Single-line bus intelligent scheduling method based on double-layer constraint fusion

Abstract

The invention relates to the technical field of bus management, in particular to a single-line bus intelligent scheduling method based on double-layer constraint fusion, and the method comprises the steps: initializing scheduling parameters; simulating the running process of each vehicle, constructing a shift event chain, and verifying the integrity of the shift event chain; constructing a double-layer constraint matrix by taking the complete dispatching event chain of one vehicle as a row and the dispatching events at the station at the same moment as a column; performing constraint verification and adjustment on each shift event in the double-layer constraint matrix based on the constraint priority; carrying out compression or smoothing processing on the abnormal time section; and comprehensively checking the compressed or smoothed scheduling scheme, and if all constraint conditions and transport capacity requirements are met, generating a final scheduling scheme. According to the method, constraints of two levels of vehicle operation and station departure are considered at the same time, more reasonable scheduling is carried out on the buses, and collaborative optimization of vehicle operation and station departure is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bus management, in particular to a single-line bus intelligent scheduling method based on double-layer constraint fusion. BACKGROUND

[0002] At present, bus scheduling mainly adopts manual experience scheduling or single constraint automatic scheduling method. Manual experience scheduling has problems such as low efficiency, difficulty in optimization, and inability to adapt to complex scenarios. Although the single constraint automatic scheduling method can improve efficiency, it often only considers the single constraint of the vehicle layer or the platform layer, resulting in many problems in the actual execution of the scheduling result:

[0003] 1. Vehicle layer: unable to reasonably arrange vehicle turnover, resulting in too long or too short vehicle stay time at the site, affecting operational efficiency;

[0004] 2. Platform layer: uneven departure interval, insufficient departure density during peak hours, and excessive vehicles during off-peak hours, causing resource waste;

[0005] 3. Constraint conflict: the constraints of the vehicle layer and the platform layer often conflict, such as sacrificing vehicle reasonable turnover time to meet the departure interval, or causing uneven departure interval to ensure vehicle turnover.

[0006] Therefore, how to consider the constraints of both the vehicle operation and the platform departure, and more reasonably schedule the buses is a problem that needs to be solved by those skilled in the art. SUMMARY

[0007] Therefore, the present application provides a single-line bus intelligent scheduling method based on double-layer constraint fusion, which considers the constraints of both the vehicle operation and the platform departure, and more reasonably schedules the buses, achieving collaborative optimization of vehicle operation and platform departure.

[0008] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0009] A single-line bus intelligent scheduling method based on double-layer constraint fusion, comprising the following steps:

[0010] S1, initializing the scheduling parameters of the buses under a certain line;

[0011] S2, assigning a first departure time to all vehicles under the line according to the first departure time and the departure interval requirement, starting from the first departure time, simulating the running process of each vehicle, constructing a scheduling event chain, and verifying the integrity of the scheduling event chain;

[0012] S3, taking a complete scheduling event chain of a vehicle as a row, and taking the scheduling events at the same time on the platform as a column, to construct a double-layer constraint matrix;

[0013] S4, dividing the whole day operation time into different time periods, extracting time period features of each time period; determining constraint priorities of each time period based on the time period features of different time periods, and performing constraint checking and adjustment on each dispatching event in the double-layer constraint matrix based on the constraint priorities;

[0014] S5, based on the time period features and operation requirements, identifying an abnormal time period, and performing compression or smoothing processing on the abnormal time period;

[0015] S6, performing comprehensive checking on the scheduling scheme after compression or smoothing processing, and if all constraint conditions and operation requirements are met, generating a final scheduling scheme.

[0016] Further, S1 includes:

[0017] S11, determining basic operation parameters according to line features, including first and last bus times and peak time period division;

[0018] S12, formulating differentiated headway requirements for different time periods, including maximum and minimum headways during peak period, flat peak period and first and last bus period;

[0019] S13, setting maximum and minimum working time lengths of a single vehicle, and minimum and maximum stop time length requirements in different time periods;

[0020] S14, dividing the whole day operation time into multiple time periods at fixed intervals, counting the running time of the vehicle at each time period, and establishing a time period-running time mapping relationship;

[0021] S15, based on the running time analysis result, calculating the single vehicle round trip cycle, and combining with the working time length limit to determine the theoretical dispatching frequency of each vehicle.

[0022] Further, S2 includes:

[0023] S21, according to the first bus time and headway requirement, assigning a first dispatching time to each vehicle to generate a first dispatching time sequence;

[0024] S22, constructing a SARIMAX model based on historical data and time period features, and predicting the baseline running time of different time periods based on the SARIMAX model;

[0025] S23, starting from the first dispatching time, simulating the running process of each vehicle under the constraint of the baseline running time of different time periods, including dispatching, arrival and turnover links;

[0026] S24, generating corresponding dispatching events for each link in the simulation process, including dispatching time, arrival time, running time and stop time, to obtain the dispatching event chain of each vehicle.

[0027] S25, integrity verification is performed on the departure event chain of each vehicle, and verification targets include that the departure time meets the first and last time range requirements, the vehicle completes the required number of departure trips, and it is ensured that the vehicle is received at the same site.

[0028] Further, S22 includes:

[0029] Anomaly detection and cleaning are performed on historical running time data, unreasonable data points are removed, and a SARIMAX model is constructed based on the processed historical running time;

[0030] The whole day operation time is divided into multiple time periods at fixed intervals, and for each time period, the historical average running time at the departure time of the time period is calculated;

[0031] For each planned departure event, the time period in which the departure event is located is located, the feature vector corresponding to the time period is extracted, including period features, weather features and passenger flow features; the historical average running time of each time period is corrected based on the SARIMAX model combined with the feature vector of each time period as the baseline running time of the planned departure event.

[0032] Further, S3 includes:

[0033] S31, initialize the matrix structure: create the basic matrix structure of the vehicle layer and the platform layer, take the vehicle layer as the row, which is used to represent the complete departure event chain of a vehicle, take the platform layer as the column, which is used to represent the departure event at the same time on the platform, and determine the matrix dimension and index relationship;

[0034] S32, map the departure event chain to the matrix, and the mapping process includes: a) fill in the row data according to the vehicle number and the departure order, establish the correspondence between the vehicle and the departure event; b) fill in the column data according to the time period and the departure interval requirement, ensure the continuity of the platform departure event;

[0035] Each element in the matrix is a departure event object, and each departure event object includes the following attributes: departure time, arrival time, running time, departure direction, departure site number, arrival site number and forced stop time;

[0036] S33, set constraints for the matrix, including stop time, departure interval and capacity demand constraints;

[0037] S34, construct a four-way linked list relationship between matrix elements, each departure event object establishes a bidirectional association with adjacent elements: a) up, indicating a link to the previous departure event in the same column, used to maintain the departure order of the platform; b) down, indicating a link to the next departure event in the same column, used to maintain the departure order of the platform; c) left, indicating a link to the previous departure event in the same row, used to track the vehicle running track; d) right, indicating a link to the next departure event in the same row, used to track the vehicle running track.

[0038] Further, S4 includes:

[0039] S41, divide the whole day operation time into multiple time periods, including the first bus, the morning peak, the flat peak, the evening peak and the last bus period;

[0040] S42, analyze the passenger flow characteristics and the demand characteristics of the operation capacity of each period, and determine the constraint priority of each period;

[0041] S43, traverse each departure event in the double-layer constraint matrix, and perform the following checks for each departure event:

[0042] Period constraint check: check whether the departure time meets the operation time requirements of the period; verify whether it meets the passenger flow and full load rate requirements of the period; confirm whether it meets the fixed-point departure rule;

[0043] Platform constraint check: verify whether the interval with the previous and next departure event meets the requirements; check whether it meets the minimum / maximum stop time length rule of the platform; for peak hours, check whether the departure density meets the requirements;

[0044] Vehicle constraint check: confirm whether the vehicle working time length is within the limit; verify whether the vehicle round trip turnaround time is reasonable; check whether it meets the vehicle rest and departure requirements;

[0045] S44, when a certain departure event violates a certain constraint condition, adjust the departure time according to the violated constraint type, and get the four-way associated elements of the current departure event, and process them in the order of up, down, left and right, and recheck the constraints for each associated element; if the adjustment leads to new constraint violation, recursively process the related elements.

[0046] Further, in S42, the passenger flow characteristics include: the maximum passenger flow of each period, the ratio of passenger flow to vehicle capacity, and the passenger flow change rate between adjacent periods;

[0047] The demand characteristics of the operation capacity include: the baseline running time, the baseline departure interval, the peak interval and the flat peak interval predicted by the SARIMAX model;

[0048] In peak hours, the minimum headway and full load rate requirements are prioritized; in flat peak hours, the balance of transport capacity and vehicle turnover is prioritized; in the first and last shift hours and rest shift hours, the operation rule requirements are prioritized.

[0049] Further, S5 includes:

[0050] S51, based on the headway deviation judgment, the section continuity judgment, the transport capacity distribution judgment and the constraint satisfaction degree judgment index, identify the abnormal time section that needs to be compressed or smoothed;

[0051] S52, evaluate the compressible range of each abnormal time section, considering vehicle operation constraints, station stop constraints and headway constraints, calculate the minimum compression unit, while not affecting subsequent and previous departure events as a prerequisite, determine the compression boundary;

[0052] S53, adopt a gradual compression strategy to compress the abnormal time section;

[0053] S54, determine the smoothing parameter according to the time period characteristics, and perform smoothing processing on the abnormal section according to the smoothing parameter; wherein the smoothing parameter includes a reference parameter and an adjustment parameter, the reference parameter includes: first bus time period reference interval, peak time period reference interval, flat peak time period reference interval and last bus time period reference interval; the adjustment parameter includes: adjustment time step, maximum iteration number and interval coefficient range.

[0054] Further, S53 includes:

[0055] S531, determine the start time point and end time point of the compression interval, which remain unchanged during the compression process; check whether the compression interval length meets the minimum compression requirement, and record the departure event information corresponding to the compression interval endpoints as the boundary constraint of the compression process;

[0056] S532, determine the target headway, and select a forward compression mode or a backward compression mode;

[0057] When the forward compression mode is selected, starting from the compression interval start time point, the new departure time is calculated in turn according to the target headway; the new time of each departure event is equal to the departure time of the previous departure event plus the target interval; the departure time of the last departure event must not exceed the termination time point of the compression interval;

[0058] When the backward compression mode is selected, starting from the compression interval termination point, the new departure time is calculated in reverse order according to the target headway; the new time of each departure event is equal to the departure time of the next event minus the target interval; the departure time of the first departure event must not be earlier than the start time point of the compression interval;

[0059] S533, performing a compression process:

[0060] Arranging the departure events in the compression interval in chronological order to establish a compression processing queue;

[0061] According to the selected compression mode, the departure time is gradually adjusted, and during the adjustment process, the single adjustment amount does not exceed the minimum compression unit, and after each adjustment, the constraint satisfaction condition is checked. If there is a constraint violation, it will be rolled back to the last feasible state;

[0062] For each adjusted departure event, its four-way associated events in the double-layer constraint matrix are obtained, and it is checked whether the adjustment affects the constraints of the associated events. If it does, the associated events are adjusted synchronously;

[0063] S534, compression result verification: verifying whether the standard deviation of the departure interval in the compressed interval meets the requirements; confirming whether all adjusted departure events meet the vehicle and platform constraints; verifying whether the connection between the compressed interval and the adjacent interval is smooth;

[0064] S535, abnormal situation processing:

[0065] When the compression interval length is insufficient to accommodate all departure events, the compression interval range is expanded, and the target departure interval is adjusted, or it is split into multiple sub-intervals for separate processing;

[0066] When there is a constraint conflict that cannot be met, the high-priority constraint is prioritized, the low-priority constraint is relaxed, and the unhandled constraint conflict is recorded for subsequent optimization.

[0067] Further, in S51, the abnormal time section determination method is:

[0068] Departure interval deviation determination: calculate the difference between the departure interval in the section and the target interval, and determine it as abnormal when the difference exceeds the threshold value, wherein the peak period threshold value is 5 minutes and the flat peak period threshold value is 15 minutes;

[0069] Section continuity determination: check whether the transition of adjacent sections is smooth;

[0070] Distribution of transport capacity determination: evaluate whether the transport capacity distribution in the section is balanced;

[0071] Constraint satisfaction degree determination: count the number of constraint violations in the section, including the number of violations of the departure interval constraint and the stop time constraint.

[0072] According to the above technical solution, compared with the prior art, the present application has the following beneficial effects:

[0073] 1. The present application considers both vehicle operation and platform departure constraints, realizes a globally optimal scheduling scheme, and makes the final scheduling scheme more reasonable.

[0074] 2、The application automatically processes constraint conflicts by constraint fusion algorithm, reduces manual intervention, and realizes intelligent scheduling of each vehicle scheduling.

[0075] 3、The application divides the whole day operation time into multiple time periods, including peak period, flat peak period, first and last shift, etc., considers specific characteristics of different time periods, and finely controls peak period, special time period, etc. scene, improves the practicability of the scheduling scheme.

[0076] 4、The application improves the utilization efficiency of vehicle and human resources by identifying abnormal time sections and compressing and smoothing the abnormal sections.

[0077] 5、The application can flexibly cope with scheduling needs of different lines and different time periods, and has strong universality. BRIEF DESCRIPTION OF DRAWINGS

[0078] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only a part of the embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.

[0079] Figure 1 The overall framework flow chart of the single line bus intelligent scheduling method based on double-layer constraint fusion provided by the present application is shown in the figure.

[0080] Figure 2 The detailed flow chart of the single line bus intelligent scheduling method based on double-layer constraint fusion provided by the present application is shown in the figure. DETAILED DESCRIPTION

[0081] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0082] As shown in the figure, the embodiment of the present application discloses a single line bus intelligent scheduling method based on double-layer constraint fusion, including the following steps: Figure 1 S1, initialize the scheduling parameters of the bus under a certain line;

[0083]

[0084] ​S2, according to the first time and the departure interval requirements, assigning the first departure time for all vehicles under the line, starting from the first departure time, simulating the running process of each vehicle, constructing the departure event chain, and verifying the integrity of the departure event chain;

[0085] S3, taking the complete departure event chain of a vehicle as a row, and the departure event at the same time on the platform as a column, constructing a double-layer constraint matrix;

[0086] S4, dividing the whole day operation time into different time periods, extracting the time period characteristics of each time period, determining the constraint priority of each time period based on the time period characteristics of different time periods, and performing constraint checking and adjustment on each departure event in the double-layer constraint matrix based on the constraint priority;

[0087] S5, based on the time period characteristics and operation requirements, identifying the abnormal time period, and performing compression or smoothing processing on the abnormal time period;

[0088] S6, performing comprehensive checking on the scheduling scheme after compression or smoothing processing, and if all constraint conditions and operation requirements are met, generating the final scheduling scheme.

[0089] Next, combined with Figure 2 , the above steps are further described in detail.

[0090] S1, initializing the scheduling parameters of the buses under a certain line, specifically including:

[0091] S11, determining the basic operation parameters according to the line characteristics, including the first and last time and the division of peak period.

[0092] S12, setting the departure interval requirements: formulating differentiated departure interval requirements for different time periods, including the maximum and minimum departure interval during peak period, flat peak period and first and last period.

[0093] S13, defining vehicle working restrictions: setting the maximum and minimum working time of a single vehicle, and the minimum and maximum stop time requirements in different time periods.

[0094] S14, analyzing the running time: dividing the whole day operation time into multiple time periods according to fixed intervals, counting the running time of the vehicle at each time period, and establishing the time period-running time mapping relationship.

[0095] S15, calculating the theoretical departure times: based on the running time analysis results, calculating the single vehicle round-trip cycle, and combining with the working time limit, determining the theoretical departure times of each vehicle.

[0096] In this step, the basic operation parameters are determined according to the actual operation characteristics of the line, including the determination of basic parameters such as the setting of the first and last bus time, the planning of the operation time, and the division of the peak period. In terms of setting the first and last bus time, according to historical operation data and actual demand, the optimal first bus departure time and last bus arrival time are determined, usually the first bus time is set between 5:30 and 6:30 in the morning, and the last bus time is set between 22:00 and 23:00 in the evening according to the passenger flow.

[0097] Differentiated departure interval requirements are formulated for different periods, especially during the morning peak (7:00-9:00) and evening peak (17:00-19:00), the departure interval is usually controlled at 3-5 minutes, during the flat peak, it can be appropriately relaxed to 8-15 minutes, and during the first and last bus, it can be extended to 15-20 minutes.

[0098] In addition, it is also necessary to clearly stipulate the working restrictions of the vehicle, including the maximum working time of each vehicle not exceeding 8 hours, the minimum working time not less than 6 hours, and the stop time requirements in different periods, among which the minimum stop time in the peak period is not less than 3 minutes, and the minimum stop time in the flat peak period is not less than 5 minutes.

[0099] Through statistical analysis of the running time of each period, an accurate period-running time mapping relationship is established, recording the average running time, standard deviation and other statistical indicators of each time period (such as 15 minutes as a time slice), providing basic data support for subsequent turnover calculation.

[0100] Finally, based on the analysis results of the running time, combined with the single vehicle round trip cycle (usually including the uplink time, downlink time and stop time at both ends of the station) and the working time limit, the system will accurately calculate the theoretical departure times of each vehicle, ensuring the reasonable utilization of vehicles.

[0101] S2, constructing a departure event chain, specifically including:

[0102] S21, according to the first bus time and the departure interval requirement, assigning the first departure time to each vehicle, and generating the first departure time sequence.

[0103] S22, based on historical data and period characteristics, constructing a SARIMAX model, predicting the baseline running time in different periods based on the SARIMAX model, specifically including:

[0104] S221, since the conditions of all vehicles on the same line are basically the same, only the relationship model between the departure time and the running time needs to be constructed, the construction process includes:

[0105] 1) Outlier detection and cleaning of historical running time data, eliminating unreasonable data points, and grouping by time period, based on the processed historical running time and time period characteristics to build a SARIMAX model.

[0106] 2) Feature engineering: build time period features (morning peak / flat peak / late peak), weather features, passenger flow features, and other exogenous variables.

[0107] 3) Model order determination: determine the model order (p, d, q) x (P, D, Q) s based on AIC and BIC criteria.

[0108] 4) Parameter estimation: estimate model parameters using maximum likelihood estimation method.

[0109] 5) Model diagnosis: verify model effectiveness through residual analysis.

[0110] S222, after the model is built, divide the whole day operation time into multiple time periods (such as 15 minutes for a time segment), for each time period, calculate the historical average running time at the departure time of that time period;

[0111] S223, for each planned departure event, locate the time period where the departure event occurs, extract the feature vector corresponding to the time period, including time period features, weather features and passenger flow features; based on the SARIMAX model combined with the feature vector of each time period, correct the historical average running time of the time period as the baseline running time of the planned departure event.

[0112] This prediction process is applicable to all vehicles on the same line, without considering individual differences, significantly simplifying the model complexity while ensuring prediction accuracy.

[0113] S23, simulate vehicle operation process: from the first departure time, under the constraint of baseline running time in different time periods, simulate the operation process of each vehicle, including departure, arrival and turnaround.

[0114] S24, generate departure events: in the simulation process, generate corresponding departure events for each link, including departure time, arrival time, running time and stop time, to get the departure event chain of each vehicle.

[0115] S25, verify the integrity of each vehicle's departure event chain, verify the following three aspects: departure time meets the first and last time range requirements, vehicle completes the required number of departure trips, and ensures that the vehicle is parked at the same station.

[0116] In this step, in the construction process of the departure event chain, first, according to the first departure time and the departure interval requirement, a reasonable first departure time is allocated for each vehicle. The allocation of the departure time needs to consider the matching relationship between the number of vehicles and the departure interval, so as to ensure that the stable departure interval can be maintained after the first bus departs.

[0117] Subsequently, based on historical data and time period characteristics, an accurate SARIMAX running time prediction model is constructed, and the model construction is completed through five key steps: first, data preprocessing, abnormal value detection and cleaning of historical running time data, and elimination of unreasonable data points; second, feature engineering, construction of external variables including time period characteristics (morning peak / flat peak / late peak), weather characteristics (sunny / rainy / temperature), passenger flow characteristics, etc.; third, model order determination, determination of the order (p, d, q) x (P, D, Q) s of the model through AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion); fourth, parameter estimation, estimation of model parameters using maximum likelihood estimation method; and finally, model diagnosis, verification of the effectiveness of the model through residual analysis.

[0118] In the prediction application stage, a day is divided into 96 15-minute time segments, a baseline running time model is established for each time segment t, the historical average running time μt of the time segment is calculated, and the baseline running time yt is predicted through the SARIMAX model combined with the feature vector xt of the current time segment. On this basis, the running process of each vehicle is simulated, including departure, arrival, turnover, etc., and the corresponding departure event is generated, and the key information of each event such as departure time, arrival time, running time, and stop time is recorded in detail. Finally, the integrity of the event chain is verified, mainly in three aspects: first, to ensure that all departure times are within the range of the first and last departure times; second, to verify whether each vehicle has completed the required number of departures; and finally, to ensure that all vehicles can be collected at the same station, ensuring the standardization of operation.

[0119] S3, construct a double-layer constraint matrix, specifically including:

[0120] S31, initialize the matrix structure: create the basic matrix structure of the vehicle layer and the platform layer, with the vehicle layer as the row, representing the complete departure event chain of a vehicle, and the platform layer as the column, representing the departure event at the same time on the platform, and determine the matrix dimension and index relationship.

[0121] S32, fill in the matrix: map the departure event chain to the matrix, the mapping process includes: a) fill in the row data according to the vehicle number and departure order, establish the correspondence between the vehicle and the departure event; b) fill in the column data according to the time period and departure interval requirement, ensure the continuity of the platform departure event;

[0122] Each element in the matrix is a departure event object, each departure event object includes the following attributes: a) departure_time: departure time; b) arrival_time: arrival time; c) runtime_minutes: running time; d) direction: departure direction (up / down); e) from_station: departure station number; f) to_station: arrival station number; g) force_stop_time: forced stop time.

[0123] S33, set constraints for the matrix, including stop time, departure interval and capacity demand constraints;

[0124] S34, establish matrix association: build a four-way linked list relationship between matrix elements, each departure event object is associated with adjacent elements in two directions: a) UP, indicating linking to the previous departure event in the same column, used to maintain the departure order of the platform; b) DOWN, indicating linking to the next departure event in the same column, used to maintain the departure order of the platform; c) LEFT, indicating linking to the previous departure event in the same row, used to track the vehicle running track; d) RIGHT, indicating linking to the next departure event in the same row, used to track the vehicle running track.

[0125] In the construction of the double-layer constraint matrix, a two-dimensional matrix structure containing vehicle layer and platform layer is created. In the horizontal axis (row) direction of the matrix, the vehicle dimension is represented, and each row records the departure event chain of a vehicle, including all events such as departure, arrival, turnaround, etc. of the vehicle throughout the day; in the vertical axis (column) direction, the platform dimension is represented, and each column records the departure event at the same time on the platform, used to manage and optimize the departure interval at the platform level. Each element in the matrix is a departure event (Departure) object, and a four-way linked list relationship is established between the matrix elements to achieve effective association and management of the departure event. This four-way linked list structure enables the system to quickly access and adjust the relevant information of any departure event, providing convenience for subsequent optimization and adjustment.

[0126] S4, perform constraint fusion optimization, the optimization process is based on historical operation data, and the following basic data needs to be provided by the user: a) passenger flow data: passenger flow distribution and trend in each period; b) vehicle data: full load rate, vehicle capacity and other capacity indicators; c) running data: historical turnaround time, interval running time, etc.; d) stop data: stop time distribution of each station. The specific optimization process includes:

[0127] S41, divide time sections: divide the whole day operation time into multiple time sections, including the first shift, morning peak, flat peak, evening peak and last shift.

[0128] S42, extract the time period characteristics: analyze the passenger flow characteristics and the demand characteristics of the operation capacity of each time period, and determine the constraint priority of each time period;

[0129] Among them, the passenger flow characteristics include: 1) the maximum cross-section passenger flow: the maximum passenger flow of each time period; 2) the full load rate: the ratio of passenger flow to vehicle capacity, the calculation formula is: (passenger flow / (number of departures*vehicle capacity))*100%; 3) passenger flow change trend: the passenger flow change rate between adjacent time periods.

[0130] The operation capacity demand characteristics include: 1) the benchmark operation time predicted by the SARIMAX model; 2) the benchmark departure interval: calculated according to the operation time and the number of departures, the formula is: operation time / (number of departures-1); 3) peak interval: take 0.7 times of the benchmark interval; 4) flat peak interval: take 1.2 times of the benchmark interval.

[0131] Constraint attributes: 1) stop time constraint: the minimum and maximum stop time requirements of each time period. 2) departure interval constraint: the minimum and maximum departure interval requirements of each time period. 3) fixed-point departure constraint: whether to depart at a fixed time.

[0132] Priority setting: 1) in peak hours (7:00-9:00, 17:00-19:00), priority is given to guarantee the minimum departure interval and full load rate requirements; 2) in flat peak hours, priority is given to balance the operation capacity and vehicle turnover; 3) in the first and last shift hours and rest standby hours, priority is given to meet the operation rules requirements.

[0133] S43, traverse each departure event in the double-layer constraint matrix, and perform the following constraint condition verification for each departure event:

[0134] 1) time period constraint verification, a) departure time verification: check whether the departure time meets the time period operation time requirements; b) passenger flow full load verification: verify whether it meets the time period passenger flow and full load rate requirements; c) fixed-point departure verification: confirm whether it meets the fixed-point departure rules.

[0135] 2) platform constraint verification, a) interval requirement verification: verify whether the interval with the previous and next departure events meets the requirements; b) stop time verification: check whether it meets the minimum / maximum stop time rules of the platform; c) peak density verification: for peak hours, verify whether the departure density meets the requirements.

[0136] 3) vehicle constraint verification, a) working time verification: confirm whether the vehicle working time is within the limit; b) turnover time verification: verify whether the vehicle round-trip turnover time is reasonable; c) rest standby verification: check whether it meets the vehicle rest standby requirements.

[0137] S44, when a certain departure event is found to violate a certain constraint condition, the following adjustment strategy is adopted:

[0138] 1) Departure time adjustment: according to the type of violated constraint, calculate a reasonable adjustment range; find a feasible new departure time within the adjustment range; prefer to choose the adjustment scheme that has the least impact on other departure events.

[0139] 2) Chain update: get the four-way associated elements of the current departure event, and process them in the order of up, down, left, and right; re-execute constraint checking for each associated element;

[0140] 3) Conflict processing: if adjustment leads to new constraint violation, recursively process related elements; record the adjustment path to avoid circular adjustment; if necessary, backtrack to alternative solutions.

[0141] S45, complete global optimization through multiple iterations, including:

[0142] 1) Departure time adjustment strategy: a) forward adjustment: try to advance the departure time, adjustment amount is 1.2 times the difference of violated constraint, to avoid still violating the constraint after adjustment. b) backward adjustment: try to delay the departure time, adjustment amount is 1.2 times the difference of violated constraint. c) interval search: search within the forward and backward adjustment range with minimum departure interval as step. d) fluctuation adjustment: when local search is in trouble, allow larger range of time adjustment to jump out of local optimum.

[0143] 2) Feasibility verification method: a) constraint satisfaction degree: calculate the satisfaction degree of each constraint after adjustment. b) chain effect: evaluate the impact range and degree of adjustment on associated departure events. c) operation index: verify the key indicators such as full load rate and departure interval after adjustment. d) boundary condition: ensure that adjustment will not cause the first and last class time or working time to exceed the limit.

[0144] 3) Optimal solution determination standard: a) constraint violation number: count the number of remaining constraint violations. b) adjustment amplitude: calculate the total time change caused by this round of adjustment. c) index improvement: evaluate the improvement degree of key operation indicators. d) stability: the improvement amplitude change trend of continuous multiple rounds of adjustment.

[0145] 4) Iteration termination condition: a) reach the maximum number of iterations (default 50 rounds). b) the improvement amplitude of the last 3 rounds is less than 1 minute. c) the number of constraint violations has not changed for 5 consecutive rounds. d) the solution is in shock (the same solution appears repeatedly).

[0146] 5) Backtracking mechanism: a) Record the complete scheme of each iteration. b) Set checkpoints to save the optimal solution at stages. c) Backtrack when the new scheme is worse than the historical optimal solution. d) Try different adjustment strategies at the backtracking point.

[0147] The constraint fusion optimization phase of this step first divides the full-day operating time into different time periods, including the first-trip period (5:30-7:00), the morning peak period (7:00-9:00), the morning off-peak period (9:00-17:00), the evening peak period (17:00-19:00), the evening off-peak period (19:00-22:00), and the last-trip period (22:00-23:00). Analyze the passenger flow characteristics and operating capacity demand characteristics of each period, and determine the constraint priority of each period through comprehensive analysis of passenger flow data, vehicle data (full load rate, vehicle capacity, etc.), operation data (historical turnaround time, interval running time, etc.), and stop data (stop time distribution of each station). Then, perform constraint checking for each departure event in the matrix, and use a gradual adjustment strategy when a constraint violation is found. Next, complete global optimization through multiple iterations, each iteration including departure time adjustment (forward adjustment, backward adjustment, interval search, and wave adjustment), feasibility verification (constraint satisfaction, chain effect, operating index, and boundary condition), and optimal solution determination (constraint violation number, adjustment amplitude, index improvement, and stability).

[0148] S5, based on the characteristics of the time period and the operating demand, identify the abnormal time section, and perform compression or smoothing processing on the abnormal time section, specifically including:

[0149] S51, identify the abnormal section:

[0150] 1) Time period classification: divide the operating time into four basic time periods: first-trip period (FIRST_TRIP), peak period (PEAK), off-peak period (OFF_PEAK), and last-trip period (LAST_TRIP).

[0151] 2) Section hierarchy: build a hierarchical time section management structure (TimeSection) to support parent-child relationship management and facilitate overall and local section control.

[0152] 3) Abnormality determination: based on departure interval deviation determination, section continuity determination, operating capacity distribution determination, and constraint satisfaction degree determination, identify the abnormal time section that needs to be compressed or smoothed:

[0153] a) Departure interval deviation determination: calculate the difference between the departure interval in the section and the target interval, and determine it as abnormal when the difference exceeds the threshold value, where the peak period threshold is 5 minutes and the off-peak period threshold is 15 minutes.

[0154] b) Segment continuity judgment: Check if the transition between adjacent segments is smooth.

[0155] c) Capacity distribution judgment: Evaluate if the capacity distribution within a segment is balanced.

[0156] d) Constraint satisfaction degree judgment: Count the number of constraint violations within a segment, including the violation of headway constraint and dwell time constraint.

[0157] S52, Calculate compression space: Evaluate the compressible range of each abnormal time segment, considering vehicle operation constraints, station stop constraints, and headway constraints, calculate the minimum compression unit, and determine the compression boundary while ensuring that it does not affect subsequent and previous departure events.

[0158] where the minimum compression unit refers to the smallest time unit that can be compressed within a given segment, and its determination process includes: 1) Operation constraint calculation: considering vehicle operation constraints, ensure that the compressed headway is not less than 3 minutes. 2) Dwell constraint calculation: considering the station stop requirement, ensure that the compressed dwell time is not less than the default minimum dwell time of 5 minutes. 3) Interval constraint calculation: considering the headway limit of different time periods, ensure that the compressed interval meets the time period characteristics.

[0159] The determination of the compression boundary includes: 1) Forward boundary calculation: calculate the maximum adjustable time for compression towards the termination point, ensuring that it does not affect subsequent departure events. 2) Backward boundary calculation: calculate the maximum adjustable time for compression towards the starting point, ensuring that it does not affect previous departure events. 3) Scheme evaluation: select the compression direction and amplitude, preferentially selecting the scheme that has a smaller impact on the overall departure plan.

[0160] S53, Adopt a gradual compression strategy to compress the abnormal time segment, specifically including:

[0161] S531, Compression interval determination, 1) Interval endpoint determination: determine the starting time point and termination time point of the compression interval, which remain unchanged during the compression process; 2) Interval range verification: check if the compression interval length meets the minimum compression requirement; 3) Boundary condition recording: record the departure event information corresponding to the compression interval endpoints as boundary constraints for the compression process.

[0162] S532, Compression direction selection: determine the target headway and select the forward compression mode or backward compression mode;

[0163] 1) Target headway calculation: calculate the ideal target headway according to the interval type (peak / flat) and interval length: a) Peak interval: target interval = min(5 minutes, interval length / number of departure events); b) Flat interval: target interval = min(15 minutes, interval length / number of departure events).

[0164] 2) When the forward compression mode is selected, i.e., compression towards the end point, the end point of the interval is fixed, and the departure events in the interval are sequentially pushed back, specifically: starting from the compression interval start time point, the new departure time is calculated according to the target departure interval; the new time of each departure event is equal to the departure time of the previous departure event plus the target interval; the departure time of the last departure event must not exceed the end time point of the compression interval.

[0165] 3) When the backward compression mode is selected, i.e., compression towards the start point, the start point of the interval is fixed, and the departure events in the interval are sequentially pushed forward, specifically: starting from the end point of the compression interval, the new departure time is calculated in reverse according to the target departure interval; the new time of each departure event is equal to the departure time of the next event minus the target interval; the departure time of the first departure event must not be earlier than the start time point of the compression interval.

[0166] S533, execute the compression process:

[0167] 1) Departure event sorting: arrange the departure events in the compression interval in chronological order to establish a compression processing queue.

[0168] 2) Progressive compression execution: adjust the departure time step by step according to the selected compression mode, and during the adjustment process, the following conditions must be met: a) the single adjustment amount must not exceed the minimum compression unit (default 2 minutes); b) check the constraint satisfaction after each adjustment; c) if there is a constraint violation, revert to the last feasible state.

[0169] 3) Associated event processing: for each adjusted departure event, obtain its four-way associated events (UP, DOWN, LEFT, RIGHT) in the double-layer constraint matrix, check if the adjustment affects the constraints of the associated events, and if so, adjust the associated events synchronously.

[0170] S534, compression result verification, mainly including the following three aspects of verification: 1) interval uniformity check: verify whether the standard deviation of the departure interval after compression meets the requirements; 2) constraint satisfaction check: confirm whether all adjusted departure events meet the vehicle and platform constraints; 3) boundary connection check: verify whether the connection between the compression interval and the adjacent interval is smooth.

[0171] S535, abnormal situation handling, mainly including:

[0172] 1) Space shortage handling: when the compression interval length is insufficient to accommodate all departure events, expand the compression interval range and adjust the target departure interval, or split it into multiple sub-intervals for separate processing.

[0173] 2) Constraint conflict handling: When there is a constraint conflict that cannot be satisfied, prioritize high-priority constraints (such as minimum headway during peak hours) and relax low-priority constraints (such as stop duration), and record the constraint conflicts that cannot be handled for subsequent optimization.

[0174] S54, determine the smoothing parameter according to the time period characteristics, and perform smoothing processing on the abnormal section according to the smoothing parameter;

[0175] The smoothing parameter includes a reference parameter and an adjustment parameter, and the reference parameter includes: a first bus period reference interval (set to 10 minutes), a peak period reference interval (set to 5 minutes), an off-peak period reference interval (set to 15 minutes), and a last bus period reference interval (set to 15 minutes).

[0176] The adjustment parameter includes: an adjustment time step (set to 2 minutes), a maximum number of iterations (10 rounds), and an interval coefficient range (minimum value 0.8, maximum value 1.5), and a satisfaction threshold is set to 0.8.

[0177] After setting the smoothing parameter, perform smoothing processing, 1) Intra-section smoothing: a) Target interval calculation: determine the ideal headway according to the time period type. b) Progressive adjustment execution: adjust the departure time step by step with a minimum step of 2 minutes. c) Constraint check execution: ensure that the adjustment does not violate vehicle and platform constraints.

[0178] 2) Optimization termination judgment: a) Iteration number judgment: terminate when the maximum number of iterations is reached, 10 rounds. b) Improvement amplitude judgment: terminate when the adjustment improvement amplitude is less than the threshold. c) Satisfaction judgment: terminate when the satisfaction reaches the target value 0.8. d) Oscillation judgment: terminate when the solution oscillates.

[0179] In the section compression smoothing link, first, the operation time is divided into four basic time periods: first bus period (FIRST_TRIP), peak period (PEAK), off-peak period (OFF_PEAK) and last bus period (LAST_TRIP) through time period classification, and a hierarchical time section management structure (TimeSection) is constructed to support parent-child relationship management.

[0180] Next, based on the headway deviation judgment (peak period threshold 5 minutes, off-peak period threshold 15 minutes), section continuity judgment, capacity distribution judgment and constraint satisfaction degree judgment, identify the time sections that need to be compressed or smoothed.

[0181] Subsequently, the compressible range of each abnormal section is evaluated, and a compression scheme is planned by calculating the minimum compression unit (considering the operation constraints, stop constraints and interval constraints) and determining the compression boundaries (forward boundary and backward boundary). Finally, the compression process is executed, and a progressive compression strategy is adopted when performing section compression.

[0182] The steps including departure event sequencing, target interval calculation, progressive compression execution and associated event processing are performed within a section to calculate target intervals, perform progressive adjustment and check constraints until the termination condition is met.

[0183] S6, a comprehensive check is performed on the scheduling scheme after compression or smoothing, mainly including:

[0184] 1) constraint checking is performed to comprehensively check whether the scheduling scheme meets all constraint conditions.

[0185] 2) time period coverage is verified to confirm whether the departure arrangement of each time period meets the transport capacity demand.

[0186] 3) a timetable is generated to arrange the optimized scheduling scheme and generate a detailed departure timetable.

[0187] When generating the final scheduling scheme, a comprehensive check is performed on whether the scheduling scheme meets all constraint conditions, including vehicle-level constraints (such as working time, turnaround time) and platform-level constraints (such as departure interval, stop time). At the same time, the departure arrangement of each time period is verified to confirm whether it meets the transport capacity demand, especially whether it can meet the passenger flow demand during peak hours and whether there is transport capacity waste during off-peak hours. If it is found that the constraint conditions are not met, the departure interval is fine-tuned. After confirming that all check items meet the requirements, a detailed departure timetable is finally generated, which contains complete information such as the departure time, arrival time and stop time of each vehicle, providing accurate guidance for actual operation.

[0188] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the related parts can be referred to the method part.

[0189] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A single-line bus intelligent scheduling method based on double-layer constraint fusion, characterized in that, The method comprises the following steps: S1, initializing scheduling parameters of buses on a certain line; S2, assigning a first departure time to all vehicles on the line according to the first departure time and the departure interval requirement, simulating the running process of each vehicle from the first departure time, constructing a departure event chain, and verifying the integrity of the departure event chain; S3, constructing a double-layer constraint matrix by taking the complete departure event chain of a vehicle as a row and taking the departure event at the same time on the platform as a column; S4, dividing the whole day operation time into different time periods, and extracting time period characteristics of each time period; determining the constraint priority of each time period based on the time period characteristics of different time periods, and performing constraint verification and adjustment on each departure event in the double-layer constraint matrix based on the constraint priority; S5, based on the time period characteristics and operation demand, identifying an abnormal time section, and performing compression or smoothing processing on the abnormal time section; S6, comprehensively checking the scheduling scheme after compression or smoothing processing, and generating a final scheduling scheme if all constraint conditions and operation demand are met.

2. The single-line bus intelligent scheduling method based on double-layer constraint fusion according to claim 1, characterized in that, S1 comprises: S11, determining basic operation parameters according to line characteristics, including first and last departure time and peak period division; S12, formulating differentiated departure interval requirements for different time periods, including maximum and minimum departure intervals during peak period, flat peak period and first and last departure period; S13, setting the maximum and minimum working time of a single vehicle, and the minimum and maximum stop time requirements of different time periods; S14, dividing the whole day operation time into multiple time periods at a fixed interval, counting the running time of the vehicle at the departure time in each time period, and establishing a time period-running time mapping relationship; S15, based on the running time analysis result, calculating the single vehicle round trip cycle, and determining the theoretical departure number of each vehicle in combination with the working time limit.

3. The single-line bus intelligent scheduling method based on double-layer constraint fusion according to claim 1, wherein S2 Comprise: S21, assigning a first departure time to each vehicle according to the first departure time and the departure interval requirement, and generating a first departure time sequence; S22, constructing a SARIMAX model based on historical data and time period characteristics, and predicting the benchmark running time of different time periods based on the SARIMAX model; S23, simulating the running process of each vehicle from the first departure time under the constraint of the benchmark running time of different time periods, including departure, arrival and turnover; S24, generating corresponding departure events for each link in the simulation process, including departure time, arrival time, running time and stop time, to obtain the departure event chain of each vehicle; S25, verifying the integrity of the departure event chain of each vehicle, and the verification targets include: the departure time meets the first and last departure time range requirement, the vehicle completes the required number of departure trips, and the vehicle is ensured to be parked at the same site.

4. The single-line bus intelligent scheduling method based on double-layer constraint fusion according to claim 3, characterized in that, S22 comprises: detecting and cleaning outliers from historical running time data, eliminating unreasonable data points, and constructing a SARIMAX model based on the processed historical running time; dividing the whole day operation time into multiple time periods at a fixed interval, and for each time period, calculating the historical average running time at the departure time of the time period; For each planned departure event, the time period in which the departure event occurs is located, and the feature vector corresponding to the time period is extracted, including period features, weather features, and passenger flow features; based on the SARIMAX model, the historical average running time corresponding to the time period is corrected based on the feature vector of each time period, as the baseline running time of the planned departure event.

5. The single-line bus intelligent scheduling method based on double-layer constraint fusion according to claim 1, characterized in that, S3 includes: S31, initialize the matrix structure: create the basic matrix structure of the vehicle layer and the platform layer, with the vehicle layer as the row, representing a complete departure event chain of a vehicle, and the platform layer as the column, representing the departure event at the same time on the platform, and determine the matrix dimension and index relationship; S32, map the departure event chain to the matrix, the mapping process includes: a) fill in the row data according to the vehicle number and the departure order, establish the correspondence between the vehicle and the departure event; b) fill in the column data according to the time period and the departure interval requirement, ensure the continuity of the platform departure event; Each element in the matrix is a departure event object, each departure event object includes the following attributes: departure time, arrival time, running time, departure direction, departure site number, arrival site number, and forced stop time; S33, set the constraint conditions for the matrix, including stop time, departure interval, and capacity demand constraints; S34, build a four-way linked list relationship between the matrix elements, each departure event object is bidirectionally associated with adjacent elements: a) up, indicating a link to the previous departure event in the same column, used to maintain the platform departure order; b) down, indicating a link to the next departure event in the same column, used to maintain the platform departure order; c) left, indicating a link to the previous departure event in the same row, used to track the vehicle running trajectory; d) right, indicating a link to the next departure event in the same row, used to track the vehicle running trajectory.

6. The single-line bus intelligent scheduling method based on double-layer constraint fusion according to claim 1, characterized in that, S4 Including: S41, divide the whole day operation time into multiple time periods, including the first bus, the morning peak, the flat peak, the evening peak, and the last bus time period; S42, analyze the passenger flow characteristics, capacity demand characteristics of each time period, and determine the constraint priority of each time period; S43, traverse each departure event in the double-layer constraint matrix, and perform the following checks for each departure event: Period constraint check: check whether the departure time meets the operation time requirements of the time period; verify whether it meets the passenger flow and full load rate requirements of the time period; confirm whether it meets the fixed-point departure rule; Platform constraint check: verify whether the interval with the previous and next departure event meets the requirements; check whether it meets the minimum / maximum stop time rules of the platform; for peak hours, check whether the departure density meets the requirements; Vehicle constraint check: confirm whether the vehicle working time is within the limit; verify whether the vehicle turnaround time is reasonable; check whether it meets the vehicle rest and departure requirements; S44, when a certain departure event violates a certain constraint condition, adjust the departure time according to the violated constraint type, and get the four-way associated elements of the current departure event, and process them in the order of up, down, left, and right, and re-execute the constraint check for each associated element; if the adjustment leads to a new constraint violation, recursively process the related elements.

7. The single-line bus intelligent scheduling method based on double-layer constraint fusion according to claim 1, characterized in that, In S42, the passenger flow characteristics include: the maximum passenger flow in each time period, the ratio of passenger flow to vehicle capacity, and the passenger flow change rate between adjacent time periods; The capacity demand characteristics include: the baseline running time predicted by the SARIMAX model, the baseline departure interval, the peak interval, and the off-peak interval; In the peak period, the minimum departure interval and the full load rate requirements are prioritized; in the off-peak period, the capacity balance and vehicle turnover are prioritized; in the first and last shift periods and the rest period, the operation rule requirements are prioritized.

8. The single-line bus intelligent scheduling method based on double-layer constraint fusion according to claim 1, wherein S5 Comprise: S51, based on the departure interval deviation judgment, the section continuity judgment, the capacity distribution judgment and the constraint satisfaction degree judgment index, identify the abnormal time period that needs to be compressed or smoothed; S52, evaluate the compressible range of each abnormal time period, considering vehicle operation constraints, station stop constraints and departure interval constraints, calculate the minimum compression unit, and determine the compression boundary while ensuring that it does not affect subsequent and previous departure events; S53, adopt a gradual compression strategy to compress the abnormal time period; S54, determine the smoothing parameters according to the time period characteristics, and perform smoothing processing on the abnormal section according to the smoothing parameters; wherein the smoothing parameters include baseline parameters and adjustment parameters, the baseline parameters include: first bus time period baseline interval, peak time period baseline interval, off-peak time period baseline interval and last bus time period baseline interval; adjustment parameters include: adjustment time step, maximum iteration number and interval coefficient range.

9. The single-line bus intelligent scheduling method based on double-layer constraint fusion according to claim 8, characterized in that, S53 includes: S531, determine the start time point and end time point of the compression interval, which remain unchanged during the compression process; check whether the compression interval length meets the minimum compression requirement, and record the departure event information corresponding to the compression interval endpoints as boundary constraints for the compression process; S532, determine the target departure interval, and select the forward compression mode or the backward compression mode; When selecting the forward compression mode, start from the compression interval start time point, and calculate the new departure time according to the target departure interval; the new time of each departure event is equal to the departure time of the previous departure event plus the target interval; the departure time of the last departure event must not exceed the end time point of the compression interval; When selecting the backward compression mode, start from the compression interval end point, and calculate the new departure time in reverse order according to the target departure interval; the new time of each departure event is equal to the departure time of the next event minus the target interval; the departure time of the first departure event must not be earlier than the start time point of the compression interval; S533, execute the compression process: Arrange the departure events in the compression interval in chronological order to establish a compression processing queue; According to the selected compression mode, gradually adjust the departure time, and during the adjustment process, the single adjustment amount must not exceed the minimum compression unit, and after each adjustment, check whether the constraints are met; if there is a constraint violation, return to the previous feasible state; For each adjusted departure event, obtain its four-way associated events in the double-layer constraint matrix, check whether the adjustment affects the constraints of the associated events, and if it does, synchronize the adjustment of the associated events; S534, verification of compression results: verify whether the standard deviation of the departure interval in the compressed interval meets the requirements; confirm whether all adjusted departure events meet the vehicle and platform constraints; verify whether the connection between the compressed interval and the adjacent interval is smooth; S535, abnormal situation handling: When the compressed interval length is insufficient to accommodate all departure events, expand the compressed interval range and adjust the target departure interval, or split it into multiple sub-intervals for separate processing; When there is a constraint conflict that cannot be met, prioritize high-priority constraints, relax low-priority constraints, and record the constraint conflict that cannot be processed for subsequent optimization.

10. The single-line bus intelligent scheduling method based on double-layer constraint fusion according to claim 8, characterized in that, In S51, the determination method of the abnormal time section is: Departure interval deviation determination: calculate the difference between the departure interval in the section and the target interval, and determine it as abnormal when the difference exceeds the threshold value, where the peak period threshold value is 5 minutes and the off-peak period threshold value is 15 minutes; Section continuity determination: check whether the transition between adjacent sections is smooth; Capacity distribution determination: evaluate whether the capacity distribution in the section is balanced; Constraint satisfaction degree determination: count the number of constraint violations in the section, including the number of violations of the departure interval constraint and the stop duration constraint.

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