Automatic Design of Large-Scale Trusses: A Comparison Between Derivative-Free Algorithms
Main Article Content
Keywords
Multi-objective metaheuristic optimization, articulated structures, trusses, large scale
Abstract
The design of steel trusses is a frequent problem in civil engineering, which requires the experience of the design engineer to achieve a structural solution with good performance and that can satisfy the established needs. In recent years, the design of these systems has been supported by the application of various methods of optimization, which allow optimal solutions, meeting the proposed design objectives, automatically and in a shorter time. This research presents the application of a series of multiobjective metaheuristic algorithms for the automatic design of large-scale trusses. The NSGA-II, MOPSO and AMOSA algorithms were applied and the structures reported in the literature were considered to be made up of a high number of elements. The performance of the algorithms was evaluated based on the computational cost, the hypervolume criterion and the behavior that the algorithms have when increasing the amount of iterations per optimization cycle. The search space used in the optimization was discrete, restricted by the W steel profiles available in the Colombian market. The results obtained show that, for the proposed problems, the MOPSO algorithm is the most efficient, followed by the AMOSA and the NSGA-II which showed a higher computational cost. Finally, it is worth mentioning that the calculation times were less than one hour, for trusses close to a thousand elements.
Downloads
Download data is not yet available.
References
[1] H. Assimi and A. Jamali, “A hybrid algorithm coupling genetic programming and nelder - mead for topology and size optimization of trusses with static and dynamic constraints,” Expert Systems with Applications, vol. 95, pp. 127–141, 2018. https://doi.org/10.1016/j.eswa.2017.11.035
[2] O. Hasançebi, “Adaptive evolution strategies in structural optimization: Enhancing their computational performance with applications to large-scale structures,” Computers and Structures, vol. 86, no. 1-2, pp. 119–132, 2008. https://doi.org/10.1016/j.compstruc.2007.05.012
[3] O. Hasançebi and S. K. Azad, “Adaptive dimensional search: A new metaheuristic algorithm for discrete truss sizing optimization,” Computers and Structures, vol. 154, pp. 1–16, 2015. https://doi.org/10.1016/j.compstruc.2015.03.014
[4] S. Degertekin, L. Lamberti, and I. Ugur, “Discrete sizing/layout/topology optimization of truss structures with an advanced jaya algorithm,” Applied Soft Computing Journal, vol. 79, pp. 363–390, 2019. https://doi.org/10.1016/j.asoc.2019.03.058
[5] K. Deb and S. Gulati, “Design of truss-structures for minimum weight using genetic algorithms,” Finite Elements in Analysis and Design, vol. 37, no. 5, pp. 447–465, may 2001. https://doi.org/10.1016/S0168-74X(00)00057-3
[6] G. G. Tejani, V. J. Savsani, V. K. Patel, and P. V. Savsani, “Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics,” Journal of Computational Design and Engineering, vol. 5, no. 2, pp. 198–214, 10 2017. https://doi.org/10.1016/j.jcde.2017.10.001
[7] H. Cao, X. Qian, and Y. Zhou, “Large-scale structural optimization using metaheuristic algorithms with elitism and a filter strategy,” Structural and Multidisciplinary Optimization, vol. 57, no. 2, pp. 799–814, feb 2018. https://doi.org/10.1007/s00158-017-1784-3
[8] M. Khatibinia and H. Yazdani, “Accelerated multi-gravitational search algorithm for size optimization of truss structures,” Swarm and Evolutionary Computation, vol. 38, no. June 2017, pp. 109–119, 2018. https://doi.org/10.1016/j.swevo.2017.07.001
[9] H. Assimi, A. Jamali, and N. Nariman-zadeh, “Sizing and topology optimization of truss structures using genetic programming,” Swarm and Evolutionary Computation, vol. 37, pp. 90–103, dec 2017. https://doi.org/10.1016/j.swevo.2017.05.009
[10] M. S. Gonçalves, R. H. Lopez, and L. F. F. Miguel, “Search group algorithm: A new metaheuristic method for the optimization of truss structures,” Computers and Structures, vol. 153, pp. 165–184, 2015. https://doi.org/10.1016/j.compstruc.2015.03.003
[11] L. F. F. Miguel, R. H. Lopez, and L. F. F. Miguel, “Multimodal size, shape, and topology optimisation of truss structures using the firefly algorithm,” Advances in Engineering Software, vol. 56, pp. 23–37, 2013. https://doi.org/10.1016/j.advengsoft.2012.11.006
[12] A. Kaveh and M. Ilchi Ghazaan, Meta-heuristic Algorithms for Optimal Design of Real-Size Structures, 1st ed. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-78780-0
[13] I. Couceiro, J. París, S. Martínez, I. Colominas, F. Navarrina, and M. Casteleiro, “Structural optimization of lattice steel transmission towers,” Engineering Structures, vol. 117, pp. 274–286, 2016. https://doi.org/10.1016/j.engstruct.2016.03.005
[14] C. Tort, S. Sahin, and O. Hasançebi, “Optimum design of steel lattice transmission line towers using simulated annealing and pls-tower,” Computers & Structures, vol. 179, pp. 75–94, 2017.
[15] R. R. de Souza, L. F. F. Miguel, R. H. Lopez, L. F. F. Miguel, and A. J. Torii, “A procedure for the size, shape and topology optimization of transmission line tower structures,” Engineering Structures, vol. 111, pp. 162–184, 2016. https://doi.org/10.1016/j.engstruct.2015.12.005
[16] S. Degertekin, L. Lamberti, and I. Ugur, “Sizing, layout and topology design optimization of truss structures using the Jaya algorithm,” Applied Soft Computing Journal, 2017. https://doi.org/10.1016/j.asoc.2017.10.001
[17] S. Gholizadeh and A. Baghchevan, “Multi-objective seismic design optimization of steel frames by a chaotic meta-heuristic algorithm,” Engineering with Computers, vol. 33, no. 4, pp. 1045–1060, oct 2017. https://doi.org/10.1007/s00366-017-0515-0
[18] V. Mokarram and M. R. Banan, “A new PSO-based algorithm for multi-objective optimization with continuous and discrete design variables,” Structural and Multidisciplinary Optimization, vol. 57, no. 2, pp. 509–533, 2018. https://doi.org/10.1007/s00158-017-1764-7
[19] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, apr 2002. https://doi.org/10.1109/4235.996017
[20] C. C. Coello and M. S. Lechuga, “Mopso: A proposal for multiple objective particle swarm optimization,” in Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No. 02TH8600), vol. 2. IEEE, 2002, pp. 1051–1056.
[21] C. A. Coello Coello, G. Toscano Pulido, and M. Salazar Lechuga, “Handling multiple objectives with particle swarm optimization,” IEEE Transactions on evolutionary computation, vol. 8, no. 3, pp. 256–279, 2004. https://doi.org/10.1109/TEVC.2004.826067
[22] S. Bandyopadhyay, S. Saha, U. Maulik, and K. Deb, “A simulated annealing-based multiobjective optimization algorithm: Amosa,” IEEE transactions on evolutionary computation, vol. 12, no. 3, pp. 269–283, 2008. https://doi.org/10.1109/TEVC.2007.900837
[23] A. Kaveh and S. Talatahari, “A particle swarm ant colony optimization for truss structures with discrete variables,” Journal of Constructional Steel Research, vol. 65, no. 8-9, pp. 1558–1568, 2009. https://doi.org/10.1016/j.jcsr.2009.04.021
[24] A. Kaveh and M. Khayatazad, “Ray optimization for size and shape optimization of truss structures,” Computers and Structures, vol. 117, pp. 82–94, 2013. https://doi.org/10.1016/j.compstruc.2012.12.010
[25] A. Kaveh and A. Zolghadr, “Comparison of nine meta-heuristic algorithms for optimal design of truss structures with frequency constraints,” Advances in Engineering Software, vol. 76, pp. 9–30, 2014. https://doi.org/10.1016/j.advengsoft.2014.05.012
[26] A. Kaveh and V. R. Mahdavi, “Colliding Bodies Optimization method for optimum discrete design of truss structures,” Computers and Structures, vol. 139, pp. 43–53, 2014.
http://dx.doi.org/10.1016/j.compstruc.2014.04.006
[27] A. Mortazavi and V. Togan, “Simultaneous size, shape, and topology optimization of truss structures using integrated particle swarm optimizer,” Structural and Multidisciplinary Optimization, vol. 54, no. 4, pp. 715–736,
2016. https://doi.org/10.1007/s00158-016-1449-7
[28] A. Mortazavi and V. Togan, “Sizing and layout design of truss structures under dynamic and static constraints with an integrated particle swarm optimization algorithm,” Applied Soft Computing Journal, vol. 51, pp. 239–252, 2017. https://doi.org/10.1016/j.asoc.2016.11.032
[29] G. Bekdas, S. M. Nigdeli, and X. S. Yang, “Sizing optimization of truss structures using flower pollination algorithm,” Applied Soft Computing Journal, vol. 37, pp. 322–331, 2015. https://doi.org/10.1016/j.asoc.2015.08.037
[30] E.-G. Talbi, Metaheuristics: from design to implementation. John Wiley & Sons, 2009, vol. 74. 87
[31] P. Ngatchou, A. Zarei, and A. El-Sharkawi, “Pareto multi objective optimization,” in Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems. IEEE, 2005, pp. 84–91.
[32] K. Deb, Multi-objective optimization using evolutionary algorithms. John Wiley & Sons, 2001, vol. 16.
[33] J. S. Arora, “Optimum Design Problem Formulation,” in Introduction to Optimum Design, 4th ed. Elsevier, 2017, pp. 19–70.
[34] K. L. Du, M. Swamy et al., “Search and optimization by metaheuristics,” Techniques and Algorithms Inspired by Nature; Birkhauser: Basel, Switzerland, 2016.
[35] MATLAB, “version 9.6.0 (2019a),” Natick, Massachusetts, 2019.
[36] M. Y. Cheng, D. Prayogo, Y. W. Wu, and M. M. Lukito, “A Hybrid Harmony Search algorithm for discrete sizing optimization of truss structure,” Automation in Construction, vol. 69, pp. 21–33, 2016. https://doi.org/10.1016/j.autcon.2016.05.023
[37] S. Fallahian, D. Hamidian, and S. M. Seyedpoor, “Optimal Design of Structures using the simultaneous perturbation stochastic approximation algorithm,” International Journal of Computational Methods, vol. 6, no. 2,
pp. 229–245, 2009. https://doi.org/10.1002/0471722138.ch7
[38] K. S. Lee and Z. W. Geem, “A new structural optimization method based on the harmony search algorithm,” Computers & structures, vol. 82, no. 9-10, pp. 781–798, 2004. https://doi.org/10.1016/j.compstruc.2004.01.002
[2] O. Hasançebi, “Adaptive evolution strategies in structural optimization: Enhancing their computational performance with applications to large-scale structures,” Computers and Structures, vol. 86, no. 1-2, pp. 119–132, 2008. https://doi.org/10.1016/j.compstruc.2007.05.012
[3] O. Hasançebi and S. K. Azad, “Adaptive dimensional search: A new metaheuristic algorithm for discrete truss sizing optimization,” Computers and Structures, vol. 154, pp. 1–16, 2015. https://doi.org/10.1016/j.compstruc.2015.03.014
[4] S. Degertekin, L. Lamberti, and I. Ugur, “Discrete sizing/layout/topology optimization of truss structures with an advanced jaya algorithm,” Applied Soft Computing Journal, vol. 79, pp. 363–390, 2019. https://doi.org/10.1016/j.asoc.2019.03.058
[5] K. Deb and S. Gulati, “Design of truss-structures for minimum weight using genetic algorithms,” Finite Elements in Analysis and Design, vol. 37, no. 5, pp. 447–465, may 2001. https://doi.org/10.1016/S0168-74X(00)00057-3
[6] G. G. Tejani, V. J. Savsani, V. K. Patel, and P. V. Savsani, “Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics,” Journal of Computational Design and Engineering, vol. 5, no. 2, pp. 198–214, 10 2017. https://doi.org/10.1016/j.jcde.2017.10.001
[7] H. Cao, X. Qian, and Y. Zhou, “Large-scale structural optimization using metaheuristic algorithms with elitism and a filter strategy,” Structural and Multidisciplinary Optimization, vol. 57, no. 2, pp. 799–814, feb 2018. https://doi.org/10.1007/s00158-017-1784-3
[8] M. Khatibinia and H. Yazdani, “Accelerated multi-gravitational search algorithm for size optimization of truss structures,” Swarm and Evolutionary Computation, vol. 38, no. June 2017, pp. 109–119, 2018. https://doi.org/10.1016/j.swevo.2017.07.001
[9] H. Assimi, A. Jamali, and N. Nariman-zadeh, “Sizing and topology optimization of truss structures using genetic programming,” Swarm and Evolutionary Computation, vol. 37, pp. 90–103, dec 2017. https://doi.org/10.1016/j.swevo.2017.05.009
[10] M. S. Gonçalves, R. H. Lopez, and L. F. F. Miguel, “Search group algorithm: A new metaheuristic method for the optimization of truss structures,” Computers and Structures, vol. 153, pp. 165–184, 2015. https://doi.org/10.1016/j.compstruc.2015.03.003
[11] L. F. F. Miguel, R. H. Lopez, and L. F. F. Miguel, “Multimodal size, shape, and topology optimisation of truss structures using the firefly algorithm,” Advances in Engineering Software, vol. 56, pp. 23–37, 2013. https://doi.org/10.1016/j.advengsoft.2012.11.006
[12] A. Kaveh and M. Ilchi Ghazaan, Meta-heuristic Algorithms for Optimal Design of Real-Size Structures, 1st ed. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-78780-0
[13] I. Couceiro, J. París, S. Martínez, I. Colominas, F. Navarrina, and M. Casteleiro, “Structural optimization of lattice steel transmission towers,” Engineering Structures, vol. 117, pp. 274–286, 2016. https://doi.org/10.1016/j.engstruct.2016.03.005
[14] C. Tort, S. Sahin, and O. Hasançebi, “Optimum design of steel lattice transmission line towers using simulated annealing and pls-tower,” Computers & Structures, vol. 179, pp. 75–94, 2017.
[15] R. R. de Souza, L. F. F. Miguel, R. H. Lopez, L. F. F. Miguel, and A. J. Torii, “A procedure for the size, shape and topology optimization of transmission line tower structures,” Engineering Structures, vol. 111, pp. 162–184, 2016. https://doi.org/10.1016/j.engstruct.2015.12.005
[16] S. Degertekin, L. Lamberti, and I. Ugur, “Sizing, layout and topology design optimization of truss structures using the Jaya algorithm,” Applied Soft Computing Journal, 2017. https://doi.org/10.1016/j.asoc.2017.10.001
[17] S. Gholizadeh and A. Baghchevan, “Multi-objective seismic design optimization of steel frames by a chaotic meta-heuristic algorithm,” Engineering with Computers, vol. 33, no. 4, pp. 1045–1060, oct 2017. https://doi.org/10.1007/s00366-017-0515-0
[18] V. Mokarram and M. R. Banan, “A new PSO-based algorithm for multi-objective optimization with continuous and discrete design variables,” Structural and Multidisciplinary Optimization, vol. 57, no. 2, pp. 509–533, 2018. https://doi.org/10.1007/s00158-017-1764-7
[19] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, apr 2002. https://doi.org/10.1109/4235.996017
[20] C. C. Coello and M. S. Lechuga, “Mopso: A proposal for multiple objective particle swarm optimization,” in Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No. 02TH8600), vol. 2. IEEE, 2002, pp. 1051–1056.
[21] C. A. Coello Coello, G. Toscano Pulido, and M. Salazar Lechuga, “Handling multiple objectives with particle swarm optimization,” IEEE Transactions on evolutionary computation, vol. 8, no. 3, pp. 256–279, 2004. https://doi.org/10.1109/TEVC.2004.826067
[22] S. Bandyopadhyay, S. Saha, U. Maulik, and K. Deb, “A simulated annealing-based multiobjective optimization algorithm: Amosa,” IEEE transactions on evolutionary computation, vol. 12, no. 3, pp. 269–283, 2008. https://doi.org/10.1109/TEVC.2007.900837
[23] A. Kaveh and S. Talatahari, “A particle swarm ant colony optimization for truss structures with discrete variables,” Journal of Constructional Steel Research, vol. 65, no. 8-9, pp. 1558–1568, 2009. https://doi.org/10.1016/j.jcsr.2009.04.021
[24] A. Kaveh and M. Khayatazad, “Ray optimization for size and shape optimization of truss structures,” Computers and Structures, vol. 117, pp. 82–94, 2013. https://doi.org/10.1016/j.compstruc.2012.12.010
[25] A. Kaveh and A. Zolghadr, “Comparison of nine meta-heuristic algorithms for optimal design of truss structures with frequency constraints,” Advances in Engineering Software, vol. 76, pp. 9–30, 2014. https://doi.org/10.1016/j.advengsoft.2014.05.012
[26] A. Kaveh and V. R. Mahdavi, “Colliding Bodies Optimization method for optimum discrete design of truss structures,” Computers and Structures, vol. 139, pp. 43–53, 2014.
http://dx.doi.org/10.1016/j.compstruc.2014.04.006
[27] A. Mortazavi and V. Togan, “Simultaneous size, shape, and topology optimization of truss structures using integrated particle swarm optimizer,” Structural and Multidisciplinary Optimization, vol. 54, no. 4, pp. 715–736,
2016. https://doi.org/10.1007/s00158-016-1449-7
[28] A. Mortazavi and V. Togan, “Sizing and layout design of truss structures under dynamic and static constraints with an integrated particle swarm optimization algorithm,” Applied Soft Computing Journal, vol. 51, pp. 239–252, 2017. https://doi.org/10.1016/j.asoc.2016.11.032
[29] G. Bekdas, S. M. Nigdeli, and X. S. Yang, “Sizing optimization of truss structures using flower pollination algorithm,” Applied Soft Computing Journal, vol. 37, pp. 322–331, 2015. https://doi.org/10.1016/j.asoc.2015.08.037
[30] E.-G. Talbi, Metaheuristics: from design to implementation. John Wiley & Sons, 2009, vol. 74. 87
[31] P. Ngatchou, A. Zarei, and A. El-Sharkawi, “Pareto multi objective optimization,” in Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems. IEEE, 2005, pp. 84–91.
[32] K. Deb, Multi-objective optimization using evolutionary algorithms. John Wiley & Sons, 2001, vol. 16.
[33] J. S. Arora, “Optimum Design Problem Formulation,” in Introduction to Optimum Design, 4th ed. Elsevier, 2017, pp. 19–70.
[34] K. L. Du, M. Swamy et al., “Search and optimization by metaheuristics,” Techniques and Algorithms Inspired by Nature; Birkhauser: Basel, Switzerland, 2016.
[35] MATLAB, “version 9.6.0 (2019a),” Natick, Massachusetts, 2019.
[36] M. Y. Cheng, D. Prayogo, Y. W. Wu, and M. M. Lukito, “A Hybrid Harmony Search algorithm for discrete sizing optimization of truss structure,” Automation in Construction, vol. 69, pp. 21–33, 2016. https://doi.org/10.1016/j.autcon.2016.05.023
[37] S. Fallahian, D. Hamidian, and S. M. Seyedpoor, “Optimal Design of Structures using the simultaneous perturbation stochastic approximation algorithm,” International Journal of Computational Methods, vol. 6, no. 2,
pp. 229–245, 2009. https://doi.org/10.1002/0471722138.ch7
[38] K. S. Lee and Z. W. Geem, “A new structural optimization method based on the harmony search algorithm,” Computers & structures, vol. 82, no. 9-10, pp. 781–798, 2004. https://doi.org/10.1016/j.compstruc.2004.01.002
Article Sidebar
Published
Nov 11, 2020
Article Details
How to Cite
Niño-Alvarez, L., Guevara-Corzo, J., & Begambre-Carrillo, O. (2020). Automatic Design of Large-Scale Trusses: A Comparison Between Derivative-Free Algorithms. Ingeniería Y Ciencia, 16(32), 83–108. https://doi.org/10.17230/ingciencia.16.32.4
Issue
Section
Articles
Supporting Agencies
Universidad Industrial de Santander
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).