A subway scheduling decision intelligent generation method based on column generation algorithm

Abstract

The present application relates to the technical field of intelligent decision-making, in particular to a subway scheduling decision-making intelligent generation method based on column generation algorithm, comprising: abstracting the subway scheduling problem as a path problem; designing a mathematical heuristic method to obtain a high-quality initial solution; dividing the problem into a main problem and a sub-problem, and constructing linear mathematical models corresponding to the main problem and the sub-problem; automatically generating an intelligent decision-making scheme according to the input solving time iterative calculation, which can quickly and accurately generate an intelligent decision-making scheme for the subway scheduling problem, reduce decision-making errors, and greatly improve the efficiency of the subway scheduling plan.

Description

Technical Field

[0001] This invention is an intelligent generation method for subway scheduling decisions based on a column generation algorithm, belonging to the field of intelligent decision-making technology. Background Technology

[0002] In modern transportation systems, efficient and accurate scheduling decisions play a crucial role in ensuring the stable operation of transportation lines, optimizing driver work efficiency, and ensuring safe driving. Traditional subway scheduling decisions often rely on human experience and simple logical judgments, such as assigning a fixed number of drivers to wait at certain stations and take turns boarding, or prioritizing special trains based on experience. This approach is not only inefficient but also highly susceptible to human factors, easily leading to problems such as excessively long waiting times for drivers, excessively long working hours, and insufficient rest intervals between work shifts, resulting in low work efficiency and potentially even safety hazards.

[0003] With the development of operations research algorithms in the transportation field, various operations research algorithm solutions are gradually being applied to traffic decision-making. Direct solutions using heuristic algorithms and integer programming (IP) can automate some decision-making tasks in traffic scenarios, improving decision-making efficiency and accuracy to some extent. However, existing intelligent transportation decision-making solutions still have many limitations. On the one hand, heuristic algorithms are prone to getting trapped in local optima, and rule design requires extensive trial and error, resulting in weak generalization ability and difficulty in widespread adoption. On the other hand, as the problem size increases, the number of variables in integer programming (IP) methods grows exponentially, leading to the "curse of dimensionality" in commercial solvers (such as CPLEX) and unacceptable solution times.

[0004] Therefore, this invention proposes an intelligent generation method for subway scheduling decisions based on a column generation algorithm. Summary of the Invention

[0005] To address the problems in existing technologies, this invention provides an intelligent generation method for subway scheduling decisions based on a column generation algorithm.

[0006] The technical solution adopted by this invention to solve its technical problem is: an intelligent generation method for subway scheduling decisions based on a column generation algorithm, comprising: Step S1: Obtain subway timetable and rule data; The subway timetable includes departure and arrival times, train arrival and departure times, and station dwell times. The rules data include minimum driving intervals, driver and vehicle resource constraints, and route connection rules; Step S2: Use mathematical heuristics to obtain alternative route plans that cover all train services; Step S3: Solve the main problem model to obtain the shadow price of all train trips in the main problem model; Step S4: Solve the subproblem model and add the obtained intersections to the main problem's candidate intersection pool; Step S5: Check whether the objective of all sub-problem models is less than the preset tolerance or reaches the time limit. If it meets the requirements, proceed to the next step; otherwise, return to step S4. Step S6: Analyze the column generation algorithm scheme and generate the corresponding route plan.

[0007] Furthermore, mathematical heuristics include: Step a1: Initialize whether the train number exists in the candidate routes. If it does, record it as 0; otherwise, record it as 1. At the same time, set N=1. Step a2: Obtain the subproblem formed by the Nth attendance point; Step a3: Solve this subproblem with the objective of maximizing the number of trains passing through routes without alternative options; Step a4: Record the alternative routes after solving the problem, update the train numbers passed by the routes, and update the train number record table. Step a5: Check if all train routes exist in the candidate routes. If so, output all candidate routes as the initial solution; otherwise, output N+1 and return to step a2.

[0008] Furthermore, the variable constants of the linear model include: Represents a set of train numbers; This represents the set of all trains among the candidate routes obtained in the callback function; This represents the total number of train trips for all candidate routes calculated in the callback function; Indicates train number Whether it has been visited or not, 0 is passed and 1 is not passed. Indicates the train number Maximum working hours during off-duty hours; Indicates the train number Minimum working hours before returning to work; Indicates whether or not attendance is required. Starting from this point, 1 represents selection, and 0 represents no selection. ; The variables in a linear model include: Indicate whether to start from train number Train numbers 1 indicates that the event has been passed, and 0 indicates that it has not been passed. ; Indicate whether to select a train number As the endpoint, 1 represents selection, and 0 represents no selection. .

[0009] Indicates the selection of train number Earliest start time ; The objective function of the linear model is: This indicates that you should try to select trains that have not yet been selected.

[0010] The constraint expressions for the linear model are: This means that each train can only pass through once; This means that the number of times each train enters and exits should be equal; This means that each train trip must meet the maximum working time limit; This indicates that each train trip must meet the minimum working hours limit.

[0011] The callback function for the linear model is: During the solution process, alternative routes are obtained, and rest time checks are performed to check if there are any segments in the train sequence that have not been allocated rest time. If illegal rest segments are found, callback constraints are added to the segments that violate the constraints. This indicates that this segment is prohibited from being selected for route selection.

[0012] Furthermore, the variables, constants, constraint expressions, and callback functions in step S4 are the same as the linear model of the subproblem in the above mathematical heuristic method; The following differs from the linear model of the subproblems in the mathematical heuristics described above: Indicates road segment The corresponding dual variable value in the main function.

[0013] The objective function is as follows: Furthermore, the objective function of the linear model of the main problem model is: The constraint expression for the linear model of the main problem model is as follows: in Indicates the set of alternative routes; Represents a set of train numbers; Indicates alternative Does it pass by train number? 1 indicates the passage was passed, and 0 indicates it was not passed. , ; Indicate alternative routes The overall cost; Indicates whether to select a path. 1 indicates selection, 0 indicates no selection. .

[0014] Furthermore, the aforementioned Based on the alternative route budget The budget includes: The cost per route is 1; The balance of working hours and length is achieved by subtracting the set expected working hours or length from the total working hours of the budgeted route and taking the absolute value. The formula for driver time utilization rate is the total driving time of a driver divided by the total route time. The weights of each part of the objective function are set through input.

[0015] Furthermore, the upper and lower limits of working hours can be different for different shifts; The departure and arrival points can be different for different shifts; The working hours, attendance point, departure point, and minimum rest interval are determined based on the input.

[0016] The beneficial effects of this invention are: This invention abstracts the subway scheduling problem into a path problem; it obtains a high-quality initial solution through a mathematical heuristic method, then divides the problem into a main problem and sub-problems, and constructs linear mathematical models corresponding to the main problem and sub-problems; it iteratively calculates based on the input solution time, and automatically generates an intelligent decision-making scheme, which can quickly and accurately generate an intelligent decision-making scheme for the subway scheduling problem, reduce decision-making errors, and significantly improve the efficiency of subway scheduling plans. This invention uses the idea of ​​decomposition, which on the one hand solves the shortcomings of heuristic algorithms that are prone to getting trapped in local optima, require a lot of trial and error in rule design, have weak generalization ability, and are not easy to generalize; on the other hand, it solves the "curse of dimensionality" faced when the problem scale increases, speeds up the solution speed, and guarantees the existence of a feasible solution through mathematical heuristic algorithms. Attached Figure Description

[0017] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart of an intelligent generation method for subway scheduling decisions based on a column generation algorithm, as described in this invention. Figure 2 This is a flowchart of the mathematical heuristic algorithm in this invention; Figure 3 A graph showing the degree of dispersion in a class using a heuristic algorithm; Figure 4 This is a graph showing the degree of dispersion of the column generation algorithm in this invention; Figure 5 This is an algorithm planning diagram of an intelligent generation method for subway scheduling decisions based on a column generation algorithm, according to the present invention. Detailed Implementation

[0018] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0019] This invention utilizes a column generation algorithm for intelligent scheduling decisions. Column Generation (CG) is a decomposition and optimization method for large-scale linear programming problems. Its core idea is to dynamically call subproblems to generate key variables through an iterative mechanism, avoiding the enumeration of all variables and thus efficiently solving combinatorial optimization problems with a large number of variables. Essentially, it transforms the search of the entire variable space into the on-demand generation of high-value variables, a classic framework for handling NP-hard large-scale problems. Based on the abstracted problem, it decomposes into a main problem and several subproblems. Each candidate departure point in a shift corresponds to a subproblem, and each subproblem is: starting from a fixed departure point, find a route that satisfies constraints and ends at a candidate departure point. The main problem is to select several routes based on the candidate routes chosen from the subproblems, covering the entire subway timetable.

[0020] The first embodiment provides an intelligent generation method for subway scheduling decisions based on a column generation algorithm, including: Step S1: Obtain subway timetable and rule data; The subway timetable includes departure and arrival times, train arrival and departure times, and station dwell times. The rules data include minimum headway, driver / vehicle resource constraints, and route connection rules; Driver / vehicle resource constraints include the maximum number of drivers, minimum rest interval, and maximum number of available trains.

[0021] Routing coordination rules include turnaround time coordination and attendance / departure coordination.

[0022] Step S2: Use mathematical heuristics to obtain alternative route plans that cover all train services; Step S3: Solve the main problem model to obtain the shadow price of all train trips in the main problem model; Step S4: Solve the subproblem model and add the obtained intersections to the main problem's candidate intersection pool; Step S5: Check whether the objective of all sub-problem models is less than the preset tolerance or reaches the time limit. If it meets the requirements, proceed to the next step; otherwise, return to step S4. Step S6: Analyze the column generation algorithm scheme and generate the corresponding route plan.

[0023] After the main problem is solved, for each required trip, a unique corresponding dual variable, i.e., the shadow price, is output and stored as a set of numerical vectors. The shadow prices corresponding to all trips are then distributed to the pricing subproblem. After receiving the complete set of shadow prices, the subproblem traverses all feasible spatiotemporal paths and searches for the optimal new route with a negative check number. If the subproblem finds a high-quality new route, it packages the trips, costs, and coverage relationships included in the route and returns them to the main problem. The main problem adds this route to the variable pool and solves it again. If no high-quality route is found, no route is returned, the iteration termination condition is triggered, and the main and subproblems alternate in a loop.

[0024] This invention addresses the problem of subway scheduling decisions. Specifically, given a subway timetable, the method of this invention arranges driver routes (the order of driver shifts) requiring all route plans to cover all trains in the subway timetable. Routes must begin at certain alternative start points and end at certain exit points. Each route requires a decision on the shift to which it belongs. Each shift has its own alternative start and end points, and must comply with the maximum working hours, minimum working hours, and rest intervals for morning, afternoon, and evening shifts, respectively.

[0025] The terms used in the above steps are defined as follows: Train number: refers to a complete operation of a subway train according to a fixed timetable, including the departure time of the origin station, the arrival time of the destination station, and the arrival and departure times of each station along the way.

[0026] Shift: refers to the time period during which a driver works, generally divided into morning shift, afternoon shift, evening shift, and substitute shift, etc.

[0027] Routes: refers to the driver duty sequence formed by combining one or more train routes according to certain rules. It stipulates that drivers start from a certain departure point, work on a certain train route, and return to the departure point after running on a specific train route. It includes the direction of operation, the origin and destination points, and the combination relationship of train routes.

[0028] Main problem: Given a number of train trips and several alternative routes, decide which alternative routes to select as the route plan so that all train trips are operated at least once. The objective is to minimize the number of routes, balance the time and length of each route as much as possible, maximize driver time utilization, and minimize the weighted sum of the start and end points of routes.

[0029] Subproblem: Given several train services, one departure point, and several alternative departure points, decide which train services and which alternative departure points to use to form a route. The objective is to maximize the sum of the shadow prices of the selected train services corresponding to the main problem.

[0030] The upper and lower limits of working hours for different shifts are as follows: there are different upper and lower limits for the working hours of the morning shift, afternoon shift, evening shift, and substitute shift. The upper and lower limits of working hours can be different for each shift. For example, the working hours for the morning shift can be set to 4-6 hours, while those for the afternoon shift can be set to 8-9 hours.

[0031] The start and end points are determined by the input, and the set of start and end points may be different for different shifts. For example, the start point for the morning shift may be station 1 or station 2, and the end point may be station 3 or station 4. The start point for the evening shift may be station 3 or station 4, and the end point may be station 1 or station 2.

[0032] The minimum rest interval is generally determined based on input, and is usually the legally mandated rest time. For example, during a continuous 2-hour duty shift, a 15-minute rest is required.

[0033] Since the column generation algorithm requires solving the main problem once to obtain the shadow prices of the subproblems, this invention designs a mathematical heuristic method to obtain a feasible initial solution. The steps of the mathematical heuristic method are as follows: Step a1: Initialize whether the train number exists in the candidate routes. If it does, record it as 0; otherwise, record it as 1. At the same time, set N=1. Step a2: Obtain the subproblem formed by the Nth attendance point; Step a3: Solve this subproblem with the objective of maximizing the number of trains passing through routes without alternative options; Step a4: Record the alternative routes after solving the problem, update the train numbers passed by the routes, and update the train number record table; Step a5: Check if all train routes exist in the candidate routes. If so, output all candidate routes as the initial solution; otherwise, output N+1 and return to step a2.

[0034] The variables, constants, objective function, constraint expressions, and callback functions in the linear model of the subproblems in the above mathematical heuristic method are as follows: The constants involved are as follows: Represents a set of train numbers; This represents the set of all trains among the candidate routes obtained in the callback function; This represents the total number of train trips for all candidate routes calculated in the callback function; Indicates train number Whether it has been visited or not, 0 is passed and 1 is not passed. Indicates the train number Maximum working hours before returning to work.

[0035] Indicates the train number Minimum working hours for returning to work.

[0036] Indicates whether or not attendance is required. As a starting point, 1 represents selection, and 0 represents no selection. ; The variables involved are as follows: Indicate whether to start from train number Train numbers 1 indicates that the event has been passed, and 0 indicates that it has not been passed. ; Indicate whether to select a train number As the endpoint, 1 represents selection, and 0 represents no selection. .

[0037] Indicates the selection of train number Earliest start time ; The specific objective functions involved are shown below: This indicates that you should try to select trains that have not yet been selected.

[0038] The specific constraint expressions involved are shown below: This means that each train can only pass through once; This means that the number of times each train enters and exits should be equal; This means that each train trip must meet the maximum working time limit; This indicates that each train trip must meet the minimum working hours limit.

[0039] The callback functions involved are as follows: During the solution process, alternative routes are obtained, and rest time checks are performed (to check if there are any segments in the train sequence that have not been allocated rest time; if illegal rest segments are found, callback constraints are added to the segments that violate the constraints). This indicates that this segment is prohibited from being selected for route selection.

[0040] The sub-problem model in step S4 above, specifically its linear model variables, constants, objective function, constraint expressions, and callback function, are as follows: The parts concerning variables, constants, constraint expressions, and callback functions are the same as the linear model of the subproblems in the mathematical heuristics described above; The following differs from the linear model of the subproblems in the mathematical heuristics described above: Indicates road segment The corresponding dual variable value in the main function.

[0041] The objective function is as follows: The variables, constants, objective function, constraint expressions, and callback functions of the linear model of the main problem model mentioned above include: The constants involved are as follows: Indicates the set of alternative routes; Represents a set of train numbers; Indicates alternative Does it pass by train number? 1 indicates the passage was passed, and 0 indicates it was not passed. , ; Indicate alternative routes The overall cost; The variables involved are as follows: Indicates whether to select a path. 1 indicates selection, 0 indicates no selection. ; The specific objective functions involved are shown below: This indicates selecting the path combination with the lowest cost.

[0042] The specific constraint expressions involved are shown below: This indicates that the selected route combination must pass through every road segment.

[0043] wherein, The calculation can be performed according to the alternative trip routes, which is specifically as follows: The cost of the number of trip routes is 1; the equalization of working hours and length is obtained by taking the absolute value of the total working hours of the calculated trip routes minus the set expected working hours or length; the formula for the driver working hour utilization rate is the total running time of the trains driven by the driver divided by the total time of the trip routes. In addition, the weight of each part of the objective function is set through input.

[0044] Preferably, the initial weights of all parts are saved as preset values after input, which are respectively the trip route number cost weight w1, the working hour over-limit weight w2, the working hour equalization weight w3, and the working hour utilization rate weight w4. Meanwhile, adjustment coefficients for each weight as well as the basic passenger flow, number of vehicles, and number of drivers are also preset in the decision algorithm. The real-time passenger flow, number of vehicles and number of drivers are acquired, and the real-time passenger flow Q_real, real-time number of vehicles V_real and real-time number of drivers S_real are divided by the basic passenger flow, basic number of vehicles and basic number of drivers respectively to obtain comparison coefficients X_pass, X_veh, X_driv respectively. The adjustment coefficients of each weight are adjusted based on the comparison coefficients, then the adjustment coefficients are multiplied by the initial weights to obtain the weights that take effect in real time, and the upper and lower limits of the adjustment coefficients of each weight are set. When the adjustment coefficient of any weight is close to the upper or lower limit, an alarm is automatically sent to the console to prompt the dispatcher to intervene for manual locking or weight correction. The whole mechanism realizes automatic weight adaptation to changes in passenger flow, transport capacity and manpower, and reserves a manual intervention channel, which not only reduces the workload of repeated manual parameter adjustment, but also prevents the scheduling decision imbalance caused by the weights staying at extreme values continuously, ensuring the stability and compliance of the trip route planning result.

[0045] Baseline passenger flow Q0; baseline vehicle quantity V0; baseline driver quantity S0.

[0046] k1=1.0 (base value of trip route number adjustment coefficient); k2=1.0 (base value of working hour over-limit adjustment coefficient); k3=1.0 (base value of equalization adjustment coefficient); k4=1.0 (base value of utilization rate adjustment coefficient); X_pass=Q_real÷Q0; X_veh=V_real÷V0; X_driv=S_real÷S0 k1=k1×X_pass÷X_driv k2=k2×Max(X_pass, 1), which means that the greater the passenger flow, the higher the working hour penalty intensity; k3=k3×X_driv÷Max(X_pass, 1), which means that when there is a surplus of drivers, the working hour equalization is prioritized; k4=k4×X_veh÷X_driv, which means that when the vehicles are sufficient and the number of drivers is relatively small, the working hour utilization rate is preferentially improved; The adjustment coefficients are uniformly limited by a threshold with a lower limit of 0.5 and an upper limit of 2.0, and values exceeding the interval after calculation are directly truncated to the boundary values; Set a critical buffer threshold of 0.2: If any adjustment coefficient k satisfies k≤0.7 or k≥1.8, the system will immediately send an alarm to the console and log. The alarm will include information such as which adjustment coefficient is approaching the extreme value, the current real-time weight value, and the current passenger flow, vehicle, and driver data. The system will remind the dispatcher to review the data manually and can manually lock the corresponding weight and pause the adaptive adjustment.

[0047] The second embodiment provides an intelligent generation method for subway scheduling decisions based on a column generation algorithm, wherein the steps of the column generation algorithm are as follows: Step b1: Read the data; Step b2: Use a mathematical heuristic algorithm to construct an initial solution; Step b3: Solve the main problem and obtain the shadow prices of the subproblems; Step b4: Determine whether the optimal conditions or the time limit have been met. If they have been met, end the algorithm. Step b5: Update the shadow price of the subproblem, solve the subproblem, add the solution to the main problem, and return to step b3.

[0048] The steps of mathematical heuristics are as follows: Step c1: Initialize the record table for whether the road segment has passed through, n=1; Step c2: Obtain the nth possible route; Step c3: Construct a linear model of the possible route path problem and solve it; Step c4: Record the route taken after solving the problem and update the route traversal record table; Step c5: If every road segment in the road segment traversal record table has been traversed, output all paths as the initial solution; otherwise, add n+1 and return to step c2.

[0049] Please refer to Table 1 for the subway timetable. The minimum and maximum working hours for each train are set to 1 and 2. .

[0050] Table 1 Subway Timetable According to the mathematical heuristic algorithm process, the algorithm first solves the subproblem starting from road segment 1; The specific objective functions involved are shown below: The specific constraint expressions involved are shown below: This means that each train can only pass through once; This means that the number of times each train enters and exits should be equal; This means that the maximum working hours limit must be met when leaving work at each departure point; This means that the maximum working hours limit must be met when leaving work at each departure point.

[0051] By calling CPLEX (or other commercial solvers), the path 1-3-5 can be obtained.

[0052] At this point, the values ​​of the paths corresponding to 1, 3, and 5 are adjusted to 0. Similarly, a mathematical model for the subproblem is constructed to obtain another path solution, 2-4-6.

[0053] At this point, the main problem has two possible route options: 1-3-5 and 2-4-6.

[0054] The objective function involved in the main problem model is shown below: This indicates selecting the path combination with the lowest cost.

[0055] The specific constraint expressions involved are shown below: This indicates that the selected route combination must pass through every train.

[0056] By calling CPLEX (or other commercial solvers) to solve the problem, the selected solution can be obtained. , .

[0057] At this point, we check whether the shadow price solution of each subproblem is less than the preset value to determine whether the optimal solution has been reached. The optimal solution is: , .

[0058] If we continue to build sub-problem models in this embodiment.

[0059] The specific objective functions involved are shown below: The specific constraint expressions involved are shown below: This means that each train can only pass through once; This means that the number of times each train enters and exits should be equal; This indicates that the maximum working hours limit must be met when leaving work at each departure point; Please refer to Table 2 for a comparison of the algorithm's performance in solving the number of intersections; Figure 3 as well as Figure 4 Table 3 shows the comparison results of labor efficiency, and Table 4 shows the comparison results of production utilization. Table 2 Comparison of Algorithm Path Number Calculation Performance Table 3 Comparison of Labor Efficiency Effects Table 4 Comparison of Production Utilization Rate According to the comparison charts, the method of the present invention reduces the number of trips by 3% to 5%, improves labor efficiency evaluation by 2.63%, increases production utilization by an average of 1.29%, and reduces ultra-short or ultra-long trips, making the work fairer among drivers.

[0060] Dimensionality reduction and efficiency improvement can enable rapid early-stage iterations and yield a better global optimal solution.

[0061] Preferably, the present invention can also achieve flexible expansion by adjusting the constraints of sub-problems and the methods for solving sub-problems, such as using the punctuation method, to further adapt to business needs and accelerate solution efficiency. The present invention can quickly generate solutions that adapt to disturbances (such as train delays) by updating data in real time, and can support online optimization.

[0062] The disturbance mechanism is as follows: When some trains are delayed or canceled, the trains can be identified by their respective schedules, and the routes of those trains can be filtered out. The routes involved in the routes are then solved locally to obtain new local route plans.

[0063] Although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for intelligent generation of subway scheduling decisions based on a column generation algorithm, characterized in that: include: S1. Obtain subway timetables and rule data; S2. Use mathematical heuristics to obtain alternative route plans that cover all train services; S3. Solve the main problem model to obtain the shadow price of all train services in the main problem model; S4. Solve the subproblem model and add the obtained intersections to the main problem's candidate intersection pool; S5. Check whether the objective of all sub-problem models is less than the preset tolerance or reaches the time limit. If it is satisfied, proceed to the next step; otherwise, return to S4. S6. Analyze the column generation algorithm scheme and generate the corresponding route plan.

2. The intelligent generation method for subway scheduling decisions based on column generation algorithm according to claim 1, characterized in that: The mathematical heuristics include: a1. Initialize whether the train number exists in the alternative routes. If it does, record it as 0; otherwise, record it as 1. Set N=1. a2. Obtain the subproblem formed by the Nth attendance point; a3. Construct a linear model of the possible route path problem and solve the subproblem; a4. Record the alternative routes taken after solving the problem, update the train numbers taken by the routes, and update the train number record table. a5. Check if all train routes exist in the candidate routes. If so, output all candidate routes as the initial solution; otherwise, output N+1 and return to a2.

3. The intelligent generation method for subway scheduling decisions based on column generation algorithm according to claim 2, characterized in that: The objective function in the linear model is: The constraint expression is: The callback function is: in, Represents a set of train numbers; This represents the set of all trains among the candidate routes obtained in the callback function; This represents the total number of train trips for all candidate routes calculated in the callback function; Indicates train number Whether it has been visited or not, 0 is passed and 1 is not passed. Indicates the train number Maximum working hours during off-duty hours; Indicates the train number Minimum working hours before returning to work; Indicates whether or not attendance is required. As a starting point, 1 represents selection, and 0 represents no selection. ; Indicate whether to start from train number Train numbers 1 indicates that the event has been passed, and 0 indicates that it has not been passed. ; Indicate whether to select a train number As the endpoint, 1 represents selection, and 0 represents no selection. ; Indicates the selection of train number Earliest start time .

4. The intelligent generation method for subway scheduling decisions based on column generation algorithm according to claim 3, characterized in that: The constraint expressions and callback functions of the linear model of the subproblem model in S4 are the same as those of the linear model of the subproblem in the mathematical heuristic method. The objective function of the linear model of the subproblem model in S4 is: in, Indicates road segment The corresponding dual variable value in the main function.

5. The intelligent generation method for subway scheduling decisions based on column generation algorithm according to claim 1, characterized in that: The objective function of the linear model of the main problem model is: The constraint expression for the linear model of the main problem model is as follows: in Indicates the set of alternative routes; Represents a set of train numbers; Indicates alternative Does it pass by train number? 1 indicates the passage was passed, and 0 indicates it was not passed. , ; Indicate alternative routes The overall cost; Indicates whether to select a path. 1 indicates selection, 0 indicates no selection. .

6. The intelligent generation method for subway scheduling decisions based on column generation algorithm according to claim 5, characterized in that: The Based on the alternative route budget The budget includes: The cost per route is 1; The balance of working hours and length is achieved by subtracting the set expected working hours or length from the total working hours of the budgeted route and taking the absolute value. The formula for driver time utilization rate is the total driving time of a driver divided by the total route time. The weights of each part of the objective function are set through input.

7. The intelligent generation method for subway scheduling decisions based on column generation algorithm according to claim 1, characterized in that: The working hours, attendance point, departure point, and minimum rest interval are determined based on the input.

8. The intelligent generation method for subway scheduling decisions based on column generation algorithm according to claim 1, characterized in that: The subway timetable includes departure and arrival times, train arrival and departure times, station stops, and train numbers. The rule data includes minimum driving interval, driver and vehicle resource constraints, route connection rules, and upper and lower limits of working hours.

9. The intelligent generation method for subway scheduling decisions based on column generation algorithm according to claim 1, characterized in that: The main problem is the decision-making process for alternative routes in the route plan, ensuring that all train trips are performed at least once. The objective of the main problem is to minimize the number of routes; balance the time and length of each route; maximize driver time utilization; and minimize the weighted sum of the start and end points of each route.

10. The intelligent generation method for subway scheduling decisions based on column generation algorithm according to claim 1, characterized in that: The sub-problem is the decision-making process of train numbers and alternative drop-off points in the route; The objective of the subproblem is to maximize the sum of the shadow prices of the main problem corresponding to the selected train number.

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