A method, device and equipment for optimizing the operation of high-speed railway freight trains

Abstract

The present invention relates to a high-speed rail freight train operation optimization method, device, and equipment, comprising: establishing a dual-objective nonlinear model for high-speed rail freight train operation optimization; decomposing it into a train candidate set restriction main model and a freight train candidate set generation submodel in different ways, and a first single-objective optimization model and a second single-objective optimization model; solving the train candidate set restriction main model and the freight train candidate set generation submodel based on the high-speed rail freight train candidate set to obtain the current optimal freight train candidate set with the initial freight train candidate set as the starting point; substituting the first single-objective optimization model and the second single-objective optimization model into the solution to obtain an optimal target value vector; and using a genetic algorithm to solve the optimal target value vector to obtain an optimal chromosome as the final optimal solution output. The present invention combines the genetic algorithm with a column generation algorithm, taking into account both economic efficiency and transportation capacity requirements, achieving matching of freight flow and train flow, and obtaining a feasible high-speed rail freight train operation optimization solution.

Description

Technical Field

[0001] The present invention belongs to the technical field of train operation plan compilation, and specifically relates to a high-speed railway freight train operation optimization method, device and equipment. Background Art

[0002] Train operation plans are based on passenger and freight volume, and are informed by the nature, characteristics, and patterns of passenger and freight flows. They scientifically and rationally arrange train operation levels, types, origins and destinations, routes, train formations, stop schedules, train capacity utilization, and vehicle floor utilization, reflecting the organizational plan for everything from passenger and freight flows to train flows. Train operation plan design encompasses numerous aspects and is influenced by various factors, making it a large-scale combinatorial optimization problem. High-speed rail freight train operation plan design, beyond traditional train operation plan design, requires full consideration of the complex high-speed rail network conditions and incorporates freight transportation organizational models and freight flow distribution characteristics. This complexity leads to core issues in actual operation, such as multi-dimensional resource coordination conflicts, the difficulty in balancing economic efficiency and timeliness, and inefficient real-time decision-making. Specifically, the lack of coordination among multiple constraints, such as station operating capacity, section throughput, and EMU turnover, can easily lead to local resource overload or idleness. Furthermore, the inefficiency of generating solutions within a high-dimensional solution space makes it difficult to efficiently generate transportation plans. Furthermore, low-cost solutions require reducing train runs and stops, which increases cargo transfer times. High-efficiency solutions require more frequent train runs and more stops, which drives up operating costs. Traditional single-objective optimization or simple weighted methods cannot balance the dynamic game between these two. Summary of the Invention

[0003] In order to overcome the above-mentioned problems existing in the prior art, the present invention provides a method, device and equipment for optimizing the operation of high-speed railway freight trains, which are used to solve the above-mentioned problems existing in the prior art.

[0004] A method for optimizing the operation of high-speed railway freight trains, the method comprising:

[0005] S1. Establish a dual-objective nonlinear model for optimizing high-speed rail freight train operations;

[0006] S2. Based on the principle of column generation algorithm, the dual-objective nonlinear model is decomposed into a main model for train candidate set restriction and a sub-model for freight train candidate set generation;

[0007] S3. Decompose the dual-objective nonlinear optimization model into a first single-objective optimization model and a second single-objective optimization model;

[0008] S4. Solve the train candidate set constraint main model and the freight train candidate set generation sub-model based on the high-speed rail freight train candidate set to obtain the current optimal freight train candidate set starting from the initial freight train candidate set;

[0009] S5. Substitute the current optimal freight train candidate set into the first single-objective optimization model and the second single-objective optimization model to obtain the optimal target value vector;

[0010] S6. The optimal target value vector is used as the fitness value of each chromosome in the genetic algorithm. Then, the optimal chromosome is obtained according to the iterative evolution of the genetic algorithm as the final optimal solution output, that is, the high-speed rail freight train operation optimization plan is obtained.

[0011] As described above and any possible implementation method, an implementation method is further provided, in which the dual-objective nonlinear model includes the objective function of minimizing the high-speed rail train operating cost, the objective function of minimizing the total freight transportation time, freight demand satisfaction constraints, train flow and freight flow coupling constraints, train carrying capacity constraints, interval passing capacity constraints, station operating capacity constraints and value constraints of model decision variables.

[0012] As described above and any possible implementation method, an implementation method is further provided, in which the main model of the train alternative set restriction includes the high-speed rail train operating cost objective function, interval passing capacity constraints, station operating capacity constraints, train carrying capacity constraints, interval section flow satisfaction constraints, train assignment constraints and train operation frequency decision variables.

[0013] According to the aspects and any possible implementation methods described above, an implementation method is further provided, in which the objective function of the freight train alternative set generation sub-model is obtained by mixed calculation of the high-speed rail train operating cost objective function, the test number and the simplex multiplier.

[0014] According to the aspects described above and any possible implementation method, an implementation method is further provided, in which the objective function of the first single-objective optimization model includes the high-speed rail train operating cost objective function, freight flow demand satisfaction constraint, train flow and freight flow coupling constraint, train carrying capacity constraint, interval passing capacity constraint, station operating capacity constraint and model decision variable value constraint.

[0015] According to the aspects described above and any possible implementation methods, an implementation method is further provided, in which the second single-objective optimization model includes the objective function of minimizing the total freight transportation time, freight flow demand satisfaction constraints, train flow and freight flow coupling constraints, train carrying capacity constraints, interval passing capacity constraints, station operating capacity constraints, model decision variable value constraints and new constraints.

[0016] According to the above aspects and any possible implementation, an implementation is further provided, wherein S4 specifically includes: S41. randomly generating an initial freight train candidate set using genetic algorithm chromosomes;

[0017] S42. Substitute the initial freight train candidate set into the train candidate set restriction master model based on the column generation algorithm, and solve the current optimal objective function value, each constraint simplex multiplier, and related test number of the train candidate set restriction master model;

[0018] S43. Substitute each constrained simplex multiplier into the freight train candidate set generation submodel based on the column generation algorithm to obtain the freight train candidate set generation submodel;

[0019] S44. Determine whether a new freight train can be added to the train candidate set. If so, return to step S42. If not, obtain the current optimal freight train candidate set starting from the initial freight train candidate set.

[0020] According to the above aspects and any possible implementation, an implementation is further provided, wherein S6 specifically includes:

[0021] S61: Save the chromosome with the best fitness value in the parent population into the offspring population list;

[0022] S62: Using a roulette wheel method, set the number of roulette wheel selections per round to m, where m ≥ 4. Generate a uniformly distributed pseudo-random number r in the interval [0, 1]. Based on the value of r, select the corresponding chromosome from the offspring population list and enter the roulette wheel candidate list. Select the two chromosomes with the best fitness values ​​from the list of m candidate chromosomes and enter the list to be crossed over and mutated.

[0023] S63: After the two best chromosomes complete the crossover and mutation operations in the list to be crossed and mutated, the new chromosomes or the parent chromosomes that have not been actually operated due to the crossover and mutation probability are saved in the offspring candidate chromosome list, and the fitness value of each chromosome in the list is calculated. The chromosome with the best fitness value is selected and saved in the offspring population.

[0024] The present invention also provides a high-speed railway freight train operation optimization device that integrates a train generation algorithm and a genetic algorithm. The device is used to implement the method described above, including:

[0025] Establish a module for building a dual-objective nonlinear model for optimizing the operation of high-speed freight trains;

[0026] A first decomposition module is used to decompose the dual-objective nonlinear model into a train candidate set restriction main model and a freight train candidate set generation sub-model based on the column generation algorithm principle;

[0027] The second decomposition module is used to decompose the dual-objective nonlinear model of operation optimization into a first single-objective optimization model and a second single-objective optimization model;

[0028] The first solving module is used to solve the train candidate set restriction main model and the freight train candidate set generation sub-model based on the high-speed rail freight train candidate set, and obtain the current optimal freight train candidate set with the initial freight train candidate set as the starting point;

[0029] A second solving module is configured to substitute the current optimal freight train candidate set into the first single-objective optimization model and the second single-objective optimization model to solve and obtain an optimal target value vector;

[0030] The optimal solution module is used to use the optimal target value vector as the fitness value of each chromosome in the genetic algorithm, and then obtain the optimal chromosome as the final optimal solution output based on the iterative evolution of the genetic algorithm, that is, to obtain the optimization plan for the operation of high-speed railway freight trains.

[0031] The present invention further provides an electronic device, comprising:

[0032] a memory storing executable instructions;

[0033] A processor is configured to execute the executable instructions in the memory to implement the method.

[0034] Beneficial effects of the present invention

[0035] The high-speed railway freight train operation optimization method of the present invention comprises: establishing a dual-objective nonlinear model for optimizing the operation of high-speed railway freight trains; decomposing the dual-objective nonlinear model into a train candidate set restriction main model, a freight train candidate set generation submodel, and a first single-objective optimization model and a second single-objective optimization model in different ways; solving the train candidate set restriction main model and the freight train candidate set generation submodel according to the high-speed railway freight train candidate set to obtain a current optimal freight train candidate set with the initial freight train candidate set as the starting point; and substituting the first single-objective optimization model and the second single-objective optimization model into the solution to obtain an optimal target value vector; and solving the optimal target value vector using a genetic algorithm to obtain an optimal chromosome as the final optimal solution output. The train generation algorithm structure part of the present invention first selects a train alternative set that takes into account both economic efficiency and capacity demand constraints, and then constructs a freight flow allocation model based on the alternative set under the goal of minimizing the operating cost of high-speed rail freight trains, realizes the matching of freight flow and train flow, and obtains a feasible high-speed rail freight train operation plan; the genetic algorithm structure part uses the train generation algorithm structure as a calculation method for the fitness value of each chromosome in the genetic algorithm, generates an initial feasible train set in the train generation algorithm through the genetic algorithm, compares the fitness value of each chromosome in each generation population, and iteratively obtains a satisfactory high-speed rail freight train operation plan, with a small number of iterations, fast calculation speed, and good optimization effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of the method of the present invention;

[0037] Figure 2 is an example diagram of a two-dimensional chromosome structure of the present invention;

[0038] Figure 3 This is an example diagram of freight OD demand of the present invention;

[0039] Figure 4 This is an example diagram of a two-dimensional matrix random train stop plan of the present invention;

[0040] Figure 5 This is an example diagram of determining the initial candidate set of the present invention;

[0041] Figure 6 This is an example diagram of random gene point crossover of the present invention;

[0042] Figure 7 This is an example diagram of random gene fragment intersection of the present invention;

[0043] Figure 8 This is an example diagram of the cross result determination of the present invention;

[0044] Figure 9 This is an example diagram of random gene site variation of the present invention;

[0045] Figure 10 This is an example diagram of random gene segment variation of the present invention;

[0046] Figure 11 It is a trend diagram of the change of the objective function values ​​of all generated chromosomes of the present invention;

[0047] Figure 12 It is a graph showing the changing trend of the optimal objective function value Z1' of each generation of the present invention;

[0048] Figure 13 This is a high-speed railway freight train operation diagram of the present invention;

[0049] Figure 14 This is a diagram of the cargo flow distribution plan for each high-speed rail freight train of the present invention;

[0050] Figure 15 It is a cross-sectional flow diagram of the present invention. DETAILED DESCRIPTION

[0051] To better understand the technical solutions of the present invention, the present invention includes but is not limited to the specific embodiments described below. Similar technologies and methods should be considered within the scope of protection of the present invention. To further clarify the technical problems, technical solutions, and advantages to be solved by the present invention, the following detailed description is provided in conjunction with the accompanying drawings and specific embodiments.

[0052] It should be understood that the embodiments described herein are only a portion of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0053] The terms used in the embodiments of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The singular forms "a", "an", "the" and "the" used in the embodiments of the present invention and the appended claims are also intended to include plural forms unless the context clearly indicates otherwise.

[0054] like Figure 1 As shown, the present invention provides a method for optimizing the operation of high-speed railway freight trains, the method comprising:

[0055] S1. Establish a dual-objective nonlinear model for optimizing high-speed rail freight train operations;

[0056] S2. Based on the principle of column generation algorithm, the dual-objective nonlinear model is decomposed into a main model for train candidate set restriction and a sub-model for freight train candidate set generation;

[0057] S3. Decompose the dual-objective nonlinear optimization model into a first single-objective optimization model and a second single-objective optimization model;

[0058] S4. Solve the train candidate set constraint main model and the freight train candidate set generation sub-model based on the high-speed rail freight train candidate set to obtain the current optimal freight train candidate set starting from the initial freight train candidate set;

[0059] S5. Substitute the current optimal freight train candidate set into the first single-objective optimization model and the second single-objective optimization model to obtain the optimal target value vector;

[0060] S6. The optimal target value vector is used as the fitness value of each chromosome in the genetic algorithm. Then, the optimal chromosome is obtained according to the iterative evolution of the genetic algorithm as the final optimal solution output, that is, the high-speed rail freight train operation optimization plan is obtained.

[0061] Furthermore, the dual-objective nonlinear model includes the objective function of minimizing the high-speed rail train operating cost, the objective function of minimizing the total freight transportation time, freight demand satisfaction constraints, train flow and freight flow coupling constraints, train carrying capacity constraints, interval passing capacity constraints, station operating capacity constraints, and value constraints of model decision variables.

[0062] Furthermore, the train alternative set constraint main model includes the high-speed rail train operating cost objective function, interval passing capacity constraint, station operation capacity constraint, train carrying capacity constraint, interval section flow satisfaction constraint, train assignment constraint and train operation frequency decision variables.

[0063] Furthermore, the objective function of the freight train alternative set generation sub-model is obtained by mixed calculation of the high-speed rail train operating cost objective function, the test number and the simplex multiplier.

[0064] Furthermore, the objective function of the first single-objective optimization model includes the high-speed rail train operating cost objective function, freight flow demand satisfaction constraint, train flow and freight flow coupling constraint, train carrying capacity constraint, interval passing capacity constraint, station operating capacity constraint and model decision variable value constraint.

[0065] Furthermore, the second single-objective optimization model includes the objective function of minimizing the total freight transportation time, freight flow demand satisfaction constraints, train flow and freight flow coupling constraints, train carrying capacity constraints, interval passing capacity constraints, station operating capacity constraints, model decision variable value constraints and new constraints.

[0066] Furthermore, the S4 specifically includes: S41. randomly generating an initial freight train candidate set using genetic algorithm chromosomes;

[0067] S42. Substitute the initial freight train candidate set into the train candidate set restriction master model based on the column generation algorithm, and solve the current optimal objective function value, each constraint simplex multiplier, and related test number of the train candidate set restriction master model;

[0068] S43. Substitute each constrained simplex multiplier into the freight train candidate set generation submodel based on the column generation algorithm to obtain the freight train candidate set generation submodel;

[0069] S44. Determine whether a new freight train can be added to the train candidate set. If so, return to step S42. If not, obtain the current optimal freight train candidate set starting from the initial freight train candidate set.

[0070] Specifically, the implementation process of the present invention is as follows: A high-speed rail freight operation optimization method integrating a train generation algorithm and a genetic algorithm comprises the following steps:

[0071] (1) The basic optimization problem of optimizing the operation plan of high-speed railway freight trains is modeled as a dual-objective nonlinear optimization model M1;

[0072] (2) Based on the train generation algorithm principle, the constructed high-speed rail freight train operation plan optimization model M1 is decomposed into the train alternative set restriction main problem model M2 and the freight train alternative set generation sub-problem model M3;

[0073] (3) Multi-objective processing and fitness value setting for the high-speed rail freight train operation plan optimization model M1;

[0074] (4) Using the set models M2 and M3, the train candidate set is solved and the fitness value is calculated using the train generation algorithm iteratively;

[0075] (5) Design a hybrid heuristic algorithm based on column generation and genetic algorithm to solve the original problem model M1 and obtain the optimal high-speed railway freight train operation plan and freight flow allocation plan;

[0076] (6) An actual high-speed railway line is selected for case analysis to obtain the high-speed railway freight train operation plan and freight flow distribution plan under the case parameters to verify the effectiveness of the proposed algorithm.

[0077] The following describes the detailed operation process of each part:

[0078] The high-speed rail freight train operation plan optimization model M1 in step (1) needs to meet the freight demand satisfaction constraint, the train flow and freight flow coupling constraint, the train carrying capacity constraint, the interval passing capacity constraint, the station operation capacity constraint, and the value constraint of the model decision variables. The relevant parameters, decision variables, objective function and constraints of the model are as follows:

[0079] Related parameters: S represents the set of high-speed rail stations, e, i, j represent the index of S, |S| represents the number of stations; O represents the starting station of the high-speed rail line; D represents the terminal station of the high-speed rail line; Z represents the interval set, represents the interval from station i to station i+1; ZL represents the interval distance set, represents the distance between station i and station i + 1; G represents the freight demand set, represents the cargo flow demand from station i to station j; Represents a collection of high-speed rail freight trains, express The index of Indicates the number of freight trains; Represents the fixed cost of cargo transportation, RMB / ton; Represents the variable cost of freight transportation, the distance-related cost part, RMB / ton-kilometer; represents the fixed cost of operating freight trains, RMB / train; represents the variable cost related to the distance of freight train operation, RMB / train-kilometer; Represents the variable cost associated with the operation and stopover of freight trains, RMB / train; Represents the interval within the unit period By capacity cap, number of columns; represents the upper limit of the operating capacity of station i within a unit period, in terms of number of trains; Represents the rated load of freight train, tons; Represents the minimum number of stops for a freight train throughout the entire journey, times; Represents the upper limit of the number of stops for a freight train throughout the entire journey, times; Represents the lower limit of the full mileage of freight trains, kilometers; Represents the upper limit of the total mileage of freight trains, kilometers; Represents the average operating speed of freight trains, km / h; Represents the stop time of freight trains at intermediate stations, in minutes; Represents the additional start and stop time caused by the freight train's intermediate stops, in minutes; M represents an infinite positive number.

[0080] Decision variables: Indicates freight train Whether to stop at station i, a 0-1 variable, 1 if stopping, 0 if not stopping; Indicates freight train Whether to pass the interval ,0-1 variable, takes 1, not 0; Indicates whether station i is a freight train The originating station, a 0-1 variable, takes 1, not 0; Indicates whether station i is a freight train The final destination, a 0-1 variable, is 1, not 0; Indicates freight train The number of lines opened during the statistical period, an integer variable; Indicates freight train Whether it can serve freight needs ,0-1 variable, takes 1, not 0; Indicates assignment to freight train The freight flow from station i to station j, an integer variable.

[0081] (1) Model objective function

[0082] Minimize the total operating cost of high-speed trains: (1), where Z1 represents the minimum total operating cost of the HSR train;

[0083] Minimize total freight transportation time: (2), where Z2 represents the minimum total freight transportation time.

[0084] (2) Model constraints

[0085] Cargo flow demand meets the constraints: (3)

[0086] Train flow and freight flow coupling constraints: (4)

[0087] Train carrying capacity constraints: (5), among which, Indicates the starting station of the line. Indicates the terminal station of the line.

[0088] Interval passing capacity constraints: (6)

[0089] Station operating capacity constraints: (7)

[0090] Model decision variable value constraints: (8) (9), where N represents the set of natural numbers.

[0091] High-speed rail freight train operation plan optimization model M1:

[0092] Objective function: Formula (1), (2)

[0093] Constraints: Formulas (3)-(7)

[0094] Decision variables: Formulas (8)-(9)

[0095] The specific steps of decomposing the high-speed rail freight train operation plan optimization model based on the train generation algorithm principle described in step (2) are as follows: According to the high-speed rail freight train operation plan algorithm process design, the overall algorithm combines the train generation algorithm to solve the train candidate set, substitutes it into the operation plan and freight flow allocation plan model to obtain the chromosome fitness value and train operation plan. Based on the train generation algorithm principle, the train candidate set solution problem is decomposed into the train candidate set restriction main problem model M2 and the freight train candidate set generation subproblem model M3. The current optimal train candidate set based on the given initial candidate set is obtained through iterative solution.

[0096] The column generation algorithm is a highly efficient algorithm for solving large-scale linear optimization problems. Essentially, it is a form of the simplex method. Its theoretical basis, proposed by Danzig and Wolfe in 1960 and known as the DW decomposition principle, decomposes the original linear programming problem into a master problem (MP) and several sub-problems (SP), essentially assigning the linear programming problem constraints to the main and subsidiary layers. Genetic algorithms are a method for searching for optimal solutions by simulating natural evolutionary processes.

[0097] For relatively small-scale models, the column generation algorithm can artificially give an initial solution that meets the conditions based on the model structure and problem characteristics, and then gradually add columns that contribute to the optimization target of the restricted main problem based on the initial solution. Since the scale of the entire solution set is limited and the overall solution scale is not large, the optimal solution can generally be found in the end. However, when facing a large-scale linear programming problem, its solution space often has too many dimensions. Since the selection of the initial feasible solution directly affects the acquisition of the MP optimal solution of the problem, different feasible initial solutions are selected for column generation algorithm solution, and different approximate solutions are often obtained. It is easy to fall into the local optimal solution by starting the iterative calculation from only a certain feasible initial solution. In order to obtain the global optimal solution or satisfactory solution, the present invention selects a suitable heuristic algorithm to compile the generation of the initial solution, continuously saves and updates the initial solution structure according to the corresponding MP optimal solution value, and finally selects a set of relatively satisfactory initial solutions to obtain the final acceptable satisfactory solution. Moreover, the MP optimal solution will not be uniquely restricted by the selection of the initial feasible solution, so there is no need to perform a global traversal of all feasible initial solutions.

[0098] A genetic algorithm begins with a population representing a set of potential solutions to a problem. A population is composed of a certain number of individuals encoded by genes, each of which is actually a chromosome-like entity with characteristics. The present invention combines a genetic algorithm with a column generation algorithm, compiling the initial solutions of the column generation algorithm as chromosomes and designing a hybrid heuristic algorithm. The column generation algorithm requires a certain scale of random initial solutions to ensure a sufficiently large search solution space coverage, and the random search characteristics of the genetic algorithm can adapt to this. At the same time, the optimization ability and convergence efficiency of the genetic algorithm are limited by the fitness value setting of the randomly generated chromosomes. The column generation algorithm solves the train candidate set, which is a further optimization of the initial train candidate set. From the perspective of overall algorithm design, it also optimizes the fitness value of the genetic algorithm chromosomes, significantly enhancing the optimization ability and convergence efficiency of the genetic algorithm and achieving good results. Therefore, the present invention combines the column generation algorithm with the genetic algorithm, using different algorithms at different processing stages.

[0099] Step 1: Based on the above train generation algorithm principle, a main train candidate set restriction model M2 based on the train generation algorithm is constructed. The solution of M2 is mainly to select a more suitable candidate set train for M1. Therefore, the transformation is based on M1, retaining only the part related to the train frequency decision variable in M1 and deleting the part related to the freight flow distribution decision variable.

[0100] The details are as follows:

[0101] (1) Objective function

[0102] Of the two objective functions of M1, the high-speed train operating cost objective function, which is expressed in formula (1), is the product of the frequency of freight train operation and the actual operating cost of a single freight train. It is only related to the frequency of train operation and can therefore be directly used as the optimization target of M2. In addition, the objective function formula (2) is related to freight demand and is therefore not considered.

[0103] (2) Constraints

[0104] The interval passing capacity constraint (Formula (6)) and station operation capacity constraint (Formula (7)) in M1 are only related to the train operation frequency decision variable, so they are directly used in M2.

[0105] The freight demand satisfaction constraints in M1 are only relevant to the freight flow allocation decision variables and are therefore discarded in M2. The train capacity constraints and train-freight flow coupling constraints in M1 are relevant to both the train operation plan decision variables and the freight flow allocation decision variables, and therefore require some transformation in M2.

[0106] 1) Transform train carrying capacity constraints into section flow satisfaction constraints

[0107] The mathematical meaning of the train carrying capacity constraint is that the carrying capacity of each train passing through any interval section must be greater than the actual carrying capacity of the train. Since the freight flow allocation decision of the train is not considered, the train carrying capacity constraint is converted into an interval section flow satisfaction constraint.

[0108] The size of the section flow depends on the train's loading capacity and the section flow demand. That is, for any section, the total OD freight demand covering that section must be less than the sum of the loading capacities of all trains that can serve that section. The section flow satisfies the following constraints: (10)

[0109] Mathematically, a flow-satisfaction constraint on a section relaxes the relationship between the flow on each train and its capacity, transforming it into a relationship between the flow of all trains passing through the section and the total capacity of all trains serving that section. From the perspective of how constraints restrict the solution space, flow-satisfaction constraints on a section reduce the constraints on the solution space.

[0110] 2) Transforming the coupling constraints of train flow and freight flow into train assignment constraints

[0111] The mathematical meaning of the train flow and freight flow coupling constraint is the matching relationship between all high-speed trains passing a certain OD demand and whether the OD demand flow is allocated to the high-speed train. In order to eliminate the freight flow allocation decision, the train flow and freight flow coupling constraint is transformed into a train assignment constraint.

[0112] The train assignment constraint states that when a certain OD demand exists, there must be a train that can serve that OD. Its expression is as follows: (11)

[0113] Mathematically, similar to the interval flow satisfaction constraint, train assignment constraints relax the coupling constraints between train and freight flows to a certain extent. The original coupling relationship between each train's service OD and the assigned OD on that train is relaxed into a relationship between a specific OD demand and the assignment of all trains to that OD. From the perspective of the constraints on the solution space, train assignment constraints reduce the constraints on the solution space.

[0114] (3) Decision variables

[0115] In the decision variable part, only the train frequency decision variable in M1 is retained.

[0116] The complete train candidate set constraint master model M2 is expressed as follows:

[0117] Objective function: Formula (1)

[0118] Constraints: Formulas (6)-(7), (10)-(11)

[0119] Decision variables: Formula (9)

[0120] The goal of solving the freight train candidate set generation subproblem is to select trains for the train candidate set that meet the conditions and can further optimize the objective function of the restricted main problem. These added trains must also have certain properties such as train starting and ending points, train running intervals, and train stop plans.

[0121] The freight train candidate set generation sub-model M3 determines its objective function by restricting the objective function of the main model M2, the test number, and the simplex multiplier. The objective function of the freight train candidate set generation sub-model M3 is expressed as:

[0122] (12)

[0123] The specific constraints related to the freight train operation conditions in model M1 are obtained through linearization as follows:

[0124] Train service OD stop constraints: (13)

[0125] (14), among which, Representing freight trains Whether to stop at station j, a 0-1 variable, 1 if stopping, 0 if not stopping.

[0126] (15)

[0127] Train stop constraints at origin and destination points: (16)

[0128] (17)

[0129] (18)

[0130] (19)

[0131] Train stop range constraints: (20), among which, Indicates whether to stop at station e. It is a 0-1 variable and takes the value 1 instead of 0.

[0132] (twenty one)

[0133] Train passing range constraints:

[0134] a. All sections between the starting and ending points of the train route are considered passing sections: (22), among which, To indicate whether station j is a freight train The final destination, a 0-1 variable, is 1, not 0.

[0135] b. The train must not pass through the section outside the origin and destination: (23), among which, Indicates whether station e is the departure station for freight trains. It is a 0-1 variable and is set to 1 instead of 0.

[0136] (twenty four)

[0137] Constraints on the number of train stops: (25)

[0138] Train mileage constraints: (26)

[0139] Constraints on the number of train origin and destination points: (27)

[0140] (28)

[0141] Train line station sequence constraints: (29)

[0142] Train stop decision variables: (30)

[0143] Train demand service decision variables: (31)

[0144] Decision variables for train passing interval: (32)

[0145] Train origin and destination decision variables: (33) (34)

[0146] Among them, in formula (12), in addition to the variables and parameters already defined in M1, represents the simplex multiplier of the freight train constrained by the interval through-capacity, i.e., the price of the “resource” referred to by the interval through-capacity; represents the simplex multiplier of the freight train constrained by the station's operating capacity, that is, the price of the "resource" referred to by the station's receiving and dispatching capacity; Indicates that the interval cross-sectional flow satisfies the constraint freight train simplex multiplier, that is, the interval cross-sectional flow satisfies the “resource” price referred to; represents the freight train simplex multiplier constraining the train assignment, i.e., the price of the “resource” to which the train assignment refers.

[0147] The complete freight train candidate set generation sub-model M3 is expressed as follows:

[0148] Objective function: Formula (12)

[0149] Constraints: Formulas (13)-(32)

[0150] Decision variables: Formulas (33)-(34)

[0151] Step (3): The specific steps of multi-objective processing and fitness value setting for model M1 are as follows:

[0152] Step 1: Use the priority method to decompose the high-speed railway freight train operation plan optimization model M1 with multiple objectives into two single-objective optimization models M4 and M5.

[0153] The single-objective optimization model M4 specifically includes:

[0154] Objective function: Formula (1)

[0155] Constraints: Formulas (3) - (7)

[0156] Decision variables: Formula (8), (9)

[0157] The single-objective optimization model M5 specifically includes:

[0158] Objective function: Formula (2)

[0159] Constraints: Formulas (3)-(7) and new constraints (35)

[0160] Among them, Z1 * The optimal target value obtained by solving model M4.

[0161] Decision variables: Formula (8), (9)

[0162] The steps of solving the multi-objective linear model M1 using the priority method are as follows: first, optimize the objective function (1) separately, that is, solve the model M4, and obtain the minimum value of the high-speed rail freight train operating cost; then, under the condition of considering the newly added constraint (35), optimize the objective function (2) separately, that is, solve the model M5, and obtain the minimum value of the total freight transportation time. The two objective function values ​​of M1 solved by the priority method are expressed as the target vector solution with priority [Z1 * , Z2 * ], which constitutes the fitness value of the chromosome in the genetic algorithm for subsequent selection.

[0163] Using a priority approach, the multi-objective model M1 is decomposed into two single-objective models, M4 and M5, prioritizing the goal of minimizing total operating costs. Total freight transport time is then secondary optimized based on optimal operating costs. This single-objective model simplifies the solution process and avoids the complexity of multi-objective algorithms. This approach aligns with the practical operational decision-making principle of "prioritizing cost control over time efficiency." While maintaining solution quality, it significantly reduces computational complexity.

[0164] Step (4): The specific steps of solving the train candidate set and calculating the fitness value based on the train generation algorithm are as follows:

[0165] Step 1: Chromosome encoding. Construct chromosome classes and clarify the structural characteristics of each chromosome. Because all freight OD requirements are required to be met, when the number of high-speed rail stations on the line is When , assuming that there is OD demand between any two stations, there are OD pairs need train service. Without considering the same train serving multiple ODs, a total of The trains correspond to ODs one by one. Combined with the requirement of “train service OD stop constraint”, the trains serving the OD demand must stop at the OD origin and destination station. Therefore, “OD-train-station” is used as the encoding object to construct a two-dimensional chromosome structure. The size of the two-dimensional matrix is , represents the stop plan of the train that can serve different OD demands, and the specific value represents the stop selection of a certain "OD-train" at the corresponding station. Figure 2 As an example, the chromosome structure matrix is ​​represented by a six-column matrix of stop plans for OD trains at four stations. Taking the first row as an example, the stop plan for OD train "0-1" serving OD demand "0-1" is [1, 1, 0, 0].

[0166] The main structure of the chromosome encoding module is a two-dimensional matrix consisting of the number of OD demands and the number of stations. Therefore, the two-dimensional "OD-train-station" is used as the encoding object to construct the chromosome main structure. According to the number of stations on the solved line |S|, the size of the two-dimensional matrix array is determined as In addition, it also includes properties such as the initial candidate set of the chromosome, the train candidate set after the chromosome solution, the fitness value of the chromosome, the operation plan and traffic allocation plan corresponding to the chromosome.

[0167] Step 2: Generate the initial train candidate set. This is used to compile the specific values ​​of the two-dimensional "OD-train-station" matrix for the new chromosomes generated in the population. At the same time, it further obtains the fitness value and other attributes of the chromosome to determine the initial candidate set information. Therefore, it can be further divided into two parts: chromosome structure assignment and initial candidate set determination.

[0168] 1) Chromosome structure assignment part

[0169] The assignment operation of the two-dimensional matrix is ​​essentially to determine the stop plan of the "OD-train". First, it is determined whether there is demand, that is, whether there is freight demand between the two stations. If OD demand does not exist, there is no need to compile a stop plan for the OD service train, and the values ​​of the train stop plan column corresponding to the OD are all set to "0"; then, following the "train service OD stop constraint" requirements, the current "OD-train" must stop at the current OD starting and ending stations, and the corresponding station position is set to "1", and other stations are randomly set to "0" or "1". And so on, the stop plan values ​​of each "OD-train" in the freight two-dimensional matrix can be completed.

[0170] Assume that the freight OD demand of the high-speed rail line is as follows Figure 3 As shown, the stop plan of each OD train is determined according to whether there is freight demand. Figure 4As shown in the figure, the OD origin and destination stations served by the train must stop at them, and the train stop plans for other stations are randomly generated. In the freight two-dimensional matrix, since the freight OD demand 0-3 flow is 0, the corresponding "OD-train" "1-3" is set to not run, that is, the stop plan for all stations is "0".

[0171] 2) Initial candidate set determination part

[0172] The determination of the initial candidate set is different from the train list after chromosome assignment. After chromosome assignment, the stop plans of several trains with OD demand are determined. In order to ensure the integrity of the chromosome structure, the generated trains are not processed. The candidate set saves the train sequence with different stop plans. Therefore, in order to obtain the initial candidate set, the chromosome train list needs to be deduplicated, that is, only trains with different stop plans are added to the initial candidate set. Figure 5 As shown in the figure, after removing duplicates, the initial candidate set containing freight trains is obtained. The specific steps include:

[0173] Step 1: Generate freight train candidate set.

[0174] Step 2: Solve the main problem of train candidate set constraints. Substitute the initial freight train candidate set into the main train candidate set constraint model M2 based on the column generation algorithm. Call the optimization solver Cplex to solve the model using branch and bound or other solution methods to obtain the current optimal objective function value, each constraint simplex multiplier, and related test number.

[0175] Step 3: Solve the freight train generation subproblem. Substitute the freight train-related simplex multipliers from the constraints solved in Step 2 into the freight train generation submodel M3 based on the column generation algorithm. Use Cplex to solve this model and obtain the new freight train to be added to the candidate set.

[0176] Step 4: Determine whether to add new freight trains to the alternative set. Determine the solution of step 3. If "① there is no solution to step 3, ② the objective function value obtained by the solution is greater than or equal to 0, that is, the test number meets the optimal solution conditions, ③ a set of freight trains with attributes such as stop plan, starting and ending points, operating section, mileage, number of stops, and operating cost are present in the current train alternative set", if any of the three conditions is met, it means that the current train alternative set can no longer optimize the objective function value of the main problem by adding new freight train types, and then go to step 5. If all three conditions are not met, then the new freight train information solved by the model in step 3 is added to the freight train alternative set, the current train alternative set is updated, and the process returns to step 2.

[0177] Step 5: Solve the operation plan, freight flow allocation plan, and fitness value. At this point, the freight train candidate set is updated, and the objective function of the constrained main problem cannot be further optimized by adding new freight train types. Therefore, the current optimal freight train candidate set is obtained, starting with the initial freight train candidate set. This current optimal freight train candidate set is sequentially substituted into the linearized equivalent models M4 and M5, and Cplex is called to use the branch and bound method to solve it, obtaining the current optimal objective function value vector, freight train operation plan, and freight flow allocation plan.

[0178] Step 6: Return the fitness vector, operation plan, and freight flow allocation plan. Assign the optimal objective function value vector obtained by solving step 3 to the fitness vector of the chromosome of the initial freight train candidate set, and save the train operation plan, freight flow allocation plan, and train candidate set in the chromosome attributes. It should be noted that since the fitness vector represents a multi-objective function value vector with priority, there is a strong correlation between the two objective functions. The high-priority objective function directly affects the solution of the low-priority objective function. Therefore, when performing the optimal fitness comparison in the genetic algorithm, objective function (1) can be directly selected for comparison until the objective function (1) is no longer optimized or the maximum number of iterations is reached, and then the objective function (2) is solved.

[0179] Step (5): Design a hybrid heuristic algorithm based on column generation and genetic algorithm to solve the original problem model M1 and obtain the optimal high-speed railway freight train operation plan and freight flow allocation plan, specifically including:

[0180] Step 1: Save the chromosome with the best fitness value in the parent population into the offspring population list.

[0181] Step 2: Use the roulette wheel method and set the number of roulette selections per round m, where m ≥ 4. Generate a uniformly distributed pseudo-random r in the interval [0, 1]. According to the value of r, select the corresponding chromosome from the offspring population list and enter the roulette wheel candidate list. Select the two chromosomes with the best fitness values ​​from the list of m candidate chromosomes and enter the list to be crossed and mutated.

[0182] Step 3: After the two best chromosomes complete the crossover and mutation operations in the list to be crossed and mutated, the new chromosomes or the parent chromosomes that have not been actually operated due to the probability of crossover and mutation are saved in the list of offspring candidate chromosomes. The fitness value of each chromosome in the list is calculated through the "train candidate set solution" process and the "operation plan and allocation plan solution" process in step (4), and the chromosome with the best fitness value is selected and saved in the offspring population.

[0183] The crossover operations include:

[0184] A crossover operation is performed on two chromosomes to be crossed that meet the crossover probability judgment and are selected by roulette in the parent population. According to the chromosome structure, two crossover methods are designed: random gene point crossover and random gene fragment crossover.

[0185] 1) Random gene point crossover

[0186] For two chromosomes to be crossed, set n gene sites to be crossed, where the gene sites are numbered positions of "OD-train", corresponding to the crossover of the n gene sites of the two chromosomes. Figure 6 As shown in the figure, the randomly selected crossover gene sites are [0, 3, 4], that is, the stop plans of the "OD-train" ["0-1", "1-2", "1-3"] are cross-exchanged. The stop plans of the two parent chromosomes at the gene sites "0" and "3" are different, and the stop plans of the two parent chromosomes at the gene site "4" are the same, so in essence only the gene sites "0" and "3" are exchanged.

[0187] 2) Random gene fragment crossover

[0188] For two chromosomes to be crossed, two endpoints of the gene segments to be crossed are set, where the gene segments are the "OD-train" gene positions contained in the endpoint number positions of the two "OD-trains", corresponding to the crossover of the gene segments of the two chromosomes. Figure 7 As shown, the randomly selected crossover gene segment is [1-3], that is, the stop scheme of the "OD-train" ["0-2", "0-3", "1-2"] is crossed and exchanged, where the stop schemes of the two parent chromosomes on the gene segment are different.

[0189] Determination of crossover results. To ensure that the two offspring chromosomes are different from the parent chromosomes after the crossover, the "initial candidate set generation module" needs to be called after the exchange to determine the initial candidate set of the two chromosomes to ensure that the two chromosomes after the crossover are different from those before the crossover. Figure 8 As shown, the initial candidate sets of the two daughter chromosomes are different from those of the parent, so they can be saved in the list to be mutated.

[0190] If the initial candidate sets of the two daughter chromosomes after the crossover are different from the parent chromosomes, it means that two new daughter chromosomes are generated, and the two daughter chromosomes are saved in the list to be mutated; if only one of the initial candidate sets of the two daughter chromosomes after the crossover is different from the two parent chromosomes, it means that only one new daughter chromosome is generated, and the chromosome is saved in the list to be mutated, and the other chromosome that is the same as the parent initial candidate set is eliminated; if the initial candidate sets of the two daughter chromosomes after the crossover are the same as the parent chromosomes, both daughter chromosomes are eliminated, and the crossover gene sites selected at this time are saved in the crossover failure list, and the crossover gene sites or gene fragments are reselected. When the randomly generated crossover gene site or fragment is not in the crossover failure list, crossover is performed according to the gene site or fragment.

[0191] If the crossover failure list reaches the maximum limit, two new parent chromosomes to be crossed are selected again through the roulette wheel method and this step is repeated.

[0192] If after the crossover operation, there is at least one chromosome to be mutated in the list to be mutated, the crossover is successful and the crossover operation ends.

[0193] The mutation operations include:

[0194] The offspring chromosomes in the list of mutations generated by crossover are mutated. According to the chromosome structure, two mutation methods are designed: random gene site mutation and random gene fragment mutation.

[0195] 1) Random gene site variation

[0196] For the mutated chromosome, set n gene sites to be mutated, follow the basic stop requirements of the gene site "OD-train", and regenerate a train stop plan that is different from the one before the mutation. Figure 9 As shown in the figure, the randomly selected mutation gene sites are [1, 3, 4], that is, the stop plan of the “OD-train” [“0-2”, “1-2”, “1-3”] is mutated and regenerated.

[0197] 2) Random gene segment mutation

[0198] For the mutated chromosome, set two endpoints of the gene segment to be mutated, follow the basic stop requirements of the "OD-train" in the gene segment, and regenerate a train stop plan that is different from the one before the mutation. Figure 10 As shown, the randomly selected mutant gene segment is [1-3], that is, the stop plan of the “OD-train” [“0-2”, “0-3”, “1-2”] is mutated and regenerated.

[0199] Similar to the "crossover operation", the mutation results of the mutated offspring chromosomes also need to be determined.

[0200] To ensure that the offspring chromosomes generated after mutation are different from the parent chromosomes, the initial candidate sets of parent and offspring chromosomes are compared.

[0201] If the initial candidate set of the mutated offspring chromosome is different from the parent chromosome, it means that a new offspring chromosome is generated, and the offspring chromosome is saved in the successful mutation list; if the initial candidate set of the mutated offspring chromosome is the same as the parent chromosome, the mutated gene site selected at this time is saved in the failed mutation list, and the mutated gene site or gene fragment is reselected. When the randomly generated mutated gene site or fragment is not in the failed mutation list, the mutation is performed according to the gene site or fragment.

[0202] If the mutation failure list reaches the maximum limit, the chromosome to be mutated is eliminated and the other chromosomes in the mutation list are mutated. If all chromosomes in the mutation list are eliminated, the mutation operation is exited and the crossover operation is returned to obtain the chromosome to be mutated again.

[0203] If after the mutation operation, there is at least one offspring chromosome in the mutation success list that has completed the crossover and mutation operations, then the offspring chromosomes in the to-be-mutated list (the offspring chromosomes that have successfully crossed over) are merged with the offspring chromosomes in the mutation success list to form a list of offspring candidate chromosomes, and the mutation operation ends.

[0204] The above steps complete the entire design and solution process of a hybrid heuristic algorithm based on column generation and genetic algorithms. This method combines a classic genetic algorithm with a column generation algorithm. Following the principle that all freight demand OD must be served, the initial candidate set required by the column generation algorithm is compiled into chromosomes in the genetic algorithm. A certain number of initial candidate sets are randomly generated using the genetic algorithm. The column generation algorithm is then used to solve the optimal target value vector, train operation plan, and traffic distribution plan for the high-speed rail freight train operation plan. The optimal target value vector is used as the fitness value of each chromosome in the genetic algorithm. Then, according to the iterative evolution of the genetic algorithm, the optimal chromosome is selected as the final approximate optimal solution after generation-by-generation solution update, thus obtaining the high-speed rail freight train operation plan.

[0205] The heuristic algorithm proposed in this invention, which is a hybrid of column generation and genetic algorithm, uses genetic algorithm encoding to construct the initial candidate set, and uses column generation algorithm to design the train candidate set solution model and freight demand and cargo flow allocation model. By continuously iterating, it selects the approximate optimal solution, reduces the difficulty of solving the original model, and improves the solution efficiency. The overall algorithm structure is designed based on the genetic algorithm framework. First, the chromosome structure form is encoded to clarify the chromosome structure form. According to the population size, a chromosome list with the initial candidate set attributes is randomly generated. The column generation algorithm is used to construct the train candidate set solution model. The current optimal train candidate set is substituted into the basic optimization model M1 to obtain the fitness value of the chromosome of the initial candidate set. The fitness value of each chromosome in the initial population is calculated one by one. Then, according to the rules of selection, crossover, and mutation of the genetic algorithm, the next generation of a new population is generated and the fitness value calculation, population genetic evolution and termination judgment are performed. Finally, the global optimal solution or a satisfactory approximate optimal solution is output, and the algorithm ends.

[0206] The core of the hybrid heuristic algorithm lies in the train candidate set solution and fitness calculation. By constructing a constrained main problem model M2 for solving the train candidate set based on a column generation algorithm and a subproblem model M3 for generating freight trains, a filtered and reduced set of candidate trains with defined operating sections, origins and destinations, out-of-bounds service conditions, and stop plans is obtained. This train candidate set is then used as a known condition to determine the train operation frequency, freight flow distribution plan, and two objective function values ​​through M4 and M5, which are decomposed using a priority method. These two objective function values ​​are then prioritized and formed into a vector form, which serves as the fitness value of the chromosome in the genetic algorithm.

[0207] (6) An actual high-speed railway line was selected for case analysis to obtain a high-speed railway freight train operation plan and freight flow allocation plan under the case parameters to verify the effectiveness of the proposed algorithm, including:

[0208] (1) Example design

[0209] As an example, a one-way high-speed railway line consisting of six stations, LZ, LN, CQ, GY, GL, and GZ, is selected. The distances between the stations on the line are known.

[0210] Since high-speed freight trains and mixed freight trains have not yet been put into operation, we used the national express delivery volume that high-speed freight can serve as the cargo source. We obtained the inter-city express delivery volume for the top 100 cities by express delivery volume in China and related cities along the example route in 2023-2024. We used principal component analysis to estimate the inter-city express delivery volume for each city in 2023, taking into account factors such as each city's express delivery volume, total freight volume, regional GDP, value added of the tertiary industry, total retail sales of consumer goods, per capita disposable income of urban and rural households, per capita consumer expenditure, and permanent population. We then designed a sharing rate model to calculate the inter-city express delivery volume in each city that could be served by high-speed freight, taking into account the timeliness, economy, and safety of four modes of transportation: road, air, high-speed rail, and conventional rail mail trains. We then used a gravity model to calculate the express delivery volume between cities, ultimately determining the freight out-of-pocket (OD) demand between stations along the example route. The unit-cycle freight OD demand was given as the initial known condition.

[0211] In addition, considering the large-scale growth of model decision variables and constraints with the increase in the number of stations and trains, in order to enable the constructed model to be solved accurately, the results of the model's exact solution and the algorithm's iterative solution were compared in detail. The time period was further divided into 4-hour units in a day, and the first time period of the day from the start time of the operating skylight at 6:00 to 10:00 am was selected for example calculation.

[0212] The relevant parameters involved in optimization model M1 are shown in Tables 1 through 3. The example design specifies various parameters, including high-speed rail line conditions, train (carriage) operating parameters, and freight transportation costs. To facilitate the calculation of the example, it is assumed that each section and station has the same throughput capacity per unit cycle, and that the high-speed rail freight train consists of eight cars, with each car identical in condition.

[0213] Table 1 Example station and section information table

[0214]

[0215] Table 2 Example cargo flow OD demand table (unit: tons / unit cycle)

[0216]

[0217] Table 3 Train and line related parameters

[0218]

[0219] (2) Analysis of solution results

[0220] A hybrid heuristic algorithm based on column generation and genetic algorithm is used to solve model M1 to obtain the high-speed railway freight train operation plan. The algorithm initialization settings are shown in Table 4.

[0221] Table 4 Initial parameter settings of hybrid heuristic algorithm

[0222]

[0223] Through the iterative calculation of the hybrid heuristic algorithm, the trend of the objective function value change of all generated chromosomes and the trend of the optimal objective function value change of each generation are obtained as follows: Figure 11 and Figure 12 shown.

[0224] In the 32nd generation population, the optimal chromosome objective function value reaches 1997704 yuan / unit cycle, and the relevant information of the final approximate optimal solution is as follows:

[0225] (1) Initial freight train set

[0226] There are 12 freight trains in the initial train set, and the stops of each train are shown in the following table.

[0227] Table 5 Initial freight train set

[0228]

[0229] (2) Train candidate set after solving the train generation algorithm

[0230] By solving the column generation algorithm, we obtain an updated set of freight train candidates, which includes 18 types of freight trains. The stop conditions of each train are shown in the following table.

[0231] Table 6 Train sets added by the train generation algorithm

[0232]

[0233] Through the train generation algorithm, 6 new freight trains are added to the train candidate set.

[0234] (3) Train operation plan and freight flow distribution plan

[0235] At this time, the 18 freight trains are substituted into the priority-based linear models M4 and M5, and after eliminating the invalid stops in the running trains, the approximately optimal train running set and freight flow distribution are obtained as follows: Figure 13 and Figure 14 shown.

[0236] As shown in the above freight train operation chart, the set of trains to be operated based on freight OD demand includes 6 types of trains, and a total of 6 freight trains need to be operated.

[0237] The cross-sectional freight flow of the six types of freight trains in operation is as follows Figure 15As shown in the figure, the algorithm for solving the high-speed railway freight train operation plan is completed, and its objective function value is [730504, 58727.8].

[0238] The heuristic algorithm of the fusion column generation algorithm and the genetic algorithm proposed by the method of the present invention is different from the existing direct solution model in the solution process and solution efficiency, which is specifically manifested as follows: (1) Solution process

[0239] The direct solution model is to include all trains that meet the basic stop number and mileage conditions into the candidate set for traversal solution. It can be understood that the number of trains stored in the train candidate set is In the hybrid heuristic algorithm solution, the initial train candidate set consists of randomly generated trains that meet the basic stop number and mileage conditions and can serve all ODs. It can be understood that the number of trains stored in the initial train candidate set is at most [OD logarithms], since various randomly generated trains can often serve multiple ODs at the same time, after removing the initial trains of the same category, the number of trains in the initial train set is greatly reduced. The updated train candidate set obtained by the column generation algorithm has a much smaller number of stored trains than the number of train candidate sets directly traversed.

[0240] (2) Solution efficiency

[0241] The efficiency of the direct solution model for obtaining the linear optimal solution increases nearly exponentially with the number of stations. The convergence rate of integer solutions within the convergence time range also decreases significantly, with the convergence accuracy ranging from [1.40% to 3.44%]. Compared to the direct solution method, the present invention randomly generates an initial set of train candidates, updates the set of train candidates using a train generation algorithm, and then solves the operation plan and freight flow allocation model, significantly improving the solution efficiency.

[0242] From the perspective of solution efficiency, as the number of stations increases, the solution efficiency of the hybrid heuristic algorithm is significantly better than the direct solution. Therefore, when facing the problem of designing train operation plans for high-speed rail lines with a large scale and a large number of stations, the use of a hybrid heuristic algorithm can more efficiently obtain train operation plans.

[0243] As an embodiment disclosed in the present invention, the present invention further provides a high-speed railway freight train operation optimization device, which is used to implement the method described above, including:

[0244] Establish a module for building a dual-objective nonlinear model for optimizing the operation of high-speed freight trains;

[0245] A first decomposition module is used to decompose the dual-objective nonlinear model into a train candidate set restriction main model and a freight train candidate set generation sub-model based on the column generation algorithm principle;

[0246] The second decomposition module is used to decompose the dual-objective nonlinear model of operation optimization into a first single-objective optimization model and a second single-objective optimization model;

[0247] The first solving module is used to solve the train candidate set restriction main model and the freight train candidate set generation sub-model based on the high-speed rail freight train candidate set, and obtain the current optimal freight train candidate set with the initial freight train candidate set as the starting point;

[0248] A second solving module is configured to substitute the current optimal freight train candidate set into the first single-objective optimization model and the second single-objective optimization model to solve and obtain an optimal target value vector;

[0249] The optimal solution module is used to use the optimal target value vector as the fitness value of each chromosome in the genetic algorithm, and then obtain the optimal chromosome as the final optimal solution output based on the iterative evolution of the genetic algorithm, that is, to obtain the optimization plan for the operation of high-speed railway freight trains.

[0250] As an embodiment disclosed in the present invention, the present invention further provides an electronic device, the electronic device comprising:

[0251] a memory storing executable instructions;

[0252] A processor is configured to execute the executable instructions in the memory to implement the method.

[0253] The foregoing description shows and describes several preferred embodiments of the present invention. However, as previously stated, it should be understood that the present invention is not limited to the form disclosed herein and should not be construed as excluding other embodiments. Rather, the present invention can be used in various other combinations, modifications, and environments and can be modified within the scope of the application concept described herein by the teachings above or by techniques or knowledge in the relevant field. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention are intended to be protected by the appended claims.

Claims

1. A method for optimizing the operation of high-speed railway freight trains, characterized in that: The method comprises: S1. Establish a dual-objective nonlinear model for optimizing high-speed rail freight train operations. The dual-objective nonlinear model includes an objective function for minimizing high-speed rail train operating costs, an objective function for minimizing total freight transportation time, constraints on freight demand satisfaction, constraints on train and freight flow coupling, constraints on train carrying capacity, constraints on section throughput capacity, constraints on station operating capacity, and constraints on the values ​​of model decision variables. S2. Based on the principles of the column generation algorithm, the dual-objective nonlinear model is decomposed into a main model for train candidate set constraints and a sub-model for freight train candidate set generation. The main model for train candidate set constraints includes a high-speed train operating cost objective function, interval throughput constraints, station operation capacity constraints, train carrying capacity constraints, interval cross-sectional flow satisfaction constraints, train assignment constraints, and train operation frequency decision variables. The objective function of the sub-model for freight train candidate set generation is calculated by mixing the high-speed train operating cost objective function, a test number, and a simplex multiplier. S3. Decompose the dual-objective nonlinear model for train operation optimization into a first single-objective optimization model and a second single-objective optimization model, wherein the objective function of the first single-objective optimization model includes the high-speed rail train operating cost objective function, freight flow demand satisfaction constraint, train flow and freight flow coupling constraint, train carrying capacity constraint, section through capacity constraint, station operation capacity constraint, and model decision variable value constraints; and the second single-objective optimization model includes the objective function of minimizing total freight transportation time, freight flow demand satisfaction constraint, train flow and freight flow coupling constraint, train carrying capacity constraint, section through capacity constraint, station operation capacity constraint, model decision variable value constraints, and newly added constraints; S4. Solve the train candidate set constraint main model and the freight train candidate set generation sub-model based on the high-speed rail freight train candidate set to obtain the current optimal freight train candidate set starting from the initial freight train candidate set; S5. Substitute the current optimal freight train candidate set into the first single-objective optimization model and the second single-objective optimization model to obtain the optimal target value vector; S6. The optimal target value vector is used as the fitness value of each chromosome in the genetic algorithm. Then, the optimal chromosome is obtained according to the iterative evolution of the genetic algorithm as the final optimal solution output, that is, the high-speed rail freight train operation optimization plan is obtained.

2. The method according to claim 1, characterized in that The S4 specifically includes: S41. Generate an initial set of freight train candidates randomly using genetic algorithm chromosomes; S42. Substitute the initial freight train candidate set into the train candidate set restriction master model based on the column generation algorithm, and solve the current optimal objective function value, each constraint simplex multiplier, and related test number of the train candidate set restriction master model; S43. Substitute each constrained simplex multiplier into the freight train candidate set generation submodel based on the column generation algorithm to obtain the freight train candidate set generation submodel; S44. Determine whether a new freight train can be added to the train candidate set. If so, return to step S42. If not, obtain the current optimal freight train candidate set starting from the initial freight train candidate set.

3. The method according to claim 1, characterized in that The S6 specifically includes: S61: Save the chromosome with the best fitness value in the parent population into the offspring population list; S62: Using a roulette wheel method, set the number of roulette wheel selections per round m, where m ≥ 4, generate a uniformly distributed pseudo-random number r in the interval [0, 1], select the corresponding chromosome from the offspring population list according to the value of r and enter the roulette wheel candidate list, and select the two chromosomes with the best fitness values ​​from the list of m candidate chromosomes and enter the list to be crossed and mutated; S63: After the two best chromosomes complete the crossover and mutation operations in the list to be crossed and mutated, the new chromosomes or the parent chromosomes that have not been actually operated due to the crossover and mutation probability are saved in the offspring candidate chromosome list, and the fitness value of each chromosome in the list is calculated. The chromosome with the best fitness value is selected and saved in the offspring population.

4. A high-speed railway freight train operation optimization device, characterized in that: The device is used to implement the method according to any one of claims 1 to 3, comprising: Establish a module for building a dual-objective nonlinear model for optimizing the operation of high-speed freight trains; A first decomposition module is used to decompose the dual-objective nonlinear model into a train candidate set restriction main model and a freight train candidate set generation sub-model based on the column generation algorithm principle; The second decomposition module is used to decompose the dual-objective nonlinear model of operation optimization into a first single-objective optimization model and a second single-objective optimization model; The first solving module is used to solve the train candidate set restriction main model and the freight train candidate set generation sub-model based on the high-speed rail freight train candidate set, and obtain the current optimal freight train candidate set with the initial freight train candidate set as the starting point; A second solving module is configured to substitute the current optimal freight train candidate set into the first single-objective optimization model and the second single-objective optimization model to solve and obtain an optimal target value vector; The optimal solution module is used to use the optimal target value vector as the fitness value of each chromosome in the genetic algorithm, and then obtain the optimal chromosome as the final optimal solution output based on the iterative evolution of the genetic algorithm, that is, to obtain the optimization plan for the operation of high-speed railway freight trains.

5. An electronic device, characterized in that: The electronic device comprises: a memory storing executable instructions; A processor, wherein the processor runs the executable instructions in the memory to implement the method according to any one of claims 1 to 3.

Images