Journal of Zhejiang University SCIENCE A

, Volume 13, Issue 6, pp 420–432 | Cite as

Multi-objective optimization design of bridge piers with hybrid heuristic algorithms

  • Francisco J. Martinez-Martin
  • Fernando Gonzalez-Vidosa
  • Antonio Hospitaler
  • Víctor YepesEmail author


This paper describes one approach to the design of reinforced concrete (RC) bridge piers, using a three-hybrid multi-objective simulated annealing (SA) algorithm with a neighborhood move based on the mutation operator from the genetic algorithms (GAs), namely MOSAMO1, MOSAMO2 and MOSAMO3. The procedure is applied to three objective functions: the economic cost, the reinforcing steel congestion and the embedded CO2 emissions. Additional results for a random walk and a descent local search multi-objective algorithm are presented. The evaluation of solutions follows the Spanish Code for structural concrete. The methodology was applied to a typical bridge pier of 23.97 m in height. This example involved 110 design variables. Results indicate that algorithm MOSAMO2 outperforms other algorithms regarding the definition of Pareto fronts. Further, the proposed procedure will help structural engineers to enhance their bridge pier designs.

Key words

Bridge piers Concrete structures Multi-objective optimization Simulated annealing (SA) Structural design 

CLC number

TU37 TP391 


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  1. Balling, R.J., Yao, X., 1997. Optimization of reinforced concrete frames. ASCE Journal of Structural Engineering, 123(2):193–202. [doi:10.1061/(ASCE)0733-9445(1997) 123:2(193)]CrossRefGoogle Scholar
  2. Bandyopadhyay, S., Saha, S., Maulik, U., Deb, K., 2008. A simulated annealing-based multi-objective optimization algorithm: AMOSA. IEEE Transactions on Evolutionary Computation, 12(3):269–283. [doi:10.1109/TEVC.2007. 900837]CrossRefGoogle Scholar
  3. Carbonell, A., Gonzalez-Vidosa, F., Yepes, V., 2011. Design of reinforced concrete road vault underpasses by heuristic optimization. Advances in Engineering Software, 42(4): 151–159. [doi:10.1016/j.advengsoft.2011.01.002]zbMATHCrossRefGoogle Scholar
  4. Catalonia Institute of Construction Technology, 2009. BEDEC PR/PCT ITEC Materials Database, Barcelona, Spain.Google Scholar
  5. Cerny, V., 1985. Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm. Journal of Optimization Theory and Applications, 45(1): 41–51. [doi:10.1007/BF00940812]MathSciNetzbMATHCrossRefGoogle Scholar
  6. Coello, C.A., Christiansen, A.D., Santos, F., 1997. A simple genetic algorithm for the design of reinforced concrete beams. Engineering with Computers, 13(4):185–196. [doi:10.1007/BF01200046]CrossRefGoogle Scholar
  7. Cohn, M.Z., Dinovitzer, A.S., 1994. Application of structural optimization. ASCE Journal of Structural Engineering, 120(2):617–649. [doi:10.1061/(ASCE)0733-9445(1994) 120:2(617)]CrossRefGoogle Scholar
  8. Deb, D., 2001. Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, New York, USA.zbMATHGoogle Scholar
  9. Dorigo, M., Maniezzo, V., Colorni, A., 1996. The ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 26(1):29–41. [doi:10.1109/3477.484436]CrossRefGoogle Scholar
  10. Holland, J.H., 1975. Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, USA.Google Scholar
  11. Kaveh, A., Talatahari, S., 2009. Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures. Computers and Structures, 87(5–6):267–283. [doi:10.1016/j.compstruc. 2009.01.003]CrossRefGoogle Scholar
  12. Kennedy, J., Eberhart, R., 1995. Particle Swarm Optimization. IEEE International Conference on Neural Networks, Perth, Australia. IEEE Service Center, Piscataway, p.1942–1948.Google Scholar
  13. Khajehzadeh, M., Taha, M.R., El-Shafie, A., Eslami, M., 2011. Modified particle swarm optimization for optimum design of spread footing and retaining wall. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 12(6):415–427. [doi:10.1631/jzus.A1000252]CrossRefGoogle Scholar
  14. Kicinger, R., Arciszewski, T., de Jong, K., 2005. Evolutionary computation and structural design: A survey of the state-of-the-art. Computers and Structures, 83(23–24): 1943–1978. [doi:10.1016/j.compstruc.2005.03.002]CrossRefGoogle Scholar
  15. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P., 1983. Optimization by simulated annealing. Science, 220(4598):671–680. [doi:10.1126/science.220.4598.671]MathSciNetzbMATHCrossRefGoogle Scholar
  16. Koumousis, V.K., Arsenis, S.J., Vasiloglou, V.B., 1996. Detailed design of reinforced concrete buildings using logic programming. Advances in Engineering Software, 25(2–3):161–176. [doi:10.1016/0965-9978(95)00092-5]CrossRefGoogle Scholar
  17. Lee, K.S., Geem, Z., 2004. A new structural optimization method based on the harmony search algorithm. Computers & Structures, 82(9–10):781–798. [doi:10. 1016/j.compstruc.2004.01.002]CrossRefGoogle Scholar
  18. Marti, J.V., Gonzalez-Vidosa, F., 2010. Design of prestressed concrete precast pedestrian bridges by heuristic optimization. Advances in Engineering Software, 41(7–8): 916–922. [doi:10.1016/j.advengsoft.2010.05.003]zbMATHCrossRefGoogle Scholar
  19. Martinez, F.J., Gonzalez-Vidosa, F., Hospitaler, A., Yepes, V., 2010. Heuristic optimization of RC bridge piers with rectangular hollow sections. Computers and Structures, 88(5–6):375–386. [doi:10.1016/j.compstruc.2009.11.009]CrossRefGoogle Scholar
  20. Ministerio de Fomento, 1998. IAP-98: Code on the Actions to be Considered for the Design of Road Bridges. Madrid, Spain (in Spanish).Google Scholar
  21. Ministerio de Fomento, 2008. EHE-08: Code of Structural Concrete. Madrid, Spain (in Spanish).Google Scholar
  22. Neville, A.M., 1981. Properties of Concrete, 3rd Edition. Pitman, London, UK.Google Scholar
  23. Paya, I., Yepes, V., Gonzalez-Vidosa, F., Hospitaler, A., 2008. Multi-objective optimization of concrete building frames by simulated annealing. Computer-Aided Civil and Infrastructure Engineering, 23(8):596–610. [doi:10.1111/j.1467-8667.2008.00561.x]CrossRefGoogle Scholar
  24. Paya-Zaforteza, I., Yepes, V., Hospitaler, A., Gonzalez-Vidosa, F., 2009. CO2-optimization of reinforced concrete frames by simulated annealing. Engineering Structures, 31(7): 1501–1508. [doi:10.1016/j.engstruct.2009.02.034]CrossRefGoogle Scholar
  25. Perea, C., Alcalá, J., Yepes, V., González-Vidosa, F., Hospitaler, A., 2008. Design of reinforced concrete bridge frames by heuristic optimization. Advances in Engineering Software, 39(8):676–688. [doi:10.1016/j.advengsoft. 2007.07.007]CrossRefGoogle Scholar
  26. Ponz-Tienda, J.L., Pellicer, E., Yepes, V., 2012. Complete fuzzy scheduling and fuzzy earned value management in construction projects. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 13(1): 56–68. [doi:10.1631/jzus.A1100160]CrossRefGoogle Scholar
  27. Serafini, P., 1992. Simulated Annealing for Multiple Objective Optimization Problems. Proceedings of the Tenth International Conference on Multiple Criteria Decision Making, Taipei, p.87–96.Google Scholar
  28. Soke, A., Bingul, Z., 2006. Hybrid genetic algorithm and simulated annealing for two-dimensional non-guillotine rectangular packing problems. Engineering Applications of Artificial Intelligence, 19(5):557–567. [doi:10.1016/j.engappai.2005.12.003]CrossRefGoogle Scholar
  29. Suppapitnarm, A., Seffen, K.A., Parks, G.T., Clarkson, P.J., 2000. A simulated annealing algorithm for multi-objective optimization. Engineering Optimization, 33(1): 59–85. [doi:10.1080/03052150008940911]CrossRefGoogle Scholar
  30. Wong, S.Y.W., 2001. Hybrid simulated annealing/genetic algorithm approach to short-term hydro-thermal scheduling with multiple thermal plants. International Journal of Electrical Power & Energy Systems, 23(7):565–575. [doi:10.1016/S0142-0615(00)00029-6]CrossRefGoogle Scholar
  31. Wu, T.H., Chung, S.H., Chang, C.C., 2009. Hybrid simulated annealing algorithm with mutation operator to the cell formation problem with alternative process routings. Expert Systems with Applications, 36(2):3652–3661. [doi:10.1016/j.eswa.2008.02.060]CrossRefGoogle Scholar
  32. Yepes, V., Medina, J.R., 2006. Economic heuristic optimization for the heterogeneous fleet VRPHESTW. ASCE Journal of Transportation Engineering, 132(4):303–311. [doi:10.1061/(ASCE)0733-947X(2006)132:4(303)]CrossRefGoogle Scholar
  33. Yepes, V., Alcala, J., Perea, C., González-Vidosa, F., 2008. A parametric study of optimum earth-retaining walls by simulated annealing. Engineering Structures, 30(3): 821–830. [doi:10.1016/j.engstruct.2007.05.023]CrossRefGoogle Scholar
  34. Yepes, V., Gonzalez-Vidosa, F., Alcala, J., Villalba, P., 2012. CO2-optimization design of reinforced concrete retaining walls based on a VNS-threshold acceptance strategy. ASCE Journal of Computing in Civil Engineering, 26(3): 378–386. [doi:10.1061/(ASCE)CP.1943-5487.0000140]CrossRefGoogle Scholar
  35. Zhang, W.M., Li, S.J., Qian, F., 2008. θ-PSO: a new strategy of particle swarm optimization. Journal of Zhejiang University-SCIENCE A, 9(6):786–790. [doi:10.1631/jzus.A071278]CrossRefGoogle Scholar

Copyright information

© Zhejiang University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Francisco J. Martinez-Martin
    • 1
  • Fernando Gonzalez-Vidosa
    • 2
  • Antonio Hospitaler
    • 2
  • Víctor Yepes
    • 2
    Email author
  1. 1.Department of Geotechnical EngineeringUniversitat Politècnica de ValènciaValenciaSpain
  2. 2.Department of Construction Engineering, ICITECHUniversitat Politècnica de ValènciaValenciaSpain

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