Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Multi-objective design of post-tensioned concrete road bridges using artificial neural networks


In order to minimize the total expected cost, bridges have to be designed for safety and durability. This paper considers the cost, the safety, and the corrosion initiation time to design post-tensioned concrete box-girder road bridges. The deck is modeled by finite elements based on problem variables such as the cross-section geometry, the concrete grade, and the reinforcing and post-tensioning steel. An integrated multi-objective harmony search with artificial neural networks (ANNs) is proposed to reduce the high computing time required for the finite-element analysis and the increment in conflicting objectives. ANNs are trained through the results of previous bridge performance evaluations. Then, ANNs are used to evaluate the constraints and provide a direction towards the Pareto front. Finally, exact methods actualize and improve the Pareto set. The results show that the harmony search parameters should be progressively changed in a diversification-intensification strategy. This methodology provides trade-off solutions that are the cheapest ones for the safety and durability levels considered. Therefore, it is possible to choose an alternative that can be easily adjusted to each need.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9


  1. Alberdi R, Khandelwal K (2015) Comparison of robustness of metaheuristic algorithms for steel frame optimization. Eng Struct 102:40–60. doi:10.1016/j.engstruct.2015.08.012

  2. Beume N, Naujoks B, Emmerich M (2007) SMS-EMOA: Multiobjective selection based on dominated hypervolume. Eur J Oper Res 181:1653–1669. doi:10.1016/j.ejor.2006.08.008

  3. Cai H, Aref AJ (2015) A genetic algorithm-based multi-objective optimization for hybrid fiber reinforced polymeric deck and cable system of cable-stayed bridges. Struct Multidiscip Optim 52:583–594. doi:10.1007/s00158-015-1266-4

  4. Cao MS, Pan LX, Gao YF, Novák D, Ding ZC, Lehký D, Li XL (2015) Neural network ensemble-based parameter sensitivity analysis in civil engineering systems. Neural Comput Appl 1–8. doi:10.1007/s00521-015-2132-4

  5. Chatterjee S, Sarkar S, Hore S, Dey N, Ashour AS, Balas VE (2016) Particle swarm optimization trained neural network for structural failure prediction of multistoried RC buildings. Neural Comput Appl. 1–12. doi: 10.1007/s00521-016-2190-2

  6. 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 191:1245–1287. doi:10.1016/S0045-7825(01)00323-1

  7. Coello CAC, Lamont GB, Veldhuizen DA Van (2006) Evolutionary algorithms for solving multi-objective problems. Springer-Verlag New York, Inc

  8. Computers and Structures Inc. (2015) Introduction to CSiBridge. Integrated 3D bridge analysis, design and rating. Berkeley, California, USA

  9. Deb K (2011) Multi-objective optimisation using evolutionary algorithms: an introduction. In: Wang L, Ng AHC, Deb K (eds) Multi-objective evolutionary optimisation for product design and manufacturing. Springer, London, pp 3–34

  10. Deb K, Nain PKS (2007) An evolutionary multi-objective adaptive meta-modeling procedure using artificial neural networks. In: Yang S, Ong Y-S, Jin Y (eds) Evolutionary computation in dynamic and uncertain environments. Springer, Berlin, pp 297–322

  11. Dong Y, Frangopol DM, Saydam D (2013) Time-variant sustainability assessment of seismically vulnerable bridges subjected to multiple hazards. Earthq Eng Struct Dyn 42:1451–1467. doi:10.1002/eqe.2281

  12. Emmerich M, Naujoks B (2004) Metamodel assisted multiobjective optimisation strategies and their application in airfoil design. In: Parmee IC (ed) Adaptive computing in design and manufacture VI. Springer, London, pp 249–260

  13. European Committee for Standardisation (2003) EN 1991–2:2003. Eurocode 1: Actions on structures-Part 2: Traffic loads bridges

  14. European Committee for Standardisation (2005) EN1992-2:2005. Eurocode 2: Design of concrete structures- Part 2: Concrete Bridge-Design and detailing rules. Brussels

  15. Fomento M (2008) EHE-08: code on structural concrete. Ministerio de Fomento, Madrid

  16. Fomento M (2011) IAP-11: code on the actions for the design of road bridges. Ministerio de Fomento, Madrid

  17. García-Segura T, Yepes V (2016) Multiobjective optimization of post-tensioned concrete box-girder road bridges considering cost, CO2 emissions, and safety. Eng Struct 125:325–336. doi:10.1016/j.engstruct.2016.07.012

  18. García-Segura T, Yepes V, Alcalá J (2014a) Life cycle greenhouse gas emissions of blended cement concrete including carbonation and durability. Int J Life Cycle Assess 19:3–12. doi:10.1007/s11367-013-0614-0

  19. García-Segura T, Yepes V, Martí JV, Alcalá J (2014b) Optimization of concrete I-beams using a new hybrid glowworm swarm algorithm. Lat Am J Solids Struct 11:1190–1205. doi:10.1590/S1679-78252014000700007

  20. García-Segura T, Yepes V, Alcalá J, Pérez-López E (2015) Hybrid harmony search for sustainable design of post-tensioned concrete box-girder pedestrian bridges. Eng Struct 92:112–122. doi:10.1016/j.engstruct.2015.03.015

  21. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68

  22. Giannakoglou KC (2002) Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence. Prog Aerosp Sci 38:43–76. doi:10.1016/S0376-0421(01)00019-7

  23. Hare W, Nutini J, Tesfamariam S (2013) A survey of non-gradient optimization methods in structural engineering. Adv Eng Softw 59:19–28. doi:10.1016/j.advengsoft.2013.03.001

  24. Martí JV, Yepes V, González-Vidosa F (2015) Memetic algorithm approach to designing precast-prestressed concrete road bridges with steel fiber reinforcement. J Struct Eng 141:4014114. doi:10.1061/(ASCE)ST.1943-541X.0001058

  25. Martí JV, García-Segura T, Yepes V (2016) Structural design of precast-prestressed concrete U-beam road bridges based on embodied energy. J Clean Prod 120:231–240. doi:10.1016/j.jclepro.2016.02.024

  26. Martinez-Martin FJ, Gonzalez-Vidosa F, Hospitaler A, Yepes V (2012) Multi-objective optimization design of bridge piers with hybrid heuristic algorithms. J Zhejiang Univ Sci A 13:420–432. doi:10.1631/jzus.A1100304

  27. Martini K (2011) Harmony search method for multimodal size, shape, and topology optimization of structural frameworks. J Struct Eng 137:1332–1339. doi:10.1061/(ASCE)ST.1943-541X.0000378

  28. Marti-Vargas JR, Ferri FJ, Yepes V (2013) Prediction of the transfer length of prestressing strands with neural networks. Comput Concr 12:187–209. doi:10.12989/cac.2013.12.2.187

  29. McGee R (1999) Modeling of durability performance of Tasmanian bridges. In: Melchers R, M.G S (eds) Applications of statistics and probability: civil engineering, reliability and risk analysis. A.A. Balkema, Rotterdam, pp 297–306

  30. Papadakis VG, Roumeliotis AP, Fardis MN, Vagenas CG (1996) Mathematical modelling of chloride effect on concrete du-rability and protection measures. In: Dhir RK, Jones MR (eds) Concrete repair, rehabilitation and protection. E&FN Spon, London, pp 165–174

  31. Paya I, Yepes V, González-Vidosa F, Hospitaler A (2008) Multiobjective optimization of reinforced concrete building frames by simulated annealing. Comput Civ Infrastruct Eng 23:596–610. doi:10.1111/j.1467-8667.2008.00561.x

  32. Protopapadakis E, Schauer M, Pierri E et al (2016) A genetically optimized neural classifier applied to numerical pile integrity tests considering concrete piles. Comput Struct 162:68–79. doi:10.1016/j.compstruc.2015.08.005

  33. Quaglia CP, Yu N, Thrall AP, Paolucci S (2014) Balancing energy efficiency and structural performance through multi-objective shape optimization: Case study of a rapidly deployable origami-inspired shelter. Energ Build 82:733–745. doi:10.1016/j.enbuild.2014.07.063

  34. Ricart J, Hüttemann G, Lima J, Barán B (2011) Multiobjective harmony search algorithm proposals. Electron Notes Theor Comput Sci 281:51–67. doi:10.1016/j.entcs.2011.11.025

  35. Sanad A, Saka MP (2001) Prediction of ultimate shear strength of reinforced-concrete deep beams using neural networks. J Struct Eng 127:818–828. doi:10.1061/(ASCE)0733-9445(2001)127:7(818)

  36. Sarma KC, Adeli H (1998) Cost optimization of concrete structures. J Struct Eng 124:570–578. doi:10.1061/(ASCE)0733-9445(1998)124:5(570)

  37. Shi X (2016) Experimental and modeling studies on installation of arc sprayed Zn anodes for protection of reinforced concrete structures. Front Struct Civ Eng 10:1–11. doi:10.1007/s11709-016-0312-7

  38. Sreehari VM, Maiti DK (2016) Buckling load enhancement of damaged composite plates under hygrothermal environment using unified particle swarm optimization. Struct Multidiscip Optim 1–11. doi:10.1007/s00158-016-1498-y

  39. Torres-Machi C, Chamorro A, Pellicer E et al (2015) Sustainable pavement management: Integrating economic, technical, and environmental aspects in decision making. Transp Res Rec J Transp Res Board 2523:56–63. doi:10.3141/2523-07

  40. Vu KAT, Stewart MG (2000) Structural reliability of concrete bridges including improved chloride-induced corrosion models. Struct Saf 22:313–333. doi:10.1016/S0167-4730(00)00018-7

  41. Xu H, Gao XZ, Wang T, Xue K (2010) Harmony search optimization algorithm: application to a reconfigurable mobile robot prototype. In: Geem ZW (ed) Recent advances in harmony search algorithm. Springer, Berlin, pp 11–22

  42. Yepes V, García-Segura T, Moreno-Jiménez JM (2015a) A cognitive approach for the multi-objective optimization of RC structural problems. Arch Civ Mech Eng 15:1024–1036. doi:10.1016/j.acme.2015.05.001

  43. Yepes V, Martí JV, García-Segura T (2015b) Cost and CO2 emission optimization of precast–prestressed concrete U-beam road bridges by a hybrid glowworm swarm algorithm. Autom Constr 49:123–134. doi:10.1016/j.autcon.2014.10.013

  44. Zavala GR, Nebro AJ, Luna F, Coello Coello CA (2013) A survey of multi-objective metaheuristics applied to structural optimization. Struct Multidiscip Optim 49:537–558. doi:10.1007/s00158-013-0996-4

  45. Zavrtanik N, Prosen J, Tušar M, Turk G (2016) The use of artificial neural networks for modeling air void content in aggregate mixture. Autom Constr 63:155–161. doi:10.1016/j.autcon.2015.12.009

  46. Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms - a comparative case study. In: Eiben AE, Bäck T, Schoenauer M, Schwefel H-P (eds) Conference on parallel problem solving from nature- PPSN V. Springer Berlin Heidelberg, Amsterdam, The Netherlands, pp 292–301

Download references


The authors acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness, along with FEDER funding (BRIDLIFE Project: BIA2014-56574-R) and the Research and Development Support Program of Universitat Politècnica de València (PAID-02-15).

Author information

Correspondence to Tatiana García-Segura.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

García-Segura, T., Yepes, V. & Frangopol, D.M. Multi-objective design of post-tensioned concrete road bridges using artificial neural networks. Struct Multidisc Optim 56, 139–150 (2017).

Download citation


  • Multi-objective harmony search
  • Artificial neural networks
  • Post-tensioned concrete bridges
  • Durability
  • Safety