Abstract
The flower pollination algorithm (FPA) is an efficient metaheuristic optimization algorithm mimicking the pollination process of flowering species. In this study, FPA is applied, for the first time, to the optimum design of reinforced concrete (RC) cantilever retaining walls. It is found that FPA offers important savings with respect to conventional design approaches and that it outperforms genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm in this design problem. Furthermore, parameter tuning reveals that the best FPA performance is achieved for switch probability values ranging between 0.4 and 0.7, a population size of 20 individuals and a Lévy flight step size scale factor of 0.5. Finally, parametric optimum designs show that the optimum cost of RC retaining walls increases rapidly with the wall height and smoothly with the magnitude of surcharge loading.
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References
Alyasseri ZAA, Khader AT, Al-Betar MA, Awadallah MA, Yang XS (2018) Variants of the flower pollination algorithm: a review. Stud Comput Intell:91–118
Aydogdu I (2017) Cost optimization of reinforced concrete cantilever retaining walls under seismic loading using a biogeography-based optimization algorithm with Levy flights. Eng Optim 49(3):381–400
Babu S, Basha MB (2008) Optimum design of cantilever retaining walls using target reliability approach. ASCE Int J Geomech 8(4):240–252
Bekdas G, Nigdeli SM, Yang XS (2015) Sizing optimization of truss structures using flower pollination algorithm. Appl Soft Comput 37:322–331
CEN (2000). Eurocode 2: design of concrete structures. Part 1-1: general rules and rules for buildings. Brussels: European standard EN 1992-1-1
CEN (2004) Eurocode 7: geotechnical design. European Standard EN, Brussels, p 1997
Ceranic B, Fryer C, Baines RW (2001) An application of simulation annealing to the optimum design of reinforced concrete retaining structures. Comput Struct 79:1569–1581
Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35
Gandomi AH, Kashani AR, Roke DA, Mousavi M (2017) Optimization of retaining wall design using evolutionary algorithms. J Struct Multidiscip Optim 55:809–825
Ghazavi M, Bonab SB (2011) Learning from ant society in optimizing concrete retaining walls. J Technol Educ 5(3):205–212
Glover BJ (2007) Understanding flowers and flowering: an integrated approach. Oxford University Press, UK
HMPW (2013) Readjustment and completion of invoices of public works. Hellenic Ministry of Public Works, Athens
Holland JH (1975) Adaptation in natural and artificial systems. An introductory analysis with application to biology, control and artificial intelligence. University of Michigan, Ann Arbor
Kaveh A, Abadi ASM (2010) Harmony search based algorithm for the optimum cost design of reinforced concrete cantilever retaining walls. Int J Civ Eng 9:1): 1–1): 8
Kaveh A, Abadi ASM (2014) Optimal design of cantilever retaining walls using ray optimization method. IJST Trans Civ Eng 38(1):261–274
Kennedy J (2011) Particle swarm optimization. Encyclopedia of machine learning. Springer, pp 760–766
Khajehzadeh M, Taha MR, El-Shafie A, Eslami M (2010) Economic design of retaining wall using particle swarm optimization with passive congregation. Aust J Basic Appl Sci 4(11):5500–5507
Khajehzadeh M, Taha MR, Eslami M (2014) Multi-objective optimisation of retaining walls using hybrid adaptive gravitational search algorithm. Civ Eng Environ Syst 31(3):229–242
Li Z, Wang W, Yan Y, Li Z (2015) PS-ABC: a hybrid algorithm based on particle swarm and artificial bee colony for high-dimensional optimization problems. Expert Syst Appl 42:8881–8895
MathWorks (2000) MATLAB R2017a – global optimization toolbox. The MathWorks Inc, Natick
Mergos (2017) Optimum seismic design of reinforced concrete frames according to Eurocode 8 and fib model code 2010. Earthq Eng Struct Dyn 46:1181–1201
Mergos (2018a) Seismic design of reinforced concrete frames for minimum embodied CO2 emissions. Energy Build 162:177–186
Mergos (2018b) Contribution to sustainable seismic design of reinforced concrete members through embodied CO2 emissions optimization. Struct Concr 19:454–462
Mergos (2019) Efficient optimum seismic design of reinforced concrete frames with nonlinear structural analysis procedures. Struct Multidiscip Optim 58:2565–2581
Mosley B, Bungey J, Hulse R (2012) Reinforced concrete design to Eurocode 2, 7th edn. Palgrave McMillan, UK
Nigdeli SM, Bekdaş G, Yang XS (2016) Application of the flower pollination algorithm in structural engineering. In: Metaheuristics and optimization in civil engineering. Springer, pp 28–42
Nigdeli SM, Bekdaş G, Yang XS (2017) Optimum tuning of mass dampers by using a hybrid method using harmony search and flower pollination algorithm. In: International conference on harmony search algorithm. Springer, pp 222–231
Papazafeiropoulos G, Plevris V, Papadrakakis M (2013) Optimum design of cantilever walls retaining linear elastic backfill by use of genetic algorithm. Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN) Conference, Kos, Greece
Pavlyukevich I (2007) Lévy flights, non-local search and simulated annealing. J Comput Phys 226:1830–1844
Pei Y, Xia Y (2012) Design of reinforced cantilever retaining walls using heuristic optimization algorithms. Procedia Earth Planet Sci 5:32–36
Rahbari P, Ravichandran N, Juang HC (2017) Seismic geotechnical robust design of cantilever retaining wall using response surface approach. J GeoEng 12(4):147–155
Saribas A, Erbatur F (1996) Optimization and sensitivity of retaining structures. ASCE J Geotechn Eng 122(8):649–656
Sheikholeslami R, Khalili BG, Sadollah A, Kim JH (2016) Optimization of reinforced concrete retaining walls via hybrid firefly algorithm with upper bound strategy. KSCE J Civ Eng 20(6):2428–2438
Wang C, Yu T, Curiel-Sosa JL, Xie N, Bui TQ (2019a) Adaptive chaotic particle swarm algorithm for isogeometric multi-objective size optimization of FG plates. J Struct Multidiscip Optim 60:757–778
Wang C, Yu T, Shao G, Nguyen TT, Bui TQ (2019b) Shape optimization of structures with cutouts by an efficient approach based on XIGA and chaotic particle swarm optimization
Yang XS (2008) Nature-inspired metaheuristic algorithms. Luniver Press, UK
Yang XS (2010) Firefly algorithm, stochastic test functions and design optimization. Int J Bio-inspired Comput 2:78–84
Yang XS (2012) Flower pollination algorithm for global optimization. Unconv Comput Nat Comput 7445:240–249
Yang XS, Deb S, Fong S (2011) Accelerated particle swarm optimization and support vector machine for business optimization and applications. In: Networked digital technologies. Springer-Verlag, Berlin, pp 53–66
Yepes V, Gonzalez-Vidosa F, Alcala J, Villalba P (2008) A parametric study of optimum earth-retaining walls by simulated annealing. Eng Struct 30:821–830
Yepes V, Alcala J, Perea C, Gonzalez-Vidosa F (2012) CO2-optimization design of reinforced concrete retaining walls based on a VNS-threshold acceptance strategy. J Comput Civ Eng 26(3):378–386
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Mergos, P.E., Mantoglou, F. Optimum design of reinforced concrete retaining walls with the flower pollination algorithm. Struct Multidisc Optim 61, 575–585 (2020). https://doi.org/10.1007/s00158-019-02380-x
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DOI: https://doi.org/10.1007/s00158-019-02380-x