A Robust Control Method for Multi-Line Collaboration of Dual-Source Trackless Trolleys

Abstract

A robust control method for multi-line coordination of dual-source trolleybuses, which relates to a control method for dual-source trolleybuses. The present invention aims to solve the problem of local space or even wider congestion caused by the failure to consider the spatial correlation of the actual stations where the vehicles are located and the vehicle coordination during the operation of dual-source trolleybuses. The model established in the present invention is a mixed-integer non-linear programming model, which belongs to the min-max optimization problem and aims to find a solution that performs well in the worst scenario. By considering the uncertainty of travel time and stop time in a dynamic environment and focusing on the operation characteristics of dual-source trolleybuses, the present invention proposes a robust control method for multi-line coordination of dual-source trolleybuses, which can maintain the stability of the operation state even in a poor situation, improve the transfer efficiency of passengers in the network, reduce the risk of vehicle bunching, and improve the regularity of the operation service of dual-source trolleybus lines, thus realizing the robustness of the static scheduling plan.

Description

Technical Field

[0001] The present invention relates to a control method for a dual-source trolleybus. Background Art

[0002] The new energy transformation of public transportation has become the development trend of urban buses. As a green travel tool, trolleybuses have served urban public transportation for more than a hundred years and have made important contributions to urban transportation and environmental protection. With the development of technology, dual-source trolleybuses have been upgraded on the basis of traditional trolleybuses. By connecting the overhead line network through a pantograph and equipping with lithium-ion batteries, a dual-source power drive is formed. Given its characteristics of high efficiency, low pollution, low cost, and good mobility, many cities are building dual-source trolleybus line networks. Therefore, the research on the operation planning and scheduling of dual-source trolleybuses has important practical significance for energy conservation and emission reduction and the realization of green transportation.

[0003] The convenience of transfer within the bus network is a key service quality factor considered by residents when choosing public transportation. An untimely transfer will lead to a long waiting time for passengers to transfer, causing serious troubles to residents' travel. However, due to the different locations of each station, the traffic conditions of the corresponding physical spaces vary greatly. For example, what is the road condition between the current station and other stations, whether it is smooth, what is the road condition between a certain station and a station with vehicle traffic connectivity, and whether it has accessibility conditions; at the same time, in an open road environment, affected by uncertain factors such as road conditions, fluctuating passenger flow, and extreme weather, the driving time and stop time of dual-source trolleybuses at a certain spatial station show huge fluctuations, which not only seriously affects the coordination effect of vehicles, may lead to congestion in local spaces (stations or roads), but also leads to the technical problem of high risk of bunching. More critically, the early arrival and delay of vehicles may affect downstream stations or even other lines, causing a chain reaction between nodes with spatial connectivity and causing congestion in a larger area. In addition, congestion in a larger area of stations / roads not only reduces the traffic efficiency, but also makes it impossible for passengers to transfer in time, and even further aggravates the congestion situation.

[0004] The uniqueness of the operation mode of dual-source trolleybuses brings greater challenges to the realization of coordinated scheduling. The traffic nodes of the dual-source trolleybus line network include not only common stations, but also line combiners, automatic catchers, and power supply network sections. As Figure 1 shown, a line combiner refers to a device that connects the original four contact lines into two contact lines when two trolleybus lines intersect. Figure 2 The automatic catcher in is a device for lifting the pantograph of a trolleybus. Under this device, the dual-source trolleybus needs to stop to complete the operation of raising the pole. When the dual-source trolleybus passes through the above-mentioned operating devices, it needs to slow down or stop, and is more vulnerable to dynamic environment interference. Figure 3The sectioning of the power supply network in it is the basic catenary unit for studying vehicle energy consumption, and adjacent sections are in an insulated state with electrical isolation. Due to the limited power of the catenary, the number of dual-source trolleybuses within a section cannot exceed the carrying capacity of the power supply network section, otherwise power outage situations such as protection and tripping will occur, affecting the stable operation state of the vehicle, and even vehicle breakdown may occur.

[0005] Currently, dynamic control methods are mainly used to cope with the disturbances in the dynamic environment. For example, strategies such as station stop, skipping stations, speed control, and replacement with spare vehicles are proposed to reduce bus operation deviations. However, the implementation of dynamic control depends on the construction of a complete intelligent road infrastructure, which requires a large amount of capital investment. In addition, these methods may harm the interests of passengers. For example, the station stop strategy will increase the waiting time of passengers in the vehicle, and the skipping stations and replacement with spare vehicles strategies may disrupt the travel plans of passengers. Compared with dynamic control, using a static scheduling strategy to generate a robust timetable to achieve coordinated scheduling is a more economical and effective method. The robust timetable can, to a certain extent, resist the volatility of travel time and stop time, and maintain the stable operation state even under poor conditions. Summary of the Invention

[0006] The present invention aims to solve the problem of local space or even wider congestion caused by the lack of consideration of the spatial correlation and vehicle coordination of the actual stations where the dual-source trolleybuses are located during the operation process, and provides a robust control method for multi-line coordination of dual-source trolleybuses.

[0007] The robust control method for multi-line coordination of dual-source trolleybuses of the present invention is carried out according to the following steps:

[0008] Step 1: Select dual-source trolleybus lines to construct a line network, and establish an attribute set of each traffic node in the network to store line and traffic node information;

[0009] The attribute set of each traffic node includes the starting station, terminal station, common stations, non-common stations, automatic catchers, line combiners, the number and location of power supply network sections, and the distribution and length of off-line sections; the common stations include transfer stations and non-transfer stations;

[0010] Step 2: According to the control period, establish a train operation status set to store train operation information;

[0011] The train operation status includes the number of departures of each line in the up and down directions during the control period, the vehicle driving path, the range of departure frequencies, the planned departure intervals, and the initial departure timetable and arrival times;

[0012] Step 3: Collect the Automatic Vehicle Location (AVL) data within the controlled time period over a certain period, calculate the travel time between adjacent stations, round it to the nearest integer in minutes, and incorporate it into the set of travel times between adjacent stations to obtain an integer set of travel times between adjacent stations with upper and lower bounds;

[0013] Step 4: Utilize the IC card and two-dimensional code data on the dual-source trolleybus to collect the boarding passenger data at each station within the same controlled time period, and calculate the average passenger arrival rate at each station on each route;

[0014] Step 5: Focus on the operating characteristics of the dual-source trolleybus and construct a robust optimization model for the multi-line coordination of the dual-source trolleybus timetable:

[0015] Several explanations need to be made before constructing the model:

[0016] 1). The present invention believes that the departure frequency of the line is determined based on the maximum passenger flow section of the line. Therefore, the vehicle carrying capacity can meet the passenger flow demand during peak hours;

[0017] 2). It is considered that the power supply facilities and catenary devices of the dual-source trolleybus operate normally and the vehicle condition is in good condition;

[0018] 3). It is considered that the same type of dual-source trolleybus model is configured for each line and the vehicle will stop at each station;

[0019] 4). It is considered that the power output of the catenary is stable and the sectional power of each power supply network is the same;

[0020] 1. Part of the vehicle motion equation

[0021] The volatility of the vehicle travel time generally shows random characteristics caused by the time-varying characteristics of different time periods and road conditions;

[0022]

[0023] Formula (1) represents the arrival time of the nth vehicle on line l at station b equals the departure time from station b - 1 plus the travel time between stations where r represents the direction of the line, a is arrival, and d is departure;

[0024]

[0025] Formula (2) represents the departure time of the nth vehicle on line l from station b equals the arrival time at station b plus the stop time at the station

[0026] The stopping time of a vehicle at a station is mainly affected by the number of passengers getting on and off at the station and shows volatility. Since the time for passengers to get off is less than the time for them to get on, it can be considered that the station stopping time is mainly composed of the time for passengers to get on and the time for the vehicle to open and close the doors. Assuming that the arrival of passengers follows a uniform distribution (that is, the number of passengers arriving at station b per unit time is constant. As soon as the previous train at station b leaves, new passengers arrive at station b. As time goes by, the number of passengers accumulates until the next train arrives at station b and takes them all on board, so the stopping time is related to the headway between two adjacent trains on the line), the station stopping time is related to the headway between adjacent trains, as shown in formula (3):

[0027]

[0028] where t0 is the time required for the vehicle to open and close the doors, and γ lb is the passenger arrival rate at station b on line l, and β is the average boarding time per passenger;

[0029] Combining formula (1) and (2) gives formula (4), which represents the arrival time at station b equal to the departure time plus the travel times of each section before station b and the stopping times at each station

[0030]

[0031] The time calculation method for a dual-source trolleybus to reach the automatic catcher, line combiner and power supply network section is the same as above;

[0032] 2. Objective function

[0033] 1) Maximizing the number of vehicle collaborations

[0034] Any common station in the overlapping section of the line can be used for transfer. However, in actual operation, passengers generally only choose to transfer at the last transferable station, and the number of passengers transferring at the other common stations is relatively small and can be regarded as non-transfer stations. The collaboration in the present invention not only includes enabling passengers to collaborate in transferring at transfer stations, but also includes enabling vehicles to collaborate in entering stations at non-common stations. Collaboration time windows are set for transfer stations and non-common stations respectively, and finally the total number of collaborations is obtained by adding them up;

[0035] The time interval between vehicles arriving at transfer stations should not be too short or too long. The shortest interval w b allows passengers enough time to transfer, while the longest interval W b ensures that the transfer waiting time will not be too long;

[0036]

[0037] In formula (5), if the time difference between the train number n of line l and the train number m of line j when arriving at the transfer station b is within the time window [w b ,W b , then the two train numbers are regarded as coordinated transfer train numbers, and the binary variable is recorded as 1, otherwise it is recorded as 0;

[0038] To avoid vehicle congestion at non-transfer stations, it is also necessary to set the arrival time window, with the shortest interval v b , and the longest interval V b . If the time difference between the train number n of line l and the train number m of line j when arriving at the non-transfer station b is greater than v b , and at the same time less than V b , then the two train numbers are regarded as coordinated arrival train numbers, and the binary variable in formula (6) is used to determine whether the train numbers arrive coordinately;

[0039]

[0040] Formula (7) represents the number of vehicle coordinations at the upstream transfer station and non-transfer stations, where the subscript 1 represents the upstream direction; formula (8) represents the number of vehicle coordinations at the downstream transfer station and non-transfer stations, and the subscript 2 is for the downstream direction; formula (9) represents the goal of maximizing the total number of coordinations;

[0041]

[0042] maxF1 = F 1 +F 2 (9)

[0043] 2) Minimization of the fleet size

[0044] The minimum number of vehicles required to complete all train number tasks is equal to the sum of the maximum reverse differences of each station yard. Combining with practice, the starting and ending stations of the line are used as the double-source trolleybus station yards, and the maximum reverse difference function is calculated and summed for each station yard respectively to obtain the minimum fleet size;

[0045] Formulas (10)-(12) represent the process of calculating the fleet size using the reverse difference function, where T1 and T2 are the start and end times of the control period, represents that the nth train number of line l has departed from the station yard d at time t; SD l,t represents the number of vehicles departing from the station yard d as of time t; represents that the nth train number of line l has arrived at the station yard d at time t, and ED l,t represents the number of vehicles arriving at the station yard d as of time t, and max(SD l,t -ED l,t ) represents the maximum reverse difference function of the station yard d;

[0046]

[0047] 3) Minimization of the headway deviation at the vehicle head

[0048] The headway is the time difference between the front ends of two consecutive vehicles passing through the same point. When the headways of the trips on a line are relatively small, the number of vehicles gathering in the same section of the power supply network will increase, resulting in a high load on the line network and possibly vehicle breakdowns. When the headways are relatively large, the number of vehicles gathering in the same section of the power supply network will decrease, causing idle power in the overhead line network. If the deviation between the actual headway and the planned headway can be reduced to make the headways more uniform, it can not only avoid vehicle congestion but also improve the utilization rate of electric energy. In addition, a smaller headway deviation can also improve the regularity of vehicle operation services;

[0049] Therefore, the present invention selects two types of nodes prone to congestion, namely common stations and automatic catchers, to analyze the headway deviation; the line departure frequency has been determined in the frequency setting stage, and the planned headway is calculated h l,n,b is the headway of the vehicle at station b, h l,n,a is the headway of the vehicle at the automatic catcher a;

[0050] Formula (13) represents the average headway deviation of all stations;

[0051]

[0052] Formula (14) represents the average headway deviation of all automatic catchers;

[0053]

[0054] Formula (15) represents the goal of minimizing the average headway deviation.

[0055] minF3 = F a +F b (15)

[0056] 3. Constraint part

[0057] 1) Departure interval constraint

[0058] In order to balance the bus service level and the revenue of the bus company, the constraint formulas (16)-(18) indicate that each trip on the line must meet the departure interval requirements, and are the minimum and maximum departure intervals of line l respectively; the departure time is T1 is the start time of the control period, and T2 is the end time of the control period; is the time of the first vehicle dispatched in the r direction of line l;

[0059]

[0060] 2) Operating device constraint

[0061] Constraint (19) indicates that the dual-source trolleybus needs to stop and raise the pole under the automatic catcher a. To avoid congestion caused by subsequent vehicles arriving simultaneously, the minimum arrival interval w is set a ;

[0062]

[0063] Constraint (20) indicates that to avoid dual-source trolleybuses arriving at the line combiner c simultaneously, the minimum arrival interval w also needs to be set c ;

[0064]

[0065] 3) Power supply network sectional load-bearing capacity constraint

[0066] Constraint (21) requires that the maximum number of vehicles DK in each section is less than the maximum number of vehicles Q1 that the section can carry. The value of Q1 should consider the charging and air-conditioning power of the vehicles and combine the proportion of the number of controlled lines to the actual number of lines in the section;

[0067] DK ≤ Q1 (21)

[0068] Formulas (22)-(24) use the inverse difference function to represent the maximum number of vehicles DK in the power supply network section k, where sK l,n,t = 1 indicates that the train number n of line l has left section k at time t, and eK l,n,t = 1 indicates that the train number n of line l has arrived at section k; SK l,t and EK l,t respectively represent the number of vehicles that have left and arrived at section k as of time t;

[0069]

[0070] 4) Off-line section speed constraint

[0071] The dual-source trolleybus is driven by on-vehicle lithium batteries on the off-line section. If the vehicle has low energy consumption on the off-line section, it is not only economical and energy-saving, but also can reduce the depth of battery discharge and extend the service life of the battery. In addition, compared with newly manufactured vehicles, the battery capacity of vehicles that have been in operation for many years has significantly decayed. Reducing energy consumption can also reduce the risk of insufficient vehicle power supply during off-line driving. The energy consumption test of the dual-source trolleybus shows that the energy consumption is low when the average speed of the vehicle is maintained in the range of 20 km / h to 30 km / h. Therefore, Constraint Formula (25) requires that the average driving speed of the vehicle on the off-line section be within the range of 20 km / h to 30 km / h:

[0072]

[0073] Constraints (16)-(21) and Formula (25) also need to meet the following requirements:

[0074]

[0075] t ∈ [T1, T2] (26);

[0076] 3. Model integration part

[0077] To reduce the impact of the fluctuations in the driving time and stop time of the dual-source trolleybus on the interests of the bus company and passengers, and to find a timetable that can perform well even in a dynamic environment, the present invention establishes a multi-objective robust optimization model and transforms the three objective functions into the form of a minimax problem:

[0078]

[0079] Step Six: Design a multi-objective minimax differential evolution algorithm for solving according to the characteristics of the model: The present invention needs to solve a multi-objective minimax optimization problem. By combining the minimax differential evolution algorithm with the fast non-dominated sorting algorithm and the crowding distance algorithm, using a penalty function to transform the constrained problem into an unconstrained problem, and improving the mutation strategy, a multi-objective minimax differential evolution algorithm is proposed. The algorithm flow chart is shown in Figure 5 ;

[0080] Step Seven: The algorithm generates Pareto solutions, selects the optimal solution, and outputs the robust timetable; Selecting the optimal solution is to select a solution that conforms to its own interests from the perspective of the bus company or passengers.

[0081] The model established in the present invention is a mixed integer non - linear programming model, belonging to the min - max optimization problem, aiming to find a solution that performs well in the worst - case scenario. As an emerging algorithm improved from the differential evolution algorithm, the min - max differential evolution algorithm avoids excessive search for the worst - case objective function of uncertain variables. In a single generation of evolution, it adopts the bottom - lifting strategy for decision variables (there is only one group, which is the departure time) and the partial regeneration strategy for uncertain variables (travel time and stop time) respectively, enabling them to evolve simultaneously in the direction that meets their optimization goals.

[0082] Advantages of the present invention:

[0083] The present invention takes into account the relevance of the site space in the set of travel times between adjacent stations, and by considering the uncertainty of travel time and stop time in a dynamic environment, focuses on the operation characteristics of dual - source trolleybuses, and proposes a robust control method for the multi - line coordination of dual - source trolleybuses. Even in a relatively poor situation, it can maintain the stability of the operation state, improve the transfer efficiency of passengers in the network, reduce the risk of vehicle bunching, and improve the regularity of the operation service of dual - source trolleybus lines, realizing the robustness of the static scheduling plan. The present invention provides a new idea for bus companies to compile the multi - line coordination timetable of dual - source trolleybuses, and is of great significance for promoting the large - scale operation of urban green public transportation. Brief Description of the Drawings

[0084] Figure 1 It is a schematic diagram of the operation of a dual - source trolleybus at the line coupler;

[0085] Figure 2 It is a schematic diagram of the operation of a dual - source trolleybus at the automatic catcher;

[0086] Figure 3 It is a schematic diagram of the sectionalization of the power supply network of a dual - source trolleybus;

[0087] Figure 4 It is the overall framework diagram of the method of the present invention;

[0088] Figure 5 It is the flow chart of the multi - objective min - max differential evolution algorithm;

[0089] Figure 6 It is a schematic diagram of the upward direction of the dual - source trolleybus line in Experiment 1;

[0090] Figure 7 It is a schematic diagram of the downward direction of the dual - source trolleybus line in Experiment 1;

[0091] Figure 8 It is the Pareto optimal front diagram in Experiment 1;

[0092] Figure 9 It is the data coding structure diagram in the algorithm of Experiment 1;

[0093] Figure 10 is the number of collaborations between stations in the up and down directions in Experiment 1;

[0094] Figure 11 are the three target output results of the two timetables under the Monte Carlo simulation in Experiment 1;

[0095] Figure 12 is the maximum number of vehicles within the power supply network section under the Monte Carlo simulation in Experiment 1. Specific implementation manner

[0096] Specific implementation manner 1: This implementation manner is a robust control method for multi-line collaboration of dual-source trolleybuses, and specifically proceeds according to the following steps:

[0097] Step 1: Select the lines of dual-source trolleybuses to construct a line network, and establish an attribute set of each traffic node in the network to store line and traffic node information;

[0098] The attribute set of each traffic node includes the starting station, terminal station, common stations, non-common stations, the number and location of automatic catchers, the number and location of line combiners, the number and location of power supply network sections, and the distribution and length of the off-line sections;

[0099] Step 2: According to the control period, establish a set of train operation statuses to store train operation information;

[0100] The train operation status includes the number of departures in the up and down directions of each line during the control period, the vehicle driving path, the range of departure frequencies, the planned headways, and the initial departure timetable and arrival times;

[0101] Step 3: Collect the Automatic Vehicle Location (AVL) data during the control period within a certain period, calculate the travel time between adjacent stations, round it to the nearest integer in minutes, and incorporate it into the set of travel times between adjacent stations to obtain an integer set of travel times between adjacent stations with upper and lower bounds;

[0102] Step 4: Use the IC card and two-dimensional code data on the dual-source trolleybuses to collect the boarding passenger data at each station during the same control period, and calculate the average passenger arrival rate at each station on each route;

[0103] Step 5: Focus on the operation characteristics of dual-source trolleybuses and construct a robust optimization model for multi-line collaboration of dual-source trolleybus timetables:

[0104] Several explanations need to be made before constructing the model:

[0105] 1). The present invention believes that the departure frequency of a line is determined based on the maximum passenger flow section of the line. Therefore, the vehicle carrying capacity can meet the passenger flow demand during peak hours;

[0106] 2) It is considered that the power supply facilities and overhead line systems of dual-source trolleybuses are operating normally, and the vehicle condition is in good running condition;

[0107] 3) It is considered that the same type of dual-source trolleybus model is configured for each line, and the vehicle stops at each station;

[0108] 4) It is considered that the power output of the overhead line is stable, and the power of each section of the power supply network is the same;

[0109] 1. Part of the vehicle motion equation

[0110] The volatility of the vehicle running time generally shows random characteristics caused by the time-varying characteristics of different periods and road conditions;

[0111]

[0112] Formula (1) represents the moment when the nth vehicle on line l arrives at station b is equal to the moment of leaving station b-1 plus the running time between stations where r represents the direction of the line, a is arrival, and d is departure;

[0113]

[0114] Formula (2) represents the moment when the nth vehicle on line l leaves station b is equal to the moment of arriving at station b plus the stop time at the station

[0115] The stop time of the vehicle at the station is mainly affected by the number of passengers getting on and off at the station and shows volatility. Since the passenger getting-off time is less than the getting-on time, it can be considered that the station stop time is mainly composed of the passenger getting-on time and the vehicle door opening and closing time; assuming that the arrival of passengers follows a uniform distribution (that is, the number of passengers arriving at station b per unit time is constant. Just after the previous train at station b leaves, new passengers arrive at station b. As time goes by, the number of passengers accumulates until the next train arrives at station b and takes them all on board, so the stop time is related to the headway between two adjacent trains on the line), then the station stop time is related to the headway between adjacent trains, as shown in formula (3):

[0116]

[0117] where t0 is the time required for the vehicle to open and close the door, γ lb is the passenger arrival rate at station b on line l, and β is the average boarding time per passenger;

[0118] Combining formula (1) and (2) gives formula (4), which represents the arrival time at station b equals the departure time plus the travel times of each section before station b and the stop times at each station

[0119]

[0120] The time calculation method for the dual-source trolleybus to reach the automatic catcher, line combiner and power supply network section is the same as above;

[0121] 2. Objective function

[0122] 1) Maximize the number of vehicle collaborations

[0123] Passengers can transfer at any common station in the overlapping section of the lines. However, in actual operation, passengers generally only choose to transfer at the last transferable station, and the number of transfers at the remaining common stations is small and can be regarded as non-transfer stations; The collaboration of the present invention not only includes enabling passengers to transfer collaboratively at transfer stations, but also includes enabling vehicles to enter the station collaboratively at non-common stations. Collaboration time windows are set for transfer stations and non-common stations respectively, and finally the total number of collaborations is obtained by adding them up;

[0124] The time interval for vehicles to reach transfer stations should not be too short or too long. The shortest interval w b allows passengers enough time to transfer, while the longest interval W b ensures that the transfer waiting time will not be too long;

[0125]

[0126] In formula (5), if the time difference between train number n of line l and train number m of line j reaching transfer station b is within the time window [w b ,W b , then the two train numbers are regarded as collaboratively transferring train numbers, and the binary variable is recorded as 1, otherwise it is recorded as 0;

[0127] To avoid vehicle congestion at non-transfer stations, it is also necessary to set an arrival time window, with the shortest interval v b , the longest interval V b , if the time difference between train number n of line l and train number m of line j reaching non-transfer station b is greater than v b , and at the same time less than V b , then the two train numbers are regarded as collaboratively entering the station train numbers, and the binary variable in formula (6) is used to determine whether the train numbers collaborate to enter the station;

[0128]

[0129] Equation (7) represents the number of vehicle collaborations between the upward transfer stations and non-transfer stations, where the superscript 1 represents the upward direction; Equation (8) represents the number of vehicle collaborations between the downward transfer stations and non-transfer stations, and the superscript 2 is for the downward direction; Equation (9) represents the goal of maximizing the total number of collaborations.

[0130]

[0131] maxF1 = F 1 +F 2 (33)

[0132] 2) Minimizing the fleet size

[0133] The minimum number of vehicles required to complete all train trips is equal to the sum of the maximum inverse differences of each station yard. Considering the practice, the starting and ending stations of the line are regarded as the double-source trolleybus station yards. Calculate the maximum inverse difference function for each station yard separately and sum them up to obtain the minimum fleet size.

[0134] Equations (10)-(12) represent the process of calculating the fleet size using the inverse difference function, where T1 and T2 are the start and end times of the control period. represents that the nth train trip of line l has departed from station yard d at time t; SD l,t represents the number of vehicles dispatched from station yard d up to time t; represents that the nth train trip of line l has arrived at station yard d at time t, ED l,t represents the number of vehicles arriving at station yard d up to time t, max(SD l,t -ED l,t ) represents the maximum inverse difference function of station yard d;

[0135]

[0136] 3) Minimizing the headway deviation

[0137] The headway is the time difference between the fronts of two consecutive vehicles passing the same point. When the headway of the train trips on the line is small, the number of vehicles gathering in the same power supply network section will increase, resulting in a high load on the line network and possible vehicle breakdowns; while when the headway is large, the number of vehicles gathering in the same power supply network section will decrease, causing idle power in the overhead line network. If the deviation between the actual headway and the planned headway can be reduced to make the headway more uniform, it can not only avoid vehicle congestion but also improve the utilization rate of electric energy; in addition, a smaller headway deviation can also improve the regularity of vehicle operation services.

[0138] Therefore, the present invention selects two types of nodes prone to congestion, namely common stations and automatic catchers, to analyze the headway deviation; the line departure frequency has been determined in the frequency setting stage, and the planned headway is calculated. h l,n,b is the headway of the vehicle at stop b, h l,n,a is the headway of the vehicle at the automatic catcher a;

[0139] Equation (13) represents the average headway deviation of all stops;

[0140]

[0141] Equation (14) represents the average headway deviation of all automatic catchers;

[0142]

[0143] Equation (15) represents the goal of minimizing the average headway deviation.

[0144] minF3 = F a +F b (39)

[0145] 3. Constraint part

[0146] 1) Headway constraint

[0147] To balance the bus service level and the bus company's revenue, the constraint equations (16)-(18) indicate that each trip of the line must meet the headway requirements, and are the minimum and maximum headways of line l respectively; the departure time is T1 is the start time of the control period, and T2 is the end time of the control period; is the time of the first vehicle dispatched in the direction r of line l;

[0148]

[0149] 2) Operating device constraint

[0150] Constraint (19) indicates that the dual-source trolleybus needs to stop and raise the pole under the automatic catcher a. To avoid congestion caused by subsequent vehicles arriving simultaneously, the minimum arrival interval w is set a ;

[0151]

[0152] Constraint (20) indicates that to avoid dual-source trolleybuses arriving at the line combiner c simultaneously, the minimum arrival interval w also needs to be set c ;

[0153]

[0154] 3) Power supply network segmented carrying capacity constraint

[0155] Constraint (21) requires that the maximum number of vehicles DK within each section be less than the maximum number of vehicles Q1 that the section can carry. The value of Q1 should consider the charging and air-conditioning power of the vehicles and combine with the ratio of the number of controlled lines to the actual number of lines in the section;

[0156] DK ≤ Q1 (45)

[0157] Formulas (22)-(24) use the inverse difference function to represent the maximum number of vehicles DK within section k of the power supply network, where sK l,n,t = 1 indicates that train number n on line l has left section k at time t, and eK l,n,t = 1 indicates that train number n on line l has arrived at section k; SK l,t and EK l,t respectively represent the number of vehicles that have left and arrived at section k as of time t;

[0158]

[0159] 4) Off-line section speed constraint

[0160] The dual-source trolleybus is driven by an on-vehicle lithium battery in the off-line section. If the vehicle has low energy consumption in the off-line section, it is not only economical and energy-saving, but also can reduce the depth of battery discharge and extend the service life of the battery; in addition, compared with newly manufactured vehicles, the battery capacity of vehicles that have been in operation for many years has decreased significantly. Reducing energy consumption can also reduce the risk of insufficient vehicle power supply during off-line driving; The energy consumption test of the dual-source trolleybus shows that the energy consumption is low when the average vehicle speed is maintained in the range of 20 km / h to 30 km / h; Therefore, constraint formula (25) requires that the average driving speed of the vehicle in the off-line section is within the range of 20 km / h to 30 km / h:

[0161]

[0162] 3. Model integration part

[0163] To reduce the impact of fluctuations in the driving time and stop time of dual-source trolleybuses on the interests of bus companies and passengers, and to find a timetable that can perform well even in a dynamic environment, the present invention establishes a multi-objective robust optimization model and transforms the three objective functions into the form of a minimax problem:

[0164]

[0165] Step 6: Design a multi-objective min-max differential evolution algorithm for solution according to the characteristics of the model: The present invention aims to solve a multi-objective min-max optimization problem. By combining the min-max differential evolution algorithm with the fast non-dominated sorting algorithm and the crowding distance algorithm, and using a penalty function to transform the constrained problem into an unconstrained problem, and improving the mutation strategy, a multi-objective min-max differential evolution algorithm is proposed. The algorithm flow chart is shown in Figure 5 ;

[0166] Step 7: The algorithm generates Pareto solutions, selects the optimal solution, and outputs the robust timetable.

[0167] Specific Embodiment 2: The difference between this embodiment and Specific Embodiment 1 is that the common stations described in Step 1 include transfer stations and non-transfer stations. Others are the same as Specific Embodiment 1.

[0168] Specific Embodiment 3: The difference between this embodiment and Specific Embodiment 1 or 2 is that the method for calculating the average passenger arrival rate of each station on each route in Step 4 is to screen the passenger boarding card swiping and code scanning data of each station during the control period, and take the mean value after summing to obtain the average passenger arrival rate of the station. Others are the same as Specific Embodiment 1 or 2.

[0169] Specific Embodiment 4: The difference between this embodiment and any one of Specific Embodiments 1 to 3 is that the following requirements should also be met for the constraint expressions (16) to (21) and (25) in the constraint part:

[0170]

[0171] t ∈ [T1, T2] (26).

[0172] Others are the same as any one of Specific Embodiments 1 to 3.

[0173] Specific Embodiment 5: The difference between this embodiment and Specific Embodiment 4 is that in Step 7, the optimal solution is selected from the perspective of the bus company or passengers to select a solution that conforms to their own interests. Others are the same as Specific Embodiment 4.

[0174] The present invention is verified by the following experiments:

[0175] Experiment 1: This experiment is a robust control method for multi-line coordination of dual-source trolleybuses, and is specifically carried out according to the following steps:

[0176] A network is formed by the dual-source trolleybus routes 101, 102, 103, and 106 in Beijing. Figure 6 is a schematic diagram of the upward direction of the dual-source trolleybus route. Figure 7It is a schematic diagram of the downward direction of the double-source trolleybus line. There are 37 common stations on the four lines, 13 common stations on three lines, and 24 common stations on two lines. Taking the morning peak period from 7:00 am to 9:00 am on December 20, 2021 as the control period, the initial timetable in Table 1 is optimized. The departure headway range of the line and the planned departure headway are shown in Table 2, and the number of vehicle trips in the original departure plan remains unchanged during the optimization process.

[0177] Table 1 Initial Timetable

[0178]

[0179] Table 2 Departure Headway Range of the Line during the Control Period

[0180]

[0181] In order to obtain the travel time between stations of the double-source trolleybus, 43,079 pieces of Automatic Vehicle Location (AVL) data during the period from 7:00 am to 9:00 am on 23 working days in the previous month are collected. After rounding, the uncertain data set of the travel time between stations is shown in Table 3. The upper and lower limit values of the travel time in the table are both integers, and the fluctuation step size is 1 minute. The unit in the brackets is minutes. On the left side of the brackets is the minimum travel time between adjacent stations, and on the right side of the brackets is the maximum travel time between the two stations.

[0182] Table 3 Travel Data between Stations of Each Line

[0183]

[0184] The double-source trolleybus is equipped with a GPS device and an automatic ticket selling system. When passengers get on and off the bus, they need to swipe the integrated circuit card or scan the QR code to record the number of passengers and the time when passengers arrive at or leave the station. Through the IC card and QR code data, the passenger boarding data during the control period on working days in the previous month is obtained, and the average passenger arrival rate of each station (excluding the first and last stations) on each route is calculated, as shown in Table 4.

[0185] Table 4 Passenger Arrival Rate γ (pax / min) of Each Station on Each Line during the Control Period

[0186]

[0187] Apply the algorithm to optimize the model and obtain the Pareto optimal frontier as Figure 8As shown in the figure. The decision maker needs to select the final solution from multiple Pareto optimal solutions. From the perspective of the bus company, the fleet size determines the vehicle acquisition cost. Therefore, the goal of the fleet size takes precedence over the goals of the number of collaborations and the deviation of headway. By comparing the Pareto optimal solutions, the solution with the smallest fleet size is selected as the optimal solution, and the robust timetable in Table 5 is obtained. The specific algorithm process is as follows:

[0188] Algorithm Design

[0189] The established model is a mixed integer non-linear programming model, which belongs to the Minimax optimization problem and aims to find a solution that performs well in the worst scenario. It is difficult to solve using mathematical analytical methods. The Minimax Differential Evolution (MMDE) algorithm, as an emerging algorithm improved from the differential evolution algorithm, avoids excessive search for the worst objective function of uncertain variables. In a single generation of evolution, the bottom-up strategy and the partial regeneration strategy are respectively adopted for decision variables and uncertain variables, enabling them to evolve simultaneously in the direction that meets their optimization goals. The present invention aims to solve the multi-objective Minimax optimization problem. Therefore, the MMDE algorithm is combined with the fast non-dominated sorting algorithm and the crowding distance algorithm, and the penalty function is used to transform the constrained problem into an unconstrained problem, and the mutation strategy is improved to propose the multi-objective Minimax differential evolution algorithm (MO-MMDE).

[0190] 1 Encoding and Initialization

[0191] As Figure 9 shown, each individual in the population includes a pair of solution and operation scenario. Therefore, the encoding of an individual is divided into the encoding of decision variables and uncertain variables, both of which adopt integer encoding. To reduce constraint limitations, the decision variable is transformed from the departure time to the headway as the gene position information of the individual, so that the headway constraints (16) and (17) are satisfied at the initialization stage. It should be noted that only the travel time in the uncertain variables is encoded in this paper, because in formula (3), the stop time changes with the headway of the station and cannot be directly encoded, but the stop time can be calculated by formula (3) in the algorithm.

[0192] Each individual is divided into two directions, up and down, and consists of the headways of all trips of each line within the control period. When the final solution is obtained, the departure timetable can be obtained by adding the obtained headway scheme to the starting time. The decision variables and uncertain variables are randomly encoded within their value ranges, thus completing the initialization of the individuals in the population.

[0193] 2 Fitness Function and Fast Non-dominated Sorting

[0194] Under the combination of driving time and stopping time of individuals in the population, the opposite number of the operation coordination times of the dual-source trolleybus fleet, the fleet size, and the deviation of the vehicle headway are calculated as the individual fitness function, as shown in Equation (27). The smaller the fitness value, the better the performance of the individual.

[0195]

[0196] The present invention incorporates a penalty function into the fast non-dominated sorting algorithm and sorts individuals according to the fitness values of individuals in the population and the number of constraint violations (see the next part). First, based on the fitness values of individuals, a preliminary sorting of individuals is obtained, and penalties are imposed on individuals that violate the constraints to increase their sorting, resulting in the final sorting of individuals, and a Pareto minimum heap (PMH) is constructed. The Pareto minimum heap is improved from the minimum heap (MH) in the MMDE algorithm. It arranges the sorted solution set according to the Pareto front rank. Assuming there are M Pareto front ranks in total, the solution set with the Pareto front rank of 1 is placed at the root node of the Pareto minimum heap. After sequential placement, the last node corresponds to the Pareto front solution set with the Pareto front rank of M. The main feature of the Pareto minimum heap is that individuals in the population are arranged from high to low according to non-dominated sorting, and each individual is located in a node, and the individual with the highest non-dominated sorting is placed on the root node.

[0197] 3 Penalty Function

[0198] The present invention uses the penalty function method to convert the problem with constraints into an unconstrained problem, and punishes infeasible solutions by increasing their non-dominated sorting to achieve intelligent search of the solution space. The penalty functions for the departure interval constraint are Formulas (28) and (29), the penalty functions for the pantograph catenary operation device constraint are Formulas (30) and (31), the penalty function for the power supply network sectional carrying capacity constraint is Formula (32), and the penalty functions for the energy consumption constraint of the derailment section are shown in Formulas (33) and (34). It should be noted that the departure interval constraints (16) and (17) have been satisfied in the population initialization stage, and the functions of the coordination constraints (19) and (20) are to count the coordination times, so the constraint penalties for these two types are not considered. Assuming that the penalty intensities for the above three types of constraint conditions are the same during the operation process, Equation (35) uses the parameter P r to represent the penalty status of the constraint conditions. Therefore, the final non-dominated sorting p' rank is shown in Equation (36).

[0199]

[0200] Pe3 = DK - Q1 (32)

[0201] Pe4 = 2s off -t off (33)

[0202] Pe5 = t off -3s off (34)

[0203]

[0204] 4 Multi - objective Bottom - lifting Strategy

[0205] The core idea of the multi - objective bottom - lifting strategy is to perform adaptive mutation, crossover, and comprehensive selection on uncertain variables, making them evolve in the direction of the maximum objective function and seeking the worst operating conditions. In each bottom - lifting, for the NF1 individuals in the root node, a total of K s ·NF1 updates of uncertain variables are performed. If the newly generated uncertain variable makes the individual objective function evolve in the increasing direction, then let this uncertain variable replace the root - node uncertain variable. The pseudo - code of the multi - objective bottom - lifting strategy is shown in Algorithm 3. The improved differential evolution operation is as follows.

[0206] (1) The DE / rand / 1 mutation strategy is improved. In Equation (37), the individual with the largest crowding distance in the root node is used as the optimal individual to guide the search direction, accelerating the convergence speed of the algorithm. Let each parent have the opportunity to enter the offspring, and at the same time randomly select different non - parent individuals from the population to calculate the difference vector, maintaining the diversity of the population. Among them, r ∈ [0,1] is the greedy factor.

[0207] (2) Adaptive parameters are set. Formula (38) indicates that the adaptive parameters are adjusted with the number of evolution generations. In the initial stage, to accelerate the convergence speed and emphasize global search, the mutation operator F and the crossover operator CR are larger, and the greedy factor r is smaller; in the later stage, to obtain better distribution and perform local search at the optimal point to avoid the destruction of the optimal solution, the values of F and CR should be reduced, and the value of r should be increased. Among them, G represents the maximum number of evolution generations, and g represents the current number of evolution generations.

[0208] (3) A comprehensive selection strategy is proposed. According to the priorities of the fitness, penalty function, and crowding distance of two individuals, the advantages and disadvantages of individuals are comprehensively compared, which is conducive to screening out potential optimal solutions when two individuals do not dominate each other.

[0209]

[0210]

[0211] Algorithm 3

[0212] Pseudo - code of the multi - objective bottom - lifting strategy

[0213]

[0214] 5 Multi - objective Partial Regeneration Strategy

[0215] The core idea of the multi-objective partial regeneration strategy is to optimize decision variables under the worst operating conditions formed by the bottom-up strategy and find the optimal solution. First, assign the decision variable values of the first T individuals with small fitness values in the Pareto minimum heap to the last T individuals in the population, enabling them to inherit the elite decision variables, and perform mutation and crossover on the elite decision variables. Randomly generate the uncertain variables within the last T individuals to increase the diversity of the uncertain variables. This strategy performs DE / current / 1 mutation and binomial crossover on the decision variables. The settings of the adaptive parameters are shown in Equation (38). The pseudocode of the multi-objective bottom-up strategy is shown in Algorithm 4.

[0216] Algorithm 4

[0217] Pseudocode of the multi-objective partial regeneration strategy

[0218]

[0219]

[0220] 6 Overall algorithm flow

[0221] The pseudocode of the MO-MMDE algorithm is shown in Algorithm 2. First, set the parameters and initialize the population, and calculate the individual fitness and penalty function. At the beginning of each generation, perform a fast non-dominated sorting on the current population to construct a Pareto minimum heap. Based on the constructed minimum heap, execute the multi-objective bottom-up scheme to update the uncertain variables, and continuously extract the individuals in the root node from the Pareto minimum heap as the Pareto optimal solutions. Finally, update the decision variables using the partial regeneration strategy, and then continue the next generation of evolution. When the maximum number of evolution generations G is reached, the optimization process terminates, and the Pareto optimal solution set is output, and the algorithm ends.

[0222] Algorithm 2

[0223] Pseudocode of the MO-MMME algorithm

[0224]

[0225] Table 5 Robust timetable

[0226]

[0227] To explore the performance of the original planned timetable and the robust timetable under the worst operating conditions, input the two timetables as fixed parameters of the algorithm, keep the other parameters unchanged, and only perform the bottom-up strategy on the uncertain variables to update the uncertain variables under the condition that the decision variables are determined, so as to seek the worst operating conditions of the timetable, and thus compare the robustness of the two timetables to adapt to the worst operating conditions.

[0228] Figure 10The number of collaborations at stations under the worst operating conditions using the initial timetable and the robust timetable is given. Figure 10 (a) shows that when using the robust timetable in the upward direction, the number of collaborations at each station is higher than that in the initial timetable. The total number of collaborations increases from 142 to 168, an increase of 18.31%. Among them, the optimization effect of the common stations b6 - b11 on the three lines is relatively significant. Figure 10 (b) shows that when using the robust timetable in the downward direction, the number of collaborations at most stations is significantly higher than that in the initial timetable. The total number of collaborations increases from 147 to 158, an increase of 7.49%.

[0229] Table 6 lists the headway deviations at each station in the upward and downward directions under the worst operating conditions. Compared with the original timetable, the headway deviations under the robust timetable change more smoothly and are always smaller than the original timetable deviations. After applying the robust timetable, the average deviation in the upward direction decreases from 2.531 min to 2.287 min, an optimization of 9.64%; the average deviation in the downward direction decreases from 1.478 min to 1.218 min, an optimization of 17.59%.

[0230] Table 6 Headway Deviations at Each Station in the Upward and Downward Directions

[0231]

[0232] Combining the collaboration performance and headway deviation performance under the worst operating conditions, the tandem congestion conditions of vehicles at common stations, automatic catchers, and line combiners are further explored. Tandem includes single - line tandem and multi - line tandem, which not only affects the service regularity of dual - source trolleybuses but also leads to the triggering of power outages in the overhead line network and increases the risk of vehicle breakdowns. The reason for tandem is that the headway of vehicles in the line network at traffic nodes is very small. Through actual observation, tandem is likely to occur when the arrival interval of dual - source trolleybuses at stations is less than 30 s. Therefore, the present invention assumes that if the arrival interval of a vehicle at a station is less than 30 s, it can be regarded as a tandem phenomenon, and an arrival interval less than 10 s at the line combiner and less than 20 s at the automatic catcher is also considered a tandem.

[0233] Table 7 lists the number of train bunching at stations, automatic catchers, and line combiners under the worst operating conditions. Under the robust timetable, the number of train bunching at all three types of traffic nodes is less than that under the initial timetable, reducing the risk of queuing congestion and vehicle breakdown to a certain extent. This is also an indirect manifestation of the robust timetable in achieving vehicle operation regularity and operation coordination. Specifically, the optimization effects in the up and down directions are roughly equivalent. The number of train bunching at common stations, automatic catchers, and line combiners in the up direction has decreased by 14.41%, 35.42%, and 29.51% respectively; the number of train bunching at common stations, automatic catchers, and line combiners in the down direction has decreased by 11.58%, 29.09%, and 33.33% respectively.

[0234] Number of train bunching at each traffic node in Table 7

[0235]

[0236] To verify that the robust timetable also has good performance in practice, the two types of timetables are placed under uncertain parameters, and the target output range and constraint violation degree are compared. Based on the travel time dataset, the Monte Carlo method is used to randomly sample the travel time 3000 times, obtaining the output sets of the three targets, which are presented in turn in Figure 11 the box plots. On each box, the red line is the median, the edges of the box are the 25th and 75th percentiles, the whiskers extend to the maximum and minimum data points, and the outliers are marked with single points. In Figure 11 (a), the median of the coordination times target under the robust timetable is improved by 6.43% compared to the initial timetable, and the maximum value is improved by 7.94%. In Figure 11 (b), the median and maximum values of the fleet size target are reduced by 2.67% and 7.59% respectively compared to the initial timetable. In Figure 11 (c), the median and maximum values of the headway deviation are reduced by 4.65% and 7.18% respectively. It can be seen that under the condition of travel time fluctuations, the robust timetable has more obvious advantages than the initial timetable in both average and worst performances. Moreover, in some extreme cases, the robust timetable can obtain extremely excellent minimum values. For example, in the first target, the maximum value of the coordination times reaches 432 times, and in the second target, the minimum value of the fleet size is only 70. In addition, Figure 11 (b) shows that the output of the fleet size under the robust timetable is more concentrated, which verifies that the robust timetable can make the output of the target more stable in a dynamic environment.

[0237] Taking the power supply network section carrying capacity constraint as an example to analyze the degree of constraint violation, when the number of vehicles in a section is greater than 6, there may be a risk of vehicles breaking down. Select the k1 section in the upstream direction and the k2 section in the downstream direction at the line intersection as the control objects, because there are more vehicles concentrated on the section after the line intersection, and the risk of breakdown increases. Using the Monte Carlo method to simulate 3000 times, a frequency distribution histogram of the maximum number of vehicles on the power supply network section for the two timetables is obtained, as shown in Figure 12 . Figure 12 (a), the maximum number of vehicles in the k1 section under the two timetables did not exceed 6. This may be because the fluctuation range of the arrival time of vehicles in the upstream direction is relatively large, and the possibility of a large number of vehicles gathering in the k1 section at the same time is small. In Figure 12 (b), there are 129 scenarios with more than 6 vehicles in the k2 section under the initial timetable, and the proportion of scenarios violating the constraint is 4.3%. While there are only 43 scenarios with more than 6 vehicles under the robust timetable, and the proportion of scenarios violating the constraint is 1.43%. This shows that the degree of violation of the section carrying capacity constraint is smaller under the robust timetable, and the vehicle operation condition is safer and more reliable.

[0238] The present invention can help bus companies compile a more robust coordinated timetable under the condition of fluctuations in driving time and stop time. Compared with the initial timetable, the target output of the robust timetable output by the model is more stable under the worst operating conditions, reducing the risk of bunching. Using the Monte Carlo method to simulate the simulation environment, the optimization effects of 6.43%, 2.67% and 4.65% are respectively achieved for the number of coordination times, fleet size and headway deviation. Therefore, the present invention can effectively reduce the impact of the dynamic environment on the coordination and service regularity of vehicle operation and improve the robustness of the static scheduling plan.

Claims

1. A robust control method for multi-line coordination of dual-source trolleybuses, characterized in that The robust control method for multi-line coordination of dual-source trolleybuses is carried out in the following steps: Step 1: Select the dual-source trolleybus line to build a line network, and establish the attribute set of each traffic node in the network to store the line and traffic node information; The attribute set of each traffic node includes the starting station, the terminal station, the common station, the non-common station, the number and location of automatic catchers, the number and location of closing devices, the number and location of power supply network segments, and the distribution and length of disconnected lines. Common sites include transfer sites and non-transfer sites; Step 2: According to the time period to be controlled, establish a train operation status set to store train operation information; The train operation status includes the number of up and down train departures on each line during the control period, the vehicle travel path, the departure frequency range, the planned departure interval, the initial departure schedule and the arrival time; Step 3: Collect the AVL data during the control period in the previous month, calculate the travel time of the adjacent sites, round it off to the nearest integer in minutes, and include it in the travel time set of the adjacent sites, thus obtaining an integer set of the travel time of the adjacent sites with upper and lower bounds; Step 4: Using the IC card and QR code data on the dual-source trolleybus, collect the boarding passenger data of each station during the control period in the previous month, and calculate the average passenger arrival rate of each station on each route; Step 5: Focus on the operating characteristics of dual-source trolleybuses and build a robust optimization model for multi-line coordination of dual-source trolleybus timetables:

1. Determine the objective function 1) Maximize the number of vehicle collaborations Passengers choose to transfer at the last transferable station, and the remaining common stations are regarded as non-transfer stations; coordination time windows are set for transfer stations and non-transfer stations respectively, and the total number of coordination times is finally added up; The shortest interval w between vehicles arriving at the transfer station b Passengers have enough time to transfer, and the longest interval W b The waiting time for transfer is guaranteed not to be too long. If the time difference between train number n of line l and train number m of line j arriving at transfer station b is within the time window [w b ,W b ], the two trains are considered as coordinated transfer trains, and the binary variable It is recorded as 1, otherwise it is recorded as 0; represents the time when the nth vehicle on line l arrives at station b, represents the time when the mth vehicle on route j arrives at station b; In order to avoid vehicle congestion at non-transfer stations, it is also necessary to set an arrival time window, with the shortest interval v b , the longest interval V b , if the time difference between train number n of line l and train number m of line j arriving at non-transfer station b is greater than v b , and is less than V b , then the two trains are regarded as coordinated trains entering the station, and the binary variable in formula (2) is used Determine whether the trains enter the station in a coordinated manner; Formula (3) represents the number of vehicle coordination between the upward transfer station and the non-transfer station, and the 1 on the superscript represents the upward direction; Formula (4) represents the number of vehicle coordination between the downward transfer station and the non-transfer station, and the 2 on the superscript represents the downward direction; Formula (5) represents the goal of maximizing the total number of coordination; maxF1=F 1 +F 2 (5) 2) Minimize the size of the fleet The minimum number of vehicles required to complete all trips is equal to the sum of the maximum deficit values ​​of each station. The first and last stations of the line are taken as the dual-source trolleybus stations. The maximum deficit function is calculated for each station and summed to obtain the minimum fleet size. Formulas (6)-(8) represent the process of calculating the fleet size using the deficit function, where T1 and T2 are the start and end times of the control period. Indicates that at time t, the nth train of line l has departed from station d; SD l,t represents the number of vehicles dispatched from station d up to time t; Indicates that at time t, the nth train of line l has arrived at station d, ED l,t represents the number of vehicles arriving at station d by time t, max(SD l,t -ED l,t ) represents the maximum deficit function of station d; 3) Minimize the headway deviation The present invention selects two types of nodes prone to congestion, common sites and automatic catchers, to analyze the headway deviation; the line departure frequency is determined in the frequency setting stage, and the planned headway is calculated. h l,n,b is the headway time of the vehicle at station b, h l,n,a is the headway of the vehicle at the automatic catcher a; Formula (9) represents the average headway deviation of all stations; Formula (10) represents the average headway deviation at all automatic catchers; Formula (11) expresses the goal of minimizing the average headway deviation, minF3=F a +F b (11) 2. The constraints include departure interval constraints, operating device constraints, power supply network segment carrying capacity constraints and off-line section speed constraints; 3. Determine the integration model In order to reduce the impact of the fluctuation of the travel time and stop time of dual-source trolleybuses on the interests of bus companies and passengers, a timetable that can perform well even in a dynamic environment is sought, a multi-objective robust optimization model is established, and the three objective functions are transformed into the form of a minimum-maximum problem: Step 6: Based on the vehicle driving constraints, the multi-objective minimum-maximum differential evolution algorithm is used to solve the minimum-maximum problem of the objective function transformation: it is required to solve the multi-objective minimum-maximum optimization problem, combine the minimum-maximum differential evolution algorithm with the fast non-dominated sorting algorithm and the crowding distance algorithm, use the penalty function to transform the constrained problem into an unconstrained problem, improve the mutation strategy, and propose a multi-objective minimum-maximum differential evolution algorithm; Step 7: The algorithm generates Pareto solutions, selects the optimal solution, and outputs a robust schedule.

2. A method for robust control of dual-source trolleybus multi-line coordination according to claim 1, characterized in that The method for calculating the average passenger arrival rate at each station on each route in step 4 is to screen the card and code swiping data of passengers boarding the bus at each station during the control period, add them up and take the average value to obtain the average passenger arrival rate of the station.

3. A method for robust control of dual-source trolleybus multi-line coordination according to claim 1, characterized in that In the robust optimization model of multi-line coordination of dual-source trolleybus timetable constructed in step 5, the time when the nth vehicle on line l arrives at station b is as follows: in The stop time at the station.

4. A method for robust control of dual-source trolleybus multi-line coordination according to claim 3, characterized in that The stop time at the station is shown in formula (12): Among them, t0 is the time required for the vehicle to open and close the door, γ lb is the passenger arrival rate at station b on line l, β is the average boarding time of each passenger; is the stop time at station b.

5. A method for robust control of dual-source trolleybus multi-line coordination according to claim 4, characterized in that The departure interval constraint is: and are the minimum departure interval and the maximum departure interval of line l respectively; the departure time is T1 is the start time of the control period, and T2 is the end time of the control period; is the time when the first vehicle is dispatched on route l in direction r.

6. A method for robust control of dual-source trolleybus multi-line coordination according to claim 5, characterized in that The operating device constraints are: Constraint (16) indicates that the dual-source trolleybus needs to stop and raise the bar under the automatic catcher a. To avoid congestion caused by the simultaneous arrival of subsequent vehicles, a minimum arrival interval w is set. a ; Constraint (17) indicates that in order to avoid the two-source trolleybuses arriving at the combiner c at the same time, a minimum arrival interval w is also required. c ; 7. A method for robust control of dual-source trolleybus multi-line coordination according to claim 6, characterized in that The power supply network segment carrying capacity constraint is: Constraint (18) requires that the maximum number of vehicles DK in each segment is less than the maximum number of vehicles Q1 that the segment can carry. The value of Q1 should take into account the charging and air conditioning power of the vehicle, and the ratio of the number of controlled routes to the actual number of routes in the section. DK≤Q1 (18) Formulas (19)-(21) use the inverse difference function to express the maximum number of vehicles DK in the power supply network segment k, where sK l,n,t =1 means that at time t, train number n on line l has left segment k, eK l,n,t =1 means that train number n of line l has arrived at segment k; SK l,t With EK l,t They represent the number of vehicles that have left and arrived at segment k by time t respectively; 8. A method for robust control of dual-source trolleybus multi-line coordination according to claim 7, characterized in that The speed constraint of the off-line section is: Average speed of vehicles on the off-line section In the range of 20km / h to 30km / h, see formula (22): 。 9. A method for robust control of dual-source trolleybus multi-line coordination according to claim 8, characterized in that In the constraint part, the constraint equations (13) to (18) and equation (22) must also meet the following requirements: t∈[T1,T2](23).

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