High-dimensional optimization method for railway longitudinal profile based on population and nonlinear gradient

Abstract

The application discloses a kind of railway longitudinal section linear high-dimensional optimization method based on population and nonlinear gradient, belong to computer aided design technical field, including steps S1, according to the longitudinal section diagram of railway starting point and terminal, establishes longitudinal section linear high-dimensional optimization model;S2, longitudinal section linear is segmented according to preset mileage interval, constructs a subgrade proxy model for each segment, and the sum of the subgrade comprehensive fee of subgrade section constitutes subgrade engineering cost in longitudinal section linear high-dimensional optimization model;S3, fusion parallel JADE optimization algorithm and nonlinear gradient optimization algorithm solve longitudinal section linear high-dimensional optimization model.The application combines the global search ability of population algorithm with the local optimization efficiency of nonlinear gradient algorithm, solves the high-dimensional railway longitudinal section optimization problem.Proposed subgrade proxy model is used to calculate the subgrade comprehensive fee of each segment, so as to quickly calculate the subgrade engineering cost in total project cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer-aided design, and particularly relates to a railway longitudinal profile line high-dimensional optimization method based on population and nonlinear gradient. BACKGROUND

[0002] Computer technology has been widely applied in many fields such as electronic commerce, manufacturing, logistics transportation, traffic planning, public management, etc. In the field of engineering design, the introduction of computers has greatly improved the design efficiency and promoted the technological progress in the engineering field. In particular, in the railway engineering design industry, basic tools such as computer-aided design (CAD) software are constantly developing towards intelligence, gradually changing the traditional design thinking and process. Railway line design is a complex process of multi-disciplinary collaboration, among which the plane and longitudinal profile of the line are important basis for design and decision-making, and the longitudinal profile design process is the basic basis for evaluating the rationality of the plane design process. The pros and cons of the railway longitudinal profile line design directly affect the feasibility and economy of the project implementation. The traditional railway design method relies on engineers to compare and analyze multiple schemes and manually fine-tune local line sections to optimize the design scheme. Due to the diversity of geographical environment, the complexity of the calculation process, and the comprehensiveness of the cost calculation, the traditional manual design method often cannot guarantee to find the optimal line scheme, and the design efficiency is low, and the engineering progress is also greatly affected. The line optimization model is to abstract the influencing factors and process of the actual line design into a pure mathematical optimization problem, and to express the geometric characteristics, engineering characteristics and economic requirements of the line through a series of variables, constraint conditions and objective functions. This abstraction makes it possible to analyze and solve the model through optimization algorithms, efficiently and scientifically replacing the manual route selection design process, more comprehensively evaluating the design scheme, and further optimizing the project cost. SUMMARY

[0003] The purpose of the present application is to provide a railway longitudinal profile line high-dimensional optimization method based on population and nonlinear gradient, which solves the above problems, combines the global search advantage of the population algorithm and the efficient local search advantage of the nonlinear gradient optimization, and improves the solving efficiency of the optimization model.

[0004] To achieve the above purpose, the technical scheme adopted by the present application is as follows: a railway longitudinal profile line high-dimensional optimization method based on population and nonlinear gradient, comprising the following steps:

[0005] S1, establishing a longitudinal profile line high-dimensional optimization model according to the railway longitudinal profile;

[0006] Among them, the longitudinal profile line in the longitudinal profile includes a starting point, an ending point and at least two slope change points between the two points.

[0007] The longitudinal profile high-dimensional optimization model comprises a target function and a constraint condition, wherein the target function is a total engineering cost related to the longitudinal profile, including a bridge engineering cost C b , a tunnel engineering cost C t , a subgrade engineering cost C s , a bridge land acquisition cost C l , a cost related to a characteristic region of the longitudinal profile C f , and an operation cost C o related to the longitudinal profile

[0008] S2, the longitudinal profile is segmented according to a preset mileage interval, a subgrade agent model for calculating a subgrade comprehensive cost is constructed for each segment, and the sum of the subgrade comprehensive costs of all segments constitutes the subgrade engineering cost C s , wherein the construction method of the subgrade agent model of a segment comprises steps S21-S24;

[0009] S21, the ground line from the starting point to the ending point is divided into several segments according to a preset mileage interval, and a rectangular space range is generated for each segment;

[0010] S22, the track surface elevation is taken as a variable, and t sampling points x1-x t are obtained by uniformly sampling at the lowest point to the highest point of the space range, and the subgrade comprehensive cost y1-y t corresponding to the sampling points x1-x t is calculated;

[0011] S23, the weight w1-w t corresponding to x1-x t is calculated according to the following formula, and a weight vector is generated;

[0012] ,

[0013] In the formula, Gij is a Gaussian kernel function in the i-th row and the j-th column of the matrix, , , is a Gaussian function, i and j are the row index and the column index of the matrix respectively, 1≤i≤t, and 1≤j≤t;

[0014] S24, a subgrade agent model of the segment is generated ;

[0015] In the formula, x is any track surface elevation in the space range of the segment, is the subgrade comprehensive cost corresponding to the segment when the track surface elevation is x;

[0016] S3, the parallel JADE optimization algorithm and the nonlinear gradient optimization algorithm are fused to solve the longitudinal profile high-dimensional optimization model, comprising S31-S34;

[0017] S31, adding a plurality of slope change points on the longitudinal profile with a preset first interval, and assigning a variable and a control rectangle to each slope change point, the variable being a slope change point coordinate (M, E), wherein M and E are the mileage and elevation of the slope change point, respectively, and the control rectangle is used to control the variable range;

[0018] S32, taking the low-dimensional longitudinal profile formed by connecting the start point to the end point through the slope change points as an individual, and randomly generating a plurality of individuals as an initial population;

[0019] S33, splitting the initial population into a plurality of sub-populations, and presetting migration conditions and iteration termination conditions;

[0020] S34, based on the parallel JADE optimizer, each sub-population independently executes an evolution process and adaptively adjusts the parameter scaling factor F and the crossover factor Cr, when the migration condition is met, a individual is randomly selected from each sub-population and migrated to an adjacent sub-population according to a ring topology, and after the iteration termination condition is met, the individual with the smallest target function value is selected as the optimal longitudinal profile;

[0021] The evolution process includes mutation, crossover, evaluation and selection, and the evaluation and selection include steps Sa1-Sa3;

[0022] Sa1, generating a trial sub-population from the current sub-population after mutation and crossover, and labeling the corresponding individuals in the current sub-population and the trial sub-population as individual 1 and individual 2, respectively, and comparing the number of constraint conflicts;

[0023] Sa2, if the number of constraint conflicts is not all 0, selecting the individual with fewer constraint conflicts as the dominant individual, and if the number of constraint conflicts is 0, performing Sa3;

[0024] Sa3, using a nonlinear gradient optimizer to optimize the longitudinal profile corresponding to individual 2 to generate a corresponding high-dimensional profile, and bringing it into the high-dimensional longitudinal profile optimization model to calculate the target function value, and selecting the individual 1 or individual 2 with the smaller target function value as the dominant individual.

[0025] As preferred: In Sa3, the method of using a nonlinear gradient optimizer to optimize the longitudinal profile to generate a high-dimensional profile includes steps Sb1-Sb6;

[0026] Sb1, dividing the longitudinal profile into a plurality of vertical curve segments and slope segments according to the slope change points, and adding a plurality of slope change points on the slope segments of the longitudinal profile with a preset second interval;

[0027] Sb2, for each slope segment, calculating its negative gradient direction;

[0028] Sb3, calculating the projection plane and the descending direction of the slope segment;

[0029] Sb4, under the condition of vertical and horizontal non-overlapping, one-dimensional search is performed to find the optimal step size in the descending direction, and the line of the current slope section is moved to the next state;

[0030] Sb5, if the optimal step size of the last five generations is less than 0.2, the iteration is terminated, and the optimized slope section line is obtained, otherwise, step Sbl is returned;

[0031] Sb6, all the optimized slope section lines are combined with the vertical curve section to obtain a high-dimensional line.

[0032] As preferred: the first interval in S31 is 8 times the length of the minimum slope section, and the second interval in Sb1 is 2 times the length of the minimum slope section.

[0033] As preferred: in S21, the mileage interval is 5m-10m; the method for generating a segmented space range is to obtain a segment, take the ground line at both ends as the two side boundaries, take the ground line center elevation as the zero point, take the maximum fill height as the highest point, and take the maximum excavation depth as the lowest point, and generate the space range of the segment.

[0034] As preferred: in S22, the subgrade comprehensive cost of the segment includes the subgrade surface layer cost, the fill and excavation cost, the retaining wall structure cost, and the subgrade land acquisition cost.

[0035] As preferred: when splitting the population, the initial population is split into N sub-populations according to the number of CPU cores N; when mutating the sub-population, a differential operator is randomly selected for each sub-population, and the differential operator includes DE / current-to-p-best / 1 / bin, DE / rand / 2 / bin, and DE / best / 1 / bin.

[0036] As preferred: the target function is , to minimize the total project cost of the longitudinal section line , and Δ is the investment efficiency coefficient.

[0037] As preferred: the number of constraint conflicts in Sa1 is + ;

[0038] N1 is the current slope section length conflict number, if the current slope section length is less than the minimum slope section length, N1 is the absolute value of the difference between them, otherwise, N1 is 0;

[0039] N2 is the current slope conflict number, if the absolute value of the slope is greater than the maximum slope, N2 is 1000 times the absolute value of the difference between them, otherwise, N2 is 0;

[0040] N3 is the slope algebraic difference conflict number, if the slope algebraic difference is greater than the maximum slope algebraic difference, N3 is 1000 times the absolute value of the difference between them, otherwise, N3 is 0.

[0041] As preferred: if there are n slope change points including the start point and the end point on the profile of the longitudinal section, the constraint conditions are fixed start and end point constraints, station slope constraints, maximum slope constraints, minimum slope section length constraints, and slope algebraic difference constraints when the non-linear gradient optimizer is used for optimization;

[0042] The fixed start and end point constraints are:

[0043] ,

[0044] In the formula, , and are respectively a 2n×4 order coefficient matrix and a corresponding 4-dimensional constant vector, , and are respectively the mileage and the elevation of the start point, , and are respectively the mileage and the elevation of the end point;

[0045] Station slope constraints;

[0046] ,

[0047] In the formula, , and are respectively a 2n×2 order coefficient matrix and a corresponding 2-dimensional constant vector; is a small mileage station slope, is a large mileage station slope, , and are respectively the mileage and the elevation of the second slope change point, , and are respectively the mileage and the elevation of the n-1th slope change point;

[0048] Maximum slope constraints;

[0049] ,

[0050] In the formula , and are respectively a 2n×(n-1) order coefficient matrix and a corresponding n-1-dimensional constant vector for the positive maximum slope; , and are respectively a 2n×(n-1) order coefficient matrix and a corresponding n-1-dimensional constant vector for the negative maximum slope;

[0051] Minimum slope section length constraints;

[0052] ,

[0053] In the formula, , and are respectively a 2n×(n-1) order coefficient matrix and a corresponding (n-1) dimensional constant vector;

[0054] Slope algebraic difference constraint;

[0055]

[0056] The above constraint satisfies AX+d≤0, wherein A, d are any element in the corresponding set respectively, and X is a decision vector composed of the mileage and elevation of the variable slope point;

[0057] Slope algebraic difference constraint;

[0058]

[0059] In the formula, is a 6x6 order coefficient matrix corresponding to the slope algebraic difference of the i variable slope points, is a 2n x (6n-12) dimensional constant vector, and the slope algebraic difference constraint satisfies the formula T is a transposition operation.

[0060] Compared with the prior art, the present application has the following advantages:

[0061] (1) The global search ability of the population algorithm is combined with the local optimization efficiency of the nonlinear gradient algorithm to solve the high-dimensional railway longitudinal section optimization problem. In the method, the longitudinal section line obtained in step S32 is taken as a low-dimensional longitudinal section line, only including the starting point, the ending point and a small amount of variable slope points, the low-dimensional longitudinal section line shape is taken as an individual to form an initial population, the parallel JADE optimization algorithm is used to divide the initial population into a plurality of sub-populations, and the evolution process is independently executed, so that the optimization efficiency is improved. In the independent evolution process of each sub-population, after the individual mutation and crossover, before the selection of the superior individual, in addition to the existing constraint conflict number comparison to select the superior individual, the nonlinear gradient algorithm is introduced to locally optimize the low-dimensional longitudinal section line of the new individual, the high-dimensional line shape of the variable slope point is brought into the high-dimensional optimization model of the longitudinal section line shape to calculate the objective function value, and the superior individual is selected by comparing the objective function values of the individual 1 and the individual 2. The method can quickly solve the high-dimensional optimization problem of the railway longitudinal section line shape.

[0062] (2) The present application proposes a new method, fitting out the subgrade proxy model of each section to calculate the subgrade comprehensive cost of each section, and the sum of the subgrade comprehensive costs of all sections in the subgrade section constitutes the subgrade engineering cost in the total project cost. The method can avoid the sampling of the subgrade slope elevation in the optimization iteration process, and realizes the efficient calculation of the subgrade engineering cost in the total project cost.

[0063] (3) The present application introduces sub-population parallel computing and ring topology individual migration in the JADE algorithm, which can balance the convergence efficiency and population diversity in the global optimization process. ​​​

[0064] (4) The present application takes the slope point mileage and elevation of the longitudinal section line as variables, lists the corresponding quadratic constraint quadratic programming longitudinal section line optimization model, and solves it by using the nonlinear gradient method, thereby improving the local search ability of the overall optimization model. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 is a railway longitudinal section map;

[0066] Figure 2 is a schematic diagram of generating a corresponding high-dimensional line for individual 2 in the subpopulation;

[0067] Figure 3 schematic diagram of dividing segments and generating a space range in step S21;

[0068] Figure 4 is a schematic diagram of a roadbed cross section;

[0069] Figure 5 is Figure 4 schematic diagram of setting up a retaining wall for the filling section on the left side;

[0070] Figure 6 is Figure 4 schematic diagram of setting up a retaining wall for the excavation section on the right side;

[0071] Figure 7 is a parallel JADE optimization algorithm framework diagram;

[0072] Figure 8 is a parallel JADE algorithm framework diagram;

[0073] Figure 9 is a nonlinear gradient optimization flowchart for a slope section;

[0074] Figure 10 is the overall flowchart of the present application. DETAILED DESCRIPTION

[0075] The present application will be further described below in conjunction with examples and drawings.

[0076] Example 1: Referring to Figures 1 to 8 , Figure 10 A railway longitudinal section line high-dimensional optimization method based on population and nonlinear gradient, comprising the following steps:

[0077] S1, establishing a longitudinal section line high-dimensional optimization model according to a railway longitudinal section map;

[0078] wherein the longitudinal section line in the longitudinal section map includes a starting point, an ending point and at least two slope change points between the two points;

[0079] The high-dimensional optimization model for longitudinal profile alignment includes an objective function and constraints. The objective function is the total project cost related to the longitudinal profile alignment, including bridge engineering costs C. b Tunnel engineering cost C t Roadbed engineering cost C s Bridge land acquisition cost C l Costs related to longitudinal profile feature areas (C) f Operating costs related to longitudinal profile alignment C o ;

[0080] S2, the longitudinal profile is divided into segments according to preset mileage intervals, and a roadbed proxy model is constructed for each segment to calculate its comprehensive roadbed cost. The sum of the comprehensive roadbed costs of all segments constitutes the roadbed engineering cost C. s The method for constructing a roadbed proxy model for one segment includes steps S21 to S24.

[0081] S21, Divide the ground line from the starting point to the end point into several segments according to the preset mileage interval, and generate a rectangular spatial range for each segment;

[0082] S22 uses the track surface elevation as a variable, and uniformly samples from the lowest to the highest point in space to obtain t sampling points x1 to x2. t The sampling points are calculated as x1~x t At that time, the comprehensive roadbed cost y1~y corresponding to this segment t ;

[0083] S23, calculate x1~x according to the following formula. t The corresponding weights w1~w t Generate weight vector ;

[0084] ,

[0085] In the formula, Let be the Gaussian kernel function in the i-th row and j-th column of its matrix. , Let be a Gaussian function, i and j be the row and column indices of the matrix, respectively, 1≤i≤t, 1≤j≤t;

[0086] S24, Generate segmented roadbed proxy models ;

[0087] Where x is the elevation of any rail surface within the segmented spatial range. When the track surface elevation is taken as x, the corresponding comprehensive cost of the roadbed for this segment;

[0088] S3, which integrates the parallel JADE optimization algorithm and the nonlinear gradient optimization algorithm to solve the high-dimensional optimization model of longitudinal profile, includes S31~S34;

[0089] S31, adding a plurality of slope change points on the longitudinal profile line at a preset first interval, and assigning a variable and a control rectangle to each slope change point, the variable being a slope change point coordinate (M, E), where M and E are the mileage and elevation of the slope change point, respectively, and the control rectangle being used to control the variable range;

[0090] S32, taking the low-dimensional longitudinal profile line formed by connecting the start point to the end point through the slope change points as an individual, and randomly generating a plurality of individuals as an initial population;

[0091] S33, splitting the initial population into a plurality of sub-populations, and presetting a migration condition and an iteration termination condition;

[0092] S34, based on a parallel JADE optimizer, each sub-population independently performs an evolution process and adaptively adjusts a parameter scaling factor F and a crossover factor Cr, when the migration condition is met, each sub-population randomly selects an individual to migrate to an adjacent sub-population according to a ring topology, and after the iteration termination condition is met, an individual with the smallest target function value is selected as an optimal longitudinal profile line;

[0093] The evolution process includes mutation, crossover, evaluation and selection, and the evaluation and selection include steps Sa1-Sa3;

[0094] Sa1, generating a trial sub-population from the current sub-population after mutation and crossover, labeling the corresponding individuals in the current sub-population and the trial sub-population as individual 1 and individual 2, respectively, and comparing the number of constraint conflicts;

[0095] Sa2, if the number of constraint conflicts is not all 0, selecting the individual with fewer constraint conflicts as the dominant individual, and if the number of constraint conflicts is all 0, performing Sa3;

[0096] Sa3, using a nonlinear gradient optimizer to optimize the longitudinal profile line corresponding to individual 2 to generate a corresponding high-dimensional line, and calculating the target function value in the longitudinal profile line high-dimensional optimization model, and selecting the individual 1 or individual 2 with the smaller target function value as the dominant individual.

[0097] Regarding Figures 4 to 6 , Figure 4 In, is the left side slope excavation sectional area, is the right side slope excavation sectional area, is the middle excavation sectional area, is the middle filling sectional area, is the left shoulder elevation, is the right shoulder elevation; Figure 5 In, is the left side slope retaining wall height, Figure 6 In, is the right side slope retaining wall height.

[0098] Embodiment 2: refer to Figures 1 to 8 、 Figure 10 In S3, the method for generating high-dimensional alignment by using a nonlinear gradient optimizer to optimize the longitudinal alignment includes steps Sb1-Sb6.

[0099] Sb1, the longitudinal alignment is divided into several vertical curve segments and slope segments according to the variable slope points, and several variable slope points are added to the slope segments of the longitudinal alignment at a preset second interval.

[0100] Sb2, for each slope segment, the negative gradient direction thereof is calculated.

[0101] Sb3, the projection plane and the falling direction of the slope segment are calculated.

[0102] Sb4, under the condition of vertical non-overlapping, a one-dimensional search is performed to find the optimal step length in the falling direction, and the alignment of the current slope segment is moved to the next state.

[0103] Sb5, if the optimal step length of the last 5 generations is less than 0.2, the iteration is terminated, and the optimized slope segment alignment is obtained, otherwise, the step Sbl is returned.

[0104] Sb6, all the optimized slope segment alignments are combined with the vertical curve segments to obtain the high-dimensional alignment.

[0105] Embodiment 3: refer to Figures 1 to 8 、 Figure 10 On the basis of Embodiment 1 and Embodiment 2, the first interval in step S31 is 8 times the minimum slope segment length, and the second interval in Sb1 is 2 times the minimum slope segment length.

[0106] In step S21, the mileage interval is 5-10 m; the method for generating the segmented space range is that a segment is obtained, the ground line at both ends thereof is taken as the two side boundaries, the ground line center elevation is taken as the zero point, the maximum fill height is taken as the highest point, and the maximum excavation depth is taken as the lowest point, and the space range of the segment is generated.

[0107] In step S22, the subgrade comprehensive cost of the segment includes the subgrade surface layer cost, the fill and excavation cost, the retaining wall structure cost, and the subgrade land acquisition cost.

[0108] When splitting the population, the initial population is split into N sub-populations according to the number N of CPU cores; when the sub-population is mutated, a differential operator is randomly selected for each sub-population, and the differential operator includes DE / current-to-p-best / 1 / bin, DE / rand / 2 / bin, and DE / best / 1 / bin.

[0109] The objective function is , to minimize the total engineering cost of the longitudinal alignment , Δ is the investment efficiency coefficient.

[0110] The number of constraint conflicts in step Sa1 + ;

[0111] N1 is the current slope length conflict number, if the current slope length is less than the minimum slope length, N1 is the absolute value of the difference between them, otherwise 0;

[0112] N2 is the current slope conflict number, if the absolute value of the slope is greater than the maximum slope, N2 is the absolute value of the difference between them multiplied by 1000, otherwise 0;

[0113] N3 is the slope algebraic difference conflict number, if the slope algebraic difference is greater than the maximum slope algebraic difference, N3 is the absolute value of the difference between them multiplied by 1000, otherwise 0.

[0114] Embodiment 4: see Figures 1 to 8 、 Figure 10 On the basis of Embodiments 1-3, if there are n slope change points including the start and end points on the vertical section alignment, when using a nonlinear gradient optimizer for optimization, the constraint conditions are fixed start and end point constraints, station slope constraints, maximum slope constraints, minimum slope length constraints, and slope algebraic difference constraints.

[0115] The fixed start and end point constraints are:

[0116] ,

[0117] In the formula, 、 and are a 2n×4 coefficient matrix and a corresponding 4-dimensional constant vector respectively, 、 and are the mileage and elevation of the start point respectively, 、 and are the mileage and elevation of the end point respectively;

[0118] Station slope constraints;

[0119] ,

[0120] In the formula, 、 and are a 2n×2 coefficient matrix and a corresponding 2-dimensional constant vector respectively; is the small mileage station slope, is the large mileage station slope, 、 and are the mileage and elevation of the second slope change point respectively, 、 and are the mileage and elevation of the n-1th slope change point respectively;

[0121] Maximum slope constraints;

[0122] ,

[0123] wherein , are the positive maximum slope 2n x (n-1) order coefficient matrix and the corresponding n-1 dimensional constant vector respectively; , are the negative maximum slope 2n x (n-1) order coefficient matrix and the corresponding n-1 dimensional constant vector respectively;

[0124] Minimum slope segment length constraint;

[0125] ,

[0126] wherein , are the 2n x (n-1) order coefficient matrix and the corresponding (n-1) dimensional constant vector respectively;

[0127] Slope algebraic difference constraint;

[0128] ,

[0129] The above constraint satisfies AX+d≤0, , wherein A, d are any element in the corresponding set respectively, and X is the decision vector composed of the mileage and elevation of the variable slope point;

[0130] Slope algebraic difference constraint;

[0131] ,

[0132] wherein is the 6 x 6 order coefficient matrix corresponding to the i variable slope point slope algebraic difference constraint, is the 2n x (6n-12) dimensional constant vector, and the slope algebraic difference constraint satisfies the formula T is the transpose operation.

[0133] Embodiment 5: see Figures 1 to 10 A high-dimensional optimization method for railway longitudinal section alignment based on population and nonlinear gradient, comprising the following steps:

[0134] S1, according to the vertical section diagram of the railway starting point and the terminal point, a vertical section line shape high-dimensional optimization model is established; the vertical section diagram contains a vertical section line shape, a ground line, and a vertical section control point, wherein the vertical section line shape includes a starting point, a terminal point, and at least two slope change points between the two points; the vertical section line shape is used to determine the elevation, length, and slope of the station; the ground line is a 100m stake or a 200m stake; the vertical section control point represents objects such as lakes, rivers, poor geology, environmental protection zones, and existing line intersection zones. The vertical section line shape design standards include the minimum station length, the shortest slope section length, the vertical curve radius, the maximum slope algebraic difference, and the like; when the railway is constructed, the total engineering cost related to the vertical section line shape includes the bridge engineering cost C b , the tunnel engineering cost C t , the subgrade engineering cost C s , the bridge land acquisition cost C l , the cost related to the vertical section characteristic area C f , and the operation cost related to the vertical section line shape C o .

[0135] The bridge engineering cost C b is calculated as follows:

[0136] ,

[0137] In the calculation formula of C b , n is the number of bridges; L i is the length of the ith bridge; U beam is the unit length price of the bridge; m i is the number of piers of the ith bridge, m i =L i / standard span; U pier is the unit length price of the pier, and U pile is the unit length cost of the pier pile under the bridge; H i,j is the height of the jth pier of the ith bridge; and r b is the growth rate of the unit length price with the length of the pier.

[0138] The tunnel engineering cost C t is calculated as follows: ,

[0139] In the calculation formula of C t , L i is the length of the ith tunnel; U t is the unit length price of the tunnel; and r t is the growth rate of the unit length price with the length of the tunnel.

[0140] The subgrade engineering cost C s includes the subgrade surface layer cost, the filling and excavation cost, the retaining wall structure cost, and the subgrade land acquisition cost, and is calculated as follows:

[0141] ,

[0142] In the calculation formula of subgrade engineering cost C s , n is the number of subgrade sections, L i is the length of the i-th subgrade, U surface is the unit price of the subgrade surface layer, C i,left is the left slope cost of the i-th subgrade, C i,center is the middle earthwork cost of the i-th subgrade, C i,right is the right slope cost of the i-th subgrade, S 1,j is the left slope filling and digging sectional area of the j-th section, S 2,j is the right slope filling and digging sectional area of the j-th section, S 3,j is the middle digging sectional area of the j-th section, S 4,j is the middle filling sectional area of the j-th section, H R1,j is the left slope retaining wall height of the j-th section, H R2,j is the right slope retaining wall height of the j-th section, L step is the calculation step length of the subgrade section, U fill is the unit volume price of filling, U fillwall is the unit area price of the filling section retaining wall, U cut is the unit volume price of digging, U cutwall is the unit area price of the digging section retaining wall.

[0143] Bridge land acquisition cost C l , ; in the formula of C l , m is the number of bridges, L i is the length of the i-th bridge, W b is the width of the bridge, U bl is the unit price of land acquisition under the bridge.

[0144] Cost related to longitudinal section characteristic area C f , ; in the calculation formula of C f , n is the number of longitudinal section characteristic areas, L i is the intersection length of the longitudinal alignment and the i-th longitudinal section characteristic area, U i,feature is the unit length price of the i-th longitudinal section characteristic area.

[0145] Operating cost related to longitudinal alignment C o :

[0146] , in the calculation formula of C o , n is the number of slope sections, L i is the length of the i-th slope section, U iThe unit length price of the train running in the uphill direction of the ith slope section is determined by the slope of the slope section; N train The number of trains in both directions for daily round trips.

[0147] The high-dimensional optimization model of the longitudinal profile line includes an objective function and constraint conditions, wherein the objective function can be represented as , The total construction cost of the longitudinal profile line is minimized , and Δ is the investment efficiency coefficient, which is taken as 0.06 in the present embodiment.

[0148] S2, same as step S2 of embodiment 1, specifically, regarding the specific steps S21-S24;

[0149] S21, the ground line from the starting point to the ending point is divided into several sections according to the preset mileage interval = 5m, and a rectangular space range is generated for each section. Taking one section as an example, the lowest point of the space range is marked as , and the highest point is marked as ;

[0150] S22-S24, same as steps S22-S24 of embodiment 1.

[0151] S3, fusion and parallel JADE optimization algorithm and nonlinear gradient optimization algorithm are used to solve the high-dimensional optimization model of the longitudinal profile line, including S31-S34;

[0152] S31, the first interval is 8 times the minimum slope section length, and the rest is the same as step S31 of embodiment 1;

[0153] S32, same as step S32 of embodiment 1, the purpose is to randomly generate multiple individuals as the initial population, each individual corresponding to a low-dimensional longitudinal profile line;

[0154] S33, same as step S33 of embodiment 1, in the present embodiment, the number of initial population = CPU core number = N;

[0155] S34, same as step S34 of embodiment 1, in particular, when the sub-population is mutated, each sub-population is randomly mutated by any one of the three difference operators DE / current-to-p-best / 1 / bin, DE / rand / 2 / bin and DE / best / 1 / bin. During the evolution of the sub-population, each sub-population independently performs the evolution process and dynamically adjusts the parameters of the scale factor F and the cross factor Cr. As for the migration condition, in this embodiment, it can be performed by means of a preset migration constant. The migration constant is compared with a temporary random number. If the random number is greater than the migration constant, the next iteration is directly entered. If the random number is less than the migration constant, the individual migration between the sub-populations is performed. When migrating, each sub-population randomly selects an individual from the dominant individuals (the first 100% P, P = max(0.03, 3 / NP)) and migrates to the adjacent sub-population according to the ring topology. As for the iteration termination condition, it can be the number of iterations or the linear convergence condition. For example, in this embodiment, when the high-dimensional longitudinal profile linearly converges to the optimal linear within a 3m area, the iteration process is terminated.

[0156] As for the generation of the high-dimensional linear by the nonlinear gradient optimizer to optimize the longitudinal profile linear, same as steps Sb1-Sb6 in embodiment 2, more specifically:

[0157] In Sb1, the second interval is 2 times the length of the minimum slope section;

[0158] In Sb2, the negative gradient direction of the slope section is composed of the mileage partial derivative and the elevation partial derivative at the slope change point, that is, The calculation formula is:

[0159] ,

[0160] ,

[0161] Sb3-Sb6, same as steps Sb3-Sb6 of embodiment 2.

[0162] Combined with Figure 9 , the process of calculating the projection surface of the slope section in Sb3 includes Sb31-Sb37;

[0163] Sb31, consider as the active constraint vector;

[0164] Sb32, normalize the constraint vector to form the constraint matrix ;

[0165] Sb33, calculate the offset constant ;

[0166] Sb34, calculate to form the constraint matrix with offset ;

[0167] Sb35, compute projection plane ;

[0168] Sb36, line search to find optimal step size

[0169] Sb37, stop if optimal step size is less than 0.2, otherwise go back to Sb31

[0170] Figure 9 in: = value of kth iteration variable = 0.01 = vector of partial derivatives of kth iteration variable = negative gradient direction; J is the set of active constraint vectors taken from ; = matrix of normalized and offset active constraint vectors = projection plane = maximum step size = jth offset constraint vector taken from ; = constant value corresponding to jth offset constraint vector taken from .

[0171] The above description is only the preferred embodiment of the application, and is not intended to limit the application. Any modification, equivalent replacement and improvement made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A railway longitudinal profile alignment high-dimensional optimization method based on population and nonlinear gradient, characterized in that: The method comprises the following steps; S1, establishing a high-dimensional optimization model of the vertical alignment according to a railway vertical profile; The vertical alignment in the vertical profile comprises a starting point, an ending point and at least two slope change points between the two points; The longitudinal profile alignment high-dimensional optimization model comprises a target function and constraint conditions, wherein the target function is the total engineering cost related to the longitudinal profile alignment, including bridge engineering cost C b , tunnel engineering cost C t , subgrade engineering cost C s , bridge land acquisition cost C l , cost related to the characteristic region of the longitudinal profile C f , operation cost related to the longitudinal profile alignment C o ; S2, segmenting the longitudinal section line according to preset mileage intervals, constructing a subgrade proxy model for calculating the subgrade comprehensive cost for each segment, and summing up the subgrade comprehensive costs of all segments to obtain the subgrade engineering cost C s The method for constructing the subgrade proxy model of one segment comprises steps S21-S24. S21, dividing the ground line from the starting point to the ending point into several segments according to a preset mileage interval, and generating a rectangular space range for each segment; S22 uses the track surface elevation as a variable, and uniformly samples from the lowest to the highest point in space to obtain t sampling points x1 to x2. t The sampling points are calculated as x1~x t At that time, the comprehensive roadbed cost y1~y corresponding to this segment t ; S23, calculate x1~x t corresponding weights w1~w t , generate weight vector ; ， In the formula, is a Gaussian kernel function in the i-th row and j-th column of the matrix in which it is located, , is a Gaussian function, i and j are the row index and column index of the matrix respectively, 1≤i≤t, 1≤j≤t; S24, generating the segmented subgrade proxy model ; Wherein, x is any track surface elevation in the segment space range, When x is the track surface elevation, the segment corresponds to the roadbed comprehensive fee; S3, solving the high-dimensional optimization model of the vertical alignment by fusing the parallel JADE optimization algorithm and the nonlinear gradient optimization algorithm, comprising S31-S34; S31, adding a plurality of slope change points to the vertical alignment at a preset first interval, and assigning a variable and a control rectangle to each slope change point, wherein the variable is a slope change point coordinate (M, E), M and E are the mileage and elevation of the slope change point respectively, and the control rectangle is used to control the change range of the variable; S32, taking the low-dimensional vertical alignment formed by connecting the starting point to the ending point through the slope change points as an individual, and randomly generating a plurality of individuals as an initial population; S33, splitting the initial population into a plurality of sub-populations, and presetting a migration condition and an iteration termination condition; S34, based on the parallel JADE optimizer, each sub-population independently performs an evolution process and adaptively adjusts a parameter scale factor F and a crossover factor Cr, when the migration condition is met, each sub-population randomly selects an individual to migrate to an adjacent sub-population according to a ring topology, and after the iteration termination condition is met, an individual with the smallest target function value is selected as an optimal vertical alignment; The evolution process comprises mutation, crossover, evaluation and selection, and the evaluation and selection comprise steps Sa1-Sa3; Sa1, generating a trial sub-population from the current sub-population after mutation and crossover, marking the corresponding individuals in the current sub-population and the trial sub-population as individual 1 and individual 2 respectively, and comparing the number of constraint conflicts; Sa2, if the number of constraint conflicts is not all 0, selecting the individual with fewer constraint conflicts as the dominant individual, and if the number of constraint conflicts is all 0, performing Sa3; Sa3, using the nonlinear gradient optimizer to optimize the vertical alignment corresponding to individual 2 to generate a corresponding high-dimensional alignment, and bringing the high-dimensional alignment into the high-dimensional optimization model of the vertical alignment to calculate the target function value, and selecting individual 1 or individual 2 with a smaller target function value as the dominant individual; In Sa3, the method for generating a high-dimensional alignment by optimizing the vertical alignment using the nonlinear gradient optimizer comprises steps Sb1-Sb6; Sb1, dividing the vertical alignment into a plurality of vertical curve segments and slope segments according to the slope change points, and adding a plurality of slope change points to the slope segments of the vertical alignment at a preset second interval; Sb2, for each slope segment, calculating the negative gradient direction thereof; Sb3, calculating the projection plane and the descent direction of the slope segment; Sb4, under the condition that the vertical buffer does not overlap, one-dimensionally searching to find the optimal step length in the descent direction, and moving the alignment of the current slope segment to the next state; Sb5, if the optimal step length of five consecutive generations is less than 0.2, terminating the iteration to obtain the optimized slope segment alignment, otherwise returning to step Sb1; Sb6, combining all the optimized slope segment alignments and the vertical curve segments to obtain a high-dimensional alignment.

2. The method for high-dimensional optimization of railway longitudinal profile alignment based on population and nonlinear gradient according to claim 1, characterized in that: In S31, the first interval is 8 times the minimum slope segment length, and in Sb1, the second interval is 2 times the minimum slope segment length.

3. The population and non-linear gradient based railway longitudinal profile alignment high dimensional optimization method of claim 1, wherein: In S21, the mileage interval is 5m-10m; the method for generating the spatial range of the section is: obtaining a section, taking the two ends of the ground line as the two side boundaries, taking the central elevation of the ground line as the zero point, taking the maximum fill height as the highest point and the maximum excavation depth as the lowest point, and generating the spatial range of the section.

4. The population and non-linear gradient based railway longitudinal profile alignment high dimensional optimization method of claim 1, wherein: In S22, the comprehensive cost of the section includes the roadbed surface layer cost, the fill and excavation cost, the retaining wall structure cost, and the roadbed land acquisition cost.

5. The population and non-linear gradient based railway longitudinal profile alignment high dimensional optimization method of claim 1, wherein: When splitting the population, the initial population is split into N sub-populations according to the number of CPU cores; when the sub-populations are mutated, each sub-population randomly selects a difference operator, and the difference operator includes DE / current-to-p-best / 1 / bin, DE / rand / 2 / bin and DE / best / 1 / bin.

6. The population and non-linear gradient based railway longitudinal profile alignment high dimensional optimization method of claim 1, wherein: The objective function is min C 总 is the total construction cost C of the longitudinal profile shape 总 Δ is the investment efficiency coefficient.

7. The population and non-linear gradient based railway longitudinal profile alignment high dimensional optimization method of claim 1, wherein: Number of constraint conflicts in Sa1 ​​ N1 is the current slope length conflict number, if the current slope length is less than the minimum slope length, N1 is the absolute value of the difference between the two, otherwise 0; N2 is the current slope conflict number, if the absolute value of the slope is greater than the maximum slope, N2 is the absolute value of the difference between the two multiplied by 1000, otherwise 0; N3 is the slope algebraic difference conflict number, if the slope algebraic difference is greater than the maximum slope algebraic difference, N3 is the absolute value of the difference between the two multiplied by 1000, otherwise 0.

8. The population and non-linear gradient based railway longitudinal profile alignment high dimensional optimization method of claim 1, wherein: If there are n slope change points including the start point and the end point on the vertical section line, when using a nonlinear gradient optimizer for optimization, the constraint conditions include fixed start and end point constraints, station slope constraints, maximum slope constraints, minimum slope length constraints, and slope algebraic difference constraints.

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