Railway line optimization method for land area minimization

Abstract

The present application provides a railway construction second line linear optimization method for land area minimization, comprising: S1. obtaining basic data; S2. constructing a plane linear parameter model; S3. setting a line constraint condition and determining a constraint line; S4. setting a target function; S5. intersection classification iterative optimization; S6. adaptive intersection number iterative optimization; S7. screening an optimal linear scheme. The present application provides an efficient and feasible technical solution for the problems of narrow feasible solution space and long iteration time in the traditional optimization method in railway construction second line linear optimization, and the core target is to minimize the railway construction land area, while improving the efficiency and quality of linear optimization, reducing the railway construction cost, meeting the actual design requirements of railway construction second line engineering, and providing technical guidance for related engineering practice.

Description

Technical Field

[0001] This invention relates to the field of railway engineering technology, and in particular to a method for optimizing the alignment of railway second-track lines to minimize land use. Background Technology

[0002] The demand for building second lines for railways continues to grow. Existing single-track railway trunk lines are generally facing problems of saturated transport capacity and weak risk resistance, making it difficult to meet the growing demand for passenger and freight transport. Building second lines has become a key measure to improve transport capacity and ensure transport safety.

[0003] However, traditional manual route selection has obvious limitations. It needs to process multi-source heterogeneous data, but the human brain has limited analytical capabilities and lacks a dynamic response mechanism, making it difficult to cope with sudden constraints. Existing various alignment optimization algorithms (such as three-dimensional dynamic programming algorithms, genetic algorithm models, and bi-objective approximate fine optimization models) all have shortcomings, such as low iteration efficiency or inability to achieve global optimization. Under strict line spacing constraints and limited optimization space, it is difficult to efficiently obtain high-quality feasible solutions, which restricts the economy and design efficiency of railway construction. Summary of the Invention

[0004] This invention provides a method for optimizing the alignment of railway second-track expansion projects by minimizing land use. Addressing the challenges of traditional optimization methods, such as narrow feasible solution spaces and excessively long iteration times, this invention offers an efficient and feasible technical solution. The core objective is to minimize the land area required for railway construction, while simultaneously improving the efficiency and quality of alignment optimization, reducing railway construction costs, meeting the actual design requirements of railway second-track expansion projects, and providing technical guidance for related engineering practices.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for optimizing the alignment of a second railway line to minimize land use includes the following steps: S1. Obtain artificial intersection data, existing railway data and corresponding minimum track spacing requirements. The artificial intersection data includes the plane coordinates of each intersection point, the length of the transition curve, and the intersection radius. S2. Based on the artificial intersection data obtained in S1, a railway horizontal alignment parameter model is constructed, and the geometric features and design specifications of the line are parametrically expressed with horizontal control points (HPI) as the core. S3. Based on the minimum track spacing requirements obtained in S1 and railway design specifications, set track constraints. The constraints include track planar constraints and minimum track spacing constraints. The track planar constraints involve minimum requirements for curve radius, circular curve length, transition curve length, and straight section length. The minimum track spacing constraints differentiate between the requirements for bridge sections and roadbed sections. At the same time, the position of the constraint line is determined according to the minimum track spacing requirements. S4. Set an objective function to minimize the total land acquisition area for railway construction. The total land acquisition area includes the land acquisition area of ​​each land acquisition area along the entire line and the area of ​​the sandwiched land between the two lines that is difficult to develop and utilize. The sandwiched land is the narrow and elongated area enclosed by the land acquisition red line of the existing railway and the newly built railway in S1. S5. Based on the planar alignment parameter model of S2 and the line constraints and constraint lines of S3, an intersection point classification and iteration mechanism is adopted to identify and distinguish conflict points, active points and passive points through geometric relationships. A directional optimization strategy is applied to different types of intersection points. The conflict point is the intersection point that violates the line constraints of S3. The active point is the intersection point that participates in the formation of both long and short straight lines and the long straight line is close to or coincides with the constraint line of S3. The passive point is the middle intersection point that avoids the rectangular protrusion of the constraint line of the bridge section. S6. Based on the planar alignment parameter model of S2, the line constraints of S3, and the objective function of S4, an adaptive intersection number iteration mechanism is adopted. Intersections are added or deleted by the branch-and-bound method according to the optimization requirements, and the number of intersections is dynamically adjusted to broaden the optimization path. S7. Combining the intersection classification iteration results of S5 and the adaptive intersection number iteration results of S6, and based on the line constraints of S3 and the objective function of S4, select and output the railway alignment scheme with the best comprehensive optimization effect.

[0006] In this specification, step S5 implements a priority iteration strategy for conflict points, while other intersection points remain in their original design positions. The planar coordinates, transition curve lengths, and intersection radii of the conflict points are individually iterated and optimized to ensure that the conflict points meet the line constraints set in S3 after iteration.

[0007] In this specification, step S5 restricts the iteration direction of the active point, allowing the active point to iterate only along the long straight line and its extension, in order to avoid violating the minimum line spacing constraint set in S3 or expanding the sandwich area after iteration.

[0008] In this specification, the passive point mentioned in step S5 and the active point connecting the long straight lines on both sides form a group. The position iteration of the passive point is bound to the position iteration of the active points on both sides. The position of the passive point is optimized by adjusting the position of the active point in a linkage manner, so that the passive point always meets the requirement of avoiding the rectangular protrusion of the constraint line of the bridge section.

[0009] In this specification, the initial position of the passive point is determined in the following way: the left and right vertices of the constraint line protrusion rectangle described in S3 are set as bridge auxiliary points, and the active point on one side and the bridge auxiliary point on the same side are connected respectively and extended to form a ray. The intersection of the two rays is the initial position of the passive point.

[0010] In this specification, the specific process of adding an intersection point in step S6 is as follows: Identify a long straight line segment between two bridge segments that are close to each other and parallel to the constraint line described in S3. When the length of the straight line segment is not less than a preset minimum value and the offset distance from the constraint line is not less than a preset minimum value, the coordinates of the new intersection point are initially confirmed by drawing a perpendicular line from the midpoint of the selected long straight line segment to the constraint line. The new intersection point is verified through iteration to ensure that it meets the line constraint conditions of S3. Finally, the coordinates of the new intersection point are determined to optimize the area of ​​the sandwiched land.

[0011] In this specification, the specific process of deleting intersection points using the branch-and-bound method in step S6 is as follows: determine the length of the straight line segments in the S2 planar linear parameter model, mark the intersection points corresponding to the straight line segments with smaller optimization space as candidate deletion points, attempt to delete the candidate deletion points in a permutation and combination manner, iteratively verify whether the line formed by the remaining intersection points satisfies the line constraint conditions of S3, and retain the deletion iteration scheme that meets the constraints and better fits the objective function of S4.

[0012] In this specification, the minimum line spacing of the bridge section in step S3 is greater than the minimum line spacing of the roadbed section, and the constraint line of the corresponding bridge section forms an outward rectangular protrusion. This protruding area is the object to be avoided by the passive point in S5.

[0013] In this manual, when selecting the optimal solution in step S7, it is necessary to verify whether the solution simultaneously meets the line constraints in S3 and the objective function requirements in S4, to ensure that the optimized line spacing, straight line length, minimum curve radius, and circular curve length are reasonably adapted to the existing railway conditions.

[0014] In this specification, when the active point and the passive point are linked and iterated, the active point is moved closer to or further away from the protruding segment of the constraint line described in S3. The area of ​​the sandwiched land corresponding to the active point and the passive point is dynamically balanced, so as to minimize the total land acquisition area required by the objective function of S4.

[0015] In summary, the present invention has at least the following beneficial effects: This invention effectively reduces waste in railway construction, optimizes the configuration of track and bridge / tunnel lengths, and improves the efficiency and economy of railway construction land use; it significantly shortens the iteration cycle of alignment optimization, reducing the time cost for designers; it breaks through the bottleneck of traditional optimization methods, broadens the optimization path, improves the efficiency and stability of obtaining high-quality feasible solutions, and makes alignment optimization more in line with actual engineering constraints, providing efficient and reliable technical support for the alignment design of railway second-line construction. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of the railway alignment optimization method for minimizing land area involved in this invention.

[0018] Figure 2 This is a schematic diagram of the basic parameters of the planar line shape involved in this invention.

[0019] Figure 3 This is a schematic diagram illustrating the optimization process of the intelligent line selection model with adaptive intersection number based on intersection classification involved in this invention.

[0020] Figure 4 This is a schematic diagram of the active point involved in the present invention.

[0021] Figure 5 This is a schematic diagram comparing the line optimization and adjustment involved in this invention. Detailed Implementation

[0022] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0023] The following disclosure provides many different implementations or examples for carrying out different structures of the embodiments of the present invention. To simplify the disclosure of the embodiments of the present invention, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. Furthermore, reference numerals and / or reference letters may be repeated in different examples of the embodiments of the present invention; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various implementations and / or arrangements discussed.

[0024] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0025] like Figure 1 As shown, this embodiment provides a method for optimizing the alignment of a second railway line to minimize land use, including the following steps: S1. Obtain artificial intersection data, existing railway data and corresponding minimum track spacing requirements. The artificial intersection data includes the plane coordinates of each intersection point, the length of the transition curve, and the intersection radius. S2. Based on the artificial intersection data obtained in S1, a railway horizontal alignment parameter model is constructed, and the geometric features and design specifications of the line are parametrically expressed with horizontal control points (HPI) as the core. S3. Based on the minimum track spacing requirements obtained in S1 and railway design specifications, set track constraints. The constraints include track planar constraints and minimum track spacing constraints. The track planar constraints involve minimum requirements for curve radius, circular curve length, transition curve length, and straight section length. The minimum track spacing constraints differentiate between the requirements for bridge sections and roadbed sections. At the same time, the position of the constraint line is determined according to the minimum track spacing requirements. S4. Set an objective function to minimize the total land acquisition area for railway construction. The total land acquisition area includes the land acquisition area of ​​each land acquisition area along the entire line and the area of ​​the sandwiched land between the two lines that is difficult to develop and utilize. The sandwiched land is the narrow and elongated area enclosed by the land acquisition red line of the existing railway and the newly built railway in S1. S5. Based on the planar alignment parameter model of S2 and the line constraints and constraint lines of S3, an intersection point classification and iteration mechanism is adopted to identify and distinguish conflict points, active points and passive points through geometric relationships. A directional optimization strategy is applied to different types of intersection points. The conflict point is the intersection point that violates the line constraints of S3. The active point is the intersection point that participates in the formation of both long and short straight lines and the long straight line is close to or coincides with the constraint line of S3. The passive point is the middle intersection point that avoids the rectangular protrusion of the constraint line of the bridge section. S6. Based on the planar alignment parameter model of S2, the line constraints of S3, and the objective function of S4, an adaptive intersection number iteration mechanism is adopted. Intersections are added or deleted by the branch-and-bound method according to the optimization requirements, and the number of intersections is dynamically adjusted to broaden the optimization path. S7. Combining the intersection classification iteration results of S5 and the adaptive intersection number iteration results of S6, and based on the line constraints of S3 and the objective function of S4, select and output the railway alignment scheme with the best comprehensive optimization effect.

[0026] In some embodiments, in step S5, a priority iteration strategy is implemented for conflict points, while other intersection points remain in their original design positions. The planar coordinates, transition curve lengths, and intersection radii of the conflict points are individually iterated and optimized to ensure that the conflict points meet the line constraints set in S3 after iteration.

[0027] In some embodiments, the iteration direction of the active point is limited in step S5, allowing the active point to iterate only along the long straight line and the extension of the long straight line, so as to avoid violating the minimum line spacing constraint set in S3 or expanding the sandwich area after iteration.

[0028] In some embodiments, the passive point in step S5 and the active point connecting the long straight lines on both sides form a group. The position iteration of the passive point is bound to the position iteration of the active points on both sides. The position of the passive point is optimized by adjusting the position of the active point in conjunction with the position, so that the passive point always meets the requirement of avoiding the rectangular protrusion of the constraint line of the bridge section.

[0029] In some embodiments, the initial position of the passive point is determined by setting the left and right vertices of the constraint line protrusion rectangle described in S3 as bridge auxiliary points, connecting the active point on one side with the bridge auxiliary point on the same side respectively and extending them to form rays, and the intersection of the two rays is the initial position of the passive point.

[0030] In some embodiments, the specific process of adding intersection points in step S6 is as follows: identify a long straight line segment between two bridge segments that are close to each other and parallel to the constraint line described in S3. When the length of the straight line segment is not less than a preset minimum value and the offset distance from the constraint line is not less than a preset minimum value, the coordinates of the new intersection point are initially confirmed by selecting the midpoint of the long straight line segment and drawing a perpendicular line to the constraint line. The new intersection point is ensured to meet the line constraint conditions of S3 through iterative verification. Finally, the coordinates of the new intersection point are determined to optimize the area of ​​the sandwiched land.

[0031] In some embodiments, the specific process of deleting intersection points using the branch-and-bound method in step S6 is as follows: determine the length of the straight line segments in the S2 planar linear parameter model, mark the intersection points corresponding to the straight line segments with smaller optimization space as candidate deletion points, try to delete the candidate deletion points in a permutation and combination manner, iteratively verify whether the line formed by the remaining intersection points satisfies the line constraint conditions of S3, and retain the deletion iteration scheme that meets the constraints and is more in line with the objective function of S4.

[0032] In some embodiments, the minimum line spacing of the bridge segment in step S3 is greater than the minimum line spacing of the roadbed segment, and the constraint lines of the corresponding bridge segment form an outward rectangular protrusion. This protrusion area is the object to be avoided by the passive point in S5.

[0033] In some embodiments, when selecting the scheme with the best comprehensive optimization effect in step S7, it is necessary to verify whether the scheme simultaneously meets the line constraint conditions of S3 and the objective function requirements of S4, so as to ensure that the optimized line spacing, straight line length, minimum curve radius and circular curve length are reasonably adapted to the existing railway conditions.

[0034] In some embodiments, when the active point and the passive point are linked and iterated, the active point is moved closer to or further away from the protruding segment of the constraint line described in S3, and the sandwich area corresponding to the active point and the passive point is dynamically balanced to achieve the minimization of the total land acquisition area required by the objective function in S4.

[0035] The technical concept of this invention is as follows: This invention proposes an intelligent alignment algorithm called "Intersection Classification and Railway Land Area Alignment Optimization (ICLA-Align)". The core of this algorithm integrates a dual mechanism of intersection classification iteration and adaptive intersection quantity iteration, and is based on a railway horizontal alignment optimization model. First, an alignment parameter model is constructed using horizontal control points (HPIs) to clarify the line's horizontal constraints and minimum line spacing constraints, with the objective function being the minimization of the total land acquisition area (including sandwiched areas). Second, the algorithm identifies conflict points, active points, and passive points and applies a directional iteration strategy. Simultaneously, it dynamically adjusts the number of intersection points by adding intersection points and deleting intersection points using a branch-and-bound method, thus broadening the optimization path. Ultimately, this achieves efficient alignment optimization for the construction of a second railway line.

[0036] 1. Railway horizontal alignment optimization model 1.1 Construction of Linear Parametric Model To facilitate subsequent route optimization calculations, the geometric characteristics and design specifications of the route need to be parametrically represented. Planar alignment elements are constrained by horizontal points of intersection (HPIs). Each control point is defined by four key parameters: the x-axis value, the y-axis value in the planar coordinate system, the length of the transition curve Ls controlling the transition characteristics of the alignment, and the intersection radius R determining the curvature of the curve. The corresponding intersection point is... The corresponding x-axis value of the intersection point The corresponding vertical axis value of the intersection point The length of the corresponding intersection transition curve The corresponding intersection radius value . For the corresponding route, g is the intersection point variable that generates the corresponding route function. f Generate the function corresponding to the intersection point for the intersection point parameter variable. For example... Figure 2 As shown. Its parameterized representation can be specifically described as: (1) (2) 1.2 Line Constraint Model This model involves two aspects of constraints: the alignment constraints and the minimum track spacing constraints between the railway and the existing railway when adding a second track.

[0037] The plane constraints of the line must meet the following requirements: (1) The curve radius at the corresponding intersection point must be greater than the minimum curve radius: (3) —The radius of the curve at the corresponding intersection point; —Minimum curve radius; (2) The length of the circular curve at the corresponding intersection point must be greater than the length of the minimum circular curve: (4) —The length of the circular curve at the corresponding intersection point; —Minimum circular curve length; (3) The length of the transition curve at the corresponding intersection point must be greater than the length of the minimum transition curve: (5) —The length of the transition curve at the corresponding intersection point; —Length of the minimum transition curve; (4) The length of the clamping line must be greater than the minimum clamping line length requirement: (6) —The length of the straight line between two adjacent intersection points; —Minimum clamping line length; (5) Given that the construction of a new railway second line may have a potential impact on the operational safety of the existing line, rigid constraints must be imposed on the vertical distance from each point on the centerline of the new railway to the centerline of the existing railway to ensure that the minimum track spacing standard is met. Especially in bridge sections, differentiated minimum track spacing technical requirements need to be formulated according to the differences in bridge structure types. At the same time, the position of the constraint line should be determined according to the corresponding minimum track spacing to facilitate subsequent iterative optimization.

[0038] (7) (8) —The perpendicular distance from a point on the centerline of the new railway line to the centerline of the existing railway line; —Minimum spacing between lines in bridge sections; —Minimum spacing between lines in the roadbed section.

[0039] 1.3 Objective Function This invention uses the total land area occupied by railway construction as the objective function of the model, as shown below.

[0040] During railway construction, existing lines have clearly defined land acquisition areas, and new lines also require separate land acquisition areas. To balance engineering economy and construction safety, a certain safety distance must be maintained between the new and existing lines, resulting in a narrow, elongated area enclosed by the land acquisition boundaries of both the existing and new lines—the "sandwich zone." According to relevant research on land use control for railway second-line construction projects, this type of land resource, due to its irregular shape and the impact of railway operations, is difficult to develop on a large scale, leading to low land use efficiency and indirectly increasing railway construction costs. Particularly noteworthy is that residences within this sandwich zone are constantly exposed to noise and vibration pollution from train operations, significantly degrading their living environment quality. Therefore, such houses typically need to be demolished during railway construction. Especially when the new line runs parallel to the existing railway for a long distance, the land acquisition compensation costs and house demolition costs in the linear sandwich zone constitute a significant portion of the total project investment, a proportion that cannot be ignored. Therefore, reducing the area of ​​the sandwich zone is of great importance for controlling the total investment scale of railway second-line construction projects.

[0041] (9) —Number of land acquisition areas along the entire route; —The area requisitioned in the corresponding region; —The area within the corresponding region that is difficult to develop and utilize due to the narrow space between the two lines; —Total land acquisition area along the entire route.

[0042] 2. Intelligent route selection model with adaptive intersection number for classifying intersections when adding a second track to an existing railway. This model can classify and iterate the intersection points, significantly reducing the iteration time. It can also adaptively increase or decrease the number of intersection points, reducing the chance of missing better solutions and optimizing the design line objective function to a greater extent. The specific overall optimization process can be found in [link to optimization process]. Figure 3 .

[0043] 2.1 Classification of intersection points A complete artificial linear curve has a large number of intersections, with some sections having more than 50 intersections, and each intersection contains... x, y Coordinates, radius R， Length of transition curve Ls The four dimensions result in a very large number of intersection combinations, making it almost impossible to exhaust all these solutions. At the same time, in some design sections, the distance between the manually designed line and the constraint line is very close, which means that it takes a lot of time just to find a solution that meets the constraints. It is even more difficult to find an optimization solution that meets the constraints and has a smaller sandwich area.

[0044] Therefore, this invention selects different iteration methods and iteration times for intersections with different characteristics, making the iteration of intersections more directional and characteristic, and significantly reducing the number of combinations of intersection iterations. The following describes the methods for classifying intersections and the corresponding iteration methods.

[0045] 2.1.1 Conflict Points In practical applications, manually designed original lines inevitably contain a small number of line segments that violate constraints. The intersections that generate these constraint-violation lines are termed "conflict points" in this invention. Because these conflict points violate constraints, their positions must be iterated upon. Since these intersections are close to the constraint lines, even slight movements will result in further constraint violations. In previous iterations without intersection point classification, these types of intersections often generated a large number of constraint-violation intersection combinations, significantly slowing down the process of finding the optimal solution. Therefore, this invention adopts a priority iteration strategy for these intersections, keeping the original design line positions of other intersections unchanged, and processing conflict points separately. x, y coordinate, R, Ls The four-dimensional attributes are iterated. The specific formula for intersection point iteration is as follows: (10) (11) (12) (13) The x-coordinate of the intersection point after iteration; The original coordinates of the intersection point before iteration; The shift value applied by the algorithm to the original coordinates, for , , The same iterative method is used.

[0046] Prioritizing individual iterations of conflict points can significantly reduce the number of intersection combinations that violate constraints. At the same time, fewer intersection points participate in subsequent iterations, which also reduces the total number of intersection combinations to some extent.

[0047] 2.1.2 Active Point In the design of long straight segments, artificially designed lines are generally made to coincide with constraint lines as much as possible. This limits the optimization space for artificially designed lines on long straight segments. When an intersection point participates in the formation of both long and short straight lines, this invention refers to it as an "active point," see [link to relevant documentation]. Figure 4 .

[0048] If the previous random iteration method is used, the active point has many possible iteration directions. However, the long straight line where the active point is located is usually close to or even coincides with the constraint line. If the active point iterates towards the existing line, it will inevitably cause the newly generated design line to cross the constraint line and violate the minimum line spacing constraint. But if the active point iterates away from the constraint line, it will definitely cause the sandwich area between the newly generated design line and the existing line to be larger than the sandwich area between the original design line and the existing line, which is contrary to the optimization direction of this invention. Therefore, the iteration direction of the active point can only be determined to move and iterate on the long straight line and its extension.

[0049] (14) (15) ——Intersection after iteration x coordinate; ——Original intersection point x coordinate; —The distance moved along the direction of the constraint line; —Constraint lines and x The angle between directions; Determining the direction of active point iteration reduces the iteration space to a straight line, further reducing the number of intersection combinations and enabling faster and better iteration.

[0050] 2.1.3 Passive Points Because the minimum line spacing in bridge sections is larger than in ordinary sections without bridges, the constraint lines of bridge sections will produce an outward rectangular protrusion. To avoid this protrusion, the artificially designed lines contain at least three intersection points. This invention treats these three intersection points as a group. The two outermost intersection points in this group are the active points connecting the long straight lines, while the middle intersection point is the "passive point" for avoiding the rectangular protrusion caused by the bridge. For ease of explanation, this invention refers to the left and right vertices of the rectangular protrusion of the constraint line as "bridge auxiliary points." By connecting the active point on one side with the bridge auxiliary point on the same side and extending it to obtain a ray, and then performing the same operation on the active point on the other side with the bridge auxiliary point, these two rays will have an intersection point. This intersection point is set as the position of the passive point. The specific mathematical formula is as follows: definition: (16) make: (17) Intersection: (18) , These are the left-side active point and the bridge auxiliary point, respectively. x coordinate; , These are the left-side active point and the bridge auxiliary point, respectively. y coordinate; , These are the right-side active point and the bridge auxiliary point, respectively. x coordinate; , These are the right-side active point and the bridge auxiliary point, respectively. y coordinate; , For passive points x, y coordinate.

[0051] As the positions of the active points on both sides are iterated, the positions of the passive points also change accordingly. When the active points on both sides move closer to the protruding segment of the constraint line, the area between the active point and the constraint line becomes smaller. However, at this time, the passive point will move away from the constraint line, causing the area between the passive point and the constraint line to become larger. Conversely, the area between the active point and the constraint line is larger, while the area between the passive point and the constraint line is smaller. Through continuous iteration of the active point positions, a better position for the active and passive points than that of manually designed lines can be found.

[0052] By binding the position iteration of passive points with the position iteration of active points, the total number of intersection points is reduced, thereby improving iteration efficiency.

[0053] 2.2 Adaptive Number of Intersections The original manual design cannot perfectly consider all factors simultaneously, thus failing to achieve overall optimization. There may be instances where adding or removing certain intersections and iterating further could achieve better results. Furthermore, between two closely spaced bridge segments, there is often space where only adding intersections can further optimize the sandwich area. Therefore, this model proposes an adaptive number of intersections, identifying potentially removable intersections and attempting to delete those that can be optimized. Simultaneously, it identifies segments with optimization potential and further reduces the sandwich area by adding intersections.

[0054] 2.2.1 Adding intersection points When two bridge segments are close together, the artificial alignment often produces a long straight segment parallel to the constraint line. The offset distance between this long straight segment and the constraint line depends on the degree of bulging of the bridge segment. When the bridge segment has a large bulge and the straight segment is long enough, a large sandwich area will be created between the original design line and the constraint line. This model optimizes the area of ​​this sandwich area by adding intersection points. The detailed steps for adding intersection points are as follows: The algorithm first traverses all straight segments in the alignment and filters out segments with optimization potential based on set empirical thresholds (e.g., the length of the straight segment must be greater than 800 meters and the offset distance from the constraint line must be greater than 8 meters). Once a straight segment that meets the above criteria is identified, the model inserts a new intersection point in the segment to divide it, thereby giving the segment more flexibility to deform and get closer to the constraint line. Subsequently, the algorithm enters the iterative optimization stage, searching and strictly verifying the alignment containing the new intersection point within the specified parameter boundaries. If the newly generated solution can obtain a smaller sandwich area than the original solution while ensuring that the geometric and minimum line spacing constraints are met, the system will update it as the current optimal solution, thereby effectively breaking through the optimization bottleneck of manual design on long straight road segments.

[0055] 2.2.2 Branch and Bound Method for Deleting Intersections Branch and bound is an algorithm for solving combinatorial optimization problems. First, it enumerates all possible combinatorial solutions, ensuring that all solutions are considered. Then, it significantly reduces the number of solutions that actually need to be calculated through branch pruning strategies. Unlike other heuristic algorithms, branch and bound can guarantee finding the global optimum.

[0056] For manually designed lines, it may be difficult to comprehensively consider the influence of multiple factors when setting intersection points. It's possible that deleting certain intersection points might actually improve the overall line quality. Therefore, this invention employs a branch-and-bound method to explore potentially deletable intersection points. After deleting intersection points, each possible combination of intersection points is iterated through. If a better result than not adding or removing intersection points is found during the iteration, that result is updated as the current optimal solution. This process continues until all intersection point combinations have been iterated through, at which point the current optimal solution is set as the final optimal solution.

[0057] The situation addressed in this invention differs slightly from the traditional branch and bound method. Therefore, a branch and bound-like method is proposed based on the branch and bound approach. The specific steps for deleting intersections are as follows: Based on the idea of ​​combinatorial optimization, all potential removable intersections in the linear shape are identified, and all possible intersection deletion combinations are enumerated to construct a set of possible solutions. Subsequently, for each combination solution after attempting to delete intersections, the system will again call the "intersection classification iteration" mechanism to reposition and optimize the parameters of the remaining intersections (including conflict points, active points, and passive points), forcing the new linear shape to adapt to the environment in terms of geometry. During this process, the algorithm will perform strict constraint verification in real time. Only when a linear solution simultaneously meets all design specifications such as minimum line spacing, curve radius, and straight line length, and its calculated sandwich area is less than the currently known optimal solution, will the system determine it as a valid optimization solution.

[0058] 3. Case Analysis The ICLA-Align algorithm proposed in this invention was applied to a railway section in northern Inner Mongolia, which is over 600 kilometers long and currently faces problems such as low track grade, insufficient transport capacity, and aging equipment. The region along this railway is rich in resources, including coal, rare earth minerals, and specialty agricultural products. Capacity expansion can significantly improve transportation efficiency, reduce logistics costs, and promote resource development and industrial upgrading. Secondly, the existing railway technology standards are low, and its capacity is insufficient to meet the growing freight demand. Capacity expansion and upgrading can effectively optimize the regional transportation network, strengthen connections with surrounding trunk lines, alleviate surrounding transportation pressure, promote the implementation of the "road-to-rail" policy, and reduce road congestion and carbon emissions.

[0059] Therefore, electrifying the existing single-track railway, adding a second track, optimizing the route alignment, and improving technical standards are particularly important. In this project, due to the large number of bridge sections with varying minimum track spacing requirements, traditional manual alignment methods struggle to effectively minimize the sandwich area, leading to some waste of land. By optimizing the sandwich area and total construction cost of the manually designed alignment, the sandwich area can be optimized without increasing the length of the track, bridges, or tunnels. The optimization results are detailed in Table 1 (where longitudinal profile data is calculated based on the original alignment). For a 20.329 km long railway, alignment optimization successfully reduced the sandwich area by 7.1%. Furthermore, after multiple tests, the time required for each iteration was consistently kept within 30 seconds.

[0060] Table 1. Algorithm Optimization Results ; Actual optimization results are as follows Figure 5As shown, the red dashed line represents the unmodified manually designed line, the pink dashed line represents the constraint line determined by the minimum line spacing, and the blue solid line represents the result after optimization by this algorithm. It can be seen that in sections where manual design is difficult, such as curves and bridges, the optimized design line is closer to and does not touch the control line, thus achieving the effect of optimizing the area of ​​the sandwiched section of the line. Moreover, this algorithm can quickly generate optimized line design schemes and can generate multiple schemes in a short time, saving designers a lot of waiting time.

[0061] 4. Conclusion In optimizing manually added second-line design lines, existing algorithms face challenges such as excessive intersection point combinations and difficulty in identifying feasible combinations when dealing with stringent line spacing constraints and a limited optimization space. This results in an inability to provide a solution that satisfies the constraints and improves the objective function within a short timeframe. To address the limitations of existing methods—namely, the large number of combinations, slow iteration, and the inability to adjust the number of intersection points beyond those provided by the original manual lines—this invention proposes adaptive intersection point iteration. This approach identifies potential optimization intervals and further optimizes the sandwich area by adding or removing intersection points, while significantly reducing the number of intersection point combinations and achieving rapid solution finding. Specific optimizations are as follows: The method of this invention was applied to a railway section in northern Inner Mongolia for testing. The experimental results show that it can achieve an optimization of the sandwich area by about 7%.

[0062] While maintaining the overall alignment of the artificial route, the algorithm makes fine adjustments to the alignment. For a route optimization task of approximately 20 kilometers, the algorithm can propose improved solutions for optimizing the total cost and the area of ​​the sandwiched land within 30 seconds, thereby reducing the time required for designers to adjust the alignment to a certain extent.

[0063] The embodiments described above are for illustrative purposes only and are not intended to limit the invention. Therefore, any changes in numerical values ​​or substitutions of equivalent elements should still fall within the scope of this invention.

[0064] The above detailed description will enable those skilled in the art to understand that the present invention can indeed achieve the aforementioned objectives and has complied with the provisions of the Patent Law.

[0065] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention. The above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

[0066] It should be noted that the above description of the process is for illustrative purposes only and does not limit the scope of this specification. Those skilled in the art can make various modifications and changes to the process under the guidance of this specification. However, these modifications and changes remain within the scope of this specification.

[0067] The basic concepts have been described above. Obviously, for those skilled in the art who have read this application, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application, and therefore, such modifications, improvements, and corrections still fall within the spirit and scope of the exemplary embodiments of this application.

[0068] Furthermore, this application uses specific terms to describe its embodiments. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different positions in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application can be appropriately combined.

[0069] Furthermore, those skilled in the art will understand that aspects of this application can be described and illustrated through several patentable types or situations, including any new and useful combination of processes, machines, products, or substances, or any new and useful improvements thereof. Therefore, aspects of this application can be implemented entirely in hardware, entirely in software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. All of the above hardware or software can be referred to as a “unit,” “module,” or “system.” Furthermore, aspects of this application can take the form of a computer program product embodied in one or more computer-readable media, wherein computer-readable program code is contained therein.

[0070] The computer program code required for the operation of each part of this application can be written in any one or more programming languages, including object-oriented programming languages ​​such as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB.NET, and Python; general programming languages ​​such as C; Visual Basic, Fortran2103, Perl, COBOL2102, PHP, and ABAP; dynamic programming languages ​​such as Python, Ruby, and Groovy; or other programming languages. This program code can run entirely on the user's computer, or as a standalone software package on the user's computer, or partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer can be connected to the user's computer via any network, such as a local area network (LAN) or wide area network (WAN), or connected to an external computer (e.g., via the Internet), or in a cloud computing environment, or used as a service such as Software as a Service (SaaS).

[0071] Furthermore, unless expressly stated in the claims, the order of processing elements and sequences, the use of numbers and letters, or other names described in this application are not intended to limit the order of the processes and methods of this application. Although some currently considered useful embodiments of the invention have been discussed in the foregoing disclosure by way of various examples, it should be understood that such details are for illustrative purposes only, and the appended claims are not limited to the disclosed embodiments; rather, the claims are intended to cover all modifications and equivalent combinations that conform to the substance and scope of the embodiments of this application. For example, although the implementation of the various components described above can be embodied in a hardware device, it can also be implemented as a purely software solution, such as an installation on an existing server or mobile device.

[0072] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments of the invention, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this approach of the present application should not be construed as reflecting an intention that the claimed subject matter requires more features than expressly recited in each claim. Rather, the subject of the invention should possess fewer features than in any single embodiment described above.

Claims

1. A method for optimizing the alignment of a second railway line to minimize land use, characterized in that: include: S1. Obtain artificial intersection data, existing railway data and corresponding minimum track spacing requirements. The artificial intersection data includes the plane coordinates of each intersection point, the length of the transition curve, and the intersection radius. S2. Based on artificial intersection data, construct a railway horizontal alignment parameter model, and use horizontal control points as the core to parametrically express the geometric features and design specifications of the line; S3. Combining the minimum track spacing requirements and railway design specifications, set track constraints, including track plan constraints and minimum track spacing constraints. Track plan constraints involve minimum requirements for curve radius, circular curve length, transition curve length, and straight section length. Minimum track spacing constraints differentiate between bridge sections and roadbed sections, and determine the position of the constraint line based on the minimum track spacing requirements. S4. Set an objective function to minimize the total land acquisition area for railway construction. The total land acquisition area includes the land acquisition area of ​​each land acquisition area along the entire line and the area of ​​the sandwiched land between the two lines. The sandwiched land is the narrow area enclosed by the land acquisition red line of the existing railway and the newly built railway. S5. Based on the planar alignment parameter model and line constraints, an intersection point classification and iteration mechanism is adopted to identify and distinguish conflict points, active points and passive points through geometric relationships. Oriented optimization strategies are applied to different types of intersection points. The conflict point is the intersection point that violates the line constraints. The active point is the intersection point that participates in the formation of both long and short straight lines and the long straight line is close to or coincides with the constraint line. The passive point is the middle intersection point that avoids the rectangular protrusion of the constraint line of the bridge section. S6. Based on the planar alignment parameter model, line constraints and objective function, an adaptive intersection number iteration mechanism is adopted. Intersections are added or deleted by the branch-and-bound method according to optimization needs, and the number of intersections is dynamically adjusted to broaden the optimization path. S7. Combining the intersection point classification iteration results and the adaptive intersection point quantity iteration results, and based on the line constraints and objective function, select the railway alignment scheme with the best comprehensive optimization effect.

2. The method for optimizing the alignment of a second railway line to minimize land use, as described in claim 1, is characterized in that... In step S5, a priority iteration strategy is implemented for conflict points, while other intersection points remain in their original design positions. The planar coordinates, transition curve lengths, and intersection radii of the conflict points are individually iterated and optimized to ensure that the conflict points meet the line constraints after iteration.

3. The method for optimizing the alignment of a second railway line to minimize land use, as described in claim 1, is characterized in that... In step S5, the iteration direction of the active point is restricted, and the active point is only allowed to iterate along the long straight line and the extension of the long straight line to avoid violating the set minimum line spacing constraint or expanding the sandwich area after iteration.

4. The method for optimizing the alignment of a second railway line to minimize land use, as described in claim 1, is characterized in that... In step S5, the passive point and the active point connecting the long straight lines on both sides form a group. The position iteration of the passive point is bound to the position iteration of the active points on both sides. The position of the passive point is optimized by adjusting the position of the active point in conjunction with the position, so that the passive point always meets the requirement of avoiding the rectangular protrusion of the constraint line of the bridge section.

5. The method for optimizing the alignment of a second railway line to minimize land use, as described in claim 4, is characterized in that... The initial position of the passive point is determined as follows: set the left and right vertices of the convex rectangle of the constraint line as bridge auxiliary points, connect the active point on one side with the bridge auxiliary point on the same side respectively and extend them to form rays. The intersection of the two rays is the initial position of the passive point.

6. The method for optimizing the alignment of a second railway line to minimize land use, as described in claim 1, is characterized in that... The specific process of adding intersection points in step S6 is as follows: Identify a long straight line segment parallel to the constraint line between two bridge segments that are close to each other. When the length of the straight line segment is not less than the preset minimum value and the offset distance from the constraint line is not less than the preset minimum value, the coordinates of the new intersection point are initially confirmed by drawing a perpendicular line from the midpoint of the selected long straight line segment to the constraint line. The new intersection point is verified through iterative verification to ensure that it meets the line constraint conditions. Finally, the coordinates of the new intersection point are determined to optimize the area of ​​the sandwiched land.

7. The method for optimizing the alignment of a second railway line to minimize land use, as described in claim 1, is characterized in that... The specific process of deleting intersection points using the branch and bound method in step S6 is as follows: determine the length of the straight line segments in the planar linear parameter model, mark the intersection points corresponding to the straight line segments with smaller optimization space as candidate deletion points, try to delete the candidate deletion points in a permutation and combination manner, iteratively verify whether the line formed by the remaining intersection points satisfies the line constraint conditions, and retain the deletion iteration scheme that meets the constraints and better fits the objective function.

8. The method for optimizing the alignment of a second railway line to minimize land use, as described in claim 1, is characterized in that... In step S3, the minimum line spacing of the bridge section is greater than the minimum line spacing of the roadbed section. The constraint lines of the corresponding bridge section form an outward rectangular protrusion. This protrusion area is the object to be avoided by the passive point.

9. The method for optimizing the alignment of a second railway line to minimize land use, as described in claim 4, is characterized in that... When the active and passive points are linked and iterated, the active points are moved closer to or further away from the protruding segments of the constraint line, and the sandwich area corresponding to each of the active and passive points is dynamically balanced to minimize the total land acquisition area required by the objective function.

10. The method for optimizing the alignment of a second railway line to minimize land use, as described in claim 1, is characterized in that... In step S7, when selecting the scheme with the best comprehensive optimization effect, it is verified whether the scheme simultaneously meets the line constraints and objective function requirements, and ensures that the optimized line spacing, straight line length, minimum curve radius and circular curve length are reasonably adapted to the existing railway conditions.

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