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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (5) : 1110-1130     https://doi.org/10.1007/s11709-020-0643-2
RESEARCH ARTICLE
Evaluation of a novel Asymmetric Genetic Algorithm to optimize the structural design of 3D regular and irregular steel frames
Mohammad Sadegh ES-HAGHI1, Aydin SHISHEGARAN2, Timon RABCZUK3,4()
1. School of Civil Engineering, Khajeh Nasir Toosi University of Technology, Tehran 19697-64499, Iran
2. School of Civil Engineering, Iran University of Science and Technology, Tehran 13114-16846, Iran
3. Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
4. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
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Abstract

We propose a new algorithm, named Asymmetric Genetic Algorithm (AGA), for solving optimization problems of steel frames. The AGA consists of a developed penalty function, which helps to find the best generation of the population. The objective function is to minimize the weight of the whole steel structure under the constraint of ultimate loads defined for structural steel buildings by the American Institute of Steel Construction (AISC). Design variables are the cross-sectional areas of elements (beams and columns) that are selected from the sets of side-flange shape steel sections provided by the AISC. The finite element method (FEM) is utilized for analyzing the behavior of steel frames. A 15-storey three-bay steel planar frame is optimized by AGA in this study, which was previously optimized by algorithms such as Particle Swarm Optimization (PSO), Particle Swarm Optimizer with Passive Congregation (PSOPC), Particle Swarm Ant Colony Optimization (HPSACO), Imperialist Competitive Algorithm (ICA), and Charged System Search (CSS). The results of AGA such as total weight of the structure and number of analyses are compared with the results of these algorithms. AGA performs better in comparison to these algorithms with respect to total weight and number of analyses. In addition, five numerical examples are optimized by AGA, Genetic Algorithm (GA), and optimization modules of SAP2000, and the results of them are compared. The results show that AGA can decrease the time of analyses, the number of analyses, and the total weight of the structure. AGA decreases the total weight of regular and irregular steel frame about 11.1% and 26.4% in comparing with the optimized results of SAP2000, respectively.

Keywords optimization      steel frame      Asymmetric Genetic Algorithm      constraints of ultimate load      constraints of serviceability limits      penalty function     
Corresponding Author(s): Timon RABCZUK   
Just Accepted Date: 06 August 2020   Online First Date: 28 September 2020    Issue Date: 16 November 2020
 Cite this article:   
Mohammad Sadegh ES-HAGHI,Aydin SHISHEGARAN,Timon RABCZUK. Evaluation of a novel Asymmetric Genetic Algorithm to optimize the structural design of 3D regular and irregular steel frames[J]. Front. Struct. Civ. Eng., 2020, 14(5): 1110-1130.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-020-0643-2
http://journal.hep.com.cn/fsce/EN/Y2020/V14/I5/1110
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Mohammad Sadegh ES-HAGHI
Aydin SHISHEGARAN
Timon RABCZUK
Fig.1  Flowchart of the optimization procedure of AGA.
kind of loads somewhere load is applied amount (kgf/m2)
dead load on roof 345
on storey of building expect roof 300
peripheral wall 530
the peripheral wall on the roof 250
live load the internal wall on storey 115
on roof 150
on storey 200
static lateral loads applied C = ABI/Ra)
Tab.1  Vertical and lateral loads in optimization problem of this study
Fig.2  The geometry of regular five-storey one-bay.
?item GA AGA
column 4BO×220×10
14BO×200×10
2BO×200×12
2BO×250×10
1BO×220×12
5BO×220×101
BO×200×12
11BO×200×10
beam 4IPE100
12IPE120
4IPE140
2IPE100
13IPE120
5IPE140
number of cross-section 6 8
total weight of the frame 5175.1 5361.6
weight of frames per area 64.68 67.02
number of structural analyses 32152 401
time (second)? 260288 3057
Tab.2  Optimal results of five-storey one-bay steel frame
Fig.3  Convergence histories of GA and AGA for solving the deterministic optimization problem of the five-storey one-bay steel frame.
Fig.4  Comparing the number of analyses of GA and AGA for solving the optimization problem of the five-storey one-bay steel frame.
Fig.5  The historical value of ϕRn/R u for each element in the best solution of the population (each color shows one element).
Fig.6  The geometry of regular nine-storey five-bay.
?item AGA SAP2000
cross-sections 47W14×38
11W12×87
100W12×40
24W10×100
39W10×39
21W10×15
142W8×48
62W8×21
47W8×15
14W8×13
33W30×148
12W27×146
27W24×146
14W24×94
38W21×122
40W21×73
39W18×106
76W18×55
42W16×57
8W14×159
28W14×74
201W14×38
10W12×210
51W12×87
8W10×100
12W10×39
1W10×15
20W8×48
35W8×21
4W8×15
8W8×13
5W33×201
8W30×292
10W27×146
52W24×146
39W21×122
24W21×73
4W18×106
287W18×55
59W14×159
29W14×74
number of selective cross section 21 20
total weight of the structure (kg) 300110 339540
weight per area (kg/m2) 66.69 75.45
number of structural analyses 6117
number of weight calculations 130200
Tab.3  The results of the best solution in the regular nine-storey five-bay
Fig.7  Convergence histories of AGA for solving the optimization problem of the regular nine-storey five-bay steel frame. (a) Number of generations; (b) number of structural analyses.
Fig.8  ϕRn/R u in solving this optimization example (a regular nine-storey five-bay steel frame) by AGA and SAP2000. (a) The results of SAP2000; (b) the results of AGA algorithm.
Fig.9  The geometry of nine-storey six-bay steel frame which is irregularities in plan and regularities in height.
item AGA SAP2000
cross-sections 116W16×57
28W14×159
55W14×74
18W14×38
24W12×210
79W12×87
58W12×40
23W10×100
66W10×39
35W8×48
1W8×21
5W36×232
15W33×201
42W30×148
52W27×146
27W24×146
43W24×94
12W21×122
116W21×73
3W18×234
8W18×106
47W18×55
16W14×74
170W14×38
8W12×87
1W12×40
5W10×100
9W10×39
18W8×48
9W8×21
13W14×159
46W30×292
6W27×307
1W27×146
10W24×146
13W21×122
42W21×73
318W18×55
92W14×455
96W14×342
number of selective cross section 22 16
total weight of the frame (kg) 414843 521396
weight per area (kg/m2) 96.03 120.69
number of structural analyses 6918
number of weight calculations 162750
Tab.4  Results of optimization for nine-storey six-bay steel frame (irregularities in plan and regularities in height)
Fig.10  Convergence histories of AGA for solving the optimization problem of the nine-storey three-bay steel frame (irregularities in plan and regularities in height). (a) Number of generations; (b) number of structural analyses.
Fig.11  ϕRn/R u in solving the optimization problem of the nine-storey six-bay steel frame (irregularities in plan and regularities in height) . (a) The results of SAP2000; (b) the results of AGA algorithm.
Fig.12  The geometry of the nine-storey five-bay steel frame (regularities in plan and irregularities in height).
?item AGA SAP2000
cross sections 36W14×74
158W14×38
44W12×87
4W12×40
8W10×100
8W10×39
8W8×48
8W8×21
24W33×201
4W27×146
60W24×146
5W24×94
44W21×122
83W21×73
4W18×106
306W18×55
60W14×159
23W16×57
8W14×455
23W14×342
3W14×159
6W14×74
44W14×38
13W12×210
5W12×87
129W12×40
7W10×100
36W10×39
21W10×15
96W8×48
60W8×21
64W8×15
20W8×13
40W36×361
16W36×232
33W33×387
5W33×201
19W30×292
4W30×148
37W27×307
3W27×146
30W24×306
5W24×146
4W24×94
3W21×122
15W21×73
16W18×234
5W18×106
71W18×55
number of selective cross section 17 32
total weight of the frame (kg) 381313 498631
weight per area (kg/m2) 84.74 110.8
number of structural analyses 8873
number of weight calculations 130200
Tab.5  Results of optimization for nine-storey five-bay steel frame (regularities in plan and irregularities in height)
Fig.13  Convergence histories of AGA for solving the optimization problem of the nine-storey five-bay steel frame (regularities in plan and irregularities in height). (a) Number of generations; (b) number of structural analyses.
Fig.14  ϕRn/R u in the solving of the nine-storey three-bay steel frame (regularities in plan and irregularities in height). (a) The results of SAP2000; (b) the results of AGA algorithm.
Fig.15  The geometry of the irregular nine-storey six-bay steel frame.
?item AGA SAP2000
cross sections 38 W14×74
172 W14×38
48 W12×87
1 W12×40
10 W10×100
9 W10×39
18 W8×48
10 W8×21
13 W33×201
6 W27×146
53 W24×146
54 W21×122
85 W21×73
1 W18×106
290 W18×55
65 W14×159
60 W10×39
55 W10×15
10 W8×48
71 W8×21
18 W8×15
396 W8×13
56 W30×292
10 W27×307
100 W14×455
74 W14×342
14 W12×87
number of selective cross section 16 11
total weight of the frame (kg) 376807 511811
weight per area (kg/m2) 87.22 118.47
number of structural analyses 6215
number of weight calculations 162750
Tab.6  Results of optimization for irregularities nine-storey three-bay steel frame
Fig.16  Convergence histories of AGA for solving the optimization problem of the irregular nine-storey six-bay steel frame. (a) Number of generations; (b) number of structural analyses.
Fig.17  ϕRn/R u in the solving of irregular nine-storey six-bay steel frame by AGA and SAP2000. (a) The results of SAP2000; (b) the results of AGA algorithm.
Fig.18  The geometry of the 15-storey three-bay steel planner frame.
element group optimal W-shaped sections
PSO [51] PSOPC [51] HPSACO [51] ICA [52] CSS [53] AGA
1 W33×118 W27×129 W21×111 W24×117 W21×147 W24×117
2 W33×263 W24×131 W18×158 W21×147 W18×143 W18×143
3 W24×76 W24×103 W10×88 W27×84 W12×87 W24×103
4 W36×256 W33×141 W30×116 W27×114 W30×108 W30×108
5 W21×73 W24×104 W21×83 W14×74 W18×76 W14×74
6 W18×86 W10×88 W24×103 W18×86 W24×103 W24×103
7 W18×65 W14×74 W21×55 W12×96 W21×68 W21×68
8 W21×68 W27×94 W27×114 W24×68 W14×61 W14×61
9 W18×60 W21×57 W10×33 W10×39 W18×35 W18×35
10 W18×65 W18×71 W18×46 W12×40 W10×33 W10×33
11 W21×44 W21×44 W21×44 W21×44 W21×44 W21×44
weight (kN) 496.68 452.34 426.36 417.466 412.62 408.31
number of analyses 5000 5000 6800 6000 5000 4287
Tab.7  Optimal design comparison for the 15-storey three-bay steel planar frame.
Fig.19  Convergence histories of AGA for solving the optimization problem of the 15-storey three-bay planar frame.
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