A railway car flow routing optimization method based on variable neighborhood search algorithm

Abstract

The present invention discloses a method for optimizing the railway car flow routing based on the variable neighborhood search algorithm. First, a mixed integer linear programming model that conforms to the tree-shaped characteristics of the railway car flow routing and the principle that a single flow cannot be split is constructed, and a heuristic algorithm adapted to the railway car flow routing optimization model is designed based on the variable neighborhood search algorithm. Then, the heuristic algorithm is used to solve the optimization model to obtain the optimal solution. The method of the present invention can optimize the railway network car flow routing problem on the basis of considering the network transportation capacity limitation and the tree-shaped characteristics of the routing, and can effectively solve problems such as the large variety of goods properties, the complex network, and the frequent goods exchange between important nodes in the railway freight transportation network; compared with the existing algorithms, it has the advantages of high solution efficiency and good solution quality, and when applied to large-scale cases, the solution efficiency is improved to a greater extent.

Description

Technical Field

[0001] The present invention relates to the technical field of railway transportation, and particularly relates to a method for optimizing railway car flow routing based on a variable neighborhood search algorithm. Background Art

[0002] The railway car flow routing is one of the most important bases and references for compiling the formation plan of freight trains. Due to the fact that China's railway freight transportation network is more complex than that of other countries, involving a wide variety of freight flow natures, and with the continuous advancement of the "highway to railway" strategy and the development of new transportation modes under the low-carbon economy, the goods exchange between important railway nodes is more frequent. Under such a background, it is obviously unreasonable and extreme to allocate the car flow on the railway network according to the shortest path. Therefore, it is of great significance to optimize the railway network car flow routing problem on the basis of considering the network transport capacity limit and the tree-like characteristics of the routing.

[0003] When organizing the car flow at technical stations in China's railway, the principles of non-splittability of single-strand car flow and merger of car flow connection need to be followed. This makes the railway car flow routing have unique tree-like characteristics, and general forms of car flow routing optimization models, such as the point-arc model and the arc-path model, cannot be directly applied to railway transportation and need to be modified. Then, a railway tree-shaped car flow routing optimization model based on the association relationship between car flow and sections is proposed according to the modeling idea of the traditional car flow routing model. Since the car flow routing and the formation plan belong to medium- and long-term plans, the quality of the plan is more critical than the time consumed in formulating the plan. Therefore, an exact algorithm that can obtain the global optimal solution is the first choice for solving the car flow routing model or the integrated optimization model with the formation plan. However, with the expansion of the problem scale, under the limited computer memory capacity, the exact algorithm may be difficult to obtain the optimal solution within an acceptable time, or even unable to obtain a feasible solution. The present invention provides a method for optimizing railway car flow routing based on a variable neighborhood search algorithm to solve the above problems. Summary of the Invention

[0004] The present invention provides a method for optimizing railway car flow routing based on a variable neighborhood search algorithm, which can obtain a relatively high-quality approximate optimal solution within an acceptable time or with limited computing resources.

[0005] The technical solution adopted by the present invention to solve the above technical problems is as follows:

[0006] A method for optimizing railway car flow routing based on a variable neighborhood search algorithm includes the following steps:

[0007] S1, constructing a model: constructing an optimization model for railway car flow routing that meets the section passing capacity;

[0008] S2, designing an algorithm: designing a heuristic algorithm adapted to the railway car flow routing optimization model based on the variable neighborhood search algorithm;

[0009] S3. Optimize model solution: Use a heuristic algorithm to solve the optimization model and obtain the optimal solution.

[0010] Furthermore, based on the modeling ideas of the classic point-arc model and arc-path model in the vehicle flow distribution model, a model is constructed. The constructed railway vehicle flow routing optimization model is a mixed integer linear programming model that conforms to the tree-like characteristics of railway vehicle flow routing and the principle that a single flow cannot be split.

[0011] Furthermore, the railway vehicle flow routing optimization model is as follows:

[0012]

[0013] The objective function (1) represents the sum of the running costs of all vehicles;

[0014] The constraint conditions are as follows:

[0015]

[0016] The constraint condition formula (2) means that for the vehicle flow routing from station i to station j, the first arc segment of it should start from station i and only one station adjacent to station i can be selected as the end point of this arc segment;

[0017]

[0018] The constraint condition formula (3) means that for the vehicle flow from station i to station j, the last arc segment of its routing should end at station j and there is only one last arc segment;

[0019]

[0020] The constraint condition formulas (4) and (5) mean that for the vehicle flow between adjacent stations, it can only be transported through the arc segment between these adjacent stations and cannot choose other arc segments for detour transportation;

[0021]

[0022] The constraint condition formula (6) is used to ensure the continuity of the vehicle flow routing; that is, for the vehicle flow from station i to station j, if its routing includes station t, then among the arc segments that make up this routing, the sum of the number of arc segments starting from station t should be equal to the sum of the number of arc segments ending at station t;

[0023]

[0024] For a certain vehicle flow in the road network, the constraint condition formula (7) is used to assist in eliminating unreasonable arc segments; for example, for the vehicle flow from station i to station j, the vehicle flow routing should obviously not include arc segments ending at station i or starting at station j;

[0025]

[0026] The constraint equation (8) indicates that the routing of the vehicle flow has a tree-like characteristic; that is, the vehicle flow from station i to station j can only select a certain forward station adjacent to station i as the first arrival station.

[0027]

[0028] The constraint equation (9) is a logical relationship expression between the decision variable and the auxiliary variable; when the vehicle flow from station i to station j selects the arc segment [s, t] for transportation, according to the tree-like mechanism of the vehicle flow routing, the vehicle flow from station s to station j must select station t as the first forward station.

[0029]

[0030] The constraint equation (10) is the mileage constraint of the detour route of the vehicle flow; the concept of the relative detour rate threshold γ Detour is introduced in the model, that is, for a certain vehicle flow, the vehicle flow routes available for it include the shortest route, and also include the routes whose physical mileage is within γ Detour times the shortest route mileage after removing the arc segment mileage shared with the shortest route.

[0031]

[0032] The constraint equation (11) is the passing capacity constraint of the line section.

[0033] In order to unify with the optimization model of the freight train formation plan, the passing capacity of the line here is given in units of trains; actually, the average number of cars formed by trains in different directions is not the same, but since the vehicle flow routing plan does not involve issues such as the distribution and selection of formation destinations during the formulation process, the average number of cars formed by trains in different directions is not distinguished in the vehicle flow routing optimization model.

[0034]

[0035] The constraint equation (12) is the flow balance constraint on the road network.

[0036]

[0037] The constraint equation (13) is the constraint on the variable value range.

[0038] The symbol definitions in the objective function and constraints are as follows:

[0039] (1) Sets,

[0040] V: The set of all stations in the railway network;

[0041] V F (i): The set of all forward stations adjacent to station i in the railway network;

[0042] E: The set of all line sections in the railway network;

[0043] (ii) Parameter,

[0044] N ij : The original traffic volume from station i to station j, unit: vehicle;

[0045] L ij : The shortest path mileage from station i to station j, unit: kilometer;

[0046] C st : The maximum passing capacity of section [s, t], unit: train;

[0047] l st : The physical mileage of section [s, t], unit: kilometer;

[0048] Λ ij : The total mileage of the common sections of the detour path and the shortest path of the traffic flow from station i to station j, unit: kilometer;

[0049] m: The average number of cars in a train formation, unit: vehicle;

[0050] α st : The passing capacity reserve coefficient of single-track railway section [s, t];

[0051] λ: The unit conversion coefficient of traffic flow running cost, unit: vehicle-hour / vehicle-kilometer;

[0052] γ Detour : The relative detour rate threshold of the traffic flow running path;

[0053] (iii) Decision variable, that is, the traffic flow-section association relationship variable,

[0054] If the traffic flow path from station i to station j includes section [s, t], then the value is 1, otherwise the value is 0, which is a Boolean variable;

[0055] (iv) Auxiliary variable,

[0056] Boolean variable, if the traffic flow from station i to station j selects station k as the first forward station, then the value is 1, otherwise the value is 0, which is a Boolean variable.

[0057] Furthermore, in the optimization model, the constraint condition (11) is more difficult to handle in form compared with other constraints, and it is necessary to preprocess the constraint condition (11); the preprocessing method is to add it to the objective function (1) by using the penalty function method and transform it into the following penalty term:

[0058]

[0059] where μ is a positive penalty factor;

[0060] The objective function (1) of the optimization model is reconstructed into the following energy function:

[0061]

[0062] Taking the reconstructed energy function (15) as the objective function of the railway car flow routing optimization model.

[0063] Furthermore, the heuristic algorithm is the Variable Neighborhood Search (VNS) algorithm, that is, the VNS algorithm. The specific design steps of the VNS algorithm are as follows:

[0064] S21, generation and feasibility of the initial solution: First, generate the initial solution of the VNS algorithm, and then check the feasibility of the initial solution;

[0065] S22, design of the shaking neighborhood structure: Design two neighborhood structures to complete the shaking process, including the Insert-Delete neighborhood structure and the Ruin-Insert neighborhood structure;

[0066] S23, design of the acceptance criterion: The acceptance criterion for the solution is that if the new solution is better than the current solution, accept the new solution and substitute it into the next iteration; otherwise, accept the new solution with a certain probability;

[0067] According to the solution vector S of the VNS algorithm VNS the value of the energy function cannot be directly obtained. It is necessary to transform the solution vector S VNS into the corresponding car flow - section association relationship variable x VNS , but since the solution vector S VNS can ensure that each car flow has a feasible and unique first forward station, the routing of each car flow can be determined, and then the value of the car flow - section association relationship variable x VNS can be obtained;

[0068] S24, determination of the termination criterion: Use the number of iterations, running time or the number of solution improvements as the termination condition of the VNS algorithm;

[0069] For cases with a relatively small calculation scale, choose to set the maximum number of iterations IMax is the termination condition.

[0070] Furthermore, the VNS algorithm uses the tree network composed of the first forward stations of all vehicle flows with the same terminal station but different origin stations as the initial solution. The generation steps of the initial solution are as follows:

[0071] S2101, generate a feasible vehicle flow routing that meets the mileage constraint according to the relative detour rate constraint formula (10);

[0072] S2102, generate the set V F (i) of the first forward stations corresponding to each vehicle flow i→j according to the feasible routing;

[0073] S2103, randomly select an element from the set V F (i) of the first forward stations of each vehicle flow. The tree network composed of these elements is the initial solution of the VNS algorithm

[0074] Furthermore, the initial solution generated through the operations of S2101 - S2103 may cause a circular routing. Therefore, in order to eliminate the first forward stations that cause such circular routings, it is necessary to perform a feasibility test on the initial solution of the VNS algorithm. The steps for performing a feasibility test on the initial solution are as follows:

[0075] S2111, extract the elements with a value of 1 from the initial solution vector and form a temporary solution vector S0′;

[0076] The dimension of the vector S′0 is related to the network characteristics of the problem. If the network of this problem consists of |V| nodes, then the dimension of the vector S′0 is |V|×(|V| - 1), expressed as

[0077] S2112, swap the indices of the vector S0′ to generate a test vector Compare the vector S0′ with element by element. If the elements with the same subscript also have the same superscript, it can be considered that the value of this element in the initial solution vector is unreasonable and will lead to a circular routing.

[0078] For the elements with the same subscript and if the superscript t is equal to i, that is then it means that the value of the element in the initial solution vector should not be 1; for the elements and if the superscript q is not equal to m, that is then it means that the element The value is reasonable;

[0079] Denote the vector composed of unreasonable elements in S0' as Denote the vector formed after removing unreasonable elements from S0' as

[0080] S2113, calculate the dimension of the vector ; if it is 0, stop the loop, let the elements in the temporary solution vector S0' take the value of 1, and the other elements in the vector take the value of 0, then a feasible initial solution vector can be obtained. Thus, the initialization of the feasible solution of the VNS algorithm is completed; otherwise, go to S2114;

[0081] S2114, let the elements in the vector take the value of 0 in the initial solution vector ; perform superscript adjustment on the elements in the vector and add the elements with superscript adjustment in the vector to the vector to form a new temporary solution vector S0', then go to S2112;

[0082] The specific adjustment operation is: to ensure that all vehicle flows can be transported to the end point, it is necessary to reselect the first forward station for the demand corresponding to the subscript of the elements in the vector . For unreasonable elements (i.e., ), let the set of the first forward stations of the demand f kj be represented as V F (k) = {..., t, u, v,...}, and the reselected first forward station should be other pivot stations except t, that is, the superscript adjustment of the elements is realized.

[0083] Through the steps of S2101 - S2103, S2111 - S2114, the initial solution of the VNS algorithm is verified and adjusted, and the generation and feasibility of the initial solution are completed.

[0084] Furthermore, as the core content of the VNS algorithm, the shaking neighborhood structure, in this embodiment, an insert - delete (Insert - Delete) neighborhood structure and a ruin - insert neighborhood structure are designed based on the idea of λ - interchange to complete the shaking process.

[0085] Among them, the specific description of the insert - delete (Insert - Delete) neighborhood structure is:

[0086] The neighborhood operation Insert is to insert an arc between two adjacent nodes. If there is already an arc connection between the two nodes, then select two other non-connected adjacent points; after inserting the arc, to satisfy the uniqueness of the first forward station, an arc connected to these two nodes before insertion should be Delete, and after deleting the arc, it should be ensured that the degree of each node in the tree-shaped network is not less than 1; each neighborhood operation only randomly selects one tree-shaped network in the current solution and performs one insertion and deletion on it to obtain a jitter solution, and only executes once. Different execution times will generate different neighborhood structures.

[0087] The specific description of the Ruin-Insert neighborhood structure is as follows:

[0088] Randomly select two tree-shaped networks in the current solution, Ruin all the associated arcs of two adjacent nodes in one network, find the arcs associated with these two adjacent nodes in the other tree-shaped network, and Insert all the arcs into the former.

[0089] Furthermore, the specific steps for solving the optimization model using the heuristic algorithm are as follows:

[0090] S31, Input the network and the original traffic flow data, and input the model and algorithm parameters;

[0091] S32, Construct a neighborhood structure set according to the relative detour rate constraint;

[0092] S33, Initialize the number of iterations and generate an initial solution, and perform a feasibility process on the initial solution;

[0093] S34, Design a jitter neighborhood structure and complete the jitter;

[0094] S35, Perform iterative operations based on the Metropolis criterion;

[0095] S36, Output the approximate optimal solution.

[0096] The beneficial effects of the present invention are as follows:

[0097] The method of the present invention can optimize the railway network traffic flow routing problem on the basis of considering the network capacity limit and the characteristics of the path tree shape, and can effectively solve problems such as the large variety of goods properties, complex network, and frequent goods exchanges between important nodes in the railway freight transport network; compared with the existing algorithms, it has the advantages of high solution efficiency and good solution quality, and when applied to large-scale cases, the solution efficiency is improved to a greater extent. Description of the Drawings

[0098] Figure 1 It is the specific flowchart of the algorithm for the railway traffic flow routing optimization method of the present invention;

[0099] Figure 2 Schematic diagram of the railway car flow routing characteristics of the present invention;

[0100] Figure 3 Schematic diagram of the overall structure of the railway network in the central region of the present invention;

[0101] Figure 4 Comparison table of line section mileage and passing capacity of the railway network of the present invention;

[0102] Figure 5 Schematic diagram of the road network structure composed of 9 pivot stations and 11 pivot stations of the present invention;

[0103] Figure 6 Schematic diagram of the road network structure composed of 13 pivot stations and 15 pivot stations of the present invention;

[0104] Figure 7 Schematic diagram of the road network structure composed of 17 pivot stations and 19 pivot stations of the present invention;

[0105] Figure 8 Schematic diagram of the road network structure composed of 21 pivot stations and 23 pivot stations of the present invention;

[0106] Figure 9 Table of example scale and road network characteristics of the present invention;

[0107] Figure 10 Comparison diagram of the solution effects of the variable neighborhood search algorithm and the exact algorithm of the present invention. Detailed implementation manners

[0108] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings of the specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0109] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.

[0110] Such as Figure 1As shown in the figure, a method for optimizing the railway car flow routing based on the variable neighborhood search algorithm includes the following steps:

[0111] S1. Construct a model: Based on the modeling ideas of the classic point-arc model and arc-path model in the car flow distribution model, construct an optimized model for the railway car flow routing that meets the section passing capacity;

[0112] Specifically, considering the mileage constraint of the detour route and the line passing capacity constraint, explore the correlation between the route of a single car flow and each line section on the road network, and establish a mixed integer linear programming model that conforms to the tree-like characteristics of the railway car flow routing and the principle that a single flow cannot be split;

[0113] S2. Design an algorithm: Design a heuristic algorithm based on the variable neighborhood search algorithm to adapt to the optimized model of the railway car flow routing;

[0114] S3. Solve the optimized model: Use the heuristic algorithm to solve the optimized model and obtain the optimal solution.

[0115] Furthermore, when the traffic volume in the railway network is determined, with the goal of minimizing the running cost of the car flow in the road network, the established optimized model for the railway car flow routing is as follows:

[0116]

[0117] The objective function (1) represents the sum of the running costs of all vehicles;

[0118] The constraint conditions are as follows:

[0119]

[0120] The constraint condition formula (2) means that for the car flow routing from station i to station j, the first arc segment should start from station i and only select a certain station adjacent to station i as the end point of this arc segment;

[0121]

[0122] The constraint condition formula (3) means that for the car flow from station i to station j, the last arc segment of its route should end at station j and there is only one last arc segment;

[0123]

[0124] The constraint condition formulas (4) and (5) mean that for the car flow between adjacent stations, it can only be transported through the arc segment between the adjacent stations and cannot choose other arc segments for detour transportation;

[0125]

[0126] The constraint equation (6) is used to ensure the continuity of the vehicle flow path; that is, for the vehicle flow from station i to station j, if its path includes station t, then among the arc segments that make up this path, the sum of the number of arc segments starting from station t should be equal to the sum of the number of arc segments ending at station t;

[0127]

[0128] For a certain vehicle flow in the road network, the constraint equation (7) is used to assist in eliminating unreasonable arc segments; for example, for the vehicle flow from station i to station j, its vehicle flow path should obviously not include arc segments ending at station i or starting at station j;

[0129]

[0130] The constraint equation (8) indicates that the vehicle flow path has a tree-like characteristic; that is, for the vehicle flow from station i to station j, only a certain forward station adjacent to station i can be selected as the first arrival station;

[0131]

[0132] The constraint equation (9) is a logical relationship expression between decision variables and auxiliary variables; when the vehicle flow from station i to station j selects the arc segment [s, t] for transportation, according to the tree-like mechanism of the vehicle flow path, the vehicle flow from station s to station j must select station t as the first forward station;

[0133]

[0134] The constraint equation (10) is the mileage constraint of the detour path of the vehicle flow; the relative detour rate threshold γ Detour is introduced in the model, that is, for a certain vehicle flow, the vehicle flow paths available for it include the shortest path, and also include paths whose physical mileage is within γ Detour times the shortest path mileage after removing the arc segment mileage shared with the shortest path;

[0135]

[0136] The constraint equation (11) is the passing capacity constraint of the line section;

[0137] To unify with the optimization model of the freight train formation plan, the line passing capacity here is given in terms of trains; actually, the average number of cars in trains in different directions is not the same, but since the vehicle flow path plan does not involve issues such as the distribution and selection of formation destinations during the formulation process, the average number of cars in trains in different directions is not distinguished in the vehicle flow path optimization model;

[0138]

[0139] The constraint equation (12) is the traffic balance constraint on the road network;

[0140]

[0141] The constraint equation (13) is the variable value range constraint.

[0142] In the above railway car flow routing optimization model, since the constraint condition (11) is more difficult to handle in form compared with other constraints, it is necessary to preprocess the constraint equation (11); the specific preprocessing method is to add it to the objective function (1) using the penalty function method and transform it into the following penalty term:

[0143]

[0144] In the formula, μ is a positive penalty factor;

[0145] After the above processing, the objective function (1) of the optimization model is reconstructed into the following energy function:

[0146]

[0147] Take the reconstructed energy function (15) as the objective function of the railway car flow routing optimization model.

[0148] The symbol definitions in the objective function and constraint conditions are as follows:

[0149] (1) Sets

[0150] V: The set of all stations in the railway network;

[0151] V F (i): The set of all forward stations adjacent to station i in the railway network;

[0152] E: The set of all line sections in the railway network;

[0153] (2) Parameters

[0154] N ij : The original traffic volume from station i to station j, unit: vehicle;

[0155] L ij : The shortest routing mileage from station i to station j, unit: kilometer;

[0156] C st : The maximum passing capacity of the section [s, t], unit: train;

[0157] l st : The physical mileage of the section [s, t], unit: kilometer;

[0158] Λij : The total mileage of the common section between the detour route and the shortest route of the traffic flow from station i to station j, unit: km;

[0159] m: The average number of cars in a train formation, unit: car;

[0160] α st : The passing capacity reserve coefficient of the single-track railway section [s, t];

[0161] λ: The unit conversion coefficient of the traffic flow running cost, unit: car-hour / car-km;

[0162] γ Detour : The relative detour rate threshold of the traffic flow running route;

[0163] (III) Decision variables, which are traffic flow-section association relationship variables,

[0164] If the traffic flow route from station i to station j includes section [s, t], the value is 1, otherwise the value is 0, which is a Boolean variable;

[0165] (IV) Auxiliary variables,

[0166] The Boolean variable, if the traffic flow from station i to station j selects station k as the first forward station, the value is 1, otherwise the value is 0, which is a Boolean variable.

[0167] The heuristic algorithm is used to solve the optimization model generated in step S1, and the principle process of using the heuristic algorithm to solve the optimization model is as follows: To ensure that the tree structure of the route is satisfied, the tree-like network formed by the first forward station is used as the initial solution, the neighborhood structure is designed to jitter the tree-like network, the local optimal solution of the traffic flow route is obtained by applying local search after generating the jitter solution, and continue to search within the neighborhood structure until the termination condition of the algorithm is met.

[0168] As Figure 1 shown, the heuristic algorithm is designed using the above principle. The heuristic algorithm is the Variable Neighborhood Search (VNS) algorithm, that is, the VNS algorithm. The specific design steps of the VNS algorithm are the generation and feasibility of the initial solution, the design of the jitter neighborhood structure, the design of the acceptance criterion, and the determination of the termination criterion.

[0169] S21, Generation and feasibility of the initial solution: First, generate the initial solution of the VNS algorithm, and then check the feasibility of the initial solution.

[0170] The VNS algorithm uses the tree - shaped network composed of the first forward stations of all vehicle flows with the same final destination but different origin stations as the initial solution, and generates the initial solution according to the operations of S2101 - S2103.

[0171] S2101, generate a feasible vehicle flow routing path that meets the mileage constraint according to the relative detour rate constraint formula (10);

[0172] S2102, generate the set V F (i) of the first forward stations corresponding to each vehicle flow i→j according to the feasible routing path;

[0173] S2103, randomly select an element from the set V F (i) of the first forward stations of each vehicle flow, and the tree - shaped network composed of these elements is the initial solution of the VNS algorithm

[0174] The initial solution generated through the operations of S2101 - S2103 may result in a circular routing path. Therefore, in order to eliminate the first forward stations that cause such circular routing paths, it is necessary to perform a feasibility check on the initial solution of the VNS algorithm and perform a feasibility check on the initial solution according to the operations of S2111 - S2114.

[0175] S2111, extract the elements with a value of 1 from the initial solution vector and form a temporary solution vector S0′;

[0176] The dimension of the vector S0′ is related to the network characteristics of the problem. If the network of this problem consists of |V| nodes, then the dimension of the vector S0′ is |V|×(|V| - 1), expressed as

[0177] S2112, swap the indices of the vector S0′ to generate a test vector Compare the elements of the vector S0′ with one by one. If the elements with the same subscript also have the same superscript, it can be considered that the value of this element in the initial solution vector is unreasonable and will lead to a circular routing path.

[0178] For the elements with the same subscript and if the superscript t is equal to i, that is then it means that the value of the element in the initial solution vector should not be 1; for the elements and if the superscript q is not equal to m, that is then it means that the value of the element is reasonable;

[0179] Denote the vector composed of unreasonable elements in S0′ as Denote the vector formed after removing unreasonable elements from S0′ as

[0180] S2113, calculate the dimension of the vector ; if it is 0, stop the loop, let the elements in the temporary solution vector S0′ take the value of 1, and the other elements in the vector take the value of 0, then the feasible initial solution vector can be obtained. Thus, the initialization of the feasible solution of the VNS algorithm is completed; otherwise, go to S2114;

[0181] S2114, let the elements in the vector take the value of 0 in the initial solution vector ; to ensure that all vehicle flows can be transported to the destination, it is necessary to reselect the first forward station for the demands corresponding to the element subscripts in the vector . For the unreasonable element (i.e., ), let the set of the first forward stations of the demand f kj be denoted as V F (k) = {..., t, u, v,...}, and the reselected first forward station should be other pivot stations except t;

[0182] Add the elements with superscript adjusted to the vector to form a new temporary solution vector S0′, and go to S2112.

[0183] Through the steps of S2101 - S2103, S2111 - S2114, generate the initial solution of the VNS algorithm, and check and adjust the feasibility of the generated initial solution to complete the generation and feasibility of the initial solution.

[0184] S22, design the shaking neighborhood structure: The shaking neighborhood structure is the core content of the VNS algorithm. The shaking solution generated by the neighborhood structure for the initial solution is related to the solution quality. Therefore, in this embodiment, based on the idea of λ - interchange, two neighborhood structures, namely the Insert - Delete neighborhood structure and the Ruin - Insert neighborhood structure, are designed to complete the shaking process.

[0185] The specific description of the Insert - Delete neighborhood structure is as follows:

[0186] The neighborhood operation Insert is to insert an arc between two adjacent nodes. If there is already an arc connection between the two nodes, then select two other non-connected adjacent points; after inserting the arc, to satisfy the uniqueness of the first forward station, an arc connected to these two nodes before insertion should be Delete, and after deleting the arc, it should be ensured that the degree of each node in the tree-shaped network is not less than 1; each neighborhood operation only randomly selects one tree-shaped network in the current solution and performs one insertion and deletion on it to obtain a jitter solution, and only executes once. Different execution times will generate different neighborhood structures.

[0187] The specific description of the Ruin-Insert neighborhood structure is as follows:

[0188] Randomly select two tree-shaped networks of the current solution, Ruin all the associated arcs of two adjacent nodes in one network, find the arcs associated with these two adjacent nodes from the other tree-shaped network, and Insert all the arcs into the former.

[0189] S23, Design the acceptance criterion: The acceptance criterion for the solution of the VNS algorithm designed in this embodiment is to judge the new solution based on the Metropolis criterion: If the new solution is better than the current solution, accept the new solution and substitute it into the next iteration; otherwise, accept the new solution with a certain probability.

[0190] According to the solution vector S of the VNS algorithm VNS the value of the energy function cannot be directly obtained. The solution vector S VNS needs to be transformed into the corresponding vehicle flow-section association relationship variable x VNS , but because the solution vector S VNS can ensure that each vehicle flow has a feasible and unique first forward station, so the running route corresponding to each vehicle flow can be determined, and then the value of the vehicle flow-section association relationship variable x VNS can be obtained.

[0191] S24, Determine the termination criterion: Use the number of iterations, running time, or the number of improvements of the solution as the termination condition of the VNS algorithm;

[0192] For cases with a relatively small computational scale, choose to set the maximum number of iterations I Max as the termination condition.

[0193] As Figure 1 shown, use the heuristic algorithm to solve the optimization model according to the steps of S31-S37.

[0194] S31, Network and original vehicle flow data, including the adjacency matrix, vehicle flow path: L ij and Λ ij , line section: lst , C st and α, O-D matrix: N ij ; model and algorithm parameters, including model parameters: λ and m, sets: V, V F (i,j) and E, maximum number of iterations: I Max ; Input the above data and parameters into the model.

[0195] S32. Construct a neighborhood structure set according to the relative detour rate constraint.

[0196] S33. Initialize the number of iterations, generate an initial solution according to the operations of S2101 - S2103, and perform feasibility processing on the initial solution according to the steps of S2111 - S2114.

[0197] S34. Design a jitter neighborhood structure and complete the jitter; the jitter solution obtained by jittering the initial solution through the jitter neighborhood structure, that is, the new solution. If the energy function value corresponding to the new solution is better than the current solution, accept the new solution and substitute it into the next iteration, otherwise enter S35.

[0198] S35. Perform iterative operations based on the Metropolis criterion.

[0199] Judge the new solution that is not better than the current solution in S34 according to the Metropolis criterion, accept the new solution that is not better than the current solution with a certain probability, and substitute the accepted new solution into the next iteration.

[0200] After the new solution in S34 and S35 is accepted, if the maximum number of iterations I Max is not reached, Max continue the iteration. If the maximum number of iterations I

[0201] is reached, ij terminate the iteration and enter S36.

[0202] As Figure 2 , 3 , as shown in Figure 4, an application example of this embodiment. A number of numerical examples of different scales are constructed based on the railway network in the central part of China. The central part of this railway network is Figure 2 the pivot network in Figure 3 the network represented by the blue lines in Figure 3 . Figure 3 A total of 25 pivot stations are included in Figure 3There are a total of 43 line sections between the middle support stations, including both the up and down directions, and the line mileage in the up and down directions is symmetrically equal. The road network composed of less than 20 support stations is classified as small-scale, the road network composed of more than 20 and less than 40 support stations is medium-scale, the road network composed of more than 40 and less than 80 support stations is large-scale, and the road network composed of more than 80 support stations is extra-large-scale. The line mileage and passing capacity between the support stations in the medium-scale road network in this example are as Figure 4 shown.

[0203] Figure 4 Lists the line section mileage and passing capacity parameters of the road network in one direction. Since this road network is composed of single-track railways, the line mileage and passing capacity in the up and down directions should be symmetrically equal. Taking the line section [Y1, Y2] as an example, the down direction is Y1 → Y2, and the line mileage l 12 in this direction is 74 kilometers, and the maximum passing capacity C 12 is 79 trains. It can be inferred that the line mileage l 21 and the maximum passing capacity C 21 in the direction of Y2 → Y1 are also 74 kilometers and 79 trains. Similarly, the mileage and passing capacity of other line sections not listed in Figure 4 can be obtained.

[0204] To test the solution efficiency of the model under the condition of gradually complex road network structure, based on the central road network represented by the blue line in Figure 3 , a total of 9 numerical examples with continuously increasing road network scales are designed. Among them, the smallest-scale road network is composed of Figure 5 9 support stations and 12 line sections in Figure 3 , and the largest-scale road network is composed of Figure 5 , 6 , 7, 8 represent the intermediate process of the road network composed of 9 support stations and 12 line sections gradually expanding into the road network composed of 25 support stations and 43 line sections. The scale and road network characteristics of each example are as Figure 9 shown.

[0205] In addition, the parameter λ is set to 0.1, the section passing capacity reserve coefficient α is set to 20%, and the average number of cars in a train formation m is set to 55 cars.

[0206] In this example, the above 9 cases with gradually increasing scales are used to analyze the solution performance and solution effect of the variable neighborhood search algorithm when solving the railway car flow routing optimization model, and the obtained approximate optimal solution is compared with the exact solution obtained by the iterative algorithm. For the variable neighborhood search algorithm, the maximum number of iterations I Maxis 500. The calculation time and the approximate optimal objective function value are as follows Figure 10 As shown, the solution of the variable neighborhood search algorithm is the optimal value in multiple consecutive experiments.

[0207] Depend on Figure 10 From (a), we can see that when solving problems with a network size of less than 19 pivot stations, the variable neighborhood search algorithm and the exact algorithm have little difference in solution time; when the network size continues to increase, the variable neighborhood search algorithm can obtain an approximate optimal solution relatively quickly. When the network size is 25 pivot stations, the solution time of the variable neighborhood search algorithm is reduced by 80% compared to the exact algorithm. Figure 10 From (b), we can see that the optimal or approximately optimal objective function values ​​obtained by the two algorithms are slightly different, among which the optimal objective function value Gap obtained by the exact algorithm is not much different, and the average Gap value is 1.91%.

[0208] The calculation method of Gap is as follows:

[0209] Gap = |optimal objective function value - approximate optimal objective function value| / |optimal objective function value|.

[0210] After comprehensive comparison, it can be seen that under the premise that the solution quality of the variable neighborhood search algorithm is very different from that of the exact algorithm, the solution speed of the variable neighborhood search algorithm is faster than that of the exact algorithm. Therefore, it can be considered that the variable neighborhood search algorithm proposed in the present invention has a better solution effect than the exact algorithm. When facing large-scale cases, the use of the variable neighborhood search algorithm can improve the solution efficiency to a greater extent while ensuring the solution quality.

[0211] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be regarded as exemplary and non-limiting from any point of view, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention, and any reference numerals in the claims should not be regarded as limiting the claims involved.

Claims

1. A railway vehicle flow path optimization method based on a variable neighborhood search algorithm, characterized in that: The following steps are included: S1, model building: building a railway vehicle flow path optimization model that meets the section's throughput capacity; S2, design algorithm: design a heuristic algorithm based on the variable neighborhood search algorithm to adapt to the railway traffic path optimization model; S3, solving the optimization model: using a heuristic algorithm to solve the optimization model and obtain the optimal solution; The railway vehicle flow path optimization model in step S1 is as follows: Objective Function Objective function (1) represents the sum of the travel costs of all vehicles; The constraints are as follows: Constraint condition (2) indicates that for the traffic flow path from station i to station j, its first arc should start from station i and only a station adjacent to station i can be selected as the end point of the arc; Constraint (3) indicates that for the traffic flow from station i to station j, the last arc of its path should end at station j and there is only one last arc; Constraints (4) and (5) indicate that the traffic between adjacent stations can only be transported through the arc between the adjacent stations, and cannot choose other arcs for detours. Constraint (6) is used to ensure the continuity of the traffic path; The constraint condition (7) is used to assist in eliminating unreasonable arc segments of a certain traffic flow in the road network; Constraint condition (8) indicates that the path of the traffic flow has a tree-like characteristic; The constraint condition (9) is the expression of the logical relationship between the decision variables and the auxiliary variables; The constraint condition (10) is the detour route mileage constraint of the traffic flow; The constraint condition (11) is the capacity constraint of the line section; The constraint condition (12) is the flow balance constraint on the road network; The constraint condition (13) is the variable value range constraint; The symbols are defined as follows: (a) Collection, V: the set of all stations in the railway network; V F (i): the set of all the forward stations adjacent to station i in the railway network; E: the set of all line segments in the railway network; (ii) Parameters, N ij : The original traffic volume from station i to station j, unit: car; L ij : The shortest path distance from station i to station j, unit: kilometers; C st : The maximum throughput capacity of the section [s, t], unit: column; l st : The physical mileage of the segment [s, t], unit: kilometers; Λ ij : The total mileage of the detour route and the shortest route from station i to station j, in kilometers; m: average number of cars in a train, unit: car; α st : The capacity reserve coefficient of the single-track railway section [s, t]; λ: unit conversion coefficient of vehicle flow running cost, unit: vehicle hour / vehicle kilometer; γ Detour : The relative detour rate threshold of the traffic path; (iii) Decision variables, If the route of the traffic flow from station i to station j includes the segment [s, t], the value is 1, otherwise the value is 0, which is a Boolean variable; (iv) Auxiliary variables, Boolean variable. If the traffic flow from station i to station j selects station k as the first forward station, the value is 1; otherwise, the value is 0. It is a Boolean variable.

2. The railway vehicle flow path optimization method based on variable neighborhood search algorithm according to claim 1 is characterized in that: The model is constructed based on the modeling ideas of the classic point-arc model and arc-path model in the traffic allocation model. The constructed railway traffic path optimization model is a mixed integer linear programming model that conforms to the tree-like characteristics of railway traffic paths and the principle that single-stream flow cannot be split.

3. The method for optimizing railway vehicle flow paths based on a variable neighborhood search algorithm according to claim 1 is characterized in that: The constraint condition (11) is preprocessed and added to the objective function (1) through the penalty function method, and converted into the following penalty term: Where μ is a positive penalty factor; The objective function (1) of the optimization model is reconstructed into the following energy function: The reconstructed energy function (15) is used as the objective function of the railway traffic path optimization model.

4. The railway vehicle flow path optimization method based on variable neighborhood search algorithm according to claim 1 is characterized in that: The heuristic algorithm is the variable neighborhood search algorithm, that is, the VNS algorithm. The specific design steps of the VNS algorithm are as follows: S21, generation and feasibility of initial solution: first generate the initial solution of the VNS algorithm, and then check the feasibility of the initial solution; S22, designing a jittering neighborhood structure: designing two neighborhood structures to complete the jittering process, including an insert-delete neighborhood structure and a remove-insert neighborhood structure; S23, design acceptance criteria: The acceptance criteria for the solution is that if the new solution is better than the current solution, the new solution is accepted and substituted into the next iteration; otherwise, the new solution is accepted with a certain probability; S24, determine the termination criterion: the number of iterations, running time or number of solution improvements are used as the termination conditions of the VNS algorithm.

5. The method for optimizing railway vehicle flow paths based on a variable neighborhood search algorithm according to claim 4 is characterized in that: The VNS algorithm uses the tree network consisting of the first forward stations of all vehicle flows with the same destination station but different origin stations as the initial solution. The steps for generating the initial solution are: S2101, generating a feasible traffic flow path that meets the mileage constraint according to the relative detour rate constraint condition formula (10); S2102: Generate the first forward station set V corresponding to each vehicle flow i→j according to the feasible path. F (i); S2103, from the first front station set V of each traffic flow F (i) A random element is selected, and the tree network composed of these elements is the initial solution of the VNS algorithm.

6. The method for optimizing railway vehicle flow paths based on a variable neighborhood search algorithm according to claim 5 is characterized by: The feasibility test steps of the initial solution are: S2111, from the initial solution vector Take out the elements with value 1 and form a temporary solution vector S′0; The dimension of vector S′0 is related to the network characteristics of the problem. If the network of the problem consists of |V| nodes, then the dimension of vector S′0 is |V|×(|V|-1), which can be expressed as S2112, swap the index of vector S′0 to generate a test vector Compare vector S′0 with If the elements in the same subscript have the same corresponding superscript, then the initial solution vector An unreasonable value of this element will lead to a circular path; The vector composed of unreasonable elements in S′0 is The vector formed by removing unreasonable elements from S′0 is S2113, Calculate vector dimension; if it is 0, stop the loop and set the element value of the temporary solution vector S′0 to 1. The other elements in are set to 0, and a feasible initial solution vector can be obtained. At this point, the feasibility of the initial solution of the VNS algorithm is completed, otherwise go to S2114; S2114, let vector The elements in the initial solution vector The value in is 0; for vector The elements in are adjusted and the adjusted vector Add the elements in to the vector A new temporary solution vector S′0 is formed and then transferred to S2112.

7. The method for optimizing railway vehicle flow paths based on a variable neighborhood search algorithm according to claim 4 is characterized by: The specific description of the insertion-deletion neighborhood structure is: Neighborhood action insertion is to insert an arc between two adjacent nodes. If there is an arc link between the two nodes, select two other adjacent points without links. After inserting the arc, in order to meet the uniqueness of the first forward station, an arc connected to the two nodes before the insertion should be deleted, and after deleting the arc, the degree of each node in the tree network should be guaranteed to be no less than 1. Each neighborhood action randomly selects a tree network in the current solution and inserts and deletes it to obtain a jitter solution, and it is only executed once. The specific description of the remove-insert neighborhood structure is: Randomly select two tree networks of the current solution, remove all the arcs associated with two adjacent nodes in one of the networks, find the arcs associated with these two adjacent nodes from the other tree network, and insert all the arcs into the former.

8. The method for optimizing railway vehicle flow paths based on a variable neighborhood search algorithm according to claim 1 is characterized by: The specific steps of solving the optimization model using the heuristic algorithm are as follows: S31, input network and original traffic data, input model and algorithm parameters; S32, constructing a neighborhood structure set according to the relative detour rate constraint; S33, initializing the number of iterations and generating an initial solution, and performing feasibility processing on the initial solution; S34, designing a jitter neighborhood structure and completing jittering; S35, iterative calculation based on the Metropolis criterion; S36, output the approximate optimal solution.

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