Integrated optimization method based on urban rail transit operation end period timetable and jump stop plan in abnormal state

Abstract

The invention discloses an integrated optimization method based on an abnormal state urban rail transit operation end period timetable and a jump stop plan. The method comprises the following steps: acquiring passenger demand data and train operation parameters in an operation end period; according to the passenger demand data and the train operation parameters, a mixed integer multi-objective optimization model is constructed, and the model comprises an objective function and constraint conditions; solving the mixed integer multi-objective optimization model by adopting a multi-objective whale optimization algorithm to obtain a Pareto optimal solution set; and outputting the Pareto optimal solution set for generating a time table and a jump stop plan of the operation end period. According to the method, the time table and the jump stop plan are integrated and optimized, so that the total waiting time of the passengers is remarkably shortened in the operation ending period, meanwhile, the number of the passengers who are not served due to jump stop is effectively reduced, and the overall operation efficiency and the service fairness are improved; according to the method, various optimization schemes can be flexibly generated, and decision basis is provided for operating enterprises.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of traffic operation optimization, in particular to an integrated optimization method based on timetable and skip-stop plan at the end of urban rail transit operation under abnormal conditions. BACKGROUND

[0002] With the acceleration of urbanization, subway, as the core carrier of large-capacity public transportation, is facing increasingly severe operation pressure. According to the statistics of China Urban Rail Transit Association, the daily passenger flow of subway in super-large cities such as Beijing, Shanghai and Guangzhou exceeded ten million person-times in 2022, and the full load rate of some lines during peak hours broke through 120%, far exceeding the designed carrying capacity. In order to alleviate congestion and improve transport capacity, some cities have tried to use the "skip-stop" strategy, that is, by dynamically adjusting the train stopping sites, reducing the train stopping time loss, and optimizing the line operation efficiency. However, the implementation of the skip-stop plan is not a universal solution, its effect is restricted by multiple factors such as passenger flow distribution, technical conditions, social fairness, and scientific decision-making basis is urgently needed.

[0003] Under abnormal operation scenarios such as holidays and large-scale activities, urban rail transit system faces the core contradiction of time-space resource mismatch at the end of operation. Its internal mechanism is as follows:

[0004] 1. The increase of demand-side time-space heterogeneity: The superimposed effect of cross-domain return flow caused by holiday-type holidays (such as Spring Festival and National Day) and instantaneous gathering flow formed by large-scale event dispersal leads to the generation of asymmetric passenger flow peaks at the end of operation in transportation hubs, commercial districts and tourism sites; Based on the path-dependent passenger selection behavior, passengers at upstream non-essential stations (such as short-distance leisure stations) occupy the physical capacity of the train in advance, resulting in the occurrence of full-load congestion at downstream key nodes (integrated transportation hubs and main line transfer stations), that is, the remaining passenger carrying capacity of the train is lower than the critical safety threshold of the platform waiting passenger flow when the train arrives.

[0005] 2. The highlight of supply-side rigid constraints: The existing dispatching system relies on fixed timetables and homogeneous stopping rules, and lacks dynamic response capability to sudden passenger flow; The traditional skip-stop strategy is based on static station classification (such as fixed skipping of low-priority stations), which is difficult to adapt to the time-space migration characteristics of passenger flow pressure source under abnormal conditions. SUMMARY

[0006] To solve the technical problems in the above background, the present application constructs a data-driven dynamic skip-stop-timetable collaborative optimization model, taking urban rail transit network as the research object, balancing uneven passenger demand and limited train capacity through skip-stop strategy and timetable optimization, considering the waiting time of all passengers in the entire network to improve the service quality of network passengers.

[0007] To achieve the above object, the application provides an integrated optimization method based on timetable and skip-stop plan at the end of urban rail transit operation under abnormal conditions, steps including:

[0008] Obtaining passenger demand data and train operation parameters in the end of operation period;

[0009] According to the passenger demand data and train operation parameters, a mixed integer multi-objective optimization model is constructed, which includes objective functions and constraint conditions;

[0010] The mixed integer multi-objective optimization model is solved by using a multi-objective whale optimization algorithm to obtain a Pareto optimal solution set;

[0011] The Pareto optimal solution set is output for generating the timetable and skip-stop plan at the end of operation period.

[0012] Preferably, the mixed integer multi-objective optimization model has the following basic conditions:

[0013] Trains are not allowed to skip two adjacent stations continuously, and trains of two adjacent trains are not allowed to skip the same station continuously, and starting stations, terminal stations and transfer stations are not allowed to skip;

[0014] At the same transfer direction of the transfer station, the transfer walking time of all passengers is consistent;

[0015] The effective path between the origin and destination adopts the structure form of physical loop-free topology;

[0016] All passengers will choose the train with the shortest arrival time on the transfer line to complete the transfer during the transfer process in the end of operation period;

[0017] Two running directions of each line are regarded as two independent lines.

[0018] Preferably, the objective function of the mixed integer multi-objective optimization model includes:

[0019] Minimizing the number of unserved passengers due to skip-stop:

[0020]

[0021] Wherein, minZ l represents minimizing the number of unserved passengers; is the number of passengers at the station s of the train j of the line l; is a 0-1 variable, 1 represents skip-stop, 0 represents stop; L represents the set of rail lines in the network, l∈L; S l represents the set of all stations on the line l, {1,2,3,...,s l}, wherein, s lis the terminal station on route l; Q l denotes the set of trains on route l, {1, 2, 3,..., j l}, where j l is the last train on route l;

[0022] and minimizing the total waiting time of passengers at the end of the operation period:

[0023] minT = T wt + T tf + T st

[0024] where minT denotes the total waiting time of passengers at the end of the operation period; T wt denotes the waiting time of newly-arriving passengers; T st denotes the total waiting time of passengers stranded at stations due to train passenger capacity limitation or skipping stops; T tf denotes the waiting time of passengers requiring transfer.

[0025] Preferably, the constraints include: skipping stop constraints, timetable transfer constraints, and train passenger capacity constraints.

[0026] Preferably, the timetable transfer constraints include: stop time constraints, headway constraints between two adjacent trains on route l, travel time constraints between two adjacent stations on route l, transfer connection success measurement constraints, and latest closing time constraints.

[0027] The train passenger capacity constraints include: waiting passenger constraints at stations, stranded passenger constraints at stations, actual boarding number constraints, remaining capacity constraints of trains, alighting number constraints, transfer number constraints, waiting time of newly-arriving passengers, total waiting time of stranded passengers, and total waiting time of transfer passengers.

[0028] Preferably, the skipping stop constraints are represented by introducing a 0-1 variable to indicate whether train j on route l stops at station s:

[0029]

[0030] where Q l denotes the set of trains on route l;

[0031] Train j on route l cannot skip two adjacent stations continuously:

[0032]

[0033] Two adjacent trains on route l cannot skip a station continuously:

[0034]

[0035] The starting station and the terminal station on the line cannot be skipped:

[0036]

[0037] wherein, denotes the starting station of the train j on the line l; denotes the terminal station of the train j on the line l; u denotes the number of the transfer station; X l denotes the set of transfer stations.

[0038] Preferably, the multi-objective whale optimization algorithm comprises the following steps:

[0039] A position matrix coding strategy is constructed, and the position matrix of each whale represents a solution to the problem, and the coding station of the position matrix of the whale, the stop time between stations, and the departure interval between adjacent trips on the same line are composed;

[0040] An initial population is generated, the population size is set to G, G initial solutions are randomly generated, all constraints in the model are verified, if all constraints are met, the current solution is feasible, otherwise, the initial solution is regenerated, until an initial whale group containing G feasible solutions is generated;

[0041] Iterative evolution, there are three kinds of iterative update strategies, which are search foraging mechanism, shrinkage surrounding mechanism and spiral update mechanism; each iteration, the position update strategy of each whale is determined by the value of random number p and the modulus of coefficient vector Through iteration, the optimal solution is found;

[0042] When the algorithm meets the termination condition, the iteration is terminated, and the Pareto optimal solution set is output.

[0043] Preferably, the termination condition of the algorithm is two, the algorithm stops when one of the following conditions is met:

[0044] Condition a): maximum iteration number iteration, when the population evolution generation reaches iteration, the algorithm is terminated, and the current Pareto front is output;

[0045] Condition b): the stability and diversity of the Pareto front are judged from two aspects of stability and diversity;

[0046] Wherein, the method for judging the stability of the Pareto front includes: measuring the change between the current generation and the last generation of the front by Euclidean distance, if the maximum distance between the two fronts is less than the preset threshold epsilon, the current Pareto front is output.

[0047] The method for judging diversity stability comprises: calculating the diversity of the current binding Pareto front, i.e., the uniformity of the distribution of solutions in the target space, and comparing the diversity with that of the last generation; evaluating the distribution of solutions by calculating the diversity with the minimum value as a reference point; and considering that the diversity has been stable if the diversity of the current Pareto front changes by less than a preset threshold compared with that of the last generation.

[0048] When the Pareto front stability and the diversity stability are both satisfied, the condition b is triggered, the algorithm is terminated, and the current set of Pareto optimal solutions is output.

[0049] The application also provides an integrated optimization system for timetable and skip-stop plan at the end of urban rail transit operation under abnormal conditions, which is used to implement the above method and comprises a collection module, a construction module, a solution module and an optimization generation module.

[0050] Compared with the prior art, the application has the following beneficial effects:

[0051] The application significantly reduces the total waiting time of passengers at the end of operation by integrating and optimizing the timetable and the skip-stop plan, effectively reduces the number of passengers not served due to skip-stop, improves the overall operation efficiency and service fairness, and can generate various optimization schemes flexibly to provide decision basis for operation enterprises, so that the operation enterprises can achieve the best balance between service coverage and operation efficiency under different passenger flow scenarios, especially during abnormal peak periods such as holidays and large events, can relieve platform congestion, optimize resource utilization, and enhance the response capability and passenger satisfaction of the rail transit system. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the application, the following briefly introduces the drawings needed in the embodiments. Obviously, the drawings in the following description only constitute some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0053] Figure 1 The flow chart of the multi-objective whale optimization algorithm of the embodiment of the application;

[0054] Figure 2 The schematic diagram of the position vector structure in the whale optimization algorithm of the embodiment of the application;

[0055] Figure 3 The distribution of the Pareto and non-Pareto solution sets of the optimization objectives under different timetables and skip-stop schemes in the embodiment of the application;

[0056] Figure 4 The Pareto and non-Pareto solution sets under the stop station time of 1-1.5 min in the embodiment of the application;

[0057] Figure 5 The stop time sensitivity analysis chart for the embodiment of the present application. DETAILED DESCRIPTION

[0058] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0059] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0060] Embodiment one

[0061] The embodiment provides an integrated optimization method based on a timetable in an abnormal state at an end-of-operation period of urban rail transit and a skip-stop plan, and steps include:

[0062] S1. Obtain passenger demand data and train operation parameters in the end-of-operation period.

[0063] In this embodiment, a certain city subway line 10 is taken as an example, and the skip-stop strategy of this line affects one-third of the subway passenger flow in the city. The hourly passenger flow of a certain train station during the holiday reaches 12,000 people, which provides a pressure test sample for the national high-speed rail hub subway connection. The line crosses multiple functional areas, and the skip-stop practice can verify the differentiated response of business, tourism and commuting passenger flow, and the conclusion has strong extrapolation and serves as an emergency, cross-area coordination and intelligent scheduling exploration.

[0064] In the parameter setting, the end-of-operation period is from 21:30 to 23:30; the stop time of each station in the timetable is 0.5-1 minute, the interval running time between stations is shown in Table 2; the minimum departure interval and the minimum departure-to-arrival interval of the station are both 4 minutes, and the maximum departure interval of the first station of the line is 6 minutes; the train capacity is 1500 people; the maximum train number in the end-of-operation period is preset to 30, and the remaining arrival rate, the alighting rate and the transfer rate are estimated according to the historical subway data in different time periods, so as to balance the resource utilization and the passenger service demand in the optimization of the operation efficiency in the end-of-operation period.

[0065] Based on the actual investigation of the night passenger flow data, the amplification simulation method is used for the abnormal state (such as holiday / large-scale activity), the in-station passenger flow of line 10 during 22:00-23:00 is expanded by 4-6 times, the "abnormal peak evacuation" scene is constructed, and the adaptability and potential of the integrated optimization of the timetable in the end-of-operation period and the skip-stop plan are analyzed.

[0066] S2. Construct a mixed integer multi-objective optimization model according to the passenger demand data and train operation parameters.

[0067] The constructed mixed integer multi-objective optimization model satisfies the following basic conditions:

[0068] 1. The train is not allowed to skip two adjacent stations continuously, and the trains of two adjacent train services are not allowed to skip the same station continuously. The starting station, terminal station and transfer station are not allowed to be skipped.

[0069] 2. It is assumed that the heterogeneity of passengers is weak at the end of the operation period, and the fluctuation degree of transfer walking time is small. Specifically, in the same transfer direction at the transfer station, the transfer walking time of all passengers is consistent.

[0070] 3. The effective path between the origin-destination (OD) adopts the structure form of physical loop-free topology.

[0071] 4. All passengers will choose the train service with the shortest arrival time on the transfer-in line to complete the transfer within the end of the operation period.

[0072] 5. The train bottom turnover is not considered, and the two running directions of each line are regarded as two independent lines.

[0073] The constructed model includes objective functions and constraint conditions:

[0074] (1) Objective function

[0075] ① Minimize the number of unserved passengers due to skipping:

[0076]

[0077] Where minZ l represents minimizing the number of unserved passengers; is the station dwell passenger of train j at station s on line l; is a 0-1 variable (1 represents skipping and 0 represents stopping); L represents the set of track lines in the network, l∈L; S l represents the set of all stations on line l, {1,2,3,...,s l}, where s l is the terminal station on line l; Q l represents the set of trains on line l, {1,2,3,...,j l}, where j l is the last train on line l; Q l represents the set of trains on line l, {1,2,3,...,j l}. The \{1} appearing below is the first bus.

[0078] ② Minimize the total waiting time of passengers at the end of the operation period

[0079] The waiting time of new passengers arriving from the outside during the two consecutive bus departures, and the waiting time of stranded passengers who did not board the previous train, and the waiting time of transfer passengers.

[0080] minT = T wt + T tf + T st

[0081] Where minT represents the total waiting time of passengers at the end of the operation period; T wt represents the waiting time of new passengers; T st represents the total waiting time of passengers stranded at the station due to train capacity restrictions or skip stops; T tf represents the waiting time of transfer passengers.

[0082] (2) Skip stop constraint

[0083] This embodiment introduces a 0-1 variable to represent whether train j on line l stops at station s, that is:

[0084]

[0085] Where Q l represents the set of trains on line l.

[0086] Train j on line l cannot skip two adjacent stations continuously, that is:

[0087]

[0088] Two adjacent trains on line l cannot skip a station continuously, that is:

[0089]

[0090] The starting station, transfer station and terminal station on line l cannot skip, that is:

[0091]

[0092] Where represents the starting station of train j on line l; represents the terminal station of train j on line l; u represents the transfer station number; X l represents the set of transfer stations.

[0093] (3) Timetable transfer constraint

[0094]

[0095] wherein, denotes the time of the jth train of line l arriving at station s; denotes the time of the jth train of line l leaving station s; denotes the time of the jth train of line l leaving the starting station; denotes the headway of line l; denotes the running time of the jth train of line l between two adjacent stations k; denotes the time of the jth train of line l stopping at station s.

[0096] ① Station stopping time constraint

[0097] In order to ensure the safety of the interval train operation and the service level of passengers, the train stopping time should be greater than the minimum stopping time and less than the maximum stopping time.

[0098]

[0099] wherein, denotes the minimum stopping time of line l at station s; denotes the maximum stopping time of line l at station s.

[0100] ② Headway constraint between two adjacent trains of line l

[0101] In order to ensure the safety of the interval train operation and the service level of passengers, the train headway time should be greater than the minimum headway time and less than the maximum headway time.

[0102]

[0103] wherein, denotes the minimum headway time; denotes the maximum headway time.

[0104] ③ Running time constraint between two adjacent stations of line l

[0105] The running time of the train between stations should meet the actual operation requirements. It should be greater than the minimum running time and less than the maximum running time.

[0106]

[0107] wherein, denotes the minimum running time; denotes the maximum running time.

[0108] To ensure the safety of station operation (string car), the interval time between the arrival time of the train and the departure time of the previous train at the same station shall not be less than the minimum departure interval time T AD .

[0109]

[0110] (4) Transfer success measurement constraints

[0111] Whether the jth train of line l successfully transfers to line l at station s / . / The 0-1 variable is introduced to represent the jth train of line l ; M is a very large positive number.

[0112]

[0113] When , it means that the l line and the l / line successfully transfer at station s, otherwise 0; It represents the general transfer walking time of line l and line l / at transfer station s; It represents the departure time of the jth train of line l / at transfer station s. / .

[0114] (5) The latest arrival time constraint

[0115] To avoid interfering with night maintenance, the arrival time of the terminal station of each line should not be later than the latest arrival time

[0116]

[0117] Where s l represents the terminal station of line l; j l represents the last train of line l.

[0118] (4) Train passenger capacity constraints

[0119] ① Station waiting passenger constraints

[0120] t0 represents the start time of the study period. For non-transfer stations, including passengers arriving at the station from the outside during the continuous two train departures, and stranded passengers who left the previous train. For transfer stations, Also includes passengers transferring from other lines. In this equation, represents the average passenger arrival rate to station s on line l, which can be obtained from historical AFC data estimates or forecasts.

[0121]

[0122] where X l,u represents; represents the transfer number of line j train at s station; / line j / train at s station;

[0123] ② Station dwell passenger constraint

[0124] l line j train after leaving the number of passengers remaining is equal to the waiting number at s station minus the number of passengers boarding

[0125]

[0126] ③ Actual boarding number constraint

[0127] When l number line j train stops at s station, the actual boarding number is the actual waiting number and the remaining capacity on the train The minimum of the two.

[0128]

[0129] where, represents.

[0130] ④ Train remaining capacity

[0131] Train remaining capacity At the starting station, it is the train capacity C max , and at the remaining s station, the remaining capacity is (s-1) station remaining number minus (s-1) station boarding number plus s station alighting number

[0132]

[0133] ⑤ Alighting number constraint

[0134] When l number line j train stops at s station, then the alighting number is equal to the alighting rate times the number of passengers on the train when arriving at s station.

[0135]

[0136] ⑥ Transfer number constraint

[0137] l number line j train transfers to l / number line j / at s station is equal to the alighting number of l number line j train at s station Transfer rate between two lines

[0138]

[0139] Waiting time of new arriving passengers

[0140] T wt represents the total waiting time of new arriving passengers, and δ is the average waiting time of passengers in the headway, which can be obtained according to historical data.

[0141]

[0142] Total waiting time of stranded passengers

[0143] T st represents the total waiting time of passengers stranded in the station due to train passenger capacity limit or skip stop:

[0144]

[0145] Total waiting time of transfer passengers

[0146] T tf represents the waiting time of transfer passengers:

[0147]

[0148] wherein, represents the train set on the line l / ; X l represents the transfer station set; represents the line l / , j / th train leaves s station at time; represents the general transfer walking time of the line l / and the line l at the transfer station s.

[0149] S3. The multi-objective whale optimization algorithm is used to solve the mixed integer multi-objective optimization model to obtain the Pareto optimal solution set.

[0150] The operation end period skip-stop plan coordination optimization model constructed in this embodiment belongs to a mixed integer nonlinear programming model. The number of decision variables and constraint conditions of the model is mainly affected by the number of lines, the number of stations of each line, and the size of the train set of each line. According to the current research, the optimization research on the timetable of each line in the network has been proved to be an NP-hard problem. Based on this, the multi-objective whale optimization algorithm (Non-Dominated Sorting Whale Optimization Algorithm, NSWOA) is used to solve this optimization model.

[0151] The flowchart of the multi-objective whale optimization algorithm is shown in Figure 1 . The detailed design process is as follows.

[0152] (1) Position matrix coding strategy

[0153] The position matrix of each whale represents a solution to the problem, and the coding of the position matrix of the whale is composed of whether the station is skipped, the stop time between stations, and the departure interval between adjacent trains on the same line. Other decision variables can be calculated by the following formula.

[0154]

[0155] The position vector structure is shown in Figure 2 , which is composed of the skip-stop matrix, the stop time matrix, and the departure interval matrix.

[0156] (2) Generate initial population

[0157] Set the population size to G, randomly generate G initial solutions, and verify all the constraints in the model. If all the constraints are met, the current solution is feasible, otherwise, regenerate the initial solution until an initial whale group containing G feasible solutions is generated.

[0158] (3) Iterative evolution

[0159] There are three iterative update strategies, which are search foraging mechanism, shrinkage surrounding mechanism and spiral update mechanism. At each iteration, the position update strategy of each whale is determined by the value of the random number p and the modulus of the coefficient vector . With the iteration, the whale population constantly converges to the optimal solution.

[0160] (4) Algorithm termination judgment

[0161] The evolution termination condition of the algorithm is two, one of which is met, the algorithm stops, and the Pareto frontier is output.

[0162] Condition a) : maximum number of iterations iteration, when the population evolution reaches iteration, the algorithm terminates and outputs the current Pareto front;

[0163] Condition b) : combination of Pareto front stability and diversity index stability;

[0164] Wherein, the method for judging the stability of the Pareto front includes: measuring the change between the current and the last generation of the front by Euclidean distance, if the maximum distance between the two fronts is less than the preset threshold epsilon, the current Pareto front is output.

[0165] The method for judging the stability of diversity includes: calculating the diversity of the current combined Pareto front, that is, the uniformity of the solution distribution in the target space, and comparing it with the diversity of the last generation; the minimum value is taken as the reference point for diversity calculation to evaluate the distribution of solutions; if the diversity of the current Pareto front changes less than the preset threshold compared with the last generation, it is considered that the diversity has been stable;

[0166] When the Pareto front stability and diversity stability are met at the same time, condition b is triggered, the algorithm terminates and outputs the current Pareto optimal solution set.

[0167] Pareto front stability: the program judges the stability by comparing the change of the Pareto front between the current generation and the last generation. The specific operation is to measure the change between the two fronts by Euclidean distance, if the maximum distance between the two fronts is less than the preset threshold epsilon, it is considered that the current front is relatively stable.

[0168] Diversity stability: the diversity stability is calculated by comparing the diversity of the current front with the diversity of the last generation. The minimum value is taken as the reference point for diversity calculation to judge the uniformity of the individual distribution in the target space.

[0169] S4. Output the Pareto optimal solution set, which is used to generate the timetable and skip-stop plan at the end of the operation period.

[0170] In order to evaluate the application effect of the proposed timetable and skip-stop plan integrated optimization model in the end of operation period, this paper compares and analyzes the sensitivity of multiple Pareto optimal solutions obtained based on whale optimization algorithm (NSWOA) with the actual operation scheme as reference. Figure 3 The distribution of Pareto and non-Pareto solutions of optimization objectives under different timetables and skip-stop plans: the number of passengers not served due to skip-stop and the total waiting time of passengers in the end of operation period. Among them, the blue star represents the distribution of Pareto optimal solutions, and the black dot represents the real unoptimized scheme.

[0171] It can be observed from the figure that there is a clear trade-off between the two objectives: as the number of unserved passengers decreases, the total passenger waiting time generally increases; conversely, as the skip-stop intensity increases, more passengers are denied service opportunities, although the overall waiting time decreases and the operation efficiency improves. This typical non-inferior solution distribution reflects the scheduling strategy space under different objective preferences, providing diversified selection basis for the operator.

[0172] For comparative analysis, Table 1 summarizes the Pareto-optimal quantitative indicators of eight typical timetables and skip-stop plan integrated optimization schemes. Figure 3 From the table, it can be seen that all optimization schemes have significantly improved the total waiting time indicator compared with the realistic scheme, with the maximum reduction of 41.39%. However, this improvement is at the cost of a certain number of passenger service coverage, i.e., 9.82% to 30.01% of passengers are unable to obtain service due to the skip-stop strategy.

[0173] Table 1

[0174]

[0175] Specifically, scheme 1 is the most "robust" optimization scheme, sacrificing only 9.82% of service coverage (4,892 person-times), but achieving a significant 12.30% reduction in total waiting time. This indicates that at the initial stage of optimization, the introduction of the skip-stop strategy can bring extremely high marginal benefits, with a small sacrifice in service coverage to achieve a significant improvement in operational efficiency.

[0176] As the optimization objective is further strengthened (from scheme 2 to scheme 7), the total waiting time continues to decrease, but the number of passengers sacrificed for each additional minute of waiting time increases dramatically. For example, from scheme 1 to scheme 2, 250 more passengers are sacrificed, and the waiting time is reduced by 9.59%; while from scheme 6 to scheme 7, 1,822 more passengers are sacrificed, and the waiting time is only reduced by 0.31%. This diminishing marginal benefit phenomenon indicates that the pursuit of extreme operational efficiency in the later stage requires a huge social cost.

[0177] Scheme 8 represents an extreme solution on the Pareto frontier, although it achieves the maximum compression of waiting time (41.39% reduction), but at the cost of a sharp drop in service coverage to 69.99%, i.e., up to 30.01% (14,952 person-times) of passengers cannot obtain service. This result means that the skip-stop strategy of this scheme is very aggressive, and its cost-effectiveness ratio decreases significantly, which needs to be carefully evaluated in practical application, as it may cause serious service fairness and social acceptance problems.

[0178] In summary, if the operator pays more attention to service fairness and passenger coverage, options 1-3 can be selected; if more attention is paid to overall efficiency improvement and station congestion relief, options 6-8 are more advantageous; options 4 and 5 are relatively balanced solutions, the number of unserved passengers is still within a controllable range, and the waiting time reduction is also more significant.

[0179] Therefore, the timetable and skip-stop plan integrated optimization model proposed in this embodiment can effectively generate a series of Pareto solutions with actual regulation value, providing decision support for the operator to balance service fairness and efficiency at the end of operation.

[0180] Embodiment Two

[0181] In order to analyze the influence of train stopping time setting on the optimization results, the minimum stopping time and the maximum stopping time of each station in the model are set to be sensitive. The original setting of the stopping time range [0.5, 1.0] minutes is adjusted to [1.0, 1.5] minutes, and under the premise of keeping other parameters unchanged, the multi-objective optimization model is run to obtain the corresponding Pareto solution set, as shown in Figure 4 , and the sensitivity analysis diagram of the stopping time is shown in Figure 5 .

[0182] As can be seen from the figure, the analysis result shows that the stopping time has a significant influence on the balance between the total waiting time of passengers and the number of passengers not served due to skipping stops, and shows a certain nonlinear trend:

[0183] Overall performance: In the interval with similar total waiting time of passengers, the number of passengers not served due to skipping stops corresponding to the stopping time of 1-1.5 minutes is generally higher than that of the stopping time of 0.5-1 minute. This is because the extended stopping time prolongs the running cycle of the whole train, and under the constraint of the end of operation and the latest closing time, the number of trains that can be arranged is reduced, thereby limiting the service capacity of the line, resulting in more passengers not being served due to skipping stops.

[0184] Local performance: In some specific cases, when the total waiting time of passengers is similar, the stopping time of 1-1.5 minutes can actually reduce the number of unserved passengers. This shows that under a specific passenger flow structure, longer stopping time can improve the efficiency of single passenger carrying, so that more passengers can successfully take the train, thereby reducing the proportion of unserved passengers. However, this will also cause the waiting time of other passengers to be prolonged, reflecting the trade-off of service quality.

[0185] In summary, the setting of stopping time has a dual influence on the optimization results, and should be reasonably set according to the actual line capacity, station spacing and passenger flow distribution characteristics, and adjusted flexibly according to the scene characteristics, in order to achieve a better balance between service and operation efficiency.

[0186] The above described embodiments are only to illustrate the preferred modes of the present application, and are not intended to limit the scope of the present application. Any modification and improvement made by those skilled in the art to the technical solutions of the present application without departing from the design spirit of the present application shall fall within the protection scope of the present application as defined by the claims.

Claims

1. An integrated optimization method based on the timetable and skip-stop plan for the end of urban rail transit operation under abnormal conditions, characterized by the following steps: include: Acquire passenger demand data and train operation parameters during the end of the operating period; Based on passenger demand data and train operation parameters, a mixed integer multi-objective optimization model is constructed, which includes an objective function and constraints. The mixed-integer multi-objective optimization model is solved using the multi-objective whale optimization algorithm to obtain the Pareto optimal solution set; Output the Pareto optimal solution set, which is used to generate the timetable and tripping plan for the end of the operation.

2. The integrated optimization method based on the timetable and skip-stop plan for the end of urban rail transit operation under abnormal conditions, as described in claim 1, is characterized in that... The mixed-integer multi-objective optimization model has the following basic conditions: Trains are not allowed to skip two adjacent stations consecutively, and two adjacent trains are not allowed to skip the same station consecutively. Skipping stops is not allowed at the origin station, destination station, and transfer station. At the transfer station, all passengers traveling in the same direction have the same transfer time; The effective path between the origin and destination points adopts a physically acyclic topology. During the transfer process, all passengers will choose the train with the shortest arrival time at the end of the operating period on the receiving line to complete the transfer. The two directions of operation of each line are regarded as two independent lines.

3. The integrated optimization method based on the timetable and skip-stop plan for the end of urban rail transit operation under abnormal conditions, as described in claim 1, is characterized in that... The objective function of the mixed-integer multi-objective optimization model includes: Minimize the number of passengers who are not served due to the stop: Where, minZ l This represents minimizing the number of unserved passengers; For passengers stranded at station S on line J; Let S be a 0-1 variable, where 1 represents a jump and 0 represents a stop; L represents the set of track lines in the network, l∈L; l Let {1,2,3,...,s} represent the set of all stations on line l. l }, where s l Q is the terminal station on route l; l Let {1,2,3,...,j} be the set of trains on line l. l }, where j l This refers to the last train on route l. And minimize the total passenger waiting time at the end of the operation: minT=T wt +T tf +T st Where minT represents minimizing the total waiting time for passengers at the end of the operation; T wt Indicates the waiting time for newly arriving passengers; T st This indicates the total waiting time for passengers stranded at the station due to train capacity limitations or train skipping stops; T tf This indicates the waiting time for passengers who need to transfer.

4. The integrated optimization method based on the timetable and skip-stop plan for the end of urban rail transit operation under abnormal conditions, as described in claim 3, is characterized in that... The constraints include: stop constraints, timetable transfer constraints, and train passenger capacity constraints.

5. The integrated optimization method based on the timetable and skip-stop plan for the end of urban rail transit operation under abnormal conditions, as described in claim 4, is characterized in that... The timetable transfer constraints include: stop time constraints, departure interval constraints between two adjacent trains on Line 1, train running time constraints between two adjacent stations on Line 1, transfer connection success measurement constraints, and latest closing time constraints. The train passenger capacity constraints include: station waiting passenger constraints, station stranded passenger constraints, actual number of passengers boarding constraints, remaining train capacity, number of passengers disembarking constraints, number of passengers transferring constraints, waiting time for newly arriving passengers, total waiting time for stranded passengers, and total waiting time for transferring passengers.

6. The integrated optimization method based on the timetable and skip-stop plan for the end of urban rail transit operation under abnormal conditions, as described in claim 4, is characterized in that... The stop constraint is achieved by introducing a 0-1 variable. This indicates whether train j on line l stops at station s: Among them, Q l This represents the set of trains on line l; Train J on line l cannot skip two adjacent stations consecutively: Two adjacent trains on line l cannot skip a station consecutively: The starting, transfer, and ending stations on Line L cannot be skipped. in, Indicates the starting station of train j on line l; Indicates the terminal station of train j on line l; u indicates the transfer station number; X l This indicates a meeting point at a transfer station.

7. The integrated optimization method based on the timetable and skip-stop plan for the end of urban rail transit operation under abnormal conditions, as described in claim 1, is characterized in that... The multi-objective whale optimization algorithm includes: A location matrix encoding strategy is constructed, where each whale's location matrix represents a solution to the problem. The encoding of the whale's location matrix consists of whether the station skips a stop, the stop time between stations, and the departure interval between adjacent trains on the same route. Generate an initial population, set the population size to G, randomly generate G initial solutions, verify all constraints in the model, if all constraints are satisfied, the current solution is feasible, otherwise regenerate the initial solution, until an initial whale pod containing G feasible solutions is generated; Iterative evolution employs three iterative update strategies: search-and-forage mechanism, shrinking encirclement mechanism, and spiral update mechanism. In each iteration, the value of a random number p and the coefficient vector are used... The model is used to determine the position update strategy for each whale; the optimal solution is found through iteration. When the algorithm meets the termination condition, the iteration terminates and the Pareto optimal solution set is output.

8. The integrated optimization method based on the timetable and skip-stop plan for the end of urban rail transit operation under abnormal conditions, as described in claim 7, is characterized in that... The algorithm terminates under two conditions; it stops if either condition is met: Condition a): Maximum number of iterations. When the number of generations of population evolution reaches iteration, the algorithm terminates and outputs the current Pareto front. Condition b): The judgment is made by combining the stability of the Pareto frontier and the stability of the diversity index; The method for determining the stability of the Pareto front includes: measuring the change between the current and previous generation fronts using Euclidean distance; if the maximum distance between the two fronts is less than a preset threshold epsilon, then the current Pareto front is output. The methods for judging the stability of diversity include: calculating the diversity of the current combined Pareto front, i.e. the uniformity of the solution distribution in the target space, and comparing it with the diversity of the previous generation; using the minimum value as a reference point to calculate diversity and evaluate the distribution of solutions; if the change in the diversity of the current Pareto front compared with the previous generation is less than a preset threshold, then the diversity is considered to be stable. When both Pareto front stability and diversity stability are satisfied, condition b is triggered, the algorithm terminates and outputs the current Pareto optimal solution set.

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