build the train number chain to the greatest extent and reduce the use of vehicles, the connection of empty trains is considered in the train number matching, that is, there will be connections of empty trains in the train number chain;

[0033]

[0034] f i represents a set showing the number of departures of route i; I represents a set of routes;

[0035] ② Time-of-use electricity price and charging strategy: The charging plan is affected by factors such as charging time, time-of-use electricity price and nonlinear charging. At present, many cities at home and abroad implement time-of-use electricity price, dividing 24 hours a day into several different time periods, charging corresponding electricity fees according to different time periods, and the rate during peak period is 2 to 3 times that of non-peak period. Most charging stations have limited scale conditions, and the charging mode is mostly conventional charging (slow charging). It takes several hours for the battery to be fully charged, and the number of vehicles with charging needs in different time periods of the day is also different. Therefore, it is possible to consider charging the bus route vehicles at night and charging during the day during the operation period to meet the daily operation needs. The constant current and constant voltage method is a charging method commonly used by electric vehicles, which can show the nonlinear charging behavior of the battery. The constant current and constant voltage process is that in the constant current (CC) stage, the charging current remains constant, and the terminal voltage of the battery continues to increase until it reaches the maximum value specified by the manufacturer. In the constant voltage (CV) stage, the terminal voltage must be maintained at the maximum value to avoid overcharging the battery. The present invention uses a piecewise linear function f(χ) to represent the change of the battery state of charge (SOC) and the charging duration χ. The charge level at each segment point can be obtained through the piecewise linear function. Therefore, the charging duration can be calculated through the charging piecewise function and the battery remaining charge level after the vehicle completes a trip. The percentage of charging capacity is in is the charging start time, The charging level at the beginning of charging. The charging strategy has a crucial impact on the number of buses in operation and the battery cycle life. If charging is not stopped until the battery is exhausted and is not stopped until it is fully charged, or the battery state of charge (SOC) changes greatly, this will accelerate the deterioration of the battery health state. Therefore, in the present invention, an appropriate charging strategy is adopted to keep the battery state of charge of each electric bus at [S min , S max ] to extend the battery cycle life;

[0036] The goal of vehicle charging scheduling is to minimize the total operating cost of the line. The total operating cost is usually measured by the minimum fleet size required, that is, the maximum number of train chains. The fleet cost is closely related to the amortization cost, depreciation cost, insurance and maintenance cost. The research object of this invention is electric buses, which need to be charged during a day's journey. Therefore, the total operating cost also includes the charging cost, which depends on the charging duration, charging amount and unit electricity price. Considering the limited scale of charging stations and the charging time, this cost is a variable cost. In order to facilitate the calculation of the charging cost, To represent the percentage of charging of the vehicle on route i at the charging station after completing trip p; because the time-of-use electricity price is considered in the charging strategy, c s Indicates the unit electricity price in period S, the number of train chain connections The objective functions of and charging cost C1 are respectively expressed as

[0037]

[0038] f i represents the set of departure times for route i; I represents the set of routes; i 1 Indicates the direction of leaving the charging station in route i, i 2 Indicates the direction toward the charging station in route i;

[0039]

[0040] in is the charging duration, is the charging start time, is the charge level at the beginning of charging;

[0041] The minimum number of electric buses required is given by the minimum fleet size theorem, that is, when implementing a given bus schedule, F i and f represent the total number of vehicles going up and down on line i and the total number of vehicles going up and down, respectively. The minimum fleet size is expressed as:

[0042]

[0043] Then the objective function of minimizing fleet cost is expressed as

[0044]

[0045] where c F represents the fixed cost of using an electric bus;

[0046] Therefore, the total operating cost of multi-station bus vehicles with the minimum total operating cost of the route is expressed as follows:

[0047] minTC=min(C1+C2) (14);

[0048] 3. Constraints

[0049] 1) Departure interval constraints

[0050]

[0051] Constraints (15) and (16) are departure interval constraints, which ensure that the consecutive departure times of each line are between the minimum and maximum departure intervals;

[0052] Constraint (17) is the departure time constraint of the first train on the route, ensuring that the first train on each route departs on time;

[0053] Constraints (18) and (19) ensure that the departure time of the last vehicle on each route is within the planning period s and no earlier than a time that is one departure interval less than s;

[0054] where h i With H i are the minimum departure interval and the maximum departure interval of line i respectively; the departure time of train p on line i is It means that the first bus of route i departs on time. The time when the last vehicle departs from route i; s i is the planning period of route i; I represents the set of routes; the departure time of train q on route j is is a value between the minimum departure interval and the maximum departure interval of line i, that is,

[0055] 2) Collaborative constraints

[0056]

[0057] Constraints (20) and (21) indicate that pure electric buses must meet the minimum and maximum time window range at the line coordination station b. Inside; M1 is a maximum positive value;

[0058] 3) Train connection constraints

[0059] Constraint (22) ensures that each train can only be connected to one subsequent train at most, and the connected train may be an empty trip;

[0060] Constraint (23) ensures that each train can only be connected to one preceding train at most, and the connected train may be an empty trip; the empty trip is to connect to more trains;

[0061]

[0062] If the same vehicle cannot complete the subsequent trip after completing the previous trip, constraints (24) and (25) force the binary auxiliary variable is 0; if the vehicle does not arrange a charging plan after completing trip p, then t pcq and All are 0, assuming that there is a charging station on the side of the upstream starting point of line i; represents the departure time of route i when it leaves the charging station, represents the departure time of route i heading towards the charging station; constraint (26) specifies the binary auxiliary variable The possible values ​​of ;

[0063]

[0064] in represents the running time of the up-trip p of line i, represents the running time of the down train q on line i; t pc is the time required for the vehicle to travel from the starting and ending stations to the charging station, t cq is the time required for the vehicle to return from the charging station to the starting and ending stations, t pcq =t pc +t cq Indicates the round-trip time of an electric bus in an empty trip between the departure station and the charging station; Indicates the charging duration of the electric bus at the charging station; M2 is a maximum positive value;

[0065] 4) Constraints on power consumption and charging facilities

[0066] Constraint (27) reflects the power constraint, which means that the remaining power of the vehicle at the charging station is not less than the total power consumed by the outbound trip and the return trip plus the safety lower limit power; Constraint (28) reflects the charging pile capacity limit of the charging station, which ensures the charging of the vehicle and provides reliable services for building the train chain;

[0067]

[0068] in Indicates the remaining power of the vehicle at the charging station; are the power consumed by completing p and q linked trains, p is the uplink train and q is the downlink train; S min Provide the battery with a safe lower limit of power for cycling; It is defined as the remaining effective charging position of charging station k in period s The number of vehicles charging demand for line i in time period s The difference between indicates the capacity limitation of the charging station;

[0069] ① Determination of effective charging position

[0070] Considering the limited number of charging piles at the charging station and the sharing of charging piles with other bus routes in a day, α s It represents the charging position utilization rate of the charging station in the current planning period, which can be converted into the remaining effective charging positions of the charging station, expressed as

[0071]

[0072] Among them C N is the total charging position;

[0073] ② Estimation and determination of the number of charging vehicles and energy consumption

[0074] The charging decision is made every time the vehicle returns to the charging station. Whether the vehicle is charged is determined by the remaining power of the vehicle at the charging station and the subsequent outbound and return trips. If the remaining power is insufficient to perform the subsequent trip tasks, charging is required. The vehicle is charged on a first-come, first-served basis. The charging piles at the charging station are numbered and the available charging time of each charging pile is compared with the charging time of the vehicle. Match; the remaining power of the vehicle Energy consumption by travel and the battery rated capacity R; when the battery rated capacity is fixed, the remaining power of the electric bus E on route i at the end of trip p is The state of charge at the start And the energy consumption of this trip Decide, expressed as follows:

[0075]

[0076] Where η is the charging power of the charging pile (kWh); Vehicles that meet the charging conditions during period s Sum; S max Cycle the battery to the safe upper limit of power;

[0077] The four variables with the highest correlation with vehicle travel energy consumption are: the mileage L traveled by the electric bus trip p p (km), vehicle measured curb weight G p (kg), driving time T p (h) and the absolute difference between the average ambient temperature and the optimal operating temperature An energy consumption estimation model for electric buses was established. Since the distances from each line to the charging station are different, the idle distance L needs to be considered. pc The energy consumption generated by (km) is added to the energy consumption model. The energy consumption estimation model is as follows:

[0078]

[0079] in and represents the estimator of the regression coefficient;

[0080] 4. Model integration

[0081] The established pure electric bus multi-line timetable collaborative optimization model and vehicle charging scheduling optimization model use the same decision variables, namely the departure time of the bus; both meet the same minimum and maximum departure intervals, and the departure time of the last bus on each line is within the planning period; these two models are integrated and the same constraints are combined to obtain the following dual-objective integrated optimization model:

[0082] Integrated dual-objective optimization model

[0083] Objective function:

[0084] Constraints: coordination constraints, coordination + charging scheduling constraints, and train chain construction constraints;

[0085] Step 6: The model established by the present invention is a mixed integer linear programming model. Due to the complexity of the dual-objective collaborative optimization model and the diversity of the elements involved, the algorithm is carried out from the following aspects: first, the problem is solved by combining the differential evolution algorithm with the heuristic basic algorithm of the lexicographic order method, and then a collaborative matching algorithm and a construction heuristic algorithm suitable for the problem background and logic are established for the collaborative and charging scheduling optimization goals respectively, so as to solve the dual-objective optimization problem;

[0086] Step 7: The algorithm generates a target convergence curve based on the target priority setting and outputs a satisfactory solution to the problem.

[0087] Advantages of the present invention:

[0088] The present invention studies the integrated optimization model of pure electric bus timetable coordination and vehicle scheduling. On the basis of vehicle charging scheduling, it also considers the charging pile scheduling under the condition of limited charging station scale. It is a rare study on the coordinated optimization model of pure electric bus. At the same time, it also considers non-uniform timetables, nonlinear charging curves and time-of-use electricity prices. Under the condition of reducing the number of vehicles and charging costs, it generates a departure schedule that maximizes the timetable coordination and a vehicle charging scheduling plan that minimizes the total operating cost, as well as the scheduling results of charging piles. These considerations can reflect more realistic operating conditions. The present invention considers the operating time of one day as the planning cycle, and the optimization involves more data and variables. It combines the collaborative matching algorithm and the construction heuristic algorithm to solve large-scale multi-line optimization problems, so that the problem is effectively solved. The method of the present invention provides a new idea for bus companies to compile multi-line coordinated timetables for pure electric buses, which is of great significance to promoting the large-scale operation of urban green buses. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 A schematic diagram of coordinated events and charging scheduling for a pure electric bus of the present invention;

[0090] Figure 2 This is a schematic diagram of the charging pile scheduling;

[0091] Figure 3 It is a constant current-constant voltage nonlinear charging curve-piecewise function fitting diagram (the vertical axis is the battery charge level);

[0092] Figure 4 This is the current layout of the pure electric bus line in Experiment 1;

[0093] Figure 5 This is a schematic diagram of the individual coding in the algorithm of Experiment 1;

[0094] Figure 6 This is the target convergence curve diagram in experiment 1;

[0095] Figure 7 This is the result diagram of the optimized dispatch of bus route 425 in experiment 1;

[0096] Figure 8 This is the result diagram after the optimization of bus route 484 scheduling in experiment 1;

[0097] Fig. 9 This is the result diagram of the optimized dispatch of bus route 569 in experiment 1;

[0098] Fig.10 This is the result diagram of the optimized dispatch of bus route 653 in experiment 1;

[0099] Fig.11 This is the result diagram of charging pile resource allocation for line 425-569 in test 1;

[0100] Fig.12 This is the result diagram of charging pile resource allocation for line 484-653 in test 1;

[0101] Fig.13 It shows the change of line coordination times before and after model optimization;

[0102] Fig.14 It shows how the fleet and charging costs change before and after the model optimization;

[0103] Fig.15 The change in the target optimization percentage before and after model optimization is shown. DETAILED DESCRIPTION

[0104] Specific implementation method 1: This implementation method is a method for integrating timetable design and vehicle scheduling for multi-line coordination of pure electric buses, which is specifically carried out in the following steps:

[0105] Step 1: Build a pure electric bus route network and establish the attribute set of each traffic node in the network;

[0106] Step 2: Collect and establish the running status set of each line according to the operating period;

[0107] The train operation status set includes the number of up and down train departures, vehicle travel routes, departure frequency range, minimum and maximum departure intervals, initial departure schedule and arrival time of each line during operation;

[0108] Step 3: Collect the AVL data during the operation period within one month, calculate the inter-station travel time of adjacent stations, round it off to the nearest integer in minutes, and include it in the set of travel time of adjacent stations. Then, an integer set of the travel time of adjacent stations is obtained, and the average of the inter-station travel time is taken.

[0109] Step 4: Use the card and code swiping data on pure electric buses to collect the boarding passenger data at each station during the operation period of one month, and calculate the average passenger arrival rate at each station on each route;

[0110] Step 5: Focus on the operation characteristics of pure electric buses and build a pure electric bus coordinated timetable and vehicle dispatch optimization model;

[0111] 1. Vehicle motion equation part

[0112] The arrival and departure times of vehicles at each station are related to the travel time between stations and the stop time at the station. The arrival time of the pth train of line i at station b is The departure time of the vehicle at the previous stop b-1 Travel time between stations The departure time at station b is determined by Arrival time and the stop time at station b The vehicle’s stop time at a station includes the door opening and closing time t° and the passenger boarding and alighting time t up , where the time required for passengers to get on and off the bus depends on the maximum value of the passenger boarding time and the passenger getting off time; and denote the number of passengers getting on and off the p-th bus of line i at station b, α1 and α2 denote the average time required for each passenger to get on and off the bus, respectively. The time required for a vehicle to get on and off passengers at station b is the product of the number of passengers getting on and off and the time of getting on and off;

[0113] In the present invention, the time when passengers get off the bus is ignored, and the formulas are expressed as follows:

[0114]

[0115]

[0116] b∈N i , N i is the set of bus stops on bus route i;

[0117] 2. Objective Function

[0118] 1) Maximize the number of timetable collaborations

[0119] For line i with collaborative station b, collaborative station b includes collaborative entry / transfer at the same platform b' and collaborative transfer at a different platform b"; define binary auxiliary variables represents the number of coordinated times of multi-line pure electric buses at coordinated station b, include and in It represents the coordination between line i and line j at the same station and the same direction at the coordinated station b', solving the problem of coordinated entry / transfer at the same station; represents the coordination between line i and line j at different platform coordinated transfer b”, solving the problem of different platform coordinated transfer; the pth train of line i is represented as train number i(p), is the main decision variable, representing the departure time of train number i(p). When the absolute difference between the time when train number i(p) arrives at the cooperative station b and train number j(q) is within the preset cooperative time window, In, a binary auxiliary variable representing the number of collaborations is 1, otherwise it is 0, which means as follows:

[0120]

[0121] represents the time when the pth train of line i arrives at the cooperative station b; represents the travel time of the p-th train of line i from the initial station to the coordinated station b, that is, the sum of the inter-station running time and the stop time at each station from the initial station to the coordinated station b;

[0122] Formula (7) below represents the number of coordinated transfers between routes i and j at the same station; Formula (8) represents the number of coordinated transfers between routes i and j at different stations; Formula (9) represents the goal of maximizing the total number of coordinated transfers between routes; f i represents the set showing the number of departures of route i; p is the number of trains of route i, q is the number of trains of route j; I represents the set of routes;

[0123]

[0124] 2) Minimize total operating costs

[0125] ① Establish a train chain: The vehicle charging scheduling gives a train schedule, each of which includes a departure station, departure time, arrival station, arrival time, charging location, and whether to charge; establish a multi-depot vehicle charging scheduling model based on train connection, with the departure time of the vehicle at the starting station as the decision variable; introduce binary auxiliary variables To measure the number of buses on bus line i 1 (p) and down train number i 2 (q) Whether they can be connected in series, i.e. whether the planned trip is carried out by the same vehicle, i 1 (p) represents the train number p of line i in the upward direction, i 2 (q) represents the train number q of line i in the down direction; the train number is integrated into the train number chain, and then the train number chain is executed by the vehicle; in order to build the train number chain to the greatest extent and reduce the use of vehicles, the connection of empty trains is considered in the train number matching, that is, there will be connections of empty trains in the train number chain;

[0126]

[0127] f i represents a set showing the number of departures of route i; I represents a set of routes;

[0128] ② The goal of vehicle charging scheduling is to minimize the total operating cost of the line. The total operating cost is usually measured by the minimum fleet size required, that is, the maximum number of train chains. The fleet cost is closely related to the amortization cost, depreciation cost, insurance and maintenance cost. The research object of this invention is electric buses, which need to be charged during a day's journey. Therefore, the total operating cost also includes the charging cost, which depends on the charging duration, charging amount and unit electricity price. Considering the limited scale of charging stations and the charging time, this cost is a variable cost. In order to facilitate the calculation of the charging cost, To represent the percentage of charging of the vehicle on route i at the charging station after completing trip p; because the time-of-use electricity price is considered in the charging strategy, c s Indicates the unit electricity price in period S, the number of train chain connections The objective functions of and charging cost C1 are respectively expressed as

[0129]

[0130] f i represents the set of departure times for route i; I represents the set of routes; i 1 Indicates the direction of leaving the charging station in route i, i 2 Indicates the direction toward the charging station in route i;

[0131]

[0132] in is the charging duration, is the charging start time, is the charge level at the beginning of charging;

[0133] The minimum number of electric buses required is given by the minimum fleet size theorem, that is, when implementing a given bus schedule, F i and f represent the total number of vehicles going up and down on line i and the total number of vehicles going up and down, respectively. The minimum fleet size is expressed as:

[0134]

[0135] Then the objective function of minimizing fleet cost is expressed as

[0136]

[0137] where c F represents the fixed cost of using an electric bus;

[0138] Therefore, the total operating cost of multi-station bus vehicles with the minimum total operating cost of the route is expressed as follows:

[0139] minTC=min(C1+C2) (14);

[0140] 3. Constraints

[0141] 1) Departure interval constraints

[0142]

[0143] Constraints (15) and (16) are departure interval constraints, which ensure that the consecutive departure times of each line are between the minimum and maximum departure intervals;

[0144] Constraint (17) is the departure time constraint of the first train on the route, ensuring that the first train on each route departs on time;

[0145] Constraints (18) and (19) ensure that the departure time of the last vehicle on each route is within the planning period s and no earlier than a time that is one departure interval less than s;

[0146] where h i With H i are the minimum departure interval and the maximum departure interval of line i respectively; the departure time of train p on line i is It means that the first bus of route i departs on time. The time when the last vehicle departs from route i; s i is the planning period of route i; I represents the set of routes; the departure time of train q on route j is is a value between the minimum departure interval and the maximum departure interval of line i, that is,

[0147] 2) Collaborative constraints

[0148]

[0149] Constraints (20) and (21) indicate that pure electric buses must meet the minimum and maximum time window range at the line coordination station b. Inside; M1 is a maximum positive value;

[0150] 3) Train connection constraints

[0151] Constraint (22) ensures that each train can only be connected to one subsequent train at most, and the connected train may be an empty trip;

[0152] Constraint (23) ensures that each train can only be connected to one preceding train at most, and the connected train may be an empty trip; the empty trip is to connect to more trains;

[0153]

[0154] If the same vehicle cannot complete the subsequent trip after completing the previous trip, constraints (24) and (25) force the binary auxiliary variable is 0; if the vehicle does not arrange a charging plan after completing trip p, then t pcq and All are 0, assuming that there is a charging station on the side of the upstream starting point of line i; represents the departure time of route i when it leaves the charging station, represents the departure time of route i heading towards the charging station; constraint (26) specifies the binary auxiliary variable The possible values ​​of ;

[0155]

[0156] in represents the running time of the up-trip p of line i, represents the running time of the down train q on line i; t pc is the time required for the vehicle to travel from the starting and ending stations to the charging station, t cq is the time required for the vehicle to return from the charging station to the starting and ending stations, t pcq =t pc +t cq Indicates the round-trip time of an electric bus in an empty trip between the departure station and the charging station; Indicates the charging duration of the electric bus at the charging station; M2 is a maximum positive value;

[0157] 4) Constraints on power consumption and charging facilities

[0158] Constraint (27) reflects the power constraint, which means that the remaining power of the vehicle at the charging station is not less than the total power consumed by the outbound trip and the return trip plus the safety lower limit power; Constraint (28) reflects the charging pile capacity limit of the charging station, which ensures the charging of the vehicle and provides reliable services for building the train chain;

[0159]

[0160] in Indicates the remaining power of the vehicle at the charging station; are the power consumed by completing p and q linked trains, p is the uplink train and q is the downlink train; S min Provide the battery with a safe lower limit of power for cycling; It is defined as the remaining effective charging position of charging station k in period s The number of vehicles charging demand for line i in time period s The difference between indicates the capacity limitation of the charging station;

[0161] ① Determination of effective charging position

[0162] Considering the limited number of charging piles at the charging station and the sharing of charging piles with other bus routes in a day, α s It represents the charging position utilization rate of the charging station in the current planning period, which can be converted into the remaining effective charging positions of the charging station, expressed as

[0163]

[0164] Among them C N is the total charging position;

[0165] ② Estimation and determination of the number of charging vehicles and energy consumption

[0166] The charging decision is made every time the vehicle returns to the charging station. Whether the vehicle is charged is determined by the remaining power of the vehicle at the charging station and the subsequent outbound and return trips. If the remaining power is insufficient to perform the subsequent trip tasks, charging is required. The vehicle is charged on a first-come, first-served basis. The charging piles at the charging station are numbered and the available charging time of each charging pile is compared with the charging time of the vehicle. Match; the remaining power of the vehicle Energy consumption by travel and the battery rated capacity R; when the battery rated capacity is fixed, the remaining power of the electric bus E on route i at the end of trip p is The state of charge at the start And the energy consumption of this trip Decide, expressed as follows:

[0167]

[0168] Where η is the charging power of the charging pile (kWh); Vehicles that meet the charging conditions during period s Sum; S max Cycle the battery to the safe upper limit of power;

[0169] The four variables with the highest correlation with vehicle travel energy consumption are: the mileage L traveled by the electric bus trip p p (km), vehicle measured curb weight G p (kg), driving time T p (h) and the absolute difference between the average ambient temperature and the optimal operating temperature An energy consumption estimation model for electric buses was established. Since the distances from each line to the charging station are different, the idle distance L needs to be considered. pc The energy consumption generated by (km) is added to the energy consumption model. The energy consumption estimation model is as follows:

[0170]

[0171] in and represents the estimator of the regression coefficient;

[0172] 4. Model integration

[0173] The established pure electric bus multi-line timetable collaborative optimization model and vehicle charging scheduling optimization model use the same decision variables, namely the departure time of the bus; both meet the same minimum and maximum departure intervals, and the departure time of the last bus on each line is within the planning period; these two models are integrated and the same constraints are combined to obtain the following dual-objective integrated optimization model:

[0174] Integrated dual-objective optimization model

[0175] Objective function:

[0176] Constraints: coordination constraints, coordination + charging scheduling constraints, and train chain construction constraints;

[0177] Step 6: The model established by the present invention is a mixed integer linear programming model. Due to the complexity of the dual-objective collaborative optimization model and the diversity of the elements involved, the algorithm is carried out from the following aspects: first, the problem is solved by combining the differential evolution algorithm with the heuristic basic algorithm of the lexicographic order method, and then a collaborative matching algorithm and a construction heuristic algorithm suitable for the problem background and logic are established for the collaborative and charging scheduling optimization goals respectively, so as to solve the dual-objective optimization problem;

[0178] Step 7: The algorithm generates a target convergence curve based on the target priority setting and outputs a satisfactory solution to the problem.

[0179] Specific implementation method 2: This implementation method is different from specific implementation method 1 in that the attribute set of each traffic node described in step 1 includes a starting station, a terminal station, a cooperative station, a non-cooperative station and a charging station. The rest is the same as specific implementation method 1.

[0180] Specific implementation method three: This implementation method is different from specific implementation method two in that: the charging station described in step one includes its location and the number of charging piles. The rest is the same as specific implementation method two.

[0181] Specific implementation method 4: This implementation method is different from specific implementation method 2 in that the cooperative station described in step 1 includes the same platform cooperative entry / transfer and different platform cooperative transfer. The rest is the same as specific implementation method 2.

[0182] Specific implementation method 5: This implementation method is different from specific implementation method 1 in that the method for calculating the average passenger arrival rate at each station of each route in step 4 is: screening the card and code swiping data of passengers boarding at each station during the operation period, adding them up and taking the average value to obtain the average passenger arrival rate at the station. The rest is the same as specific implementation method 1.

[0183] Specific implementation method 6: This implementation method is different from the specific implementation method 1 in that: in step 5, the following conditions need to be met before model building:

[0184] 1) The vehicle travel time is fixed;

[0185] 2) The charging preparation time of the vehicle at the charging station is negligible;

[0186] 3) The planning cycle is discretized in minutes, that is, the vehicle departure time is a discrete integer variable;

[0187] 4) The usage and performance of vehicles on each route are the same; the vehicle capacity is sufficient to meet the needs of passengers;

[0188] 5) The first bus on the route departs on time and the bus driver fully adheres to the planned vehicle itinerary and timetable.

[0189] The rest is the same as the first specific implementation mode.

[0190] Specific implementation method 7: This implementation method is different from specific implementation method 6 in that the satisfactory solution in step 7 is the target convergence solution iterated according to the target priority set by the algorithm, that is, a satisfactory solution that meets the interests of the bus company or the passengers themselves. Other aspects are the same as specific implementation method 6.

[0191] The present invention is verified by the following tests:

[0192] Experiment 1: This experiment is a timetable design and vehicle scheduling integration method for multi-line coordinated pure electric buses, which is carried out in the following steps:

[0193] like Figure 4As shown, the line network is formed by Beijing Bus No. 484 (Route 484 is the light blue line, and has overlapping parts with the green and red lines) (the upper line is between the Third Hospital of Peking University and Beiyuan Home), Route 425 (green line) (the upper line is between Xiaoying Bus Station and Nanwu), Route 653 (red line) (the upper line is between Haidian Wuluju and Beiyuan Home) and Route 569 (dark blue line) (the upper line is between Beijing Conference Center and Xiaoying Bus Station). The upward mileage of Beijing Bus Routes 484, 425, 653 and 569 are 15 kilometers, 19 kilometers, 28 kilometers and 11.8 kilometers respectively, covering 21, 30, 41 and 20 stations respectively, and the downward mileage is 15 kilometers, 19 kilometers and 28 kilometers respectively. and 6.4 kilometers, covering 23, 31, 41 and 14 stations respectively; the routes use three types of vehicles, the 484 route is the Foton Auman BJ6180EVCA-1 pure electric bus, with a curb weight of 18,500kg and a battery rated capacity of 196 kWh; the 425 and 653 routes are the GTQ6131BEVST3 pure electric double-decker city buses, with a curb weight of 20,150kg and a battery rated capacity of 139 kWh; the 569 route is the second-generation BJ6123EVCA-3 pure electric bus, with a curb weight of 13,000kg and a battery rated capacity of 131 kWh; for safety reasons, the SOC of the pure electric bus battery is set within the range. The fixed cost of operating a pure electric bus is 318.28 yuan / day. The four routes are charged at two charging stations: Routes 484 and 653 depart from Beiyuanjiayuan Bus Station, which has 16 fast-charging charging piles deployed at the station, with a charging power of 90kw; Routes 425 and 569 depart from Xiaoying Bus Station, which has 32 charging piles deployed at the station, with a charging power of 90kw. The preset load is met during the use of the charging station. In order to meet the line operation requirements and economy, the charging time is the time required to charge the remaining power at the beginning of charging to 80% of the power;

[0194] The operation and passenger flow data used were collected on December 20, 2021. The passenger flow data were obtained from the Beijing bus card swiping data of four lines, including the card swiping data and code swiping data of passengers getting on and off the bus. The one-day planning cycle is used as the research operation period, which includes the low-peak, flat-peak and peak periods of the line, and is representative for the research. Line departure intervals, vehicle operating hours, time-of-use electricity prices and daily hourly average temperatures are collected from multiple source data, including the timetable published on the Beijing Bus Data website, the Gaode Map application and on-site surveys. There is a lot of data, which is stored in a Microsoft Excel spreadsheet after preprocessing for easy Python processing. The charging station's charging position utilization rate, charging standards for different time periods, line operating hours and minimum and maximum departure intervals, and daily hourly average temperature information during operation are shown in Tables 1, 2, 3 and 4, respectively:

[0195] Table 1 Utilization rate of charging piles at charging stations

[0196] line The sum of the charging pile utilization rates of the two lines / % 484 and 653 50 425 and 569 45

[0197] Table 2 Time-of-use electricity prices

[0198] Time period <![CDATA[Electricity price (yuan·kWh -1 )]]> 10:00-15:00、18:00-21:00 1.8044 7:00-10:00、15:00-18:00、21:00-23:00 1.4950 23:00-7:00 the next day 1.1946

[0199] Table 3 Bus route operation time and minimum and maximum departure intervals

[0200] line Operating hours Minimum departure interval / min Maximum departure interval / min Average running time / h 484 Road Up 6:10-23:00 3 18 1 484 downlink 5:30-22:20 3 18 1.1 425 Road Up 5:30-23:00 4 15 1.32 Route 425 Down 5:30-23:00 4 15 1.32 653 Road Up 6:00-22:00 1 18 1.83 Route 653 Down 5:30-22:00 1 18 1.76 569 Road Up 5:50-22:20 2 19 0.63 Route 569 Down 5:30-22:00 7 19 0.40

[0201] Table 4 Daily hourly average temperature during bus line operation

[0202] Time period Average temperature(℃) Time period Average temperature(℃) 5:00-6:00 -3 15:00-16:00 12 6:00-8:00 -4 16:00-17:00 10 8:00-9:00 -3 17:00-18:00 6 9:00-10:00 0 18:00-19:00 4 10:00-11:00 4 19:00-20:00 2 11:00-12:00 7 20:00-21:00 1 12:00-14:00 9 21:00-22:00 0 14:00-15:00 10 22:00-23:00 -1

[0203] In normal charging mode, the charging curve of the CV phase is approximately a piecewise linear function, such as Figure 3 Therefore, the vehicle charging piecewise function involved in pure electric bus routes 425, 653, and 569 is shown in formula f(χ1), indicating that the time required for the battery to be fully charged from exhaustion is 1.5h:

[0204]

[0205] The charging piecewise function of the pure electric bus line 484 is shown in formula f(χ2), which means that the time required for the battery to be fully charged from exhausted is 2.25h:

[0206]

[0207] Apply the algorithm to optimize the model, obtain the target convergence curve and get a satisfactory solution. The specific algorithm process is as follows:

[0208] Algorithm Design

[0209] The established model is a mixed integer linear programming model. Considering the complexity of the dual-objective collaborative optimization model and the diversity of the elements involved, the established algorithm is carried out from the following aspects: first, the problem is solved by combining the differential evolution algorithm with the heuristic basic algorithm of the lexicographic order method, and then a collaborative matching algorithm and a construction heuristic algorithm suitable for the problem background and logic are established for the collaborative and charging scheduling optimization goals respectively to achieve the solution of the dual-objective optimization problem.

[0210] 1. Differential Evolution Algorithm Combined with Lexicographic Order Method

[0211] 1. Individual coding method

[0212] The model is a mixed integer optimization model. The departure time of each line is an integer (the value of seconds is 0), so integer coding is used. Each individual coded is the adjustment time of all train departure times of all lines in the planning period. It consists of two directions, uplink and downlink, and D is the dimension of the problem to be solved; Figure 5 As shown, the first trains all departed on time, including It means that the second train of the first line in the upward direction will be adjusted to the left by one minute (a negative value means it will be adjusted to the left to start earlier, a positive value means it will be adjusted to the right to start later, and 0 means it remains unchanged).

[0213] 2. Fitness evaluation

[0214] The fitness function accepts a candidate solution to the problem and returns a value representing the quality of the solution. There are two objective functions: the total number of coordinated times of multi-line pure electric buses at each coordinated station on the up and down routes is maximized, which is solved by the coordinated matching algorithm of timetable coordination (Algorithm 2); the total operating cost (fleet and charging) of multi-line pure electric buses is minimized, which is solved by the construction heuristic algorithm of vehicle charging scheduling (Algorithm 3). For the dual-objective problem, this study uses the lexicographic order method to evaluate the fitness of the solution.

[0215] 3. Initial population

[0216] Set the population size N pop , taking the departure time adjustment interval defined in the objective function as the search space, it can be seen that the position information is the entire search space, and the uniformly distributed initial population position P is randomly generated in the search space pops . Initialize all schedule population positions. Each individual is represented as follows:

[0217]

[0218] Among them, i represents the number of individuals in the population, j represents the gene position (the value of the jth dimension of individual i), and G represents the evolutionary generation.

[0219] 4. Mutation, crossover, selection

[0220] The individual mutation of the differential evolution algorithm is achieved through the differential strategy. That is, by randomly selecting two different individuals in the population, scaling their vector difference and synthesizing the vector with the individual to be mutated. The mutation vector is generated as follows:

[0221] V i,G+1 =x r1,G +F·(x r2,G -x r3,G )

[0222] Among them, the randomly selected individual serial number r1≠r2≠r3≠i, and the mutation operator F∈[0,2].

[0223] Perform a general crossover of the mutation vector and the target vector. In order to increase the diversity of the interference parameter vector, a crossover operation is introduced, and the test vector becomes:

[0224]

[0225] Where randb(j) represents the jth estimated value of a random number generator between [0,1]. rnbr(i)∈(1,2,…,D) represents a randomly selected sequence. CR is the crossover operator, which ranges from [0,1].

[0226] The selection operation is a greedy-based selection mechanism that compares the trial vector with the target vector in the current population. In the next generation, if the target vector is good, the target vector is selected, and if the trial vector is good, the trial vector is selected.

[0227] 5. Lexicographical method

[0228] The lexicographic order method is used to process the non-dominated sorting of multiple objective functions to determine the pros and cons of individuals, and plays a key role in selecting and retaining the optimal solution. By assigning priorities to each goal, conflicts and trade-offs between goals can be better handled. The main principle is: for two solutions x and y, if f1(x) < f1(y) or f1(x) = f1(y) and f2(x) < f2(y), then x is better than y.

[0229] In bus scheduling, bus planners are more concerned about the changes in the number of line cooperative connections caused by adding (reducing) a vehicle, as well as the changes in variable charging costs, that is, optimizing the total number of line cooperative connections while minimizing the total operating cost. Algorithm 1 is a pseudo code implemented by the differential evolution algorithm combined with the lexicographic order method: Algorithm 1:

[0230]

[0231] 2. Collaborative Matching Algorithm

[0232] The purpose of the collaborative matching algorithm is to find a multi-line feasible timetable with at least one collaboration between the lines. This discards the multi-line feasible timetable without collaboration between the lines, improving the efficiency of the planner in formulating the initial plan. The core idea of ​​the algorithm is: establish a line collaborative time window through two types of stations and line departure intervals, calculate the difference between the arrival time of the previous vehicle and the arrival time of the next vehicle at each collaborative station, and judge whether it meets the collaborative time window constraint. If it does, record one collaboration. Calculate the number of collaborative transfers for all stations within the operation cycle, and discard the solution with a collaborative number of 0. The corresponding pseudo code of the algorithm is shown in Algorithm 2:

[0233] Algorithm 2:

[0234]

[0235]

[0236] 3. Constructing Heuristic Algorithms

[0237] The optimization part of vehicle charging scheduling is created by using a construction heuristic algorithm to generate feasible solutions for pure electric bus operations. The core idea of ​​the algorithm is mainly divided into the following three parts: the first step is to plan the vehicle scheduling without considering the charging scheduling, including the determination of the departure time of each line, the maximum matching connection of the up and down trains, and the insertion of empty trains (up trains connected to down trains (empty) and down trains connected to up trains (empty)). The operation of empty trains is to balance the inequality of the daily operating times of up and down trains on the line and better build a train chain to reduce the number of vehicles used; the second step is to schedule the vehicle charging without considering the effective resources of charging stations and charging piles. First, it is divided into two situations: there are charging stations on both sides of the line and there are charging stations on only one side of the line. Secondly, check whether the current vehicle is on the side of the charging station. Finally, check whether the vehicle needs to be charged according to the power consumption, that is, whether the current remaining power of the vehicle after executing the outbound train and the return train is greater than the set power limit; the third step is the charging pile scheduling. Determine the time when the vehicle arrives at the charging station, calculate the vehicle charging time and charging amount according to the model parameters, and number the available charging piles, check the available charging time period of each charging pile, that is, the charging time of any vehicle with charging demand at any time, split the available charging time period of the available charging piles, and convert the available resources of the piles into a match between the vehicle charging time and the available time period of the piles. The pseudo code for implementing the key steps is shown in Algorithm 3.

[0238] Algorithm 3

[0239]

[0240] All optimization modes and solving algorithms are implemented in Python 3.7 and solved on an AMD Ryzen 7 5800H with Radeon Graphics 3.20GHz, 16.0GB RAM, 64-bit Windows 10 operating system, x64-based processor. The number of iterations of the differential evolution algorithm is set to 500, the population size is 30, the crossover operator is 0.8, and the mutation operator is 0.2. Figure 6 The convergence curve graph of the optimization objective of this paper is shown. It can be observed that through the established integrated optimization model and the set solution algorithm, we can obtain a satisfactory convergence solution within an effective iteration time and number of iterations, that is, as the number of vehicles used decreases, the total number of collaborative times and variable charging costs change accordingly.

[0241] Current actual value

[0242] The planning period is from the first to the last train of each line in a day. These four lines operate a total of 686 train tasks on that day. Based on basic information such as line stations, departure intervals, and passenger card swiping data, this paper will coordinate the entry / transfer time window at the same platform. Set to [1,3] to set the time window for coordinated transfers at different platforms Set to [3,5].

[0243] The detailed data of each line station name, station running time and passenger arrival rate are stored in Excel. By sorting out the line coordination station data, the coordination number between each line under the existing departure timetable can be calculated based on the basic data, as shown in Table 5:

[0244] Table 5 Actual results of line coordination times during operation before optimization

[0245]

[0246] By constructing the operating train chain based on the existing timetable and charging strategy, it can be calculated that the number of vehicles used is 85 and the total operating cost is 42,363.21 yuan. The operation scheduling results are shown in Table 6:

[0247] Table 6 Actual results of line vehicle use and charging costs during operation before optimization

[0248]

[0249] The total number of coordinated times, vehicle operation numbers and variable charging cost of the optimized line are shown in Table 7 and Table 8 respectively. The total operating cost of the line is 38,318.47 yuan, of which the fleet cost is 22,597.88 yuan, the charging cost is 15,720.59 yuan, and the total number of coordinated times of the line is 1,399 times.

[0250] Table 7 Results after optimization of line coordination times during operation

[0251]

[0252] Table 8 Results of optimized line vehicle use and charging costs during operation

[0253]

[0254] One of the optimization goals is to establish a line station collaborative optimization model under a non-uniform timetable. The planning period is one day of operation time. The line collaborative departure timetable under integrated optimization is calculated through the solution algorithm we set. The specific optimization results are shown in Table 9 using bus line 484:

[0255] Table 9 Optimized departure timetable for Route 484

[0256]

[0257] The second optimization goal is to establish a vehicle charging scheduling optimization model that takes into account vehicle charging scheduling and charging station charging pile resource scheduling. Combined with the line operation needs, the vehicle charging scheduling plan and the bus company's consideration of line coordination while taking into account its own costs to reduce the number of vehicles used, and in order to better build train connections and further reduce the number of vehicles used, the corresponding empty trips are considered in the operation optimization. The coordinated timetable is obtained through algorithm iteration and convergence, and the vehicle charging scheduling results are calculated. The scheduling results of each line are as follows Figure 7-10 As shown, ( Figure 7 Medium to dark green means the train is going up (outbound), light green means the train is going down, orange means the train is charging, and blue means the train is empty);

[0258] Considering that there are many trains to be optimized throughout the day, the specific operation scheduling optimization results are shown here with a train chain of one train per line in one day, including the executing vehicles of the line operation, the operating direction and location status, the operating time period, the operating status of the train or charging, the power consumption status and the train sequence. The optimization results are shown in Tables 10 to 13:

[0259] Table 10 425 bus route operation optimization results

[0260] line vehicle Location Status Run time Running status Power changes Sorting 425 v01 Up 5:30-6:51 Execute the trip 139.000-113.810 1 425 v01 Downside 6:54-8:18 Execute the trip 113.810-88.259 2 425 v01 Up 8:21-9:42 Execute the trip 88.259-63.086 3 425 v01 Downside 9:45-11:09 Execute the trip 63.086-37.598 4 425 v01 Charging Station 11:09-11:49 Charge 37.598-111.200 5 425 v01 Up 11:52-13:13 Execute the trip 111.200-86.128 6 425 v01 Downside 13:17-14:41 Execute the trip 86.128-60.706 7 425 v01 Charging Station 14:41-15:08 Charge 60.706-111.200 8 425 v01 Up 15:10-16:31 Execute the trip 111.200-86.163 9 425 v01 Downside 16:32-17:56 Execute the trip 86.163-60.715 10 425 v01 Charging Station 17:56-18:23 Charge 60.715-111.200 11 425 v01 Up 18:25-19:46 Execute the trip 111.200-86.063 12 425 v01 Downside 19:53-21:17 Execute the trip 86.063-60.549 13 425 v01 Charging Station 21:17-21:44 Charge 60.549-111.200 14 425 v01 Up 21:47-23:08 Execute the trip 111.200-86.031 15

[0261] Table 11 484 bus route operation optimization results

[0262] line vehicle Location Status Run time Running status Power changes Sorting 484 v01 Downside 5:30-6:40 Execute the trip 196.000-175.551 1 484 v01 Up 6:52-7:56 Execute the trip 175.551-155.802 2 484 v01 Downside 8:02-9:12 Execute the trip 155.802-135.359 3 484 v01 Up 9:18-10:22 Execute the trip 135.359-115.643 4 484 v01 Downside 10:25-11:35 Execute the trip 115.643-95.258 5 484 v01 Up 11:42-12:46 Execute the trip 95.258-75.600 6 484 v01 Downside 12:54-14:04 Execute the trip 75.600-55.248 7 484 v01 Up 14:16-15:20 Execute the trip 55.248-35.613 8 484 v01 Charging Station 15:20-16:29 Charge 35.613-156.800 9 484 v01 Downside 16:33-17:43 Execute the trip 156.800-136.434 10 484 v01 Up 17:53-18:57 Execute the trip 136.434-116.739 11 484 v01 Downside 19:03-20:13 Execute the trip 116.739-96.324 12 484 v01 Up 20:16-21:20 Execute the trip 96.324-76.604 13 484 v01 Downside 21:27-22:37 Execute the trip 76.604-56.173 14 484 v01 Up 22:41-23:45 Execute the trip 56.173-36.442 15

[0263] Table 12 653 bus route operation optimization results

[0264] line vehicle Location Status Run time Running status Power changes Sorting 653 v01 Downside 5:30-7:25 Execute the trip 139.000-103.587 1 653 v01 Up 7:31-9:31 Execute the trip 103.587-67.757 2 653 v01 Charging Station 9:31-9:54 Charge 67.757-111.200 3 653 v01 Downside 10:10-12:05 Execute the trip 111.200-75.904 4 653 v01 Up 12:18-14:18 Execute the trip 75.904-40.236 5 653 v01 Charging Station 14:18-14:56 Charge 40.236-111.200 6 653 v01 Downside 15:01-16:56 Execute the trip 111.200-75.998 7 653 v01 Up 17:08-19:08 Execute the trip 75.998-40.257 8 653 v01 Charging Station 19:08-19:46 Charge 40.257-111.200 9 653 v01 Downside 19:47-21:42 Execute the trip 111.200-75.836 10 653 v01 Up 21:47-23:47 Execute the trip 75.836-40.023 11

[0265] Table 13 569 bus route operation optimization results

[0266] line vehicle Location Status Run time Running status Power changes Sorting 569 v01 Downside 5:30-5:58 Execute the trip 131.000-124.278 1 569 v01 Up 6:03-6:47 Execute the trip 124.278-113.210 2 569 v01 Downside 6:57-7:25 Execute the trip 113.210-106.486 3 569 v01 Up 7:34-8:18 Execute the trip 106.486-95.419 4 569 v01 Downside 8:26-8:54 Execute the trip 95.419-88.698 5 569 v01 Up 8:54-9:38 Execute the trip 88.698-77.641 6 569 v01 Downside 9:41-10:09 Execute the trip 77.641-70.929 7 569 v01 Up 10:14-10:58 Execute the trip 70.929-59.889 8 569 v01 Downside 11:05-11:33 Execute the trip 59.889-53.192 9 569 v01 Up 11:34-12:18 Execute the trip 53.192-42.171 10 569 v01 Downside 12:24-12:52 Execute the trip 42.171-35.480 11 569 v01 Up 12:52-13:36 Execute the trip 35.480-24.465 12 569 v01 Charging Station 13:36-14:22 Charge 24.465-104.800 13 569 v01 Downside 14:36-15:04 Execute the trip 104.800-98.114 14 569 v01 Up 15:15-15:59 Execute the trip 98.114-87.119 15 569 v01 Downside 16:02-16:30 Execute the trip 87.119-80.431 16 569 v01 Up 16:38-17:22 Execute the trip 80.431-69.412 17 569 v01 Downside 17:37-18:05 Execute the trip 69.412-62.711 18 569 v01 Up 18:09-18:53 Execute the trip 62.711-51.672 19 569 v01 Downside 18:56-19:24 Execute the trip 51.672-44.961 20 569 v01 Up 19:31-20:15 Execute the trip 44.961-33.913 21 569 v01 Downside 20:33-21:01 Execute the trip 33.913-27.199 22 569 v01 Up 21:09-21:53 Execute the trip 27.199-16.144 23

[0267] The established model is a coordinated optimization model of pure electric bus route timetable and vehicle charging scheduling optimization model under the condition of limited charging station scale. In order to avoid centralized charging of vehicles and reduce the waiting time for vehicle charging, the available charging time of each charging pile is sliced, the nearest available charging pile is found, the vehicle charging time is matched, and the charging and operation of the vehicle are guaranteed. Therefore, on the basis of charging scheduling, this paper also considers the charging pile scheduling of the charging station to realize the resource allocation of the charging pile. The charging pile resource scheduling obtained by the scheduling strategy is as follows Fig.11 and Fig.12 shown.

[0268] The specific scheduling results of the charging piles when the bus on route 484 is charging at the charging station are shown, including the number of the charging pile, the usage time interval, the charged vehicle, the charging amount and the corresponding charging cost. The specific scheduling results are shown in Table 14:

[0269] Table 14 The results of the charging station scheduling for bus line 484

[0270] line Charging Station Use time period vehicle Charging capacity Charging costs 484 P_01 15:20-16:29 v01 121.187 181.174 484 p_02 15:33-16:42 v02 121.163 181.139 484 p_03 15:46-16:55 v03 121.140 181.104 484 p_04 15:59-17:08 v04 121.116 181.068 484 p_05 14:28-15:26 v05 100.804 168.141 484 p_06 16:29-17:38 v06 121.082 181.018 484 p_07 14:41-15:38 v07 100.786 161.105 484 p_08 16:42-17:51 v08 121.065 180.992 484 p_04 14:54-15:51 v09 100.768 154.070 484 p_05 17:34-18:43 v10 121.059 204.235 484 p_07 18:43-19:52 v11 121.064 218.447

[0271] Fig.13 The changes in the number of line coordination times before and after model optimization are shown (corresponding to Table 5 and Table 7). Fig.14 The changes in fleet and charging costs before and after model optimization are shown (corresponding to Table 6 and Table 8). Fig.15The change of the target optimization percentage before and after model optimization is shown (corresponding to Table 15). By analyzing the current results and the results obtained by our optimization convergence within the number of iterations, the numerical calculation results show that the total line coordination target has increased from the original 1330 times to 1399 times, an increase of 5.19%, which shows that the line coordination rate has been improved, and the passenger transfer waiting time and the congestion of common stations in the overlapping sections of the lines have been effectively reduced. The total operating cost target has dropped from the original 42363.21 yuan to 38318.47 yuan, a decrease of 9.55%, indicating that we have effectively guaranteed the interests of the bus company. Among them, the fleet cost has dropped from the original 27053.80 yuan to 22597.88 yuan, a decrease of 16.47%, and the charging cost has increased slightly, from the original 15309.41 yuan to 15720.59 yuan, an increase of 2.69%. The comparison of the optimization results is shown in Table 15. The increase in charging costs is due to the reduction in the use of vehicles on the line. Another reason is that empty trains are taken into account in the connection between up and down trains on the line. This will make the train chain more tightly constructed and the scheduling more reasonable. The cost of running one more vehicle is greater. At the same time, reducing the number of vehicles can also operate trains more efficiently and make more reasonable use of charging pile resources, with a better overall optimization effect.

[0272] Table 15 Comparison of optimization results

[0273] Target Optimization Before optimization After optimization Optimization percentage % Total collaboration times 1330 1399 5.19 Total operating cost (yuan) 42363.21 38318.47 9.55 Fleet cost (yuan) 27053.80 22597.88 16.47 Charging cost (yuan) 15309.41 15720.59 -2.69

[0274] The model and solution method proposed in this invention are effective, significantly improving line coordination, reducing the total number of vehicles in use, and saving operating power consumption. That is, it improves passenger travel efficiency and satisfaction, saves the operating costs of bus companies, and can be applied on a large scale to the actual operation and scheduling of pure electric buses, providing technical support for the networked operation of urban pure electric buses. These findings provide some valuable management insights for making wise decisions on the coordinated optimization of pure electric buses within the framework of integrated timetable coordination and charging scheduling optimization, which can significantly improve system efficiency, enhance the attractiveness of pure electric bus travel, and serve the development of urban new energy public transportation.

Claims

1. A method for integrating timetable design and vehicle scheduling for multi-line coordinated pure electric buses, characterized in that The timetable design and vehicle scheduling integration method for multi-line coordinated pure electric buses is carried out in the following steps: Step 1: Build a pure electric bus route network and establish the attribute set of each traffic node in the network; Step 2: Collect and establish the running status set of each line according to the operating period; The train operation status set includes the number of up and down train departures, vehicle travel routes, departure frequency range, minimum and maximum departure intervals, initial departure schedule and arrival time of each line during operation; Step 3: Collect the AVL data during the operation period within one month, calculate the inter-station travel time of adjacent stations, round it off to the nearest integer in minutes, and include it in the set of travel time of adjacent stations. Then, an integer set of the travel time of adjacent stations is obtained, and the average of the inter-station travel time is taken. Step 4: Use the card and code swiping data on pure electric buses to collect the boarding passenger data at each station during the operation period of one month, and calculate the average passenger arrival rate at each station on each route; Step 5: Focus on the operation characteristics of pure electric buses and build a pure electric bus coordinated timetable and vehicle dispatch optimization model; 1. Vehicle motion equation part The arrival and departure times of vehicles at each station are related to the travel time between stations and the stop time at the station. The arrival time of the pth train of line i at station b is The departure time of the vehicle at the previous stop b-1 Travel time between stations The departure time at station b is determined by Arrival time and the stop time at station b The vehicle’s stop time at a station includes the door opening and closing time t° and the passenger boarding and alighting time t up , where the time required for passengers to get on and off the bus depends on the maximum value of the passenger boarding time and the passenger getting off time; and denote the number of passengers getting on and off the p-th bus of line i at station b, α1 and α2 denote the average time required for each passenger to get on and off the bus, respectively. The time required for a vehicle to get on and off passengers at station b is the product of the number of passengers getting on and off and the time of getting on and off; In the present invention, the time when passengers get off the bus is ignored, and the formulas are expressed as follows: b∈N i , N i is the set of stops for bus line i; 2. Objective Function 1) Maximize the number of timetable collaborations For line i with collaborative station b, collaborative station b includes collaborative entry / transfer at the same platform b' and collaborative transfer at a different platform b"; define binary auxiliary variables represents the number of coordinated times of multi-line pure electric buses at coordinated station b, include and in It represents the coordination between line i and line j at the same station and the same direction at the coordinated station b', solving the problem of coordinated entry / transfer at the same station; It represents the coordination between line i and line j at the coordinated transfer point b” at different platforms, solving the problem of coordinated transfer at different platforms; The pth train number of line i is denoted as train number i(p), is the main decision variable, representing the departure time of train number i(p). When the absolute difference between the time when train number i(p) arrives at the cooperative station b and train number j(q) is within the preset cooperative time window, In, a binary auxiliary variable representing the number of collaborations is 1, otherwise it is 0, which means as follows: represents the time when the pth train of line i arrives at the cooperative station b; represents the travel time of the p-th train of line i from the initial station to the cooperative station b, that is, the sum of the inter-station running time and the stop time at each station from the initial station to the cooperative station b; Formula (7) below represents the number of coordinated transfers between routes i and j at the same station; Formula (8) represents the number of coordinated transfers between routes i and j at different stations; Formula (9) represents the goal of maximizing the total number of coordinated transfers between routes; f i represents the set of departure times of route i; p is the departure times of route i, q is the departure times of route j; I represents the set of routes; 2) Minimize total operating costs ① Establish a train chain: The vehicle charging scheduling gives a train schedule, each of which includes a departure station, departure time, arrival station, arrival time, charging location, and whether to charge; establish a multi-depot vehicle charging scheduling model based on train connection, with the departure time of the vehicle at the starting station as the decision variable; Introducing binary auxiliary variables To measure the number of buses on bus line i 1 (p) and down train number i 2 (q) Whether they can be connected in series, i.e. whether the planned trip is carried out by the same vehicle, i 1 (p) represents the train number p of line i in the upward direction, i 2 (q) represents the train number q of line i in the down direction; the train number is integrated into the train number chain, and then the train number chain is executed by the vehicle; in order to build the train number chain to the greatest extent and reduce the use of vehicles, the connection of empty trains is considered in the train number matching, that is, there will be connections of empty trains in the train number chain; f i represents the set of departure times of route i; I represents the set of routes; ② The goal of vehicle charging scheduling is to minimize the total operating cost of the line. The total operating cost is usually measured by the minimum fleet size required, that is, the maximum number of train chains. The fleet cost is closely related to the amortization cost, depreciation cost, insurance and maintenance cost. The research object of this invention is electric buses, which need to be charged during a day's journey. Therefore, the total operating cost also includes the charging cost, which depends on the charging duration, charging amount and unit electricity price. Considering the limited scale of charging stations and the charging time, this cost is a variable cost. In order to facilitate the calculation of the charging cost, To represent the percentage of charging of the vehicle on route i at the charging station after completing trip p; because the time-of-use electricity price is considered in the charging strategy, c s Indicates the unit electricity price in period S, the number of train chain connections N i1i2 The objective functions of and charging cost C1 are respectively expressed as f i represents the set of departure times of route i; I represents the set of routes; i 1 Indicates the direction of leaving the charging station in route i, i 2 Indicates the direction toward the charging station in route i; in is the charging duration, is the charging start time, is the charge level at the beginning of charging; The minimum number of electric buses required is given by the minimum fleet size theorem, that is, when implementing a given bus schedule, F i and f represent the total number of vehicles going up and down on line i and the total number of vehicles going up and down, respectively. The minimum fleet size is expressed as: Then the objective function of minimizing fleet cost is expressed as where c F represents the fixed cost of using an electric bus; Therefore, the total operating cost of multi-station bus vehicles with the minimum total operating cost of the route is expressed as follows: minTC=min(C1+C2) (14); 3. Constraints 1) Departure interval constraints Constraints (15) and (16) are departure interval constraints, which ensure that the consecutive departure times of each line are between the minimum and maximum departure intervals; Constraint (17) is the departure time constraint of the first train on the route, ensuring that the first train on each route departs on time; Constraints (18) and (19) ensure that the departure time of the last vehicle on each route is within the planning period s and no earlier than a time that is one departure interval less than s; where h i With H i are the minimum departure interval and the maximum departure interval of line i respectively; the departure time of train p on line i is It means that the first bus of route i departs on time. The time when the last vehicle departs from route i; s i is the planning period of route i; I represents the set of routes; the departure time of train q on route j is is a value between the minimum departure interval and the maximum departure interval of line i, that is, 2) Collaborative constraints Constraints (20) and (21) indicate that pure electric buses must meet the minimum and maximum time window range at the line coordination station b. Inside; M1 is a maximum positive value; 3) Train connection constraints Constraint (22) ensures that each train can only be connected to one subsequent train at most, and the connected train may be an empty trip; Constraint (23) ensures that each train can only be connected to one preceding train at most, and the connected train may be an empty trip; the empty trip is to connect to more trains; If the same vehicle cannot complete the subsequent trip after completing the previous trip, constraints (24) and (25) force the binary auxiliary variable is 0; If the vehicle does not arrange a charging plan after completing trip p, then t pcq and All are 0, assuming that there is a charging station on the side of the upstream starting point of line i; represents the departure time of route i when it leaves the charging station, represents the departure time of route i heading towards the charging station; constraint (26) specifies the binary auxiliary variable The possible values ​​of ; in represents the running time of the up-trip p of line i, represents the running time of the down train q on line i; t pc is the time required for the vehicle to travel from the starting and ending stations to the charging station, t cq is the time required for the vehicle to return from the charging station to the starting and ending stations, t pcq =t pc +t cq Indicates the round-trip time of an electric bus in an empty trip between the departure station and the charging station; Indicates the charging duration of the electric bus at the charging station; M2 is a maximum positive value; 4) Constraints on power consumption and charging facilities Constraint (27) reflects the power constraint, which means that the remaining power of the vehicle at the charging station is not less than the total power consumed by the outbound trip and the return trip plus the safety lower limit power; Constraint (28) reflects the charging pile capacity limit of the charging station, which ensures the charging of the vehicle and provides reliable services for building the train chain; in Indicates the remaining power of the vehicle at the charging station; are the power consumed by completing p and q linked trains, p is the uplink train and q is the downlink train; S min Provide the battery with a safe lower limit of power for cycling; It is defined as the remaining effective charging position of charging station k in period s. The number of vehicles charging demand for line i in time period s The difference between indicates the capacity limitation of the charging station; ① Determination of effective charging position Considering the limited number of charging piles at the charging station and the sharing of charging piles with other bus routes in a day, α s It represents the charging position utilization rate of the charging station in the current planning period, which can be converted into the remaining effective charging positions of the charging station, expressed as Among them C N is the total charging position; ② Estimation and determination of the number of charging vehicles and energy consumption The charging decision is made every time the vehicle returns to the charging station. Whether the vehicle is charged is determined by the remaining power of the vehicle at the charging station and the subsequent outbound and return trips. If the remaining power is insufficient to perform the subsequent trip tasks, charging is required. The vehicle is charged on a first-come, first-served basis. The charging piles at the charging station are numbered and the available charging time of each charging pile is compared with the charging time of the vehicle. Match; the remaining power of the vehicle Energy consumption by travel and the battery rated capacity R; when the battery rated capacity is fixed, the remaining power of the electric bus E on route i at the end of trip p is The state of charge at the start And the energy consumption of this trip Decide, expressed as follows: Where η is the charging power of the charging pile (kWh); Vehicles that meet the charging conditions during period s Sum; S max Cycle the battery to the safe upper limit of power; The four variables with the highest correlation with vehicle travel energy consumption are: the mileage L traveled by the electric bus trip p p (km), vehicle measured curb weight G p (kg), driving time T p (h) and the absolute difference between the average ambient temperature and the optimal operating temperature An energy consumption estimation model for electric buses was established. Since the distances from each line to the charging station are different, the idle distance L needs to be considered. pc The energy consumption generated by (km) is added to the energy consumption model. The energy consumption estimation model is as follows: in and represents the estimator of the regression coefficient; 4. Model integration The established pure electric bus multi-line timetable collaborative optimization model and vehicle charging scheduling optimization model use the same decision variables, namely the departure time of the bus; both meet the same minimum and maximum departure intervals, and the departure time of the last bus on each line is within the planning period; these two models are integrated and the same constraints are combined to obtain the following dual-objective integrated optimization model: Integrated dual-objective optimization model Objective function: Constraints: coordination constraints, coordination + charging scheduling constraints, and train chain construction constraints; Step 6: The model established by the present invention is a mixed integer linear programming model. Due to the complexity of the dual-objective collaborative optimization model and the diversity of the elements involved, the algorithm is carried out from the following aspects: first, the problem is solved by combining the differential evolution algorithm with the heuristic basic algorithm of the lexicographic order method, and then a collaborative matching algorithm and a construction heuristic algorithm suitable for the problem background and logic are established for the collaborative and charging scheduling optimization goals respectively, so as to solve the dual-objective optimization problem; Step 7: The algorithm generates a target convergence curve based on the target priority setting and outputs a satisfactory solution to the problem.

2. A method for integrating timetable design and vehicle scheduling for multi-line coordination of pure electric buses according to claim 1, characterized in that The attribute set of each transportation node described in step 1 includes a starting station, a terminal station, a coordinated station, a non-coordinated station, and a charging station.

3. The method for integrating timetable design and vehicle scheduling for multi-line coordination of pure electric buses according to claim 2 is characterized in that The charging station described in step 1 includes its location and the number of charging piles.

4. The method for integrating timetable design and vehicle scheduling for multi-line coordination of pure electric buses according to claim 1 is characterized in that The coordinated stations described in step one include coordinated entry / transfer at the same platform and coordinated transfer at different platforms.

5. The method for integrating timetable design and vehicle scheduling for multi-line coordination of pure electric buses according to claim 1 is characterized in that The method for calculating the average passenger arrival rate at each station on each route in step 4 is: filter the card and code swiping data of passengers boarding the bus at each station during the operating period, add them up and take the average value to obtain the average passenger arrival rate of the station.

6. The method for integrating timetable design and vehicle scheduling for multi-line coordination of pure electric buses according to claim 1 is characterized in that In step 5, the following conditions must be met before building the model: (1) The vehicle travel time is fixed; (2) The charging preparation time of the vehicle at the charging station is negligible; (3) The planning cycle is discretized in minutes, that is, the vehicle departure time is a discrete integer variable; (4) The usage and performance of vehicles on each route are the same; the vehicle capacity is sufficient to meet the needs of passengers; (5) The first bus on the route departs on time and the bus driver fully adheres to the planned vehicle itinerary and timetable.

7. The method for integrating timetable design and vehicle scheduling for multi-line coordination of pure electric buses according to claim 1 is characterized in that The satisfactory solution in step seven is the target convergence solution iterated according to the target priority set by the algorithm, that is, a satisfactory solution that meets the interests of the bus company or the passengers themselves.

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