Abstract
The newly proposed Generalized Normal Distribution Optimization (GNDO) algorithm is used to design the truss structures with optimal weight. All trusses optimized have frequency constraints, which make them very challenging optimization problems. A large number of locally optimal solutions and non-convexity of search space make them difficult to solve, therefore, they are suitable for testing the performance of optimization algorithm. This work investigates whether the proposed algorithm is capable of coping with such problems. To evaluate the GNDO algorithm, three benchmark truss optimization problems are considered with frequency constraints. Numerical data show GNDO’s reliability, stability, and efficiency for structural optimization problems than other meta-heuristic algorithms. We thoroughly analyse and investigate the performance of GNDO in this engineering area for the first time in the literature.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Erbatur F, Hasançebi O, Tütüncü I, Kılıç H (2000) Optimal design of planar and space structures with genetic algorithms. Comput Struct 75(2):209–224
Kaveh A, Kalatjari V (2004) Size/geometry optimization of trusses by the force method and genetic algorithm. ZAMM J Appl Math Mech für Angew Math und Mech Appl Math Mech 84(5):347–357
Li LJ, Huang ZB, Liu F (2009) A heuristic particle swarm optimization method for truss structures with discrete variables. Comput Struct 87(7–8):435–443
Kaveh A, Talatahari S, Khodadadi N (2020) Stochastic paint optimizer: theory and application in civil engineering. Eng Comput:1–32
Kaveh A, Khodadadi N, Azar BF, and Talatahari S, (2020) “Optimal design of large-scale frames with an advanced charged system search algorithm using box-shaped sections,” Eng Comput 1–21
Pierezan J, dos Santos Coelho L, Mariani VC, de Vasconcelos Segundo EH, Prayogo D (2021) Chaotic coyote algorithm applied to truss optimization problems. Comput Struct 242:106353
Kaveh A, Eslamlou AD, Khodadadi N (2020) Dynamic water strider algorithm for optimal Design of Skeletal Structures. Period Polytech Civ Eng 64(3):904–916
Bellagamba L, Yang TY (1981) Minimum-mass truss structures with constraints on fundamental natural frequency. AIAA J 19(11):1452–1458
Camp CV (2007) Design of space trusses using big bang–big crunch optimization. J Struct Eng 133(7):999–1008
Azad SK, Aminbakhsh S (2021) High-dimensional optimization of large-scale steel truss structures using guided stochastic search. Structures 33:1439–1456
Kaveh A, Talatahari S, Khodadadi N (2019) The hybrid invasive weed optimization-shuffled frog-leaping algorithm applied to optimal Design of Frame Structures. Period Polytech Civ Eng 63(3):882–897
Huynh TN, Do DTT, Lee J (2021) Q-learning-based parameter control in differential evolution for structural optimization. Appl Soft Comput 107:107464
Kaveh A, Khodadadi N, Talatahari S (2021) A comparative study for the optimal design of steel structures using Css and Acss algorithms. Iran Univ Sci Technol 11(1):31–54
Hasançebi O (2008) Adaptive evolution strategies in structural optimization: enhancing their computational performance with applications to large-scale structures. Comput Struct 86(1–2):119–132
Khodadadi N, Azizi M, Talatahari S, and Sareh P, (2021) “Multi-Objective Crystal Structure Algorithm (MOCryStAl): Introduction and Performance Evaluation,” IEEE Access
Wang D, Zhang WH, Jiang JS (2004) Truss optimization on shape and sizing with frequency constraints. AIAA J 42(3):622–630
Sedaghati R, Suleman A, Tabarrok B (2002) Structural optimization with frequency constraints using the finite element force method. AIAA J 40(2):382–388
Gomes HM (2011) Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst Appl 38(1):957–968
Miguel LFF, Miguel LFF (2012) Shape and size optimization of truss structures considering dynamic constraints through modern metaheuristic algorithms. Expert Syst Appl 39(10):9458–9467
Farshchin M, Camp CV, Maniat M (2016) Optimal design of truss structures for size and shape with frequency constraints using a collaborative optimization strategy. Expert Syst Appl 66:203–218
Kaveh A, Zolghadr A (2012) Truss optimization with natural frequency constraints using a hybridized CSS-BBBC algorithm with trap recognition capability. Comput Struct 102:14–27
Kaveh A, Ghazaan MI (2017) Vibrating particles system algorithm for truss optimization with multiple natural frequency constraints. Acta Mech 228(1):307–322
Millan-Paramo C and Abdalla Filho JE, (2019)“Size and shape optimization of truss structures with natural frequency constraints using modified simulated annealing algorithm,” Arab J Sci Eng pp. 1–15
Zuo W, Bai J, Li B (2014) A hybrid OC–GA approach for fast and global truss optimization with frequency constraints. Appl Soft Comput 14:528–535
Kaveh A, Javadi SM (2014) Shape and size optimization of trusses with multiple frequency constraints using harmony search and ray optimizer for enhancing the particle swarm optimization algorithm. Acta Mech 225(6):1595–1605
Tejani GG, Savsani VJ, Patel VK (2016) Modified sub-population teaching-learning-based optimization for design of truss structures with natural frequency constraints. Mech Based Des Struct Mach 44(4):495–513
Farshchin M, Camp CV, Maniat M (2016) Multi-class teaching–learning-based optimization for truss design with frequency constraints. Eng Struct 106:355–369
Kaveh A, Talatahari S, and Khodadadi N, (2019) “Hybrid invasive weed optimization-shuffled frog-leaping algorithm for optimal design of truss structures,” Iran J Sci Technol Trans Civ Eng 1–16
Li L-J, Huang ZB, Liu F, Wu QH (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85(7–8):340–349
Coello CAC (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191(11–12):1245–1287
Zhang Y, Jin Z, Mirjalili S (2020) Generalized normal distribution optimization and its applications in parameter extraction of photovoltaic models. Energy Convers Manag 224:113301
Konzelman CJ, (1986) Dual methods and approximation concepts for structural optimization
Kaveh A, Zolghadr A (2017) Truss shape and size optimization with frequency constraints using tug of war optimization. Asian J Civ Eng 7(2):311–333
Kaveh A, Zolghadr A (2015) An improved CSS for damage detection of truss structures using changes in natural frequencies and mode shapes. Adv Eng Softw 80:93–100
Tejani GG, Savsani VJ, Patel VK (2016) Adaptive symbiotic organisms search (SOS) algorithm for structural design optimization. J Comput Des Eng 3(3):226–249
Kaveh A, Mahdavi VR (2015) Colliding-bodies optimization for truss optimization with multiple frequency constraints. J Comput Civ Eng 29(5):4014078
Kaveh A, Zolghadr A (2014) Democratic PSO for truss layout and size optimization with frequency constraints. Comput Struct 130:10–21
Kaveh A, Mahdavi VR (2013) Optimal design of structures with multiple natural frequency constraints using a hybridized BB-BC/quasi-Newton algorithm. Period Polytech Civ Eng 57(1):27–38
Kaveh A, Ilchi Ghazaan M (2016) Truss optimization with dynamic constraints using UECBO. Adv Comput Des 1(2):119–138
Kaveh A, Ghazaan MI (2015) Enhanced colliding bodies algorithm for truss optimization with frequency constraints. J Comput Civ Eng 29(6):4014104
Kaveh A, Ghazaan MI (2015) Hybridized optimization algorithms for design of trusses with multiple natural frequency constraints. Adv Eng Softw 79:137–147
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Khodadadi, N., Mirjalili, S. Truss optimization with natural frequency constraints using generalized normal distribution optimization. Appl Intell 52, 10384–10397 (2022). https://doi.org/10.1007/s10489-021-03051-5
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10489-021-03051-5