Urban rail train operation scheme optimization method based on target full load rate control

Abstract

This invention provides a method for optimizing urban rail transit train operation schemes based on target load factor control. This method, under the condition of a predetermined maximum train load factor control requirement for the line, fully considers the spatiotemporal distribution of passenger flow and aims to determine the optimal train interval and route scheme with capacity-capacity matching as the objective. In a case study, optimizing the morning peak train operation scheme based on passenger flow data reduced the maximum train load factor on the shared section of the downlink route by 21%, while the maximum train load factor on the non-shared section reached the predetermined target load factor of 80%, resulting in better capacity-capacity matching. After optimization, the maximum train load factor in the downlink direction reached 80%, meeting the predetermined target load factor control requirement. This invention plays a crucial role in balancing the load factor across different sections and achieving optimal coupling between passenger flow and vehicles, providing a reference for further optimizing train operation schemes and improving urban rail transit capacity.

Description

Technical Field

[0001] This invention relates to the field of urban rail transit, and in particular to an optimization method for urban rail train operation schemes based on target load factor control. Background Technology

[0002] With the continuous growth of passenger demand in urban rail transit, and given the limitations of fixed facilities and equipment such as power supply and signaling, optimizing train operation has become a major research direction for alleviating passenger flow pressure and further improving the capacity of urban rail transit.

[0003] Existing technologies include: 1) theoretical research on complex train operation organization methods (multi-route, express and local trains, variable formation) for different passenger flow characteristics of urban rail transit lines; 2) a mixed integer programming model for urban rail transit train scheduling based on passenger flow demand for lines with multiple depots or parking lots; 3) an optimization model for multi-formation train operation schemes of intercity railways, taking the passenger flow demand of the line as the objective function and minimizing the overall passenger travel time; 4) a nonlinear integer programming model with linear constraints, considering time-varying passenger flow demand and train skip-stop strategies, with minimizing the average waiting time of passengers as the optimization objective; 5) evaluation and optimization of train operation schemes based on the production efficiency of operating enterprises and passenger travel services; and 6) an optimization model for multi-route train operation schemes, considering the spatial unevenness of line transport capacity utilization, with the objectives of maximizing line transport capacity utilization, minimizing the number of train sets in operation and passenger travel costs, and with route form, departure frequency, and train formation as decision variables. Other studies use minimizing train energy consumption, train travel time, or passenger waiting time costs as objective functions, but these will not be elaborated upon here.

[0004] There is a lot of theoretical research on train operation plan optimization both at home and abroad, which has laid a theoretical foundation for operation plan optimization. However, due to the strong assumptions of theoretical models and the lack of specific constraints, it is still difficult to fully apply them to the practice of timetable optimization, especially for the special full load rate target constraints during major emergencies. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention, under the predetermined maximum load factor control requirement of the line, analyzes the spatiotemporal distribution of passenger flow and proposes an optimization method for urban rail train operation based on target load factor control, with capacity and passenger volume matching as the objective. This aims to provide methodological support for routine transportation organization and offer a reference for improving operational service levels and the construction and operation of smart urban rail transit. The specific technical solution adopted is as follows:

[0006] An optimization method for urban rail transit train operation schemes based on target load factor control, the method comprising the following steps:

[0007] (1) Determine the strategy for developing train operation plans

[0008] Analyzing the spatiotemporal distribution characteristics of passenger flow, including cross-sectional passenger flow, inbound / outbound passenger flow, and transfer passenger flow, the unevenness of passenger flow in time and space is determined. Train intervals, train routes, and station dwell times for different time periods are calculated. Based on the basic conditions of the line's equipment and facilities, and considering transfer connections between lines, the train operation plan is optimized and adjusted to ultimately form a train operation plan. The specific steps include:

[0009] (1.1) Analysis of passenger flow time imbalance

[0010] The time-based balance of passenger flow is determined based on the time imbalance coefficient:

[0011]

[0012] In the formula, is the time imbalance coefficient in the t-th time period along the s direction; is the maximum cross-sectional passenger flow in the t-th time period in the s direction, in people; T is the total operating time of the line.

[0013] (1.2) Analysis of Spatial Imbalance in Passenger Flow

[0014] The spatial imbalance coefficient is used to determine the spatial balance of passenger flow, and to ascertain whether the conditions for multi-route passenger flow operation are met.

[0015]

[0016] In the formula, is the spatial imbalance coefficient of the e-th cross section in the s direction within a certain time period; The maximum passenger flow at the e-th cross-section in the s direction; E is the total number of cross-sections;

[0017] (2) Establish a train operation scheme optimization model

[0018] Based on the train operation plan preparation strategy in step (1), and under the established full load rate control requirements, a train operation plan optimization model with the goal of matching transport capacity and transport volume is established.

[0019] (2.1) Model Objective

[0020]

[0021] In the formula, D represents the train's capacity; L t N represents the predetermined full load rate requirement for trains in the t-th time period; t Let be the number of trains in the t-th time period;

[0022] (2.2) Constraints

[0023] (2.2.1) Train interval constraints

[0024]

[0025] In the formula, Let I be the train interval in the t-th time period in the s direction; max This refers to the maximum train interval; I min The minimum train interval; T is the statistical time period;

[0026] The minimum train interval constraint includes power supply system capacity constraints and signaling system capacity constraints, namely:

[0027] I min ≥max(I′ min ,I″ min (5)

[0028] In the formula, I′ min This indicates the minimum headway that the power supply system can meet; I″ min This represents the minimum headway required to meet the requirements of the signaling system.

[0029] (2.2.2) Maximum cross-sectional train load factor constraint

[0030] The maximum cross-sectional train occupancy rate during time period T meets the following requirements:

[0031]

[0032] In the formula, L max This is the maximum train load factor requirement.

[0033] (2.2.3) Applying total vehicle quantity constraints

[0034]

[0035] In the formula, k r K represents the number of train pairs on the r-th route; K represents the total number of available cars.

[0036] (2.2.4) Distance constraints of short-route train operating sections

[0037] Z min ≤S end -S start +1≤Z max ,1≤S start <S end ≤N(8)

[0038] In the formula, S start and S endZ represents the start and end points of the short-haul route, where N is the total number of stations on the route. When N ≥ 25, Z... min = (1 / 4)·N, Z max = (3 / 4)·N; When the total number of stations N on the line is less than 25, Z min = (1 / 3)·N, Z max = (3 / 4)·N;

[0039] (2.2.5) Passenger load factor constraints for short-route trains clearing passengers and turning back at turnaround stations

[0040] L z ≤L′ (9)

[0041] In the formula, L z L represents the full load rate of the turnaround train; L′ represents the maximum full load rate of the train before passengers are cleared and the train turns around.

[0042] (2.2.6) Restrictions on the number of routes

[0043] Let the maximum number of intersections be m, and the constraint condition for limiting the number of intersections is:

[0044]

[0045] In the formula, Q represents the number of stations with train turnaround conditions; X i,j It is a 0-1 variable.

[0046] Preferably, the method further includes the following steps:

[0047] (3) Algorithm for solving train operation route schemes based on candidate route sets

[0048] In the algorithm, q e,max This represents the maximum cross-sectional passenger flow at the e-th cross-section during time period T. The specific calculation steps are as follows:

[0049] Step 1: If the line spatial imbalance coefficient during a certain period If only a single main route is operated, proceed to Step 6; otherwise, adopt a multi-route operation scheme and proceed to Step 2.

[0050] Step 2: Based on the turnaround situation of the line stations, all operating routes are obtained by enumeration. The route set is then filtered according to the section with a large cross-sectional passenger flow that the route should cover, to obtain a candidate route set.

[0051] Step 3: For the set of candidate routes, calculate the passenger flow distribution matching for each route during the time period. The calculation formula is as follows:

[0052]

[0053]

[0054]

[0055] In the formula, k i,j For route S i,j The passenger flow distribution matching coefficient, S′ i,j For S i,j The adjacent small intersections, q i,j,max For route S i,j Maximum cross-sectional passenger flow, q′ i,j,max S′ i,j Maximum cross-sectional passenger flow, q′ e′,max The maximum cross-sectional passenger flow at the e′-th cross-section;

[0056] Step 4: Calculate the passenger flow distribution matching under different route combinations during different time periods. The evaluation parameter calculation formula is as follows:

[0057]

[0058] In the formula, R is the evaluation parameter for the matching of passenger flow distribution during time periods;

[0059] Step 5: Under the conditions of satisfying constraints (8) to (10), solve formula (15) to obtain the train operation route scheme with the optimal evaluation parameter R based on the basic route:

[0060] minR

[0061] stX 1,Q =1 (15)

[0062] In the formula, X 1,Q =1 represents selecting the basic route;

[0063] Step 6: After determining the unique time-sharing train operation route scheme, conduct passenger flow statistics according to the combined route scheme, and determine the number of trains to be operated in combination with constraints (4) to (7). Attached Figure Description

[0064] Figure 1 It is a flowchart for train operation plan preparation.

[0065] Figure 2 This is a flowchart for analyzing uneven passenger flow times.

[0066] Figure 3 This is a flowchart for analyzing spatial imbalances in passenger flow.

[0067] Figure 4 This is a schematic diagram of all intersections.

[0068] Figure 5 This is the wiring diagram for Line 8 (North Section).

[0069] Figure 6 This is a chart showing the maximum cross-sectional passenger flow during different times for both directions.

[0070] Figure 7 It is the passenger flow time imbalance coefficient of Line 8 (North Section).

[0071] Figure 8 This represents the peak hourly passenger flow.

[0072] Figure 9 It is the coefficient of spatial imbalance of passenger flow during the morning rush hour.

[0073] Figure 10 It is an evaluation parameter for the matching of passenger flow distribution under different combination schemes. Detailed Implementation

[0074] (1) Train operation plan development strategy

[0075] Following the principle of precisely matching transport capacity and passenger volume throughout the day, the system accurately analyzes the spatiotemporal distribution characteristics of passenger flow, including cross-sectional passenger flow, inbound and outbound passenger flow, and transfer passenger flow. This identifies the unevenness of passenger flow in time and space, allowing for the calculation of train intervals, train routes, and station dwell times at different times. Based on the basic conditions of the line's equipment and facilities, and considering transfer connections between lines, the train operation plan is optimized and adjusted, ultimately forming the train operation plan. The basic process is as follows: Figure 1 As shown.

[0076] (1.1) Analysis of passenger flow time imbalance

[0077] A time imbalance coefficient is introduced to determine the balance of passenger flow over time. The time imbalance coefficient is the ratio of the maximum hourly passenger flow in one direction to the average hourly passenger flow in that direction. The calculation formula is as follows:

[0078]

[0079] In the formula, is the time imbalance coefficient in the t-th time period along the s direction; denoted as s, representing the maximum cross-sectional passenger flow in the t-th time period, in persons; T represents the total operating time of the line, in hours.

[0080] When calculating whether the time distribution of passenger flow on a route is balanced, if the time imbalance coefficient... If passenger flow is balanced, it is considered relatively even; otherwise, it is considered uneven. Therefore, peak and off-peak periods can be determined based on passenger flow at different time intervals. The analysis process for passenger flow time balance is as follows: Figure 2 .

[0081] (1.2) Analysis of Spatial Imbalance in Passenger Flow

[0082] A spatial imbalance coefficient is introduced to determine the spatial balance of passenger flow. The coefficient determines whether the passenger flow conditions for multi-route operation are met, and based on this, the turnaround points for multi-route operation are determined in conjunction with route conditions. The spatial imbalance coefficient is the ratio of the maximum unidirectional cross-sectional passenger flow to the average passenger flow of all cross-sections in that direction within a certain time period. The calculation formula is:

[0083]

[0084] In the formula, is the spatial imbalance coefficient of the e-th cross section in the s direction within a certain time period; Let E be the maximum passenger flow of the e-th cross-section in the s direction, expressed in people; E is the total number of cross-sections.

[0085] when When the flow rate approaches 1, the passenger flow cross-section is relatively balanced; when... At that time, the passenger flow across the cross-section was significantly uneven. Therefore, when calculating whether a route is suitable for multiple inter-route passenger flow adjustments, the following should be considered: As a basis for judgment, if Short-route trains can then be operated. The analysis process for passenger flow spatial balance is as follows: Figure 3 .

[0086] When determining the turnaround stations for short-route trains, in addition to ensuring the necessary track conditions, factors such as the load factor and headway of long-route trains should be comprehensively considered. The turnaround points for short-route trains should, as far as possible, be located at stations where the cross-sectional imbalance coefficient in both directions is less than 1.5. Furthermore, route optimization should be carried out according to the principles of reducing train load factor, reducing operating costs, and reducing the complexity of passenger transport organization, ultimately determining the train route settings.

[0087] (2) Train operation scheme optimization model

[0088] Based on the train operation plan development strategy, and under the established full load rate control requirements, an optimization model for train operation plans with the goal of matching transport capacity and passenger volume is established.

[0089] (2.1) Model Objective

[0090]

[0091] In the formula, D represents the train's passenger capacity, with a unit of one person; L t N represents the predetermined full load rate requirement for trains in the t-th time period, expressed as a percentage. t Let t represent the number of trains in the t-th time period, in columns.

[0092] (2.2) Constraints

[0093] (2.2.1) Train interval constraints

[0094]

[0095] In the formula, Let I be the train interval in the t-th time period in the s direction; max This refers to the maximum train interval; generally, the maximum train interval during off-peak hours is 10 minutes. min The minimum train interval is defined as T, where T is the statistical time period. The minimum train interval constraint includes both power supply system capacity constraints and signaling system capacity constraints, namely:

[0096] I min ≥max(I′ min ,I″ min (5)

[0097] In the formula, I′ min This indicates the minimum headway that the power supply system can meet; I″ min This represents the minimum headway required to meet the signaling system's capabilities.

[0098] (2.2.2) Maximum cross-sectional train load factor constraint

[0099] The maximum cross-sectional train occupancy rate during time period T must meet the following requirements:

[0100]

[0101] In the formula, L max This represents the maximum train occupancy rate requirement.

[0102] (2.2.3) Applying total vehicle quantity constraints

[0103]

[0104] In the formula, k r Let k represent the number of train pairs on the r-th route. r ∈Z; K represents the total number of vehicles available.

[0105] (2.2.4) Distance constraints of short-route train operating sections

[0106] The operating distance of short-route trains should not be too short or too long. Too short a distance leads to frequent train turnsarounds to clear passengers, affecting service quality; too long a distance prevents the cost-saving and efficiency-enhancing advantages of short-route trains from being realized. Therefore, short-route trains require:

[0107] Z min ≤S end -S start +1≤Z max ,1≤S start <S end ≤N (8)

[0108] In the formula, S start and S end Let Z be the start and end points of the short-haul route, and N be the total number of stations on the route. Here, when N≥25, Z... min = (1 / 4)·N, Z max = (3 / 4)·N; When the total number of stations N on the line is less than 25, Z min = (1 / 3)·N, Z max = (3 / 4)·N.

[0109] (2.2.5) Passenger load factor constraints for short-route trains clearing passengers and turning back at turnaround stations

[0110] L z ≤L′ (9)

[0111] In the formula, L z L represents the full load rate of the turnaround train; L′ represents the maximum full load rate of the train before the passengers are cleared and the train turns around.

[0112] (2.2.6) Restrictions on the number of routes

[0113] An excessive number of train routes will cause difficulties for passenger boarding and train operation organization. Therefore, the maximum number of train routes is set to m, where m takes a value between 1 and 5. The constraint condition for limiting the number of train routes is then:

[0114]

[0115] In the formula, Q represents the number of stations with train turnaround conditions; X i,j For variables of 0-1, if the intersection S is open... i,j Then X i,j The value is 1 if it is not 0 otherwise.

[0116] (3) Algorithm for solving train operation route schemes based on candidate route sets

[0117] First, the algorithm determines whether different routes need to be operated based on the spatial imbalance coefficient of the line. Then, it forms a set of all routes based on the station turnaround situation and filters candidate routes according to the maximum cross-sectional passenger flow that each route should cover. Next, it calculates the passenger flow distribution matching under different route combinations during time period T, thus obtaining the best operating route scheme with the best capacity-volume fit. Note that for simplicity, the algorithm uses q... e,max This represents the maximum cross-sectional passenger flow at the e-th cross-section during time period T. The specific calculation steps are as follows:

[0118] Step 1: If the line spatial imbalance coefficient during a certain period If the first route is selected, proceed to Step 6; otherwise, proceed to Step 2.

[0119] Step 2: Based on the station turnaround situation, obtain all operating routes through enumeration. Then, filter the route set according to the area that the route should cover, resulting in a candidate route set. For example... Figure 4 As shown, there are 4 stations with turnaround capabilities, and the set of all routes is {S}. 1,2 ,S 1,3 ,S 1,4 ,S 2,3 ,S 2,4 ,S 3,4 Due to route S 2,3 The largest cross-section with high passenger flow is not covered. 2,max Or q 5,max Therefore, the set of candidate routes after filtering is {S}. 1,2 ,S 1,3 ,S 1,4 ,S 2,4 ,S 3,4}

[0120] Step 3: For the set of candidate routes, calculate the passenger flow distribution matching for each route during the time period. The calculation formula is as follows:

[0121]

[0122]

[0123]

[0124] In the formula, k i,j For route S i,j The passenger flow distribution matching coefficient, S′ i,j For S i,j The adjacent small intersections, q i,j,max For route S i,j Maximum cross-sectional passenger flow, q′ i,j,max S′ i,j Maximum cross-sectional passenger flow, q′ e′,max Let be the maximum cross-sectional passenger flow at the e′-th cross-section. Here, let k be the passenger flow distribution matching coefficient of the basic route. 1,Q The value is 1.

[0125] Step 4: Calculate the passenger flow distribution matching under different route combinations during different time periods. The evaluation parameter calculation formula is as follows:

[0126]

[0127] In the formula, R is the evaluation parameter for the matching of passenger flow distribution during time periods. The larger R is, the higher the degree of matching between routes and passenger flow is considered.

[0128] Step 5: Under the condition of satisfying constraints (8) to (10), call the CPLEX software to solve formula (15) to obtain the train operation route scheme with the optimal evaluation parameter R based on the basic route (large route):

[0129] minR

[0130] stX 1,Q =1 (15)

[0131] In the formula, X 1,Q =1 represents selecting the basic route.

[0132] Step 6: After determining the unique time-sharing train operation route scheme, conduct passenger flow statistics according to the combined route scheme, and determine the number of trains to be operated in combination with constraints (4) to (7).

[0133] (4) Application Cases

[0134] Taking the actual data of the morning rush hour of Metro Line 8 (North Section) in a certain city as an example, the effectiveness and feasibility of the urban rail train operation scheme optimization method based on target load factor control proposed in this invention are verified.

[0135] Line 8 (North Section) runs from Zhuxinzhuang in the north to the National Art Museum of China in the south, with 19 stations, including 6 interchange stations. The line has secondary tracks at Huilongguan East Street, Yongtaizhuang, and the South Gate of Forest Park for turnaround. The turnaround time at Zhuxinzhuang is 2 minutes, and at the National Art Museum of China it is 2 minutes and 30 seconds. The track layout of Line 8 (North Section) is as follows: Figure 5 As shown.

[0136] Based on the maximum cross-sectional passenger flow at different times of a certain day, an optimization study of train operation plans is conducted. The statistical results of the maximum cross-sectional passenger flow at different times for both the up and down directions are as follows: Figure 6 As shown in the figure, the peak hourly passenger flow is during the downhill direction from 8:00 to 9:00.

[0137] Calculate the passenger flow time imbalance coefficient according to formula (1) (e.g.) Figure 7 As shown in the figure, we can see that: 1) the time imbalance coefficient of the upward direction from 17:30 to 20:30 is greater than 1.5. Therefore, the evening peak period of the upward direction can be determined to be from 17:30 to 20:30; 2) the time imbalance coefficient of the downward direction from 7:00 to 10:00 is greater than 1.5. Therefore, the morning peak period of the downward direction can be determined to be from 7:00 to 10:00.

[0138] Spatial imbalance analysis was conducted on the peak hourly passenger flow period (8:00-9:00) for the downhill direction during the morning rush hour (e.g., Figure 8As shown): 1) The passenger flow distribution in the downbound direction is significantly uneven, with some sections having a peak hour load factor of less than 30% (from Zhuxinzhuang Station to Yuzhilu Station, and from Gulou Dajie Station to National Art Museum Station), while some sections have a load factor of more than 90% (from Lincuiqiao Station to Olympic Park); 2) Overall, the passenger flow in the downbound direction is relatively high, with 11 sections having a peak hour load factor of more than 50%.

[0139] The spatial imbalance coefficient of passenger flow in the downward direction during the morning peak is calculated according to equation (2), such as... Figure 9 As shown in the figure, the spatial imbalance coefficient between Yongtaizhuang Station and Olympic Park Station is greater than 1.5, while the spatial imbalance coefficient between Gulou Dajie Station and National Art Museum of China Station is less than 0.5. Therefore, a multi-route operation scheme is adopted.

[0140] Based on passenger flow data, the maximum cross-sectional load factor of Line 8 (North Section) in the northbound direction is 27.6%. According to operational experience, L′ = 50%. Therefore, the northbound direction meets the maximum load factor requirement for trains before passenger clearing and turnaround. Based on the turnaround situation at the stations, there are a total of 10 routes. The passenger flow distribution and matching of each route during the 8:00-9:00 time period are shown in Table 1. Among them, the 5 stations with turnaround capabilities are numbered sequentially starting from 1, such as S... 1,2 This refers to the route from Zhuxinzhuang to Huilongguan East Street. Based on the maximum cross-sectional passenger flow data, there are 9 alternative routes, and the set of alternative routes is {S}. 1,3 ,S 1,4 ,S 1,5 ,S 2,3 ,S 2,4 ,S 2,5 ,S 3,4 ,S 3,5 ,S 4,5}

[0141] Table 1 Matching coefficients of passenger flow distribution along transportation routes

[0142]

[0143] The evaluation parameter R-value for the matching of passenger flow distribution during different time periods was calculated, and the results are shown in [the table below]. Figure 10 Based on this, and considering the constraints, the route S is selected. 1,5 and S 2,5 (R value is 2.8716), which means operating the long route from Zhuxinzhuang to the National Art Museum of China and the short route from Huilongguan East Street to the National Art Museum of China.

[0144] The train has a capacity of 1468 passengers, with a predetermined load factor control condition of 80% during peak hours. While passenger flow in the upbound direction is relatively low, to maintain consistent service quality, the headway in the upbound direction remains unchanged at 152 seconds. The urban rail train operation optimization method based on target load factor control proposed in this invention is used to optimize the train operation plan in the downbound direction during the morning peak hours (7:00-9:00). Based on passenger flow data, route S... 1,5 and S 2,5 Under combined conditions, the specific number of rows and columns for non-collinear segments and collinear segments are as follows:

[0145] 17765 ÷ (1468 * 0.8) ≈ 15 (columns)

[0146] 35249 ÷ (1468 * 0.8) ≈ 30 (columns)

[0147] Therefore, route S 1,5 The number of rows and columns k1 = 15, and the intersection S 2,5 The number of trains operating is k2 = 30 - k1 = 15. Line 8 (North Section) has K = 50 trains; therefore, k1 + k2 < K, satisfying the total number of trains in operation constraint. The ratio of long and short routes is approximately 1:1. The minimum headway required by the power supply and signaling systems of Line 8 (North Section) is 2 minutes. Statistical analysis of various parameters before and after train operation plan optimization is shown in Table 2.

[0148] Table 2 Comparison of parameters before and after optimization of train operation plan (downward direction)

[0149]

[0150] For the morning rush hour on the southbound direction: the minimum departure interval has been shortened from 152 seconds to 120 seconds, increasing capacity by 21.1% and reducing the average passenger waiting time by 16 seconds; the ratio of large-scale to small-scale routes is 1:1; the maximum train load factor on shared sections of large-scale and small-scale routes has decreased from 101% to 80%, a reduction of 21%; the maximum train load factor on non-shared sections has reached the target of 80%, resulting in better capacity-volume matching. Under the constraints of the established load factor, the load factor across different sections on the southbound direction is more balanced.

[0151] This invention proposes an optimized train operation model that aligns with the predetermined maximum load factor, taking into account constraints such as the line's signaling system capacity, power supply system capacity, and turnaround capacity. This model aims to achieve the desired maximum load factor while fully meeting passenger travel demands. An application analysis is conducted using the morning peak hours of Line 8 (North Section) as a case study. In the case study, through model optimization, the maximum train load factor on the shared section of the southbound line during the morning peak hours was reduced by 21%, and the capacity-volume matching effect on the non-shared section was improved. The maximum train load factor reached the predetermined target of 80%, and the southbound line also met the target load factor control requirement of 80%. The results show that the optimization method proposed in this invention is highly effective. Under the load factor control requirements, the optimized method achieves a more balanced load factor across different sections, realizing the goal of optimal coupling between passenger and train flows.

Claims

1. A method for optimizing an urban rail train operation scheme based on target full load rate control, characterized in that, The method includes the following steps: (1) Determine the strategy for train operation plan preparation This study analyzes the spatiotemporal distribution characteristics of passenger flow at cross-sections, inbound / outbound passenger flow, and transfer passenger flow to determine the temporal and spatial imbalances in passenger flow. It then calculates train intervals, train routes, and station dwell times for different time periods. Based on the basic conditions of the line's equipment and facilities, and considering transfer connections between lines, the train operation plan is optimized and adjusted to ultimately form a train operation plan. The specific steps include: (1.1) Analysis of passenger flow time imbalance The time-based balance of passenger flow is determined based on the time imbalance coefficient: （1） In the formula, is s direction of the first t time imbalance coefficient of the first time period; is s direction of the first t maximum cross-sectional passenger flow of the first time period, in units of people; is the total length of line operation; (1.2) Analysis of Spatial Imbalance in Passenger Flow The spatial imbalance coefficient is used to determine the spatial balance of passenger flow, and to ascertain whether the conditions for multi-route passenger flow operation are met. （2） In the formula, is the number of passengers in the certain period of time s direction of the e space imbalance coefficient of the section; is s direction of the e maximum section passenger flow of the section; E is the total number of sections; (2) Establish a train operation plan optimization model Based on the train operation plan preparation strategy in step (1), under the established full load rate control requirements, a train operation plan optimization model with the goal of matching transport capacity and transport volume is established. (2.1) Model Objective （3） wherein is the train crew; is the train full load factor requirement for the t th time period; is the train number for the t th time period; (2.2) Constraints (2.2.1) Train interval constraints （4） In the formula, is s direction of the t train operation interval of the time period; is the maximum train operation interval; is the minimum train operation interval; is the statistical time period; The minimum train interval constraint includes power supply system capacity constraints and signaling system capacity constraints, namely: （5） In the formula, represents the minimum headway that the power supply system capacity meets; represents the minimum headway that the signal system capacity meets; (2.2.2) Maximum cross-section train load factor constraint The period maximum cross-section train full load rate satisfies: （6） In the formula, is the maximum train full load rate requirement value; (2.2.3) Applying total vehicle quantity constraints （7） In the formula, indicates the number of trains of the route; indicates the number of trains of the route; indicates the total amount of available vehicles; (2.2.4) Distance constraints of short-route train operating sections （8） wherein and is the starting point of the small circuit, is the total number of stations included in the line, when , , ; when the total number of stations included in the line is , , ; (2.2.5) Passenger load factor constraints for short-route trains clearing passengers and turning back at turnaround stations （9） In the formula, is the full load rate of the turnaround train; is the maximum full load rate of the train before passenger cleaning and turnaround; (2.2.6) Restriction on the number of routes The maximum value of the number of routes is set as m , and the number of routes limit constraint condition is: （10） In the formula, is the number of stations with a train turnaround condition; is a 0-1 variable.

2. The target full load rate control based urban rail train operation scheme optimization method according to claim 1, characterized in that, The method also includes the following steps: (3) Algorithm for solving train operation route schemes based on candidate route sets In the algorithm, the maximum cross-sectional passenger flow of each cross section in each time period is represented as The maximum cross-sectional passenger flow of each cross section in each time period is calculated as follows: the maximum cross-sectional passenger flow of each cross section in each time period is calculated as follows:​ Step 1: If the line space imbalance coefficient of a certain period is then only a single large interline is operated, and Step 6 is turned to; otherwise, a multi-interline operation scheme is adopted, and Step 2 is turned to; Step 2: Based on the turnaround situation of the line stations, all operating routes are obtained by enumeration. The route set is then filtered according to the section with a large cross-sectional passenger flow that the route should cover, to obtain a candidate route set. Step 3: For the set of candidate routes, calculate the passenger flow distribution matching for each route during the time period. The calculation formula is as follows: （11） （12） （13） In the formula, For the route The passenger flow distribution matching coefficient for Adjacent small intersections, For the route Maximum cross-sectional passenger flow for Maximum cross-sectional passenger flow For the first The maximum cross-sectional passenger flow of each section; Step 4: Calculate the passenger flow distribution matching under different route combinations during different time periods. The evaluation parameter calculation formula is as follows: （14） In the formula, is an evaluation parameter for matching the time period passenger flow distribution; Step 5: Solve formula (15) under the condition of meeting constraints (8)-(10) to obtain the evaluation parameter on the basis of the basic train operation route Optimal train operation route scheme: （15） In the formula, representing the selection of a base route; Step 6: After determining the unique time-sharing train operation route scheme, conduct passenger flow statistics according to the combined route scheme, and determine the number of trains to be operated in combination with constraints (4) to (7).

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