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This paper deals with the economic optimization of high-performance post-tensioned concrete box- girder pedestrian bridges. To this end, a program analyzes and evaluates the structural restrictions following Spanish codes for structural concrete and bridge design loads. This problem includes 33 discrete design variables that define the geometry, the concrete, the reinforcing steel bars and the post-tensioned steel. Various acceptance criteria are proposed to modify a variant of the simulated annealing algorithm with a neighborhood move based on the mutation operator from the genetic algorithms (SAMO). An objective methodology based on the extreme value theory is used to determine the number of experimental tests required to provide a solution with user-defined accuracy as compared to a global optimum solution. Results indicate that the local optima found by SAMO2 fits a three- parameter Weibull distribution and improves the cost results for this structural problem. The minimum value obtained by SAMO2 differed just 0.34% compared to the theoretical minimum value so that, from the structural engineering perspective, the divergence was small enough to be accepted. High- strength concrete performance was further studied in a concrete strength parametric study to acquire more evidence-based knowledge on its implications for economic efficiency. Finally, the study showed that high-strength concrete decreases the cost by 4.5% and the amount of concrete by 26%.
box-girder bridge, extreme value theory, high-strength concrete, post-tensioned concrete, simulated annealing, Structural optimization
[1] Yepes, V., Díaz, J., González-Vidosa, F. & Alcalá, J.. Statistical characterization of prestressed concrete road bridge decks. Revista de la Construcción, 8(2), pp. 95–108, 2009.
[2] Aparicio, A.C., Casas, J.R. & Ramos, G., Computer aided design of prestressed concrete highway bridges. Computers & Structures, 60(6), pp. 957–969, 1996. https://doi.org/10.1016/0045-7949(96)00033-8
[3] Hassanain, M.A. & loov, R.E., Cost optimization of concrete bridge infrastructure. Canadian Journal of Civil Engineering, 30(5), pp. 841–849, 2003. https://doi.org/10.1139/l03-045
[4] Penadés-Plà, V., García-Segura, T., Martí, J.V. & Yepes, V., A review of multicriteria decision making methods applied to the sustainable bridge design. Sustainability, 8(12), pp. 1295, 2016. https://doi.org/10.3390/su8121295
[5] Hernández, S., Fontan, A.N., Díaz, J. & Marcos, D., VTOP. An improved software for design optimization of prestressed concrete beams. Advances in Engineering Software, 41(3), pp. 415–421, 2010. https://doi.org/10.1016/j.advengsoft.2009.03.009
[6] Cohn, M.Z. & Dinovitzer, A.S., Application of structural optimization. Journal of Structural Engineering, 120(2), pp. 617–649, 1994. https://doi.org/10.1061/(asce)0733-9445(1994)120:2(617)
[7] García-Segura, T., Yepes, V., Martí, J.V. & Alcalá, J., Optimization of concrete I-beams using a new hybrid glowworm swarm algorithm. Latin American Journal of Solids and Structures, 11(7), pp. 1190–1205, 2014. https://doi.org/10.1590/s1679-78252014000700007
[8] García-Segura, T., Yepes, V., Alcalá, J. & Pérez-lópez, E., Hybrid harmony search for sustainable design of post-tensioned concrete box-girder pedestrian bridges. Engineering Structures, 92, pp. 112–122, 2015. https://doi.org/10.1016/j.engstruct.2015.03.015
[9] Hasançebi, O. & Kazemzadeh Azad, S., Improving computational efficiency of bat- inspired algorithm in optimal structural design. Advances in Structural Engineering, 18(7), pp. 1003–1015, 2015. https://doi.org/10.1260/1369-4332.18.7.1003
[10] Kaveh, A. & Mahjoubi, S., Design of multi-span steel box girder using lion pride optimization algorithm. Smart Structures and Systems, 20(5), pp. 607–618, 2017.
[11] Mokarram, V. & Banan, M.R., A new PSO-based algorithm for multi-objective optimization with continuous and discrete design variables. Structural and Multidisciplinary Optimization, 57(2), pp. 509–533, 2018. https://doi.org/10.1007/s00158-017-1764-7
[12] 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. Computers & Structures, 195, pp. 99–112, 2018. https://doi.org/10.1016/j.compstruc.2017.06.016
[13] Carbonell, A., González-Vidosa, F. & Yepes, V., Design of reinforced concrete road vault underpasses by heuristic optimization. Advances in Engineering Software, 42(4), pp. 151–159, 2011. https://doi.org/10.1016/j.advengsoft.2011.01.002
[14] Martínez-Martín, F.J., González-Vidosa, F., Hospitaler, A. & Yepes, V., Multi-objec- tive optimization design of bridge piers with hybrid heuristic algorithms. Journal of Zhejiang University-SCIENCE A, 13(6), pp. 420–432, 2012. https://doi.org/10.1631/jzus.a1100304
[15] luz, A., Yepes, V., González-Vidosa, F. & Martí, J.V., Design of open reinforced con- crete abutments road bridges with hybrid stochastic hill climbing algorithms. Informes de la Construcción, 67(540), pp. e114, 2015. https://doi.org/10.3989/ic.14.089
[16] Yepes, V., García-Segura, T. & Moreno-Jiménez, J.M., A cognitive approach for the multi-objective optimization of RC structural problems. Archives of Civil and Mechanical Engineering, 15(4), pp. 1024–1036, 2015. https://doi.org/10.1016/j.acme.2015.05.001
[17] Martí, J.V., García-Segura, T. & Yepes, V., Structural design of precast-prestressed con- crete U-beam road bridges based on embodied energy. Journal of Cleaner Production, 120, pp. 231–240, 2016. https://doi.org/10.1016/j.jclepro.2016.02.024
[18] Yepes, V., Martí, J.V., García-Segura, T. & González-Vidosa, F., Heuristics in optimal detailed design of precast road bridges. Archives of Civil and Mechanical Engineering, 17(4), pp. 738–749, 2017. https://doi.org/10.1016/j.acme.2017.02.006
[19] Torres-Machí, C., Yepes, V., Alcalá, J. & Pellicer, E., Optimization of high-performance concrete structures by variable neighborhood search. International Journal of Civil Engineering, 11(2), pp. 90–99, 2013.
[20] BEDEC PR/PCT ITEC Materials Database, Catalonia Institute of Construction Tech- nology, available at www.itec.cat (Accessed 10 September 2017)
[21] Schlaich, J. & Scheff H., Concrete Box-girder Bridges, International Association for Bridge and Structural Engineering: Zürich, Switzerland, 1982.
[22] Fomento, M., IAP-98: Code on the actions for the design of road bridges, Ministerio de Fomento, Madrid, Spain, 1998.
[23] Fomento, M., EHE-08: Code on structural concrete, Ministerio de Fomento, Madrid, Spain, 2008.
[24] Fomento, M., Recommendations for steel-concrete composite road bridges project, Ministerio de Fomento, Madrid, Spain, 1995.
[25] Kirkpatrick, S., Gelatt, C.D. & Vecchi, M.P., Optimization by simulated annealing.
Science, 220(4598), pp. 671–680, 1983. https://doi.org/10.1126/science.220.4598.671
[26] Černý, V., Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm. Journal of Optimization Theory and Applications, 45(1), pp. 41–51, 1985. https://doi.org/10.1007/bf00940812
[27] Dreo, J., Petrowsky, A., Siarry, P. & Taillard, E., Metaheuristics for hard optimization. Methods and case studies, Springer, Berlin (Heidelberg), 2006.
[28] Holland, J.H., Adaptation in Natural and Artificial Systems, Ann Arbor MI University of Michigan Press, 1975.
[29] Castilho, V.C. de, El Debs, M.K. & Carmo Nicoletti, M. do, Using a modified genetic algorithm to minimize the production costs for slabs of precast prestressed concrete joists. Engineering Applications of Artificial Intelligence, 20(4), pp. 519–530, 2007. https://doi.org/10.1016/j.engappai.2006.09.003
[30] Martí, J.V., Gonzalez-Vidosa, F., Yepes, V. & Alcalá, J., Design of prestressed concrete precast road bridges with hybrid simulated annealing. Engineering Structures, 48, pp. 342–352, 2013. https://doi.org/10.1016/j.engstruct.2012.09.014
[31] Junghans, l. & Darde, N., Hybrid single objective genetic algorithm coupled with the simulated annealing optimization method for building optimization. Energy and Buildings, 86, pp. 651–662, 2015. https://doi.org/10.1016/j.enbuild.2014.10.039
[32] Medina, J.R., Estimation of Incident and Reflected Waves Using Simulated Anneal- ing. Journal of Waterway, Port, Coastal, and Ocean Engineering, 127(4), pp. 213–221, 2001. https://doi.org/10.1061/(asce)0733-950x(2001)127:4(213)
[33] Payá-Zaforteza, I., Yepes, V., González-Vidosa, F. & Hospitaler, A., On the Weibull cost estimation of building frames designed by simulated annealing. Meccanica, 45(5), pp. 693–704, 2010. https://doi.org/10.1007/s11012-010-9285-0
[34] Carbonell, A., Yepes, V. & González-Vidosa, F., Automatic design of concrete vaults using iterated local search and extreme value estimation. Latin American Journal of Solids and Structures, 9(6), pp. 675–689, 2012.
[35] García-Segura, T., Yepes, V. & Alcalá, J., life cycle greenhouse gas emissions of blended cement concrete including carbonation and durability. International Journal of Life Cycle Assessment, 19(1), pp. 3–12, 2014. https://doi.org/10.1007/s11367-013-0614-0