Evaluation of a novel Asymmetric Genetic Algorithm to optimize the structural design of 3D regular and irregular steel frames

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

References

[1] Le L A, Bui-Vinh T, Ho-Huu V, Nguyen-Thoi T. An efficient coupled numerical method for reliability-based design optimization of steel frames. Journal of Constructional Steel Research, 2017, 138: 389–400

[2] Pezeshk S, Camp C V, Chen D. Design of nonlinear framed structures using genetic optimization. Journal of Structural Engineering, 2000, 126(3): 382–388

[3] Camp C V, Bichon B J, Stovall S P. Design of steel frames using ant colony optimization. Journal of Structural Engineering, 2005, 131(3): 369–379

[4] Hasançebi O, Carbas S. Bat inspired algorithm for discrete size optimization of steel frames. Advances in Engineering Software, 2014, 67: 173–185

[5] Degertekin S O. Optimum design of steel frames using harmony search algorithm. Structural and Multidisciplinary Optimization, 2008, 36(4): 393–401

[6] Saka M P. Optimum design of steel sway frames to BS5950 using harmony search algorithm. Journal of Constructional Steel Research, 2009, 65(1): 36–43

[7] Murren P, Khandelwal K. Design-driven harmony search (DDHS) in steel frame optimization. Engineering Structures, 2014, 59: 798–808

[8] Kaveh A, Talatahari S. An improved ant colony optimization for the design of planar steel frames. Engineering Structures, 2010, 32(3): 864–873

[9] Aydoğdu İ, Saka M P. Ant colony optimization of irregular steel frames including elemental warping effect. Advances in Engineering Software, 2012, 44(1): 150–169

[10] Hasançebi O, Kazemzadeh Azad S. An exponential big bang-big crunch algorithm for discrete design optimization of steel frames. Computers & Structures, 2012, 110: 167–179

[11] Kaveh A, Abbasgholiha H. Optimum design of steel sway frames using big bang-big crunch algorithm. Asian Journal of Civil Engineering, 2011, 12(3): 293–317

[12] ANSI/AISC 360-10. Specification for Structural Steel Buildings. American National Standard, 2010, 1–612

[13] Cardoso J B, de Almeida J R, Dias J M, Coelho P G. Structural reliability analysis using Monte Carlo simulation and neural networks. Advances in Engineering Software, 2008, 39(6): 505–513

[14] Papadrakakis M, Tsompanakis Y, Lagaros N D, Friagiadakis M. Reliability based optimization of steel frames under seismic loading conditions using evolutionary computation. Journal of Theoretical and Applied Mechanics, 2004, 42: 585–608

[15] Ghasemi M R, Yousefi M. Reliability-based optimization of steel frame structures using modified genetic algorithm. Asian Journal of Civil Engineering, 2011, 12(4): 449–475

[16] Shayanfar M, Abbasnia R, Khodam A. Development of a GA-based method for reliability-based optimization of structures with discrete and continuous design variables using OpenSees and Tcl. Finite Elements in Analysis and Design, 2014, 90: 61–73

[17] Li F, Wu T, Badiru A, Hu M, Soni S. A single-loop deterministic method for reliability-based design optimization. Engineering Optimization, 2013, 45(4): 435–458

[18] Tu J, Choi K K, Park Y H. A new study on reliability-based design optimization. Journal of Mechanical Design, 1999, 121(4): 557–564

[19] Grandhi R V, Wang L. Reliability-based structural optimization using improved two-point adaptive nonlinear approximations. Finite Elements in Analysis and Design, 1998, 29(1): 35–48

[20] Wu Y T. Computational methods for efficient structural reliability and reliability sensitivity analysis. AIAA Journal, 1994, 32(8): 1717–1723

[21] Wu Y, Kakushima K, Ahmet P, Nishiyama A. An innovative framework for reliability-based MDO. In: The 41st Structures, Structural Dynnamics, Materials Conference and Exhibit. Atlanta, GA: American Institute of Aeronautics and Astronautics, 2000,100–108

[22] Wu Y T, Shin Y, Sues R, Cesare M. Safety-factor based approach for probability-based design optimization. In: The 19th AIAA Applied Aerodynamics Conference. Anaheim, CA: AIAA, 2001

[23] Du X, Chen W. Sequential optimization and reliability assessment method for efficient probabilistic design. In: ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference American Society of Mechanical Engineers. Montreal, 2002, 871–880

[24] Storn R, Price K. Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 1997, 11(4): 341–359

[25] Ho-Huu V, Nguyen-Thoi T, Le-Anh L, Nguyen-Trang T. An effective reliability-based improved constrained differential evolution for reliability-based design optimization of truss structures. Advances in Engineering Software, 2016, 92: 48–56

[26] Ho-Huu V, Nguyen-Thoi T, Vo-Duy T, Nguyen-Trang T. An adaptive elitist differential evolution for optimization of truss structures with discrete design variables. Computers & Structures, 2016, 165: 59–75

[27] Ho-Huu V, Vo-Duy T, Luu-Van T, Le-Anh L, Nguyen-Thoi T. Optimal design of truss structures with frequency constraints using improved differential evolution algorithm based on an adaptive mutation scheme. Automation in Construction, 2016, 68: 81–94

[28] Wang Z, Tang H, Li P. Optimum design of truss structures based on differential evolution strategy. In: 2009 International Conference on Information Engineering and Computer Science. Los Angeles: IEEE, 2009,1–5

[29] Ho-Huu V, Do-Thi T D, Dang-Trung H, Vo-Duy T, Nguyen-Thoi T. Optimization of laminated composite plates for maximizing buckling load using improved differential evolution and smoothed finite element method. Composite Structures, 2016, 146: 132–147

[30] Le-Anh L, Nguyen-Thoi T, Ho-Huu V, Dang-Trung H, Bui-Xuan T. Static and frequency optimization of folded laminated composite plates using an adjusted differential evolution algorithm and a smoothed triangular plate element. Composite Structures, 2015, 127: 382–394

[31] Vo-Duy T, Ho-Huu V, Dang-Trung H, Nguyen-Thoi T. A two-step approach for damage detection in laminated composite structures using modal strain energy method and an improved differential evolution algorithm. Composite Structures, 2016, 147: 42–53

[32] Vo-Duy T, Ho-Huu V, Dang-Trung H, Dinh-Cong D, Nguyen-Thoi T. Damage detection in laminated composite plates using modal strain energy and improved differential evolution algorithm. Procedia Engineering, 2016, 142: 182–189

[33] Dinh-Cong D, Vo-Duy T, Ho-Huu V, Dang-Trung H, Nguyen-Thoi T. An efficient multi-stage optimization approach for damage detection in plate structures. Advances in Engineering Software, 2017, 112: 76–87

[34] Dinh-Cong D, Vo-Duy T, Nguyen-Minh N, Ho-Huu V, Nguyen-Thoi T. A two-stage assessment method using damage locating vector method and differential evolution algorithm for damage identification of cross-ply laminated composite beams. Advances in Structural Engineering, 2017, 20(12): 1807–1827

[35] Ilonen J, Kamarainen J K, Lampinen J. Differential evolution training algorithm for feed-forward neural networks. Neural Processing Letters, 2003, 17(1): 93–105

[36] Xu G, Li M, Mourrain B, Rabczuk T, Xu J, Bordas S P. Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization. Computer Methods in Applied Mechanics and Engineering, 2018, 328: 175–200

[37] Ghasemi H, Kerfriden P, Bordas S P, Muthu J, Zi G, Rabczuk T. Interfacial shear stress optimization in sandwich beams with polymeric core using non-uniform distribution of reinforcing ingredients. Composite Structures, 2015, 120: 221–230

[38] Ghasemi H, Park H S, Rabczuk T. A level-set based IGA formulation for topology optimization of flexoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 239–258

[39] Ghasemi H, Brighenti R, Zhuang X, Muthu J, Rabczuk T. Optimal fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach. Structural and Multidisciplinary Optimization, 2015, 51(1): 99–112

[40] Ghasemi H, Kerfriden P, Bordas S P, Muthu J, Zi G, Rabczuk T. Probabilistic multiconstraints optimization of cooling channels in ceramic matrix composites. Composites. Part B, Engineering, 2015, 81: 107–119

[41] Nanthakumar S S, Zhuang X, Park H S, Rabczuk T. Topology optimization of flexoelectric structures. Journal of the Mechanics and Physics of Solids, 2017, 105: 217–234

[42] Ghasemi H, Rafiee R, Zhuang X, Muthu J, Rabczuk T. Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multi-scale modeling. Computational Materials Science, 2014, 85: 295–305

[43] Nanthakumar S S, Valizadeh N, Park H S, Rabczuk T. Surface effects on shape and topology optimization of nanostructures. Computational Mechanics, 2015, 56(1): 97–112

[44] Ghasemi H, Brighenti R, Zhuang X, Muthu J, Rabczuk T. Optimization of fiber distribution in fiber reinforced composite by using NURBS functions. Computational Materials Science, 2014, 83: 463–473

[45] Ho-Huu V, Nguyen-Thoi T, Truong-Khac T, Le-Anh L, Vo-Duy T. An improved differential evolution based on roulette wheel selection for shape and size optimization of truss structures with frequency constraints. Neural Computing & Applications, 2018, 29(1): 167–185

[46] Holland J. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Application to Biology, Control and artificial Intelligence. Ann Arbor: University of Michigan Press, 1975

[47] Goldberg D E, Holland J H. Genetic algorithms and machine learning. Machine Learning, 1988, 3(2): 95–99

[48] Bel Hadj Ali N, Sellami M, Cutting-Decelle A F, Mangin J C. Multi-stage production cost optimization of semi-rigid steel frames using genetic algorithms. Engineering Structures, 2009, 31(11): 2766–2778

[49] Akbari J, Ayubirad M S. Seismic optimum design of steel structures using gradient-based and genetic algorithm methods. International Journal of Civil Engineering, 2017, 15(2): 135–148

[50] Arora J S. Introduction to Optimum Design. Lowa: Elsevier, 2004

[51] Gholizadeh S, Samavati O A. Structural optimization by wavelet transforms and neural networks. Applied Mathematical Modelling, 2011, 35(2): 915–929

[52] Kaveh A, Talatahari S. Hybrid algorithm of harmony search, particle swarm and ant colony for structural design optimization. Studies in Computational Intelligence, 2009, 239: 159–198

[53] Kaveh A, Talatahari S. Optimum design of skeletal structures using imperialist competitive algorithm. Computers & Structures, 2010, 88(21-22): 1220–1229

[54] Kaveh A, Talatahari S. Charged system search for optimal design of frame structures. Applied Soft Computing, 2012, 12(1): 382–393

[55] Zhou S, Rabczuk T, Zhuang X. Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies. Advances in Engineering Software, 2018, 122: 31–49

[56] Zhou S, Zhuang X, Rabczuk T. Phase-field modeling of fluid-driven dynamic cracking in porous media. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 169–198

[57] Zhou S, Zhuang X, Rabczuk T. A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology, 2018, 240: 189–203

[58] Zhou S, Zhuang X, Zhu H, Rabczuk T. Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics, 2018, 96: 174–192

[59] Zhou S, Zhuang X, Rabczuk T. Phase field modeling of brittle compressive-shear fractures in rock-like materials: A new driving force and a hybrid formulation. Computer Methods in Applied Mechanics and Engineering, 2019, 355: 729–752

RIGHTS & PERMISSIONS

2020 Higher Education Press