CN113554467B - Railway three-dimensional linear intelligent design method based on co-evolution - Google Patents

Railway three-dimensional linear intelligent design method based on co-evolution Download PDF

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CN113554467B
CN113554467B CN202110848678.5A CN202110848678A CN113554467B CN 113554467 B CN113554467 B CN 113554467B CN 202110848678 A CN202110848678 A CN 202110848678A CN 113554467 B CN113554467 B CN 113554467B
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缪鹍
周启航
冯倩
戴炎林
李洵贻
李挺
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Abstract

The invention discloses a railway three-dimensional linear intelligent design method based on coevolution, which comprises the steps of firstly establishing two three-dimensional linear design objective functions, and simultaneously solving the quantity and the parameters of plane intersection points and the quantity and the parameters of slope changing points of a three-dimensional linear based on an ArcGIS platform by adopting a coevolution differential algorithm according to the line grade of a railway, the constraint conditions of planes and longitudinal sections and unit price cost to realize the railway three-dimensional linear intelligent design; the three-dimensional linear shape of the intelligent design method can comprehensively consider engineering cost and operation cost, well avoid obstacles and adapt to terrains, and provide early design reference for engineering designers.

Description

Intelligent railway three-dimensional linear design method based on co-evolution
Technical Field
The invention relates to the field of railway line selection, in particular to a railway three-dimensional line intelligent design method based on coevolution.
Background
The intelligent design of three-dimensional linear shape of railway means that the intelligent calculation method is adopted to solve the constructed three-dimensional linear model so as to realize the automatic wiring and automatic design of the three-dimensional linear shape of railway and simultaneously require the minimum objective function of the scheme. The objective function is usually not trivial because it is obtained by interpolation of the digital elevation model and involves various costs. When the railway line is long and has more intersection points and slope changing points, numerous decision variables need to be involved in the process of three-dimensional linear intelligent design, numerous complex factors in project construction are considered, and the factors interact and mutually restrict, so that the railway three-dimensional linear intelligent design is a large-scale complex problem. In the prior art, the intelligent design of the line selection problem is usually to solve all decision variables of a line simultaneously, so that the calculation efficiency is low, and even the local optimal solution is easy to fall into.
The differential algorithm has excellent global optimization performance, better parallelism and robustness, can execute evolution operation according to the distribution condition of individuals in a group, better solves the problem of early convergence of the algorithm, but has slower convergence speed and depends very on the adopted variation strategy and parameter setting. Meanwhile, the coevolution framework can carry out grouping solution on the variables, and efficiently solves the problem of large-scale variable optimization.
Because the existing railway three-dimensional linear intelligent design method can not directly identify, analyze and utilize geographic information, the line selection result is not satisfactory, and the practical application is difficult to realize. The Geographic Information System (GIS) has strong spatial retrieval and analysis capability, can reasonably and quickly process and analyze complex and various surface feature, terrain and landform in the railway three-dimensional linear intelligent design process, and can be visually expressed. However, the prior art does not provide a railway three-dimensional linear intelligent design method combining GIS and co-evolution.
Disclosure of Invention
In order to solve the problems in the existing route selection design, the invention aims to provide a railway three-dimensional linear intelligent design method based on coevolution. The method utilizes the excellent performance of the coevolution in the large-scale multi-target design problem to more efficiently solve the problem of complex route selection design.
The intelligent design method for the three-dimensional linear shape of the railway based on the coevolution comprises the steps of firstly establishing two target functions for the three-dimensional linear shape design, and simultaneously solving the quantity and the parameters of the intersection points of the three-dimensional linear shape based on the ArcGIS platform and the quantity and the parameters of the slope changing points of the longitudinal section by adopting a coevolution differential algorithm according to the line grade of the railway, the constraint conditions of the plane and the longitudinal section and the unit price cost, so that the intelligent design of the three-dimensional linear shape of the railway is realized.
The number and parameters of the three-dimensional linear plane intersections and the number and parameters of the longitudinal section slope-changing points refer to the number, coordinates, radiuses and easement curves of the plane intersections, the number, coordinates, radiuses and easement curves of the longitudinal plane intersections;
the three-dimensional linear plane intersection point and vertical section slope-changing point parameters refer to plane coordinates (x, y), radius R and slow length l of the plane intersection point, and vertical section slope-changing point mileage lzAnd elevation z.
The three-dimensional linear intelligent design method for the railway based on the coevolution is characterized by comprising the following steps of:
step 1: two target functions F for respectively establishing railway three-dimensional line shapes1And F2：
Figure GDA0003687358450000021
F2＝KN·LCp+365·(NH+η·NK)·∑ε1 (2)
Wherein, F1The engineering cost index is a railway three-dimensional linear engineering cost index; l is the cross section serial number; b is the serial number of the bridge; t is the serial number of the tunnel; l is the number of cross sections in the linear design interval; b is the number of bridge seats in the linear design interval; t is the number of the tunnel seats in the design interval; cLThe unit price of the earthwork project is; cBThe unit price of each linear meter of the bridge; cTThe unit price of each linear meter of the tunnel; d is the distance between two adjacent cross sections; a. thelThe area of the first design cross section; a. thel+1The area of the designed cross section is the (l + 1) th; l is a radical of an alcoholbThe length of the b-th bridge; l istThe length of the t-th seat tunnel;
F2the operation cost index is a railway three-dimensional linear operation cost index; kNIs an unrelated rate; LC (liquid Crystal)pThe total length of the line; n is a radical of hydrogenHThe number of the rows of the truck; eta is a conversion coefficient of the travelling train travelling cost; n is a radical ofKThe number of passenger car rows; sigma epsilon1The sum of the running fee of each freight train for one round trip;
step 2: setting a three-dimensional linear plane constraint condition, a longitudinal section constraint condition and a three-dimensional linear design target area constraint condition;
(1) plane constraint condition
(a) Number of intersections constraint, number of intersections n of three-dimensional line shapepThe specification or the artificially specified allowable number should be satisfied, that is: n ispmin≤np≤npmax；
Wherein n ispminA minimum number of intersections specified for specification or human; n ispmaxA maximum number of intersections specified for normative or artificial;
(b) minimum circular curve radius constraint, plane intersection point PiRadius of the circular curve RJDiNot less than the minimum circular curve radius RminNamely: rmin≤RJDi(i＝1,2,…,np-1)；
(c) Minimum circular curve length constraint, plane intersection point PiLength L of the circular curveRiNot less than the minimum circular curve length LRminNamely: l isRmin≤LRi＝RJDi·|αi|(i＝1,2,…,np-1)；
Wherein alpha isiIs a plane intersection point PiThe steering angle of (d);
(d) minimum relaxed curve length constraint, plane intersection point PiLength of the relaxation curve l0JDiNot less than the minimum relief curve length l0minNamely: l. the0min≤l0JDi(i＝1,2,…,np-1)；
(e) Minimum clip line length constraint, clip line length L between two adjacent easement curves of different intersection pointsjiNot less than the minimum clip line length LjminNamely: l isjmin≤Lji＝Li,i+1-Ti-Ti+1(i＝1,2,…,np-1)；
Wherein L isi,i+1Is a plane intersection point PiTo the plane intersection point Pi+1The distance of (a); t is a unit ofiIs a plane intersection point PiThe tangent length of (2); t is a unit ofi+1Is a plane intersection point Pi+1The tangent length of (2);
(2) longitudinal section constraint condition
(a) The number of the variable slope points is restrained, and the number of the three-dimensional linear variable slope points is nzThe specification or a human-defined allowed number should be met, i.e.: n is a radical of an alkyl radicalzmin≤nz≤nzmax；
Wherein n iszminThe minimum number of the grade changing points is specified by a standard or a person; n is a radical of an alkyl radicalzmaxThe maximum number of grade change points specified for the norm or the human;
(b) minimum slope length constraint, distance L between two adjacent slope change pointspjNot less than the minimum slope length LpminNamely: l is a radical of an alcoholpmin≤Lpj＝XBPDj+1-XBPDj(j＝1,2,…,nz-1)；
Wherein XBPDjFor changing the slope point HjMileage of (2); xBPDj+1To change the slope point Hj+1Mileage of (1);
(c) longitudinal section slope constraint, slope i of two adjacent points of variationBPDjThe allowed gradient should be met, either by specification or by human regulation, i.e.:
Figure GDA0003687358450000031
wherein iminA minimum slope segment length specified for regulatory or human; i.e. imaxMaximum length of slope, Z, specified for regulation or manmadeBPDjFor changing the slope point HjElevation of (d); zBPDj+1To change the slope point Hj+1Elevation of (d);
(d) the slope difference of adjacent slope segments is constrained and the slope difference of adjacent slope segments is delta iBPDjNot greater than a standard or artificially specified maximum gradient difference Δ imaxNamely: delta iBPDj＝|iBPDj-iBPDj-1|≤Δimax；
(3) The three-dimensional linear design target area constraint, the three-dimensional linear design target area (x, y), should satisfy the range specified by the human, namely: x is the number ofmin≤x≤xmax，ymin≤y≤ymax
And 3, step 3: searching for an optimal linear shape by adopting a co-evolution differential algorithm from a three-dimensional linear design target area;
a, step a: setting population size NP, a variation factor, a cross factor, a greedy factor, maximum function evaluation times and an iteration cycle of random grouping;
step b: taking the number and parameters of all plane intersection points and the number and parameters of longitudinal section gradient-changing points on a three-dimensional line as individuals, wherein the individuals comprise n-dimensional variables, and randomly distributing the n-dimensional variables to s groups Pi(i ═ 1,2, …, s), each group comprising m dimensions of variables, each group being assigned a sub-individual of size NP, each group being initialized according to the upper and lower limit values corresponding to the m dimensions of the variables for which each group is responsible for optimization;
step c: according to an inter-group cooperation mode, each sub-individual is cooperated with sub-individuals of other groups, the fitness value of the sub-individuals in each group is calculated by adopting a railway three-dimensional linear objective function, each group is subjected to rapid non-dominant sorting based on the fitness value, the non-dominant grade of each sub-individual is obtained, and the congestion distance value of each sub-individual in each group is calculated at the same time;
the specific implementation manner of inter-group cooperation is as follows:
because the sub-individuals in each sub-population only contain partial dimensionality of the three-dimensional linear variable, the fitness evaluation cannot be independently completed, and the sub-individuals in a certain sub-population must cooperate with other sub-populations to complete the fitness evaluation, namely, the inter-group cooperation:
f(i,j)＝f(P1y,…Pj-1y,z,Pj+1y,…Psy) (3)
wherein f (i, j) represents the fitness of the jth sub-individual in the ith sub-population; p isjy represents the position of a random sub-individual at the highest non-dominant level in other sub-populations; z represents the current position of the jth sub-individual in the ith sub-population;
step d: for all groups Pi(i-1, 2, …, s) performing a mutation operation and a crossover operation of a differential algorithm to generate a subgroup Qi(i is 1,2, …, s), and the method of inter-group cooperation is adopted according to the purpose of three-dimensional line shape of the railwayCalculating the fitness value of each sub-group neutron individual by the standard function, and then updating an external archive set;
wherein, the external archive set is updated as follows:
1) if the current group PiOf (b) dominates the progeny group QiSelecting the current group PiThe child individuals of (2) enter an external archive set; 2) if the child group QiDominates the current group PiSelecting a progeny group QiThe child individuals enter an external archive set; 3) if the child group QiAnd the current group PiThe two sub-individuals are selected and stored in an external file set;
step e: performing non-domination sorting on all the sub-individuals of the external archive set, calculating the non-domination level and the crowded distance value of each sub-individual, selecting NP sub-individuals as a new group according to the non-domination level and the crowded distance value of the sub-individuals, and entering next generation for updating;
wherein, the non-dominating ordering mode is as follows:
1) for all the sub-individuals, finding out all non-dominated sub-individuals according to a Pareto domination relation, using the non-dominated sub-individuals as a first-level non-dominated layer, and recording the non-dominated ranking values Rank of the sub-individuals as 1;
2) removing the individuals which have obtained the non-dominant grade values from the whole external archive set, and carrying out next round of comparison on the remaining sub-individuals to obtain a second-level non-dominant layer; and so on until all individuals obtain their non-dominant rank values;
step f: judging whether the current function evaluation times reach the maximum function evaluation times, if the current function evaluation times meet the termination condition, obtaining a final complete non-dominated solution set containing all variable dimensions from the optimal front edge (the sub-individual with the domination level of 1) of the external archive set, outputting the solution set, obtaining the optimal three-dimensional linear shape of the railway, and ending; if the evaluation times do not meet the algorithm termination condition, judging whether the current function evaluation times meet the iteration period of the random grouping, if so, executing the updating group number s, returning to the step d to continue updating, and if not, directly returning to the step d to continue updating.
The invention provides a railway three-dimensional linear intelligent design method based on coevolution, which can be known by analyzing the test result of railway three-dimensional linear intelligent design of a research area as follows: the invention can rapidly and efficiently select and solve the line of the plane and the vertical section of the line at the same time, and the three-dimensional line of the intelligent design method can comprehensively consider the engineering cost and the operation cost, better avoid the obstacle and adapt to the terrain, and provide the early design reference for engineering designers. In addition, the invention has the following beneficial effects:
(1) the scheme has good diversity and high efficiency. And finally, generating an optimal scheme group which comprises different characteristics such as a bypass scheme and a bridge and tunnel erecting scheme instead of a single scheme. By utilizing the co-evolution, the diversity of the intelligent designed circuit scheme is ensured, more than selection schemes with reference values are provided for circuit designers, and the omission of feasible schemes due to subjective factors of the designers is avoided.
(2) Is suitable for large-scale and large-range line selection. The GIS has strong space analysis capability and mass data processing capability, can conveniently and quickly process large-scale landforms, and provides a strong support system for large-scale line selection. The three-dimensional route selection problem of large-scale variables can be divided into a plurality of low-dimensional sub-problems by the aid of the co-evolution, and then each sub-problem is solved independently, so that the calculation efficiency of the three-dimensional route selection problem of the large-scale variables is improved.
Drawings
FIG. 1 is a flow diagram of co-evolution;
FIG. 2 is a schematic illustration of an example topographical plan view;
FIG. 3 is a flow chart of model optimization;
FIG. 4 is a schematic illustration of inter-group collaboration;
FIG. 5 is a schematic diagram of a three-dimensional linear design scheme set.
Detailed Description
The invention is further illustrated with reference to the following figures and examples:
the invention provides a railway three-dimensional linear intelligent design method based on coevolution, which comprises the steps of firstly establishing two three-dimensional linear design objective functions, and simultaneously solving the quantity and the parameters of plane intersection points and the quantity and the parameters of slope changing points of a three-dimensional linear based on an ArcGIS platform by adopting a coevolution differential algorithm according to the line grade of a railway, the constraint conditions of planes and longitudinal sections and unit price cost, so as to realize the railway three-dimensional linear intelligent design.
The number and parameters of the three-dimensional linear plane intersection points and the number and parameters of the vertical section slope changing points refer to the number, coordinates, radiuses and easement curves of the plane intersection points, the number, coordinates, radiuses and easement curves of the vertical section intersection points;
the three-dimensional linear plane intersection point and vertical section slope-changing point parameters refer to plane coordinates (x, y), radius R and slow length l of the plane intersection point, and vertical section slope-changing point mileage lzAnd elevation z.
The co-evolution flow chart is shown in fig. 1.
The example covers 220.8km with the east of Chongqing City in China2And taking a mountainous area terrain with the altitude of 255-1445 m as a research area, and testing the developed road three-dimensional linear intelligent design method, as shown in figure 1. The specific topographic data of the research area is TIFF file of the terrain obtained from the Earth of Google, then Global Mapper is adopted to convert the TIFF file into contour lines in DWG format, and finally Arcmap is utilized to convert line elements of the contour lines into point elements which can be identified by ArcGIS.
The line selection is to design a three-level road with the length of about 12km in a line selection area by applying the invention, and as shown in fig. 2, the line selection area is a mountain and heavy hill area, and has the defects of undulation of terrains and vertical and horizontal gullies and no bad geological conditions. Setting parameters according to specific conditions: the designed speed per hour is 80 km/h; the range of plane intersection points is [5,15 ]](ii) a The minimum curve radius is 500 m; the minimum circular curve length is 50 m; a minimum relief curve length of 60 m; the minimum clamping line length is 50 m; the range of the longitudinal gradient change point is [5,15 ]](ii) a The length of the minimum slope section is 200 m; maximum limit slope 22%; the maximum longitudinal slope difference is 22%; the unit price of the filled earthwork is 65 yuan/m3(ii) a The unit price of the square earth and stone is 35 yuan/m3(ii) a The unit price of the bridge is 30000 yuan/m2(ii) a The unit price of the tunnel is 28000 yuan/m2。
Fig. 3 shows a flow chart of model optimization.
Step 1: respectively establishing two target functions F of railway three-dimensional line shape1And F2：
Figure GDA0003687358450000061
F2＝KN·LCp+365·(NH+η·Nk)·∑ε1 (5)
Wherein, F1The engineering cost index is a railway three-dimensional linear engineering cost index; l is the serial number of the cross section; b is the serial number of the bridge; t is the serial number of the tunnel; l is the number of cross sections in the linear design interval; b is the number of bridge seats in the linear design interval; t is the number of the tunnel seats in the design interval; cLThe unit price of the earthwork project is; cBThe unit price of each linear meter of the bridge; cTThe unit price of each linear meter of the tunnel; d is the distance between two adjacent cross sections; a. thelThe area of the first design cross section; a. thel+1The area of the designed cross section is the (l + 1) th; l isbThe length of the b-th bridge; l is a radical of an alcoholtThe length of the t-th seat tunnel;
F2the operation cost index is a railway three-dimensional linear operation cost index; kNIs an unrelated rate; LC (liquid Crystal)pIs the total length of the line; n is a radical ofHThe number of the rows of the trucks is; eta is a travel cost conversion coefficient of the travelling train; n is a radical of hydrogenKThe number of passenger car rows; sigma epsilon1The sum of the running fees of each freight train for one round trip;
step 2: setting a three-dimensional linear plane constraint condition, a longitudinal section constraint condition and a three-dimensional linear design target area constraint condition;
(1) plane constraint condition
(a) Number of intersections constraint, number of intersections n of three-dimensional linepThe specification or a human-defined allowed number should be met, i.e.: n ispmin≤np≤npmax；
Wherein n ispminMinimum number of intersections specified for specification or human；npmaxA maximum number of intersections specified for specification or human;
(b) minimum circular curve radius constraint, plane intersection point PiRadius of the circular curve RJDiNot less than the minimum circular curve radius RminNamely: r ismin≤RJDi(i＝1,2,…,np-1)；
(c) Minimum circular curve length constraint, plane intersection point PiLength L of the circular curveRiNot less than the minimum circular curve length LRminNamely: l isRmin≤LRi＝RJDi·|αi|(i＝1,2,…,np-1)；
Wherein alpha isiIs a plane intersection point PiThe steering angle of (d);
(d) minimum relaxed curve length constraint, plane intersection point PiLength of the relaxation curve l0JDiNot less than the minimum relief curve length l0minNamely: l0min≤l0JDi(i＝1,2,…,np-1)；
(e) Minimum clip line length constraint, clip line length L between two adjacent easement curves of different intersection pointsjiNot less than the minimum clip line length LjminNamely: l isjmin≤Lji＝Li,i+1-Ti-Ti+1(i＝1,2,…,np-1)；
Wherein L isi,i+1Is a plane intersection point PiTo the plane intersection point Pi+1The distance of (d); t isiIs a plane intersection point PiThe tangent length of (2); t isi+1Is a plane intersection point Pi+1The tangent length of (2);
(2) longitudinal section constraint condition
(a) The number of the variable slope points is restrained, and the number n of the three-dimensional linear variable slope pointszThe specification or a human-defined allowed number should be met, i.e.: n is a radical of an alkyl radicalzmin≤nz≤nzmax；
Wherein n iszminThe minimum number of grade changing points specified for the standard or man-made; n is a radical of an alkyl radicalzmaxThe maximum number of grade change points specified for the norm or the human;
(b) minimum slope segment lengthConstraint, distance L between two adjacent grade-changing pointspjNot less than the minimum slope length LpminNamely: l ispmin≤Lpj＝XBPDj+1-XBPDj(j＝1,2,…,nz-1)；
Wherein XBPDjFor changing the slope point HjMileage of (2); xBPDj+1For changing the slope point Hj+1Mileage of (2);
(c) longitudinal section slope constraint, slope i of two adjacent slope-changing pointsBPDjThe allowed gradient should be met, either by specification or by human regulation, i.e.:
Figure GDA0003687358450000071
wherein iminA minimum slope segment length that is normative or artificially specified; i.e. imaxMaximum length of slope, Z, specified for regulation or manmadeBPDjFor changing the slope point HjElevation of (d); zBPDj+1To change the slope point Hj+1Elevation of (d);
(d) the slope difference of the adjacent slope sections is restrained, and the slope difference of the adjacent slope sections is delta iBPDjNot greater than a standard or artificially specified maximum gradient difference Δ imaxNamely: Δ iBPDj＝|iBPDj-iBPDj-1|≤Δimax；
(3) The three-dimensional linear design target area constraint, the three-dimensional linear design target area (x, y), should satisfy the range specified by the human, namely: x is the number ofmin≤x≤xmax，ymin≤y≤ymax
And 3, step 3: searching for an optimal linear shape by adopting a co-evolution differential algorithm from a three-dimensional linear design target area;
step a: setting population size NP, variation factors, cross factors, greedy factors, maximum function evaluation times and an iteration cycle of random grouping;
step b: taking the number and parameters of all plane intersection points and the number and parameters of longitudinal section gradient-changing points on a three-dimensional line as individuals, wherein the individuals comprise n-dimensional variables, and randomly distributing the n-dimensional variables to s groups Pi(i-1, 2, …, s), each group containing m dimensions of the variable, each group being assigned a large numberInitializing each group according to upper limit values and lower limit values corresponding to m dimensions of variables for each group to be responsible for optimization, wherein each sub-individual is small as NP;
step c: according to an inter-group cooperation mode, each sub-individual is cooperated with sub-individuals of other groups, the fitness value of the sub-individuals in each group is calculated by adopting a railway three-dimensional linear objective function, each group is subjected to rapid non-dominant sorting based on the fitness value, the non-dominant grade of each sub-individual is obtained, and the crowding distance value of each sub-individual in each group is calculated at the same time;
the specific implementation mode of the inter-group cooperation is as follows:
because the sub-individuals in each sub-population only contain partial dimensionality of the three-dimensional linear variable, the fitness evaluation cannot be independently completed, and the sub-individuals in a certain sub-population must cooperate with other sub-populations to complete the fitness evaluation, namely, the inter-group cooperation:
f(i,j)＝f(P1y,…Pj-1y,z,Pj+1y,…Psy) (6)
wherein f (i, h) represents the fitness of the jth individual in the ith sub-population; pjy represents the position of a random one of the other sub-populations at the highest non-dominant level; z represents the current position of the jth sub-individual in the ith sub-population;
step d: for all groups Pi(i-1, 2, …, s) performing a mutation operation and a crossover operation of a differential algorithm to generate a child group Qi(i-1, 2, …, s), calculating the fitness value of each sub-group neutron individual according to the target function of the railway three-dimensional linear shape by adopting an inter-group cooperation mode, and then updating an external file set;
wherein, the external archive set is updated as follows:
1) if the current group PiOf (2) dominates the progeny group QiSelecting the current group PiThe child individuals enter an external archive set; 2) if the child group QiDominates the current group PiSelecting a progeny group QiThe child individuals of (2) enter an external archive set; 3) if it is usedSubgroup QiAnd the current group PiThe two sub-individuals are selected and stored in an external archive set;
step e: performing non-domination sorting on all the sub-individuals of the external archive set, calculating the non-domination level and the crowding distance value of each sub-individual, selecting NP sub-individuals as a new group according to the non-domination level and the crowding distance value of the sub-individuals, and entering next generation for updating;
wherein, the non-dominating ordering mode is as follows:
1) for all the sub-individuals, finding out all non-dominated sub-individuals according to a Pareto domination relation to serve as a first-level non-dominated layer, and marking the non-dominated ranking values Rank of the sub-individuals as 1;
2) removing the individuals with the non-dominance grade values from the whole external archive set, and performing the next round of comparison on the remaining sub-individuals to obtain a second-level non-dominance layer; and so on until all individuals obtain their non-dominant rank values;
step f: judging whether the current function evaluation times reach the maximum function evaluation times, if the current function evaluation times meet the termination condition, obtaining a final complete non-dominated solution set containing all variable dimensions from the optimal front edge (the sub-individual with the domination level of 1) of the external archive set, outputting the solution set, obtaining the optimal three-dimensional linear shape of the railway, and ending; if the evaluation times do not meet the algorithm termination condition, judging whether the current function evaluation times meet the iteration period of the random grouping, if so, executing the updating group number s, returning to the step d to continue updating, and if not, directly returning to the step d to continue updating.
FIG. 4 is a schematic diagram of group cooperation.
After the basic parameters of line selection are set, the three-dimensional linear design scheme set of the line is generated by inputting the coordinates of the starting point and the coordinates of the end point and adopting the method provided by the invention, as shown in fig. 5. The scheme set comprises 26 schemes which can avoid plane elevation obstacles well.
Through the above steps, information of the whole line can be obtained, and table 2 shows target values and partial information of the first seven obtained schemes of the 26 schemes; taking the first solution as an example, the plane intersection data of the first solution is shown in table 3, and the vertical section gradient point data of the first solution is shown in table 4.
TABLE 2 target values and partial information for seven schemes
Figure GDA0003687358450000091
Table 3 plan one intersection data
Figure GDA0003687358450000092
Table 4 plan one of the vertical section slope changing data
Figure GDA0003687358450000101

Claims (1)

1. A three-dimensional linear intelligent design method for a railway based on co-evolution is characterized by comprising the following steps:
step 1: respectively establishing two target functions F of railway three-dimensional line shape1And F2：
Figure FDA0003678336240000011
F2＝KN·LCp+365·(NH+η·NK)·∑ε1 (2)
Wherein, F1The engineering cost index is a railway three-dimensional linear engineering cost index; l is the cross section serial number; b is the serial number of the bridge; t is the serial number of the tunnel; l is the number of cross sections in the linear design interval; b is the number of bridge seats in the linear design interval; t is the number of the tunnel seats in the design interval; cLThe unit price of the earthwork project is; cBThe unit price of each linear meter of the bridge; cTThe unit price of each linear meter of the tunnel; d is between two adjacent cross sectionsA distance; a. thelThe area of the first design cross section; a. thel+1The area of the designed cross section is the (l + 1) th; l isbThe length of the b-th bridge; l is a radical of an alcoholtThe length of the t-th seat tunnel;
F2the operation cost index is a railway three-dimensional linear operation cost index; kNIs an unrelated rate; LC (liquid Crystal)pIs the total length of the line; n is a radical of hydrogenHThe number of the rows of the truck; eta is a conversion coefficient of the travelling train travelling cost; n is a radical ofKThe number of passenger train rows; sigma epsilon1The sum of the running fees of each freight train for one round trip;
and 2, step: setting linear design target area constraint conditions according to the line grade of a railway, constraint conditions of planes and longitudinal sections and unit cost, and simultaneously solving the quantity and parameters of three-dimensional linear plane intersection points and the quantity and parameters of longitudinal section slope changing points based on the ArcGIS platform by adopting a coevolution differential algorithm;
the number and parameters of the three-dimensional linear plane intersections and the number and parameters of the longitudinal section slope-changing points refer to the number, coordinates, radii and relaxation curves of the plane intersections, the number, coordinates, radii and relaxation curves of the longitudinal plane intersections;
(1) plane constraint condition
(a) Number of intersections constraint, number of intersections n of three-dimensional linepThe specification or the artificially specified allowable number should be satisfied, that is: n ispmin≤np≤npmax；
Wherein n ispminA minimum number of intersections specified for specification or human; n ispmaxA maximum number of intersections specified for specification or human;
(b) minimum circular curve radius constraint, plane intersection point PiRadius of the circular curve RJDiNot less than the minimum circular curve radius RminNamely: r ismin≤RJDi(i＝1，2，…，np-1)；
(c) Minimum circular curve length constraint, plane intersection point PiLength L of the circular curveRiNot less than the minimum circular curve length LRminNamely: l isRmin≤LRi＝RJDi·|αi|(i＝1，2，…，np-1)；
Wherein alpha isiIs a plane intersection point PiThe steering angle of (d);
(d) minimum relaxed curve length constraint, plane intersection point PiLength of the relaxation curve l0JDiNot less than the minimum relief curve length l0minNamely: l. the0min≤l0JDi(i＝1，2，…，np-1)；
(e) Minimum clip line length constraint, clip line length L between two adjacent easement curves at different intersection pointsjiNot less than the minimum clip line length LjminNamely: l is a radical of an alcoholjmin≤Lji＝Li，i+1-Ti-Ti+1(i＝1，2，…，np-1)；
Wherein L isi，i+1Is a plane intersection point PiTo the plane intersection point Pi+1The distance of (a); t isiIs a plane intersection point PiThe tangent length of (2); t is a unit ofi+1Is a plane intersection point Pi+1The tangent length of (2);
(2) longitudinal section constraint condition
(a) The number of the variable slope points is restrained, and the number of the three-dimensional linear variable slope points is nzThe specification or a human-defined allowed number should be met, i.e.: n iszmin≤nz≤nzmax；
Wherein n iszminThe minimum number of the grade changing points is specified by a standard or a person; n iszmaxThe maximum number of grade change points specified for the norm or the human;
(b) minimum slope length constraint, distance L between two adjacent slope change pointspjNot less than the minimum slope length LpminNamely: l is a radical of an alcoholpmin≤Lpj＝XBPDj+1-XBPDj(j＝1，2，…，nz-1)；
Wherein, XBPDjFor changing the slope point HjMileage of (1); xBPDj+1For changing the slope point Hj+1Mileage of (2);
(c) longitudinal section slope constraint, slope i of jth slope segmentBPDjThe allowed gradient should be met, either by specification or by human regulation, i.e.:
Figure FDA0003678336240000021
wherein iminA minimum slope segment length that is normative or artificially specified; i all right anglemaxMaximum length of slope, Z, specified for regulation or for human purposesBPDjFor changing the slope point HjElevation of (d); zBPDj+1To change the slope point Hj+1Elevation of (d);
(d) the slope difference of the adjacent slope sections is restrained, and the slope difference of the adjacent slope sections is delta iBPDjNot greater than a standard or artificially specified maximum difference in grade Δ imaxNamely: delta iBPDj＝|iBPDj-iBPDj-1|≤Δimax；
Wherein iBPDj-1The gradient of the j-1 th slope section;
(3) the three-dimensional linear design target area constraint, the three-dimensional linear design target area (x, y), should satisfy the range area specified by human, namely: x is the number ofmin≤x≤xmax，ymin≤y≤ymax；
Wherein (x)min，ymin) Is a point at the lower left corner of the range area defined by human beings, (x)max，ymax) Is a point at the upper right corner of the manually specified range region;
and step 3: searching for an optimal linear shape by adopting a co-evolution differential algorithm from a three-dimensional linear design target area;
a, step a: setting population size NP, variation factors, cross factors, greedy factors, maximum function evaluation times and an iteration cycle of random grouping;
step b: taking the number and parameters of all plane intersection points and the number and parameters of longitudinal section gradient-changing points on a three-dimensional line as individuals, wherein the individuals comprise n-dimensional variables, and randomly distributing the n-dimensional variables to s groups Pi(i ═ 1,2, …, s), each group containing m dimensions of variables, each group being assigned to children of size NP, each group being initialized according to the upper and lower limit values corresponding to the m dimensions of the variables for which each group is responsible for optimization;
step c: according to an inter-group cooperation mode, each sub-individual is cooperated with sub-individuals of other groups, the fitness value of the sub-individuals in each group is calculated by adopting a railway three-dimensional linear objective function, each group is subjected to rapid non-dominant sorting based on the fitness value, the non-dominant grade of each sub-individual is obtained, and the crowding distance value of each sub-individual in each group is calculated at the same time;
the specific implementation mode of the inter-group cooperation is as follows:
because the sub-individuals in each sub-population only contain partial dimensionality of the three-dimensional linear variable, the fitness evaluation cannot be independently completed, and the sub-individuals in a certain sub-population must cooperate with other sub-populations to complete the fitness evaluation, namely, inter-group cooperation:
f(i，j)＝f(P1y，…Pj-1y，z，Pj+1y，…Psy) (3)
wherein f (i, j) is the fitness of the jth sub-individual in the ith sub-population; pjy is the position of a random sub-individual at the highest non-dominant level in other sub-populations; z is the current position of the jth sub-individual in the ith sub-population;
step d: for all groups Pi(i-1, 2, …, s) performing a mutation operation and a crossover operation of a differential algorithm to generate a subgroup Qi(i is 1,2, …, s), calculating the fitness value of each sub group neutron individual according to the target function of the railway three-dimensional linear shape by adopting an inter-group cooperation mode, and then updating an external archive set;
the mutation operation and the crossover operation of the difference algorithm are as follows:
1) mutation operation: the differential algorithm generates variant individuals for each individual in the population through a variant strategy, namely:
Figure FDA0003678336240000031
wherein, Vi GIs the ith individual
Figure FDA0003678336240000032
Variant individuals at passage G;
Figure FDA0003678336240000033
are randomly selected individuals from the current population,
Figure FDA0003678336240000034
Figure FDA0003678336240000035
is an individual randomly selected from the current population and an external archive set;
Figure FDA0003678336240000036
is an individual randomly selected from an algorithm non-dominated solution set; f is a variation factor; r and rnd are two between [0, 1 ]]A random number of ranges;
2) and (3) cross operation: after mutation operation is executed to obtain a mutation individual, combining the target individual and the mutation individual by adopting a binomial crossover operator to obtain an offspring individual, namely:
Figure FDA0003678336240000037
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003678336240000038
represents the j dimension of the ith test subject in the G generation,
Figure FDA0003678336240000039
represents the j dimension of the ith variant individual in the G generation,
Figure FDA00036783362400000310
represents the j dimension, rand, of the ith individual in the G generationi，j() Represents [0, 1 ]]Random numbers uniformly distributed in the range, Cr denotes crossover operator, jrandRepresents [0, n]Random integers uniformly distributed within the range;
wherein, the external archive set is updated as follows:
1) if the current group PiOf (b) dominates the progeny group QiSelecting the current group PiThe child individuals enter an external archive set; 2) if the child group QiDominates the current group PiSelecting a progeny group QiThe child individuals enter an external archive set; 3) if the child group QiAnd the current group PiThe two sub-individuals are selected and stored in an external file set;
step e: performing non-domination sorting on all the sub-individuals of the external archive set, calculating the non-domination level and the crowded distance value of each sub-individual, selecting NP sub-individuals as a new group according to the non-domination level and the crowded distance value of the sub-individuals, and entering next generation for updating;
wherein, the non-dominating ordering mode is as follows:
1) for all the sub-individuals, finding out all non-dominated sub-individuals according to a Pareto domination relation, using the non-dominated sub-individuals as a first-level non-dominated layer, and recording the non-dominated ranking values Rank of the sub-individuals as 1;
2) removing the individuals with the non-dominance grade values from the whole external archive set, and performing the next round of comparison on the remaining sub-individuals to obtain a second-level non-dominance layer; and so on until all individuals have obtained their non-dominant rank values;
step f: judging whether the current function evaluation times reach the maximum function evaluation times, if the current function evaluation times meet the termination condition, obtaining a final complete non-dominated solution set containing all variable dimensions from the optimal front edge of an external archive set, namely a sub-individual with a domination level of 1, outputting the solution set, obtaining the optimal three-dimensional linear shape of the railway, and ending; if the algorithm termination condition is not met, judging whether the current function evaluation times meet the iteration period of the random grouping, if so, executing the updating group number s, returning to the step d to continue updating, and if not, directly returning to the step d to continue updating.
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