Optimizing earthquake design of reinforced concrete bridge infrastructures based on evolutionary computation techniques

  • Vítor T. CamachoEmail author
  • Nuno Horta
  • Mário Lopes
  • Carlos S. Oliveira
Research Paper


This paper presents a methodology for the earthquake design of reinforced concrete (RC) bridge infrastructures based on the application of multi-objective evolutionary techniques. The purpose of the methodology is to allow better decision-making for the earthquake design of bridges by proposing optimized solutions which offer trade-offs between material quantities, performance/robustness, and cost. For this, two multi-objective problems (MOPs) were defined with two sets of objectives: the first objective set optimizes the amount of material used in the piers; the second set of objectives comprises a cost function and a performance metric. The NSGA-II algorithm was adapted and applied with real coded variables and multiple non-linear dynamic analyses performed in each fitness evaluation. The results of the runs show different Pareto fronts strongly associated with solution schema of pier-deck connections and steel distribution between piers. The results also allow to perceive the influence of ductility through the impact that certain variables in certain piers have on the performance of solutions. The importance of support conditions/connections between infrastructure and deck and of confinement of piers is clear. The results of the two MOPs show that sub-optimal solutions in terms of volume of materials used may be interesting in terms of reliability gain. In the end, the results of applying the methodology present solutions which offer trade-offs and information gain valuable for bridge design.


Evolutionary algorithms Multi-objective structural optimization Bridge earthquake design Non-linear dynamic analysis 



We acknowledge CERIS/DECivil from IST for all the support.

Funding information

Vítor T. Camacho has a grant (grant number PD/BD/127802/2016) from Fundação para a Ciência e Tecnologia (FCT).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

158_2019_2407_MOESM1_ESM.tcl (25 kb)
ESM 1 (TCL 24 kb)
158_2019_2407_MOESM2_ESM.tcl (66 kb)
ESM 2 (TCL 66 kb)


  1. Alam MI, Kanagarajan B, Jana P (2019) Optimal design of thin-walled open cross-section column for maximum buckling load. Thin-Walled StructGoogle Scholar
  2. Antoniou S, Pinho R (2004) Development and verification of a displacement-based adaptive pushover procedure. J Earthq Eng 8(5):643–661. CrossRefGoogle Scholar
  3. Arellano H, Tolentino D, Gómez R (2018) Optimum criss crossing cables in multi-span cable-stayed bridges using genetic algorithms. KSCE J Civ Eng.
  4. Azizi M, Ejlali RG, Ghasemi SA, Talatahari S (2019) Upgraded whale optimization algorithm for fuzzy logic based vibration control of nonlinear steel structure. Eng Struct 192:53–70CrossRefGoogle Scholar
  5. Beume N, Fonseca CM, Lopez-Ibanez M, Paquete L, Vahrenhold J (2009) On the complexity of computing the hypervolume indicator. IEEE Trans Evol Comput 13(5):1075–1082. CrossRefGoogle Scholar
  6. Bybordiani M, Kazemzadeh Azad S (2019) Optimum design of steel braced frames considering dynamic soil-structure interaction. Struct Multidiscip Optim.
  7. Casarotti C, Pinho R (2007) An adaptive capacity spectrum method for assessment of bridges subjected to earthquake action. Bull Earthq Eng 5(3):377–390Google Scholar
  8. Chikahiro Y, Ario I, Pawlowski P, Graczykowski C (2019) Optimization of reinforcement layout of scissor-type bridge using differential evolution algorithm. Computer-Aided Civil and Infrastructure EngineeringGoogle Scholar
  9. Chow CK, Yuen SY (2012) A multiobjective evolutionary algorithm that diversifies population by its density. IEEE Trans Evol Comput 16(2):149–172Google Scholar
  10. Curadelli O, Amani M (2014) Integrated structure-passive control design of linear structures under seismic excitations. Eng Struct 81:256–264CrossRefGoogle Scholar
  11. Deb K (2001) Multi-objective optimization using evolutionary algorithms. John Wiley & Sons, Inc, New YorkzbMATHGoogle Scholar
  12. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  13. EN 1998-2 (2005) Eurocode 8: Design of structures for earthquake resistance - part 2: bridges. CEN - European Committee for StandardisationGoogle Scholar
  14. EN1998-1 (2005) Eurocode 8: Design of structures for earthquake resistance - part 1: general rules, seismic actions and rules for buildings. CEN - European Committee for StandardisationGoogle Scholar
  15. Esfandiari MJ, Urgessa GS, Sheikholarefin S, Manshadi SH (2018) Optimization of reinforced concrete frames subjected to historical time-history loadings using DMPSO algorithm. Struct Multidiscip Optim 58(5):2119–2134.
  16. Fonseca CM, Fleming PJ (1996) On the performance assessment and comparison of stochastic multiobjective optimizers. 4th International Conference on Parallel Problem Solving from Nature, PPSN IV. Springer-Verlag, London, pp 584–593Google Scholar
  17. Fonseca CM, Guerreiro AP, López-Ibáñez M, Paquete L (2011) On the computation of the empirical attainment function. In: Takahashi RHC, Deb K, Wanner EF, Greco S (eds) Evolutionary Multi-Criterion Optimization. EMO 2011. Lecture Notes in Computer Science, vol. 6576. Springer, Berlin, pp 106–120.
  18. Fragiadakis M, Papadrakakis M (2008) Performance-based optimum seismic design of reinforced concrete structures. Earthq Eng Struct Dyn 37(6):825–844.
  19. Geem ZW, Lee KS (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82(9–10):781–798Google Scholar
  20. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68.
  21. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Boston: Addison-Wesley Longman Publishing Co., Inc.Google Scholar
  22. Ha M-H, Vu Q-A, Truong V-H (2018) Optimum design of stay cables of steel cable-stayed bridges using nonlinear inelastic analysis and genetic algorithm. StructuresGoogle Scholar
  23. Kappos AJ, Saiidi MS, Aydinoglu MN, Isakovic T (2012) Seismic design and assessment of bridges, Inelastic Methods of Analysis and Case Studies (Geotechnical, Geological and Earthquake Engineering), vol 21. Springer, New York. CrossRefGoogle Scholar
  24. Lagaros ND, Papadrakakis M (2007) Robust seismic design optimization of steel structures. Structural and Multidisciplinary Optimization 33(6):457–469.
  25. Lagaros ND, Tsompanakis Y (2007) Intelligent computational paradigms in earthquake engineering. Idea Group Inc, HersheyCrossRefGoogle Scholar
  26. Lee J (2019) Multi-objective optimization case study with active and passive design in building engineering. Struct Multidiscip Optim 59(2):507–519.
  27. Liu M, Burns SA, Wen YK (2003) Optimal seismic design of steel frame buildings based on life cycle cost considerations. Earthq Eng Struct Dyn 32(9):1313–1332Google Scholar
  28. Martínez CA, Curadelli O, Compagnoni ME (2014) Optimal placement of nonlinear hysteretic dampers on planar structures under seismic excitation. Engineering StructuresGoogle Scholar
  29. McKenna F, Fenves G (1999) OpenSEES-open system for earthquake engineering simulation. The Regents of the University of California, BerkeleyGoogle Scholar
  30. Mergos PE (2018) Efficient optimum seismic design of reinforced concrete frames with nonlinear structural analysis procedures. Struct Multidiscip Optim 58(6):2565–2581.
  31. Papadrakakis M, Lagaros ND (2002) Reliability-based structural optimization using neural networks and Monte Carlo simulation. Comput Methods Appl Mech Eng 191(32):3491–3507Google Scholar
  32. Parreiras R, Vasconcelos J (2009) Decision making in multiobjective optimization aided by the multicriteria tournament decision method. Nonlinear Anal Theory Methods Appl 71(12):191–198MathSciNetCrossRefGoogle Scholar
  33. Pedro R, Demarche J, Miguel L, Lopez R (2017) An efficient approach for the optimization of simply supported steel-concrete composite I-girder bridges. Adv Eng Softw 112:31–45Google Scholar
  34. Plevris V, Mitropoulou CC, Lagaros ND (2012) Structural seismic design optimization and earthquake engineering: formulations and applications. Hershey: IGI GlobalGoogle Scholar
  35. Priestley MN (2003) Myths and fallacies in earthquake engineering, revisited. IUSS Press, PaviaGoogle Scholar
  36. Rao SS, Sundararaju K, Prakash BG, Balakrishna C (1992) Fuzzy goal programming approach for structural optimization. American Institute of Aeronautics and AstronauticsGoogle Scholar
  37. Rojas HA, Foley C, Pezeshk S (2011) Risk-based seismic design for optimal structural and nonstructural system performance. Earthquake Spectra 27(3):857–880Google Scholar
  38. Sarma KC, Adeli H (2000) Fuzzy genetic algorithm for optimization of steel structures. J Struct Eng 126(5):596–604Google Scholar
  39. SeismoSoft (2016) SeismoSpect v2016. Retrieved from
  40. Soh CK, Yang J (1996) Fuzzy controlled genetic algorithm search for shape optimization. J Comput Civ Eng 10(2):143–150CrossRefGoogle Scholar
  41. Tsompanakis Y, Papadrakakis M (2004) Large-scale reliability-based structural optimization. Struct Multidiscip Optim 26(6):429–440. CrossRefGoogle Scholar
  42. Tugilimana A, Coelho R, Thrall A (2019) An integrated design methodology for modular trusses including dynamic grouping, module spatial orientation, and topology optimization. Struct Multidiscip Optim.
  43. Wang J-Q, Li S, Dezfuli FH, Alam MS (2019) Sensitivity analysis and multi-criteria optimization of SMA cable restrainers for longitudinal seismic protection of isolated simply supported highway bridges. Eng Struct 189:509–522CrossRefGoogle Scholar
  44. Zavala GR, Nebro AJ, Luna F, Coello Coello CA (2013) A survey of multi-objective metaheuristics applied to structural optimization. Struct Multidiscip Optim 49(4):537–558. MathSciNetCrossRefGoogle Scholar
  45. Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731. CrossRefGoogle Scholar
  46. Zhang Q, Chen JC, Chong PP (2004) Decision consolidation: criteria weight determination using multiple preference formats. Decis Support Syst 38(2):247–258CrossRefGoogle Scholar
  47. Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms-a comparative case study, 5th International Conference on Parallel Problem Solving from Nature, PPSN V. Springer-Verlag, London, UK, pp 292–304Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.CERIS, Department of Civil EngineeringInstituto Superior TécnicoLisbonPortugal
  2. 2.Instituto de Telecomunicações, Instituto Superior TécnicoLisbonPortugal

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