# 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
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
 Download: PDF(4703 KB)   HTML Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
 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. 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
 Fig.1  Flowchart of the optimization procedure of AGA. Tab.1  Vertical and lateral loads in optimization problem of this study Fig.2  The geometry of regular five-storey one-bay. 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. 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. 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). 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. 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. 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.