[1] Li F, Liu J, Wen G, Rong J. (2019). Extending SORA method for reliability-based design optimization using probability and convex set mixed models. Struct Multidiscip Optim ;59:1163–79. https://doi.org/10.1007/s00158-018-2120-2.
[2] Haftka RT, GurdalL Z. (1992). Elements of Structural Optimization: Third Edition (Google eBook). Springer Science & Business Media;
[3] Shobeiri V, Ahmadi-Nedushan B. (2017). Bi-directional evolutionary structural optimization for strut-and-tie modelling of three-dimensional structural concrete. Eng Optim ;49:2055–78. https://doi.org/10.1080/0305215X.2017.1292382.
[4] Fathnejat H, Ahmadi-Nedushan B. (2020). An efficient two-stage approach for structural damage detection using meta-heuristic algorithms and group method of data handling surrogate model. Front Struct Civ Eng ;14:907–29. https://doi.org/10.1007/s11709-020-0628-1.
[5] Ahmadi-Nedushan B, Varaee H. (2009). Optimal Design of Reinforced Concrete Retaining Walls using a Swarm Intelligence Technique. Proc First Int Conf Soft Comput Technol Civil, Struct Environ Eng ;92. https://doi.org/10.4203/ccp.92.26.
[6] Shakiba M, Ahmadi-Nedushan B. (2009). Engineering Optimization using Opposition Based Differential Evolution. Proc First Int Conf Soft Comput Technol Civil, Struct Environ Eng ;92. https://doi.org/10.4203/ccp.92.23.
[7] Ahmadi-Nedushan B, Varaee H. (2011). Minimum cost design of concrete slabs using particle swarm optimization with time varying acceleration coefficients. World Appl Sci J ;13:2484–94.
[8] Mohaddese S, VahidReza K, Pahlavan H. (2022). Optimization of Single-Objective and Multi-Objective Special Truss Moment Frame Using Island Genetic Algorithm. J Struct Constr Eng ;8:124–42. https://doi.org/10.22065/JSCE.2021.257179.2290.
[9] Abbas K, Kiani A, Seraji M, Dashti H. (2022). Optimization of structure using hybrid Harris hawks and genetic algorithm. J Struct Constr Eng . https://doi.org/10.22065/JSCE.2022.338161.2788.
[10] Arani AS, Ahmadi-Nedushan B, Bondarabadi HA. (2017). Optimal Design of Curved Portal Frame with Consideration of Stressed Skin Action Using the Equivalent Spring Theory. J Struct Constr Eng. https://doi.org/10.22065/JSCE.2017.91588.1261.
[11] Chen X, Hasselman TK, Neill DJ. (1997). Reliability based structural design optimization for practical applications. Collect Tech Pap - AIAA/ASME/ASCE/AHS/ASC .In: Struct Dyn Mater Conf ;4:2724–32. https://doi.org/10.2514/6.1997-1403.
[12] Du X, Chen W. (2002). Sequential optimization and reliability assessment method for efficient probabilistic design. In: Proc ASME Des Eng Tech Conf ;2:871–80. https://doi.org/10.1115/detc2002/dac-34127.
[13] Wang P, Hu C, Youn BD. (2011). A generalized complementary intersection method (GCIM) for system reliability analysis. J Mech Des Trans ASME;133. https://doi.org/10.1115/1.4004198.
[14] B.D Y, K.K C, L D. (2005). Adaptive probability analysis using an enhanced hybrid mean value method. Struct Multidiscip Optim ;29:134–48.
[15] Liu J, Wen G, Xie YM. (2016). Layout optimization of continuum structures considering the probabilistic and fuzzy directional uncertainty of applied loads based on the cloud model. Struct Multidiscip Optim ;53:81–100. https://doi.org/10.1007/s00158-015-1334-9.
[16] Liu J, Wen G. (2018). Continuum topology optimization considering uncertainties in load locations based on the cloud model. Eng Optim ;50:1041–60. https://doi.org/10.1080/0305215X.2017.1361417.
[17] Irani H, Kalatjari VR, Dibaei Bonab M. (2013). Reliability Assessment of Three-dimensional Moment Resisting Frames Designed According to the Iranian National Building Code, Part 10: Steel Structures, 2008 and 2013 Editions. J Struct Constr Eng 2021;8:173–90. https://doi.org/10.22065/jsce.2020.185303.1858.
[18] Fan L, Teresa W, Adedeji B, Mengqi H, Som S. (2013). A single-loop deterministic method for reliability-based design optimization. Eng Optim ;45:435–58.
[19] Chen Z, Qiu H, Gao L, Su L, Li P. (2013). An adaptive decoupling approach for reliability-based design optimization. Comput Struct ;117:58–66. https://doi.org/10.1016/j.compstruc.2012.12.001.
[20] Valdebenito MA, Schuëller GI. (2010). A survey on approaches for reliability-based optimization. Struct Multidiscip Optim ;42:645–63. https://doi.org/10.1007/s00158-010-0518-6.
[21] Du X, Sudjianto A, Chen W. (2004). An integrated framework for optimization under uncertainty using inverse reliability strategy. J Mech Des Trans ASME ;126:562–70. https://doi.org/10.1115/1.1759358.
[22] Du X, Guo J, Beeram H. (2008). Sequential optimization and reliability assessment for multidisciplinary systems design. Struct Multidiscip Optim ;35:117–30. https://doi.org/10.1007/s00158-007-0121-7.
[23] Du X, Chen W. (2004). Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des Trans ASME ;126:225–33. https://doi.org/10.1115/1.1649968.
[24] Ho-Huu V, Nguyen-Thoi T, Le-Anh L, Nguyen-Trang T. (2016). An effective reliability-based improved constrained differential evolution for reliability-based design optimization of truss structures. Adv Eng Softw ;92:48–56. https://doi.org/10.1016/j.advengsoft.2015.11.001.
[25] Khodam A, Farajzadeh MS, Shayanfar MA. (2021). Reliability-Based Design Optimization of Structures using Firefly Algorithm. J Struct Constr Eng ;8:333–44. https://doi.org/10.22065/jsce.2020.203929.1962.
[26] Kaveh A, Ghazaan MI. (2015). Structural reliability assessment utilizing four metaheuristic algorithms. Int J Optim Civ Eng ;5:205–25.
[27] Gholizadeh S, Aligholizadeh V. (2019). Reliability-based optimum seismic design of RC frames by a metamodel and metaheuristics. Struct Des Tall Spec Build ;28. https://doi.org/10.1002/tal.1552.
[28] Papadrakakis M, Lagaros ND. (2002). Reliability-based structural optimization using neural networks and Monte Carlo simulation. Comput Methods Appl Mech Eng ;191:3491–507. https://doi.org/10.1016/S0045-7825(02)00287-6.
[29] Liu Y, Lu N, Yin X. (2016). A Hybrid Method for Structural System Reliability-Based Design Optimization and its Application to Trusses. Qual Reliab Eng Int ;32:595–608. https://doi.org/10.1002/qre.1775.
[30] Kaveh A, Gholipour Y, Rahami H. (2008). Optimal design of transmission towers using genetic algorithm and neural networks. Int J Sp Struct;23:1–19. https://doi.org/10.1260/026635108785342073.
[31] Taheri F, Ghasemi MR, Dizangian B. (2020) Practical optimization of power transmission towers using the RBF-based ABC algorithm. Struct Eng Mech ;73:463–79. https://doi.org/10.12989/sem.2020.73.4.463.
[32] Nguyen TH, Vu AT. (2022). Speeding up Composite Differential Evolution for structural optimization using neural networks. J Inf Telecommun;6:101–20. https://doi.org/10.1080/24751839.2021.1946740.
[33] Papadrakakis M, Lagaros ND, Tsompanakis Y. (1998). Structural optimization using evolution strategies and neural networks. Comput Methods Appl Mech Eng;156:309–33. https://doi.org/10.1016/S0045-7825(97)00215-6.
[34] Lagaros ND, Papadrakakis M. (2012). Applied soft computing for optimum design of structures. Struct Multidiscip Optim ;45:787–99. https://doi.org/10.1007/s00158-011-0741-9.
[35] Javanmardi R, Ahmadi-Nedushan B. (2021). Cost Optimization of Steel-Concrete Composite I- Girder Bridges With Skew Angle and Longitudinal Slope , Using the SM Toolbox and the Parallel Pattern Search Algorithm. Int J Optim Civ Eng;11:357–82.
[36] Csi computers & structures.Inc https://www.csiamerica.com/.
[37] Ahmadi Nedushan B, Chouinard LE. (2003). Use of artificial neural networks for real time analysis of dam monitoring data. Proceedings, Annu Conf - Can Soc Civ Eng;2003:1987–94.
[38] Ahmadi-Nedushan B. (2012). Prediction of elastic modulus of normal and high strength concrete using ANFIS and optimal nonlinear regression models. Constr Build Mater;36:665–73. https://doi.org/10.1016/j.conbuildmat.2012.06.002.
[39] Deng J, Gu D, Li X, Yue ZQ. (2005). Structural reliability analysis for implicit performance functions using artificial neural network. Struct Saf ;27:25–48. https://doi.org/10.1016/j.strusafe.2004.03.004.
[40] Mukhopadhyay A, Iqbal A. (2006). Comparison of ANN and MARS in prediction of property of steel strips. Adv Soft Comput;34:329–41. https://doi.org/10.1007/3-540-31662-0_26.
[41] Shahani AR, Setayeshi S, Nodamaie SA, Asadi MA, Rezaie S. (2009). Prediction of influence parameters on the hot rolling process using finite element method and neural network. J Mater Process Technol;209:1920–35. https://doi.org/10.1016/j.jmatprotec.2008.04.055.
[42] Moodi Y, Eslami E, Mousavi SR, Dizangian B, Mirshekar H. (2022). Applying neural networks for estimating the compressive strength of confined circular concrete columns with FRP sheets. J Struct Constr Eng ;9. https://doi.org/10.22065/jsce.2021.178649.1825.
[43] Fathi A, Peyman F. (2021). Combining Neural Network Models to Prediction the Bond Strength of Glass FRP to Concrete. J Struct Constr Eng;8:313–32. https://doi.org/10.22065/jsce.2020.216063.2051.
[44] Labibzadeh M, Dadak M. (2019). Determining of Load Bearing Capacity of Rectangular Concrete Columns Reinforced with Longitudinal Spirals Using FEM and ANN Methods. J Struct Constr Eng ;6:157–76. https://doi.org/10.22065/jsce.2018.101469.1351.
[45] Nguyen TH, Vu AT. (2020). Using Neural Networks as Surrogate Models in Differential Evolution Optimization of Truss Structures. Lect Notes Comput Sci (Including Subser Lect Notes Artif Intell Lect Notes Bioinformatics);12496 LNAI:152–63. https://doi.org/10.1007/978-3-030-63007-2_12.
[46] Booker AJ, Dennis JE, Frank PD, Serafini DB, Torczon V, Trosset MW. (1999). A rigorous framework for optimization of expensive functions by surrogates. Struct Optim;17:1–13. https://doi.org/10.1007/BF01197708.
[47] The Mathworks Inc. (2012). Matlab documentation. Matlab :R2012b.
[48] Nowak AS, Kevin R C. (2012). Reliability of Structures. CRC press;
[49] The Mathworks Inc. (2019). Matlab documentation. Matlab :R2019b.
[50] The joint committee on structural safety. vol. 11. 1992. https://doi.org/10.1016/0167-4730(92)90025-i.
[51] Hu Z, Du X. (2015). A random field approach to reliability analysis with random and interval variables. ASCE-ASME J Risk Uncertain Eng Syst Part B Mech Eng;1. https://doi.org/10.1115/1.4030437.
[52] Wang L, Wang X, Wang R, Chen X. (2016). Reliability-based design optimization under mixture of random, interval and convex uncertainties. Arch Appl Mech ;86:1341–67. https://doi.org/10.1007/s00419-016-1121-0.