Railway traffic flow path optimization method based on variable neighborhood search algorithm

Abstract

The invention discloses a railway traffic flow path optimization method based on a variable neighborhood search algorithm, and the method comprises the steps: firstly constructing a mixed integer linear programming model which accords with the tree-shaped features of a railway traffic flow path and the principle that a single stream cannot be split, and designing a heuristic algorithm suitable for a railway traffic flow path optimization model based on the variable neighborhood search algorithm; and then solving the optimization model by using a heuristic algorithm to obtain an optimal solution. According to the method, the railway network traffic flow path problem can be optimized on the basis of considering the road network transport capacity limitation and path tree-shaped characteristics, and the problems that a railway cargo transportation network relates to various cargo properties, the network is complex, and cargo communication among important nodes is frequent can be effectively solved; compared with an existing algorithm, the method has the advantages of being high in solving efficiency and good in solving quality, and the solving efficiency is improved to a greater extent when the method is applied to large-scale cases.

Description

Technical Field

[0001] The invention relates to the technical field of railway transportation, and in particular to a railway vehicle flow path optimization method based on a variable neighborhood search algorithm. Background Art

[0002] Railway traffic routing is one of the most important foundations and bases for preparing freight train formation plans. Since my country's railway freight transportation network is more complex than that of other countries, the nature of the freight involved is diverse, and with the continuous advancement of the "road to rail" strategy and the development of new transportation modes under the low-carbon economy, the exchange of goods between important railway nodes is more frequent. In this context, if the traffic on the road network is distributed according to the shortest path, it is obviously an unreasonable and extreme method. How to optimize the railway network traffic routing problem based on the network capacity constraints and path tree characteristics is of great significance.

[0003] When organizing the traffic flow of technical stations, my country's railways must follow the principle that single-stream traffic flow cannot be split and the principle that traffic flow continues and merges, which makes the railway traffic flow path have a unique tree-like feature. The general form of traffic flow path optimization model, such as the point-arc model and the arc-path model, cannot be directly applied to railway transportation and needs to be modified to a certain extent. Then, according to the modeling idea of ​​the traditional traffic flow path model, a railway tree-shaped traffic flow path optimization model based on the traffic flow-section association relationship is proposed. Since the traffic flow path and the formation plan belong to the medium- and long-term plan, the quality of the plan is more critical than the time consumed in formulating the plan. Therefore, an accurate algorithm that can obtain the global optimal solution is the first choice for solving the traffic flow path model or the comprehensive optimization model with the formation plan. However, as the scale of the problem expands, the accurate algorithm may be difficult to obtain the optimal solution within an acceptable time when the computer memory capacity is limited, or even unable to obtain a feasible solution. The present invention provides a railway traffic flow path optimization method based on a variable neighborhood search algorithm to solve the above problems. Summary of the invention

[0004] The present invention provides a railway vehicle flow path optimization method based on a variable neighborhood search algorithm, which can obtain a 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:

[0006] A railway vehicle flow path optimization method based on a variable neighborhood search algorithm comprises the following steps:

[0007] S1, model building: building a railway vehicle flow path optimization model that meets the section's throughput capacity;

[0008] S2, design algorithm: design a heuristic algorithm based on the variable neighborhood search algorithm to adapt to the railway traffic path optimization model;

[0009] S3, solving the optimization model: using a heuristic algorithm to solve the optimization model and obtain the optimal solution.

[0010] Furthermore, a 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 the railway traffic path and the principle that a single flow cannot be split.

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

[0012]

[0013] Objective function (1) represents the sum of the travel costs of all vehicles;

[0014] The constraints are as follows:

[0015]

[0016] 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;

[0017]

[0018] 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;

[0019]

[0020] 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.

[0021]

[0022] Constraint condition (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 arcs constituting the path, the sum of the number of arcs starting from station t should be equal to the sum of the number of arcs ending at station t.

[0023]

[0024] For a certain traffic flow in the road network, the constraint condition (7) is used to assist in eliminating unreasonable arcs; for example, for the traffic flow from station i to station j, its traffic flow path should obviously not include an arc with station i as the end point or station j as the start point;

[0025]

[0026] Constraint condition (8) indicates that the path of the traffic flow has a tree-like characteristic; that is, the traffic flow from station i to station j can only choose a certain forward station adjacent to station i as the first destination;

[0027]

[0028] Constraint condition formula (9) is the logical relationship expression between decision variables and auxiliary variables. When the traffic flow from station i to station j selects the arc segment [s, t] for transportation, according to the tree-forming mechanism of traffic flow paths, the traffic flow from station s to station j must select station t as the first forward station.

[0029]

[0030] The constraint condition (10) is the detour route mileage constraint of the traffic flow; the relative detour rate threshold γ is introduced into the model Detour The concept of is that for a certain traffic flow, the traffic flow paths available for selection include the shortest path, and also include the physical mileage of the shortest path mileage γ after removing the arc mileage shared with the shortest path. Detour A path within times;

[0031]

[0032] The constraint condition (11) is the capacity constraint of the line section;

[0033] In order to unify with the freight train formation plan optimization model, the line capacity here is given in units of trains; in fact, the average number of train formations in different directions is different, but since the traffic flow routing plan does not involve the distribution and selection of the destination of the formation during the formulation process, the average number of train formations in different directions is not distinguished in the traffic flow routing optimization model;

[0034]

[0035] The constraint condition (12) is the flow balance constraint on the road network;

[0036]

[0037] The constraint condition (13) is the variable value range constraint;

[0038] The symbols in the objective function and constraints are defined as follows:

[0039] (a) Collection,

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

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

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

[0043] (ii) Parameters,

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

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

[0046] C st : The maximum throughput capacity of the section [s, t], unit: column;

[0047] l st : The physical mileage of the segment [s, t], unit: kilometers;

[0048] Λ ij : The total mileage of the detour route and the shortest route from station i to station j, in kilometers;

[0049] m: average number of cars in a train, unit: car;

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

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

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

[0053] (III) Decision variables, i.e., traffic-section correlation variables,

[0054] 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;

[0055] (iv) Auxiliary variables,

[0056] 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.

[0057] Furthermore, in the optimization model, constraint (11) is more difficult to handle in form than other constraints, and it is necessary to preprocess constraint (11); the preprocessing method is to use the penalty function method to add it to the objective function (1) and convert 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] The reconstructed energy function (15) is used as the objective function of the railway traffic path optimization model.

[0063] Furthermore, the heuristic algorithm is a variable neighborhood search (VNS) algorithm, that is, a VNS algorithm. The specific design steps of the VNS algorithm are as follows:

[0064] 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;

[0065] S22, designing a jittering neighborhood structure: designing two neighborhood structures to complete the jittering process, including an Insert-Delete neighborhood structure and a Ruin-Insert neighborhood structure;

[0066] 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;

[0067] According to the solution vector S of the VNS algorithm VNS The value of the energy function cannot be obtained directly. The solution vector S VNS Transformed into the corresponding traffic-section association variable x VNS , but since the solution vector S VNS It can be ensured that each traffic flow has a feasible and unique first front station, so the corresponding route of each traffic flow can be determined, and then the traffic flow-section association variable x can be obtained VNS The value of

[0068] S24, determining the termination criterion: the number of iterations, the running time or the number of solution improvements are used as the termination conditions of the VNS algorithm;

[0069] For smaller computational cases, select 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 destination station but different origin stations as the initial solution. The steps for generating the initial solution are:

[0071] S2101, generating a feasible traffic flow path that meets the mileage constraint according to the relative detour rate constraint condition formula (10);

[0072] S2102: Generate the first forward station set V corresponding to each vehicle flow i→j according to the feasible path. F (i);

[0073] 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.

[0074] Further, the initial solution generated by the operations of S2101-S2103 This may cause a loop path. Therefore, in order to eliminate the first forward station that may cause a loop path, the initial solution of the VNS algorithm needs to be Conduct feasibility test. The steps for conducting feasibility test on the initial solution are as follows:

[0075] S2111, from the initial solution vector Take out the elements with value 1 and form a temporary solution vector S 0 ′;

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

[0077] S2112, vector S 0 ′Index is swapped to generate a test vector Compare vector S one by one 0 'and 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.

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

[0079] Remember S 0 The vector composed of unreasonable elements in ′ is Remember S 0 The vector formed by removing unreasonable elements from ′ is

[0080] S2113, Calculate vector Dimension; if it is 0, stop the loop and let the temporary solution vector S 0 ′ takes the value of 1, and the vector 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;

[0081] S2114, let vector The elements in the initial solution vector The value in is 0; for vector The elements in are superscripted and the vector The superscript-adjusted elements in are added to the vector A new temporary solution vector S is formed in 0 ', transfer to S2112;

[0082] The specific adjustment operation is: to ensure that all vehicles can be transported to the destination, the vector The demand corresponding to the element index in the middle reselects the first forward station, and for unreasonable elements (Right now ), let the demand f kj The first forward station set is denoted as V F (k) = {..., t, u, v, ...}, the first forward station reselected should be a pivot station other than t, that is, the superscript adjustment of the element is achieved.

[0083] The initial solution of the VNS algorithm is tested and adjusted through steps S2101-S2103 and S2111-S2114 to complete the generation and feasibility of the initial solution.

[0084] Furthermore, as the core content of the VNS algorithm, the jittering neighborhood structure is designed in this embodiment based on the idea of ​​λ-interchange to complete the jittering process by using two neighborhood structures: Insert-Delete neighborhood structure and Ruin-Insert neighborhood structure.

[0085] The specific description of the Insert-Delete neighborhood structure is as follows:

[0086] The neighborhood action Insert is to insert an arc between two adjacent nodes. If there is an arc link between the two nodes, two other adjacent points without links are selected. After inserting the arc, in order to meet the uniqueness of the first forward station, an arc connected to the two nodes before 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 only randomly selects a tree network in the current solution to insert and delete it once to obtain a jitter solution, and it is only executed once. Different execution times will produce different neighborhood structures.

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

[0088] Randomly select two tree networks of the current solution, Ruin (remove) all the associated arcs of 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.

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

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

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

[0092] S33, initializing the number of iterations and generating an initial solution, and performing feasibility processing on the initial solution;

[0093] S34, designing a jitter neighborhood structure and completing jittering;

[0094] S35, iterative calculation 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 vehicle flow routing problem on the basis of considering the network capacity constraints and the tree-like characteristics of the routing, and can effectively solve the problems of the railway freight transportation network involving a variety of cargo properties, complex networks, and frequent cargo exchanges between important nodes. Compared with the existing algorithms, the method has the advantages of high solution efficiency and good solution quality, and when applied to large-scale cases, the solution efficiency is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 It is a specific flow chart of the algorithm of the railway vehicle flow path optimization method of the present invention;

[0099] Figure 2 A schematic diagram of the characteristics of the railway vehicle flow path of the present invention;

[0100] Figure 3 It is a schematic diagram of the overall structure of the railway network in the central region of the present invention;

[0101] Figure 4 A comparison table of line section mileage and throughput capacity of the railway network of the present invention;

[0102] Figure 5 It is a schematic diagram of the road network structure composed of 9 supporting stations and 11 supporting stations of the present invention;

[0103] Figure 6 It is a schematic diagram of the road network structure composed of 13 supporting stations and 15 supporting stations of the present invention;

[0104] Figure 7 It is a schematic diagram of the road network structure composed of 17 supporting stations and 19 supporting stations of the present invention;

[0105] Figure 8 It is a schematic diagram of the road network structure composed of 21 supporting stations and 23 supporting stations of the present invention;

[0106] Fig. 9 The example scale and road network characteristic table of the present invention;

[0107] Fig.10 This is a comparison chart of the solution effects of the variable neighborhood search algorithm and the exact algorithm of the present invention. DETAILED DESCRIPTION

[0108] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings of the specification. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0109] In the description of the present invention, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship are based on the orientation or position relationship shown in the drawings, and are 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 cannot be understood as a limitation on the present invention.

[0110] like Figure 1 As shown, a railway vehicle flow path optimization method based on a variable neighborhood search algorithm includes the following steps:

[0111] S1, model building: Based on the modeling ideas of the classic point-arc model and arc-path model in the traffic distribution model, a railway traffic path optimization model that meets the section capacity is constructed;

[0112] Specifically, the relationship between the route of a single vehicle flow and each line section on the road network is explored under the constraints of detour route mileage and line capacity, and a mixed integer linear programming model is established that conforms to the tree-like characteristics of railway vehicle flow routes and the principle that a single vehicle flow cannot be split.

[0113] S2, design algorithm: design a heuristic algorithm based on the variable neighborhood search algorithm to adapt to the railway traffic path optimization model;

[0114] S3, solving the optimization model: using a heuristic algorithm to solve the optimization model and obtain the optimal solution.

[0115] Furthermore, when the traffic volume in the railway network is determined, the railway traffic route optimization model is established with the goal of minimizing the running cost of the traffic in the network as the optimization goal as follows:

[0116]

[0117] Objective function (1) represents the sum of the travel costs of all vehicles;

[0118] The constraints are as follows:

[0119]

[0120] 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;

[0121]

[0122] 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;

[0123]

[0124] 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.

[0125]

[0126] Constraint condition (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 arcs constituting the path, the sum of the number of arcs starting from station t should be equal to the sum of the number of arcs ending at station t.

[0127]

[0128] For a certain traffic flow in the road network, the constraint condition (7) is used to assist in eliminating unreasonable arcs; for example, for the traffic flow from station i to station j, its traffic flow path should obviously not include an arc with station i as the end point or station j as the start point;

[0129]

[0130] Constraint condition (8) indicates that the path of the traffic flow has a tree-like characteristic; that is, the traffic flow from station i to station j can only choose a certain forward station adjacent to station i as the first destination;

[0131]

[0132] Constraint condition formula (9) is the logical relationship expression between decision variables and auxiliary variables. When the traffic flow from station i to station j selects the arc segment [s, t] for transportation, according to the tree-forming mechanism of traffic flow paths, the traffic flow from station s to station j must select station t as the first forward station.

[0133]

[0134] The constraint condition (10) is the detour route mileage constraint of the traffic flow; the relative detour rate threshold γ is introduced into the model Detour The concept of is that for a certain traffic flow, the traffic flow paths available for selection include the shortest path, and also include the physical mileage of the shortest path mileage γ after removing the arc mileage shared with the shortest path. Detour A path within times;

[0135]

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

[0137] In order to unify with the freight train formation plan optimization model, the line capacity here is given in units of trains; in fact, the average number of train formations in different directions is different, but since the traffic flow routing plan does not involve the distribution and selection of the destination of the formation during the formulation process, the average number of train formations in different directions is not distinguished in the traffic flow routing optimization model;

[0138]

[0139] The constraint condition (12) is the flow balance constraint on the road network;

[0140]

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

[0142] In the above railway vehicle flow route optimization model, since constraint (11) is more difficult to handle in form than other constraints, it is necessary to preprocess constraint (11); the specific preprocessing method is to use the penalty function method to add it to the objective function (1) and convert it into the following penalty term:

[0143]

[0144] Where 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] The reconstructed energy function (15) is used as the objective function of the railway traffic path optimization model.

[0148] The symbols in the objective function and constraints are defined as follows:

[0149] (a) Collection,

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

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

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

[0153] (ii) Parameters,

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

[0155] L ij : The shortest path distance from station i to station j, unit: kilometers;

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

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

[0158] Λ ij : The total mileage of the detour route and the shortest route from station i to station j, in kilometers;

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

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

[0161] λ: unit conversion coefficient of vehicle flow running cost, unit: vehicle hour / vehicle kilometer;

[0162] γ Detour : The relative detour rate threshold of the traffic path;

[0163] (III) Decision variables, i.e., traffic flow-section correlation variables,

[0164] 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;

[0165] (iv) Auxiliary variables,

[0166] 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.

[0167] A 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 path is satisfied, the tree network formed by the first front station is used as the initial solution, and a neighborhood structure is designed to jitter the tree network. After the jittered solution is generated, a local search is applied to obtain the local optimal solution of the traffic path, and the search is continued within the neighborhood structure until the termination condition of the algorithm is met.

[0168] like Figure 1 As shown, the above principle is used to design a heuristic algorithm, which is a variable neighborhood search (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 criteria and the determination of the termination criteria.

[0169] 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.

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

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

[0172] S2102: Generate the first forward station set V corresponding to each vehicle flow i→j according to the feasible path. F (i);

[0173] 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.

[0174] The initial solution generated by the operations of S2101-S2103 This may cause a loop path. Therefore, in order to eliminate the first forward station that may cause a loop path, the initial solution of the VNS algorithm needs to be Perform a feasibility check on the initial solution according to operations S2111-S2114.

[0175] S2111, from the initial solution vector Take out the elements with value 1 and form a temporary solution vector S 0 ′;

[0176] Vector S′ 0 The dimension of is related to the network characteristics of the problem. If the network of the problem consists of |V| nodes, then the vector S′ 0 The dimension is |V|×(|V|-1), which can be expressed as

[0177] S2112, vector S 0 ′Index is swapped to generate a test vector Compare vector S one by one 0 'and 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.

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

[0179] Remember S 0 The vector composed of unreasonable elements in ′ is Remember S 0 The vector formed by removing unreasonable elements from ′ is

[0180] S2113, Calculate vector Dimension; if it is 0, stop the loop and let the temporary solution vector S 0 ′ takes the value of 1, and the vector 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;

[0181] S2114, let vector The elements in the initial solution vector The value of is 0; to ensure that all vehicles can be transported to the destination, it is necessary to be a vector The demand corresponding to the element index in the middle reselects the first forward station, and for unreasonable elements (Right now ), let the demand f kj The first forward station set is denoted as V F (k) = {..., t, u, v, ...}, the first forward station reselected should be a fulcrum station other than t;

[0182] Add the superscript-adjusted elements to the vector A new temporary solution vector S is formed in 0 ′, transfer to S2112.

[0183] The initial solution of the VNS algorithm is generated through steps S2101-S2103 and S2111-S2114, and the feasibility of the generated initial solution is tested and adjusted to complete the generation and feasibility of the initial solution.

[0184] S22, designing a jittering neighborhood structure: The jittering neighborhood structure is the core content of the VNS algorithm. The jittering solution generated by the neighborhood structure jittering the initial solution is related to the solution quality. Therefore, this embodiment designs two neighborhood structures, Insert-Delete neighborhood structure and Ruin-Insert neighborhood structure, based on the idea of ​​λ-interchange to complete the jittering process.

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

[0186] The neighborhood action Insert is to insert an arc between two adjacent nodes. If there is an arc link between the two nodes, two other adjacent points without links are selected. After inserting the arc, in order to meet the uniqueness of the first forward station, an arc connected to the two nodes before 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 only randomly selects a tree network in the current solution to insert and delete it once to obtain a jitter solution, and it is only executed once. Different execution times will produce different neighborhood structures.

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

[0188] Randomly select two tree networks of the current solution, Ruin (remove) all the associated arcs of 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.

[0189] S23, design acceptance criteria: The acceptance criteria of 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, the new solution is accepted and substituted into the next iteration; otherwise, the new solution is accepted with a certain probability.

[0190] According to the solution vector S of the VNS algorithm VNS The value of the energy function cannot be obtained directly. The solution vector S VNS Transformed into the corresponding traffic-section association variable x VNS , but since the solution vector S VNS It can be ensured that each traffic flow has a feasible and unique first front station, so the corresponding route of each traffic flow can be determined, and then the traffic flow-section association variable x can be obtained VNS The value of .

[0191] S24, determining the termination criterion: the number of iterations, the running time or the number of solution improvements are used as the termination conditions of the VNS algorithm;

[0192] For cases with smaller computational scale, choose to set the maximum number of iterations I Max is the termination condition.

[0193] like Figure 1 As shown, the optimization model is solved according to steps S31-S37 using a heuristic algorithm.

[0194] S31, network and original traffic data, including adjacency matrix, traffic path: L ij and Λ ij 、Line section: l st , C st and α, OD 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, constructing a neighborhood structure set according to the relative detour rate constraint.

[0196] S33, initialize the number of iterations and 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 jittering neighborhood structure and complete jittering; the initial solution is jittered to obtain a jittering solution, i.e., a new solution, after the jittering of the jittering neighborhood structure. If the energy function value corresponding to the new solution is better than the current solution, the new solution is accepted and substituted into the next iteration, otherwise enter S35.

[0198] S35, performs iterative calculations based on the Metropolis criterion.

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

[0200] After the new solution in S34 and S35 is accepted, if the maximum number of iterations I is not reached Max Then continue to iterate. If the maximum number of iterations I is reached Max The iteration is terminated and the process proceeds to S36.

[0201] S36: Output the approximate optimal solution after reaching the termination condition. The optimal solution includes the total travel cost, the traffic flow routing scheme, and the traffic flow routing mileage L. ij , through capacity utilization and relative detour rate under the approximate optimal solution.

[0202] like Figure 2 , 3 , 4, are examples of the application of this embodiment. Several numerical examples of different scales are constructed based on the railway network in central my country. Figure 2 The pivot network in Figure 3 The blue lines represent the network, and the overall structure of the road network is as follows Figure 3 shown. Figure 3There are 25 support stations in total. Each support station name has a corresponding number in brackets. In the parameter introduction and optimization result analysis, the names of each support station are in the form of numbers. The lines in this example are all single-track railways. Figure 3 There are 43 line sections between the middle pivot stations, all of which include both the upward and downward directions, and the line mileage in the upward and downward directions is symmetrical and equal. The road network consisting of less than 20 pivot stations is classified as small-scale, the road network consisting of more than 20 pivot stations and less than 40 pivot stations is classified as medium-scale, the road network consisting of more than 40 pivot stations and less than 80 pivot stations is classified as large-scale, and the road network consisting of more than 80 pivot stations is classified as super-large-scale. The line mileage and throughput capacity between pivot stations in the medium-scale road network in this example are as follows: Figure 4 shown.

[0203] Figure 4 The line section mileage and capacity parameters of the road network in a single direction are listed. Since the road network consists of a single-track railway, the line mileage and capacity in the up and down directions should be symmetrical and equal. 1 ,Y 2 ] as an example, the downward direction is Y 1 →Y 2 , the line mileage in this direction is l 12 74 km, maximum capacity C 12 There are 79 columns. It can be inferred that the direction is Y 2 →Y 1 Line mileage 21 and maximum capacity C 21 The same is 74 kilometers and 79 trains. Figure 4 The mileage and capacity of other line sections not listed.

[0204] In order to test the model's efficiency in solving increasingly complex road network structures, Figure 3 The central road network represented by the blue line is used as the basis for expansion. A total of 9 numerical examples with increasing road network scales are designed. Among them, the smallest road network is Figure 5 The largest network consists of 9 branch stations and 12 line sections. Figure 3 It consists of 25 supporting stations and 43 line sections. Figure 5 , 6 , 7, and 8 represent the intermediate process of a network consisting of 9 supporting stations and 12 line sections gradually expanding to a network consisting of 25 supporting stations and 43 line sections. Fig. 9 shown.

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

[0206] This example uses the above 9 cases with gradually increasing scales to analyze the performance and effect of the variable neighborhood search algorithm in solving the railway traffic path optimization model, and compares the approximate optimal solution obtained with the exact solution obtained by the iterative algorithm. For the variable neighborhood search algorithm, the maximum number of iterations in the termination criterion I Max is 500. The calculation time and the approximate optimal objective function value are as follows Fig.10 As shown, the solution of the variable neighborhood search algorithm is the optimal value in multiple consecutive experiments.

[0207] Depend on Fig.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. Fig.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.

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 railway vehicle flow path optimization method based on variable neighborhood search algorithm according to claim 1 is characterized in that: The railway vehicle flow path optimization model 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.

4. The method for optimizing railway vehicle flow paths based on a variable neighborhood search algorithm according to claim 3 is characterized by: 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.

5. The railway vehicle flow path optimization method based on variable neighborhood search algorithm according to claim 3 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.

6. The method for optimizing railway vehicle flow paths based on a variable neighborhood search algorithm according to claim 5 is characterized by: 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.

7. The method for optimizing railway vehicle flow paths based on a variable neighborhood search algorithm according to claim 6 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, 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.

8. The method for optimizing railway vehicle flow paths based on a variable neighborhood search algorithm according to claim 5 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.

9. 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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