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Frontiers of Structural and Civil Engineering

ISSN 2095-2430

ISSN 2095-2449(Online)

CN 10-1023/X

邮发代号 80-968

2019 Impact Factor: 1.68

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Frontiers of Structural and Civil Engineering  2024, Vol. 18 Issue (1): 89-103   https://doi.org/10.1007/s11709-024-1037-7
  本期目录
Multi-population particle swarm optimization algorithm for automatic design of steel frames
Wenchen SHAN1, Jiepeng LIU2, Yao DING2, Y. Frank CHEN3, Junwen ZHOU2()
1. Institute of Smart City and Intelligent Transportation, Southwest Jiaotong University, Chengdu 610000, China
2. School of Civil Engineering, Chongqing University, Chongqing 400045, China
3. Department of Civil Engineering, the Pennsylvania State University, Middletown, PA 17057, USA
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Abstract：

Steel structures are widely used; however, their traditional design method is a trial-and-error procedure which is neither efficient nor cost effective. Therefore, a multi-population particle swarm optimization (MPPSO) algorithm is developed to optimize the weight of steel frames according to standard design codes. Modifications are made to improve the algorithm performances including the constraint-based strategy, piecewise mean learning strategy and multi-population cooperative strategy. The proposed method is tested against the representative frame taken from American standards and against other steel frames matching Chinese design codes. The related parameter influences on optimization results are discussed. For the representative frame, MPPSO can achieve greater efficiency through reduction of the number of analyses by more than 65% and can obtain frame with the weight for at least 2.4% lighter. A similar trend can also be observed in cases subjected to Chinese design codes. In addition, a migration interval of 1 and the number of populations as 5 are recommended to obtain better MPPSO results. The purpose of the study is to propose a method with high efficiency and robustness that is not confined to structural scales and design codes. It aims to provide a reference for automatic structural optimization design problems even with dimensional complexity. The proposed method can be easily generalized to the optimization problem of other structural systems.
Key words： steel frame    multi-population particle swarm optimization    automatic structural optimization design
收稿日期: 2023-02-02      出版日期: 2024-05-24
Corresponding Author(s): Junwen ZHOU   
 引用本文:   
. [J]. Frontiers of Structural and Civil Engineering, 2024, 18(1): 89-103.
Wenchen SHAN, Jiepeng LIU, Yao DING, Y. Frank CHEN, Junwen ZHOU. Multi-population particle swarm optimization algorithm for automatic design of steel frames. Front. Struct. Civ. Eng., 2024, 18(1): 89-103.
 链接本文:  
https://academic.hep.com.cn/fsce/CN/10.1007/s11709-024-1037-7
https://academic.hep.com.cn/fsce/CN/Y2024/V18/I1/89
Parameter Range Increment
Total height [100, 600] 2
Flange width [50, 400] 2
Web thickness [4,14] 1
Flange thickness [4,20] 1
Tab.1  
Fig.1  
Fig.2  
  
  
  
  
Fig.3  
  
Algorithm Parameter
SA Pop: 100, T0: 100, T1: 1, DR: 0.9
DBAGA Pop: 100, pc1: 0.9, pc2: 0.5, pm1: 0.5, pm2: 0.2, pm3: 0.01, c: 2, b: 2
APSO Pop: 100, c1: 3, c2: 1, ωmax: 0.8, ωmin: 0.5
MPGA Pop: 50, pc1: [0.7, 0.99], pc2: [0.4,0.7], c [1, 2], b [1, 2], pm1: [0.4, 0.6], pm2: [0.1, 0.3], pm3: [0.001, 0.02], tm: 1, mp: 5
MPPSO Pop: 50, c1 [2, 3], c2: 4- c1, ωmax: [0.7, 0.9], ωmin: [0.3, 0.5], p1: 0.5, p2: 0.3, tm: 1, mp: 5
Tab.2  
Fig.4  
Group SBO [32] ACO [38] IACO [39] HS [40] MPPSO
1 W30 × 90 W30 × 90 W30 × 99 W30 × 90 W30 × 90
2 W8 × 18 W8 × 18 W16 × 26 W10 × 22 W27 × 129
3 W24 × 55 W24 × 55 W18 × 35 W18 × 40 W24 × 55
4 W6 × 8.5 W8 × 21 W14 × 22 W12 × 16 W24 × 104
5 W14 × 193 W14 × 145 W14 × 145 W14 × 176 W14 × 145
6 W14 × 145 W14 × 132 W14 × 132 W14 × 176 W14 × 120
7 W14 × 120 W14 × 132 W14 × 120 W14 × 132 W14 × 132
8 W14 × 82 W14 × 132 W14 × 109 W14 × 109 W14 × 74
9 W14 × 53 W14 × 68 W14 × 48 W14 × 82 W14 × 90
10 W14 × 53 W14 × 53 W14 × 48 W14 × 74 W14 × 53
11 W14 × 38 W14 × 43 W14 × 34 W14 × 34 W14 × 26
12 W14 × 22 W14 × 43 W14 × 30 W14 × 22 W14 × 22
13 W14 × 120 W14 × 145 W14 × 159 W14 × 145 W14 × 99
14 W14 × 132 W14 × 145 W14 × 120 W14 × 132 W14 × 109
15 W14 × 120 W14 × 120 W14 × 109 W14 × 109 W14 × 99
16 W14 × 109 W14 × 90 W14 × 99 W14 × 82 W14 × 99
17 W14 × 99 W14 × 90 W14 × 82 W14 × 61 W14 × 68
18 W14 × 61 W14 × 61 W14 × 53 W14 × 48 W14 × 53
19 W14 × 34 W14 × 30 W14 × 38 W14 × 30 W14 × 53
20 W12 × 19 W14 × 26 W14 × 26 W14 × 22 W14 × 22
Min. (lb) 216306 220465 217464 214896 209814
Mean (lb) 224310 229555 – 222620 219823
Std. (lb) 6855 4561 – – 6983
Analyses 14817 15500 – 14651 4912
Tab.3  
Fig.5  
Algorithm Frame Optimal (t) Average (t) Worst (t) Std. (t) Analyses
SA Planar 13.7 144.5 216.5 78.0 5135
Spatial 39.6 192.8 348.7 96.0 5930
DBAGA Planar 19.5 89.3 321.3 89.1 3204
Spatial 59.8 162.5 264.5 57.7 3470
APSO Planar 11.8 12.3 13.4 0.4 9835
Spatial 27.5 31.2 34.7 1.8 13850
MPGA Planar 13.3 15.6 17.5 1.2 6352
Spatial 30.4 43.1 54.3 7.1 6242
MPPSO Planar 11.3 11.6 12.0 0.2 3710
Spatial 24.7 28.2 32.9 2.3 5597
Tab.4  
Fig.6  
Fig.7  
Fig.8  
Fig.9  
Parameter Optimal (t) Average (t) Worst (t) Std. (t) Analyses
Migration interval
tm = 5 25.2 28.5 37.0 3.1 4770
tm = 10 25.6 33.3 47.1 6.0 3618
Multiple populations
mp = 8 24.8 27.2 32.5 1.7 6083
mp = 3 26.9 31.0 36.9 2.8 5163
tm = 1, mp = 5 24.7 28.2 32.9 2.3 5597
Tab.5  
Fig.10  
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