Intelligent train dynamic marshalling scheduling method for heavy haul railway marshalling station

Abstract

According to the intelligent train dynamic marshalling scheduling method for the heavy haul railway marshalling station, a train dynamic marshalling scheduling mixed integer linear programming model for the heavy haul railway marshalling station is established, and the target function is to minimize the dwell time of a train in the marshalling station; the decision variables comprise a train dynamic marshalling strategy, a departure sequence and departure time; the mixed integer linear programming model is expanded into a two-stage robust optimization model, the first stage decides a marshalling scheme of a departure train, and the second stage optimizes a departure time sequence based on a worst operation time scene; solving the two-stage robust optimization model by using an improved column sum constraint generation method, and determining an optimal departure sequence and time by combining a dynamic programming algorithm; and verifying the performance of the dynamic marshalling scheduling strategy through a numerical experiment. The optimal scheduling strategy is generated under the condition that the operation time of the train marshalling station is uncertain, and the scheduling strategy obtained by solving can be ensured to have better robustness in test cases of different scales.

Description

Technical Field

[0001] The present invention relates to the field of intelligent rail transit technical equipment, and specifically to a train dynamic formation scheduling method for the intelligence of heavy-haul railway marshalling yards. Background Technique

[0002] Heavy-haul railways are an important part of the railway freight field. Marshalling yards are the core facility nodes of heavy-haul railways, mainly responsible for the formation of heavy-haul trains and the decomposition of empty trains. In the composition of the turnover time of railway freight trains in China, the residence time of trains in marshalling yards accounts for a relatively large proportion. Therefore, the efficiency level of the operation organization of marshalling yards will directly determine the overall transportation efficiency of the railway freight system.

[0003] Currently, heavy-haul railway marshalling yards generally adopt a static scheduling mode based on manual experience. The formulation of scheduling plans highly depends on the individual experience accumulation of dispatchers, with problems such as strong subjective experience dependence, lack of real-time and dynamic adaptability, lack of theoretical decision-making guidance and intelligent scheduling decision-making support, and it is difficult to meet the high-efficiency and intelligent requirements of modern heavy-haul railway transportation. In complex operation scenarios, due to the dynamic coupling of the train formation operation process, the time-varying characteristics of multi-type equipment collaboration, and the uncertainty of train technical operation time, traditional scheduling methods are difficult to respond in real time to the dynamic changes of the operation status in the marshalling yard. There is an urgent need to construct a train dynamic formation intelligent scheduling method considering the uncertainty of operation time, through collaborative optimization of train formation strategies and intelligent decision-making on departure timings, so as to reduce the residence time of trains in marshalling yards, thereby improving the intelligent level of transportation organization and the overall operation efficiency of marshalling yards. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a train dynamic formation scheduling method for the intelligence of heavy-haul railway marshalling yards, including the following steps: Establish a mixed-integer linear programming model for train dynamic formation scheduling in a heavy-haul railway marshalling yard, with the objective function of minimizing the stop time of trains in the marshalling yard, and the decision variables including train dynamic formation strategies, departure order, and departure time; Expand the mixed-integer linear programming model into a two-stage robust optimization model, where the first-stage decision is the formation plan of departing trains, and the second stage optimizes the departure timings based on the worst-case operation time scenario; Use an improved column-and-constraint generation method to solve the two-stage robust optimization model, and combine the dynamic programming algorithm to determine the optimal departure order and time; Verify the performance of the dynamic formation scheduling strategy through numerical experiments.

[0005] Furthermore, the mixed-integer linear programming model includes the following constraints: Each arriving train can only be incorporated into one departing train; Full load, full length and full axle restrictions of departure trains; Constraints on the connecting train types of arrival and departure trains; Constraints on the setting time and departure interval of departure trains.

[0006] Furthermore, in the two-stage robust optimization model, the uncertainty of operation time is estimated through historical data, and the fluctuation range and robust control coefficient are defined to ensure the robustness of the scheduling plan.

[0007] Furthermore, the two-stage robust optimization model is processed by an improved column sum constraint generation method, specifically including: Construct a scenario subset to solve the relaxation model, and iteratively update the scenario subset until the termination condition is met; In the second stage, use a dynamic programming program to allocate robust parameters and optimize the departure time sequence.

[0008] Furthermore, the dynamic programming program includes: The first dynamic programming program allocates robust parameters to non-empty departure trains and calculates the maximum stop time; The second dynamic programming program recursively allocates the total robust parameters to all non-empty trains to determine the optimal allocation plan.

[0009] Furthermore, the modeling process of the mixed integer linear programming model specifically includes establishing a deterministic model, assuming that all time-related variables are integers, ; The objective function (1) aims to minimize the total residence time cost of trains in the marshalling station, where is the index of the arriving train, is the set of arriving trains, is the unit residence time cost of the arriving train , is the actual departure time of the arriving train, is the arriving train ; ; The constraint condition (2) ensures that each arriving train can only be incorporated into one departure train, where is the set of departure trains, is the index of the departure train, is a 0-1 binary variable, indicates that the arriving train is formed into the departure train ; ; ; Constraints (3) and (4) ensure that the departing trains meet the full weight and full length restrictions respectively. The parameter defines the maximum and minimum allowable lengths and weight restrictions of the departing trains, where respectively represent the maximum and minimum lengths of the departing train operation, respectively represent the maximum and minimum weights allowed for the departing trains, is a 0-1 binary variable. If the departing train meets the full weight restriction, then , otherwise . Similarly, is a 0-1 binary variable. If the departing train meets the full length restriction, then , otherwise . Otherwise ; ; Constraint (5) ensures that each departing train complies with the full axle regulation, is the maximum allowable formation number for the departing train ; ; Constraint (6) stipulates the formation number restriction of the departing train, where is a 0-1 binary variable. If the departing train is formed by two or more arriving trains, then , otherwise ; ; Constraint (7) defines the connecting vehicle type constraint for arriving and departing trains. is the number of inside gondolas in the arriving train , is the type of inside gondolas in the arriving train , is the number of inside gondolas in the arriving train , is the number of inside gondolas in the arriving train , is the optional combination type of the departing train, which refers to the complete set of the number of inside gondolas that meet the formation rules and their corresponding gondola types. It defines all compliant car body combination schemes that make up the departing train, representing the combination set of the gondola types and quantities that can be formed into the departing train; ; Constraint (8) ensures that two arriving trains and can be formed only when their terminal stations are the same. is the arriving train The terminal station, is the terminal station for the arriving train ; ; Constraint (9) is used to determine whether the departing train is an empty car; where is a 0-1 binary variable. If the departing train is not empty, then , otherwise ; ; Constraint (10) defines the setting time for each departing train. is an integer variable representing the setting time of the departing train , is the formation time of the departing train , is the departure interval that should be satisfied when the departing train departs from the formation station, is the departure inspection time of the departing train ; ; ; Constraints (11) and (12) calculate the actual departure times of the departing train and the arriving train respectively. Among them, is the operation start time of the departing train , is the operation time of the departing train , and represent the actual departure times of trains and respectively; ; Constraint (13) ensures that the operation start time of each departing train is after the operation completion time of the previous departing train ; ; Constraint (14) ensures that the formation operation of the departing train must start after all the constituent traffic flows (arriving trains ) have arrived at the formation station. is the arrival time of the arriving train; ; Constraint (15) ensures that the departing train The operation time is at least as long as that of any arriving train in its formation train. For the arriving train Operation time; ; ; ; ; Formulas (16)-(19) are the range constraints of decision variables.

[0010] Furthermore, the extension is a two-stage robust optimization model. Specifically, by considering the uncertainty of the operation time of trains in the marshalling station, the model is extended to a two-stage robust optimization model to minimize the dwell time of trains in the marshalling station under uncertain operation times; For the arriving train , its average operation time can be estimated by analyzing historical data as well as the lower limit of the operation time and the upper limit . For each arriving train, define and to represent the positive and negative deviations of the average operation time respectively. Use the set to define the uncertainty of the operation time: ; where is the robust parameter used to limit the deviation of the train operation time from its average value, represents whether there will be a deviation in the operation time of each arriving train , is the vector composed of all , and this vector is defined by the set : ; Based on the above analysis, construct a two-stage robust optimization model , where the first stage determines the formation strategy of departure trains: ; Subject to: Constraints (2)-(9), (16), (17). The above first-stage model aims to solve the train formation strategy that meets the constraint conditions and use it as the input of the second-stage model. is the formation decision vector solved by Constraints (2)-(9), (16) and (17); the objective function​ It is evaluated through the following second-stage problem, aiming to minimize the marshalling station stop time cost of the train under a given marshalling decision. The decision variables of the second-stage decision include the departure time and departure order of the departing trains: ; ; Subject to: Constraints (10)-(15), (18), (19). ; It is relatively difficult to directly solve the above problem. Therefore, an improved column and constraint generation method is designed to handle the established two-stage robust optimization model: Since the operation time will be different under different scenarios, define as the set of all scenarios . For each scenario is the value of the vector under this scenario, is the implementation of the variables defined by Constraints (18)-(19) under scenario . Then the two-stage robust optimization model is further expressed in the following form: ; Subject to: Constraints (2)-(9), (16), (17). ; ; ; ; ; ; In problem , by introducing an auxiliary variable , the objective function of the original problem is converted into Constraint (26); using the column and constraint generation method, a relaxation model is constructed based on a subset of the scenario set. This relaxation model is used as the master problem in the column and constraint generation method, and the master problem is solved. The optimal value of the solved master problem provides an effective lower bound for problem . The optimal solution of the master problem is then used as the input for the second stage. In the second stage (i.e., the sub-problem), solving this problem can obtain the optimal value , thus providing an upper bound for problem ; The solution of the second-stage problem is then used to determine the worst-case scenario , after the second stage of solution, it is determined whether the termination condition is satisfied, that is, whether the difference between the upper bound and the lower bound is within an acceptable threshold range. If the termination condition is not satisfied, the scenario obtained from the sub-problem solution is used. Construct a new subset , and solve the master problem again on this subset, and repeat the above process until the gap between the current optimal upper bound and the lower bound is within an acceptable range.

[0011] Furthermore, when using the improved column sum and constraint generation method to solve the two-stage robust optimization model, the optimal departure order and time are determined in combination with the dynamic programming algorithm, specifically including: Step 1: Initialize the scenario subset , where the scenario is arbitrarily selected from , and the upper bound and the lower bound are initialized, that is ; Step 2: Solve the relaxation model of the problem on the subset , obtain the solution and the value of the objective function , and update the lower bound: ; Step 3: According to the formation decision , solve the second-stage model, obtain the value of the objective function and the vector as well as the solution , and update the upper bound: ; Step 4: If , terminate the algorithm and output as the optimal solution, otherwise, update the scenario subset and go to Step 2.

[0012] Furthermore, the dynamic programming program specifically includes In the first dynamic programming, the robust parameters are assigned to a group of departing trains to dynamically optimize the departure time and order of trains at the marshalling station. Specifically, the given robust parameters are assigned to a non-empty group of departing trains, and the departure time of this group of trains and the maximum marshalling station stop time corresponding to this allocation method are calculated. If the current allocation does not meet the time constraints, the allocation method needs to be adjusted until all conditions are satisfied. Through this dynamic programming, a set of allocation schemes is finally determined to maximize the stop time of this non-empty group of trains at the marshalling station; The second dynamic programming program is to determine how to allocate the total robust parameters to all non-empty departure trains. For each departure train, the stop time of each train at the marshalling station is obtained by calculating the operation start time and the operation time. Based on the first dynamic programming, the optimal allocation method of the current non-empty trains is obtained, and the optimal allocation scheme of allocating the robust parameters to all non-empty trains is obtained through the recurrence relation, so that the total stop time of all trains at the marshalling station is maximized.

[0013] Furthermore, the performance of the dynamic marshalling scheduling strategy is verified through numerical experiments, specifically including, through real data, randomly generating the weight, composition type, and technical station of the trains, conducting small-scale and large-scale numerical experiments, and comparing the performance of the deterministic model, the robust optimization method combined with the dynamic programming algorithm, and the first-come-first-served method.

[0014] Advantages of the present invention: Aiming at the problem of dynamic marshalling of trains at the marshalling station of heavy-haul railways, the present invention constructs a two-stage robust optimization model and designs an improved column-and-constraint generation method combined with the dynamic programming algorithm to solve the two-stage robust optimization model, ensuring that an optimal scheduling strategy is generated in the case of uncertain operation time at the train marshalling station, and also ensuring that the obtained scheduling strategy has good robustness in different-scale test cases. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The present invention has the following drawings: Figure 1 Schematic diagram of train marshalling at the marshalling station of heavy-haul railways; Figure 2 Example diagram of the scheduling plan of loaded trains under different operation time scenarios; Figure 3 Scheduling plan solved by the robust optimization method combined with the dynamic programming algorithm in a small-scale scenario; Figure 4 Scheduling plan solved by the deterministic model method in a small-scale scenario; Figure 5 Improvement of the proposed method compared with the existing method in a large-scale scenario. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0016] To make the purpose, technical solutions, and advantages of the present application clearer, the following further describes the present application in detail with reference to specific embodiments and the attached Figures 1-5 , and further elaborates on the present application.

[0017] Such as Figure 1 and Figure 2As shown in the figure, heavy-haul trains need to be dynamically formed at the marshalling station. However, different train formation times will result in different formation plans and departure timings. Therefore, it is necessary to consider the train dynamic formation scheduling plan under uncertain operation times. First, based on the assumption that the operation times of trains at the marshalling station are known, a mixed-integer linear programming model for train dynamic formation scheduling at the heavy-haul railway marshalling station is established, with the objective function of minimizing the residence time cost of arriving trains in the marshalling station. On this basis, aiming at the uncertain factors existing in actual operation, a two-stage robust optimization model considering the uncertainty of operation times is further established: by introducing the operation time fluctuation interval parameter and the robust control coefficient, a robust train formation strategy generation mechanism is constructed to ensure that in the situation where it is difficult to determine the train operation time in the station due to complex working conditions such as changes in infrastructure conditions and fluctuations in personnel operation efficiency, the effectiveness of the scheduling plan can still be maintained, and intelligent train dynamic formation scheduling can be realized. Different from the deterministic model, the two-stage robust optimization model solves the problem in two stages. In the first stage, the formation plan is determined, that is, the arriving trains are incorporated into the departing trains, In the second stage, based on the decision in the first stage, the minimum residence time of trains in the marshalling station is achieved by dynamically adjusting the departure time and departure order.

[0018] First, a deterministic model is established, assuming that all time-related variables are integers.

[0019] ; The objective function (1) aims to minimize the total residence time cost of trains in the marshalling station, where is the index of the arriving train, is the set of arriving trains, is the arriving train 's unit residence time cost, is the actual departure time of the arriving train , is the arriving train 's arrival time.

[0020] ; The constraint condition (2) ensures that each arriving train can only be incorporated into one departing train, where is the set of departing trains, is the index of the departing train. is a 0-1 binary variable, indicating that the arriving train is formed into the departing train .

[0021] ; ; Constraints (3) and (4) ensure that the departure train complies with the full weight and full length constraints respectively. Departure train defined The maximum and minimum length and weight restrictions are as follows: Respectively represent the maximum and minimum lengths of departure train runs, Respectively represent the maximum and minimum weight allowed for a departing train. It is a 0-1 binary variable. If the train is leaving If the full weight restriction is met, then ,otherwise Similarly, It is a 0-1 binary variable. If the train is departing If the full length limit is met, ,otherwise .

[0022] ; Constraint (5) ensures that each departing train complies with the full axle requirement, For departure train The maximum number of groups allowed.

[0023] ; Constraint (6) specifies the number of trains that can be formed. It is a 0-1 binary variable. If the train is departing If the train is composed of two or more arriving trains, ,otherwise .

[0024] ; Constraint (7) defines the vehicle type constraints for the arrival and departure trains. For arriving train The number of open wagons, For arriving train Type of open car, For arriving train The number of open wagons in For arriving train The number of open wagons in The optional combination types for a departing train refer to the complete set of gondola car numbers and corresponding gondola car models that meet the marshaling rules. This defines all legal vehicle combinations that can form the departing train. This represents the set of possible gondola car model and quantity combinations that can form the departing train.

[0025] ; Constraint (8) ensures that if and only if two arriving trains and can be marshaled only when their terminal stations are the same. is the terminal station of the arriving train . is the terminal station of the arriving train.

[0026] ; Constraint (9) is used to determine whether the departing train is empty; where is a 0-1 binary variable. If the departing train is not empty, then , otherwise .

[0027] ; Constraint (10) defines the setting time for each departing train. is an integer variable representing the setting time of the departing train , is the marshalling time of the departing train , is the departure interval that should be satisfied when the departing train departs from the marshalling station, is the departure inspection time of the departing train .

[0028] ; ; Constraints (11) and (12) calculate the actual departure times of the departing train and the arriving train respectively. Among them, is the start time of the operation of the departing train , is the operation time of the departing train , and represent the actual departure times of trains and respectively.

[0029] ; Constraint (13) ensures that the start time of the operation of each departing train needs to be after the completion time of the operation of the previous departing train .

[0030] ; Constraint (14) ensures that the marshalling operation of the departing train must be after all its constituent traffic flows (arriving trains ) It can only start after arriving at the marshalling station. is the arrival time of the arriving train.

[0031] ; Constraint (15) ensures that the operation time of the departing train is at least as long as the operation time of any arriving train in its formation train. is the operation time of the arriving train operation time.

[0032] ; ; ; ; (16)-(19) are the decision variable range constraints.

[0033] Furthermore, by considering the uncertainty of the operation time of trains in the marshalling station, the model is extended to a two-stage robust optimization model to minimize the dwell time of trains in the marshalling station under uncertain operation times.

[0034] For the arriving train , its average operation time and the lower limit and upper limit of the operation time can be estimated by analyzing historical data. For each arriving train, define and to represent the positive and negative deviations of the average operation time respectively. Use the set to define the uncertainty of the operation time: ; where is the robust parameter used to limit the deviation of the train operation time from its average value. represents whether the operation time of each arriving train will deviate, is the vector composed of all , and this vector is defined by the set : ; Based on the above analysis, a two-stage robust optimization model is constructed. Among them, the first stage determines the formation strategy of the departing train: ; Subject to: Constraints (2)-(9), (16), (17). The above first-stage model aims to solve the train formation strategy that meets the constraint conditions and uses it as the input of the second-stage model. Is the formation decision vector solved by Constraints (2)-(9), (16) and (17). The objective function Is evaluated through the following second-stage problem, aiming to minimize the yard dwell time cost of the train under the given formation decision The decision variables of the second-stage decision include the departure time and departure order of the departing trains: ; Subject to: Constraints (10)-(14), (18), (19). ; It is relatively difficult to directly solve the above problem. Therefore, an improved column and constraint generation method is designed to handle the established two-stage robust optimization model. Since the operation time varies under different scenarios, define As the set of all scenarios . For each scenario , Is the value of the vector Under this scenario, Is the implementation of the variables defined by Constraints (18)-(19) under scenario . Then the two-stage robust optimization model can be further expressed in the following form: ; Subject to: Constraints (2)-(9), (16), (17). ; ; ; ; ; ; In problem , by introducing the auxiliary variable , the objective function of the original problem is converted into Constraint (26). The scenario set Is usually too large to enumerate all constraints and directly solve problem . Using the column and constraint generation method, based on the subset of the scenario set A relaxation model is constructed and used as the master problem in the column-and-constraint generation method, and the master problem is solved. The optimal value of the solved master problem is the value of the problem which provides a valid lower bound. The optimal solution of the master problem is then used as the input for the second stage. In the second stage (i.e., the subproblem), solving this problem gives the optimal value , thus providing an upper bound for the problem . The solution of the second-stage problem is then used to determine the worst-case scenario . After solving the second stage, it is judged whether the termination condition is satisfied, that is, whether the difference between the upper bound and the lower bound is within an acceptable threshold range. If the termination condition is not satisfied, a new subset is constructed using the scenario obtained from solving the subproblem, and the master problem is solved again on this subset. The above process is repeated until the gap between the current optimal upper bound and lower bound is within an acceptable range.

[0035] Based on the above description, the used column-and-constraint generation method is summarized in the following algorithm: Step 1: Initialize the scenario subset , where the scenario can be arbitrarily selected from . And initialize the upper bound and the lower bound. That is .

[0036] Step 2: Solve the relaxation model of the problem on the subset to obtain the solution and the value of the objective function . Update the lower bound: .

[0037] Step 3: According to the formation decision , solve the second-stage model to obtain the objective function value and the vector and the solution . Update the upper bound: .

[0038] Formation strategy of the train: ; Subject to: Constraints (2)-(9), (16), (17). The above first-stage model aims to solve the train formation strategy that meets the constraint conditions and use it as the input for the second-stage model is the formation decision vector solved by Constraints (2)-(9), (16) and (17). The objective function Evaluate through the following second-stage problem, aiming to minimize the marshalling station stop time cost of the train under a given marshalling decision. The decision variables of the second-stage decision include the departure time and departure order of the departing trains: Subject to: Constraints (10)-(14), (18),(19). ; It is difficult to directly solve the above problem. Therefore, an improved column and constraint generation method is designed to handle the established two-stage robust optimization model. Since the operation time will be different under different scenarios, define ; as the set of all scenarios . For each scenario , is the value of the vector under this scenario, is the implementation of the variables defined by Constraints (18)-(19) under scenario . Then the two-stage robust optimization model can be further expressed in the following form: ; Subject to: Constraints (2)-(9), (16),(17). ; ; ; ; ; ; In problem , by introducing the auxiliary variable , the objective function of the original problem is converted into Constraint (26). The scenario set is usually too large to enumerate all constraints and directly solve problem . Using the column and constraint generation method, a relaxation model is constructed based on a subset of the scenario set. This relaxation model is used as the master problem in the column and constraint generation method, and the master problem is solved. The optimal value of the solved master problem provides an effective lower bound for problem . The optimal solution of the master problem is then used as the input for the second stage. In the second stage (i.e., the sub-problem), solving this problem gives the optimal value , thus providing an upper bound for problem . The solution of the second-stage problem is then used to determine the worst-case scenario After solving the second stage, it is judged whether the termination condition is satisfied, that is, whether the difference between the upper bound and the lower bound is within an acceptable threshold range. If the termination condition is not satisfied, the scenarios obtained from the sub-problem solving are used Construct a new subset and solve the master problem again on this subset. Repeat the above process until the gap between the current optimal upper bound and the lower bound is within an acceptable range.

[0039] Based on the above description, the column and constraint generation method used is summarized in the following algorithm: Step 1: Initialize the scenario subset , where the scenario can be arbitrarily selected from . And initialize the upper bound and the lower bound. That is .

[0040] Step 2: Solve the relaxation model of the problem on the subset to obtain the solution and the value of the objective function . Update the lower bound: .

[0041] Step 3: According to the grouping decision , solve the second-stage model to obtain the objective function value and the vector as well as the solution . Update the upper bound: .

[0042] Step 4: If , terminate the algorithm and output as the optimal solution. Otherwise, update the scenario subset and go to Step 2.

[0043] The solution of the second-stage model in the column and constraint generation method takes a lot of time. To solve this problem, a solution method using dynamic programming is introduced, which can efficiently solve the second-stage problem based on the first-stage solution . The proposed column and constraint generation method based on dynamic programming consists of two dynamic programming programs.

[0044] In the first dynamic programming, robust parameters are assigned to a set of departure trains to dynamically optimize the departure time and departure order of trains at the marshalling station. Specifically, the given robust parameter is assigned to a non - empty set of departure trains, and the departure times of this set of trains and the maximum marshalling station stop time corresponding to this allocation method are calculated. If the current allocation does not meet the time constraints, the allocation method needs to be adjusted until all conditions are satisfied. Through this dynamic programming, a set of allocation schemes is finally determined to maximize the stop time of this set of non - empty trains at the marshalling station. The second dynamic programming program is to determine how to allocate the total robust parameter to all non - empty departure trains. For each departure train, the stop time of each train at the marshalling station can be obtained by calculating the operation start time and operation time. Based on the first dynamic programming, the optimal allocation method for the current non - empty trains can be obtained. Through the recursive relationship, the optimal allocation scheme for allocating the robust parameter to all non - empty trains is obtained to maximize the total stop time of all trains at the marshalling station.

[0045] Using the operation times of each train under uncertainty obtained from the above dynamic programming program, the constraint (31) in the problem can be considered as a constant. Subsequently, other variables can be calculated according to other constraint conditions in the problem , and then the optimal solution under the robust optimization model can be obtained.

[0046] Through Figure 3 , Figure 4 and Figure 5 , the performance of the proposed train dynamic marshalling and scheduling method for the intelligentization of heavy - haul railway marshalling stations is verified.

[0047] In the numerical experiments, the real - world data of the Datong - Qinhuangdao heavy - haul railway (Daqin Line) in China is used to verify the effectiveness and efficiency of the proposed method. On the Daqin Line, there are three commonly used gondola car models, which are , , and . The heavy - haul trains on the Daqin Line operate in unit trains and there are a total of 9 main technical stations. In the numerical experiments, data such as the weight, composition type, and technical stations of the trains will be randomly generated.

[0048] First, in the small - scale numerical experiment, the comparison between the deterministic model (DM) and the robust optimization method combined with the dynamic programming algorithm (Robust Optimization - Dynamic Planning, RO - DP) is carried out. There are a total of 10 inbound trains, and the robust parameter of the intelligent scheduling method is set to . The optimal marshalling and scheduling strategies are shown in Figure 3 and Figure 4 . Figure 3 represents the scheduling strategy obtained by the intelligent scheduling method, Figure 4It is represented by what is obtained by DM. The vertical axis represents the incoming trains, and the horizontal axis represents the dwell time of the incoming trains at the marshalling station. Lines of the same color indicate that two incoming trains are marshalled into the same outgoing train and depart simultaneously. The results prove that both DM and RO-DP can effectively determine the optimal scheduling strategy. From Figure 3 and Figure 4 As can be seen, due to the terminal station and full-axle constraints, the scheduling strategies obtained by the two methods are the same, but the departure times and departure orders are different. For example, in the scheduling strategy obtained by DM, incoming trains 2 and 3 are marshalled into the second outgoing train and depart simultaneously, while in RO-DP, in order to cope with the uncertainty of operation time and minimize the total dwell time, incoming trains 2 and 3 are marshalled into the fourth departing train. The objective function values of DM and the intelligent scheduling method are 1904 and 2386 respectively, indicating that the total dwell time cost of RO-DP is greater than that of the DM method. This is because RO-DP is designed to minimize the total dwell time cost in the worst case, so the objective function value will be larger than that of the DM method.

[0049] To further reveal the effectiveness and performance of RO-DP, three scales of test cases were constructed, which are , and , indicating that there are 40, 60, and 80 incoming trains in each scale, and there are three test cases in each scale. In large-scale numerical experiments, DM, RO-DP, and the First-come, First-served (FCFS) method were used for comparison respectively. The robust parameter of RO-DP was set to , and the results are as Figure 5 shown. Figure 5 It represents the comparison of the improvement rates of the three methods for the objective function value. It can be seen that the performance of DM and RO-DP in all test cases is always better than that of the experience-based FCFS, verifying the effectiveness of RO-DP. It is worth noting that the improvement rate of RO-DP increases with the increase in the complexity of the test cases, indicating its robustness in solving the problem of train operation time uncertainty.

[0050] The embodiments of the present application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the embodiments of the present application shall be included within the protection scope of the present application.

Claims

1. A train dynamic formation dispatching method for the intelligence of heavy-haul railway marshalling yards, characterized in that It includes the following steps: Establish a mixed-integer linear programming model for train dynamic formation scheduling in heavy-haul railway marshalling yards, with the objective function of minimizing the dwell time of trains in the marshalling yard. The decision variables include train dynamic formation strategies, departure order, and departure time; Expand the mixed-integer linear programming model into a two-stage robust optimization model, where the formation plan of departing trains is determined in the first stage, and the departure time sequence is optimized based on the worst-case operation time scenario in the second stage; Use an improved column-and-constraint generation method to solve the two-stage robust optimization model, and combine the dynamic programming algorithm to determine the optimal departure order and time; Verify the performance of the dynamic formation scheduling strategy through numerical experiments.

2. The train dynamic formation dispatching method for the intelligence of heavy-haul railway marshalling yards according to claim 1, wherein The mixed-integer linear programming model includes the following constraints: Each arriving train can only be incorporated into one departing train; The full-load, full-length, and full-axle restrictions of departing trains; The constraint on the consecutive train types of arriving and departing trains; The setting time and departure interval constraints of departing trains.

3. The train dynamic formation dispatching method for the intelligence of a heavy-haul railway marshalling station according to claim 1, wherein In the two-stage robust optimization model, the uncertainty of operation time is estimated through historical data, and the fluctuation interval and robust control coefficient are defined to ensure the robustness of the scheduling plan.

4. The train dynamic formation dispatching method for the intelligent marshalling yard of heavy-haul railways according to claim 1, wherein The two-stage robust optimization model is processed by an improved column-and-constraint generation method, specifically including: Construct a scenario subset to solve the relaxed model, and iteratively update the scenario subset until the termination condition is met; In the second stage, use the dynamic programming program to allocate robust parameters and optimize the departure time sequence.

5. The train dynamic formation scheduling method for the intelligent heavy-haul railway marshalling station according to claim 4, wherein, The dynamic programming program includes: The first dynamic programming program allocates robust parameters to non-empty departing trains and calculates the maximum dwell time; The second dynamic programming program recursively allocates the total robust parameters to all non-empty trains to determine the optimal allocation plan.

6. The train dynamic formation dispatching method for the intelligence of heavy-haul railway marshalling yards as described in claim 5, characterized in that, The modeling process of the mixed-integer linear programming model specifically includes establishing a deterministic model, assuming that all time-related variables are integers, ； The objective function (1) aims to minimize the total residence time cost of trains in the marshalling station, where is the index of the arriving train, is the set of arriving trains, is the unit residence time cost of the arriving train , is the actual departure time of the arriving train , is the arrival time of the arriving train . ； Constraint (2) ensures that each arriving train can only be incorporated into one departing train, where is the set of departing trains, is the index of the departing train, is a 0-1 binary variable, indicating that the arriving train is formed into the departing train ; ； ； Constraints (3) and (4) ensure that the departing trains meet the full - weight and full - length restrictions respectively. The parameter defines the maximum and minimum allowable lengths and weight restrictions of the departing trains, where represent the maximum and minimum lengths of the departing train's operation respectively, represent the maximum and minimum weights allowed for the departing train respectively, is a binary variable. If the departing train meets the full - weight restriction, then , otherwise . Similarly, is a 0 - 1 binary variable. If the departing train meets the full - length restriction, then , otherwise ; otherwise ; ； Constraint (5) ensures that each departing train complies with the full-axle requirement, for the departing train the maximum allowable formation number; ； Constraint (6) specifies the limit on the formation number of departure trains, where is a 0-1 binary variable. If the departure train is formed by two or more arriving trains, then , otherwise ; ； Constraint (7) defines the constraint on the consecutive train types for arrival and departure trains. For arrival trains The number of gondola cars within For arrival trains The type of gondola cars within For arrival trains The number of gondola cars within For arrival trains The number of gondola cars within The combinatorial types available for departure trains refer to the complete set of the number of gondola cars that meet the formation rules and their corresponding gondola car types, which defines all compliant car formation schemes for the departure train and represents the set of combinations of gondola car types and numbers that can be formed into the departure train. ； Constraint (8) ensures that trains and can be marshaled if and only if their destination stations are the same. Let be the destination station of arriving train , and be the destination station of arriving train . and can be marshaled if and only if their destination stations are the same. Let be the destination station of arriving train , and be the destination station of arriving train . ； Constraint (9) is used to determine whether the departing train is an empty car; among them is a 0-1 binary variable. If the departing train is not empty, then , otherwise ; ； Constraint (10) defines the setup time for each departing train, which is an integer variable representing the departing train 's setup time, is the formation time for the departing train and is the headway that should be satisfied when the departing train departs from the marshalling station, is the departure inspection time for the departing train ; ； ； Constraints (11) and (12) calculate the actual departure times of departing trains and arriving trains respectively, where is the start time of the operation of the departing train , is the operation time of the departing train , and represent the actual departure times of trains and respectively; ； Constraint (13) ensures that the operation start time of each departing train is after the operation completion time of the previous departing train ; ； The constraint condition (14) ensures that the formation operation of the departing train must start after all the constituent train flows, i.e., the arriving trains , have arrived at the marshalling station. is the arrival time of the arriving train; ； Constraint (15) ensures that the operation time of the departing train is at least as long as the operation time of any arriving train within its formation train, for the operation time of the arriving train operation time; ； ； ； ； Formulas (16)-(19) are the range constraints of decision variables.

7. The train dynamic formation dispatching method for the intelligent heavy-haul railway marshalling station according to claim 6, wherein The expansion is a two-stage robust optimization model, specifically including, by considering the uncertainty of the operation time of trains in the marshalling station, the model is expanded into a two-stage robust optimization model to minimize the dwell time of trains in the marshalling station under uncertain operation times; For the arriving trains , the average operation time can be estimated by analyzing historical data as well as the lower limit of the operation time and the upper limit . For each arriving train, define and to represent the positive and negative deviations of the average operation time respectively, and use the set to define the uncertainty of the operation time: ； Among them, is a robust parameter used to limit the deviation of the train operation time from its average value, represents whether there will be a deviation in the operation time of each arriving train , is a vector composed of all and is defined by the set : ； Based on the above analysis, a two-stage robust optimization model is constructed , where the formation strategy of the departing trains is determined in the first stage: ； Subject to: Constraints (2)-(9), (16), (17). The above first-stage model aims to solve the train formation strategy that meets the constraint conditions and use it as the input of the second-stage model. is the formation decision vector solved by constraints (2)-(9), (16) and (17); the objective function is evaluated through the following second-stage problem, aiming to minimize the dwell time cost of the train at the marshalling station under the given formation decision. The decision variables of the second-stage decision include the departure time and departure order of the departing trains. ； Subject to: Constraints (10)-(15), (18), (19). ； It is relatively difficult to directly solve the above problem. Therefore, an improved column sum constraint generation method is designed to handle the established two-stage robust optimization model: Since the operation time varies under different scenarios, define as the set of all scenarios . For each scenario , is the value of the vector under this scenario, is the implementation of the variables defined by constraints (18)-(19) under scenario . Then the two-stage robust optimization model is further expressed in the following form: ； Subject to: Constraints (2)-(9), (16), (17). ； ； ； ； ； ； In problem ,by introducing an auxiliary variable ,the objective function of the original problem is transformed into constraint (26); using the column sum constraint generation method, a relaxation model is constructed based on a subset of the scenario set ,and this relaxation model is used as the master problem in the column sum constraint generation method, and the master problem is solved. The optimal value of the master problem obtained by solving provides an effective lower bound for problem ,and the optimal solution of the master problem is then used as the input for the second stage. In the second stage, that is, the sub-problem, solving this problem can obtain the optimal value ,thus providing an upper bound for problem ; the solution of the second stage problem is then used to determine the worst-case scenario . After solving the second stage, it is judged whether the termination condition is satisfied, that is, whether the difference between the upper bound and the lower bound is within an acceptable threshold range. If the termination condition is not satisfied, a new subset is constructed using the scenario obtained from the sub-problem solution ,and the master problem is solved again on this subset, and the above process is repeated until the gap between the current optimal upper bound and lower bound is within an acceptable range.

8. The train dynamic formation dispatching method for the intelligence of heavy-haul railway marshalling yards as claimed in claim 7, wherein Using the improved column-and-constraint generation method to solve the two-stage robust optimization model and combining the dynamic programming algorithm to determine the optimal departure order and time specifically includes: Step 1: Initialize the scene subset , where the scene can be arbitrarily selected from , and the upper and lower bounds are initialized, that is ; Step 2: Solve the relaxation model of the problem on the subset to obtain the solution and the value of the objective function , and update the lower bound: ; Step 3: According to the grouping decision , solve the second-stage model to obtain the objective function value and vector as well as the solution , and update the upper bound: ; Step 4: If , terminate the algorithm and output as the optimal solution; otherwise, update the scenario subset and go to Step 2.

9. The train dynamic formation dispatching method for the intelligence of heavy-haul railway marshalling yards according to claim 8, characterized in that, The dynamic programming program specifically includes, In the first dynamic programming, robust parameters are assigned to a set of departing trains to dynamically optimize the departure time and departure sequence of trains at the marshalling station. Specifically, the given robust parameters are assigned to a non-empty set of departing trains, and the departure time of this set of trains and the maximum dwell time at the marshalling station corresponding to this allocation method are calculated. If the current allocation does not meet the time constraints, the allocation method needs to be adjusted until all conditions are satisfied. Through this dynamic programming, a set of allocation schemes is finally determined to maximize the dwell time of this set of non-empty trains at the marshalling station; The second dynamic programming program is to determine how to allocate the total robust parameters to all non-empty departure trains. For each departure train, the dwell time of each train at the marshalling station is obtained by calculating the operation start time and the operation time. Based on the first dynamic programming, the optimal allocation method of the current non-empty trains is obtained, and the optimal allocation scheme of allocating the robust parameters to all non-empty trains is obtained through the recurrence relation, so that the total dwell time of all trains at the marshalling station is maximized.

10. The train dynamic formation dispatching method for the intelligent marshalling station of heavy-haul railways according to claim 9, characterized in that, Verifying the performance of the dynamic formation scheduling strategy through numerical experiments specifically includes, through real data, randomly generating the weights, composition types, and technical stations of trains, conducting small-scale and large-scale numerical experiments, and comparing the performance of the deterministic model, the robust optimization method combined with the dynamic programming algorithm, and the first-come-first-served method.

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