Railway operation scheduling method based on four-layer graph integer programming modeling

Abstract

The present application provides a railway operation scheduling method based on four-layer graph integer programming modeling, comprising: S1. obtaining a standardized data set; S2. obtaining time-related data; S3. updating the standardized data set; S4. constructing a constraint system; S5. constructing a four-layer graph structure; S6. constructing a MILP model; S7. hybrid solving; S8. calculation acceleration; S9. calibrating the upper limit of the optimal single-day task number; S10. based on the solving result of S7, outputting a scheduling plan, a resource allocation scheme, path information and a visualization chart. The present application aims to provide a comprehensive scheme of "unified modeling + efficient solving + feasibility guarantee + calculation acceleration", which can quickly generate an executable railway operation scheduling plan that meets the requirements of engineering practice under the conditions of multiple tasks, multiple resources and strict window constraints, and improve the intelligent level and implementation efficiency of operation and maintenance management.

Description

Technical Field

[0001] This invention relates to the field of railway infrastructure operation and maintenance management and intelligent scheduling optimization technology, and in particular to a railway operation and maintenance scheduling method based on four-layer graph integer programming modeling. Background Technology

[0002] As the scale and complexity of railway networks continue to grow, critical infrastructure such as tracks, bridges, tunnels, and roadbeds are prone to fatigue and structural deterioration under high-frequency loads and environmental influences, which can seriously affect operational safety and service quality. Modern railway operation and maintenance also face practical constraints such as rising labor costs, aging equipment, and limited maintenance windows, making efficient and executable maintenance organization within limited maintenance windows a prominent challenge.

[0003] Railway routine maintenance tasks are diverse, generally categorized into track inspection, condition-based maintenance, periodic maintenance, and preventative maintenance. These tasks differ significantly in triggering mechanisms, execution objectives, closure methods, duration, and required resources. For example, dynamic inspections often require the entire track to be closed, prohibiting other track work; static inspection duration is related to the length of the inspection section; rail flaw detection time depends primarily on the number of welds; condition-based maintenance is triggered by defects / anomalies and is typically urgent and has higher priority; periodic maintenance must meet fixed maintenance intervals; and preventative maintenance emphasizes completion within a specified timeframe to prevent further deterioration. Therefore, maintenance scheduling models need to consider the comprehensive constraints arising from task heterogeneity, such as track opening times, priorities, resource consumption, and mutually exclusive parallel operations.

[0004] Existing computational methods for intelligent operation and maintenance optimization can be summarized into three categories: heuristic algorithms, deep reinforcement learning, and mixed-integer programming. Deep reinforcement learning focuses on learning state-action policies, but it suffers from high training time, large computational overhead, limited transferability, and complex reward function design, and is often used in simpler scenarios. Heuristic algorithms and mixed-integer programming are more suitable for the business characteristics of railway operation and maintenance, which involves weekly / monthly planning. In terms of constraint modeling, existing intelligent operation and maintenance models mainly cover maintenance operation constraints, track availability constraints, and acceptable track state / safety threshold constraints.

[0005] However, the existing implementation routes that are closest to the technical solution of this application and are most common in engineering often break down "task scheduling, resource allocation, and maintenance / operation vehicle path planning" into independent problems and solve them separately, or are based on simplification assumptions. This makes it difficult to reflect the coupling relationship between resources, time windows and path continuity in the same framework. As a result, key operational constraints such as priority conflicts, simultaneous operation restrictions and strict track window lengths are easily ignored, thus limiting the direct usability of the model in real railway operation and maintenance scenarios.

[0006] Existing technical solutions typically include the following technical features: 1. Maintenance task generation method: When predictions or detections indicate that the track condition has reached or is approaching limits, the system generates corresponding maintenance tasks and assigns priorities according to task urgency or preset rules. Some solutions distinguish between mandatory and general maintenance tasks, but priority assignment is mostly based on static rules.

[0007] 2. Maintenance scheduling and resource allocation During the maintenance scheduling phase, existing technologies typically treat maintenance tasks as work nodes, using mixed-integer programming or heuristic algorithms to allocate maintenance personnel, machinery, and maintenance vehicles, and arrange the task execution order within a given work time window.

[0008] 3. Maintenance vehicle route planning Some existing solutions further consider the driving sequence of maintenance vehicles between different work points, combining the vehicle routing problem with the maintenance scheduling problem in a combined model. However, they often reduce the complexity of the problem by simplifying assumptions, such as ignoring some resource conflicts or time continuity constraints.

[0009] In general, the existing technical solutions mentioned above mostly adopt a serial processing approach of "task generation - scheduling optimization - path planning," with limited coupling between modules, and often require significant simplification of the model under complex constraints. Although existing technologies have made some progress in track maintenance decision-making and scheduling optimization, the following shortcomings still exist: Disadvantage 1: It is difficult to simultaneously satisfy coupling constraints such as "task sequencing - resource mutual exclusion - vehicle path continuity - time window / slot length" within the same framework, resulting in insufficient executability of the planned engineering.

[0010] Existing research and implementation schemes often break down maintenance task scheduling, resource allocation, and track maintenance vehicle path planning into independent problems for separate solutions, or employ simplified assumptions. This makes it difficult to uniformly characterize the inherent coupling between resources, time windows, and path continuity. Consequently, key operational constraints such as priority conflicts, simultaneous operation limitations, and strict maintenance window durations are easily ignored or can only be addressed through post-event manual adjustments, reducing the feasibility and stability of the scheme in real railway operation and maintenance scenarios.

[0011] Disadvantage 2: Pure MILP global solution takes a long time to solve as the task size increases and the constraints become more complex, making it difficult to meet the timeliness requirements of engineering decision-making.

[0012] In actual operation and maintenance, multiple tasks need to be scheduled simultaneously, which brings a large number of decision variables and complex logical constraints. Although existing solutions can use MILP to find the global optimum, when the number of tasks increases and the constraints involve multiple resource types, transit time, time windows and task order, the branch and bound and cutting plane iterations in the solution process cause the solution time to increase rapidly, often reaching an unacceptable level for engineering applications, making it difficult to output a usable scheduling plan within the specified time.

[0013] Disadvantage 3: Heuristic / genetic search generation schemes are prone to producing infeasible results, causing forced tasks to be missed / overdue or overloaded on a single day, thereby reducing feasibility and slowing down evaluation efficiency.

[0014] Existing heuristic / genetic frameworks have difficulty guaranteeing that all hard constraints are always satisfied during initialization, crossover, and mutation. Typical manifestations include: mandatory tasks with strict deadlines / allowed date sets may not be assigned or may fall into unallowed dates; at the same time, tasks may be over-concentrated on a certain day, making it difficult to simultaneously satisfy constraints such as window length, resource mutual exclusion, transit and path continuity, resulting in a significant decrease in the feasibility rate of intraday subproblems, slower solver evaluation, or even failure to find a feasible solution within the limited window time.

[0015] Disadvantage 4: Repeatedly solving subproblems incurs additional computational overhead, reducing the throughput and convergence speed of heuristic search.

[0016] In genetic evaluation, different individuals may repeatedly exhibit the same or highly similar "daily task combinations". If the intraday MIP subproblem is reconstructed and solved each time, it will result in a large amount of redundant computation, significantly increasing the overall time cost and reducing search throughput and convergence efficiency. Summary of the Invention

[0017] This invention provides a railway operation and maintenance scheduling method based on four-layer graph integer programming modeling. Addressing core issues in existing technologies such as "segmentation-resource-vehicle path fragmentation, easy omission of key constraints," "low efficiency in solving large-scale problems," "insufficient feasibility of heuristic solutions," and "high overhead of repetitive computation," this invention aims to provide a comprehensive solution integrating "unified modeling + efficient solution + feasibility assurance + computational acceleration." Under multi-task, multi-resource, and strict window constraints, it rapidly generates executable railway operation and maintenance scheduling plans that meet actual engineering requirements, thereby improving the intelligence level and implementation efficiency of operation and maintenance management.

[0018] To achieve the above objectives, the present invention adopts the following technical solution: A railway operation and maintenance scheduling method based on four-level graph integer programming modeling includes: S1. Acquire data on tasks to be scheduled, maintenance bases and resource capabilities, maintenance windows and work slots, and form a standardized data set; S2. Based on the task location-related data in the standardized dataset, combined with the preset maintenance vehicle driving rules, calculate the transfer time between any two tasks and from the maintenance base to each task location, forming time-related data; S3. Classify the tasks to be scheduled in the standardized dataset according to their job characteristics, set duration estimation rules for each type of task, determine the standard duration of each task, and update it to the standardized dataset. S4. Based on a standardized dataset, construct a window and task execution time constraint system based on date and intraday time slot dimensions; S5. Based on a standardized dataset, a four-layer graph structure is constructed to represent the relationship between tasks, resources, vehicle paths, and time windows using event sequences; S6. Construct a MILP model based on standardized datasets, time-related data, constraint systems, and a four-layer graph structure; S7. A mechanism combining heuristic global search and intraday MILP sub-problem verification is adopted. The tasks to be scheduled are encoded as chromosome sequences. The feasibility is verified by the MILP model and offspring are generated. When repairing chromosomes, forced tasks are added, and the task volume is adjusted by calling the optimal daily task limit pre-calibrated by S9. S8. In the search process of S7, the MILP subproblems are simplified and a cache mapping is established to accelerate computation; S9. Based on the tasks to be scheduled and the MILP model, determine the upper limit of the optimal number of tasks per day; S10. Based on the solution results of S7, output the scheduling plan, resource allocation scheme, path information and visualization charts.

[0019] In this specification, the preset driving rules for maintenance vehicles in S2 include: determining the driving speed of maintenance vehicles on different sections of the railway line by combining information on speed-limited sections, turnout distribution, construction restricted areas, and the driving speed limits corresponding to the type and load of the maintenance vehicle.

[0020] In this specification, the tasks to be scheduled in S3 are divided into daily maintenance tasks, emergency repair tasks, and special maintenance tasks according to their operational characteristics. The duration estimation rules for each type of task are established based on historical operation data, equipment models, number of operators, and operational environment parameters.

[0021] In this specification, the constraint system in S4 includes: constraints on the opening and closing time of the maintenance sunroof and the available working time within the sunroof; constraints on the earliest start time and latest completion time of the tasks to be scheduled; and constraints on the priority execution time of the forced tasks.

[0022] In this specification, in the four-layer graph structure of S5, the skylight start event corresponds to the opening time node of the maintenance skylight, the task start event corresponds to the start time node after the task is allocated resources, the task end event corresponds to the time node when the task is completed and resources are released, and the skylight end event corresponds to the closing time node of the maintenance skylight; directed edges are used to represent the temporal relationship between events, and the weight of the edge is the time interval or resource consumption cost between events.

[0023] In this specification, the core constraints of the MILP model in S6 include resource capacity constraints, task timing constraints, vehicle path continuity constraints, and time window constraints. The objective function is a weighted combination of at least one or more of the following: maximizing the forced task completion rate, minimizing the total operation and maintenance cost, and minimizing resource idle time.

[0024] In this specification, the heuristic global search algorithm in S7 is a hybrid algorithm of one or more of the following: genetic algorithm, simulated annealing algorithm, and particle swarm optimization algorithm; in the chromosome sequence, gene positions represent tasks to be scheduled, the order of gene positions represents the execution order of tasks, and date separators are used to divide task groups of different dates.

[0025] In this specification, the simplified MILP subproblem in S8 refers to removing the resource optimization allocation constraints in the MILP model and retaining only the task feasibility constraints, time window constraints, and vehicle path continuity constraints; the key of the cache mapping is a combination of daily tasks, and the value is the corresponding feasibility verification result and the optimal execution time.

[0026] In this specification, when determining the optimal daily task limit in S9, a daily task group is constructed based on the type distribution and priority distribution of the tasks to be scheduled. The range of the candidate limit is 1 to 1.5 times the historical average number of tasks executed per day. The optimal daily task limit is determined by comparing the task feasibility rate, model solution time and resource utilization rate under different candidate limits.

[0027] In this specification, the visualization charts in S10 include a task execution Gantt chart, a resource load distribution chart, a maintenance vehicle path planning topology chart, and a task completion rate statistical bar chart.

[0028] In summary, the present invention has at least the following beneficial effects: 1. Improve the reliability of track condition prediction: By using a Gaussian process model to predict track condition probabilistically, the prediction results can simultaneously reflect trend, periodic and uncertainty factors, thereby avoiding the risks of making maintenance decisions based on a single prediction value.

[0029] 2. Achieve dynamic correlation between maintenance task priority and track risk level: By directly incorporating the TQI exceedance probability into the maintenance task generation and priority allocation process, maintenance scheduling can prioritize coverage of high-risk track sections, thereby improving the ability to ensure train operation safety.

[0030] 3. Improve the feasibility and stability of maintenance scheduling schemes: By coordinating and optimizing maintenance task scheduling, resource allocation and maintenance vehicle routes in a unified model, problems such as resource conflicts, path discontinuity and time window violations are effectively avoided, making the generated maintenance plan more in line with actual execution conditions.

[0031] 4. Enhance engineering applicability under complex constraints: By explicitly introducing maintenance windows, personnel and equipment capacity limits, and continuous operation constraints into the model, the scheduling scheme can be applied to the actual working conditions of high-speed railway maintenance tasks being intensive and resources being limited.

[0032] In summary, this invention can improve the intelligence level and engineering feasibility of high-speed railway maintenance plans while ensuring safety, and has good technical promotion value and application prospects. Attached Figure Description

[0033] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a schematic diagram of the railway operation and maintenance scheduling method based on four-layer graph integer programming modeling involved in this invention.

[0035] Figure 2 This is a schematic diagram of the railway operation and maintenance scheduling modeling structure based on a four-layer directed graph involved in this invention.

[0036] Figure 3 This is a schematic diagram illustrating the coupling decomposition relationship of the railway operation and maintenance scheduling problem involved in this invention.

[0037] Figure 4 This is a schematic diagram of the scheduling solution structure based on heuristic algorithms and mixed integer programming involved in this invention.

[0038] Figure 5 This is a schematic diagram illustrating the sorting, crossing, variation, and repair process of maintenance tasks involved in this invention.

[0039] Figure 6 This is a schematic diagram of the integrated scheduling results of multi-day maintenance tasks, resources, and vehicle routes involved in this invention. Detailed Implementation

[0040] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0041] The following disclosure provides many different implementations or examples for carrying out different structures of the embodiments of the present invention. To simplify the disclosure of the embodiments of the present invention, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. Furthermore, reference numerals and / or reference letters may be repeated in different examples of the embodiments of the present invention; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various implementations and / or arrangements discussed.

[0042] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0043] like Figure 1 As shown, this embodiment provides a railway operation and maintenance scheduling method based on four-level graph integer programming modeling, including: S1. Acquire data on tasks to be scheduled, maintenance bases and resource capabilities, maintenance windows and work slots, and form a standardized data set; S2. Based on the task location-related data in the standardized dataset, combined with the preset maintenance vehicle driving rules, calculate the transfer time between any two tasks and from the maintenance base to each task location, forming time-related data; S3. Classify the tasks to be scheduled in the standardized dataset according to their job characteristics, set duration estimation rules for each type of task, determine the standard duration of each task, and update it to the standardized dataset. S4. Based on a standardized dataset, construct a window and task execution time constraint system based on date and intraday time slot dimensions; S5. Based on a standardized dataset, a four-layer graph structure is constructed to represent the relationship between tasks, resources, vehicle paths, and time windows using event sequences; S6. Construct a MILP model based on standardized datasets, time-related data, constraint systems, and a four-layer graph structure; S7. A mechanism combining heuristic global search and intraday MILP sub-problem verification is adopted. The tasks to be scheduled are encoded as chromosome sequences. The feasibility is verified by the MILP model and offspring are generated. When repairing chromosomes, forced tasks are added, and the task volume is adjusted by calling the optimal daily task limit pre-calibrated by S9. S8. In the search process of S7, the MILP subproblems are simplified and a cache mapping is established to accelerate computation; S9. Based on the tasks to be scheduled and the MILP model, determine the upper limit of the optimal number of tasks per day; S10. Based on the solution results of S7, output the scheduling plan, resource allocation scheme, path information and visualization charts.

[0044] In some embodiments, the preset driving rules for maintenance vehicles in S2 include: determining the driving speed of maintenance vehicles on different road sections by combining information on speed-limited sections of railway lines, turnout distribution, construction restricted areas, and driving speed limits corresponding to the type and load of the maintenance vehicle.

[0045] In some embodiments, the tasks to be scheduled in S3 are classified into daily maintenance tasks, emergency repair tasks, and special maintenance tasks according to their operational characteristics. The duration estimation rules for each type of task are established based on historical operational data, equipment models, number of operational personnel, and operational environment parameters.

[0046] In some embodiments, the constraint system in S4 includes: constraints on the opening and closing time of the maintenance sunroof and the available working time within the sunroof; constraints on the earliest start time and latest completion time of the tasks to be scheduled; and constraints on the priority execution time of the forced tasks.

[0047] In some embodiments, in the four-layer graph structure of S5, the skylight start event corresponds to the opening time node of the maintenance skylight, the task start event corresponds to the start time node after the task is allocated resources, the task end event corresponds to the time node when the task is completed and resources are released, and the skylight end event corresponds to the closing time node of the maintenance skylight; directed edges are used to represent the temporal relationship between events, and the weight of the edge is the time interval or resource consumption cost between events.

[0048] In some embodiments, the core constraints of the MILP model in S6 include resource capacity constraints, task timing constraints, vehicle path continuity constraints, and time window constraints. The objective function is a weighted combination of at least one or more of the following: maximizing the forced task completion rate, minimizing the total operation and maintenance cost, and minimizing resource idle time.

[0049] In some embodiments, the heuristic global search algorithm in S7 is a hybrid algorithm of one or more of the following: genetic algorithm, simulated annealing algorithm, and particle swarm optimization algorithm; in the chromosome sequence, gene positions represent tasks to be scheduled, the order of gene positions represents the execution order of tasks, and date separators are used to divide task groups of different dates.

[0050] In some embodiments, the simplification of the MILP subproblem in S8 refers to removing the resource optimization allocation constraints in the MILP model and retaining only the task feasibility constraints, time window constraints, and vehicle path continuity constraints; the key of the cache mapping is a combination of daily tasks, and the value is the corresponding feasibility verification result and the optimal execution time.

[0051] In some embodiments, when determining the optimal daily task limit in S9, a daily task group is constructed by sampling based on the type distribution and priority distribution of the tasks to be scheduled. The range of the candidate limit is 1 to 1.5 times the historical average number of tasks executed per day. The optimal daily task limit is determined by comparing the task feasibility rate, model solution time and resource utilization rate under different candidate limits.

[0052] In some embodiments, the visualization charts in S10 include a task execution Gantt chart, a resource load distribution chart, a maintenance vehicle path planning topology chart, and a task completion rate statistical bar chart.

[0053] The technical concept of this invention is as follows: To address the problems of existing technologies, such as "segmentation-resource-vehicle path fragmentation, easy omission of key engineering constraints," "pure MILP global solution's computational efficiency is insufficient to meet engineering timeliness requirements when the task scale is large," "heuristic generation schemes are prone to forced task omission / overdue and single-day task overload leading to infeasibility," and "repeated solution of subproblems within the day causing additional overhead," the purpose of this invention is: 1) Provides a unified modeling method for railway operation and maintenance, which expresses the ordering of maintenance tasks, resource occupation and the continuity of track maintenance vehicle paths in the same framework, and realizes the synchronous characterization and consistent constraint of engineering executable constraints such as track window time, resource mutual exclusion, task start and end on the same day, transfer time, path continuity and no loop. 2) Provides an efficient solution strategy for engineering applications. Under the conditions of multiple tasks, multiple resources, and strict windowing, it avoids the time explosion of pure MILP on large-scale problems by using a hybrid mechanism of "heuristic global search + intraday MIP subproblem feasibility verification" and outputs an executable daily plan within an acceptable time. 3) Provide a feasibility assurance mechanism tailored to the characteristics of railway operation and maintenance scheduling. By mandating task repair and adjusting the daily task limit, reduce the infeasibility risks introduced by crossover / variation, ensure that mandating tasks with hard date constraints are allocated, and avoid excessive concentration of daily tasks that makes it difficult to meet the constraints of maintenance window time / resources / paths. 4) Provide a computation acceleration mechanism. In the heuristic search phase, the model with embedded solver is simplified to "only retaining the feasibility judgment of hard constraints" and a "task combination - fitness / feasibility" cache is established to reduce the overhead of solving repeated subproblems and improve the overall search throughput and convergence speed.

[0054] The core process is as follows: Acquire basic data such as tasks, resources, and sunroof maintenance information, and perform structured modeling; Quantitatively calculate the transfer time between tasks and the duration of tasks, and construct window and calendar constraints; The four-layer diagram structure of "skylight start - mission start - mission end - skylight end" is used to uniformly represent the coupling relationship between mission, resources, vehicles, and time window; Establish a mixed-integer linear programming (MILP) model with constraints such as vehicle routing, event time, and resource conflicts; A hybrid solution strategy of "heuristic global search + intraday MILP subproblem feasibility verification" is adopted, combined with optimization methods such as chromosome repair, sub-model simplification, cache reuse, and daily task limit calibration. Output daily scheduling plans and visualizations such as resource-task Gantt charts and maintenance vehicle route diagrams.

[0055] This invention, under the given planning period and daily maintenance window conditions, comprehensively considers constraints such as task time window, task duration, resource consumption, maintenance vehicle route continuity, and transfer time to generate an executable multi-day maintenance scheduling scheme. The method includes at least the following steps: Step S1: Acquisition of Operation and Maintenance Scheduling Input Data and Structured Modeling S1.1 Obtain basic data for tasks and routes.

[0056] Obtain the set of tasks to be scheduled from the operation and maintenance management system / defect database / job log, including but not limited to: task type, task location, type and quantity of resources required by the task, whether the task requires the participation of a maintenance vehicle, set of days on which the task can be executed, task priority / level, etc. Refer to Table 1 for determining the task priority.

[0057] Table 1. Task Priority Importance-Urgency Matrix ; S1.2 Obtain data on maintenance bases and resource capabilities.

[0058] Obtain information on maintenance bases and available resources, including but not limited to: work teams, inspection trolleys / inspection equipment, tamping / grinding tools, maintenance vehicles, etc., and record the quantity, available time periods, and compatibility of each resource.

[0059] S1.3 Obtain maintenance sunroof / operation time slot data.

[0060] Obtain the daily maintenance window length or time period boundary within the planning period, record the start and end times of each maintenance window length and the constraints on allowed operations, and form a "maintenance window set".

[0061] S1.4 Establish the input data table and symbol system.

[0062] The above data is unified into computable model input fields, forming structured tables that include at least "task list" and "task-resource requirement mapping table" for subsequent model calls, as shown in Tables 2 and 3.

[0063] Table 2. Structured Task Data ; Note: Tasks marked with * are mandatory and must be completed within the specified time.

[0064] Table 3. Resources Required for Each Task ; Step S2: Calculation of inter-task transfer / travel time S2.1 Calculate the distance between tasks.

[0065] Calculate the linear distance or equivalent distance between any two tasks based on their locations, and optionally consider the distance from the base to the task point.

[0066] S2.2 Calculate the travel / transfer time between tasks.

[0067] Set the vehicle speed or speed rules for different sections, and calculate the travel time from task i to task j; if necessary, fixed times for arrival preparation / completion can be added. This forms a travel time matrix between tasks.

[0068] S2.3 Transfer time from computing base to mission point.

[0069] Calculate the transfer time from the maintenance base to each task location, and form a base-task transfer time vector or matrix.

[0070] Step S3: Task Duration Estimation and Standardization S3.1 Task Classification.

[0071] Operation and maintenance tasks can be categorized according to their duration and formation mechanism, such as segmented tasks and point-based tasks: 1. Sectional tasks: Continuous operations along the route, with execution time and work length showing a linear or segmented linear relationship; 2. Point-type tasks: These tasks handle local defects, and their execution time can be approximated as a fixed value or a function related to the number of defects.

[0072] S3.2 Decompose the task into work phases and estimate the duration.

[0073] The total duration of each task is broken down into stages such as "preparation - execution - withdrawal," and a rule for estimating the total duration is given: 1. Segment type: Execution time is linearly related to segment length; 2. Point-type: The execution time is taken as a fixed value or estimated according to empirical formulas.

[0074] S3.3 Create a table of task duration parameters.

[0075] Write the minimum / standard duration of each task into the task table and use it as input for subsequent "Event Time Constraint" and "Window Length Constraint".

[0076] Step S4: Maintain skylight modeling and calendar constraint construction S4.1 models the planning period using a "date dimension + intraday time slot dimension".

[0077] Date dimension: Determines which day within the planning period each task is assigned to; Time slot dimension: Within the same daily window period, tasks are sorted, resources are allocated, and maintenance vehicle routes are arranged (satisfying the window period length and timing constraints).

[0078] S4.2 Construct constraints on skylight length and return-to-warehouse.

[0079] Set a sunroof length for each workday and require maintenance vehicles to return to the base or complete necessary follow-up before the sunroof ends.

[0080] S4.3 Build the set of executable dates for tasks / hard deadline constraints.

[0081] For tasks with hard deadlines or that must be completed within a specified set of dates, establish a constraint that "execution can only be performed on one day from the allowed set of days".

[0082] Step S5: A four-layer graph is used to uniformly represent the coupling relationship between task, resources, vehicles, and time window. S5.1 defines event nodes and levels.

[0083] Construct a four-layer graph structure: Skylight start event – ​​Task start event – ​​Task end event – ​​Skylight end event. Each task corresponds to a pair of events, and the time difference between events covers the entire process of "preparation, execution, and withdrawal." See attached diagram. Figure 2 As shown. Figure 2 This paper demonstrates the four-layer directed graph modeling structure used in this invention, where each node represents a maintenance-related event, and each directed edge represents the temporal sequence or path constraint relationship between events. This four-layer structure is used to uniformly characterize the coupling relationship between maintenance tasks, operation time windows, resource consumption, and maintenance vehicle operation paths. It is the core modeling method of this invention for achieving collaborative optimization of maintenance task scheduling, resource allocation, and vehicle path routing.

[0084] S5.2 defines directed edges and reachability relations.

[0085] In a four-level graph, directed edges represent the sequence of events: The path for a repair vehicle to move from one event to the next is formed. Whether tasks can be executed continuously is determined by reachability, travel time, and resource availability. Fully connected or restricted connections can be established between adjacent layers and within layers to represent a "transferable candidate set".

[0086] S5.3 Definition of coupling variables.

[0087] Using "event sequence / event ordering" as the coupling variable between the vehicle routing problem and the resource-constrained scheduling problem: The sequence of events determines the order in which the repair vehicle is accessed; The timing of the event and the availability of resources determine the feasibility of operations within the same day's window.

[0088] The coupling relationship of the combined structure of "path subproblem + resource / time subproblem" is shown in the figure. Figure 3 . Figure 3 This diagram illustrates the coupling relationship between the maintenance vehicle routing subproblem and the resource-constrained task scheduling subproblem in railway operation and maintenance scheduling. It demonstrates that this invention uses maintenance task sequencing as a coupling variable, simultaneously constraining vehicle path continuity and maintenance resource conflicts within a unified framework. This avoids the feasibility issues arising from treating the two types of problems separately in existing technologies.

[0089] Step S6: Establish a MILP model for operation and maintenance scheduling S6.1 Define model parameters and decision variables.

[0090] Define the relevant parameters and variables, as shown in Table 4-5: Table 4. Model Parameter List ; Table 5. List of Model Variables ; S6.2 Vehicle path continuity and acyclic constraints.

[0091] Establish a constraint that the maintenance vehicle has "one and only one first event and one last event" in each workday. The constraint is shown in Equation 1.1-1.3.

[0092] (1.1) (1.2) (1.3) Establish flow conservation constraints to ensure that each event (except the first and last events) has exactly one incoming edge and one outgoing edge; and introduce cycle cancellation constraints to avoid forming unreasonable loop paths. The relevant constraints are shown in Equations 1.4-1.7.

[0093] (1.4) (1.5) (1.6) (1.7) S6.3 Event sequence and time feasibility constraints.

[0094] The order of an ending event should be higher than that of a starting event, as shown in Equation 1.8.

[0095] For any task, the time slot for the end event should be at least equal to the start event time plus the task duration, as shown in Equation 1.9.

[0096] If event i occurs before event j, and events i and j are scheduled on the same day, then the time of event i should be earlier than that of event j, and vice versa. As shown in equations 1.10-1.11.

[0097] If two tasks share the same resource, their durations cannot overlap, and the start event should have a higher priority than the end event, as shown in Equations 1.12-1.13.

[0098] (1.8) (1.9) (1.10) (1.11) (1.12) (1.13) S6.4 Resource capacity and resource conflict constraints.

[0099] For each task, resource allocation must meet its resource requirements; for tasks sharing the same resource, the time periods they occupy within the same window must not overlap. The relevant constraints are shown in Equation 1.14.

[0100] (1.14) S6.5 Date Assignment and Working Day Activation Constraints.

[0101] Each event must be assigned to the appropriate set of dates; if there are no tasks scheduled on a day, that day is not enabled (rest day); if there are tasks scheduled on a day, that day is enabled. The relevant constraints are shown in Equations 1.15-1.17.

[0102] (1.15) (1.16) (1.17) S6.6 Coupling Constraints.

[0103] If there is an edge in the repair vehicle path, then event i must precede event j, thus achieving consistency between the "path adjacency variable" and the "event sequence variable / time variable"; the relevant constraints are represented by Equation 1.18.

[0104] (1.18) S6.7 Construction of the objective function.

[0105] Construct a dual-objective or weighted single-objective form that balances "maximizing task benefits / priority" and "minimizing the number of working days / operational maintenance overhead". The objective function is represented by Equation 1.19.

[0106] (1.19) Step S7: Employ a hybrid solution process combining heuristic search and MILP subproblem feasibility / optimality checks. S7.1 chromosome encoding.

[0107] Candidate scheduling schemes are encoded as chromosome sequences: genes represent tasks; date separators are introduced to divide tasks into different days; segments before and after the separator represent the task sets within the corresponding day; tasks after the last separator indicate unscheduled tasks. The encoding structure is shown in the attached figure. Figure 5 As shown. Figure 5 This diagram illustrates the crossover, mutation, and infeasibility repair processes of maintenance task sorting codes during heuristic solution. It demonstrates how this invention maintains maintenance task priority constraints and operational feasibility during scheduling optimization, thereby generating a maintenance plan that meets actual engineering constraints.

[0108] S7.2 Subproblem decomposition and solution.

[0109] For each day's task group in the chromosome, construct a small-scale MILP subproblem that "removes the date dimension"; call the solver to verify the feasibility of the day's task group and obtain feasible sorting / resource allocation / path schemes; add feasible tasks to the completion set.

[0110] S7.3 Fitness Calculation.

[0111] The fitness of an individual is determined by the weighted sum of priorities for completing the set size or the task, which guides the direction of the evolutionary search.

[0112] S7.4 Genetic Operations: Crossover and Mutation.

[0113] To address the characteristics of "task sorting / path continuity", a crossover operator that preserves the sequence structure is used to generate offspring; mutation can be performed by exchange mutation or other operations that do not violate the legality of the encoding, and parameters such as crossover probability and mutation probability are set.

[0114] S7.5 chromosome repair.

[0115] To improve feasibility and solution efficiency, the following fixes will be implemented: For individuals with unassigned hard-dead / mandatory tasks, mandatory tasks are inserted into feasible days by swapping them with non-mandatory tasks or adjusting the position of separators. If a day's workload is too heavy, making subproblems unfeasible within the window, move the date separator or shift / set the last task to unscheduled to control the daily task size. See the fix logic below. Figure 5 As shown.

[0116] Step S8: Engineering Acceleration Strategy S8.1 Simplification of the sub-model with feasibility as the priority.

[0117] In the early screening stage of heuristic search, the embedded MILP subproblems are simplified into feasibility models that "only retain hard constraints" to quickly determine whether candidate day task groups are feasible, thereby significantly reducing the solution overhead for each evaluation.

[0118] S8.2 fitness cache reuse.

[0119] Construct a cached mapping of "task combination → fitness / feasibility result". When the daily task group of a new individual is consistent with the historically evaluated combination or meets the reuse condition, the cached result is read directly to avoid repeated calls to the solver.

[0120] Step S9: Setting the maximum number of tasks per day S9.1 sets the upper limit set of candidates.

[0121] Given a set of candidate "maximum daily task limit k".

[0122] S9.2 Benchmark Sampling and Daily Solution Experiment.

[0123] Random sampling is performed from the real task set according to task type and resource requirement distribution to construct daily task groups; for each k, the corresponding daily MILP is solved, and the solution time and feasibility rate are recorded.

[0124] S9.3 Choose the optimal compromise k.

[0125] Based on a trade-off between feasibility and solution time, an upper limit k for the number of daily tasks is selected for the main experiment / main deployment, and used as a hard or soft threshold in genetic repair.

[0126] Step S10: Output the executable plan and visualization results S10.1 outputs the daily scheduling plan.

[0127] Output the daily task set, task execution order, start / end time of each task, resource allocation results, and access path for the repair vehicle, etc.

[0128] S10.2 outputs a graphical executable file.

[0129] The results will generate resource-task Gantt charts, repair vehicle path diagrams, etc. (See attached diagram for illustrations.) Figure 6 As shown, it is used for on-site execution and management review.

[0130] Example 1: Modeling and Solving of Railway Operation and Maintenance Task Scheduling under the Constraints of Track Window and Resource Coupling (I) Implementation Environment and Basic Data This embodiment uses the operation and maintenance task scheduling of a high-speed railway line as an example. The line is 75km long, and there are a total of 52 operation and maintenance tasks during the planning period. The tasks are derived from actual maintenance operation logs and cover types such as periodic inspections, condition-based maintenance, and preventive maintenance. The available operational resources in this embodiment include: 4 work teams, 2 inspection trolleys, 1 railway maintenance car, and 1 pair of tamping machines.

[0131] At the implementation level, this embodiment calls GurobiOptimizer to solve the subproblem in a MacBook Air (Apple M2, 8GB RAM) environment, with the evolutionary parameters set as follows: population size 50, number of iterations 200, crossover probability 0.7, and mutation probability 0.05.

[0132] (II) Time Dimension and Priority Rules for Problem Modeling As stated in the problem statement of the paper, this embodiment divides the scheduling solution structure into a "date dimension" and a "window dimension": in the date dimension, maintenance tasks are assigned to specific dates within the planning period; in the window dimension, tasks on the same day are sorted to avoid resource conflicts and meet the maintenance vehicle travel continuity constraint.

[0133] Regarding the determination of task priorities at the date dimension, this embodiment uses an Important-Urgent Matrix to classify tasks and guide scheduling priority settings, as shown in Table 6.

[0134] Table 6. Task Priority Importance-Urgency Matrix ; (III) Coupled Modeling of Four-Layer Diagrams and Event Sequences like Figure 3 As shown, this embodiment establishes a four-layer graph structure with sunroof operation as the core, where each node represents an event and each directed edge represents the event sequence; each task includes a "task start event" and a "task end event", with the interval between the two events corresponding to the task duration. Under the four-layer graph structure, this embodiment treats maintenance resources as capacity-constrained resources and describes the event sequence of the maintenance vehicle from the sunroof start node to the sunroof end node on the sunroof timeline.

[0135] like Figure 4 As shown, Figure 4 This paper illustrates the scheduling solution structure employed in this invention, where candidate maintenance task execution schemes are generated through heuristic search, and a subset of daily tasks is embedded into a mixed-integer programming model for feasibility verification. This figure serves to explain the overall approach of this invention to improve the solution efficiency of complex railway operation and maintenance scheduling problems while ensuring the feasibility of the scheduling scheme.

[0136] This embodiment treats the maintenance scheduling problem as a coupling of the "vehicle routing problem" and the "resource-constrained flexible job shop scheduling problem", with the event sequence as the coupling variable of the two sub-problems, thereby simultaneously handling task ordering, resource conflicts and routing continuity under a unified model framework.

[0137] (iv) Scheduling Input Preparation Process Before solving the model, this embodiment constructs the scheduling input according to the following process: retrieve the defect type, defect location, and set of machinery and equipment resources involved in the construction process from the database; calculate the travel time between two tasks based on the distance between tasks and the speed of the maintenance vehicle; Based on on-site operational experience, the duration of each maintenance task is estimated, and maintenance activities are divided into "segment-type tasks" and "point-type tasks". The total duration of the task consists of three stages: preparation, execution, and withdrawal. The execution time of segment-type tasks is linearly related to the length of the work segment, while the execution time of point-type tasks is a fixed value. The maintenance window duration is incorporated into the model and corresponding constraints are established.

[0138] Furthermore, all embodiments in this example assume that the railway maintenance vehicle travels at a speed of 60 km / h.

[0139] (V) Hybrid Heuristic-MIP Solution Process and Computational Acceleration Strategies To improve the efficiency of solving large-scale scheduling problems, this embodiment adopts a hybrid framework that combines heuristic search with MIP feasibility / precision verification, and introduces the following two computation acceleration strategies in solving subproblems.

[0140] In the early stages of heuristic search, the objective function of the embedded Gurobi model is removed, and only hard constraints are retained for the feasibility verification of candidate solutions, thereby reducing the time for solving a single evaluation. A dictionary cache structure of "task combination - fitness value" is constructed. Before evaluating a new individual, the cache is queried. If a match is found, the fitness value is directly reused. If a match is not found, the simplified Gurobi model is solved to obtain the fitness value and then written back to the cache to avoid repeated solving.

[0141] (vi) Setting the maximum number of tasks per day To improve intraday feasibility under realistic constraints such as the "4-hour window," this embodiment calibrates the "maximum number of tasks that can be scheduled per day." For different upper limits, a task set is randomly sampled while maintaining the task type and resource distribution characteristics. These sets are then used as solutions for the daily MIP model, and the solution time and feasibility indicators are recorded to form comparative data, as shown in Table 7. Based on the calibration results, this embodiment selects a maximum of 5 tasks per day as the compromise solution for the main experiment.

[0142] Table 7. Baseline results for different daily maximum task limits ; (vii) Execution results and output format After completing the preparation process, this embodiment starts the solution process, with an overall solution time of about 30 minutes. During the evolutionary iteration, the population entropy and fitness quantiles are calculated to characterize convergence and diversity.

[0143] Finally, this embodiment outputs a 7-day task-resource Gantt chart and maintenance vehicle route results, see [link / details]. Figure 6 As shown, the daily window length meets the 4-hour requirement, there are no resource conflicts between tasks on the same day, and the maintenance vehicle path is consistent with the task event sequence, thus forming an operation and maintenance scheduling plan that can be directly executed. Figure 6 This diagram illustrates the scheduling results of different maintenance tasks under various resource constraints and operation time windows within a multi-day maintenance plan cycle, including the occupancy of maintenance personnel and equipment resources, as well as the travel routes of maintenance vehicles. This figure serves to demonstrate the feasibility and stability of the maintenance scheduling scheme generated by this invention under actual engineering constraints.

[0144] The embodiments described above are for illustrative purposes only and are not intended to limit the invention. Therefore, any changes in numerical values ​​or substitutions of equivalent elements should still fall within the scope of this invention.

[0145] The above detailed description will enable those skilled in the art to understand that the present invention can indeed achieve the aforementioned objectives and has complied with the provisions of the Patent Law.

[0146] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention. The above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

[0147] It should be noted that the above description of the process is for illustrative purposes only and does not limit the scope of this specification. Those skilled in the art can make various modifications and changes to the process under the guidance of this specification. However, these modifications and changes remain within the scope of this specification.

[0148] The basic concepts have been described above. Obviously, for those skilled in the art who have read this application, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application, and therefore, such modifications, improvements, and corrections still fall within the spirit and scope of the exemplary embodiments of this application.

[0149] Furthermore, this application uses specific terms to describe its embodiments. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different positions in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application can be appropriately combined.

[0150] Furthermore, those skilled in the art will understand that aspects of this application can be described and illustrated through several patentable types or situations, including any new and useful combination of processes, machines, products, or substances, or any new and useful improvements thereof. Therefore, aspects of this application can be implemented entirely in hardware, entirely in software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. All of the above hardware or software can be referred to as a “unit,” “module,” or “system.” Furthermore, aspects of this application can take the form of a computer program product embodied in one or more computer-readable media, wherein computer-readable program code is contained therein.

[0151] The computer program code required for the operation of each part of this application can be written in any one or more programming languages, including object-oriented programming languages ​​such as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB.NET, and Python; general programming languages ​​such as C; Visual Basic, Fortran2103, Perl, COBOL2102, PHP, and ABAP; dynamic programming languages ​​such as Python, Ruby, and Groovy; or other programming languages. This program code can run entirely on the user's computer, or as a standalone software package on the user's computer, or partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer can be connected to the user's computer via any network, such as a local area network (LAN) or wide area network (WAN), or connected to an external computer (e.g., via the Internet), or in a cloud computing environment, or used as a service such as Software as a Service (SaaS).

[0152] Furthermore, unless expressly stated in the claims, the order of processing elements and sequences, the use of numbers and letters, or other names described in this application are not intended to limit the order of the processes and methods of this application. Although some currently considered useful embodiments of the invention have been discussed in the foregoing disclosure by way of various examples, it should be understood that such details are for illustrative purposes only, and the appended claims are not limited to the disclosed embodiments; rather, the claims are intended to cover all modifications and equivalent combinations that conform to the substance and scope of the embodiments of this application. For example, although the implementation of the various components described above can be embodied in a hardware device, it can also be implemented as a purely software solution, such as an installation on an existing server or mobile device.

[0153] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments of the invention, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this approach of the present application should not be construed as reflecting an intention that the claimed subject matter requires more features than expressly recited in each claim. Rather, the subject of the invention should possess fewer features than in any single embodiment described above.

Claims

1. A railway operation and maintenance scheduling method based on four-level graph integer programming modeling, characterized in that, include: S1. Acquire data on tasks to be scheduled, maintenance bases and resource capabilities, maintenance windows and work slots, and form a standardized data set; S2. Based on the task location-related data in the standardized dataset, combined with the preset maintenance vehicle driving rules, calculate the transfer time between any two tasks and from the maintenance base to each task location, forming time-related data; S3. Classify the tasks to be scheduled in the standardized dataset according to their job characteristics, set duration estimation rules for each type of task, determine the standard duration of each task, and update it to the standardized dataset. S4. Based on a standardized dataset, construct a window and task execution time constraint system based on date and intraday time slot dimensions; S5. Based on a standardized dataset, a four-layer graph structure is constructed to represent the relationship between tasks, resources, vehicle paths, and time windows using event sequences; S6. Construct a MILP model based on standardized datasets, time-related data, constraint systems, and a four-layer graph structure; S7. A mechanism combining heuristic global search and intraday MILP sub-problem verification is adopted. The tasks to be scheduled are encoded as chromosome sequences. The feasibility is verified by the MILP model and offspring are generated. When repairing chromosomes, forced tasks are added, and the task volume is adjusted by calling the optimal daily task limit pre-calibrated by S9. S8. In the search process of S7, the MILP subproblems are simplified and a cache mapping is established to accelerate computation; S9. Based on the tasks to be scheduled and the MILP model, determine the upper limit of the optimal number of tasks per day; S10. Based on the solution results of S7, output the scheduling plan, resource allocation scheme, path information and visualization charts.

2. The railway operation and maintenance scheduling method based on four-layer graph integer programming modeling according to claim 1, characterized in that, The preset driving rules for maintenance vehicles in S2 include: determining the driving speed of maintenance vehicles on different road sections by combining information on the speed limit sections, turnout distribution, and construction restricted areas of the railway line, as well as the driving speed limits corresponding to the type and load of the maintenance vehicle.

3. The railway operation and maintenance scheduling method based on four-layer graph integer programming modeling according to claim 1, characterized in that, In S3, the tasks to be scheduled are divided into daily maintenance tasks, emergency repair tasks, and special maintenance tasks according to their operational characteristics. The duration estimation rules for each type of task are established based on historical operation data, equipment models, number of operators, and operational environment parameters.

4. The railway operation and maintenance scheduling method based on four-layer graph integer programming modeling according to claim 1, characterized in that, The constraint system in S4 includes: constraints on the opening and closing time of maintenance skylights and the available working time within the skylights; constraints on the earliest start time and latest completion time of tasks to be scheduled; and constraints on the priority execution time of mandatory tasks.

5. The railway operation and maintenance scheduling method based on four-layer graph integer programming modeling according to claim 1, characterized in that, In the four-layer graph structure of S5, the skylight start event corresponds to the opening time node of the maintenance skylight, the task start event corresponds to the start time node after the task is allocated resources, the task end event corresponds to the time node when the task is completed and resources are released, and the skylight end event corresponds to the closing time node of the maintenance skylight; directed edges are used to represent the temporal relationship between events, and the weight of the edge is the time interval or resource consumption cost between events.

6. The railway operation and maintenance scheduling method based on four-layer graph integer programming modeling according to claim 1, characterized in that, The core constraints of the MILP model in S6 include resource capacity constraints, task timing constraints, vehicle path continuity constraints, and time window constraints. The objective function is a weighted combination of at least one or more of the following: maximizing the forced task completion rate, minimizing the total operation and maintenance cost, and minimizing resource idle time.

7. The railway operation and maintenance scheduling method based on four-level graph integer programming modeling according to claim 1, characterized in that, The heuristic global search algorithm in S7 is a hybrid algorithm of one or more of the following: genetic algorithm, simulated annealing algorithm, and particle swarm optimization algorithm; in the chromosome sequence, gene positions represent tasks to be scheduled, the order of gene positions represents the execution order of tasks, and date separators are used to divide task groups of different dates.

8. The railway operation and maintenance scheduling method based on four-level graph integer programming modeling according to claim 1, characterized in that, The simplification of the MILP subproblem in S8 refers to removing the resource optimization allocation constraints in the MILP model and retaining only the task feasibility constraints, time window constraints, and vehicle path continuity constraints; the key of the cache mapping is the daily task combination, and the value is the corresponding feasibility verification result and the optimal execution time.

9. The railway operation and maintenance scheduling method based on four-layer graph integer programming modeling according to claim 1, characterized in that, When determining the optimal daily task limit in S9, a daily task group is constructed by sampling based on the type distribution and priority distribution of the tasks to be scheduled. The range of the candidate limit is 1 to 1.5 times the historical average number of tasks executed per day. The optimal daily task limit is determined by comparing the task feasibility rate, model solution time and resource utilization rate under different candidate limits.

10. The railway operation and maintenance scheduling method based on four-layer graph integer programming modeling according to claim 1, characterized in that, The visualization charts in S10 include a task execution Gantt chart, a resource load distribution chart, a maintenance vehicle path planning topology chart, and a task completion rate statistics bar chart.

Images