Collaborative optimization method for dispatching electric buses and drivers with multiple charging modes

Abstract

The present invention discloses a method for collaborative optimization of multi-charging mode electric bus and driver scheduling, comprising the following steps: 1: extracting the shift data of the selected actual operating route based on the actual operating status of the selected actual operating route; 2: determining the relevant characteristic parameters of the electric bus on the selected actual operating route and the driver's scheduling rule parameters; 3: constructing a collaborative optimization model for vehicle and driver scheduling of the electric bus system with the goal of minimizing driver cost, vehicle cost, and charging cost; 4: using a tree enumeration-based labeling algorithm to enumerate all shift chains that meet the relevant constraints of the collaborative optimization model; and 5: constructing a set covering model and using a column generation algorithm to solve the constructed set covering problem. With the goal of minimizing cost, the present invention provides vehicle scheduling and personnel scheduling suggestions for electric bus operating routes, accurately serving users in need and improving operating revenue.

Description

Technical Field

[0001] The present invention relates to the technical field of electric bus systems, and in particular to a collaborative optimization method for vehicle dispatching and driver scheduling for bus routes with multiple charging modes. Background Art

[0002] Environmental pollution, traffic congestion, and other issues have intensified with the advancement of urbanization in my country. In recent years, with the development of electric vehicle technology, the electrification of public transportation, owing to its energy-saving and environmentally friendly advantages, has attracted widespread attention and rapid adoption worldwide. In China, statistics from the Ministry of Transport indicate that by the end of 2020, the country had 704,400 pure electric buses in urban areas, accounting for 53.8% of the total public transportation fleet. Pure electric bus systems not only contribute to building green cities and supporting the achievement of the dual carbon emission goals, but also enhance the service quality of urban public transportation systems with their quiet and comfortable ride experience, attracting more public transportation users and, to a certain extent, alleviating urban traffic congestion. However, the technical characteristics of electric buses, particularly the constraints on driving range and charging time, have limited their development to a certain extent and created new challenges in bus scheduling, charging, and crew scheduling.

[0003] Currently, there are three main charging modes for electric buses: fast charging, slow charging, and battery swapping. Each charging mode has its own technical advantages and disadvantages. Slow charging is low-cost but time-consuming; fast charging is relatively expensive but time-consuming; and battery swapping is the most expensive but time-efficient. Choosing the appropriate charging mode for electric buses significantly impacts the scheduling of electric bus systems. Furthermore, because electric bus driver performance evaluations are based on vehicle wear and tear caused by driver behavior, a driver-vehicle-bound scheduling model is employed. This forces drivers to take breaks during charging, and the varying charging times for the three charging modes complicates scheduling. The key and challenge in scheduling electric buses lies in charging plans and modes. Different charging modes require varying charging times, and the constraints of driver-vehicle ties often force drivers to take breaks during charging. A rational and effective selection of charging modes can effectively utilize driver work time, improve the operational efficiency of electric bus systems, and reduce operating costs.

[0004] At present, extensive and in-depth research has been carried out on the optimization of electric bus line operations, but there are still some key issues to be resolved. Current research on the optimization of electric bus line operations mainly focuses on the impact of a single charging mode on vehicle scheduling. However, there are currently multiple charging modes. What is the mechanism of their impact on vehicle scheduling and scheduling in the bus system? How to consider multiple charging modes and propose a collaborative optimization strategy for vehicle scheduling, charging plan and personnel scheduling? These issues have an important impact on improving the operational efficiency and reducing operating costs of electric bus systems. Therefore, the present invention considers three charging modes: fast charging, slow charging and battery replacement, and constructs a collaborative optimization model for vehicle scheduling, charging plan and personnel scheduling. The model aims to minimize the costs related to drivers, vehicles, charging, etc.; and fully explores the operational constraints of the electric bus system, including driving range constraints, driver work intensity constraints, shift connection constraints, etc. After verification by examples, the scheduling scheme obtained by the present invention is feasible and the algorithm is effective. Summary of the Invention

[0005] The electric bus system is the most widespread bus system in many cities. Due to its limited driving range, vehicle scheduling is more complicated, and the current charging modes are: fast charging, slow charging, and battery replacement. An efficient collaborative scheduling solution for buses and drivers can not only improve passengers' travel satisfaction, but also effectively reduce the costs of operating companies. The present invention provides a collaborative optimization method for vehicle scheduling and driver scheduling for multi-charging mode bus routes, which can collaboratively optimize the vehicle scheduling, charging plan and personnel scheduling stages of the electric bus system, and provide certain theoretical guidance for electric bus operation routes.

[0006] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0007] A method for collaborative optimization of multi-charging mode electric bus and driver scheduling, characterized by comprising the following steps:

[0008] Step 1: Extract the shift data of the selected actual operating line based on the actual operating status of the selected actual operating line. The shift data includes the start time, end time, start station, and end station of all shifts of the actual operating line;

[0009] Step 2: Based on the actual operating route selected in Step 1, determine the relevant characteristic parameters of the electric bus and the driver scheduling parameters for the selected actual operating route; the relevant characteristic parameters include the electric bus's fast charging mode, slow charging mode, and battery replacement mode, and the driver scheduling parameters are determined based on actual operation management;

[0010] Step 3: Based on step 2, establish the bus-related characteristic parameters and driver scheduling rule parameters, and build a vehicle and driver scheduling collaborative optimization model for the electric bus system with the goal of minimizing driver cost, vehicle cost, and charging cost.

[0011] The process of constructing the vehicle and driver scheduling collaborative optimization model of the electric bus system in step 3 is specifically as follows:

[0012] Target 1: Driver salary costs;

[0013] The driver's salary cost is divided into daily wages and hourly wages, which are expressed as:

[0014]

[0015]

[0016] Where D represents the set of drivers, T represents the set of shifts, A driver's daily wage, represents a driver's hourly wage, represents the start time of shift j, represents the end time of shift j, Indicates whether driver d will execute shift j after completing shift i. If yes, it is 1, otherwise it is 0. Indicates whether driver d will execute shift j when departing from the station;

[0017] Objective 2: Bus costs; bus costs include bus purchase costs and operating costs; the purchase and operating costs of buses are expressed as:

[0018]

[0019]

[0020] Where V represents the set of electric buses, It represents the purchase cost of an electric bus, calculated on a daily basis. represents the unit mileage operating cost of electric buses, l j represents the operating mileage of flight j, Indicates whether bus v will execute shift j after completing shift i. If so, it is 1, otherwise 0. Indicates whether bus v departs from the station and executes the schedule j;

[0021] Target 3: Costs associated with bus charging; including the electricity cost of battery charging, the fixed cost of charging piles, and the battery cost required for battery replacement, which are expressed as follows:

[0022]

[0023]

[0024]

[0025] in, Indicates the unit charging cost of fast charging. Indicates the unit charging cost of slow charging. Indicates the unit battery cost generated by battery replacement, represents the purchase cost of a single charging pile corresponding to the kth charging mode, P k represents the charging power of the kth charging mode, where k∈{1,2} represents fast charging and slow charging respectively, Q k Indicates the number of charging piles corresponding to the kth charging mode represents the charging time required for bus v to be charged using the kth charging mode before executing the jth shift, Indicates whether bus v uses the kth charging mode to charge after completing the trip i and before starting the trip j. If it is charged, the value is 1; otherwise, it will not be charged in the kth charging mode.

[0026] According to the above description of the cost of electric bus system, the objective function of the model is expressed as:

[0027]

[0028] Constraints:

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Among them, D 1max The maximum number of drivers that can perform the morning shift on this route, D 2max Indicates the maximum number of drivers that can perform the lunch shift on this route, H 1max Indicates the latest time for the morning shift driver to get off work on this route, H 2min Indicates the earliest working time for the noon shift driver on this route, B max Indicates the maximum number of electric buses that can operate on this route. represents the starting station of shift j, represents the end station of shift j, g w represents the shortest time required for a shift change, g r Indicates the maximum time required for a shift change, Indicates the driver's maximum continuous working time, t max Indicates the maximum working time of the driver per day, N min Indicates the minimum number of shifts a driver performs in a day, N max Indicates the maximum number of shifts a driver performs in a day, E max Indicates the battery capacity when it is fully charged, E l represents the power consumption per unit mileage, r represents the battery power warning level, that is, to ensure that the bus can return to the bus station smoothly and ensure that the battery power of the bus is higher than the warning level after completing the shift mission, t replace Indicates the time required for battery replacement. Indicates whether the driver d is bound to the bus v, if so, it is 1, otherwise it is 0. Indicates the continuous working time of driver d before performing shift j, It represents the amount of electricity of bus v before it performs shift j. represents the time set of starting charging using the kth charging mode, where k∈{1,2}, and represents the time set of starting charging for fast charging and slow charging for all electric buses on this line during one day of operation. represents the time set of charging end using the kth charging mode, where k∈{1,2}, and represents the time set of charging end points for fast charging and slow charging of all electric buses on this line during one day of operation. Indicates the time point corresponding to the kth charging mode being used for the nth time during line operation, where k∈{1,2}. The time point includes the start time point and the end time point of charging, and the two exist independently. Indicates that the time node in the kth charging mode is The number of charging piles in use at the time;

[0070] Formulas (9) and (10) ensure that each shift is executed by the driver and the bus respectively; Formulas (11) and (12) ensure that each driver only executes one shift chain and each bus only executes one bus chain; Formulas (13) and (14) ensure that each driver only executes one shift chain and each bus only executes one bus chain. (14) is the shift connection constraint, that is, the shifts executed by each driver and bus can form a shift chain and a bus chain; formulas (15), (16), and (17) respectively meet the maximum number of drivers and the maximum number of buses; formula (18) is used to determine whether there is a binding relationship between the bus and the driver; formula (19) means that if the driver is bound to the bus, the shift executed by the driver will definitely be executed by the corresponding bus; formulas (20) and (21) ensure that the shift change time of the bus and the driver is greater than the shortest time required for the shift change; formulas (22) and (23) are the shift change location constraints; formula (24) defines the driver's continuous working hours and sets the initial value to 0; formula (25) is the update of the continuous working hours. Here, if it exceeds the maximum time required for the shift change, it is assumed that the driver has rested and the continuous working hours are 0; formulas (26) and (27) are to meet the continuous working hours limit and total working hours limit stipulated by labor laws and regulations; formulas (28) and (29) are the driver's Two-shift mode; Formula (30) ensures fairness among drivers, that is, the number of shifts performed by each driver is not much different; Formula (31) defines the power of the bus and sets the initial state to be full power; Formula (32) is the update of power; Formula (33) is the remaining power of the bus after completing the shift is above the warning power; Formulas (34) and (35) define the charging time used by the bus to select the three charging modes respectively; Formula (36) ensures that the charging plan is between the adjacent shifts performed by the corresponding bus; Formula (37) ensures that the bus meets the charging time limit when performing the next shift; Formulas (38), (39), and (40) define the starting charging time point set, the ending charging time point set, and the total time node set of fast charging and slow charging; Formulas (41), (42), (43), (44), and (45) extract the maximum number of charging piles required for fast charging and slow charging in one day; Formulas (46), (47), and (48) are variable type constraints, defining 0-1 decision variables.

[0071] Step 4: Based on the relevant constraints in the vehicle and driver scheduling collaborative optimization model of the electric bus system in step 3, use the labeling algorithm based on tree enumeration to enumerate all the shift chains that meet the relevant constraints;

[0072] Step 4 is as follows:

[0073] Step 4.1: Initialize shift data; shift data is used Indicates that i represents the index corresponding to the shift. Respectively represent the starting and ending locations of flight i, Respectively represent the start time and end time of shift i, and sort the shift data by start time;

[0074] Step 4.2: Initialize the set of feasible shift chains; Initialize the set of feasible shift chains The data of one feasible shift chain is represented by (f, d, c), where f represents the set of shifts and charging combinations included in this feasible shift chain, d represents the number of drivers required to execute this feasible shift, and c is the cost required to execute this feasible shift chain. The initial shift number i = 1 is selected;

[0075] Step 4.3: Take shift i as the starting shift of a feasible shift chain; design a label (e, w, t) for the shift chain, where e represents the battery state of the electric bus before the current shift, w represents the continuous working hours of the driver before the current shift, and t represents the total working hours of the driver before the current shift. Initialize e2 = e max , w=0, t=0;

[0076] Step 4.4: Expand the subsequent shifts; expand from the current shift i in the shift data to the subsequent shift j; assuming that the shift chain label before executing the current shift is (e1, w1, t1), after connecting with the subsequent shift, the shift chain label becomes (e2, w2, t2);

[0077] The step 4.4 is specifically as follows:

[0078] Step 4.4.1: Basic constraint judgment; if the current shift i and the subsequent shift j meet where t min If represents the shortest time required for shift conversion, the basic constraints are met. Otherwise, it cannot be connected with the subsequent shift j, and the search for a feasible connecting shift continues;

[0079] Step 4.4.2: Update and judge the battery level; if fast charging or slow charging is performed between shifts, then e2 = e c +e1-e t , where e c is the total amount of electricity charged, e t is the power consumption for the current shift, e2≤e max ; If the battery is replaced, then e2=e max; Otherwise e2=e1-e t If e2-e t ≤e min , where e min is the minimum power limit, e t The power consumption for executing the subsequent shift satisfies the energy-range constraint; otherwise, the subsequent shift cannot be connected, and the search for a feasible connecting shift continues.

[0080] Step 4.4.3: Update and judge continuous working hours; if the inter-shift transfer time is greater than the specified maximum shift change time, then w2 = 0; otherwise like where w max If the maximum continuous working hours are met, the continuous working hours can be continued; otherwise, the driver performs a rest task and the shift cannot be continued, or a new driver is added for this bus and w2=0;

[0081] Step 4.4.4: Determine if the driver is on two shifts; if the driver is on the morning shift and the end time of the subsequent shift is less than or equal to the latest end time of the morning shift, then Where H 1max If is the latest off-duty time of the shift, then this driver can perform this shift j; And the starting time of the shift is greater than or equal to the earliest working time of the afternoon shift, that is Then add a driver for the afternoon shift to perform this bus j; if neither of the conditions are met, the current driver will perform the bus j;

[0082] Step 4.4.5: Update and judge the total working hours; if the bus driver is replaced before the subsequent shift j, the total working hours before the subsequent shift j is set to t2 = 0; otherwise like where t max If it is the maximum formula specified, the total working hours constraint is satisfied; otherwise, a new driver needs to be added to this bus, and w2 = 0 and t2 = 0;

[0083] Step 4.5: Obtain feasible shift chains; backtrack all obtained feasible shift chains, obtain the shift set f and the number of drivers d contained in them, and calculate their corresponding costs c. Add this shift data (f, d, c) to the feasible shift chain set. If i <= T, set i = i + 1; otherwise, the algorithm ends and outputs the feasible shift chain set F.

[0084] Step 5: Use all the shift chains generated in step 4 to build a set covering model, and use the column generation algorithm to solve the constructed set covering problem; output the vehicle and driver scheduling results.

[0085] The step 5 is specifically as follows:

[0086] Step 5.1: Get an initial feasible solution; select a shift chain: [t,,t], [t,...,t],..., [t m ] as the initial feasible solution;

[0087] Step 5.2: Construct a set covering the main problem. Each column in the main problem represents a column constructed from the initial feasible solution, that is, the corresponding shift chain;

[0088] Step 5.3: Solve the main problem and the shadow price of the main problem. When solving the main problem, use branch and bound to obtain a 0-1 integer solution. The shadow price of the main problem can be solved based on the dual problem of the main problem. The solution of the dual problem is the shadow price of the main problem.

[0089] Step 5.4: Construct the price sub-problem;

[0090] Step 5.5: Solve the price subproblem and determine whether there is a carry-in variable. The optimal solution to the price subproblem is the solution corresponding to the column with the smallest test number in the main problem. If the test number is less than 0, there is a carry-in variable, and go to step 5.6. If the test number is greater than or equal to 0, there is no carry-in variable, the algorithm ends, and the solution to the main problem is output.

[0091] Step 5.6: Add the columns or shift chains corresponding to the incoming base variables to the main problem and go to step 5.3.

[0092] Beneficial effects of the present invention: The present invention provides a method for collaborative optimization of vehicle scheduling, charging planning, and personnel scheduling for electric bus systems based on the coexistence of multiple charging point modes. Taking into account the three charging modes of fast charging, slow charging, and battery replacement, a collaborative optimization model for vehicle scheduling, charging planning, and personnel scheduling is constructed. The model aims to minimize the costs related to drivers, vehicles, charging, etc.; and fully explores the operational constraints of the electric bus system, including driving range constraints, driver work intensity constraints, shift connection constraints, etc. The shift data required by the present invention is the basic data, which can be extracted according to the line operation status and is easy to obtain. The labeling algorithm and column growth algorithm adopted by the present invention are universal for solving similar models, and the calculated planning results are relatively reasonable. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] The present invention has the following accompanying drawings:

[0094] Figure 1 It is a flowchart of the overall process of the present invention;

[0095] Figure 2 This is a schematic diagram of Beijing's No. 3 bus route;

[0096] Figure 3 This is a schematic diagram of vehicle scheduling in fast charging mode;

[0097] Figure 4 This is a diagram of driver scheduling in fast charging mode;

[0098] Figure 5 This is a schematic diagram of vehicle scheduling in slow charging mode;

[0099] Figure 6 This is a diagram of driver scheduling in slow charging mode;

[0100] Figure 7 This is a schematic diagram of vehicle scheduling in battery swap mode;

[0101] Figure 8 This is a diagram of driver scheduling in battery swap mode;

[0102] Figure 9 This is a schematic diagram of vehicle scheduling in multiple charging modes;

[0103] Figure 10 Schematic diagram of driver scheduling in multiple charging modes. DETAILED DESCRIPTION

[0104] The present invention will be further described in detail below with reference to the accompanying drawings.

[0105] like Figure 1 As shown, the vehicle and driver scheduling collaborative optimization method based on a multi-charging mode electric bus system according to the present invention includes the following steps:

[0106] Step 1: Extract the shift data of the selected route based on its actual operating conditions. The shift data includes the start time, end time, start station, and end station of all shifts.

[0107] Step 2: Based on the actual operating route selected in Step 1, determine the relevant characteristics of the electric buses on the route and the driver scheduling rules;

[0108] Step 3: Combined with Step 2, the bus-related characteristics and driver scheduling rules are established. Considering three charging modes: fast charging, slow charging, and battery swapping, and aiming to minimize the costs associated with drivers, vehicles, and charging, a collaborative optimization model for vehicle and driver scheduling in the electric bus system is constructed.

[0109] Step 4: Incorporating the relevant constraints in the vehicle and driver scheduling collaborative optimization model for the electric bus system in Step 3, use a tree enumeration-based labeling algorithm to enumerate all shift chains that meet the relevant constraints. Tree enumeration can comprehensively consider various link situations and ensure that all shift chains that meet the relevant conditions are enumerated. The labeling algorithm can clearly represent the driver hours and electric bus power consumption in the shift chain, so that the hours and power consumption can be updated in combination with the relevant constraints in the model, simplifying the relevant complex constraints.

[0110] Step 5: Combine all the shift chains generated in Step 4 to construct a set covering model. Since each column of the constraint matrix in the set covering problem can represent a solution, and the column generation algorithm is suitable for solving a class of combinatorial optimization problems where each decision solution corresponds to a column of the constraint matrix in the overall planning model, in this step, the column generation algorithm is used to solve the constructed set covering problem.

[0111] Step 6 is specifically: analyzing the optimal solution of step 5 to prove the rationality of this optimization method and the effectiveness of the algorithm.

[0112] Based on the above solution, step 1 is as follows:

[0113] Step 1.1: Without loss of generality, let's take Beijing Bus Route 3 as an example. This bus route is located within the Third Ring Road of Beijing. The route is 20 kilometers long and has 34 stops. The operating hours for the upward direction are from 5:30 to 22:00, and the operating hours for the downward direction are from 6:00 to 22:00. The peak departure frequency is 5 minutes to 10 minutes, and the off-peak departure frequency is 10 minutes to 15 minutes. The peak running time is 65 minutes, and the off-peak running time is 50 minutes. Figure 2 A schematic diagram of Beijing's No. 3 bus route is given;

[0114] Step 1.2: The operating parameters of the bus schedule are set according to the actual operating conditions of Beijing Bus Line 3. The schedule-related data includes the start time, end time, start station, and end station of all schedules.

[0115] Based on the above solution, step 2 is as follows:

[0116] Step 2.1: Determine the characteristics of electric buses. The available charging modes for electric buses are: fast charging, slow charging, and battery swapping. Each of these three charging modes has its own advantages: slow charging is low-cost and takes a long time; fast charging is relatively high-cost and takes a relatively short time; and battery swapping is high-cost and takes a short time.

[0117] Step 2.2: Determine the driver scheduling rules. This incorporates the two-shift scheduling model commonly used in bus system operations. The so-called two-shift system divides drivers into two groups based on their working hours: the morning shift starts at 5:00 AM and ends at 1:00 PM; the afternoon shift starts at 12:00 PM and ends after completing all shift tasks.

[0118] Step 2.3: Determine the relationship between drivers and buses. Because China's driver performance evaluations need to account for vehicle wear and tear, electric bus system scheduling employs a driver-vehicle binding strategy. This means a driver can only drive one bus, while a bus can be driven by multiple drivers. While an electric bus is charging, its driver must rest.

[0119] Based on the above solution, step 3 is as follows:

[0120] Objective 1: Driver salary cost. Since each driver has different working hours per day, in order to ensure fairness for drivers, the driver salary cost is divided into daily wages and hourly wages, which are expressed as:

[0121]

[0122]

[0123] Where D represents the set of drivers, T represents the set of shifts, A driver's daily wage, represents a driver's hourly wage, represents the start time of shift j, represents the end time of shift j, Indicates whether driver d will execute shift j after completing shift i. If yes, it is 1, otherwise it is 0. Indicates whether driver d will execute shift j when departing from the station;

[0124] Objective 2: Bus costs. Bus costs consist of two parts: bus purchase cost and operating cost. This article averages the purchase cost on a daily basis based on the bus's service life. The operating cost of the bus mainly includes depreciation, repair costs, and amortization of some intangible assets. The purchase and operating costs of the bus are expressed as:

[0125]

[0126]

[0127] Where V represents the set of electric buses, It represents the purchase cost of an electric bus, calculated on a daily basis. represents the unit mileage operating cost of electric buses, l j represents the operating mileage of flight j, Indicates whether bus v will execute shift j after completing shift i. If so, it is 1, otherwise 0. Indicates whether bus v departs from the station and executes the schedule j;

[0128] Objective 3: Bus charging-related costs. This mainly includes the electricity cost of battery charging, the fixed cost of charging piles, and the battery cost required for battery replacement, which are expressed as follows:

[0129]

[0130]

[0131]

[0132] in, Indicates the unit charging cost of fast charging. Indicates the unit charging cost of slow charging. Indicates the unit battery cost generated by battery replacement, represents the purchase cost of a single charging pile corresponding to the kth charging mode, P k represents the charging power of the kth charging mode, where k∈{1,2} represents fast charging and slow charging respectively, Q k Indicates the number of charging piles corresponding to the kth charging mode represents the charging time required for bus v to be charged using the kth charging mode before executing the jth shift, Indicates whether bus v uses the kth charging mode to charge after completing the trip i and before starting the trip j. If it is charged, the value is 1; otherwise, it will not be charged in the kth charging mode.

[0133] According to the above description of the cost of electric bus system, the objective function of the model is expressed as:

[0134]

[0135] Constraints:

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171]

[0172]

[0173]

[0174]

[0175]

[0176] Among them, D 1max The maximum number of drivers that can perform the morning shift on this route, D 2max Indicates the maximum number of drivers that can perform the lunch shift on this route, H 1max Indicates the latest time for the morning shift driver to get off work on this route, H 2min Indicates the earliest working time for the noon shift driver on this route, B max Indicates the maximum number of electric buses that can operate on this route. represents the starting station of shift j, represents the end station of shift j, g w represents the shortest time required for a shift change, g r Indicates the maximum time required for a shift change, Indicates the driver's maximum continuous working time, t max Indicates the maximum working time of the driver per day, N min Indicates the minimum number of shifts a driver performs in a day, N max Indicates the maximum number of shifts a driver performs in a day, E max Indicates the battery capacity when it is fully charged, E l represents the power consumption per unit mileage, r represents the battery power warning level, that is, to ensure that the bus can return to the bus station smoothly and ensure that the battery power of the bus is higher than the warning level after completing the shift mission, t replace Indicates the time required for battery replacement. Indicates whether the driver d is bound to the bus v, if so, it is 1, otherwise it is 0. Indicates the continuous working time of driver d before performing shift j, It represents the amount of electricity of bus v before it performs shift j. represents the time set of starting charging using the kth charging mode, where k∈{1,2}, and represents the time set of starting charging for fast charging and slow charging for all electric buses on this line during one day of operation. represents the time set of charging end using the kth charging mode, where k∈{1,2}, and represents the time set of charging end points for fast charging and slow charging of all electric buses on this line during one day of operation. Indicates the time point corresponding to the kth charging mode being used for the nth time during line operation, where k∈{1,2}. The time point includes the start time point and the end time point of charging, and the two exist independently. Indicates that the time node in the kth charging mode is The number of charging piles in use at the time;

[0177] Formulas (9) and (10) ensure that each shift is executed by the driver and the bus respectively; Formulas (11) and (12) ensure that each driver only executes one shift chain and each bus only executes one bus chain; Formulas (13) and (14) ensure that each driver only executes one shift chain and each bus only executes one bus chain. (14) is the shift connection constraint, that is, the shifts executed by each driver and bus can form a shift chain and a bus chain; formulas (15), (16), and (17) respectively meet the maximum number of drivers and the maximum number of buses; formula (18) is used to determine whether there is a binding relationship between the bus and the driver; formula (19) means that if the driver is bound to the bus, the shift executed by the driver will definitely be executed by the corresponding bus; formulas (20) and (21) ensure that the shift change time of the bus and the driver is greater than the shortest time required for the shift change; formulas (22) and (23) are the shift change location constraints; formula (24) defines the driver's continuous working hours and sets the initial value to 0; formula (25) is the update of the continuous working hours. Here, if it exceeds the maximum time required for the shift change, it is assumed that the driver has rested and the continuous working hours are 0; formulas (26) and (27) are to meet the continuous working hours limit and total working hours limit stipulated by labor laws and regulations; formulas (28) and (29) are the driver's Two-shift mode; Formula (30) ensures fairness among drivers, that is, the number of shifts performed by each driver is not much different; Formula (31) defines the power of the bus and sets the initial state to be full power; Formula (32) is the update of power; Formula (33) is the remaining power of the bus after completing the shift is above the warning power; Formulas (34) and (35) define the charging time used by the bus to select the three charging modes respectively; Formula (36) ensures that the charging plan is between the adjacent shifts performed by the corresponding bus; Formula (37) ensures that the bus meets the charging time limit when performing the next shift; Formulas (38), (39), and (40) define the starting charging time point set, the ending charging time point set, and the total time node set of fast charging and slow charging; Formulas (41), (42), (43), (44), and (45) extract the maximum number of charging piles required for fast charging and slow charging in one day; Formulas (46), (47), and (48) are variable type constraints, defining 0-1 decision variables.

[0178] Based on the above solution, step 4 is as follows:

[0179] Step 4.1: Initialize the shift data. Indicates that i represents the index corresponding to the shift. Respectively represent the starting and ending locations of flight i, Respectively represent the start time and end time of shift i, and sort the shift data by start time;

[0180] Step 4.2: Initialize the set of feasible shift chains. Initialize the set of feasible shift chains The data of one feasible shift chain is represented by (f, d, c), where f represents the set of shifts and charging combinations included in this feasible shift chain, d represents the number of drivers required to execute this feasible shift, and c is the cost required to execute this feasible shift chain. The initial shift number i = 1 is selected;

[0181] Step 4.3: Take shift i as the starting shift of a feasible shift chain. Design a label (e, w, t) for the shift chain, where e represents the battery state of the electric bus before the current shift, w represents the continuous working hours of the driver before the current shift, and t represents the total working hours of the driver before the current shift. Initialize e2 = e max , w=0, t=0;

[0182] Step 4.4: Expand the subsequent shifts. Expand the current shift i to the subsequent shift j in the shift data. Assume that the shift chain label before executing the current shift is (e1, w1, t1). After connecting with the subsequent shift, the shift chain label becomes (e2, w2, t2).

[0183] Step 4.5: Obtain a feasible shift chain. Backtrack through all feasible shift chains to obtain the set of shifts f and the number of drivers d they contain, and calculate their corresponding costs c. Add this shift data (f, d, c) to the set of feasible shift chains. If i <= T, set i = i + 1; otherwise, the algorithm ends and outputs the feasible shift chain set F.

[0184] Among them, step 4.4 is specifically as follows:

[0185] Step 4.4.1: Basic constraint judgment. If the current shift i and the subsequent shift j meet where t min If represents the shortest time required for shift conversion, the basic constraints are met. Otherwise, it cannot be connected with the subsequent shift j, and the search for a feasible connecting shift continues;

[0186] Step 4.4.2: Update and judge the battery level. If fast charging or slow charging is performed between shifts, then e2 = e c +e1-e t , where e c is the total amount of electricity charged, e t is the power consumption for the current shift, e2≤e max ; If the battery is replaced, then e2=e max ; Otherwise e2=e1-et If e2-e t ≤e min , where e min is the minimum power limit, e t The power consumption for executing the subsequent shift satisfies the energy-range constraint; otherwise, the subsequent shift cannot be connected, and the search for a feasible connecting shift continues.

[0187] Step 4.4.3: Update and judge continuous working hours. If the inter-shift transfer time is greater than the specified maximum shift time, then w2 = 0; otherwise like where w max If the maximum continuous working hours are met, the continuous working hours can be continued; otherwise, the driver performs a rest task and the shift cannot be continued, or a new driver is added for this bus and w2=0;

[0188] Step 4.4.4: Determine if the driver is on two shifts. If the driver is on the morning shift and the end time of the subsequent shift is less than or equal to the latest end time of the morning shift, then Where H 1max If is the latest off-duty time of the shift, then this driver can perform this shift j; And the starting time of the shift is greater than or equal to the earliest working time of the afternoon shift, that is Then add a driver for the afternoon shift to perform this bus j; if neither of the conditions are met, the current driver will perform the bus j;

[0189] Step 4.4.5: Update and judge the total working hours. If the bus driver is changed before the subsequent shift j, the total working hours before the subsequent shift j is set to t2 = 0; otherwise like where t max If it is the maximum formula specified, the total working hours constraint is satisfied; otherwise, a new driver needs to be added to this bus, and w2 = 0 and t2 = 0;

[0190] Based on the above solution, step 5 is as follows:

[0191] Step 5.1: Get an initial feasible solution. Select a shift chain: [t1,...,t i ],[t2,...,t j ],...,[t m ] as the initial feasible solution;

[0192] Step 5.2: Construct a set covering the main problem. Each column in the main problem represents a column constructed from the initial feasible solution, that is, the corresponding shift chain;

[0193] Step 5.3: Solve the main problem and the shadow price of the main problem. When solving the main problem, use branch and bound to obtain a 0-1 integer solution. The shadow price of the main problem can be solved based on the dual problem of the main problem. The solution of the dual problem is the shadow price of the main problem.

[0194] Step 5.4: Construct the price sub-problem;

[0195] Step 5.5: Solve the price subproblem and determine if there is a carry-in variable. The optimal solution to the price subproblem is the solution corresponding to the column with the smallest test number in the main problem. If the test number is less than 0, there is a carry-in variable, and go to step 5.6. If the test number is greater than or equal to 0, there is no carry-in variable, and the algorithm ends, outputting the solution to the main problem.

[0196] Step 5.6: Add the columns or shift chains corresponding to the incoming base variables to the main problem and go to step 5.3.

[0197] Based on the above solution, step 6 specifically involves solving the model using the above algorithm and judging the rationality of the model and the effectiveness of the algorithm based on the convergence and scheduling solution. Finally, the vehicle scheduling and crew scheduling results of the model are presented for fast charging, slow charging, battery swapping, and multiple charging point modes.

[0198] Figure 3 A schematic diagram of vehicle scheduling in fast charging mode is given; Figure 4 A schematic diagram of driver scheduling in fast charging mode is given; Figure 5 A schematic diagram of vehicle scheduling in slow charging mode is given; Figure 6 A schematic diagram of driver scheduling in slow charging mode is given; Figure 7 A schematic diagram of vehicle scheduling in battery swap mode is given; Figure 8 A schematic diagram of driver scheduling in battery swap mode is given; Figure 9 A schematic diagram of vehicle scheduling in multiple charging modes is given; Figure 10 A schematic diagram of driver scheduling under multiple charging modes is given.

[0199] The above embodiments are only used to illustrate the present invention, and are not intended to limit the present invention. Ordinary technicians in the relevant technical field can make various changes and modifications without departing from the essence and scope of the present invention. Therefore, all equivalent technical solutions also fall within the scope of protection of the present invention.

[0200] The contents not described in detail in this specification belong to the prior art known to those skilled in the art.

Claims

1. A method for collaborative optimization of multi-charging mode electric bus and driver scheduling, characterized in that: The following steps are involved: Step 1: Extract the shift data of the selected actual operating line based on the actual operating status of the selected actual operating line. The shift data includes the start time, end time, start station, and end station of all shifts of the actual operating line; Step 2: Based on the actual operating route selected in Step 1, determine the relevant characteristic parameters of the electric bus and the driver scheduling parameters for the selected actual operating route; the relevant characteristic parameters include the electric bus's fast charging mode, slow charging mode, and battery replacement mode, and the driver scheduling parameters are determined based on actual operation management; Step 3: Based on step 2, establish the bus-related characteristic parameters and driver scheduling rule parameters, and build a vehicle and driver scheduling collaborative optimization model for the electric bus system with the goal of minimizing driver cost, vehicle cost, and charging cost. Step 4: Based on the relevant constraints in the vehicle and driver scheduling collaborative optimization model of the electric bus system in step 3, use the labeling algorithm based on tree enumeration to enumerate all the shift chains that meet the relevant constraints; Step 5: Use all the shift chains generated in step 4 to construct a set covering model, and use the column generation algorithm to solve the constructed set covering problem; output the vehicle and driver scheduling results; in, The process of constructing the vehicle and driver scheduling collaborative optimization model of the electric bus system in step 3 is specifically as follows: Target 1: Driver salary costs; The driver's salary cost is divided into daily wages and hourly wages, which are expressed as: Where D represents the set of drivers, T represents the set of shifts, A driver's daily wage, represents a driver's hourly wage, represents the start time of shift j, represents the end time of shift j, Indicates whether driver d will execute shift j after completing shift i. If yes, it is 1, otherwise it is 0. Indicates whether driver d will execute shift j when departing from the station; Objective 2: Bus costs; bus costs include bus purchase costs and operating costs; the purchase and operating costs of buses are expressed as: Where V represents the set of electric buses, It represents the purchase cost of an electric bus, calculated on a daily basis. represents the unit mileage operating cost of electric buses, l j represents the operating mileage of flight j, Indicates whether bus v will execute shift j after completing shift i. If so, it is 1, otherwise 0. Indicates whether bus v departs from the station and executes the schedule j; Target 3: Costs associated with bus charging; including the electricity cost of battery charging, the fixed cost of charging piles, and the battery cost required for battery replacement, which are expressed as follows: in, Indicates the unit charging cost of fast charging. Indicates the unit charging cost of slow charging. Indicates the unit battery cost generated by battery replacement, represents the purchase cost of a single charging pile corresponding to the kth charging mode, P k represents the charging power of the kth charging mode, where k∈{1,2} represents fast charging and slow charging respectively, Q k Indicates the number of charging piles corresponding to the kth charging mode represents the charging time required for bus v to be charged using the kth charging mode before executing the jth shift, Indicates whether bus v uses the kth charging mode to charge after completing the trip i and before starting the trip j. If it is charged, the value is 1; otherwise, it will not be charged in the kth charging mode. According to the above description of the cost of electric bus system, the objective function of the model is expressed as: Constraints: Among them, D 1max The maximum number of drivers that can perform the morning shift on this route, D 2max Indicates the maximum number of drivers that can perform the lunch shift on this route, H 1max Indicates the latest time for the morning shift driver to get off work on this route, H 2min Indicates the earliest working time for the noon shift driver on this route, B max Indicates the maximum number of electric buses that can operate on this route. represents the starting station of shift j, represents the end station of shift j, g w represents the shortest time required for a shift change, g r Indicates the maximum time required for a shift change, Indicates the driver's maximum continuous working time, t max Indicates the maximum working time of the driver per day, N min Indicates the minimum number of shifts a driver performs in a day, N max Indicates the maximum number of shifts a driver performs in a day, E max Indicates the battery capacity when it is fully charged, E l represents the power consumption per unit mileage, r represents the battery power warning level, that is, to ensure that the bus can return to the bus station smoothly and ensure that the battery power of the bus is higher than the warning level after completing the shift mission, t replace Indicates the time required for battery replacement. Indicates whether the driver d is bound to the bus v, if so, it is 1, otherwise it is 0. Indicates the continuous working time of driver d before performing shift j, It represents the amount of electricity of bus v before it performs shift j. represents the time set of starting charging using the kth charging mode, where k∈{1,2}, and represents the time set of starting charging for fast charging and slow charging for all electric buses on this line during one day of operation. represents the time set of charging end using the kth charging mode, where k∈{1,2}, and represents the time set of charging end points for fast charging and slow charging of all electric buses on this line during one day of operation. Indicates the time point corresponding to the kth charging mode being used for the nth time during line operation, where k∈{1,2}. The time point includes the start time point and the end time point of charging, and the two exist independently. Indicates that the time node in the kth charging mode is The number of charging piles in use at the time; Formulas (9) and (10) ensure that each shift is executed by the driver and the bus respectively; Formulas (11) and (12) ensure that each driver only executes one shift chain and each bus only executes one bus chain; Formulas (13) and (14) are shift connection constraints, that is, the shifts executed by each driver and bus can form a shift chain and a bus chain; Formulas (15), (16) and (17) respectively meet the maximum number of drivers and the maximum number of buses; Formula (18) is used to determine whether there is a binding relationship between the bus and the driver; Formula ( 19) indicates that if a driver is bound to a bus, the shift executed by the driver will definitely be executed by the corresponding bus; Formulas (20) and (21) ensure that the shift change time between buses and drivers is greater than the shortest time required for shift change; Formulas (22) and (23) are the shift change location restrictions; Formula (24) defines the driver's continuous working hours and sets the initial value to 0; Formula (25) is the update of continuous working hours. Here, if the maximum time required for shift change is exceeded, it is assumed that the driver has rested and the continuous working hours are 0; Formulas (26) and (27) ) is to meet the continuous working hours limit and total working hours limit stipulated by labor laws and regulations; Formulas (28) and (29) are the two-shift mode of drivers; Formula (30) ensures fairness among drivers, that is, the number of shifts performed by each driver is not much different; Formula (31) defines the power of the bus and makes the initial state full power; Formula (32) is the update of power; Formula (33) is the remaining power of the bus after completing the shift and is above the warning power; Formulas (34) and (35) define the charging time used by the bus to select the three charging modes respectively; Formula (3 6) Ensure that the charging plan is between the adjacent shifts of the corresponding bus; Formula (37) ensures that the bus meets the charging time limit when executing the next shift; Formulas (38), (39), and (40) define the set of starting charging time points, the set of ending charging time points, and the total set of time nodes for fast charging and slow charging; Formulas (41), (42), (43), (44), and (45) extract the maximum number of charging piles required for fast charging and slow charging in one day; Formulas (46), (47), and (48) are variable type constraints, which define 0-1 decision variables.

2. The method for collaborative optimization of multi-charging mode electric bus and driver scheduling according to claim 1, characterized in that: Step 4 is as follows: Step 4.1: Initialize shift data; shift data is used Indicates that i represents the index corresponding to the shift. Respectively represent the starting and ending locations of flight i, Respectively represent the start time and end time of shift i, and sort the shift data by start time; Step 4.2: Initialize the set of feasible shift chains; Initialize the set of feasible shift chains The data of one feasible shift chain is represented by (f, d, c), where f represents the set of shifts and charging combinations included in this feasible shift chain, d represents the number of drivers required to execute this feasible shift, and c is the cost required to execute this feasible shift chain. The initial shift number i = 1 is selected; Step 4.3: Take shift i as the starting shift of a feasible shift chain; design a label (e, w, t) for the shift chain, where e represents the battery state of the electric bus before the current shift, w represents the continuous working hours of the driver before the current shift, and t represents the total working hours of the driver before the current shift. Initialize e2 = e max , w=0, t=0; Step 4.4: Expand the subsequent shifts; expand from the current shift i in the shift data to the subsequent shift j; assuming that the shift chain label before executing the current shift is (e1, w1, t1), after connecting with the subsequent shift, the shift chain label becomes (e2, w2, t2); Step 4.5: Obtain feasible shift chains; backtrack all obtained feasible shift chains, obtain the shift set f and the number of drivers d contained in them, and calculate their corresponding costs c. Add this shift data (f, d, c) to the feasible shift chain set. If i <= T, set i = i + 1; otherwise, the algorithm ends and outputs the feasible shift chain set F.

3. The method for collaborative optimization of multi-charging mode electric bus and driver scheduling according to claim 2, characterized in that: The step 4.4 is specifically as follows: Step 4.4.1: Basic constraint judgment; if the current shift i and the subsequent shift j meet where t min If represents the shortest time required for shift conversion, the basic constraints are met. Otherwise, it cannot be connected with the subsequent shift j, and the search for a feasible connecting shift continues; Step 4.4.2: Update and judge the battery level; if fast charging or slow charging is performed between shifts, then e2 = e c +e1-e t , where e c is the total amount of electricity charged, e t is the power consumption for the current shift, e2≤e max ; If the battery is replaced, then e2=e max ; Otherwise e2=e1-e t ; If e2-e t ≤e min , where e min is the minimum power limit, e t The power consumption for executing the subsequent shift satisfies the energy-range constraint; otherwise, the subsequent shift cannot be connected, and the search for a feasible connecting shift continues. Step 4.4.3: Update and judge continuous working hours; if the inter-shift transfer time is greater than the specified maximum shift change time, then w2 = 0; otherwise like where w max If the maximum continuous working hours are met, the continuous working hours can be continued; otherwise, the driver performs a rest task and the shift cannot be continued, or a new driver is added for this bus and w2=0; Step 4.4.4: Determine if the driver is on two shifts; if the driver is on the morning shift and the end time of the subsequent shift is less than or equal to the latest end time of the morning shift, then Where H 1max If is the latest off-duty time of the shift, then this driver can perform this shift j; And the starting time of the shift is greater than or equal to the earliest working time of the afternoon shift, that is Then add a new afternoon shift driver to perform this bus j; If neither condition is met, the current driver will perform shift j; Step 4.4.5: Update and judge the total working hours; if the bus driver is replaced before the subsequent shift j, the total working hours before the subsequent shift j is set to t2 = 0; otherwise like where t max If it is the maximum formula specified, the total working hours constraint is satisfied; otherwise, a new driver needs to be added to this bus, and w2=0 and t2=0.

4. The method for collaborative optimization of multi-charging mode electric bus and driver scheduling according to claim 1, characterized in that: The step 5 is specifically as follows: Step 5.1: Obtain an initial feasible solution; Select shift chain: [t1,…,t i ],[t2,…,t j ],…,[t m ] as the initial feasible solution; Step 5.2: Construct a set covering the main problem. Each column in the main problem represents a column constructed from the initial feasible solution, that is, the corresponding shift chain; Step 5.3: Solve the main problem and the shadow price of the main problem. When solving the main problem, use branch and bound to obtain a 0-1 integer solution. The shadow price of the main problem can be solved based on the dual problem of the main problem. The solution of the dual problem is the shadow price of the main problem. Step 5.4: Construct the price sub-problem; Step 5.5: Solve the price subproblem and determine whether there is a carry-in variable. The optimal solution to the price subproblem is the solution corresponding to the column with the smallest test number in the main problem. If the test number is less than 0, there is a carry-in variable, and go to step 5.

6. If the test number is greater than or equal to 0, there is no carry-in variable, the algorithm ends, and the solution to the main problem is output. Step 5.6: Add the columns or shift chains corresponding to the incoming base variables to the main problem and go to step 5.3.

Images