High-speed rail freight train operation optimization method, device and equipment

Abstract

The invention relates to a high-speed rail freight train operation optimization method, device and equipment. The high-speed rail freight train operation optimization method comprises the following steps: establishing an operation optimization double-target nonlinear model of a high-speed rail freight train; decomposing into a train alternative set limitation main model, a freight train alternative set generation sub-model, a first single-target optimization model and a second single-target optimization model according to different modes; solving a train alternative set limitation main model and a freight train alternative set generation sub-model according to the high-speed rail freight train alternative set to obtain a current optimal freight train alternative set taking the initial freight train alternative set as a starting point; substituting into the first single-target optimization model and the second single-target optimization model to solve and obtain an optimal target value vector; and solving the optimal target value vector by adopting a genetic algorithm to obtain an optimal chromosome, and outputting the optimal chromosome as a final optimal solution. According to the method, the genetic algorithm and the column generation algorithm are combined, economical efficiency and transport capacity requirements are considered, matching of cargo flow and train flow is achieved, and a feasible high-speed rail freight train operation optimization scheme is obtained.

Description

Technical Field

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

[0002] The train operation plan is based on passenger and freight volumes, and is based on the nature, characteristics, and laws of passenger and freight flows. It scientifically and reasonably arranges the content including train operation grades, types, starting and ending points, passing routes, formation content, stop plans, train capacity utilization, car body operation, etc., reflecting the organization plan from passenger and freight flows to train flows. The design of the train operation plan involves many contents and is affected by various factors, belonging to a large-scale combinatorial optimization problem. For the design problem of the high-speed rail freight train operation plan, on the basis of the traditional train operation plan design problem, it is necessary to fully consider the complex road network conditions of high-speed rail transportation, and combine the freight transportation organization mode and the characteristics of freight flow distribution to design the high-speed rail freight train operation plan, and the solution difficulty is more complex. The complexity of the solution difficulty of the high-speed rail freight train operation plan design directly leads to core problems such as multi-dimensional resource coordination conflicts, difficulty in balancing economic and timeliness objectives, and low real-time decision-making efficiency in actual operation. Specifically, the coordination of multiple constraints such as station operation capacity, section passing capacity, and EMU turnover is insufficient, which is prone to cause local resource overload or idleness; in addition, the efficiency of generating plans in a high-dimensional solution space is low, and it is difficult to generate transportation plans efficiently. In addition, a low-cost plan needs to reduce the train operation frequency and the number of stops, but it will prolong the goods transfer time; a high-timeliness plan needs to run trains intensively and increase stops, but it will push up the operation cost, and the traditional single-objective optimization or simple weighting method cannot balance the dynamic game relationship between the two. Summary of the Invention

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

[0004] A method for optimizing the operation of high-speed rail freight trains, the method comprising: S1. Establish a bi-objective nonlinear model for optimizing the operation of high-speed rail freight trains; S2. Based on the principle of column generation algorithm, decompose the bi-objective nonlinear model into a train alternative set restricted master model and a freight train alternative set generation sub-model; S3. Decompose the bi-objective nonlinear model for optimizing the operation into a first single-objective optimization model and a second single-objective optimization model; S4. Solve the train alternative set restricted master model and the freight train alternative set generation sub-model according to the high-speed rail freight train alternative set to obtain the current optimal freight train alternative set starting from the initial freight train alternative set; S5. Substitute the current optimal freight train alternative set into the first single-objective optimization model and the second single-objective optimization model to solve for the optimal objective value vector; S6. Use the optimal objective value vector as the fitness value of each chromosome in the genetic algorithm, and then solve through the iterative evolution of the genetic algorithm to obtain the optimal chromosome as the final optimal solution for output, that is, obtain the optimized plan for the operation of high-speed rail freight trains.

[0005] In the aspect and any possible implementation manner as described above, a further implementation manner is provided. The bi-objective non-linear model includes an objective function for minimizing the operation cost of high-speed rail trains, an objective function for minimizing the total freight transportation time, a freight demand satisfaction constraint, a coupling constraint between train flow and freight flow, a train carrying capacity constraint, a section passing capacity constraint, a station operation capacity constraint, and a value constraint for the decision variables of the model.

[0006] In the aspect and any possible implementation manner as described above, a further implementation manner is provided. The train alternative set restriction main model includes an objective function for the operation cost of high-speed rail trains, a section passing capacity constraint, a station operation capacity constraint, a train carrying capacity constraint, a section flow satisfaction constraint, a train assignment constraint, and a decision variable for the train operation frequency.

[0007] In the aspect and any possible implementation manner as described above, a further implementation manner is provided. The objective function of the freight train alternative set generation sub-model is obtained by a mixed calculation of the objective function for the operation cost of high-speed rail trains, the reduced cost, and the simplex multiplier.

[0008] In the aspect and any possible implementation manner as described above, a further implementation manner is provided. The objective function of the first single-objective optimization model includes an objective function for the operation cost of high-speed rail trains, a freight flow demand satisfaction constraint, a coupling constraint between train flow and freight flow, a train carrying capacity constraint, a section passing capacity constraint, a station operation capacity constraint, and a value constraint for the decision variables of the model.

[0009] In the aspect and any possible implementation manner as described above, a further implementation manner is provided. The second single-objective optimization model includes an objective function for minimizing the total freight transportation time, a freight flow demand satisfaction constraint, a coupling constraint between train flow and freight flow, a train carrying capacity constraint, a section passing capacity constraint, a station operation capacity constraint, a value constraint for the decision variables of the model, and an additional constraint.

[0010] In the aspect and any possible implementation manner as described above, a further implementation manner is provided. Specifically, S4 includes: S41. Use the genetic algorithm chromosome to randomly generate an initial freight train alternative set; S42. Substitute the initial freight train alternative set into the train alternative set restricted master model based on the column generation algorithm, and solve to obtain the current optimal objective function value of the train alternative set restricted master model, the simplex multipliers of each constraint, and the relevant test numbers; S43. Substitute the simplex multipliers of each constraint into the freight train alternative set generation sub-model based on the column generation algorithm, and solve to obtain the freight train alternative set generation sub-model; S44. Determine whether a new freight train can be added to the train alternative set. If so, return to step S42. If not, obtain the current optimal freight train alternative set starting from the initial freight train alternative set.

[0011] In the above aspects and any possible implementation manners, a further implementation manner is provided. The S6 specifically includes: S61: Save the chromosome with the optimal fitness value in the parent population into the offspring population list; S62: Adopt the roulette wheel method, set the number of roulette wheel selections m per round, where m≥4. Generate a uniformly distributed pseudo-random number r in the interval [0, 1]. Select the chromosome corresponding to r in the offspring population list to enter the roulette wheel candidate list, and select the two chromosomes with the best fitness values from the list of m candidate chromosomes to enter the list for crossover and mutation; S63: After completing the crossover operation and mutation operation on the two best chromosomes in the list for crossover and mutation, save the new-born chromosomes or the parent chromosomes that have not undergone actual operations due to the crossover and mutation probabilities into the offspring alternative chromosome list. Calculate the fitness values of each chromosome in the list, and select the chromosome with the optimal fitness value among them to save into the offspring population.

[0012] The present invention also provides a high-speed rail freight train operation optimization device integrating the column generation algorithm and the genetic algorithm. The device is used to implement the above method, and includes: A building module, used to build a double-objective non-linear model for optimizing the operation of high-speed rail freight trains; A first decomposition module, used to decompose the double-objective non-linear model into a train alternative set restricted master model and a freight train alternative set generation sub-model based on the principle of the column generation algorithm; A second decomposition module, used to decompose the double-objective non-linear model for operation optimization into a first single-objective optimization model and a second single-objective optimization model; A first solving module, used to solve the train alternative set restricted master model and the freight train alternative set generation sub-model according to the high-speed rail freight train alternative set, and obtain the current optimal freight train alternative set starting from the initial freight train alternative set; A second solution module, configured to substitute the current optimal freight train alternative set into a first single-objective optimization model and a second single-objective optimization model to solve and obtain an optimal objective value vector; An optimal solution calculation module, configured to use the optimal objective value vector as the fitness value of each chromosome in the genetic algorithm, and then solve through iterative evolution of the genetic algorithm to obtain the optimal chromosome as the final optimal solution for output, that is, to obtain an optimized high-speed rail freight train operation plan.

[0013] The present invention also provides an electronic device, which includes: A memory storing executable instructions; A processor that runs the executable instructions in the memory to implement the method.

[0014] Advantages of the present invention The optimized high-speed rail freight train operation method of the present invention includes: establishing an optimized double-objective non-linear model for high-speed rail freight train operation; decomposing the double-objective non-linear model into a train alternative set restricted main model, a freight train alternative set generation sub-model, a first single-objective optimization model, and a second single-objective optimization model in different ways; solving the train alternative set restricted main model and the freight train alternative set generation sub-model according to the high-speed rail freight train alternative set to obtain a current optimal freight train alternative set starting from the initial freight train alternative set; substituting it into the first single-objective optimization model and the second single-objective optimization model to solve and obtain an optimal objective value vector; using the genetic algorithm to solve the optimal objective value vector to obtain the optimal chromosome as the final optimal solution for output. In the column generation algorithm structure part of the present invention, first, a train alternative set that takes into account both economy and transport capacity demand constraints is selected. Secondly, a freight flow distribution model is constructed under the goal of minimizing the operation cost of high-speed rail freight trains based on the alternative set to achieve the matching of freight flow and train flow, and a feasible high-speed rail freight train operation plan is obtained. The genetic algorithm structure part uses the column generation algorithm structure as the calculation method of the fitness value of each chromosome in the genetic algorithm, generates an initial feasible train set in the column generation algorithm through the genetic algorithm, compares the fitness values of each chromosome in each generation of the population, and iteratively obtains a satisfactory high-speed rail freight train operation plan. It has fewer iteration times, faster calculation speed, and better optimization effect. Description of the drawings

[0015] Figure 1 is the flowchart of the method of the present invention; Figure 2 is an example diagram of a two-dimensional chromosome structure of the present invention; Figure 3 is an example diagram of freight OD demand of the present invention; Figure 4 is an example diagram of a two-dimensional matrix random train stop plan of the present invention; Figure 5It is an example diagram for determining the initial alternative set of the present invention; Figure 6 It is an example diagram for random gene locus crossover of the present invention; Figure 7 It is an example diagram for random gene fragment crossover of the present invention; Figure 8 It is an example diagram for determining the crossover result of the present invention; Figure 9 It is an example diagram for random gene locus mutation of the present invention; Figure 10 It is an example diagram for random gene fragment mutation of the present invention; Figure 11 It is a trend diagram of the objective function values of all generated chromosomes of the present invention; Figure 12 It is the optimal objective function value Z of each generation of the present invention 1 ' trend diagram; Figure 13 It is a diagram of the operating set of high - speed rail freight trains of the present invention; Figure 14 It is a diagram of the freight flow distribution plan for each high - speed rail freight special train of the present invention; Figure 15 It is a cross - section flow diagram of the present invention. Detailed implementation manners

[0016] For a better understanding of the technical solution of the present invention, the content of the present invention includes but is not limited to the following detailed implementation manners. Similar technologies and methods should be regarded as within the scope of protection of the present invention. To make the technical problems, technical solutions and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the drawings and specific embodiments.

[0017] It should be clear that the embodiments described in the present invention are only a part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts belong to the scope of protection of the present invention.

[0018] 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 of "a", "the" and "said" used in the embodiments of the present invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0019] As Figure 1 shown, the present invention provides an optimization method for operating high - speed rail freight trains, and the method includes: S1. Establish a bi - objective non - linear model for optimizing the operation of high - speed rail freight trains; S2. Based on the principle of column generation algorithm, the dual-objective nonlinear model is decomposed into a train candidate set restriction main model and a freight train candidate set generation sub-model; S3. Decomposing the dual-objective nonlinear model of the optimization of the operation into a first single-objective optimization model and a second single-objective optimization model; S4. solving the train candidate set restriction main model and the freight train candidate set generation sub-model according to the high-speed rail freight train candidate set, and obtaining the current optimal freight train candidate set starting from the initial freight train candidate set; S5. Substituting 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, and 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 railway freight train operation optimization plan is obtained.

[0020] Furthermore, the dual-objective nonlinear model includes an objective function of minimizing the operating cost of high-speed rail trains, an objective function of minimizing the total freight transportation time, freight demand satisfaction constraints, train flow and freight flow coupling constraints, train carrying capacity constraints, section passing capacity constraints, station operating capacity constraints, and value constraints on model decision variables.

[0021] Furthermore, the train alternative set restriction main model includes high-speed rail train operating cost objective function, section throughput capacity constraints, station operation capacity constraints, train carrying capacity constraints, section flow satisfaction constraints, train assignment constraints and train operation frequency decision variables.

[0022] Furthermore, the objective function of the freight train candidate set generation sub-model is obtained by mixed calculation of the high-speed rail train operation cost objective function, the test number and the simplex multiplier.

[0023] 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 constraints, train flow and freight flow coupling constraints, train carrying capacity constraints, section passing capacity constraints, station operating capacity constraints and model decision variable value constraints.

[0024] 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, section passing capacity constraints, station operating capacity constraints, model decision variable value constraints and new constraints.

[0025] Furthermore, the S4 specifically includes: S41. using genetic algorithm chromosomes to randomly generate an initial freight train candidate set; S42. Substitute the initial freight train alternative set into the train alternative set restricted master model based on the column generation algorithm, and solve to obtain the current optimal objective function value, each constraint simplex multiplier, and related test numbers of the train alternative set restricted master model; S43. Substitute each constraint simplex multiplier into the freight train alternative set generation sub-model based on the column generation algorithm, and solve to obtain the freight train alternative set generation sub-model; S44. Determine whether a new freight train can be added to the train alternative set. If yes, return to step S42; if not, obtain the current optimal freight train alternative set starting from the initial freight train alternative set.

[0026] Specifically, the implementation process of the present invention is as follows: A high-speed rail freight operation optimization method integrating the column generation algorithm and the genetic algorithm specifically includes the following steps: (1) Model the basic optimization problem of the high-speed rail freight train operation plan as a bi-objective non-linear optimization model M1; (2) Based on the principle of the column generation algorithm, decompose the constructed high-speed rail freight train operation plan optimization model M1 into a train alternative set restricted master problem model M2 and a freight train alternative set generation sub-problem model M3; (3) Perform multi-objective processing and fitness value setting on the high-speed rail freight train operation plan optimization model M1; (4) Use the set models M2 and M3, and adopt the column generation algorithm to iteratively solve the train alternative set and calculate the fitness value; (5) Design a hybrid heuristic algorithm based on the column generation and genetic algorithm to solve the original problem model M1, and obtain the optimal high-speed rail freight train operation plan and freight flow distribution plan; (6) Select an actual high-speed rail line for case analysis, obtain the high-speed rail freight train operation plan and freight flow distribution plan under the case parameters, and verify the effectiveness of the proposed algorithm.

[0027] The following specifically describes the detailed operation process of each part: The high-speed rail freight train operation plan optimization model M1 in step (1) needs to satisfy the freight demand satisfaction constraint, the train flow and freight flow coupling constraint, the train carrying capacity constraint, the section 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 constraint conditions of the model are as follows: Relevant parameters: S represents the set of high-speed rail stations, e, i, j represent the indices 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 set of sections, represents the section from station i to station i + 1; ZL represents the set of section distances, Denote the distance between station \(i\) and station \(i + 1\); \(G\) represents the set of freight demands. Denote the freight flow demand from station \(i\) to station \(j\). Represents the set of high - speed freight trains. Denote The index of Denote the number of freight trains. Represents the fixed cost of freight transportation, yuan / ton. Represents the variable cost of freight transportation, the part related to distance cost, yuan / ton - km. Represents the fixed cost of operating a freight train, yuan / train. Represents the variable cost of operating a freight train related to distance, yuan / train - km. Represents the variable cost of operating a freight train related to stops, yuan / train - stop. Represents the upper limit of the carrying capacity of the section within a unit period, number of trains. Represents the upper limit of the operating capacity of station \(i\) within a unit period, number of trains. Represents the fixed load capacity of a freight train, tons. Represents the lower limit of the number of stops of a freight train throughout the journey, stops. Represents the upper limit of the number of stops of a freight train throughout the journey, stops. Represents the lower limit of the total running mileage of a freight train, km. Represents the upper limit of the total running mileage of a freight train, km. Represents the average running speed of a freight train, km / h. Represents the stop time of a freight train during intermediate stops, minutes. Represents the additional starting and stopping time generated during the intermediate stops of a freight train, minutes; \(M\) represents an infinitely large positive number.

[0028] Decision variables: Denote whether the freight train stops at station \(i\), a 0 - 1 variable, taking 1 if it stops and 0 if it doesn't stop. Denote whether the freight train passes through the section , a 0 - 1 variable, taking 1 if it does and 0 if it doesn't. Denote whether station \(i\) is the origin station of the freight train , a 0 - 1 variable, taking 1 if it is and 0 if it isn't. Denote whether station \(i\) is the destination station of the freight train , a 0 - 1 variable, taking 1 if it is and 0 if it isn't. Denote the number of trips of the freight train during the statistical period, an integer variable. Denote whether the freight train can serve the freight demand The 0-1 variable takes the value of 1 instead of 0; represents the freight flow assigned to the freight train from station i to station j on the freight train, which is an integer variable.

[0029] (1) Model objective function Minimize the total operating cost of high-speed rail trains: (1), where Z 1 represents the minimum total operating cost of high-speed rail trains; Minimize the total freight transportation time: (2), where Z 2 represents the minimum total freight transportation time.

[0030] (2) Model constraint conditions Freight flow demand satisfaction constraint: (3) Train flow and freight flow coupling constraint: (4) Train carrying capacity constraint: (5), where represents the starting station of the line, represents the terminal station of the line.

[0031] Section passing capacity constraint: (6) Station operation capacity constraint: (7) Model decision variable value constraint: (8) (9), where N represents the set of natural numbers.

[0032] Optimization model M1 for the operation plan of high-speed rail freight trains: Objective function: Formulas (1), (2) Constraint conditions: Formulas (3)-(7) Decision variables: Formulas (8)-(9) The specific steps of decomposing the optimization model of the operation plan of high-speed rail freight trains based on the principle of column generation algorithm in step (2) are as follows: According to the design of the algorithm flow of the operation plan of high-speed rail freight trains, the column generation algorithm is combined in the overall algorithm to solve the train alternative set, and the chromosome fitness value and the train operation plan are obtained by substituting them into the operation plan and the freight flow distribution plan model. Based on the principle of the column generation algorithm, the problem of solving the train alternative set is decomposed into the train alternative set restricted master problem model M2 and the freight train alternative set generation sub-problem model M3, and the current optimal train alternative set based on the given initial alternative set is obtained through iterative solution.

[0033] The column generation algorithm is a very efficient algorithm for solving large-scale linear optimization problems. Essentially, the column generation algorithm is a form of the simplex method, and its theoretical basis was proposed by Danzig and Wolfe in 1960, known as the DW decomposition principle. It decomposes the original linear programming problem into a master problem (MP) and several sub-problems (SP), that is, allocates the linear programming problem constraints to the main layer and the attached layer. The genetic algorithm is a method for searching for the optimal solution by simulating the natural evolution process.

[0034] For models with relatively small scales, the column generation algorithm can, according to the model structure and problem characteristics, artificially give an initial solution that meets the conditions, and then gradually add columns that contribute to restricting the optimization objective of the master problem based on the initial solution. Since the scale of the entire solution set is limited and the overall solution scale is not large, generally the optimal solution can be found eventually. However, when faced with large-scale linear programming problems, their solution spaces often have too many dimensions. Since the selection of the initial feasible solution directly affects the acquisition of the optimal solution of problem MP, choosing different feasible initial solutions to solve using the column generation algorithm often results in different approximate solutions, and it is easy to fall into a local optimal solution when starting iterative calculations from only a certain feasible initial solution. In order to obtain the global optimal solution or a 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 group of relatively satisfactory initial solutions to find a finally acceptable satisfactory solution, and the MP optimal solution is not uniquely restricted by the selection of the initial feasible solution, so it is not necessary to globally traverse all feasible initial solutions.

[0035] The genetic algorithm starts from a population representing the possible potential solution set of the problem, and a population is composed of a certain number of individuals encoded by genes. Each individual is actually an entity with characteristics of a chromosome. The present invention combines the genetic algorithm with the column generation algorithm, compiles the initial solution of the column generation algorithm as a chromosome, and designs a hybrid heuristic algorithm. The column generation algorithm requires the generation of a certain scale of random initial solutions to ensure a sufficient large search solution space coverage range, and the random search characteristics of the genetic algorithm can be adapted to it. At the same time, the optimization ability and convergence efficiency of the genetic algorithm are limited by the setting of the fitness value of the randomly generated chromosomes. The column generation algorithm solves the train alternative set to further optimize the initial train alternative set. From the perspective of the overall algorithm design, it is also an optimization process for the fitness value of the genetic algorithm chromosomes, significantly enhancing the optimization ability and convergence efficiency of the genetic algorithm, and having good effects. Therefore, the present invention combines the column generation algorithm and the genetic algorithm, and uses different algorithms at different processing stages.

[0036] Step 1: According to the above-mentioned column generation algorithm principle, construct the restricted master model M2 of the train alternative set based on the column generation algorithm. The solution of M2 mainly selects a more suitable alternative set of trains for M1. Therefore, based on M1, only the part related to the train operation frequency decision variables in M1 is retained, and the part related to the freight flow allocation decision variables is deleted.

[0037] Specifically as follows: (1) Objective function part Among the two objective functions of M1, the objective function of the high-speed train operation cost, that is, formula (1), is expressed as the product of the freight train operation frequency and the actual operation cost of a single freight train, which is only related to the train operation frequency. Therefore, it can be directly used as the optimization objective of M2. In addition, the objective function formula (2) is related to the freight demand, so it is not considered.

[0038] (2) Constraint condition part The section passing capacity constraint (formula (6)) and the station operation capacity constraint (formula (7)) in M1 are only related to the train operation frequency decision variables. Therefore, they are directly used in M2.

[0039] The part of the freight demand satisfaction constraint in M1 is only related to the freight flow allocation decision variables. Therefore, it is directly discarded in M2. The part of the train carrying capacity constraint, the coupling constraint of the train flow and the freight flow in M1 are related to both the train operation plan decision variables and the freight flow allocation decision variables. Therefore, certain transformation processing is required in M2.

[0040] 1) The train carrying capacity constraint is transformed into the section flow satisfaction constraint The mathematical meaning of the train carrying capacity constraint part is that the carrying capacity of each train passing through any section should 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 transformed into the section flow satisfaction constraint.

[0041] The size of the section flow depends on the loading capacity of the train and the section flow demand. That is, for any section, the total freight demand of all OD freight demands covering this section should be less than the sum of the loading capacities of all trains that can serve this section. The section flow satisfaction constraint is as follows: (10) Mathematically, the section flow satisfaction constraint relaxes the relationship between the flow satisfaction of each train and the carrying capacity of each train, and transforms it into the relationship between the flow satisfaction of all flows passing through this section and the total carrying capacity of all trains serving this section. From the perspective of the restriction of the constraint condition on the solution space, the section flow satisfaction constraint reduces the restriction on the solution space.

[0042] 2) The coupling constraint between train flow and freight flow is transformed into a train assignment constraint. The mathematical meaning of the coupling constraint between train flow and freight flow is the matching relationship between all high-speed trains passing through a certain OD demand and whether the OD demand flow is allocated to the high-speed train. In order to remove the freight flow allocation decision, the coupling constraint between train flow and freight flow is transformed into a train assignment constraint.

[0043] The train assignment constraint means that when there is a certain OD demand, there must be a train serving this OD. Its expression is as follows: (11) Mathematically, similar to the constraint satisfied by the sectional flow, the train assignment constraint relaxes the coupling constraint between train flow and freight flow to a certain extent. It relaxes the coupling relationship between each train serving an OD and the OD allocated on the train to the assignment relationship between a certain OD demand and all trains serving this OD. From the perspective of the restriction of the constraint condition on the solution space, the train assignment constraint reduces the restriction on the solution space.

[0044] (3) Decision variable part Only the train operation frequency decision variables in M1 are retained in the decision variable part.

[0045] The complete restricted master model M2 of the train alternative set is expressed as follows: Objective function: Equation (1) Constraint conditions: Equations (6)-(7), (10)-(11) Decision variables: Equation (9) The solution objective of the freight train alternative set generation sub-problem is to select trains that meet the conditions and can further optimize the objective function of the restricted master problem for the train alternative set. These added trains also need to have attributes such as the definite origin and destination of the train, the train operation section, and the train stop plan.

[0046] The objective function of the freight train alternative set generation sub-model M3 is determined by the objective function, the reduced cost, and the simplex multipliers of the restricted master model M2. The objective function of the freight train alternative set generation sub-model M3 is expressed as: (12) The specific constraint conditions are obtained by linearizing the constraints related to the freight train operation conditions in model M1 as follows: Train service OD stop constraint: (13) (14), where represents the freight train whether it stops at station j, a 0-1 variable, taking 1 if it stops and 0 if it does not stop.

[0047] (15) Train origin and destination stop constraints: (16) (17) (18) (19) Train stop range constraints: (20), where indicates whether to stop at station e, a 0-1 variable, taking 1 if yes and 0 if no.

[0048] (21) Train passing interval range constraints: a. All intervals between the origin and destination of the train operation line are passing intervals: (22), where indicates whether station j is the final destination of the freight train , a 0-1 variable, taking 1 if yes and 0 if no.

[0049] b. The train must not pass through intervals outside the origin and destination: (23), where indicates whether station e is the origin station of the freight train, a 0-1 variable, taking 1 if yes and 0 if no.

[0050] (24) Train stop number constraints: (25) Train running mileage constraints: (26) Train origin and destination quantity constraints: (27) (28) Train line station sequence constraints: (29) Train stop decision variable: (30) Train demand service decision variable: (31) Train passing interval decision variable: (32) Train origin and destination decision variable: (33) (34) Among them, in formula (12), except for the variables and parameters already defined in M1, Denote the simplex multiplier of freight trains for the passing capacity constraint of sections, i.e., the "resource" price represented by the passing capacity of sections; Denote the simplex multiplier of freight trains for the station operation capacity constraint, i.e., the "resource" price represented by the receiving and dispatching capacity of stations; Denote the simplex multiplier of freight trains for the constraint that the sectional flow meets the requirements, i.e., the "resource" price represented by the sectional flow meeting the requirements; Denote the simplex multiplier of freight trains for the train assignment constraint, i.e., the "resource" price represented by the train assignment.

[0051] The complete sub-model M3 for generating the alternative set of freight trains is expressed as follows: Objective function: Equation (12) Constraint conditions: Equations (13)-(32) Decision variables: Equations (33)-(34) Step (3): The specific steps for multi-objective processing and fitness value setting of model M1 are as follows: Step 1: Use the priority method to decompose the operation plan optimization model M1 of high-speed rail freight trains with multiple objectives into two single-objective optimization models M4 and M5.

[0052] The single-objective optimization model M4 specifically includes: Objective function: Equation (1) Constraint conditions: Equations (3)-(7) Decision variables: Equations (8), (9) The single-objective optimization model M5 specifically includes: Objective function: Equation (2) Constraint conditions: Equations (3)-(7) and new constraints (35) where Z 1 * is the optimal objective value obtained by solving model M4.

[0053] Decision variables: Equations (8), (9) The steps for solving the multi-objective linear model M1 using the priority method are as follows: First, optimize the objective function (1) alone, i.e., solve model M4, to obtain the minimum value of the operation cost of high-speed rail freight trains; subsequently, under the condition of considering the new constraint (35), optimize the objective function (2) alone, i.e., solve model M5, to obtain the minimum value of the total cargo transportation time. Express the two objective function values of M1 obtained by solving through the priority method as a target vector solution with priorities [Z1 * , Z2 * , and use this to form the fitness value of the chromosome in the genetic algorithm for subsequent comparison and selection.

[0054] The multi-objective model M1 is decomposed into two single-objective models M4 and M5 by the priority method to achieve the goal of preferentially optimizing the minimization of the total operating cost. The total freight transportation time is secondarily optimized on the basis of the optimal operating cost. The single-objective model simplifies the solution process and avoids the complexity of the multi-objective algorithm. This processing conforms to the decision-making logic of "cost control first and timeliness improvement second" in actual operation. While ensuring the quality of the solution, the computational complexity is significantly reduced.

[0055] Step (4): The specific steps for solving the train alternative set and calculating the fitness value based on the column generation algorithm are as follows: Step 1: Chromosome encoding. Construct a chromosome class and clarify the structural characteristics of each chromosome. Since all freight OD demands are required to be met, when the number of high-speed railway stations on the line is assuming that there are OD demands between any two stations, there are a total of OD pairs that require train service. Without considering the case where a single train serves multiple OD pairs, a total of trains need to be selected to correspond to the OD one by one. Combining the requirements of the "train service OD stop constraint", the trains corresponding to the OD demand must stop at the origin and destination stations of the OD. Therefore, taking "OD-train-station" as the encoding object, a two-dimensional chromosome structure is constructed, and the scale of the two-dimensional matrix is which represents the stop plan of the trains corresponding to different OD demands. The specific values therein represent the stop selection of a certain "OD-train" at the corresponding station. Taking the Figure 2 two-dimensional matrix as an example, the chromosome structure two-dimensional matrix represents the stop plan matrix of 6 columns of "OD-trains" at 4 stations. Taking the first row as an example, the stop plan of the "OD-train" "0-1" serving the OD demand "0-1" is [1, 1, 0, 0].

[0056] The main structure of the chromosome encoding module is a two-dimensional matrix composed of the number of OD demands and the number of stations. Therefore, taking the two-dimensional "OD-train-station" as the encoding object, the chromosome main structure is constructed. According to the number of stations |S| on the line to be solved, the scale of the two-dimensional matrix array is determined to be In addition, it also includes attributes such as the initial alternative set of this chromosome, the train alternative set after the solution of this chromosome, the fitness value of this chromosome, the train operation plan and the flow allocation plan corresponding to this chromosome.

[0057] Step 2: Generation of the initial train alternative set. It is used to compile the specific values of the two-dimensional "OD-train-station" matrix for the new chromosomes generated in the population, and at the same time determine the initial alternative set information for the chromosomes to further obtain attributes such as fitness values. Therefore, it can be further divided into two parts: chromosome structure assignment and initial alternative set determination.

[0058] 1) Chromosome structure assignment part The operation of assigning values to the two-dimensional matrix is essentially to determine the stop plans of the "OD-trains". First, it is necessary to judge whether there is a demand, that is, whether there is a freight demand between two stations. If the OD demand does not exist, there is no need to determine the stop plan of the OD-compiled service train, and all the values of the train stop plan list corresponding to this OD are set to "0"; then, following the requirements of the "Train Service OD Stop Constraint", the current "OD-train" must stop at the starting and ending stations of the current OD, and the corresponding station positions are taken as "1", and the other stations are randomly taken as "0" or "1". By analogy, the stop plan values of each "OD-train" in the freight two-dimensional matrix can be completed.

[0059] Suppose the freight OD demand of the high-speed rail line is as Figure 3 shown. The stop plans of each OD train are determined respectively according to whether there is a freight demand as Figure 4 shown. Among them, the starting and ending stations of the OD served by the train must stop, and the stop plans of the trains at other stations are randomly generated. In the freight two-dimensional matrix, since the freight OD demand flow from 0 to 3 is 0, the corresponding "OD-train" "1-3" is set not to run, that is, all the stops at the stations are taken as "0".

[0060] 2) Initial alternative set determination part The determination of the initial alternative set is different from the train list after chromosome assignment. After chromosome assignment, the stop plans of the OD demand logarithm trains are determined. To ensure the integrity of the chromosome structure, the generated trains are not processed. What the alternative set saves is the train sequence with different stop plans. Therefore, to obtain the initial alternative set, it is necessary to de-duplicate the chromosome train list, that is, only add the trains with different stop plans into the initial alternative set. As Figure 5 shown, after de-duplication, the initial alternative set containing freight trains is obtained. Specifically, it includes the following steps: Step 1: Generation of the freight train alternative set.

[0061] Step 2: Solving the master problem of the train alternative set restriction. Substitute the initial freight train alternative set into the train alternative set restriction master model M2 based on the column generation algorithm, and call the optimization solver Cplex to solve this model using the branch and bound method or other solution methods to obtain the current optimal objective function value of this model, the simplex multipliers of each constraint, and the relevant test numbers.

[0062] Step 3: Solving the sub-problem of generating freight trains. Substitute the simplex multipliers related to freight trains in each constraint obtained in Step 2 into the freight train generation sub-model M3 based on the column generation algorithm, and use Cplex to solve this model to obtain the new freight trains to be added to the alternative set through the solution.

[0063] Step 4: Determination of adding freight train alternatives. Determine the solution result of Step 3. If "① there is no solution in Step 3, ② the obtained objective function value is greater than or equal to 0, that is, the test number meets the optimal solution condition, ③ a group of freight trains with attributes such as stop plans, driving starting and ending points, operation sections, driving mileage, stop times, and operation costs obtained by solving exists in the current train alternative set". If any of the three determination conditions is met, it means that the current train alternative set can no longer optimize the restricted master problem objective function by adding new types of freight trains. At this time, enter Step 5; if all three determination conditions are not met, add the new freight train information solved by the model in Step 3 into the freight train alternative set, update the current train alternative set, and return to Step 2.

[0064] Step 5: Solve the train operation plan, cargo flow distribution plan, and fitness value. At this time, the update of the freight train alternative set is completed, and the restricted master problem objective function cannot be further optimized by adding new types of freight trains. Therefore, the current optimal freight train alternative set starting from the initial freight train alternative set is obtained. Substitute the current optimal freight train alternative set into the linearized equivalent models M4 and M5 in turn, and call Cplex to solve using the branch and bound method to obtain the current optimal objective function value vector, freight train operation plan, and cargo flow distribution plan.

[0065] Step 6: Return the fitness value vector, train operation plan, and cargo flow distribution plan. Assign the optimal objective function value vector obtained by solving according to Step 3 to the fitness value vector of the chromosome of the initial freight train alternative set, and save the train operation plan, cargo flow distribution plan, and train alternative set in the chromosome attributes. It should be noted that since the fitness value vector represents a multi-objective function value vector with priorities, and 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 selection in the genetic algorithm, the objective function (1) can be directly selected for comparison until the objective function (1) no longer improves further or reaches the maximum number of iterations, and then the objective function (2) is solved.

[0066] 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 cargo flow distribution plan, specifically including: Step 1: Save the chromosome with the optimal fitness value in the parent population into the offspring population list.

[0067] Step 2: Use the roulette wheel selection method to set the number of selections m in each round of roulette wheel comparison, where m ≥ 4. Generate a pseudo-random number r uniformly distributed in the interval [0, 1]. According to the value of r, select the corresponding chromosome in the list of the offspring population to enter the roulette wheel candidate list. Select the two chromosomes with the best fitness values from the list of m candidate chromosomes to enter the list for crossover and mutation.

[0068] Step 3: After completing the crossover operation and mutation operation on the two best chromosomes in the list for crossover and mutation, save the newly generated chromosomes or the parent chromosomes that have not undergone actual operations due to crossover and mutation probabilities into the list of alternative chromosomes for the offspring. Calculate the fitness values of each chromosome in the list through the "solution process of train alternative sets" and the "solution process of train operation plans and flow allocation plans" in step (4), and select the chromosome with the optimal fitness value among them to save into the offspring population.

[0069] The specific crossover operation includes: Perform crossover operations on the two chromosomes to be crossed selected through roulette wheel selection in the parent population. According to the chromosome structure form, design two crossover methods: random gene point crossover and random gene segment crossover.

[0070] 1) Random gene point crossover For the two chromosomes to be crossed, set n gene points to be crossed, where the gene points are the numbered positions of "OD - train". Correspondingly, cross - exchange the n gene points of the two chromosomes. As Figure 6 shown, the randomly selected crossover gene points are [0, 3, 4], that is, cross - exchange the stop - station plans of the "OD - train" ["0 - 1", "1 - 2", "1 - 3"]. Among them, the stop - station plans of the two parent chromosomes corresponding to the trains at gene points "0" and "3" are different, and the stop - station plans of the two parent chromosomes corresponding to the trains at gene point "4" are the same. So essentially, only gene points "0" and "3" are exchanged.

[0071] 2) Random gene segment crossover For the two chromosomes to be crossed, set 2 endpoints of gene segments to be crossed, where the gene segments are the "OD - train" gene positions included in the endpoint numbers of 2 "OD - trains". Correspondingly, cross - exchange the gene segments of the two chromosomes. As Figure 7 shown, the randomly selected crossover gene segment is [1 - 3], that is, cross - exchange the stop - station plans of the "OD - train" ["0 - 2", "0 - 3", "1 - 2"]. Among them, the stop - station plans of the two parent chromosomes corresponding to the trains on the gene segment are different.

[0072] Cross result determination. To ensure that the two offspring chromosomes generated after crossing are different from the parent chromosomes, after the exchange, the "initial alternative set generation module" needs to be called to determine the initial alternative sets of the two chromosomes to ensure that the two chromosomes after crossing are different from those before crossing. Take gene point crossing as shown in Figure 8 As shown, the initial alternative sets of the two offspring chromosomes are different from those of the parent, so they can be saved into the list of chromosomes to be mutated.

[0073] If the initial alternative sets of the two offspring chromosomes after crossing are different from those of the parent chromosomes respectively, it means that two new offspring chromosomes are generated, and the two offspring chromosomes are saved into the list of chromosomes to be mutated; if only one of the initial alternative sets of the two offspring chromosomes after crossing is different from the two parent chromosomes, it means that only one new offspring chromosome is generated, and this chromosome is saved into the list of chromosomes to be mutated, and the other chromosome with the same initial alternative set as the parent is eliminated; if the initial alternative sets of the two offspring chromosomes after crossing are the same as those of the parent chromosomes, then both offspring chromosomes are eliminated, and the crossed gene points selected at this time are saved into the cross failure list, and the crossed gene points or gene segments are reselected. When the randomly generated crossed gene points or segments are not in the cross failure list, cross according to this gene point or segment.

[0074] If the cross failure list reaches the maximum limit number, two new parent chromosomes to be crossed are reselected by roulette wheel method, and this step is carried out again.

[0075] If there is at least one chromosome to be mutated in the list of chromosomes to be mutated after the crossing operation, the crossing is successful and the crossing operation ends.

[0076] The mutation operation specifically includes: Perform mutation operations on the offspring chromosomes in the list of chromosomes to be mutated generated after crossing. According to the chromosome structure form, two mutation methods of random gene point mutation and random gene segment mutation are designed.

[0077] 1) Random gene point mutation For the chromosome to be mutated, set n gene points to be mutated, and follow the basic stop requirements of the "OD - train" at the gene points to regenerate a train stop plan different from that before mutation. As shown in Figure 9 As shown, the randomly selected mutated gene points are [1, 3, 4], that is, the stop plan of the "OD - train" ["0 - 2", "1 - 2", "1 - 3"] is mutated and regenerated.

[0078] 2) Random gene segment mutation For the chromosome to be mutated, set the endpoints of 2 gene segments to be mutated, and follow the basic stop requirements of the "OD - train" in the gene segments to regenerate a train stop plan different from that before mutation. As shown in Figure 10As shown, the randomly selected mutated gene segment is [1-3], that is, the stop plan of the "OD-train" ["0-2", "0-3", "1-2"] is mutated and regenerated.

[0079] Similar to the "crossover operation", it is also necessary to judge the mutation result of the mutated offspring chromosome.

[0080] To ensure that the offspring chromosome generated after mutation is different from the parent chromosome, compare the initial alternative sets of the parent and offspring chromosomes.

[0081] If the initial alternative set of the mutated offspring chromosome is different from that of the parent chromosome, it means that a new offspring chromosome has been generated, and then this offspring chromosome is saved into the successful mutation list; if the initial alternative set of the mutated offspring chromosome is the same as that of the parent chromosome, the selected mutated gene position at this time is saved into the failed mutation list, and a new mutated gene position or gene segment is selected. When the randomly generated mutated gene position or segment is not in the failed mutation list, mutate according to this gene position or segment.

[0082] If the failed mutation list reaches the maximum limit number, then eliminate this chromosome to be mutated and mutate other chromosomes in the list to be mutated. If all the chromosomes in the list to be mutated are eliminated, then exit the mutation operation and return to the crossover operation to obtain chromosomes to be mutated again.

[0083] If after the mutation operation, there is at least one offspring chromosome that has completed the crossover and mutation operations in the successful mutation list, then combine the offspring chromosomes (successfully crossed offspring chromosomes) in the list to be mutated with the offspring chromosomes in the successful mutation list to form a list of alternative offspring chromosomes, and the mutation operation ends.

[0084] Through the above steps, the entire process of the design and solution of the hybrid heuristic algorithm based on column generation and genetic algorithm is completed. This method combines the classic genetic algorithm and the column generation algorithm, follows the principle that all freight demand OD must be served, compiles the initial alternative set required by the column generation algorithm into the chromosomes in the genetic algorithm, randomly generates a certain number of initial alternative sets through the genetic algorithm, uses the column generation algorithm to solve the optimal objective value vector, train operation plan and flow allocation plan of the high-speed rail freight train operation plan, and uses the optimal objective value vector 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 generation by generation after updating and output as the final approximate optimal solution, and the high-speed rail freight train operation plan can be obtained.

[0085] The heuristic algorithm combining column generation and genetic algorithm proposed by the present invention constructs an initial alternative set by using genetic algorithm encoding, designs a train alternative set solution model and a freight demand freight flow allocation model by using column generation algorithm, and selects an approximate optimal solution through continuous iteration, reducing the solution difficulty of the original model and improving the solution efficiency. The overall algorithm structure is designed based on the genetic algorithm framework. First, the chromosome structure form is clearly encoded, a chromosome list with the attributes of the initial alternative set is randomly generated according to the population size, the train alternative set solution model is constructed by using column generation algorithm, the current optimal train alternative set is substituted into the basic optimization model M1 to obtain the fitness value of the chromosome of this initial alternative set, the fitness values of each chromosome in the initial population are calculated one by one, and then according to the rules of selection, crossover and mutation of genetic algorithm, a new population of the next generation is generated for fitness value calculation, population genetic evolution and termination judgment, and finally the global optimal solution or a satisfactory approximate optimal solution is output, and the algorithm ends.

[0086] The core part of the entire hybrid heuristic algorithm is the train alternative set solution and fitness value calculation part. By constructing a train alternative set solution restricted master problem model M2 and a freight train generation sub-problem model M3 based on column generation algorithm, a set of alternative train sets with screened and reduced scale, having operation sections, starting and ending points, OD service conditions, and stop plans can be obtained. Next, taking this train alternative set as a known condition, the train operation frequency, freight flow allocation plan and two objective function values are further determined through M4 and M5 decomposed by the priority method, and the two objective function values of this model are formed into a vector form according to the priority ranking as the fitness value of the chromosome in the genetic algorithm.

[0087] (6)Select an actual high-speed railway line for case analysis, obtain the high-speed railway freight train operation plan and freight flow allocation plan under the case parameters, and verify the effectiveness of the proposed algorithm, specifically including: (1)Example design The example selects a one-way high-speed railway line composed of six stations LZ, LN, CQ, GY, GL, and GZ on a certain high-speed railway line, and the distances between the stations on the line are known.

[0088] Since high-speed rail freight trains and freight mixed trains have not been actually operated, the volume of express delivery services across the country that high-speed rail freight can serve is used as the source of goods. The off-site express delivery volume of the top 100 cities in the country and relevant cities on the example routes in 2023-2024 is obtained. Considering various factors such as the express delivery volume, total freight volume, regional GDP, added value of the tertiary industry, total retail sales of social consumer goods, per capita disposable income of urban and rural household, per capita consumption expenditure of residents, and permanent population in each city, the off-site express delivery volume of each city in 2023 is calculated through the principal component analysis method. Considering the timeliness, economy, and safety of four transportation modes, namely highway, aviation, high-speed rail, and express train on the general speed railway, a sharing rate model is designed to calculate the off-site express delivery volume of each city that can be served by high-speed rail freight. Further, the express delivery volume between cities is calculated through the gravity model, and finally, the freight flow OD demand between stations on the example route is determined. The freight OD demand in the unit cycle is given as the initial known condition.

[0089] In addition, considering the large-scale growth of the model decision variables and constraint conditions with the increase in the number of stations and trains, in order to enable the established model to be accurately solved and to compare the results of accurate model solution and algorithm iteration solution in detail, the unit time period is further divided into 4-hour units in a day, and the first time period from 6:00, the start time of the operation skylight, to 10:00 in the morning is selected for example calculation.

[0090] The relevant parameters involved in the optimization model M1 are shown in Tables 1 to 3. Various parameters such as the high-speed rail operation line conditions, train (carriage) operation related parameters, and cargo transportation costs are specified in the example design. Among them, for the convenience of example solution calculation, it is assumed that the passing operation capacity of each station in each interval is the same within the unit cycle, the formation structure of the high-speed rail freight train is 8-car formation, and the situation of each carriage is exactly the same.

[0091] Table 1 Information Table of Example Stations and Intervals

[0092] Table 2 Example Freight Flow OD Demand Table (Unit: ton / unit cycle)

[0093] Table 3 Table of Train and Line Related Parameters

[0094] (2)Analysis of Solution Results The hybrid heuristic algorithm based on column generation and genetic algorithm is used to solve the model M1 to obtain the operation plan of high-speed rail freight trains. The initial settings of the algorithm are shown in Table 4.

[0095] Table 4 Initial Parameter Settings of Hybrid Heuristic Algorithm

[0096] Through iterative calculation of the hybrid heuristic algorithm, the change trends of the objective function values of all generated chromosomes and the change trends of the optimal objective function values of each generation are as follows Figure 11 and Figure 12 shown

[0097] In the 32nd generation population, the objective function value of the optimal chromosome reaches 1,997,704 yuan / unit cycle. The relevant information of the finally generated approximate optimal solution is as follows (1) Initial freight train set In the initial train set, there are 12 freight trains in total. The stop conditions of each train are shown in the following table

[0098] Table 5 Initial freight train set

[0099] (2) Train alternative set after solving by column generation algorithm Through the solution of the column generation algorithm, an updated freight train alternative set is obtained, in which there are 18 freight trains. The stop conditions of each train are shown in the following table

[0100] Table 6 Train set added by column generation algorithm update

[0101] By solving with the column generation algorithm, 6 new freight trains are added to the train alternative set

[0102] (3) Train operation plan and freight flow distribution plan At this time, substituting 18 freight trains into the priority-based linear models M4 and M5, after removing the invalid stops in the operating trains, the approximate optimal train operation set and freight flow distribution are as follows Figure 13 and Figure 14 shown

[0103] As shown in the above freight train operation chart, the obtained train operation set based on freight OD demand includes 6 types of trains in total, and 6 freight trains need to be operated

[0104] The sectional freight flow of the 6 operated freight trains is as follows Figure 15 shown. Thus, the algorithm for solving the high-speed rail freight train operation plan ends, and its objective function value is [730,504, 58,727.8]

[0105] The heuristic algorithm that combines the 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. The specific manifestations are as follows: (1) In terms of the solution process The direct solution model includes all trains that meet the conditions of the basic stop times and running mileage in the alternative set for traversal and solution. It can be understood that the number of trains stored in the train alternative set is . In the solution of the hybrid heuristic algorithm, the initial train alternative set is composed of trains randomly generated that meet the conditions of the basic stop times and running mileage and can correspondingly serve all OD pairs. It can be understood that the maximum number of trains stored in the initial train alternative set is [the number of OD pairs]. Since various randomly generated trains can often serve multiple OD pairs at the same time, after removing the initial trains of the same category, the number of trains in the initial train set is significantly reduced. After obtaining the updated train alternative set through the column generation algorithm, the number of stored trains is also much smaller than the number of trains in the alternative set traversed by the direct solution.

[0106] (2)In terms of solution efficiency The solution efficiency of the direct solution model to obtain the linear optimal solution shows nearly exponential growth with the increase in the number of stations. The convergence speed of the integer solution within the convergence time range also decreases significantly, and the convergence accuracy range is between [1.40%, 3.44%]. Compared with the direct solution method, the present invention randomly generates the initial train alternative set, updates the train alternative set through the column generation algorithm, and then solves the train operation plan and the cargo flow distribution plan model, resulting in a significant improvement in solution efficiency.

[0107] From the perspective of solution efficiency, as the number of stations increases, the solution efficiency of the hybrid heuristic algorithm is significantly better than that of the direct solution. Therefore, in the face of the problem of designing the train operation plan for high-speed railway lines with a large scale and a large number of stations, the hybrid heuristic algorithm can obtain the train operation plan more efficiently.

[0108] As an embodiment disclosed in the present invention, the present invention also provides an optimization device for the operation of high-speed railway freight trains. The device is used to implement the method, including: A building module, used to build a double-objective nonlinear model for the optimization of the operation of high-speed railway freight trains; A first decomposition module, used to decompose the double-objective nonlinear model into a main model restricted by the train alternative set and a sub-model for generating the freight train alternative set based on the principle of the column generation algorithm; A second decomposition module, used to decompose the double-objective nonlinear model for the optimization of the operation into a first single-objective optimization model and a second single-objective optimization model; A first solution module, used to solve the main model restricted by the train alternative set and the sub-model for generating the freight train alternative set according to the freight train alternative set of high-speed railway trains, and obtain the current optimal freight train alternative set starting from the initial freight train alternative set; A second solution module, used to substitute the current optimal freight train alternative set into the first single-objective optimization model and the second single-objective optimization model to solve and obtain the optimal objective value vector; The optimal solution calculation module is used to take the optimal objective value vector as the fitness value of each chromosome in the genetic algorithm, and then solve through the iterative evolution of the genetic algorithm to obtain the optimal chromosome as the final optimal solution output, that is, to obtain the optimized operation plan for high-speed rail freight trains.

[0109] As an embodiment disclosed in the present invention, the present invention also provides an electronic device, which includes: A memory storing executable instructions; A processor that runs the executable instructions in the memory to implement the described method.

[0110] The above description shows and describes several preferred embodiments of the present invention. However, as mentioned above, it should be understood that the present invention is not limited to the form disclosed herein, should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications, and environments, and can be changed within the scope of the application concept described herein through the above teachings or the technology or knowledge in related fields. And the changes and modifications made by those skilled in the art that do not depart from the spirit and scope of the present invention should all be within the protection scope of the appended claims of the present invention.

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 the operation of high-speed rail freight trains; S2. Based on the principle of column generation algorithm, the dual-objective nonlinear model is decomposed into a train candidate set restriction main model and a freight train candidate set generation sub-model; S3. Decomposing the dual-objective nonlinear model of the optimization of the operation into a first single-objective optimization model and a second single-objective optimization model; S4. solving the train candidate set restriction main model and the freight train candidate set generation sub-model according to the high-speed rail freight train candidate set, and obtaining the current optimal freight train candidate set starting from the initial freight train candidate set; S5. Substituting 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, and then the optimal chromosome is obtained according to the iterative evolution of the genetic algorithm as the final optimal solution output, that is, the optimization plan for the operation of high-speed railway freight trains is obtained.

2. The method according to claim 1, characterized in that The dual-objective nonlinear model includes an objective function of minimizing the operating cost of high-speed rail trains, an objective function of minimizing the total freight transportation time, freight demand satisfaction constraints, train flow and freight flow coupling constraints, train carrying capacity constraints, section passing capacity constraints, station operating capacity constraints, and value constraints of model decision variables.

3. The method according to claim 1, characterized in that The train alternative set restriction main model includes high-speed rail train operation cost objective function, section throughput capacity constraint, station operation capacity constraint, train carrying capacity constraint, section flow satisfaction constraint, train assignment constraint and train operation frequency decision variables.

4. The method according to claim 3, characterized in that The objective function of the freight train candidate set generation sub-model is obtained by mixed calculation of the high-speed rail train operation cost objective function, the test number and the simplex multiplier.

5. The method according to claim 2, characterized in that: The objective functions of the first single-objective optimization model include the high-speed rail train operating cost objective function, freight flow demand satisfaction constraints, train flow and freight flow coupling constraints, train carrying capacity constraints, section passing capacity constraints, station operating capacity constraints and model decision variable value constraints.

6. The method according to claim 2, characterized in that 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, section passing capacity constraints, station operating capacity constraints, model decision variable value constraints and new constraints.

7. The method according to claim 1, characterized in that The S4 specifically includes: S41. Generate an initial freight train candidate set randomly using genetic algorithm chromosomes; S42. Substitute the initial freight train candidate set into the train candidate set restriction main 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 main 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 yes, return to step S42. If no, obtain the current optimal freight train candidate set starting from the initial freight train candidate set.

8. 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 child population list; S62: Using a roulette wheel method, set the number of roulette wheel comparisons in each round m, where m≥4, generate a uniformly distributed pseudo-random r in the interval [0, 1], select the corresponding chromosome in 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 to enter the list to be crossed and mutated; S63: After the best two chromosomes complete the crossover operation and mutation operation 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 candidate chromosomes for the offspring, and the fitness value of each chromosome in the list is calculated, and the chromosome with the best fitness value is selected and saved in the offspring population.

9. 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 8, comprising: Establish a module for establishing 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 according to 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 used 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.

10. 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 8.

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