Virtual marshalling and regenerative braking energy coordinated train timetable optimization method and system

Abstract

This invention provides a method and system for optimizing train timetables using virtual train formation and regenerative braking energy, relating to the field of data processing technology. The method includes: calculating the time overlap area of ​​the running curves of traction and braking trains within the same power supply zone based on an updated passenger flow allocation scheme and the new solution to quantify the recoverable amount of regenerative braking energy, thus obtaining a quantification result; calculating the traction energy consumption in operating costs based on the quantification result to obtain a performance evaluation value for the new solution; and determining whether to accept the new solution based on the performance evaluation value of the new solution and the performance evaluation value of the current solution, thereby updating the current solution. This invention enhances the opportunity for energy matching between trains.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method and system for optimizing train timetables in conjunction with virtual train formation and regenerative braking energy. Background Technology

[0002] Urban rail transit systems, as the backbone of urban public transportation, possess advantages such as large capacity, high efficiency, and green, low-carbon operation. However, with accelerated urbanization and continuous passenger growth, these systems face severe challenges in controlling operating costs, managing energy consumption, and improving service quality. Traction energy consumption often accounts for over 50% of total operating costs, becoming a key factor affecting the system's economic viability. Simultaneously, the uneven spatial and temporal distribution of passenger flow leads to inefficient capacity allocation, with localized congestion and capacity waste coexisting, resulting in prolonged passenger waiting times and severely impacting service levels.

[0003] To address these issues, existing research mainly focuses on two directions: first, demand-oriented timetable optimization, which dynamically adjusts train capacity configuration through virtual train formations, skip-station operations, and combinations of express and local trains to shorten passenger waiting and travel times; second, energy-saving timetable optimization, which improves the utilization efficiency of regenerative braking energy and reduces traction energy consumption by optimizing train arrival and departure times and speed curves. In recent years, some scholars have attempted to combine these two approaches, exploring energy-saving optimization under virtual train formation conditions, and have initially achieved the synergy between precise capacity allocation and energy consumption control.

[0004] However, existing research still has significant shortcomings: most methods treat virtual train formation strategies and regenerative braking energy recovery as independent problems, lacking system modeling and collaborative optimization of the inherent coupling mechanism between the two. Dynamic adjustments to the number of train formations not only affect the train's own traction / braking performance and stopping time, but also alter the spatiotemporal relationships between trains, thus impacting the transmission conditions and utilization efficiency of regenerative braking energy. Furthermore, traditional optimization models often neglect the dual impact of speed curve selection on energy consumption and running time, making it difficult to achieve overall system energy efficiency improvements while ensuring service quality. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method and system for optimizing train timetables in conjunction with virtual train formation and regenerative braking energy. Under the premise of meeting operational safety, service quality and system constraints, the method and system achieve integrated and coordinated optimization of train formation configuration, departure time, speed curve and energy transmission strategy, so as to achieve a multi-objective balance between operating cost, energy consumption and service quality.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0007] Firstly, a method for optimizing train timetables using virtual train formation and regenerative braking energy, the method comprising:

[0008] Step 1: Obtain the initial train formation configuration, initial timetable, and passenger flow allocation scheme as the initial current solution;

[0009] Step 2: Based on the initial current solution, calculate the value of a multi-objective function that includes operating costs, passenger waiting time, and passenger travel time;

[0010] Step 3: Perturb the current solution to generate a new solution that includes the dynamically adjusted number of train formations, the selected train speed curve, and the adjusted train departure time.

[0011] Step 4: Based on the train formation quantity, speed curve and departure time in the new solution, and combined with the constraints of train running time and station dwell time, generate a new full-journey train timetable;

[0012] Step 5: Based on the new full-journey train timetable, redistribute passenger flow to generate an updated passenger flow allocation scheme corresponding to the new timetable;

[0013] Step 6: Based on the updated passenger flow allocation scheme and the new solution, calculate the time overlap area of ​​the running curves of traction trains and braking trains within the same power supply area to quantify the recoverable amount of regenerative braking energy, so as to obtain the quantification result; calculate the traction energy consumption in the operating cost based on the quantification result, so as to obtain the performance evaluation value of the new solution; based on the performance evaluation value of the new solution and the performance evaluation value of the current solution, determine whether to accept the new solution, so as to update the current solution.

[0014] Step 7: Repeat steps 3 to 6 until the preset termination condition is met, and finally output the current solution as the collaboratively optimized train timetable.

[0015] Secondly, the virtual train formation and regenerative braking energy coordinated train timetable optimization system includes:

[0016] The acquisition module is used to acquire the initial train formation configuration, initial timetable, and passenger flow allocation scheme as the initial current solution;

[0017] The calculation module is used to calculate a multi-objective function value including operating costs, passenger waiting time, and passenger travel time based on the initial current solution; to perform a perturbation operation on the current solution to generate a new solution including dynamically adjusted train formation number, selected train speed curve, and adjusted train departure time; and to generate a new full-journey train timetable based on the train formation number, speed curve, and departure time in the new solution, combined with train travel time and station dwell time constraints.

[0018] The allocation module is used to redistribute passenger flow based on the new full-journey train timetable and generate an updated passenger flow allocation scheme corresponding to the new timetable.

[0019] The update module is used to calculate the recoverable amount of regenerative braking energy by quantifying the time overlap area of ​​the running curves of traction trains and braking trains within the same power supply area based on the updated passenger flow allocation scheme and the new solution, so as to obtain the quantification result; calculate the traction energy consumption in the operating cost based on the quantification result, so as to obtain the performance evaluation value of the new solution; determine whether to accept the new solution based on the performance evaluation value of the new solution and the performance evaluation value of the current solution, so as to update the current solution, until the preset termination condition is met, and finally output the obtained current solution as the collaboratively optimized train timetable.

[0020] Thirdly, a computing device includes:

[0021] One or more processors;

[0022] A storage device for storing one or more programs that, when executed by one or more processors, cause the one or more processors to implement the method.

[0023] Fourthly, a computer-readable storage medium storing a program that, when executed by a processor, implements the method.

[0024] The above-described solution of the present invention has at least the following beneficial effects:

[0025] This invention is the first to deeply integrate and optimize virtual train formation strategy, multi-level speed curve selection and regenerative braking energy utilization. By constructing a unified multi-objective optimization model, it simultaneously decides on the number of train formations, departure time, speed curve and energy transmission strategy, overcoming the limitation of traditional methods that treat these factors in isolation.

[0026] By accurately quantifying the time overlap area of ​​traction and braking train operation curves within the same power supply area, this invention can precisely assess and maximize the recoverable amount of regenerative braking energy. Combined with the dynamic adjustment of train spatiotemporal distribution through virtual train formation, it enhances the opportunity for energy matching between trains. The optimized scheme of this invention achieves effective management of operating costs by reducing traction energy consumption costs, optimizing train formation configuration to reduce fixed costs, and reasonably controlling train formation adjustment costs.

[0027] The virtual train formation mechanism can flexibly adjust the number of train formations according to the spatiotemporal dynamic fluctuations of passenger flow. This dynamic capacity allocation capability effectively solves the contradiction between insufficient capacity during peak periods and wasted capacity during off-peak periods. While ensuring service levels, it avoids unnecessary energy consumption and improves the level of operational refinement. Attached Figure Description

[0028] Figure 1 This is a circuit diagram of the present invention.

[0029] Figure 2 This is a schematic diagram of the power supply and RBE utilization of the present invention.

[0030] Figure 3 This is a schematic diagram of the train speed curve of the present invention.

[0031] Figure 4 This is a schematic diagram of the simulated annealing algorithm of the present invention.

[0032] Figure 5 This is a schematic diagram of the circuit information of the present invention.

[0033] Figure 6 This is a schematic diagram of passenger demand distribution according to the present invention.

[0034] Figure 7 This is the original train schedule of the present invention.

[0035] Figure 8 This is the optimized running diagram of the present invention. Detailed Implementation

[0036] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0037] like Figure 1 As shown, embodiments of the present invention propose a method for optimizing train timetables using virtual formation and regenerative braking energy, the method comprising the following steps:

[0038] Step 1: Obtain the initial train formation configuration, initial timetable, and passenger flow allocation scheme as the initial current solution;

[0039] Step 2: Based on the initial current solution, calculate the value of a multi-objective function that includes operating costs, passenger waiting time, and passenger travel time;

[0040] Step 3: Perturb the current solution to generate a new solution that includes the dynamically adjusted number of train formations, the selected train speed curve, and the adjusted train departure time.

[0041] Step 4: Based on the train formation quantity, speed curve and departure time in the new solution, and combined with the constraints of train running time and station dwell time, generate a new full-journey train timetable;

[0042] Step 5: Based on the new full-journey train timetable, redistribute passenger flow to generate an updated passenger flow allocation scheme corresponding to the new timetable;

[0043] Step 6: Based on the updated passenger flow allocation scheme and the new solution, calculate the time overlap area of ​​the running curves of traction trains and braking trains within the same power supply area to quantify the recoverable amount of regenerative braking energy, so as to obtain the quantification result; calculate the traction energy consumption in the operating cost based on the quantification result, so as to obtain the performance evaluation value of the new solution; based on the performance evaluation value of the new solution and the performance evaluation value of the current solution, determine whether to accept the new solution, so as to update the current solution.

[0044] Step 7: Repeat steps 3 to 6 until the preset termination condition is met, and finally output the current solution as the collaboratively optimized train timetable.

[0045] In this embodiment of the invention, passenger waiting time and travel time are optimized to reduce travel time and congestion, thereby improving travel satisfaction. Combined with quantitative analysis of regenerative braking energy recovery, traction energy consumption is reduced. By dynamically adjusting the number of train formations to match passenger flow demand, capacity waste is avoided, resulting in a double reduction in operating costs. The time overlap between traction and braking trains within the same power supply area is quantified to maximize the recoverable amount of regenerative braking energy, achieving energy saving and efficiency improvement. Dynamically adjusting train formations, speed curves, and departure times, combined with passenger flow redistribution, makes the timetable more closely reflect actual passenger flow changes, improving the accuracy and adaptability of operational scheduling. This comprehensively balances operating costs and passenger service quality, avoiding the limitations of single-objective optimization and achieving optimal overall system efficiency.

[0046] In a preferred embodiment of the present invention, step 1, obtaining the initial train formation configuration, initial timetable, and passenger flow allocation scheme as the initial current solution, includes:

[0047] Based on the existing operating vehicle parameters of the line (such as using Type B cars), determine the core physical and operational parameters of a single car, such as the train type (such as Type B cars), the mass of a single car, and the maximum passenger capacity of a single car; determine the smallest grouping unit composition (such as each grouping unit contains 3 cars), and set the initial grouping unit selection range (such as 1 unit / 3 cars, 2 units / 6 cars) to avoid exceeding the depot's decoupling / reconnection capacity.

[0048] Based on the historical peak-hour capacity demand of the line (such as the peak passenger flow during the study period [7:00-9:30]), an initial unified train formation scheme is determined, referring to existing operating strategies (such as initially setting the trains to stop at every station with 2 units), to ensure that the initial train formation can cover 70%-80% of the historical peak passenger flow, and to avoid serious shortage or waste of initial capacity; record the initial train formation adjustment constraint parameters, such as train formation adjustment time, fixed cost coefficient of a single carriage, and adjustment cost.

[0049] Confirm that the initial train formation meets the line dynamics and power supply constraints:

[0050] The initial total mass of the train formation (carriage mass and estimated passenger mass) must match the maximum traction and braking force of the line to avoid exceeding the upper limit of the train's traction / braking performance; the traction power requirement of the initial train formation must be within the capacity of the power supply area (if the total traction power of the initial train formation operating simultaneously in the same power supply area does not exceed the rated power of the power supply arm).

[0051] The initial timetable needs to be generated based on the existing operation plan of the line, the physical characteristics of the section, and safety constraints to ensure that the initial timetable meets the basic operation rules of stopping at every station. The specific steps are as follows:

[0052] Determine the time frame for the optimization study: Based on peak passenger flow periods (e.g., the morning peak period [7:00-9:30]), determine the train running direction within the study period; set the initial total number of trains, referencing existing operating frequencies (e.g., 25 trains each way), ensuring the initial number of trains can cover the basic passenger flow demand within the study period; adopt the line's conventional stopping pattern (e.g., stopping at every station initially), without considering complex strategies such as skipping stations, simplifying the complexity of the initial solution; calculate the initial running time for each section based on the line section length (e.g., a total line length of 13.413km, 14 stations) and the default speed curve of the existing ATO system (e.g., standard speed curve), and ensure that the minimum / maximum running time constraints for each section are met; set the initial stopping time for each station based on historical passenger boarding and alighting times (e.g., 30s for off-peak stations, 60s for peak stations), and ensure that the minimum / maximum stopping time constraints for each station are met; set the initial headway to a fixed value, and ensure that the minimum / maximum headway constraints are met to ensure safe train tracking.

[0053] Taking the starting point of the study period (e.g., 7:00) as the departure time of the first train going up, based on the above-mentioned interval travel time and stop time, the arrival and departure times of each train at each station are calculated in turn; the same applies to the down train (e.g., 7:02 as the departure time of the first train), and finally an initial full timetable is formed that includes train number, direction, arrival and departure times at each station, interval travel time and stop time.

[0054] The initial passenger flow allocation plan needs to be based on real passenger travel data, matching the initial timetable according to the first-come-first-served principle to ensure a basic match between the initial passenger flow and train capacity. The specific steps are as follows:

[0055] The core data sources are historical data from the line's AFC (Automatic Fare Collection) system (such as passenger entry time, entry station, and exit station (OD pair) during the study period [7:00-9:30]) and passenger flow statistics from station gates; passenger flow completion is achieved by using the historical average passenger flow for missing parts of the AFC data (such as passengers without cards) to generate a passenger flow demand matrix for each time period and OD pair within the study period.

[0056] Constructing the initial OD matrix and allocation rules:

[0057] The OD matrix is ​​a four-dimensional OD matrix constructed using 5-minute time slices, representing departure time, origin station, destination station, and passenger number (e.g., passenger demand distribution). It adopts a first-come, first-served principle, meaning that passengers are assigned to the earliest train that arrives at the station and can directly reach the destination station based on their arrival time. If a train has reached its maximum passenger capacity (initial total capacity of the formation, such as 1200 people for 2 units / 6 cars), subsequent passengers will be deferred to the next train in the same direction. Based on the train's arrival and departure times at stations in the initial timetable, passengers within the corresponding time slices are assigned to trains. The number of passengers boarding, alighting, and remaining passengers on each train at each station is recorded to ensure that the number of passengers boarding at any station does not exceed the train's available capacity. Finally, the initial passenger flow allocation scheme is output, consisting of train number, station, number of passengers boarding, number of passengers alighting, and total number of passengers on board. The initial train formation configuration (including train type, number of formations, and cost parameters), the initial train timetable (including arrival and departure times at each station, and running / stopping times), and the initial passenger flow allocation scheme (including passenger flow data for each train and station) are integrated into a structured dataset, which serves as the initial current solution for algorithm iteration, ensuring that subsequent steps can directly call this solution to calculate the multi-objective function value.

[0058] In a preferred embodiment of the present invention, step 2, based on the initial current solution, calculates a multi-objective function value including operating costs, passenger waiting time, and passenger travel time, including:

[0059] Step 21: Based on the train formation quantity and speed curve in the initial current solution, calculate the traction energy consumption of each train within the operating section, including:

[0060] Traction energy consumption is a core component of operating costs. It needs to be calculated by combining train formation quality, speed curve conditions (traction / cruising / braking), and regenerative braking energy recovery, and then summed up to achieve the total energy consumption logic. Specific steps are as follows:

[0061] Extracting basic calculation parameters: Retrieving core parameters from the initial current solution and parameter library:

[0062] The number of train formations nc in each section (dynamic formation value in the initial current solution, such as 2 units / 6 cars), and the mass m of a single car. c =1.99×105 kg, maximum passenger capacity per carriage C max = 200 people / train; related to passenger flow, i.e., the total number of passengers n on the train at each station. in (Initial passenger flow allocation plan), individual passenger mass m p =60kg; energy consumption related, i.e., traction power conversion rate η t =80%, Regenerative Braking Energy Conversion Efficiency η r =80%, unit energy price c energy = 0.8 yuan / kWh; speed curve related, i.e., the traction phase time t of the selected speed curve in each interval. t Cruise phase time t c Braking phase time t r ; Traction phase speed v t Cruise phase speed v c ; Traction phase acceleration a t Deceleration a during braking phase b (Initial current solution uses preset velocity curve parameters, such as the parameters corresponding to the standard velocity curve).

[0063] The total mass of the train, including the weight of the carriages and the mass of the passengers, is calculated using the dynamic constraint formula: m total =n c ×m c +n in ×m p (Example: When there are 6 carriages and 100 passengers, m) total = 6 × 1.99 × 10 5 +100×60=1.194×10 6 +6×10 3 =1.2×10 6 kg); Calculating energy consumption during traction and cruise phases: Traction energy consumption consists of traction phase energy consumption and cruise phase energy consumption, and the traction force and power for each phase must be calculated first:

[0064] Traction force F during traction phase t To overcome line resistance and acceleration resistance, according to the dynamic formula:

[0065] F t =m total ×(a t +g×sinθ+f×v t ), where g = 9.8 m / s 2 Let f be the acceleration due to gravity, θ be the gradient angle of the track, and f = 1.36 × 10⁻⁶. -4 Line resistance coefficient; traction stage power P t Considering power conversion efficiency, the formula is: P t =(F t ×vt ) / η t， Unit: W, needs to be converted to kW, i.e., divide by 1000; Traction phase energy consumption E t E t =P t ×t t / 3600, unit: kWh, dividing by 3600 converts seconds to hours;

[0066] Cruise phase traction F c Overcoming only the track resistance (uniform speed, acceleration resistance is 0), the formula is:

[0067] F c =m total ×(g×sinθ+f×v c );

[0068] Cruise phase power P c P c =F c ×v c No need to divide by η t There is no additional power loss during the cruise phase.

[0069] Cruise phase energy consumption E c E c =P c ×t c / 3600, unit: kWh;

[0070] Total energy consumption E for single-section traction / cruising tc =E t +E c .

[0071] The regenerative braking energy recoverable amount needs to be calculated by deducting conversion losses from the regenerative energy generated during the braking phase. The formula is: E r =(F b ×v b ×t r ×η r ) / 3600, where F b For braking force, press F. b =m total ×a b Calculate; v b The average speed during the braking phase is taken from the speed curve parameters.

[0072] Net traction energy consumption is calculated as the total traction / cruising energy consumption minus the recoverable regenerative braking energy, i.e.: E net =E tc -E r (If E) r >E tc Then E net=0, indicating that regenerated energy completely offsets traction energy consumption); finally, sum up the E values ​​of each train across all operating sections. net The total traction energy consumption of a single train is obtained, and then the traction energy consumption of all trains is summed up.

[0073] Step 22, based on the passenger flow allocation scheme in the initial current solution, calculate the waiting time of passengers on the platform and the travel time on the train, including:

[0074] Timetable data, i.e., the arrival time t of each train at each station. arr Departure time t dep Initial current solution timetable; passenger flow data, i.e., time slices (e.g., 5 minutes / slice), OD pairs (originating station - destination station) passenger entry time t parr Number of passengers n p Capacity data, i.e., the number of passengers (n) remaining in each train at each station. empty Initial passenger flow allocation plan; the total passenger waiting time is calculated based on a first-come, first-served principle. The passenger waiting time is the train departure time minus the passenger arrival time, and the total waiting time is the sum of the waiting times of all passengers.

[0075] Single passenger waiting time: t waitp =t dep -t parr (If t) parr >t dep If the passenger is delayed, they will be transferred to the next train. waitp Press the button on a train t dep (Calculation); total waiting time within the time slice, T waitslice =sum(n p ×t waitp ), n p The number of passengers assigned to this train within this slice; Total passenger waiting time: T wait =sum(T) waitslice This section summarizes the waiting times for all time slices and all stations, in minutes. Seconds need to be converted to minutes by dividing by 60. The total passenger travel time is calculated as the train's arrival time at the destination station minus its departure time. The total travel time is the sum of all passenger travel times.

[0076] Single passenger travel time: t tripp =t arrdest -t deporigin , t arrdest t is the time it takes for the train to reach the passenger's destination station. deporigin The time when the train departs from the passenger's departure station; OD to total travel time: T tripod =sum(n p ×t tripp ), np The number of passengers for this OD pair; Total passenger travel time: T trip =sum(T) tripod Summarize the travel times of all OD pairs, in minutes.

[0077] Total passenger demand at the station within the time slice: N demand =sum(n p The number of passengers arriving at the station for all OD pairs within this slice; the maximum number of passengers that can be assigned to a train within this slice: N alloc =sum(n empty The available capacity of all trains stopping at the station within this slice;

[0078] Step 23: Normalize the traction energy consumption, passenger waiting time, and travel time to obtain normalized traction energy consumption, passenger waiting time, and passenger travel time, including:

[0079] Because the dimensions of traction energy consumption, passenger waiting time, and passenger travel time differ greatly (e.g., traction energy consumption is in kWh, and waiting time is in min), directly involving them in the calculation would lead to an imbalance in the weights of the indicators. Therefore, it is necessary to convert all indicators into dimensionless values ​​in the interval [0, 1] through linear normalization, and to uniformly optimize them by making the smaller the values ​​better. The specific implementation is as follows:

[0080] Determine the boundary values ​​(Maxx and Minx) for each indicator. The boundary values ​​for each indicator should be determined based on case data, historical operating records, or theoretical extreme values ​​to ensure complete coverage of the actual values ​​of the indicator in the initial current solution.

[0081] For traction energy consumption Enet, the maximum value MaxE can be referenced to the historical maximum traction energy consumption of a fixed train formation without considering regenerative braking energy recovery schemes (e.g., 3120 kWh), and the minimum value MinE is the theoretical minimum energy consumption when the train only overcomes the track foundation resistance (e.g., 500 kWh, calculated based on parameters such as track gradient and resistance coefficient); for passenger waiting time T... wait The maximum value (MaxTw) can be the actual waiting time in the initial current solution (e.g., 244102.5 min before optimization), and the minimum value (MinTw) is set to 0 (ideally, passengers have no waiting time); for the passenger travel time T trip The maximum value MaxTt can be referenced from the actual travel time in the initial current solution (e.g., 642948 min before optimization), and the minimum value MinTt is the shortest travel time when the train runs at the maximum speed allowed by the line.

[0082] If complete historical data is lacking, the maximum value can be set to 1.2 times the value of the indicator corresponding to the initial current solution, and the minimum value can be set to 0.5 times the value of the indicator corresponding to the initial current solution. For each indicator, a cost-based indicator normalization formula is used (since all indicators need to be minimized). The normalized value (Normx) = (actual indicator value x - minimum indicator value Minx) / (maximum indicator value Maxx - minimum indicator value Minx). Normalized traction energy consumption NormE: calculated using the formula (Enet - MinE) / (MaxE - MinE). The closer Enet is to MinE, the closer NormE is to 0, indicating better traction energy consumption. If Enet equals MaxE and NormE equals 1, it represents the worst traction energy consumption; Normalized passenger waiting time NormTw: calculated by the formula (Twait-MinTw) / (MaxTw-MinTw), with the same logic as above. The shorter the waiting time, the closer NormTw is to 0; Normalized passenger travel time NormTt: calculated by the formula (Ttrip-MinTt) / (MaxTt-MinTt). The shorter the travel time, the closer NormTt is to 0; If there is a special case where the maximum and minimum values ​​of the index are equal, Maxx = Minx, in order to avoid the denominator being 0, the normalized value of this index is uniformly set to 0.5.

[0083] Step 24: Add the normalized traction energy consumption to the train formation adjustment cost and the fixed train usage cost to obtain the comprehensive operating cost; then, perform a weighted summation of the comprehensive operating cost, the normalized passenger waiting time, and the passenger-specific passenger travel time to finally obtain the calculated multi-objective function value, including:

[0084] Extract the fixed cost coefficient per carriage, the actual number of carriages in each train formation, and the total running time of each train during the study period (calculated from the train's departure time from the first station and arrival time at the last station in the timetable) recorded in Step 1. Multiply the fixed cost coefficient per carriage by the number of carriages in the formation, and then multiply by the total running time of the train to obtain the fixed operating cost per train. Summarize the fixed operating costs of all trains to form the total fixed operating cost of trains during the study period.

[0085] Step 2: Calculate the cost of train formation adjustment

[0086] Based on the train formation adjustment cost parameters in step 1 and the number of train formation adjustments recorded in step 3 (e.g., adjusting from unit 1 to unit 2 is counted as 1 adjustment), the formation adjustment cost of a single train is calculated by multiplying the cost of a single adjustment by the number of adjustments. The total cost of train formation adjustments for all trains that have undergone formation adjustments is obtained by summing up the costs of all trains that have undergone formation adjustments. If a train has not undergone formation adjustments, its adjustment cost is recorded as 0.

[0087] Step 3: Normalize fixed operating costs and adjustment costs

[0088] Referring to the linear normalization logic in step 23, determine the boundary values ​​for the total fixed operating cost and the total cost of train formation adjustment, respectively. The maximum value can be set to 1.2 times the cost value corresponding to the initial current solution, and the minimum value can be set to 0.5 times the cost value corresponding to the initial current solution. If complete historical operating data is available, the historical maximum and minimum values ​​can be used as boundaries. Using a cost-type index normalization method, the total fixed operating cost and the total cost of train formation adjustment are converted into dimensionless values ​​in the interval [0,1]. If the maximum and minimum values ​​of a certain type of cost are equal, their normalized value is uniformly set to 0.5.

[0089] Step 4: Calculate the overall operating cost

[0090] The normalized traction energy consumption (NormE) obtained in step 23, the normalized fixed operating cost obtained in step 3, and the normalized train adjustment cost are summed together. The summation result is the dimensionless comprehensive operating cost. The smaller this value, the better the operating cost.

[0091] Step 5: Set the weights for multiple objective indicators

[0092] Based on the route operation priorities (e.g., prioritizing passenger service quality during peak hours and operational cost control during off-peak hours), set weight coefficients for comprehensive operating cost, normalized passenger waiting time (NormTw), and normalized passenger travel time (NormTt). The sum of the three weight coefficients must be 1, and can be determined through expert scoring or calibration using historical operating data (e.g., comprehensive operating cost weight 0.4, waiting time weight 0.3, and travel time weight 0.3).

[0093] Step 6: Calculate the multi-objective function values

[0094] Multiply the overall operating cost by its corresponding weight coefficient, the normalized passenger waiting time by its corresponding weight coefficient, and the normalized passenger travel time by its corresponding weight coefficient. Add the three products together to obtain the final multi-objective function value. The smaller this value, the better the current solution performs in terms of overall performance across the three dimensions of operating cost, passenger waiting time, and passenger travel time.

[0095] In a preferred embodiment of the present invention, step 3, which involves perturbing the current solution to generate a new solution including the dynamically adjusted train formation number, the selected train speed curve, and the adjusted train departure time, includes:

[0096] Step 31: Randomly select some trains and switch their train formation unit numbers among several preset selectable unit numbers, including:

[0097] Extract the core parameters from the current solution:

[0098] Each train formation unit contains 3 carriages. Formation can be done with 1 or 2 units, with the set of selectable units being {1, 2}, corresponding to 3 or 6 carriages respectively. Extract the initial number of formation units for each train in the current solution (e.g., initial solutions all have 2 units, i.e., 6 carriages) and the corresponding station's formation adjustment time. Check each train sequentially to determine if a formation disturbance has been triggered. Perform the following operations on all trains in the current solution (processed sequentially in the up / down direction):

[0099] For the k-th train, generate a uniformly random number randc in the interval [0, 1]. If the current number of train formation units is 1 (3 cars), switch to 2 (6 cars); if the current number is 2 (6 cars), switch to 1 (3 cars), ensuring that the switch only occurs between preset selectable number of units. After the switch, it is necessary to confirm that the train has the corresponding de-forming / re-forming conditions at the stopping station. If the conditions are not met (e.g., no formation adjustment capability at intermediate stations), the switch is abandoned and the original formation is maintained. For trains that trigger and successfully switch, record the adjusted number of formation units. For trains that do not trigger or fail the verification, use the original formation information to form a preliminary set of adjusted formation numbers.

[0100] Step 32: Randomly select alternative speed curves for each train in each section of its operation. The alternative speed curves are selected from a preset set of speed curves containing different energy consumption and travel time characteristics, including:

[0101] Identify the four curve types and their corresponding dynamic parameters:

[0102] The fast curve, i.e., a maximum speed of 80 km / h and an acceleration of 1.2 m / s². 2 20% coasting ratio (prioritizing shorter running time, higher energy consumption); standard curve, i.e., maximum speed 70km / h, acceleration 1.0m / s². 2 30% coasting ratio (balancing time and energy consumption); energy-saving curve, i.e., maximum speed 65km / h, acceleration 0.8m / s². 2 40% coasting ratio (prioritizing energy reduction, slightly longer duration); ultra-energy-saving curve, i.e., maximum speed 60km / h, acceleration 0.6m / s². 2 50% coasting ratio (lowest energy consumption, longest running time); current solution curve information, that is, extracting the speed curve type selected by each train in each operating section in the current solution.

[0103] The system checks whether curve disturbances are triggered column by column and interval by interval. It iterates through all running tasks in the order of train arrival at intervals. That is, for the i-th interval of the k-th train, it generates a uniform random number randv in the interval [0, 1].

[0104] The currently used curve is excluded from the four preset curves, and one of the remaining three curves is randomly selected as the replacement curve (to avoid the curve remaining unchanged after disturbance and to ensure exploration). The dynamic parameters of the replacement curve must meet the constraints of the corresponding section, such as the maximum speed of the replacement curve not exceeding the maximum speed of the line in the section and the acceleration not exceeding the maximum acceleration of the section. If the constraints are not met, a new random selection is made until the constraints are met. For train-section combinations that are triggered and successfully replaced, the type of replacement curve and the corresponding parameters are recorded. For combinations that are not triggered or fail to be verified, the original curve information is used to form an adjusted speed curve selection set.

[0105] Step 33: Based on the preset departure time disturbance probability and disturbance amplitude, randomly adjust the departure time of the selected train to generate a new solution that includes the adjusted train formation number, speed curve selection, and departure time, including:

[0106] Preset disturbance range: set to [-2, 2] minutes, that is, the adjustment amount is a random integer in -2, -1, 0, 1, 2 (0 means no adjustment, but it needs to be combined with probability triggering. Here, 0 is only an amplitude option and is not required); Current solution time information, extract the departure time of each train in the current solution (e.g., the departure time of the first train on the up line is 7:00, and subsequent trains are arranged according to the initial train interval), and the minimum / maximum train interval of the line.

[0107] The timetable adjustment calculation is as follows: the adjusted departure time = current departure time + Δt (e.g., if the current time is 7:05 and Δt = -1, then the adjusted time is 7:04; if Δt = 2, then the adjusted time is 7:07). After adjustment, it must be ensured that the headway between the train and the preceding train in the same direction is not less than the minimum headway (e.g., if the minimum headway is 10 minutes, then the adjusted headway must be ≥ 10 minutes). If this is not met, Δt is regenerated (e.g., if the original headway is 10 minutes and Δt = 2 results in a headway of 8 minutes, then Δt needs to be reselected as -1 or 0) until the initial constraints are met. For trains that trigger and successfully adjust, their adjusted departure time is recorded. For trains that do not trigger or fail the verification, the original departure time is used to form a set of adjusted departure times.

[0108] The new solution integrates the adjusted train formation set obtained in step 31, the adjusted speed curve selection set obtained in step 32, and the adjusted departure time set obtained in step 33 in a structured manner, ensuring that the train formation number, speed curve of each section, and departure time of each train correspond one-to-one, forming a complete new solution. During the integration process, it is necessary to reconfirm that there are no conflicts among the adjustment items (such as the train mass corresponding to the adjusted train formation number matching the traction requirement of the speed curve). If there are conflicts, the corresponding step is backtracked to re-perturb the problem, and finally a new solution that meets the basic constraints is output, providing input for generating a new timetable in step 4.

[0109] In a preferred embodiment of the present invention, step 4, based on the train formation quantity, speed curve, and departure time in the new solution, and combined with the constraints of train travel time and station dwell time, generates a new full-journey train timetable, including:

[0110] Step 41: Based on the speed curves selected for each train in the new solution, determine the corresponding operating parameters for each speed curve; calculate the total mass of the train based on the train formation quantity in the new solution, and calculate the interval travel time of each train in each operating section in combination with the operating parameters and track conditions, specifically including:

[0111] Four types of speed curves are preset: fast, standard, energy-saving, and ultra-energy-saving. Each type of curve corresponds to fixed operating parameters for the three stages of traction, cruise, and braking. The speed curve type selected by the current train in the target section is extracted from the new solution and matched with the following parameters: maximum speed of 80 km / h and acceleration of 1.2 m / s² during the traction stage of the fast curve. 2 The maximum speed during cruising is 75 km / h, and the deceleration during braking is 1.4 m / s². 2 The coasting phase accounts for 20% of the total speed; the maximum speed and acceleration during the standard curve traction phase are 70 km / h and 1.0 m / s². 2 The maximum speed during cruising is 65 km / h, and the deceleration during braking is 1.2 m / s². 2 The coasting phase accounts for 30%; the maximum speed during the traction phase of the energy-saving curve is 65 km / h, and the acceleration is 0.8 m / s². 2 The maximum speed during cruising is 60 km / h, and the deceleration during braking is 1.0 m / s². 2 The coasting section accounts for 40% of the total speed; the maximum speed and acceleration during the ultra-energy-saving curve traction phase are 60 km / h and 0.6 m / s². 2 The maximum speed during cruising is 55 km / h, and the deceleration during braking is 0.8 m / s². 2 The coasting section accounts for 50%. Simultaneously, fixed conditions for the target operating section are extracted: section length (e.g., a section of 1.2km), line gradient angle, and line resistance coefficient (valued at 1.36 × 10⁻⁶). -4 ), and the maximum speed limit for the section (e.g., 70km / h, you must ensure that the cruising speed of the speed curve does not exceed this limit).

[0112] The total mass of the train consists of the weight of the carriages themselves and the total mass of the passengers. The calculation formula is: Total mass of the train = Number of carriages in the formation × Mass of a single carriage + Total number of passengers in the train × Average mass of a single passenger. The number of carriages in the formation is obtained from the new solution (2 units correspond to 6 carriages, 1 unit corresponds to 3 carriages); the mass of a single carriage is taken as 1.99 × 10⁻⁶. 5 kg; the total number of people in the vehicle is extracted from the passenger flow allocation scheme corresponding to the new solution (e.g., 120 people); the average weight of a single passenger is taken as 60 kg.

[0113] Section running time = traction phase time + cruise phase time + braking phase time. The calculation method for each phase time is as follows:

[0114] Traction phase time: The train accelerates from rest to cruising speed. According to the kinematic equation, cruising speed = acceleration × traction phase time (ignoring initial speed), we get traction phase time = cruising speed ÷ acceleration. When calculating, the cruising speed unit needs to be converted from km / h to m / s (e.g., 70 km / h ≈ 19.44 m / s). Taking the standard curve as an example, its cruising speed is 65 km / h (≈ 18.06 m / s) and its acceleration is 1.0 m / s². 2 The calculated traction phase time is approximately 18.06 seconds.

[0115] Braking phase time: The train decelerates from cruising speed to 0. Similarly, the braking phase time = cruising speed ÷ deceleration. Taking the standard curve as an example, its deceleration is 1.2 m / s². 2 The calculated braking phase time is approximately 15.05 seconds.

[0116] Cruise phase time: First traction phase distance = 0.5 × acceleration × traction phase time 2 Calculate the traction phase distance, and the braking phase distance = 0.5 × deceleration × braking phase time. 2 Calculate the braking phase distance; then subtract the traction and braking phase distances from the total interval length (converted to meters, e.g., 1.2km = 1200m) to obtain the cruising phase travel distance; finally, divide the cruising phase travel distance by the cruising speed (in meters per second) to obtain the cruising phase time.

[0117] After the calculation is completed, check whether the interval running time meets the interval's maximum and minimum running time constraints (e.g., a minimum of 120s and a maximum of 300s for a certain interval). If it exceeds the constraints, adjust the speed curve type (e.g., if the ultra-energy-saving curve time is too long, change it to an energy-saving curve) until the constraints are met.

[0118] Step 42: Starting from the adjusted train departure time in the new solution, the running time of each section and the dwell time of each station are accumulated sequentially to calculate the arrival and departure times of each train at all stations. The dwell time at each station must meet the preset minimum and maximum dwell time constraints to form a preliminary train timetable, which specifically includes:

[0119] Obtain the adjusted departure time of the current train from the new solution (e.g., 7:02:00 for the up line and 7:03:30 for the down line), with the originating station being the line's terminal station (e.g., S1 or S14). Initialize arrival and departure time variables: Set the originating station as station 0, and the subsequent stations as station 1, station 2, ..., station n. Set the departure time of the originating station to the obtained departure time, and the arrival time of station 1 is to be calculated.

[0120] Arrival time at station 1: Arrival time at station 1 = Departure time from originating station + Travel time for section 0-1 (calculated in step 41). For example, if the departure time from originating station is 7:02:00 and the travel time for section 0-1 is 180s, then the arrival time at station 1 = 7:02:00 + 0:03:00 = 7:05:00.

[0121] The first stop time is calculated as follows: Stop Time = Basic Stop Time (e.g., 30s) + Number of Boarding Passengers × Time Taken per Passenger Boarding (e.g., 1s / person) + Number of Alighting Passengers × Time Taken per Passenger Alighting (e.g., 1s / person). The number of boarding and alighting passengers is extracted from the newly solved passenger flow allocation scheme. Then, it is checked whether the stop time meets the station's maximum and minimum stop time constraints (e.g., minimum 20s, maximum 120s): If the calculated value is less than the minimum stop time, the minimum stop time is used; if the calculated value is greater than the maximum stop time, the maximum stop time is used (at the same time, the possible risk of passenger congestion at this station is recorded for verification during subsequent passenger flow allocation).

[0122] The departure time of the first station is equal to the arrival time of the first station plus the dwell time at the first station.

[0123] Subsequent station calculations: Repeating the logic that the arrival time of a certain station = the departure time of the previous station + the travel time between the two stations, and the departure time of a certain station = the arrival time of that station + the dwell time of that station, the arrival and departure times of all stations on the line are calculated in sequence to form a preliminary arrival and departure time sequence for a single train.

[0124] The trains going up and down are grouped by direction, and each group is sorted by departure time from morning to evening (e.g., there are 25 trains going up from 7:00 to 9:30, which are sorted in order). A preliminary timetable data table is constructed with the fields of train number, direction, station number, arrival time, departure time, section travel time, and stop time to ensure that the arrival and departure times of each train are logically consistent (e.g., the departure time of a train at station S3 is greater than its arrival time at station S3).

[0125] Step 43: Check the following interval between consecutive trains running in the same section of the preliminary train timetable to determine whether the preset minimum safe headway and maximum headway constraints are met. If any following interval is found to be non-compliant, the station departure time of subsequent trains is delayed until all following intervals meet the safe headway constraints, thereby generating a new full-journey train timetable, specifically including:

[0126] Obtain safety interval constraints for trains traveling in the same direction: minimum safe headway 100s (to ensure trains do not rear-end each other), maximum headway 600s (to avoid excessive passenger waiting); for the tracking interval of two consecutive trains traveling in the same direction (let's call them train k and train k+1), priority is given to the difference in departure time of the two trains at the same station, and the calculation formula is: tracking interval = departure time of train k+1 at a certain station - departure time of train k at that station (this station can be any station, such as station S2).

[0127] The inspection is conducted in directional and chronological order: Taking the upstream trains as an example, starting with the earliest departing train 1, the tracking intervals between trains 1 and 2, 2 and 3, and so on, are checked sequentially, from train 24 to train 25. For each group of consecutive trains, key stations in the middle of the line (such as stations with high passenger flow, S5 and S8) and long sections (such as the S6-S7 section) are selected, and the tracking intervals at 3-5 points are calculated. If the tracking intervals at all points are between 100s and 600s, the intervals are considered acceptable, and the inspection continues with the next group of trains. If the tracking interval at any point is less than 100s (safety risk) or greater than 600s (service degradation), the interval adjustment mechanism is triggered.

[0128] The adjustment follows the principle of only delaying the following train and not advancing the preceding train (to avoid disrupting the arrival and departure time logic of the preceding train), and starts the adjustment from the following train with an unqualified interval (such as train k+1):

[0129] Calculate the adjustment time: If the tracking interval is less than 100s, the adjustment time = 100s - current tracking interval + 10s (add an extra 10s redundancy); if the tracking interval is greater than 600s, the adjustment time = current tracking interval - 600s (shorten to the maximum driving interval).

[0130] After adjusting the arrival and departure times of the train, the arrival and departure times of train k+1 at all stations will be increased by the adjustment amount (for example, the original arrival time of train k+1 at station S3 is 7:15:00, which will be delayed by 30 seconds to 7:15:30, and the departure time will be delayed accordingly).

[0131] Chain check of subsequent trains: After adjusting train k+1, recheck the tracking interval between train k+1 and train k+2 (delaying train k+1 may reduce its interval with k+2). If the new interval is still not qualified, delay train k+2 according to the same logic until the tracking interval of all trains in that direction meets the constraints.

[0132] After the adjustment is completed, a second verification will be performed:

[0133] The single-train arrival and departure time logic ensures that the departure time of each train at any station is greater than its arrival time at that station, and that the interval travel time still meets the constraints of step 41; it also ensures that the adjusted arrival and departure times allow for a time overlap window between braking trains and traction trains, thus avoiding a significant decrease in energy recovery efficiency.

[0134] Passenger flow matching means confirming that the adjusted stop times can meet the needs of passengers getting on and off the train without excessive congestion. If all verifications pass, a structured full-journey train timetable is generated with train number, direction, arrival time at each station, departure time at each station, number of train sets, and speed curve type as the core fields. This timetable serves as the final output of the collaborative optimization.

[0135] In this embodiment, by matching the actually selected speed curve parameters (such as the traction and cruise parameters of the fast / energy-saving curves), and combining the total train mass (number of trains and passenger weight) with the line conditions (section length, gradient, etc.), the section running time is calculated. This avoids the deviation between theoretical values ​​and actual operation, and balances energy consumption (such as reducing energy consumption with energy-saving curves) and operating efficiency (such as shortening time with fast curves) through speed curve selection. This ensures the quality of station services and avoids passenger congestion and time waste. Step 42 calculates the arrival and departure times station by station according to the departure time, section running time, and constrained stopping time, where the stopping time strictly conforms to the minimum / maximum constraints. Minimum stop time ensures passengers have ample time to board and alight, preventing missed trains; maximum stop time prevents excessive train dwell time from causing delays to subsequent trains. Simultaneously, by linking stop durations to passenger flow data, unnecessary waiting is reduced, improving the passenger travel experience. Ensuring driving safety and balancing service intervals with operational order is crucial. Step 43 involves checking and adjusting train intervals to minimize the risk of rear-end collisions with the minimum safe interval and minimize passenger waiting time with the maximum interval. Furthermore, the principle of only delaying subsequent trains is adopted, without disrupting the calculated operating logic of preceding trains, ensuring the overall consistency of the timetable. The final generated timetable meets both the safety operation baseline and maintains a stable service frequency.

[0136] In a preferred embodiment of the present invention, step 5, based on the new full-journey train timetable, involves redistributing passenger flow to generate an updated passenger flow allocation scheme corresponding to the new timetable, including:

[0137] Step 51: Based on historical passenger flow data, obtain passenger arrival times and origin / destination station information for each station during the study period, specifically including:

[0138] The research period was selected as [7:00, 9:30] (morning peak hours, matching the peak passenger flow characteristics of the line). The core data came from the historical data of the line's automatic fare collection (AFC) system, including passenger entry time, entry station (starting station), exit station (ending station), ticket collection records, and other information. Auxiliary data supplemented the passenger flow statistics of the station gates to cross-validate the completeness of the AFC data.

[0139] Data was screened within the research period, meaning all passenger records with timestamps within the range of [7:00, 9:30] were extracted from the AFC system, and invalid data (such as duplicate ticket checks or abnormal records caused by gate malfunctions) were removed. Time slicing was performed, dividing the data into 5-minute segments (e.g., 7:00-7:05, 7:05-7:10) to assign passenger entry times to the corresponding slices, facilitating subsequent train matching by time dimension. Missing data was filled in, meaning missing passenger destination (final station) information in the AFC data was filled using data from the same time period at the same station. The mean distribution of passenger travel origin-destination (OD) points in the slices is completed; for record gaps caused by cardless travel (such as emergency ticketing), the data is proportionally distributed to each time slice based on manual passenger flow counting data at the station; a structured information matrix is ​​constructed using the fields of time slice, entering station, passenger ID, entering time, origin station, and destination station, where the origin station is the passenger's entering station and the destination station is the destination station selected by the passenger through the AFC system (or the completed destination station), ensuring that each passenger record contains a unique origin and destination station and an accurate entering time.

[0140] Step 52: Based on the arrival and departure times of each train at each station in the new full-journey train timetable, passengers at each station are assigned to specific train services according to the first-come, first-served principle to obtain the allocation results; wherein, when the passenger capacity of any train reaches its maximum capacity determined based on the number of train formations, subsequently arriving passengers will be automatically deferred to the next available train, specifically including:

[0141] Direction matching means that passengers are only assigned to trains that match their travel direction (e.g., for trains traveling north, only passengers whose origin and destination are S1 or S14 are assigned, and vice versa for trains traveling south). Time matching means that the passenger's arrival time at the station must be earlier than the train's departure time at that station, and the train's arrival time at that station must be earlier than the passenger's arrival time (ensuring that passengers can catch the train). Destination matching means that the train must stop at the passenger's destination station (because of the all-stop mode, all trains cover all stations on the line, and there is no need to filter for skipped stations). Capacity constraint means that the maximum passenger capacity of the train = number of carriages in the formation × capacity of a single carriage, where the capacity of a single carriage is 200 people, and each formation unit contains 3 carriages (i.e., the maximum capacity of 1 formation unit = 3 × 200 = 600 people, the maximum capacity of 2 formation units = 6 × 200 = 1200 people). This capacity value is extracted from the new solution based on the number of train formations.

[0142] The system sorts passengers by time slice, ranking them from earliest to latest by arrival time (following a first-come, first-served principle). It then matches passengers to trains at each station, extracting all trains traveling in the same direction from the new timetable and sorting them by departure time. Finally, it assigns passengers one by one, prioritizing the earliest departing train that meets the direction and destination criteria, and determining the train's remaining capacity (initial remaining capacity = maximum capacity, decreasing as more passengers are assigned).

[0143] If the remaining capacity is greater than or equal to 1, passengers will be assigned to this train, and the remaining passenger capacity of the train will be reduced by 1.

[0144] If the remaining capacity is 0 (train is full), the current train is skipped, and the next train in the same direction that meets the conditions is matched, and the capacity judgment is repeated. If there are no subsequent available trains in the time slice, the passenger is marked as a stranded passenger and is redistributed to the first train of the next time slice. Passengers crossing time slices, i.e., if a passenger's entry time is at the intersection of two time slices (e.g., 7:05:02), are assigned to the next time slice (7:05-7:10). High-frequency processing for full capacity during peak hours, i.e., for stations with high passenger flow (e.g., intermediate transfer stations on the line), the remaining train capacity is monitored in real time. When three consecutive trains are full, the peak of the stranded passengers at that station during that time period is recorded, and 2-unit trains are given priority for subsequent allocation to that station.

[0145] Step 53: Based on the allocation results, count and update the number of passengers boarding and alighting at each station for each train, as well as the passenger capacity on board when leaving the station, to form an updated passenger flow allocation scheme corresponding to the new full-journey train timetable. This includes:

[0146] Based on the allocation results in step 52, the following is summarized by train number - station number: the number of passengers boarding a train at a station = the total number of passengers assigned to that train and whose starting station is that station, and recorded in the train-station boarding passenger statistics table.

[0147] The number of passengers disembarking at each station for each train is counted based on the passenger's origin and destination station information, matched by train number - station number: the number of passengers disembarking at a station for a certain train = the total number of passengers assigned to that train and whose destination station is that station (i.e., the passenger's origin station ≠ that station, and the number of passengers whose destination station = that station), and recorded in the train-station disembarkation statistics table.

[0148] The initial value is set as follows: the passenger capacity of the train when it departs from the originating station (such as S1 or S14) = the number of passengers boarding the train at the originating station (if there are no passengers before the originating station, the number of passengers boarding is the initial passenger capacity); station-by-station iterative calculation is performed: for non-originating stations, the passenger capacity of the train when it leaves the station = the passenger capacity of the train when it left the previous station + the number of passengers boarding at the station - the number of passengers alighting at the station; if the calculated passenger capacity exceeds the maximum passenger capacity of the train (number of train sets × 3 × 200), step 52 needs to be backtracked to confirm whether the allocation is incorrect, and after correction, the calculation is recalculated to ensure that the passenger capacity does not exceed the upper limit; a structured updated passenger flow allocation scheme is constructed with train number - direction of travel - station number - arrival time - departure time - number of passengers boarding - number of passengers alighting - passenger capacity at departure as the core fields. The scheme needs to cover all trains and all stations within the study period to ensure that the passenger flow data of each train corresponds one-to-one with the arrival and departure times of the new timetable.

[0149] In this embodiment, by extracting historical data from the AFC system, supplementing missing information, and constructing a structured travel matrix, the system accurately obtains passenger arrival times and origin / destination station information, avoiding allocation misalignment caused by data deviations. This ensures the matching of passenger flow data with the research period (e.g., morning peak [7:00, 9:30]) and the actual passenger flow characteristics of the line, reducing the waste of capacity or passenger congestion caused by unfounded allocation. Allocation is based on the first-come, first-served principle to avoid differences in waiting time due to unfair allocation rules, thus improving the passenger travel experience. Strict adherence to the maximum passenger capacity constraint based on the number of train sets (e.g., 600 people in unit 1, 1200 people in unit 2) prevents train overloading and ensures driving safety. At the same time, through the full-capacity delay mechanism, passengers who cannot board are automatically matched to the next train, reducing on-site congestion and ineffective passenger waiting, and balancing capacity supply and passenger demand. By statistically analyzing the number of passengers boarding, alighting, and departing at each station for each train, a structured and updated passenger flow plan is formed. This not only provides a direct reflection of the passenger load at each station and on each train (such as the concentration of passengers boarding at a transfer station during the morning rush hour), but also provides accurate data for subsequent calculations of operating costs (such as traction energy consumption based on passenger load) and evaluation of service quality (such as passenger waiting time). This helps to further optimize train formation configuration and timetables, and achieve coordinated matching of passenger flow, transport capacity, and energy consumption.

[0150] In a preferred embodiment of the present invention, step 6, based on the updated passenger flow allocation scheme and the new solution, calculates the recoverable amount of regenerative braking energy by quantifying the time overlap area of ​​the running curves of traction trains and braking trains within the same power supply area, to obtain a quantification result; calculates the traction energy consumption in the operating cost based on the quantification result, to obtain the performance evaluation value of the new solution; and determines whether to accept the new solution based on the performance evaluation value of the new solution and the performance evaluation value of the current solution, so as to update the current solution, including:

[0151] Step 61, based on the new full-journey train timetable, identifies traction and braking trains that are within the same power supply zone and have overlapping running times, specifically including:

[0152] Extract power supply zone division data for the line: clarify the power supply zone number corresponding to each section and station (e.g., S1-S3 belong to power supply zone 1, S4-S6 belong to power supply zone 2, S7-S9 belong to power supply zone 3, etc.) to ensure electrical isolation between power supply zones, and that only trains within the same power supply zone can transmit energy; extract train operating condition-time-location correlation data, that is, from the newly solved speed curve parameters and the new full-journey train timetable, obtain the start and end times of the traction phase (acceleration, cruising) of each train (e.g., train k is in traction condition from 7:05:00 to 7:08:30) and the start and end times of the braking phase (e.g., train k' is in braking condition from 7:06:10 to 7:07:20), and determine the power supply zone to which the train belongs under each operating condition through the correspondence between the train position and the power supply zone division.

[0153] Grouping by power supply area, trains traveling in the same power supply area are grouped together (e.g., trains traveling in the same area, such as k1 and k2, and trains traveling in the same area, such as k3 and k4, in power supply area 2). The braking time periods of all braking trains and the traction time periods of all traction trains within each group are iterated, and candidate train pairs with overlapping braking and traction time periods are selected (e.g., train k''s braking time 7:06:10-7:07:20 and train k's traction time 7:05:00-7:08:30 overlap and are listed as candidates). The distance between the two trains is calculated using the position data of the trains during the overlapping time periods. Candidate pairs with distances exceeding the maximum allowable energy transmission distance (e.g., 500m) are excluded, and finally, traction-braking train pairs from the same power supply area, with overlapping times and compliant distances are retained.

[0154] Step 62: Determine the braking time period of the braking train and the traction time period of the traction train, and calculate the overlap interval between the two time periods. Specifically, this includes: Determining the braking time period: Extracting the braking start time of the braking train k' from the train braking condition data. (e.g., 7:06:10) and braking end time (e.g., 7:07:20), this time boundary is determined by matching the braking phase parameters (braking start time, braking duration) of the speed curve with the new timetable; the traction time period is determined by extracting the traction train from the train traction condition data. Traction start time (e.g., 7:05:00) and traction end time (e.g., 7:08:30), this time boundary is determined by matching the traction phase parameters (traction start time, traction duration) of the speed curve with the new timetable.

[0155] The interval intersection algorithm is used: the start time of the overlapping interval is taken as the later start time of the braking and traction time interval, that is... The end time of the overlapping interval is taken as the end time before the braking and traction time interval, i.e. ;

[0156] Verify validity: If Then it is determined to be a valid overlapping interval (e.g. The valid interval is 7:06:10-7:07:20). If there is no valid overlap, the calculation for that train is terminated.

[0157] Step 63: Based on the braking power curve of the braking train and the traction power curve of the traction train within the overlapping interval, calculate the area of ​​overlap between the two power curves on the time axis, specifically including:

[0158] Step 1: Extract the core operating parameters of the two trains in the overlapping section. From the updated passenger flow allocation scheme, obtain the real-time passenger load of the braking train and the traction train in the overlapping section. Combined with the train formation number in the new solution, calculate the total mass of the two trains (the sum of the car's tare weight and the total passenger mass). From the speed curve parameters of the new solution, extract the braking deceleration and actual operating speed of the braking train at each time point in the overlapping section, as well as the traction acceleration and actual operating speed of the traction train at each time point in the overlapping section. At the same time, retrieve the basic line parameters (such as the line gradient angle and resistance coefficient) to provide a basis for power calculation.

[0159] Step 2: Refine the power data within the overlapping interval by time slice. Divide the effective overlapping interval determined in step 62 into fixed time slices (e.g., 0.5 seconds / slice) to ensure that the train's operating status (speed, acceleration / deceleration) within each time slice can be considered constant, reducing calculation errors caused by power fluctuations; for each time slice, calculate the braking power of the braking train and the traction power of the traction train respectively:

[0160] Braking power: Based on the total mass of the braking train, braking deceleration and current operating speed, combined with the physical relationship logic between braking force and power, the instantaneous braking power within this time slice is calculated;

[0161] Traction power: Based on the total mass of the traction train, traction acceleration, current operating speed, and track resistance (gradient resistance, frictional resistance), combined with the physical relationship between traction force and power, the instantaneous traction power within this time slice is calculated.

[0162] The instantaneous power of all time slices is arranged in chronological order to form the time-braking power curve data sequence of the braking train and the time-traction power curve data sequence of the traction train.

[0163] Step 3: Construct a dual power curve coordinate system and define the boundary of the overlapping area. Establish a two-dimensional coordinate system with time as the horizontal axis (unit: seconds) and power as the vertical axis (unit: kW). Map the above two power curve data sequences to the coordinate system to form a continuous braking power curve and traction power curve. Use the effective overlap interval determined in step 62 as the horizontal axis boundary and the power value of the two curves in each time slice as the vertical axis boundary to define the closed area jointly covered by the two curves in the coordinate system. This area is the physical range corresponding to the power overlap area to be calculated.

[0164] Step 4: Calculate the total overlap area by accumulating the data from each time slice. For each time slice, calculate the vertical projection area between the two power curves within that slice: If the braking power value is greater than or equal to the traction power value within the same time slice, then the overlap area of ​​that slice is the time slice length × the traction power value; if the braking power value is less than the traction power value, then the overlap area of ​​that slice is the time slice length × the braking power value (i.e., take the smaller of the two values ​​and multiply it by the time slice length to ensure that the area corresponds to the actual energy supply and demand that can be matched); calculate the overlap area of ​​all time slices in sequence, and sum the area values ​​of all slices to obtain the total overlap area of ​​the two power curves within the effective overlap interval. The physical meaning of this area is the power-time integral value corresponding to the total amount of energy that the braking train can transmit to the traction train.

[0165] Step 64: Based on the power overlap area, regenerative braking energy conversion efficiency, and unit energy consumption price, calculate the recoverable amount of regenerative braking energy as a quantification result, specifically including:

[0166] Step 1: Convert the power overlap area into initial recoverable energy by retrieving the preset energy conversion coefficient (this coefficient is determined based on the physical conversion relationship between the area of ​​the power-time curve and the energy unit, and is used to convert the area value in kW·s unit into the energy value in kWh unit); multiply the total power overlap area calculated in step 63 by this energy conversion coefficient to obtain the initial recoverable energy of the traction-braking train pair in the overlap interval (i.e., the total theoretical regenerative energy without deducting any losses).

[0167] Step 2: Subtract energy losses from multiple stages to obtain net recoverable energy. Retrieve core efficiency parameters from the parameter library: regenerative braking energy conversion efficiency (the efficiency of the train braking system in converting mechanical energy into electrical energy), traction system energy receiving efficiency (the efficiency of the traction train in converting electrical energy into mechanical energy), and power supply line transmission loss rate (the proportion of electrical energy lost during transmission in the power supply line). Correct the initial recoverable energy sequentially according to the following logic:

[0168] First, deduct the braking conversion loss: multiply the initial recoverable energy by the regenerative braking energy conversion efficiency to obtain the total electrical energy output by the braking system;

[0169] After deducting line transmission losses: multiply the total electrical energy output by the braking system by (1 - power supply line transmission loss rate) to obtain the total electrical energy actually received by the traction train.

[0170] Finally, after deducting traction conversion losses: multiply the total electrical energy actually received by the traction train by the energy receiving efficiency of the traction system to obtain the net recoverable energy that can ultimately be utilized by the traction train.

[0171] If any step in the correction process results in a negative value or zero, the train is deemed to have no effective recoverable energy, and the net recoverable energy is recorded as 0.

[0172] Step 3: Summarize the total recoverable energy in the same power supply area and verify its rationality. For all traction-braking train pairs with effective overlapping sections in the same power supply area, repeat the first two steps of steps 61 to 64 to calculate and summarize the net recoverable energy of all train pairs to obtain the total recoverable regenerative braking energy of the power supply area during the study period. Perform rationality verification: compare the total recoverable energy with the total traction energy consumption demand of all traction trains in the same power supply area during the same period. If the total recoverable energy exceeds the total traction energy consumption demand, then the total recoverable amount is corrected according to the total traction energy consumption demand (i.e., the regenerative energy can at most completely offset the traction energy consumption and cannot be negative); if the total recoverable energy is negative or exceeds the rated recovery capacity of the equipment, then it is corrected according to the rated recovery capacity of the equipment or zero value to ensure that the quantification results meet the actual operational constraints.

[0173] Step 4: Output structured quantitative results. The core fields are the power supply area number, study period, traction-braking train pair number, overlapping interval duration, power overlap area, initial recoverable energy, loss rate of each link, net recoverable energy, and total recoverable energy. A structured quantitative result table is constructed. Among them, the total recoverable energy is the final quantitative result of the recoverable regenerative braking energy of the power supply area, which serves as the core input data for subsequent calculation of traction energy consumption and evaluation of the performance of the new solution.

[0174] Step 65: Based on the quantification results of regenerative braking energy, subtract the recoverable energy portion from the total traction energy consumption to calculate the net traction energy consumption, specifically including:

[0175] Energy consumption during the traction phase, according to the formula calculate, For traction power, The traction phase duration is given by the formula. For example, if a train has a traction phase power of 250kW and a duration of 0.5h, the traction energy consumption = 250 × 0.5 = 125kWh. The cruise phase energy consumption is calculated using the formula... calculate, For cruise power, The cruise phase duration is expressed in hours (h). For example, with a cruise power of 200kW and a duration of 0.3h, the cruise energy consumption would be 200 × 0.3 = 60kWh; total traction energy consumption... For example, the total traction energy consumption of the train is 125 + 60 = 185 kWh.

[0176] Net energy consumption is calculated after deducting recoverable energy:

[0177] Net traction energy consumption formula: , The total recoverable energy summarized in step 64, =80% is the energy conversion efficiency, and transmission losses need to be taken into account; constraint correction, if ,but If the regenerated energy cannot offset the excess, the net energy consumption is 0; for example, a certain train ,but .

[0178] Step 66: Based on net traction energy consumption, train formation adjustment costs, fixed operating costs, and passenger waiting time and travel time in the updated passenger flow allocation scheme, the performance evaluation value of the new solution is obtained through weighted summation, specifically including: operating cost indicators:

[0179] Traction energy consumption cost / kWh (unit energy consumption price is 0.8 yuan / kWh), such as Energy consumption cost = 25 × 0.8 = 20 yuan; train adjustment cost, , Adjusting the number of carriages in train formations at each station incurs a unit adjustment cost of 100 yuan per carriage. For example, if a train adjusts 3 carriages, the adjustment cost would be 3 × 100 = 300 yuan; fixed operating costs... nc represents the number of carriages in the train set, Trun represents the train's running time in hours (h), and the fixed cost coefficient is 590 yuan / carriage·h. For example, with 6 carriages and a running time of 1.5 hours, the fixed cost would be 6 × 590 × 1.5 = 5310 yuan; the total operating cost... For example, the total operating cost of the train mentioned above = 20 + 300 + 5310 = 5630 yuan;

[0180] Passenger-related metrics:

[0181] Total passenger waiting time Extracted from the updated passenger flow allocation scheme (in minutes), e.g., 244102.5 minutes; total passenger travel time. Extracted from the updated passenger flow allocation scheme (unit: min), such as 642948min.

[0182] Indicator normalization and weighted summation:

[0183] Normalization converts each indicator into a dimensionless value in the interval [0, 1]. The formula is as follows: , and These represent the historical minimum and maximum values ​​of the indicator, respectively.

[0184] like , Yuan;

[0185] but ;

[0186] Set weighting coefficients, and take (Operating costs) (Waiting time) (Travel time);

[0187] Calculate performance evaluation values:

[0188] .

[0189] Step 67: Compare the performance evaluation value of the new solution with the performance evaluation value of the current solution. If the new solution has a better performance evaluation value, accept it as the current solution; if the new solution has a worse performance evaluation value, accept it as the current solution with a certain probability according to the Metropolis criterion; otherwise, retain the original current solution. Specifically, this includes:

[0190] Extract the current solution performance evaluation value (e.g., 0.55); if (If the new solution is 0.492 < the current solution is 0.55), the new solution has better performance, so we will directly accept the new solution and update the current solution's timetable, passenger flow plan, energy consumption data, etc., to the new solution's data simultaneously; if (If the new solution is 0.58, which is greater than the current solution of 0.55), the new solution has poor performance and will be subject to the Metropolis criterion for probability judgment.

[0191] Metropolis Criterion Probability Judgment:

[0192] Calculate the acceptance probability using the formula. Calculate, where T is the current simulated annealing temperature (e.g., initial temperature 100, current temperature 50 after iteration with a cooling rate of 0.95); compare random numbers to generate a uniformly distributed random number rand (e.g., 0.72) in the interval [0, 1]; if (e.g., 0.72 < 0.9994), accept the new solution and update the current solution; if If a new solution is rejected, all data of the current solution is retained, and the performance evaluation value and solution status of this iteration are recorded. If a new solution is accepted, the next iteration is based on the new solution for perturbation. If a new solution is rejected, the current solution is still used as the basis, and the iteration returns to step 3 to continue.

[0193] For example, a suburban railway line is 13.413 km long and has 14 stations (S1 to S14). S1 and S14 are depots. The line from S1 to S14 is the northbound direction, and the line from S1 to S14 is the southbound direction. The study period is the weekday morning peak from 7:00 to 9:30, with 25 trains planned to run in each direction.

[0194] Train parameters: Type B trains are used, with a capacity of 200 people per car. Three cars form one train unit, supporting one unit (3 cars, maximum passenger capacity of 600 people) or two units (6 cars, maximum passenger capacity of 1200 people) trains; four speed curves are preset: fast, standard, energy-saving, and super energy-saving (traction / cruising / braking parameters are described in step 41 above).

[0195] Passenger flow data: Based on historical AFC system data, the total passenger flow of each station during the study period was approximately 52,000. During peak hours (7:30-8:30), passenger flow was concentrated at transfer stations such as S5 and S8, with the highest hourly passenger flow at a single station reaching 8,000.

[0196] Improved simulated annealing algorithm parameters and implementation process, algorithm parameter initialization:

[0197] =100, termination temperature =1, rate of temperature decrease =0.95, =50; objective function weights, operating costs Passenger waiting time Travel time Disturbance factor, number of train cars in a formation. Timetable disturbance factor .

[0198] Using the existing operational plan as the initial solution:

[0199] Train formation: All trains on the line use a 2-unit (6-car) formation; Speed ​​curve: A standard speed curve (traction acceleration 1.0 m / s²) is used uniformly. 2 The cruising speed is 65km / h); the timetable is set so that the interval between the start of trains in both directions is fixed at 6 minutes (360 seconds), and the stop time at each station is uniformly 30 seconds; the initial objective function value Z1 = 1.86, and after normalization, the smaller the value, the better. The operating cost accounts for 62%, mainly due to the high energy consumption and equipment usage cost of fixed train sets.

[0200] Disturb each train in turn:

[0201] For train formation perturbation, a random number random(0,1) is generated. If the value is ≥0.7 (i.e., 1−λ1=0.7), the 2-unit formation is changed to 1 unit (or vice versa). For example, the 8th train going up is perturbed into a 1-unit formation due to low passenger flow in the S5-S8 section. For departure time perturbation, a random number random(0,1) is generated. If the value is ≥0.5 (i.e., 1−λ2=0.5), the time is adjusted by ±1 or ±2 minutes. For example, the departure time of the 12th train going down is delayed from 7:42:00 to 7:44:00 to match the energy recovery window of the subsequent section. Based on the disturbed train formation and departure times, combined with the interval travel time (e.g., 160 seconds for the fast curve and 200 seconds for the energy-saving curve in the S1-S2 interval) and the stop time (calculated in step 42; for example, the stop time at S5 station is adjusted to 45 seconds due to a large number of passengers boarding), a preliminary timetable is generated. For trains that do not meet the minimum tracking interval (100 seconds), the departure time is delayed one by one (e.g., the initial interval between the 5th and 6th trains going up is 80 seconds, so the 6th train is delayed by 20 seconds to ensure an interval of 100 seconds). Passenger flow is allocated according to the first-come, first-served principle: 1200 passengers arriving at S5 station between 7:35 and 7:40 are given priority to the 2nd unit train (carrying 1200 passengers) departing at 7:40:00, and the subsequent 50 passengers are deferred to the 1st unit train (with a remaining capacity of 100 passengers) departing at 7:42:00, with no delays; at S8 station, due to two consecutive 1st unit trains being full, 120 passengers are deferred to the next 2nd unit train.

[0202] Regenerative braking energy calculation identifies traction-braking train pairs within the same power supply area (e.g., S5-S8 belong to power supply area 3): the 10th train downhill (braking time 8:10:00-8:11:10) and the 15th train uphill (traction time 8:09:30-8:12:00) have a 70-second overlap, and the recoverable energy is calculated to be 0.485 kWh. The total recoverable energy for the entire line is approximately 245 kWh.

[0203] New objective function:

[0204] Z l =1.23 (a decrease of 33.9% from the initial solution), because Z l <Z current The solution is directly accepted as the current solution; after 1500 iterations, the objective function tends to stabilize (Z = 0.14), satisfying the convergence condition.

[0205] This invention allows for flexible adjustment of train formations (1 / 2 unit switching) to match passenger flow fluctuations and reduce ineffective capacity consumption; regenerative braking energy recovery (quantified through time overlap intervals) can directly reduce traction energy consumption, especially in power supply areas where multiple trains converge; the optimized scheme has significant advantages in overall objectives, energy consumption, and cost control. Although passenger travel time and waiting time increase slightly, the overall comprehensive benefits are better, making it suitable for efficient operation of suburban railways during peak hours.

[0206] A virtual train formation and regenerative braking energy coordinated train timetable optimization system includes:

[0207] The acquisition module is used to acquire the initial train formation configuration, initial timetable, and passenger flow allocation scheme as the initial current solution;

[0208] The calculation module is used to calculate a multi-objective function value including operating costs, passenger waiting time, and passenger travel time based on the initial current solution; to perform a perturbation operation on the current solution to generate a new solution including dynamically adjusted train formation number, selected train speed curve, and adjusted train departure time; and to generate a new full-journey train timetable based on the train formation number, speed curve, and departure time in the new solution, combined with train travel time and station dwell time constraints.

[0209] The allocation module is used to redistribute passenger flow based on the new full-journey train timetable and generate an updated passenger flow allocation scheme corresponding to the new timetable.

[0210] The update module is used to calculate the recoverable amount of regenerative braking energy by quantifying the time overlap area of ​​the running curves of traction trains and braking trains within the same power supply area based on the updated passenger flow allocation scheme and the new solution, so as to obtain the quantification result; calculate the traction energy consumption in the operating cost based on the quantification result, so as to obtain the performance evaluation value of the new solution; determine whether to accept the new solution based on the performance evaluation value of the new solution and the performance evaluation value of the current solution, so as to update the current solution, until the preset termination condition is met, and finally output the obtained current solution as the collaboratively optimized train timetable.

[0211] The line studied in this invention is a two-way rail transit system with a turnaround function, such as... Figure 1 As shown, a total of One station and two depots, supporting virtual train formation at the depots or turnaround stations. Indicates train The number of train units affects the quality of the train. traction force Braking force and stop time This, in turn, affects train running time and energy consumption levels. More importantly, adjustments to the formation of different trains will restructure their relative positions in time and space and their departure times, thereby affecting the overall energy overlap structure of the system.

[0212] This invention also considers the efficient utilization of regenerative braking energy. The regenerative braking device can release energy during train deceleration and feed it back to the system via the overhead contact line. The utilization of regenerative energy depends on the energy receiving conditions within the system: instantaneous energy absorption can only be achieved when a traction train is present in the power supply area at the same time the braking train releases energy. The regenerative energy generated during braking can be used by the train being pulled simultaneously. Regenerated energy that is absorbed and utilized but cannot be utilized will be dissipated through resistors, resulting in energy waste and increasing energy costs. To describe this process, this invention will denote the train assembly as... The set of operating intervals is denoted as The power supply area is collected as follows When the train Does the braking state occur at a certain moment? Both located in the power supply area And it is in a traction state, such as Figure 2 As shown, this will determine the availability of renewable energy.

[0213] Furthermore, to improve system operating efficiency and energy consumption control capabilities, this invention introduces a preset set of speed curves. This is available for each train to use in different operating sections, such as Figure 3 As shown. Various velocity curves. It consists of three phases: traction, cruise, and braking, each corresponding to different maximum speeds, accelerations, and coasting ratios. Combined with the ATO (Automatic Train Control) system, it achieves precise train control. In the operating range Select speed curve This allows for proactive adjustment of operating rhythm and energy consumption. Different choices of speed curves will affect train travel time. Traction energy consumption wait.

[0214] Therefore, taking into account the grouping strategy Speed ​​curve selection and renewable energy availability function A spatiotemporally coupled, energy-transfer-sensitive integrated optimization model is constructed. This model must coordinate the operational strategies of multiple trains across multiple sections and power supply areas, while satisfying multiple constraints such as running time, station stops, power supply capacity, and passenger service, to achieve cost reduction and efficiency improvement.

[0215] This model takes the weighted minimization of operating costs, passenger waiting time, and passenger travel time as its optimization objective, and the calculation formula is as follows:

[0216]

[0217] (1) Minimum operating cost

[0218] Operating cost calculations include the impact of traction energy consumption costs, train decoupling costs, and fixed train usage costs. Traction energy consumption costs Determined by the speed curve and the required traction energy consumption, the specific calculation formula is as follows:

[0219]

[0220] Required traction energy consumption The cost is determined by the energy consumption of the train under traction and cruising conditions. Traction energy consumption cost is the remaining amount after subtracting recoverable regenerative braking energy from the total traction energy consumption generated under traction / cruising conditions, calculated as follows:

[0221]

[0222] Under traction conditions, power is affected by traction force, speed, and traction force conversion rate. Under cruising conditions, the train's power is directly proportional to traction force and speed. Power during the traction phase... and cruise phase power The calculation formula is:

[0223]

[0224] During braking, the applied braking force is converted into electrical energy through electric motor braking, resulting in regenerative braking energy per unit time. It can be approximated as:

[0225]

[0226] Indicates train In the power supply area Up, according to the speed curve During operation, it can transfer regenerative braking energy to other trains. The efficiency of this energy transfer is determined by a coefficient. This indicates that the energy loss during the transfer process is reflected, and the calculation formula is:

[0227]

[0228] In reality, it can be used by trains and its subsequent trains Utilizing regenerative braking energy It is determined by the minimum value between the train's traction energy consumption requirement and the transferable regenerative braking energy, and the calculation formula is:

[0229]

[0230] When virtual train formation is performed at a train turnaround station, corresponding train formation adjustment costs are incurred. These costs are closely related to changes in the number of carriages. Therefore, the cost of virtual formation can be calculated using the following formula:

[0231]

[0232] Trains incur fixed costs during operation, such as depreciation, leasing, and maintenance expenses. To accurately reflect these fixed costs, the following formula is provided:

[0233]

[0234] Total train operating cost The sum of the above three parts is:

[0235]

[0236] (2) Minimum passenger waiting time

[0237] This study accurately extracts passenger arrival times from AFC data and combines this with departure times from train schedules to achieve a matching analysis between passengers and specific train numbers. Specifically, the passenger arrival time at the originating platform is determined by time... This indicates the total passenger waiting time, calculated by subtracting the passenger's arrival time at the originating platform from the train's departure time. The formula for calculation is:

[0238]

[0239] (3) Minimum passenger travel time

[0240] Minimum passenger travel time is used to measure the operational efficiency of rail transit. This indicator reflects the total travel time of passengers on the train by summing up the travel times of all passengers, where travel time is defined as the time the train takes to arrive at the station. The moment leaving the station The moment The difference. Passenger travel time The calculation formula is as follows:

[0241]

[0242] The constraints of this model include seven aspects: dynamics, time overlap, regenerative braking energy matching, virtual train formation, passenger flow, timetable, and train speed curve.

[0243] (1) Dynamic constraints:

[0244] During operation, the train experiences three different conditions: traction, cruising, and braking, each corresponding to different traction or braking forces. During traction, the train needs to overcome resistance and accelerate; during braking, the train's power system converts the generated kinetic energy into regenerative electrical or thermal energy. Based on the principles of dynamics, the train's traction force... and braking force Describe it using the following equation:

[0245]

[0246] The model uses kinematic equations to describe the train's acceleration at different stages of operation, with the following constraints:

[0247]

[0248] The model considers the total resistance of the train in operation, including gradient resistance. and line resistance ,train In the interval Total resistance The calculation formula is:

[0249]

[0250]

[0251]

[0252] train traction force generated and braking force It cannot be negative, nor can it exceed the maximum limit. The constraint formula is:

[0253]

[0254]

[0255] Under traction conditions, the train accelerates under the action of traction force. Under cruise conditions, the train maintains a constant speed and travels at a uniform speed. Upon entering braking conditions, braking force is applied to decelerate the train until it finally comes to a stop. The speed and displacement at each stage are subject to corresponding dynamic constraints, expressed as follows:

[0256]

[0257]

[0258] For any time traction train and braking train Distance between Represented as:

[0259]

[0260] A 0-1 variable used to indicate in Time Train With the train The distance between them must satisfy the energy transfer requirements. If it does, the value is 1; otherwise, it is 0. The constraint is as follows:

[0261]

[0262] (2) Time overlap constraint

[0263] During train braking, other trains must be in traction mode for the generated regenerative energy to be effectively absorbed. Therefore, the regenerative energy can only be effectively transferred when the braking time of one train overlaps with the traction time of another train. The constraint is as follows:

[0264]

[0265] (3) Regenerative braking energy matching constraint

[0266] This invention considers two modes of regenerative braking energy transmission. The first is same-zone, same-direction transmission, where the braking energy of a down-going train is transferred to a down-going traction train within the same power supply zone. The second is same-zone, opposite-direction transmission, where the braking energy of a down-going train is transferred to an up-going traction train within the same power supply zone. This process uses a binary indicator variable. This means that constraints can be expressed as:

[0267]

[0268] For regenerative braking energy to be transferred between two trains, the following conditions must be met simultaneously: they must be in the same power supply zone, the braking train's occurrence time overlaps with the traction train's occurrence time, and the relative positions of the two trains transferring energy must satisfy the maximum distance for energy transfer. Therefore, the energy transfer indicator variable... Represented as:

[0269]

[0270] train Total amount of regenerative braking generated The law of conservation of energy must be satisfied, which means it must be equal to the regenerative braking energy that is effectively utilized. With the loss of regenerative braking energy sum.

[0271]

[0272] (4) Virtual grouping constraints

[0273] The total mass of the train consists of the sum of the train's own weight and the passenger weight, where the passenger weight is the mass of each passenger and the weight of the first passenger. Station train The product of the total number of passengers is given by the following constraint:

[0274]

[0275]

[0276] (5) Passenger flow constraints

[0277] At every moment and each pair of stations Above, the total number of passengers on all trains must be less than or equal to the number of passengers at that station. The maximum capacity at that moment. The constraint is:

[0278]

[0279] train The passenger capacity of a station is the total number of passengers who boarded at the current station and previous stations and disembarked at stations after this station, with the following constraint:

[0280]

[0281] To ensure Time Train exist No more than Station train The passenger carrying capacity is constrained by the following formula:

[0282]

[0283] (6) Train safety interval constraints

[0284] To ensure safe train operation, train intervals cannot be less than the minimum interval or greater than the maximum interval. The constraint is as follows:

[0285]

[0286]

[0287]

[0288] train In the interval The running time is equal to the train On the site Arrival time and train On the site Departure time.

[0289]

[0290] To ensure passengers can board the train On the site The stopping time must be greater than the minimum stopping time and not exceed the maximum stopping time. In other words, due to the safety interval between trains, the train's travel time within the section should meet the following requirements:

[0291]

[0292] train The time for uncoupling and rejoining operations must not be less than the sum of the marshalling adjustment time and the minimum stopping time.

[0293]

[0294] (7) Train speed curve constraints:

[0295] This model presupposes four speed curve levels. Higher levels represent a pursuit of operational efficiency, while lower levels tend to sacrifice some operating time for lower energy consumption. The decision variable for selecting the speed curve is... Only one velocity curve can be selected for a given interval, and the constraint is as follows:

[0296]

[0297]

[0298] Each speed level corresponds to specific operating parameters, which are determined by the selected speed level. Determine the running parameters: (The rest of the text appears to be a list of parameters and their meanings, possibly related to a specific program or event.) The train is in the section The final maximum speed parameter used. and the corresponding maximum acceleration parameters And so on, depending on the level it chooses. Corresponding The constraint is:

[0299]

[0300] Figure 4 The aforementioned model, a mixed-integer nonlinear programming model, is characterized by high dimensionality and strong nonlinear coupling, making it difficult to solve effectively by traditional commercial solvers. This invention proposes an improved Simulated Annealing (SA) algorithm that enhances search capabilities by dynamically adjusting the neighborhood structure. In each iteration, this improved method adaptively selects neighborhood operations based on the current solution quality, perturbing variables such as train frequency, train formation, and timetable.

[0301] Step 1: Parameter initialization. Set the initial temperature. Termination temperature Temperature drop rate and the length of the Markov chain Initialize the number of iterations. and the number of iterations at the current temperature .

[0302] Step 2: Multi-objective function normalization. Multiple objective functions are normalized into a single objective function using a linear weighting method. , , Set weight coefficients respectively , , The normalized objective function is shown in the following equation.

[0303]

[0304] Step 3: Initial Solution Generation. Input the existing train formation number, train timetable, and passenger flow allocation scheme as the initial solution for the algorithm.

[0305] Step 4: Calculate the objective function under the existing scheme according to formula (1), denoted as... , .

[0306] Step 5: Disturbances to train formation, speed level, and departure time.

[0307] From the train Initially, the disturbance factor for the number of train cars in the formation is set to be... Generate random numbers (Generate a random real number between [0,1]), if Then the train The number of carriages in a train can be changed from 6 to 3, or from 3 to 6. Based on timetable constraints and energy optimization requirements, if the train... If a tight tracking interval or time conflict occurs in Step 6, the speed level is increased to reduce travel time; if there is ample time and no constraint conflict, the speed level is decreased to save energy. When both speed increase and speed decrease conditions are met simultaneously, the constraint satisfaction requirement is prioritized, and the speed increase adjustment is executed. Let the train timetable disturbance factor be... Generate random numbers ,if Then for the train The starting time (The adjustment involves generating a random integer between [-2, 2]). After processing, let... Continue to disturb the next train until all trains have been dealt with.

[0308] Step 6: Train Timetable Generation. A full timetable is generated based on the constraints of train interval travel time and stop time. If the train tracking interval does not meet the constraints, the departure of each train is delayed sequentially from the second train onwards until all interval constraints are met.

[0309] Step 7: Passenger flow allocation plan generation. A first-come, first-served principle is adopted, allocating passengers according to their arrival time and origin / destination stations. If a train is already full, subsequent passengers will be transferred to the next train.

[0310] Step 8: Calculate the new objective function Generate a new solution And calculate its objective function value. .

[0311] Step 9 uses the Metropolis criterion to determine whether a new solution is acceptable.

[0312] The Metropolis criterion accepts deteriorating solutions with a certain probability, thus allowing the algorithm to escape the trap of local optima. The mechanism for updating solutions is: if the new solution is better than the current solution, then the new solution is accepted; otherwise, the Metropolis criterion is used to determine whether to accept the new solution. The formula for the acceptance probability is shown in equation (43). The Boltzmann mechanism is used to accept new individuals, that is: In this case, the newly generated solution is used. Replace the original solution Otherwise, I will not accept it. The formula for the Metropolis improved criterion is shown in equation (22).

[0313] (46)

[0314] In the formula This indicates the adjustment parameter of the Metropolis criterion.

[0315] Step 10: Determine if the length of the Markov chain under isothermal conditions has been reached. .if Proceed to Step 11; otherwise, Return to Step 5.

[0316] Step 11: Termination condition check. When... Then let If the algorithm fails, return to Step 5; otherwise, the algorithm terminates and outputs the optimal solution.

[0317] like Figure 5 As shown, this invention takes the actual operating data of a suburban railway as an example. The line is 13.413km long and has 14 stations. Stations 1 to 14 are named S1, S2, ..., S14, where S1 and S14 are depots. The direction from S1 to S14 is defined as uphill, and the opposite direction is downhill.

[0318] Based on historical passenger flow data for a specific workday, the passenger demand at each station during the research period can be obtained, such as... Figure 6 As shown.

[0319] The train uses Type B cars, with a capacity of 200 people per car. -1 Each trainset consists of 3 carriages, and can be configured with 1 or 2 units. The initial configuration is 2 units for all-stop trains. To adapt to different operating scenarios and energy consumption targets, four speed curves are preset: fast, standard, energy-saving, and ultra-energy-saving. The study period is selected as [7:00, 9:30], during which 25 trains are planned to run in each direction.

[0320] The convergence process of each objective function is as follows: Figure 7As shown, with increasing iterations, both the total objective and train operating costs show a decreasing trend, stabilizing after 1500 iterations; passenger waiting time and passenger travel time show a significant increasing trend, stabilizing after 1500 and 500 iterations respectively. The original running diagram is shown below. Figure 7 As shown, all are grouped into 2 units.

[0321] The optimized runtime graph is as follows Figure 8 As shown in the diagram, thick and thin lines represent 2-unit and 1-unit train formations, respectively, and different colors represent different train speed levels.

[0322] Compared to a fixed-formation scheme that considers regenerative energy recovery, the scheme proposed in this invention reduces the overall target by 92.1%, traction energy consumption by 17.8%, and travel time by only 0.8%, demonstrating a significant advantage in reducing overall operating costs and traction energy consumption. Compared to a scheme that only considers virtual formation, the scheme proposed in this invention reduces the overall target by 14.2%, traction energy consumption by 6.9%, and travel time by slightly increasing, indicating that considering regenerative braking energy recovery under virtual formation conditions can further improve overall energy efficiency, but passenger travel efficiency is slightly affected. Compared to a scheme that only considers fixed formation, the scheme proposed in this invention reduces the overall target by 62.9% and energy consumption by 31.1%, showing a more prominent advantage. However, in terms of travel time, fixed formation performs better, while the scheme proposed in this invention shows a significant increase. In summary, the scheme proposed in this invention demonstrates outstanding advantages in terms of overall target, energy consumption, and cost control, but in practical applications, a trade-off must be made between service levels and operating costs.

[0323] This invention studies the optimization of original train timetables by integrating virtual train formation and regenerative braking energy coordination strategies. Addressing the mixed-integer nonlinear characteristics of the model, an improved simulated annealing algorithm is proposed. Finally, a case study is conducted using a suburban railway as an example. By comparing the proposed solution with three traditional schemes, its advantages in energy saving and efficiency improvement are verified. Experimental results show that the optimized scheme of this invention is superior to other schemes in several aspects. Specific conclusions are as follows:

[0324] (1) Passenger travel time and energy consumption optimization: Compared with the traditional scheme that only considers fixed formation and recovers regenerative braking energy, the optimized scheme reduces the total target by 92.1% and energy consumption by 17.8%. This result verifies that the combination of virtual formation and regenerative energy recovery can effectively improve operating efficiency and reduce energy consumption.

[0325] (2) Synergistic effect of virtual grouping and regenerative energy recovery: Compared with the scheme that only considers virtual grouping, the optimized scheme shows better performance in terms of passenger travel time and energy consumption. Specifically, the optimized scheme reduces the total target by 14.2% and energy consumption by 13.9%, which shows that the synergistic effect of virtual grouping and regenerative energy recovery can further improve the overall efficiency of the system.

[0326] (3) Compared with the fixed formation scheme without considering regenerative braking energy recovery, the optimization effect on passenger waiting time and passenger travel time is reduced. However, by combining virtual formation and regenerative energy recovery, the optimization scheme reduces the total target by 62.9% and traction energy consumption by 31.1%. These results indicate that the optimization scheme is particularly suitable for peak hours, can significantly improve energy efficiency and effectively alleviate the operational pressure during periods of high passenger flow.

[0327] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing train timetables using virtual train formation and regenerative braking energy, characterized in that, The method includes: Step 1: Obtain the initial train formation configuration, initial timetable, and passenger flow allocation scheme as the initial current solution; Step 2: Based on the initial current solution, calculate the value of a multi-objective function that includes operating costs, passenger waiting time, and passenger travel time; Step 3: Perturb the current solution to generate a new solution that includes the dynamically adjusted number of train formations, the selected train speed curve, and the adjusted train departure time. Step 4: Based on the train formation quantity, speed curve and departure time in the new solution, and combined with the constraints of train running time and station dwell time, generate a new full-journey train timetable; Step 5: Based on the new full-journey train timetable, redistribute passenger flow to generate an updated passenger flow allocation scheme corresponding to the new timetable; Step 6: Based on the updated passenger flow allocation scheme and the new solution, calculate the time overlap area of ​​the running curves of traction trains and braking trains within the same power supply area to quantify the recoverable amount of regenerative braking energy, so as to obtain the quantification result; calculate the traction energy consumption in the operating cost based on the quantification result, so as to obtain the performance evaluation value of the new solution; based on the performance evaluation value of the new solution and the performance evaluation value of the current solution, determine whether to accept the new solution, so as to update the current solution. Step 7: Repeat steps 3 to 6 until the preset termination condition is met, and finally output the current solution as the collaboratively optimized train timetable.

2. The method for optimizing train timetables using virtual formation and regenerative braking energy as described in claim 1, characterized in that, Step 2, based on the initial current solution, calculate the value of a multi-objective function including operating costs, passenger waiting time, and passenger travel time, including: Step 21: Calculate the traction energy consumption of each train within the operating section based on the train formation quantity and operating speed curve in the initial current solution; Step 22: Based on the passenger flow allocation scheme in the initial current solution, calculate the waiting time of passengers on the platform and the travel time on the train; Step 23: Normalize the traction energy consumption, passenger waiting time, and passenger travel time respectively to obtain the normalized traction energy consumption, passenger waiting time, and passenger travel time. Step 24: Add the normalized traction energy consumption to the train formation adjustment cost and the fixed use cost of the train to obtain the comprehensive operating cost; then, perform a weighted summation of the comprehensive operating cost, the normalized passenger waiting time, and the passenger-specific passenger travel time to finally calculate the multi-objective function value.

3. The method for optimizing train timetables using virtual formation and regenerative braking energy as described in claim 2, characterized in that, The current solution is perturbed to generate a new solution that includes dynamically adjusted train formation numbers, selected train speed curves, and adjusted train departure times, including: Randomly select some trains and switch the number of their formation units between several preset selectable numbers; For each train, an alternative speed curve is randomly selected for each section of its operation. The alternative speed curve is selected from a preset set of speed curves that contain different energy consumption and running time characteristics. Based on the disturbance magnitude, the departure time of the selected train is randomly adjusted to generate a new solution that includes the adjusted number of train formations, speed curve selection, and departure time.

4. The method for optimizing train timetables using virtual formation and regenerative braking energy as described in claim 3, characterized in that, Based on the train formation quantity, speed curve, and departure time in the new solution, and combined with the constraints of train travel time and station dwell time, a new full-journey train timetable is generated, including: Based on the speed curves selected for each train in the new solution, determine the corresponding operating parameters for each speed curve; calculate the total mass of the train based on the number of train formations in the new solution, and calculate the interval travel time of each train in each operating section by combining the operating parameters and track conditions; Starting from the adjusted train departure time in the new solution, the running time of each section and the stopping time of each station are added up sequentially to calculate the arrival and departure times of each train at all stations. The stopping time of each station must meet the preset minimum and maximum stopping time constraints to form a preliminary train timetable. The system checks the tracking interval between consecutive trains running in the same section within the preliminary train timetable to determine whether the preset minimum safe headway and maximum headway constraints are met. If any tracking interval is found to be non-compliant, the station departure time of subsequent trains is delayed until all tracking intervals meet the safe headway constraints, thereby generating a new full-journey train timetable.

5. The method for optimizing train timetables using virtual formation and regenerative braking energy as described in claim 4, characterized in that, Based on the new full-journey train timetable, passenger flow is redistributed to generate an updated passenger flow allocation scheme corresponding to the new timetable, including: Based on historical passenger flow data, we obtained passenger arrival times and their origin and destination information for each station during the study period. Based on the arrival and departure times of each train at each station in the new full-journey train timetable, passengers at each station are assigned to specific train services according to the first-come, first-served principle to obtain the allocation results; among them, when the passenger capacity of any train reaches its maximum capacity determined based on the number of train formations, the passengers arriving later will be automatically postponed to the next available train. Based on the allocation results, the number of passengers boarding and alighting at each station and the passenger capacity on board each train when leaving the station are counted and updated to form an updated passenger flow allocation scheme corresponding to the new full-journey train timetable.

6. The method for optimizing train timetables using virtual formation and regenerative braking energy as described in claim 5, characterized in that, Based on the updated passenger flow allocation scheme and the new solution, the recoverable amount of regenerative braking energy is quantified by calculating the time overlap area of ​​the running curves of traction trains and braking trains within the same power supply area, to obtain the quantification results, including: Based on the new full-journey train timetable, identify traction trains and braking trains that are in the same power supply area and have overlapping running times; Determine the braking time period of the braking train and the traction time period of the traction train, and calculate the overlap interval between the two time periods. Based on the braking power curve of the braking train and the traction power curve of the traction train within the overlapping interval, calculate the overlapping area of ​​the two power curves on the time axis. Based on the power overlap area, regenerative braking energy conversion efficiency, and unit energy consumption price, the recoverable amount of regenerative braking energy is calculated as a quantitative result.

7. The method for optimizing train timetables using virtual formation and regenerative braking energy as described in claim 6, characterized in that, The traction energy consumption in the operating cost is calculated based on the quantification results to obtain the performance evaluation value of the new solution; Based on the performance evaluation values ​​of the new solution and the current solution, determine whether to accept the new solution and update the current solution, including: Based on the quantification results of regenerative braking energy, the net traction energy consumption is calculated by deducting the recoverable energy portion from the total traction energy consumption. Based on net traction energy consumption, train formation adjustment costs, fixed operating costs, and passenger waiting time and travel time in the updated passenger flow allocation scheme, the performance evaluation value of the new solution is obtained by weighted summation. The performance evaluation value of the new solution is compared with that of the current solution. If the performance evaluation value of the new solution is better, the new solution is accepted as the current solution. If the performance evaluation value of the new solution is worse, the new solution is accepted as the current solution with a certain probability according to the Metropolis criterion. Otherwise, the original current solution is retained.

8. A virtual train formation and regenerative braking energy coordinated train timetable optimization system, wherein the system implements the method as described in any one of claims 1 to 7, characterized in that, include: The acquisition module is used to acquire the initial train formation configuration, initial timetable, and passenger flow allocation scheme as the initial current solution; The calculation module is used to calculate a multi-objective function value, including operating costs, passenger waiting time, and passenger travel time, based on the initial current solution. The current solution is perturbed to generate a new solution that includes the dynamically adjusted number of train formations, the selected train speed curve, and the adjusted train departure time. Based on the number of train formations, speed curve, and departure time in the new solution, and combined with the constraints of train travel time and station dwell time, a new full-journey train timetable is generated. The allocation module is used to redistribute passenger flow based on the new full-journey train timetable and generate an updated passenger flow allocation scheme corresponding to the new timetable. The update module is used to calculate the recoverable amount of regenerative braking energy based on the updated passenger flow allocation scheme and the new solution, by calculating the time overlap area of ​​the running curves of traction trains and braking trains in the same power supply area, so as to obtain the quantification result. The traction energy consumption in the operating cost is calculated based on the quantification results to obtain the performance evaluation value of the new solution. Based on the performance evaluation value of the new solution and the performance evaluation value of the current solution, it is determined whether to accept the new solution to update the current solution until the preset termination condition is met. Finally, the obtained current solution is output as the collaboratively optimized train timetable.

9. A computing device, characterized in that, include: One or more processors; A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that, when executed by a processor, implements the method as described in any one of claims 1 to 7.

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