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Seismic design optimization of engineering structures: a comprehensive review

  • Review and Perspective in Mechanics (by Invitation Only)
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Abstract

In the last decades, design optimization of structures received significant attention to reconcile economic aspects, after the recent advances in computer technology. Many solution methods have been developed in order to solve different kinds of optimization problems defined for design of structures. Concerning various types of structural loads, earthquake loading is a crucial factor influencing structural design. The procedures for analysis and design of structures to resist seismic excitations are in a progressive state of development, for which numerous optimization problems have been proposed. This article presents an overview of seismic design optimization of structures, focusing on common solution methods, types of optimization problem and goals of optimization. Past and recent developments are reviewed, and current gaps as well as some open concerns deserving more research in future studies are discussed.

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References

  1. Kaveh, A.: Optimal Structural Analysis, 2nd edn. Wiley, Chichester (2006)

    MATH  Google Scholar 

  2. Bathe, K.J.: Finite Element Procedures, 1st edn. Prentice Hall (1996)

    MATH  Google Scholar 

  3. Kaveh, A.: Computational Structural Analysis and Finite Element Methods. Springer, Switzerland (2013)

    MATH  Google Scholar 

  4. Zakian, P., Khaji, N., Kaveh, A.: Graph theoretical methods for efficient stochastic finite element analysis of structures. Comput. Struct. 178, 29–46 (2017)

    Google Scholar 

  5. Elnashai, A.S., Di Sarno, L.: Fundamentals of Earthquake Engineering: From Source to Fragility. Wiley (2015)

    Google Scholar 

  6. Kang, B.-S., Park, G.-J., Arora, J.S.: A review of optimization of structures subjected to transient loads. Struct. Multidiscip. Optim. 31, 81–95 (2006)

    MathSciNet  MATH  Google Scholar 

  7. Hare, W., Nutini, J., Tesfamariam, S.: A survey of non-gradient optimization methods in structural engineering. Adv. Eng. Softw. 59, 19–28 (2013)

    Google Scholar 

  8. Zavala, G.R., Nebro, A.J., Luna, F., Coello Coello, C.A.: A survey of multi-objective metaheuristics applied to structural optimization. Struct. Multidiscip. Optim. 49, 537–558 (2014)

    MathSciNet  Google Scholar 

  9. Topping, B.H.V.: Shape optimization of skeletal structures: a review. J. Struct. Eng. 109, 1933–1951 (1983)

    Google Scholar 

  10. Hsu, Y.-L.: A review of structural shape optimization. Comput. Ind. 25, 3–13 (1994)

    Google Scholar 

  11. Munk, D.J., Vio, G.A., Steven, G.P.: Topology and shape optimization methods using evolutionary algorithms: a review. Struct. Multidiscip. Optim. 52, 613–631 (2015)

    MathSciNet  Google Scholar 

  12. Hassani, B., Hinton, E.: A review of homogenization and topology optimization I—homogenization theory for media with periodic structure. Comput. Struct. 69, 707–717 (1998)

    MATH  Google Scholar 

  13. Rozvany, G.I.N.: Stress ratio and compliance based methods in topology optimization—a critical review. Struct. Multidiscip. Optim. 21, 109–119 (2001)

    Google Scholar 

  14. Sigmund, O., Maute, K.: Topology optimization approaches. Struct. Multidiscip. Optim. 48, 1031–1055 (2013)

    MathSciNet  Google Scholar 

  15. van Dijk, N.P., Maute, K., Langelaar, M., van Keulen, F.: Level-set methods for structural topology optimization: a review. Struct. Multidiscip. Optim. 48, 437–472 (2013)

    MathSciNet  Google Scholar 

  16. Deaton, J.D., Grandhi, R.V.: A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct. Multidiscip. Optim. 49, 1–38 (2014)

    MathSciNet  Google Scholar 

  17. Huang, X., Xie, Y.-M.: A further review of ESO type methods for topology optimization. Struct. Multidiscip. Optim. 41, 671–683 (2010)

    Google Scholar 

  18. Fragiadakis, M., Lagaros, N.D.: An overview to structural seismic design optimisation frameworks. Comput. Struct. 89, 1155–1165 (2011)

    Google Scholar 

  19. Yang, X.S.: Engineering Optimization: An Introduction with Metaheuristic Applications. Wiley (2010)

    Google Scholar 

  20. Arora, J.S.: Introduction to Optimum Design. Elsevier (2004)

    Google Scholar 

  21. Christensen, P.W., Klarbring, A.: An Introduction to Structural Optimization. Springer (2008)

    MATH  Google Scholar 

  22. Hassani, B., Hinton, E.: Homogenization and Structural Topology Optimization: Theory, Practice and Software. Springer (2012)

    MATH  Google Scholar 

  23. Dorigo, M., Birattari, M., Stutzle, T.: Ant colony optimization. IEEE Comput. Intell. Mag. 1, 28–39 (2006)

    Google Scholar 

  24. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    MathSciNet  MATH  Google Scholar 

  25. Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 1995 MHS'95. IEEE, pp. 39–43 (1995)

  26. Holland, J.H.: Genetic algorithms. Sci. Am. 267, 66–73 (1992)

    Google Scholar 

  27. Yang, X.S., Hossein, G.A.: Bat algorithm: a novel approach for global engineering optimization. Eng. Comput. 29, 464–483 (2012)

    Google Scholar 

  28. Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)

    MathSciNet  MATH  Google Scholar 

  29. Zong Woo, G., Joong Hoon, K., Loganathan, G.V.: A new heuristic optimization algorithm: harmony search. SIMULATION 76, 60–68 (2001)

    Google Scholar 

  30. Erol, O.K., Eksin, I.: A new optimization method: Big Bang-Big Crunch. Adv. Eng. Softw. 37, 106–111 (2006)

    Google Scholar 

  31. Rao, R.V., Savsani, V.J., Vakharia, D.P.: Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43, 303–315 (2011)

    Google Scholar 

  32. Kaveh, A., Mahdavi, V.R.: Colliding bodies optimization: a novel meta-heuristic method. Comput. Struct. 139, 18–27 (2014)

    Google Scholar 

  33. Kaveh, A., Mahdavi, V.R.: Colliding Bodies Optimization: Extensions and Applications. Springer, Switzerland (2015)

    MATH  Google Scholar 

  34. Yang, X.-S., Deb, S.: Cuckoo search via Lévy flights. In: 2009 NaBIC 2009 World Congress on Nature & Biologically Inspired Computing. IEEE, pp. 210–4 (2009)

  35. Kaveh, A., Talatahari, S.: A novel heuristic optimization method: charged system search. Acta Mech. 213, 267–289 (2010)

    MATH  Google Scholar 

  36. Zakian, P., Kaveh, A.: Economic dispatch of power systems using an adaptive charged system search algorithm. Appl. Soft Comput. 73, 607–622 (2018)

    Google Scholar 

  37. Kaveh, A., Zakian, P.: Improved GWO algorithm for optimal design of truss structures. Eng. Comput. 34, 685–707 (2018)

    Google Scholar 

  38. Kaveh, A.: Advances in Metaheuristic Algorithms for Optimal Design of Structures. 3rd edn, Springer (2021)

    MATH  Google Scholar 

  39. Saka, M.P., Hasançebi, O., Geem, Z.W.: Metaheuristics in structural optimization and discussions on harmony search algorithm. Swarm Evol. Comput. 28, 88–97 (2016)

    Google Scholar 

  40. Aydoğdu, İ, Akın, A., Saka, M.P.: Design optimization of real world steel space frames using artificial bee colony algorithm with Levy flight distribution. Adv. Eng. Softw. 92, 1–14 (2016)

    Google Scholar 

  41. Lamberti, L.: An efficient simulated annealing algorithm for design optimization of truss structures. Comput. Struct. 86, 1936–1953 (2008)

    Google Scholar 

  42. Zakian, P., Nadi, M., Tohidi, M.: Finite cell method for detection of flaws in plate structures using dynamic responses. Structures. 34, 327–338 (2021)

    Google Scholar 

  43. Kaveh, A.: Applications of Metaheuristic Optimization Algorithms in Civil Engineering. Springer (2017)

    MATH  Google Scholar 

  44. Kaveh, A., Hassani, B., Shojaee, S., Tavakkoli, S.M.: Structural topology optimization using ant colony methodology. Eng. Struct. 30, 2559–2565 (2008)

    Google Scholar 

  45. Sigmund, O.: On the usefulness of non-gradient approaches in topology optimization. Struct. Multidiscip. Optim. 43, 589–596 (2011)

    MathSciNet  MATH  Google Scholar 

  46. Svanberg, K.: The method of moving asymptotes—a new method for structural optimization. Int. J. Numer. Methods Eng. 24, 359–373 (1987)

    MathSciNet  MATH  Google Scholar 

  47. Moharrami, H., Grierson, D.E.: Computer-automated design of reinforced concrete frameworks. J. Struct. Eng. 119, 2036–2058 (1993)

    Google Scholar 

  48. Pezeshk, S.: Design of framed structures: an integrated non-linear analysis and optimal minimum weight design. Int. J. Numer. Methods Eng. 41, 459–471 (1998)

    MATH  Google Scholar 

  49. ASCE: Minimum Design Loads and Associated Criteria for Buildings and Other Structures. ASCE 7-16. American Society of Civil Engineers, Reston (2017)

  50. Fajfar, P.: Analysis in seismic provisions for buildings: past, present and future. Bull. Earthq. Eng. 16, 2567–2608 (2018)

    Google Scholar 

  51. ASCE: Seismic Evaluation and Retrofit of Existing Buildings. ASCE 41-17. American Society of Civil Engineers, Reston (2017)

  52. Priestley, M.J.N., Calvi, G.M., Kowalsky, M.J.: Displacement-Based Seismic Design of Structures. IUSS Press (2007)

    Google Scholar 

  53. Rojas, H.A., Foley, C., Pezeshk, S.: Risk-based seismic design for optimal structural and nonstructural system performance. Earthq. Spectra 27, 857–880 (2011)

    Google Scholar 

  54. Cornell, C.A., Krawinkler, H.: A framework for performance-based seismic design. In: Structures 2001: A Structural Engineering Odyssey. American Society of Civil Engineers, Washington (2001)

  55. Clough, R.W., Penzien, J.: Dynamics of Structures, 3rd edn. Computers & Structures Inc (2003)

    MATH  Google Scholar 

  56. Chopra, A.K.: Dynamics of Structures: Theory and Applications to Earthquake Engineering, 4th edn. Pearson Education (2012)

    Google Scholar 

  57. Vamvatsikos, D., Cornell, C.A.: Incremental dynamic analysis. Earthq. Eng. Struct. Dyn. 31, 491–514 (2002)

    Google Scholar 

  58. Jalayer, F., Cornell, C.A.: Alternative non-linear demand estimation methods for probability-based seismic assessments. Earthq. Eng. Struct. Dyn. 38, 951–972 (2009)

    Google Scholar 

  59. Jalayer, F., De Risi, R., Manfredi, G.: Bayesian Cloud Analysis: efficient structural fragility assessment using linear regression. Bull. Earthq. Eng. 13, 1183–1203 (2015)

    Google Scholar 

  60. Lagaros, N.D., Fragiadakis, M., Papadrakakis, M., Tsompanakis, Y.: Structural optimization: a tool for evaluating seismic design procedures. Eng. Struct. 28, 1623–1633 (2006)

    Google Scholar 

  61. Kaveh, A., Zakian, P.: Optimal design of steel frames under seismic loading using two meta-heuristic algorithms. J. Constr. Steel Res. 82, 111–130 (2013)

    Google Scholar 

  62. Saadat, S., Camp, C.V., Pezeshk, S.: Seismic performance-based design optimization considering direct economic loss and direct social loss. Eng. Struct. 76, 193–201 (2014)

    Google Scholar 

  63. Kaveh, A., Zakian, P.: Optimal seismic design of reinforced concrete shear wall-frame structures. KSCE J. Civ. Eng. 18, 2181–2190 (2014)

    Google Scholar 

  64. Gholizadeh, S.: Performance-based optimum seismic design of steel structures by a modified firefly algorithm and a new neural network. Adv. Eng. Softw. 81, 50–65 (2015)

    Google Scholar 

  65. Kaveh, A., Ghafari, M.H., Gholipour, Y.: Optimal seismic design of 3D steel moment frames: different ductility types. Struct. Multidiscip. Optim. 56, 1353–1368 (2017)

    Google Scholar 

  66. Kaveh, A., Zakian, P.: An efficient seismic analysis of regular skeletal structures via graph product rules and canonical forms. Earthq. Struct. 10, 25–51 (2016)

    Google Scholar 

  67. Zou, X.-K., Chan, C.-M.: An optimal resizing technique for seismic drift design of concrete buildings subjected to response spectrum and time history loadings. Comput. Struct. 83, 1689–1704 (2005)

    Google Scholar 

  68. Foley, C.M., Pezeshk, S., Alimoradi, A.: Probabilistic performance-based optimal design of steel moment-resisting frames. I: formulation. J. Struct. Eng. 133, 757–766 (2007)

    Google Scholar 

  69. Lagaros, N.D., Garavelas, A.T., Papadrakakis, M.: Innovative seismic design optimization with reliability constraints. Comput. Methods Appl. Mech. Eng. 198, 28–41 (2008)

    MATH  Google Scholar 

  70. Asgarian, B., Ordoubadi, B.: Effects of structural uncertainties on seismic performance of steel moment resisting frames. J. Constr. Steel Res. 120, 132–142 (2016)

    Google Scholar 

  71. Gholizadeh, S., Aligholizadeh, V.: Reliability-based optimum seismic design of RC frames by a metamodel and metaheuristics. Struct. Des. Tall Spec. Build. 28, e1552 (2019)

    Google Scholar 

  72. Zakian, P., Khaji, N.: A stochastic spectral finite element method for solution of faulting-induced wave propagation in materially random continua without explicitly modeled discontinuities. Comput. Mech. 64, 1017–1048 (2019)

    MathSciNet  MATH  Google Scholar 

  73. Gong, Y., Xu, L., Grierson, D.E.: Performance-based design sensitivity analysis of steel moment frames under earthquake loading. Int. J. Numer. Methods Eng. 63, 1229–1249 (2005)

    MATH  Google Scholar 

  74. Moghaddam, H., Hajirasouliha, I., Doostan, A.: Optimum seismic design of concentrically braced steel frames: concepts and design procedures. J. Constr. Steel Res. 61, 151–166 (2005)

    Google Scholar 

  75. Salajegheh, E., Heidari, A.: Time history dynamic analysis of structures using filter banks and wavelet transforms. Comput. Struct. 83, 53–68 (2005)

    Google Scholar 

  76. Salajegheh, E., Heidari, A.: Optimum design of structures against earthquake by wavelet neural network and filter banks. Earthq. Eng. Struct. Dyn. 34, 67–82 (2005)

    Google Scholar 

  77. Salajegheh, E., Heidari, A., Saryazdi, S.: Optimum design of structures against earthquake by discrete wavelet transform. Int. J. Numer. Methods Eng. 62, 2178–2192 (2005)

    MATH  Google Scholar 

  78. Salajegheh, E., Heidari, A.: Optimum design of structures against earthquake by adaptive genetic algorithm using wavelet networks. Struct. Multidiscip. Optim. 28, 277–285 (2004)

    Google Scholar 

  79. Gholizadeh, S., Salajegheh, E.: Optimal seismic design of steel structures by an efficient soft computing based algorithm. J. Constr. Steel Res. 66, 85–95 (2010)

    Google Scholar 

  80. Gholizadeh, S., Samavati, O.A.: Structural optimization by wavelet transforms and neural networks. Appl. Math. Model. 35, 915–929 (2011)

    MathSciNet  MATH  Google Scholar 

  81. CEN: Eurocode 8: Design of Structures for Earthquake Resistance—Part 1: General Rules, Seismic Actions and Rules for Buildings. European Standard EN 1998-1. European Committee for Standardization, Brussels (2004)

  82. Jármai, K., Farkas, J., Kurobane, Y.: Optimum seismic design of a multi-storey steel frame. Eng. Struct. 28, 1038–1048 (2006)

    Google Scholar 

  83. Rojas, H.A., Pezeshk, S., Foley, C.M.: Performance-based optimization considering both structural and nonstructural components. Earthq. Spectra 23, 685–709 (2007)

    Google Scholar 

  84. FEMA: Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings. FEMA 350. Federal Emergency Management Agency, Washington (2000)

  85. Gholizadeh, S., Salajegheh, E.: Optimal design of structures subjected to time history loading by swarm intelligence and an advanced metamodel. Comput. Methods Appl. Mech. Eng. 198, 2936–2949 (2009)

    MATH  Google Scholar 

  86. Kaveh, A., Farahmand Azar, B., Hadidi, A., Rezazadeh Sorochi, F., Talatahari, S.: Performance-based seismic design of steel frames using ant colony optimization. J. Constr. Steel Res. 66, 566–574 (2010)

    Google Scholar 

  87. Kaveh, A., Nasrollahi, A.: Performance-based seismic design of steel frames utilizing charged system search optimization. Appl. Soft Comput. 22, 213–221 (2014)

    Google Scholar 

  88. Liu, M.: Progressive collapse design of seismic steel frames using structural optimization. J. Constr. Steel Res. 67, 322–332 (2011)

    Google Scholar 

  89. Li, G., Jiang, Y., Yang, D.: Modified-modal-pushover-based seismic optimum design for steel structures considering life-cycle cost. Struct. Multidiscip. Optim. 45, 861–874 (2012)

    MathSciNet  MATH  Google Scholar 

  90. Oskouei, A.V., Fard, S.S., Aksogan, O.: Using genetic algorithm for the optimization of seismic behavior of steel planar frames with semi-rigid connections. Struct. Multidiscip. Optim. 45, 287–302 (2012)

    Google Scholar 

  91. Kaveh, A., Aghakouchak, A., Zakian, P.: Reduced record method for efficient time history dynamic analysis and optimal design. Earthq. Struct. 35, 637–661 (2015)

    Google Scholar 

  92. Kaveh, A., Rahami, H., Shojaei, I.: An efficient method for seismic analysis of structures. Eng. Comput. 32, 1708–1721 (2015)

    MATH  Google Scholar 

  93. Gholizadeh, S., Moghadas, R.K.: Performance-based optimum design of steel frames by an improved quantum particle swarm optimization. Adv. Struct. Eng. 17, 143–156 (2014)

    Google Scholar 

  94. FEMA: Prestandard Commentary for the Seismic Rehabilitation of Buildings. FEMA 356. Federal Emergency Management Agency, Washington (2000)

  95. Kaveh, A., Bakhshpoori, T., Azimi, M.: Seismic optimal design of 3D steel frames using cuckoo search algorithm. Struct. Des. Tall Spec. Build. 24, 210–227 (2015)

    Google Scholar 

  96. Kaveh, A., Ghafari, M.H., Gholipour, Y.: Optimum seismic design of steel frames considering the connection types. J. Constr. Steel Res. 130, 79–87 (2017)

    Google Scholar 

  97. Kaveh, A., Ilchi Ghazaan, M.: Optimum seismic design of 3D irregular steel frames using recently developed metaheuristic algorithms. J. Comput. Civ. Eng. 32, 04018015 (2018)

    Google Scholar 

  98. Gholizadeh, S., Fattahi, F.: Damage-controlled performance-based design optimization of steel moment frames. Struct. Des. Tall Spec. Build. 27, e1498 (2018)

    Google Scholar 

  99. Fattahi, F., Gholizadeh, S.: Seismic fragility assessment of optimally designed steel moment frames. Eng. Struct. 179, 37–51 (2019)

    Google Scholar 

  100. Bybordiani, M., Kazemzadeh, A.S.: Optimum design of steel braced frames considering dynamic soil-structure interaction. Struct. Multidiscip. Optim. 60, 1123–1137 (2019)

    Google Scholar 

  101. Degertekin, S.O., Tutar, H., Lamberti, L.: School-based optimization for performance-based optimum seismic design of steel frames. Eng. Comput. 37, 3283–3297 (2020)

    Google Scholar 

  102. Ha, M.-H., Vu, Q.-V., Truong, V.-H.: Optimization of nonlinear inelastic steel frames considering panel zones. Adv. Eng. Softw. 142, 102771 (2020)

    Google Scholar 

  103. Takewaki, I.: Optimal frequency design of tower structures via an approximation concept. Comput. Struct. 58, 445–452 (1996)

    Google Scholar 

  104. Gomes, H.M.: Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst. Appl. 38, 957–968 (2011)

    Google Scholar 

  105. Kaveh, A., Zakian, P.: Enhanced bat algorithm for optimal design of skeletal structures. Asian J. Civ. Eng. 15, 179–212 (2014)

    Google Scholar 

  106. Pham, H.A.: Truss optimization with frequency constraints using enhanced differential evolution based on adaptive directional mutation and nearest neighbor comparison. Adv. Eng. Softw. 102, 142–154 (2016)

    Google Scholar 

  107. McGee, O.G., Phan, K.F.: Adaptable optimality criterion techniques for large-scale space frames with multiple frequency constraints. Comput. Struct. 42, 197–210 (1992)

    MATH  Google Scholar 

  108. McGee, O.G., Phan, K.F.: A robust optimality criteria procedure for cross-sectional optimization of frame structures with multiple frequency limits. Comput. Struct. 38, 485–500 (1991)

    MATH  Google Scholar 

  109. Salajegheh, E.: Optimum design of steel space frames with frequency constraints using three point Rayleigh quotient approximation. J. Constr. Steel Res. 54, 305–313 (2000)

    Google Scholar 

  110. Salajegheh, E.: Optimum design of structures with high-quality approximation of frequency constraints. Adv. Eng. Softw. 31, 381–384 (2000)

    Google Scholar 

  111. Zakian, P.: Meta-heuristic design optimization of steel moment resisting frames subjected to natural frequency constraints. Adv. Eng. Softw. 135, 102686 (2019)

    Google Scholar 

  112. Ganzerli, S., Pantelides, C.P., Reaveley, L.D.: Performance-based design using structural optimization. Earthq. Eng. Struct. Dyn. 29, 1677–1690 (2000)

    Google Scholar 

  113. Chan, C.-M., Zou, X.-K.: Elastic and inelastic drift performance optimization for reinforced concrete buildings under earthquake loads. Earthq. Eng. Struct. Dyn. 33, 929–950 (2004)

    Google Scholar 

  114. Zou, X.K., Chan, C.M.: Optimal seismic performance-based design of reinforced concrete buildings using nonlinear pushover analysis. Eng. Struct. 27, 1289–1302 (2005)

    Google Scholar 

  115. Zou, X.K., Teng, J.G., De Lorenzis, L., Xia, S.H.: Optimal performance-based design of FRP jackets for seismic retrofit of reinforced concrete frames. Compos. B Eng. 38, 584–597 (2007)

    Google Scholar 

  116. Zou, X.K.: Integrated design optimization of base-isolated concrete buildings under spectrum loading. Struct. Multidiscip. Optim. 36, 493 (2008)

    Google Scholar 

  117. Zou, X.-K., Wang, Q., Li, G., Chan, C.-M.: Integrated reliability-based seismic drift design optimization of base-isolated concrete buildings. J. Struct. Eng. 136, 1282–1295 (2010)

    Google Scholar 

  118. Fragiadakis, M., Papadrakakis, M.: Performance-based optimum seismic design of reinforced concrete structures. Earthq. Eng. Struct. Dyn. 37, 825–844 (2008)

    Google Scholar 

  119. Liu, Q., Zhang, J., Yan, L.: An optimal method for seismic drift design of concrete buildings using gradient and Hessian matrix calculations. Arch. Appl. Mech. 80, 1225–1242 (2010)

    MATH  Google Scholar 

  120. Khatibinia, M., Salajegheh, E., Salajegheh, J., Fadaee, M.J.: Reliability-based design optimization of reinforced concrete structures including soil–structure interaction using a discrete gravitational search algorithm and a proposed metamodel. Eng. Optim. 45, 1147–1165 (2013)

    MathSciNet  Google Scholar 

  121. Kaveh, A., Zakian, P.: Performance based optimal seismic design of RC shear walls incorporating soil-structure interaction using CSS algorithm. Int. J. Optim. Civ. Eng. 2, 383–405 (2012)

    Google Scholar 

  122. ACI: Building Code Requirements for Structural Concrete. ACI 318-11. American Concrete Institute, Farmington Hills (2011)

  123. Kaveh, A., Zakian, P.: Seismic design optimisation of RC moment frames and dual shear wall-frame structures via CSS algorithm. Asian J. Civ. Eng. 15, 435–465 (2014)

    Google Scholar 

  124. Akin, A., Saka, M.P.: Harmony search algorithm based optimum detailed design of reinforced concrete plane frames subject to ACI 318–05 provisions. Comput. Struct. 147, 79–95 (2015)

    Google Scholar 

  125. Gharehbaghi, S., Khatibinia, M.: Optimal seismic design of reinforced concrete structures under time-history earthquake loads using an intelligent hybrid algorithm. Earthq. Eng. Eng. Vib. 14, 97–109 (2015)

    Google Scholar 

  126. Esfandiari, M.J., Urgessa, G.S., Sheikholarefin, S., Dehghan Manshadi, S.H.: Optimization of reinforced concrete frames subjected to historical time-history loadings using DMPSO algorithm. Struct. Multidiscip. Optim. 58, 2119–2134 (2018)

    MathSciNet  Google Scholar 

  127. Esfandiari, M.J., Urgessa, G.S., Sheikholarefin, S., Manshadi, S.H.D.: Optimum design of 3D reinforced concrete frames using DMPSO algorithm. Adv. Eng. Softw. 115, 149–160 (2018)

    Google Scholar 

  128. Mergos, P.E.: Efficient optimum seismic design of reinforced concrete frames with nonlinear structural analysis procedures. Struct. Multidiscip. Optim. 58, 2565–2581 (2018)

    Google Scholar 

  129. Mergos, P.E.: Optimum seismic design of reinforced concrete frames according to Eurocode 8 and fib Model Code 2010. Earthq. Eng. Struct. Dyn. 46, 1181–1201 (2017)

    Google Scholar 

  130. Franchin, P., Petrini, F., Mollaioli, F.: Improved risk-targeted performance-based seismic design of reinforced concrete frame structures. Earthq. Eng. Struct. Dyn. 47, 49–67 (2018)

    Google Scholar 

  131. Franchin, P., Pinto, P.E.: Method for probabilistic displacement-based design of RC structures. J. Struct. Eng. 138, 585–591 (2012)

    Google Scholar 

  132. Sung, Y.-C., Su, C.-K.: Fuzzy genetic optimization on performance-based seismic design of reinforced concrete bridge piers with single-column type. Optim. Eng. 11, 471–496 (2010)

    MathSciNet  MATH  Google Scholar 

  133. Taniwaki, K., Ohkubo, S.: Optimal synthesis method for transmission tower truss structures subjected to static and seismic loads. Struct. Multidiscip. Optim. 26, 441–454 (2004)

    Google Scholar 

  134. Taflanidis, A.A.: Optimal probabilistic design of seismic dampers for the protection of isolated bridges against near-fault seismic excitations. Eng. Struct. 33, 3496–3508 (2011)

    Google Scholar 

  135. Zakian, P., Ordoubadi, B., Alavi, E.: Optimal design of steel pipe rack structures using PSO, GWO, and IGWO algorithms. Adv. Struct. Eng. 13694332211004116 (2021)

  136. Özakça, M., Hinton, E.: Free vibration analysis and optimisation of axisymmetric plates and shells—II. Shape optimisation. Comput. Struct. 52, 1199–1211 (1994)

    MATH  Google Scholar 

  137. Barthold, F.J., Stander, N., Stein, E.: Performance comparison of SAM and SQP methods for structural shape optimization. Struct. Optim. 11, 102–112 (1996)

    Google Scholar 

  138. Seyedpoor, S.M., Salajegheh, J., Salajegheh, E., Gholizadeh, S.: Optimal design of arch dams subjected to earthquake loading by a combination of simultaneous perturbation stochastic approximation and particle swarm algorithms. Appl. Soft Comput. 11, 39–48 (2011)

    Google Scholar 

  139. Akbari, J., Ahmadi, M.T., Moharrami, H.: Advances in concrete arch dams shape optimization. Appl. Math. Model. 35, 3316–3333 (2011)

    MATH  Google Scholar 

  140. Kaveh, A., Zakian, P.: Stability based optimum design of concrete gravity dam using CSS, CBO and ECBO algorithms. Int. J. Optim. Civ. Eng. 5, 419–431 (2015)

    Google Scholar 

  141. Deepika, R., Suribabu, C.: Optimal design of gravity dam using differential evolution algorithm. Int. J. Optim. Civ. Eng. 5, 255–266 (2015)

    Google Scholar 

  142. Khatibinia, M., Khosravi, S.: A hybrid approach based on an improved gravitational search algorithm and orthogonal crossover for optimal shape design of concrete gravity dams. Appl. Soft Comput. 16, 223–233 (2014)

    Google Scholar 

  143. Ghabraie, K., Chan, R., Huang, X., Xie, Y.M.: Shape optimization of metallic yielding devices for passive mitigation of seismic energy. Eng. Struct. 32, 2258–2267 (2010)

    Google Scholar 

  144. Lieu, Q.X., Do, D.T.T., Lee, J.: An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints. Comput. Struct. 195, 99–112 (2018)

    Google Scholar 

  145. Kaveh, A., Zolghadr, A.: Meta-heuristic methods for optimization of truss structures with vibration frequency constraints. Acta Mech. 229, 3971–3992 (2018)

    MathSciNet  Google Scholar 

  146. Mijar, A.R., Swan, C.C., Arora, J.S., Kosaka, I.: Continuum topology optimization for concept design of frame bracing systems. J. Struct. Eng. 124, 541–550 (1998)

    Google Scholar 

  147. Allahdadian, S., Boroomand, B.: Topology optimization of planar frames under seismic loads induced by actual and artificial earthquake records. Eng. Struct. 115, 140–154 (2016)

    Google Scholar 

  148. Hassanzadeh, A., Gholizadeh, S.: Collapse-performance-aided design optimization of steel concentrically braced frames. Eng. Struct. 197, 109411 (2019)

    Google Scholar 

  149. Gholizadeh, S., Ebadijalal, M.: Performance based discrete topology optimization of steel braced frames by a new metaheuristic. Adv. Eng. Softw. 123, 77–92 (2018)

    Google Scholar 

  150. Zakian, P., Kaveh, A.: Topology optimization of shear wall structures under seismic loading. Earthq. Eng. Eng. Vib. 19, 105–116 (2020)

    Google Scholar 

  151. Guan, H., Chen, Y.-J., Loo, Y.-C., Xie, Y.-M., Steven, G.P.: Bridge topology optimisation with stress, displacement and frequency constraints. Comput. Struct. 81, 131–145 (2003)

    Google Scholar 

  152. Hajirasouliha, I., Pilakoutas, K., Moghaddam, H.: Topology optimization for the seismic design of truss-like structures. Comput. Struct. 89, 702–711 (2011)

    Google Scholar 

  153. Papavasileiou, G.S., Charmpis, D.C.: Seismic design optimization of multi–storey steel–concrete composite buildings. Comput. Struct. 170, 49–61 (2016)

    Google Scholar 

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Zakian, P., Kaveh, A. Seismic design optimization of engineering structures: a comprehensive review. Acta Mech 234, 1305–1330 (2023). https://doi.org/10.1007/s00707-022-03470-6

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