CONCURRENT OPTIMIZATION OF RAILWAY …docs.trb.org/prp/17-02741.pdf1 CONCURRENT OPTIMIZATION OF RAILWAY ALIGNMENT AND STATION ... 4 5 Hao Pu 6 School of Civil Engineering ... 2 Railway

CONCURRENT OPTIMIZATION OF RAILWAY ALIGNMENT AND STATION 1

LOCATIONS IN MOUNTAINS TERRAIN 2

3

4

Hao Pu 5

School of Civil Engineering 6

National Engineering Laboratory for High Speed Railway Construction 7

Central South University 8

22 Shaoshan South Rd, Changsha, China 410075 9

Tel: +86 139-7311-9632 Fax: +86-731-8557-1736; Email: [email protected] 10

11

Hong Zhang 12






18

Wei Li, Corresponding Author 19






25

Lei Wang 26






32

Jiaxing Xiong 33






39

Word count: 4,877 words text + 10 tables/figures × 250 words (each) = 7,377 words 40

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Submission Date: July 31, 2016 43

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Submitted for presentation at the 96th Annual Meeting of the Transportation Research Board and for 45 publication in the Transportation Research Record 46

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mailto:[email protected]

mailto:[email protected]

Pu, Zhang, Li, Wang, Xiong 2

ABSTRACT 1

Railway location design is a complex work, which involves the determination of station locations and track 2

alignment. Whereas most existing studies emphasize either alignment optimization or station locations 3

optimization and rarely consider the coupling constraints among environment , railway alignment, station and 4

other structures (i.e. bridges and tunnels) which are very critical in mountainous areas. This paper proposes a 5

methodology for concurrently optimizing railway alignment and station locations while satisfying coupling 6

constraints in mountainous areas. 7

Firstly, we formulate a concurrent optimization model incorporating the objective function and 8

multiple constraints. Then, an improved distance transform algorithm is proposed to search promising railway 9

path and station locations using the concurrent optimization model to minimize the comprehensive cost while 10

handling multiple constraints. Finally, we refine the generated combined alternatives of paths with stations to 11

the optimized alignment with stations using the mesh adaptive direct search algorithm. 12

The effectiveness of the method is verified through a real-world case study in a complex mountainous 13

area. The result shows this method can automatically find various promising alignments with stations while 14

satisfying multiple constraints. 15

16

Keywords: Railway, Station location, Alignment, Concurrent optimization, Coupling constraints 17

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INTRODUCTION 1

The goal of railway location design is to find the connection alternative between two given points that is 2

cheapest to build. While there are an infinite number of possible alternatives. Moreover, multiple constraints, 3

such as geometry constraints, location constraints and structure constraints, put these issues in the realm of 4

constrained problems. How to find the optimized connection alternative satisfying multiple constraints is a 5

complex work. Traditional railway location design methods have typically been based on the experiences of 6

engineers with a trial-and-error process. Only limited number of alternatives can be selected. Such a process is 7

time consuming and cannot guarantee its results are near to optimal. 8

Numerous studies in the literature of road and railway location design can be found. Most researches 9

have addressed the optimization of road and railway alignment, involving horizontal alignment optimization 10

(1-4), vertical alignment optimization (5, 6) and three-dimensional alignment optimization (7-11). 11

Some other studies have attempted to find the optimized station locations. Correlation studies fall into 12

two categories. The first category locates railway stations along a given railway alignment (12, 13), whereas 13

the second category, without knowing the alignment, tries to select stations from a set of candidate sites (14, 14

15). 15

However, fewer studies have been directed toward concurrent optimization of railway alignment and 16

station locations. Lai (16, 17) proposed a concurrent railway alignment and station locations optimization 17

method for urban areas. Firstly, it constructed the candidate pool of potential rail transit stations based on the 18

consideration of various site requirements regarding topological features and land availability. Then these 19

candidates were selected along with the alignment between each pair of neighboring stations minimizing the 20

comprehensive cost while satisfying geometry constraints. However, this method does not consider the 21

coupling constraints which are also crucial in complex mountainous areas, where the natural terrain gradient 22

between the start and end points greatly exceeds the maximum allowed design gradient. 23

In such mountainous area, to overcome the huge elevation difference between start and end points, the 24

horizontal alignment should be circuitous to guarantee enough length and the vertical design elevation should 25

be continuously increased or reduced with the allowed maximum gradient to reach the target elevation. 26

Besides, numerous bridges and tunnels are needed in these complex mountains. While stations should be set on 27

horizontal tangents to provide drivers good vision lines to signs and signals, and they also need to be set on flat 28

slope sections to prevent trains from sliding. Since maximum design gradient cannot be used in stations, the 29

alignment must be more circuitous to reach target elevation. All these make it very difficult to find long 30

enough tangents with flat slope to locate the stations. Furthermore, stations have to bypass forbidden areas 31

(nature protection areas and geological hazards areas) and should avoid overlapping with tunnels or bridges. 32

The distances between each pair of adjacent stations are also limited in a range to satisfy the required traffic 33

capacity of the alignment and guarantee the safety of operation. Therefore, it is a great challenge to optimize 34

railway alignment jointly with station locations while satisfying such coupling constraints in mountainous 35

areas. 36

This paper proposes a concurrent railway alignment and station locations optimization method for 37

mountainous areas. Multiple coupling constraints are handled during the optimization process. 38

39

CONCURRENT OPTIMIZATION MODEL 40

It is desirable that a model for optimizing railway alignment should exploit a GIS database because massive 41

spatial data are essential for railway alignment design. We use a comprehensive geographic information model 42


(CGIM) to store and manage these data. The study area can be represented using a regular rectangular lattice 1

with three dimensions. All the needed geographic information including coordinate, topography, soil 2

conditions, forbidden areas, unit costs of earthwork, bridges, tunnels and right of way is stored in the cells. The 3

detailed development of CGIM can be found in the authors’ earlier publication (11). Based on the CGIM, we 4

develop a concurrent optimization model incorporating the objective function and multiple constraints. 5

6

Objective Function 7

Railway planners intend to find alternatives which save constructions costs, operating cost and have minimal 8

negative impacts on the environment. So the objective function can be formulated as follow: 9

Min Ctotal = Δ (CE + CB + CT + CR + CL + CS + CI) + CG + CA + CM + CW (1) 10

where Δ = capital recovery factor, which converts the total constructions costs to annual constructions 11

costs: 12

(2) 13

where i is interest rate (%per period), n is the number of compounding periods (economic life). 14

It is usually set as 30 years in China. 15

Ctotal = annual total comprehensive cost (¥), 16

CE = earthwork cost (¥), 17

CB = bridge construction cost (¥), 18

CT = tunnel construction cost (¥), 19

CR = right of way cost (¥), 20

CL = length dependent construction cost (¥), 21

CS = station construction cost (¥), 22

CI = environment impact cost (¥), 23

CG = operating cost sensitive to gradient (¥), 24

CA = operating cost sensitive to the turning angle of horizontal (¥), 25

CM = operating cost sensitive to length (¥), 26

CW = operating cost sensitive to the number of stations (¥). 27

The station construction cost CS and operating cost sensitive to the number of stations CW are 28

formulated as below, others (CE, CB, CT, CR, CL, CG, CA, CM and CI) can be found in the authors’ earlier 29

publication (11) and are not duplicated in this section. 30

The station construction cost CS can be calculated as follow: 31

(3) 32

where Penlt = penalty factor of setting a station in a tunnel, 33

γt = binary variable that equals 1 if the station lies in a tunnel and 0 if it lies outside the tunnel, 34

Penlb = penalty factor of setting a station on a bridge, 35

γb = binary variable that equals 1 if the station lies on a bridge and 0 if it lies outside the bridge, 36

m = number of fill cells within the station (integer), 37

n = number of cut cells within the station (integer), 38


CFi = unit fill cost of the ith cell within the station (¥/m3), 1

CCi = unit cut cost of the ith cell within the station (¥/m3), 2

Hi = ground elevation of the ith cell (m), 3

H0 = design elevation of the station (m), 4

w = cell width (m). 5

The operating cost sensitive to the number of stations CW can be calculated as follow: 6

CW = UW × NW (4) 7

where UW = statistical factor related to the station type, locomotive and effective lengths of 8

receiving-departure track (¥/station). It can be found in the China Railway Engineering Design 9

Manual-Alignment (18), 10

NW = number of stations (integer). 11

12

Multiple Constraints 13

There are multiple constraints affecting the railway location design, including geometry constraints, location 14

constraints, structure constraints, and coupling constraints. The detailed formulations of coupling constraints 15

are presented in this section, others can be found in the author’s earlier publication (11). 16

Coupling constraints are critical. However, most existing studies overlook these constraints. In this 17

section, we classify coupling constraints into three categories: coupling constraints between station locations 18

and railway alignment; coupling constraints between station locations and structures (bridges or tunnels), 19

coupling constraints between station locations and environment. 20

21

Coupling Constraints between Station Locations and Railway Alignment 22

(1) Horizontal coupling constraint (CSTRHC) 23

The station should be set on a tangent. There are various signal equipment in a station. If a station is set 24

on a curve, it will hinder the driver’s vision and result in a safety hazard. Assuming PS and PE are the two ends 25

of the station on the alignment (FIGURE1a). DP is the linear distance from PS to PE and LP is the corresponding 26

distance along the alignment. Comparing DP with LP, we can judge whether the station is set on the curve or not. 27

If LP > DP, the station is set on the curve (station B in FIGURE1a); if LP = DP the station is set on the tangent 28

(station A in FIGURE1a). 29

30

31

(a) Horizontal coupling constraint 32


1

(b) Vertical coupling constraint 2

3

FIGURE 1 Horizontal and vertical coupling constraints between station locations and alignment 4

5

(2) Vertical coupling constraint (CSTRVC) 6

The station should be set on a flat gradient section to prevent trains from sliding. So if there is a need to 7

set a station on a local path between two cells (e.g. pi,j and pm,n). The gradient between pi,j and pm,n must satisfy 8

equation (5) to ensure that setting a flat gradient section along the station (FIGURE1b), the local path still 9

satisfies the gradient constraint. 10

is ≤ ismax (5) 11

where is = gradient of the local path (‰). 12

(6) 13

where hi,j = elevation of pi,j (m), 14

hm,n = elevation of pm,n (m), 15

xi,j, yi,j = coordinate of pi,j (m), 16

xm,n,, ym,n = coordinate of pm,n (m). 17

ismax = maximum gradient when there is a need to set a station on the local path (‰). 18

(7) 19

where imax = maximum gradient according to design specification (‰). 20

(3) Station spacing constraint (CSTRD) 21

According to the demand of traffic capacity and operation safety, railway designers calculate the 22

maximum and minimum spacing between two adjacent stations. Stations distribution should satisfy the station 23

spacing constraint. 24

Dmin ≤ Ds ≤ Dmax (8) 25

where Ds = spacing between two adjacent stations (km), 26

Dmin = minimum spacing required between two adjacent stations (km), 27


Dmax = maximum spacing required between two adjacent stations (km). 1

2

Coupling Constraints between Station Locations and Structures 3

(1) Station-tunnel constraint (CSTRT) 4

Setting a station in a tunnel will significantly increase the construction investment and difficulty of 5

construction and maintenance. So station location should avoid overlapping with tunnels. During the railway 6

location design process if the excavated depth exceeds a given boundary value (HT) which determined by 7

designers, a tunnel has to be set. So we can use the elevation difference between ground elevation (HG) and 8

design elevation of the station (H0) to constrain the station location. If HG ≥ H0, then the design elevation of 9

the station should satisfy equation (9). 10

HG - H0 < HT (9) 11

(2) Station-bridge constraint (CSTRB) 12

Similarly , setting a station on a bridge also has the same problems. So station location should also 13

avoid overlapping with bridges. If HG < H0, then the design elevation of the station should satisfy equation (10). 14

Where HB is the fill boundary height to determine whether to set a bridge. 15

H0 - HG < HB (10) 16

17

Coupling Constraints between Station Locations and Environment 18

To protect the environment or bypass high cost areas, the station should be avoided setting in forbidden areas 19

such as wetlands, geologic hazard areas and residential areas. According to CGIM (11), we check the cells 20

within the station, if one of them is in forbidden areas, this station is omitted. 21

22

SEARCHING ALGORITHM 23

In this section, a short overview of the authors’ former distance transform algorithm is presented. The 24

algorithm can optimize railway alignment in mountainous areas, but it overlooks station locations. Then, an 25

improved distance transform algorithm based on this algorithm is proposed. Two improvements of the 26

algorithm are discussed. The improved algorithm can search railway alignment and station locations 27

simultaneously. 28

29

Former Distance Transform Algorithm 30

The authors have already proposed a generalized distance transform algorithm for railway alignment 31

optimization (11). The algorithm represents the distance using path cost and sets the starting point or endpoint 32

as the target point to search the optimized path linking the railway start and end points. An adaptive 33

neighboring mask and bidirectional scanning strategy are proposed to promote the success possibility of 34

generating path satisfied complex constraints in mountainous areas. Nonlinear optimization with mesh 35

adaptive direct search (19, 20) is used to refine the path to the final alignment. 36

Assuming pi,j is one random cell in the lattice of CGIM (11), C(pi,j), Δr(pi,j) and Δc(pi,j) are stored in 37

this cell. Where C(pi,j) is the minimum cost from pi,j to the target point, Δr(pi,j) and Δc(pi,j) are the incremental 38

row and column movements at pi,j in the corresponding minimum cost path. 39

Firstly, the method initializes C(pi,j), Δr(pi,j), Δc(pi,j) for all cells: 40

41


Δr(pi,j) = 0 1

Δc(pi,j) = 0 (11) 2

Where B is the target points set. 3

Then, setting the start point as the target point and a two-pass scan of the lattice data is conducted: a 4

forward scan from the top left to the bottom right, and then a backward scan from the bottom right to the top 5

left. When one cell is scanned, the center of the neighboring mask is placed over it, and the local cost Cx,y (i.e. 6

cost between neighboring cells) is added to the value of the cell, as shown in FIGURE2. The values are 7

refreshed by equation (12). 8

C(pi,j) = min {C(pm,n)+Cx,y} 9

Δr(pi,j) = x 10

Δc(pi,j) = y (12) 11

Where C(pi,j) = new cost value at pi,j, 12

pm,n = one random cell in the neighboring mask as shown in FIGURE2, 13

C(pm,n) = cost value at pm,n, 14

Cx,y = local cost from pi,j to pm,n, 15

x , y = values of incremental row and column movements at pi,j in the corresponding 16

minimum cost path. 17

Iterating the two-pass scan process until the values of each cell are static, then the start distance image 18

DTS is generated. The final C(pi,j) in DTS is the minimum cost from pi,j to the target point, the corresponding 19

shortest path can be generated by ΔR(pi,j) and ΔC(pi,j), as shown in FIGURE2. 20

21

22

23

FIGURE 2 Generation of the shortest path from pi,j to the target point 24

25

Similarly, the end distance image DTE is formed by setting the endpoint as the target point. 26

Finally, various paths are generated by traversing all the cells. The paths from pi,j to the start and end 27

point can be found, respectively, by DTS and DTE. Linking the above two paths, the integrated path via pi,j is 28

generated (FIGURE 3). 29

30


1

2

FIGURE 3 Generating paths 3

4

After refining the generated paths to alignments, the above algorithm can effectively optimize railway 5

alignments in mountainous area. However, it overlooks station locations, which are equally important in the 6

railway location design. 7

8

Improved Distance Transform Algorithm 9

In this section, we improve the former algorithm. Station locations are considered while searching the railway 10

path. Two improvements are added to the former algorithm. 11

i. The station spacing constraint is handled during searching the promising path. 12

ii. A method named “Tracking Station Center” is proposed to search the optimized station. 13

14

Detection of Station Spacing 15

During searching the railway path, station spacing is calculated at the same time. We create a station spacing 16

attribute DistToSta for all cells in the lattice to store the distance value from current cell to the nearest station 17

which has already generated in the previous searching process, and use it to determine when to start searching 18

the station location. 19

Assuming pi,j is the current cell, pm,n is one random cell in its neighboring mask. If DistToSta (pm,n) < 20

Dmax, then the value of DistToSta (pi,j) is renewed by equation (13). 21

DistToSta (pi,j) = DistToSta (pm,n) + Li,j (13) 22

where Li,j = distance between pi,j and pm,n (m). 23

If DistToSta (pm,n) ≥ Dmax, then backtrack the generated path until the cell pb,d whose DistToSta (pb,d) 24

≤ Dmin and search the optimized station location from pb,d to pm,n along the backtracking path. The searching 25

process will be discussed in section 3.2. After setting the new station, the costs of the cells with larger 26

DistToSta value than the new station’s should be recalculated, their values of DistToSta also need renewing. 27

Assuming the new station is set between pp,q and pr,c as shown in FIGURE4, then pr,c and pm,n need renewing, 28

C(pr,c) and C(pm,n) are recalculated by equation (1), the values of DistToSta (pr,c) and DistToSta (pm,n) are 29

renewed as follow: 30

DistToSta (pr,c) = [(xr,c – xC)2 + (yr,c, – yC)

2]

0.5 (14) 31

DistToSta (pm,n) = DistToSta (pr,c) + Lm,n (15) 32

where xr,c, yr,c = coordinate of the center point of cell pr,c (m). 33

xC, yC = coordinate of the new station center (m), 34

Lm,n = distance between pm,n and pr,c (m). 35

36


1 2

FIGURE4 Backtrack the generated path until cell pb,d 3

4

Searching the Optimized Station Location on Local Path 5

The railway station can be regarded as a rectangle mask with a given length and width by the designers. The 6

location of the rectangle mask (railway station) can be determined when the rectangle mask center (station 7

center) and the rectangle macro-axis direction (the direction of the station) are determined. When a local path 8

is generated, the station can be tracked along the local path, the station’s direction can be kept the same as the 9

local path’s direction. Thus, the process of searching a station location on a local path can be regarded as a 10

tracking process of the railway station center. 11

A method named “Tracking Station Center” is proposed to search the optimized station location on the 12

local path. During the searching process, multiple constraints are handled at the same time (FIGURE5). 13


Yes

No

Han

dle

Cou

pli

ng C

on

stra

ints

Determine moving scope

of the station center

Feasible station

alternative found?

Select the minimum

costs station alternative

Test of Forbidden area constraint

Test of Station-tunnel constraint

Test of Station-bridge constraint

Create Nsc candidate station centers along the local

path with equal interval distance

Calculate the value of

DisToSta of the station center

Dmin≤ DisToSta ≤ Dmax

Select a local path

Calculate the local path’s gradient is

according to equation (6)

is ≤ ismax

Select the ith station center

set i=i++

Determine the ith station area

according to the given station

length and width

Set flat slope along the

station longitudinal

The local path canot

set a station

Set γt =1

Set γb =1

Yes

No

Yes

No

No

No

No

Yes

Yes

Yes No

i ≤ Nsc

Test of geometry constraint

Calculate comprehensive costs

according to equation(1)

Yes

No

Yes

1

2

FIGURE 5 Searching the optimized railway station process 3

4

Step1: Select a local path. 5

Step2: Calculate the gradient (is) of the local path by equation (6), if it satisfies the vertical coupling 6

constraint in section 2.2.1, go to Step3, otherwise the local path cannot set a station. 7


Step3: Determine the moving range of the station center, as shown in FIGURE6a. It can ensure that 1

the station within the local path. 2

Step5: Create Nsc station centers along the local alignment with equal interval distance (FIGURE6a), 3

the distance is given by the designer. 4

Step6: Select the ith station center and set i=i++. 5

Step7: Judge whether the station satisfies the multiple constraints in section 2.2. 6

Step8: If all the constraints are satisfied, go to Step9, otherwise, go back to Step6. 7

Step9: Calculate comprehensive cost according to equation (1), then go back to Step6 until all station 8

centers are scanned. And select the minimum cost alternative (FIGURE6). 9

10

11

(a) Horizontal 12

13

(b) Vertical 14

15

FIGURE 6 Select station centers along the local alignment 16

17

Through the proposed procedures, we can find an optimized station location on the local path 18

satisfying multiple constraints. 19

20

REFINING PROCESS 21

Benefitting from the improved distance transform algorithm, a set of combined alternatives of polyline paths 22


and stations satisfying multiple constraints is generated. But the polyline path is not a smooth curve 1

conforming to the railway alignment geometry requirements. They have to be refined. The refining process 2

includes initializing and optimizing the alternatives. First, we use the successive subdivision method to select 3

control points in the polyline path as the points of intersection to generate the initial alternative with the 4

minimum circular curve radii. Then the mesh adaptive direct search algorithm (19, 20) is employed to optimize 5

the initial alternative, the detailed process can be found in the authors’ earlier publication (11). 6

7

A REAL-WORD CASE STUDY 8

To test the method’s effectiveness, Luding-Kangding section of the Sichuan-Tibet railway was selected as a 9

case study. 10

11

Railway Project Profile 12

The Sichuan-Tibet railway is 1,629km long. Perched at over 3,000m above sea level, and with more than 74 13

percent of its length running on bridges or in tunnels, the railway will meander through the mountains, the 14

highest of which exceeds 7,000m. This railway presents its builder multiple difficulties to overcome, such as 15

avalanches, landslides, earthquakes and so on. The accumulated height it will climb reaches over 14,000m. It is 16

believed to be one of the most difficult railway projects to build on Earth (21). 17

Luding-Kangding, one of the most difficult sections in this railway is used as a case study. The size of 18

the study area is 910sq. kilometer (35km × 26km). We represent this area using rectangular lattices, in which 19

1167 × 867 cells are included. The width of every cell is 30m. The topography is shown in FIGURE7. The start 20

and end coordinates are S (34520356.9010, 3315505.7570, 1355.611), E (34493105.5363, 3333594.2374, 21

2810.732). The elevation difference between start and end is 1,455.121m, and the straight-line distance is only 22

32.7km. The natural terrain gradient between the start and end points is 44.5‰, far more exceeding the 23

maximum allowed design gradient of 20‰. 24

25

Parameters 26

The selected locomotive is SS4, whose weight is 184 tons, and the design train’s tonnage is 3500 tons. The 27

input parameters are divided in three groups (TABLE1): 28

i. The constraints parameters. 29

ii. The parameters for setting structures (e.g. stations, bridges, tunnels). 30

iii. The parameters for calculating costs. 31

32

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TABLE 1 Values of Input Parameters 1

2

Constraint parameters

Geometric constraints Minimum radius of curve (Rmin) 600m

Maximum gradient (imax) 20‰

Minimum length of tangent between horizontal curves (LTmin) 60m

Minimum length of horizontal circular curve (LCmin) 60m

Station siting constraints Minimum station spacing (Dmin) 12km

Maximum station spacing (Dmax) 20km

Parameters for setting structures

Stations Length of the station (Ls) 1000.00m

Width of the station (Ws) 200.00m

Moving interval of station center (Is) 300.00m

Bridges and Tunnels Excavated boundary depth to auto-set a tunnel (HT) 12.00m

Fill boundary height to auto-set a bridge (HB) 8.00m

Parameters for cost calculation

Item Unit Cost Item Unit Cost

Rail track (¥/m) 3,710 Right of way(¥/m2) 73.5

Cutting earthwork(¥/m3) 20 Filling earthwork(¥/m

3) 18

(H<50) bridge (¥/m) 37,800 (L≥1000m)Tunnel (¥/m) 60,000

(H≥50, L≥500m)bridge(¥/m) 58,800 (L≥400m)Tunnel (¥/m) 56,000

(H≥50, L<500m)bridge(¥/m) 48,000 (L<400m) tunnel(¥/m) 54,000

Penalty cost for environmentally

sensitive zone (¥/m2)

500 Penalty factor of setting a station on

a bridge (Penlb) 30

Penalty factor of setting a station in

a tunnel (Penlt) 50 Capital recovery factor (Δ) 0.065

3

Optimization Results 4

The program runs on the HP Z600 workstation (Intel Xeon E5506 2.13 G processor, 4GB RAM, 500GB Hard 5

disk). The elapsed time is 1h36m46s and 81 alternatives are generated. The alternatives are sorted by their 6

costs. We choose the computed best alternative and compare it with the manually developed alternative 7

designed by experienced designers at China Railway Eryuan Engineering Group CO, LTD. The results are 8

shown in FIGURE7, FIGURE8 and TABLE2. 9

10

11


1

2

FIGURE 7 Topography and alternatives in the study area 3

4

5

(a) Computer-generated vertical alternative 6


1

(b) Manual vertical alternative 2

3

FIGURE 8 Vertical alternative 4

5

TABLE 2 Computer-generated Best Alignment Compared with Manual Work 6

7

Index Manual alternative Computer-generated best

alternative

Length (m) 74962 74489

Right of way (m2) 99449 131376

Embankment volume (m3) 95909 245092

Excavated volume (m3) 60498 116099

(H≥50m)bridge (Number-m) 0-0 0-0

(H<50m)bridge (Number-m) 9-3499 8-3078

(L≥1000m)tunnel (Number-m) 7-69957 11-68012

(L≥400m)tunnel (Number-m) 0-0 1-962

(L<400m)tunnel (Number-m) 1-244 0-0

Total constructions costs (million ¥) 4631.284 4543.942

Annual constructions costs (Δ=0.065) (million ¥) 301.033 295.356

Annual operating cost (million ¥) 32.560 30.176

Annual comprehensive cost (million ¥) 333.593 325.532

Annual comprehensive cost saving (million ¥) 8.061

8

From the result, we can know station spacing between any two adjacent stations of the 9

computer-generated best alternative satisfies the station spacing constraint. All the four stations are set on 10

horizontal tangents with flat slope and avoid overlapping with tunnels. But as the study area is extremely 11

complex, it is inevitable that some parts of the stations overlap with bridges (both in manual works and 12

computer generated alternatives). The total alignment length, the bridge length and the tunnel length of the 13

computer-generated best alternative are all shorter than those of the manual alternative. But the manual 14


alternative has fewer embankment and excavated volume. The comprehensive cost of the manually designed 1

alternative can be reduced by about 2.4%. These results show that the proposed method can find more 2

economical alternatives satisfying coupling constraints and reduce the time required for railway planning and 3

design significantly. 4

5

CONCULUSIONS 6

This paper proposes a concurrent railway alignment and station locations optimization methodology for 7

mountainous areas. Multiple constraints including coupling constraints are handled during the optimization 8

process. It can generate a set of promising alternatives satisfying all the complex constraints. The effectiveness 9

of the algorithm is verified with a real-world case study. Two important characteristics of the methodology are 10

summarized as below: 11

(1) Complex coupling constraints between station locations and railway alignment, structures (e.g. 12

bridges, tunnels), and environment are handled during the optimization process. 13

(2) Compared with previous concurrent railway alignment and station locations optimization (16, 17), 14

which first construct the candidate pool of potential railway stations then optimize railway alignment and station 15

locations concurrently. This paper proposes a methodology which can set station locations automatically while 16

searching the railway alignment and handle multiple constraints at the same time. It is more suitable for 17

mountain areas. 18

Despite the methodology’s capabilities demonstrated in this paper, it still can be improved to become 19

more realistic and flexible in use. The current methodology rarely considers the user cost and the connection 20

with existing road or railway network in mountainous areas. While in plains areas, other researchers have 21

explored correlation studies. Future work will progress in this direction. 22

23

Acknowledgements 24

This work was partially funded by National Science Foundation China (NSFC) with award number 51378512 25

and Hunan Open Fund for University Innovation Platform, China number 12K007. The authors are very grateful 26

to Professor Paul Schonfeld from University of Maryland, Doctor Michael J. de Smith from the University 27

College, and Guangchang Hu and Jianping Hu from China Railway Eryuan Engineering Group CO.LTD. They 28

kindly provided some good suggestions and real cases for this study. 29

30

REFERENCE 31

1. Jong, J. C, M. K. Jha, and P. Schonfeld. Preliminary Highway Design with Genetic Algorithms and 32

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