Abstract
This paper proposes the design of trusses using simultaneous topology, shape, and size design variables and reliability optimization. Objective functions consist of structural mass and reliability, while the probability of failure is set as a design constraint. Design variables are treated to simultaneously determine structural topology, shape, and sizes. Six test problems are posed and solved by a number of multi-objective evolutionary algorithms, and it is found that Hybridized Real-Code Population-Based Incremental Learning and Differential Evolution is the best performer. This work is considered an initial study for the combination of reliability optimization and simultaneous topology, shape, and sizing optimization of trusses.
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References
Karagöz S, Yıldız AR (2017) A comparison of recent metaheuristic algorithms for crashworthiness optimisation of vehicle thin-walled tubes considering sheet metal forming effects. Int J Veh Des 73(1–3):179–188
Kiani M, Yildiz AR (2015) A comparative study of non-traditional methods for vehicle crashworthiness and NVH optimization. Arch Comput Methods Eng 23(4):723–734
Yıldız AR, Kurtuluş E, Demirci E, Yıldız BS, Karagöz S (2016) Optimization of thin-wall structures using hybrid gravitational search and Nelder–Mead algorithm. Mater Test 58(1):75–78
Yıldız BS, Yıldız AR (2018) Comparison of grey wolf, whale, water cycle, ant lion and sine-cosine algorithms for the optimization of a vehicle engine connecting rod. Mater Test 60(3):311–315
Yıldız BS, Yıldız AR (2017) Moth-flame optimization algorithm to determine optimal machining parameters in manufacturing processes. Mater Test 59(5):425–429
Yıldız BS (2017) A comparative investigation of eight recent population-based optimisation algorithms for mechanical and structural design problems. Int J Veh Des 73(1–3):208–2187
Yıldız BS (2017) Yıldız AR, Pholdee N, Bureerat S (2017) Hybrid real-code population-based incremental learning and differential evolution for many-objective optimisation of an automotive floor-frame. Int J Veh Des 73(1–3):20–538
Yıldız AR, Öztürk F (2010) Hybrid Taguchi-harmony search approach for shape optimization. Recent Adv Harmon Search Algorithm 8:89–98
Yildiz AR (2013) Comparison of evolutionary-based optimization algorithms for structural design optimization. Eng Appl Artif Intell 26(1):327–333
Yildiz AR, Saitou K (2011) Topology synthesis of multicomponent structural assemblies in continuum domains. J Mech Des 133(1):011008–011009
Yildiz BS, Lekesiz H, Yildiz AR (2016) Structural design of vehicle components using gravitational search and charged system search algorithms. Mater Test 58(1):79–81
Victoria M, Querin OM, Díaz C, Martí P (2016) liteITD a MATLAB graphical user interface (GUI) program for topology design of continuum structures. Adv Eng Softw 100:126–147
Savsani VJ, Tejani GG, Patel VK, Savsani P (2017) Modified meta-heuristics using random mutation for truss topology optimization with static and dynamic constraints. J Comput Des Eng 4(2):106–130
Assimi H, Jamali A, Nariman-zadeh N (2017) Sizing and topology optimization of truss structures using genetic programming. Swarm Evolut Comput 37:90–103
Kaveh A, Ilchi Ghazaan M (2015) Hybridized optimization algorithms for design of trusses with multiple natural frequency constraints. Adv Eng Softw 79:137–147
Rahami H, Kaveh A, Gholipour Y (2008) Sizing, geometry and topology optimization of trusses via force method and genetic algorithm. Eng Struct 30(9):2360–2369
Assimi H, Jamali A (2018) A hybrid algorithm coupling genetic programming and Nelder–Mead for topology and size optimization of trusses with static and dynamic constraints. Expert Syst Appl 95:127–141
Tejani GG, Savsani VJ, Bureerat S, Patel VK (2018) Topology and size optimization of trusses with static and dynamic bounds by modified symbiotic organisms search. J Comput Civil Eng 32(2):04017085–04017011
Tejani GG, Savsani VJ, Bureerat S, Patel VK, Savsani P (2018) Topology optimization of truss subjected to static and dynamic constraints by integrating simulated annealing into passing vehicle search algorithms. Eng Comput. https://doi.org/10.1007/s00366-018-0612-8
Kaveh A, Zolghadr A (2011) Shape and size optimization of truss structures with frequency constraints using enhanced charged system search algorithm. Asian J Civil Eng 12:487–509
Šilih S, Kravanja S, Premrov M (2010) Shape and discrete sizing optimization of timber trusses by considering joint flexibility. Adv Eng Softw 41(2):286–294
Lieu Q, Do DTT, Lee J (2018) An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints. Comput Struct 195:99–112
Tejani GG, Savsani VJ, Patel VK (2016) Adaptive symbiotic organisms search (SOS) algorithm for structural design optimization. J Comput Des Eng 3(3):226–249
Panagant N, Bureerat S (2018) Truss topology, shape and sizing optimization by fully stressed design based on hybrid grey wolf optimization and adaptive differential evolution. Eng Optim 47:1–17
Noilublao N, Bureerat S (2011) Simultaneous topology, shape and sizing optimisation of a three-dimensional slender truss tower using multiobjective evolutionary algorithms. Comput Struct 89(23–24):2531–2538
Mortazavi A, Toğan V (2016) Simultaneous size, shape, and topology optimization of truss structures using integrated particle swarm optimizer. Struct Multidiscip Optim 54(4):715–736
Tomšič P, Duhovnik J (2014) Simultaneous topology and size optimization of 2D and 3D trusses using evolutionary structural optimization with regard to commonly used topologies. Adv Mech Eng 6:864–867
Zhou M, Pagaldipti N, Thomas HL, Shyy YK (2004) An integrated approach to topology, sizing, and shape optimization. Struct Multidiscip Optim 26(5):308–317
Tejani GG, Savsani VJ, Patel VK, Mirjalili S (2018) An improved heat transfer search algorithm for unconstrained optimization problems. J Comput Des Eng
Tejani GG, Savsani VJ, Patel VK, Savsani PV (2018) Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics. J Comput Des Eng 5(2):198–214
Tejani GG, Savsani VJ, Patel VK, Bureerat S (2017) Topology, shape, and size optimization of truss structures using modified teaching-learning based optimization. Adv Comput Des 2:313–331
Gomes HM (2011) Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst Appl 38(1):957–968
Kaveh A, Zolghadr A (2014) Democratic PSO for truss layout and size optimization with frequency constraints. Comput Struct 130:10–21
Yang IT, Hsieh YH (2012) Reliability-based design optimization with cooperation between support vector machine and particle swarm optimization. Eng Comput 29(2):151–163
Kaveh A, Talatahari S (2010) A charged system search with a fly to boundary method for discrete optimum design of truss structures. Asian J Civ Eng 11:277–293
Kaveh A, Zakian P (2014) Enhanced bat algorithm for optimal design of skeletal structures. Asian J Civil Eng 15:179–212
Kaveh A, Jafari L, Farhoudi (2015) Truss optimization with natural frequency constraints using a dolphin echolocation algorithm. Asian J Civil Eng 16:29–46
Mandhyan A, Srivastava G, Krishnamoorthi S (2016) A novel method for prediction of truss geometry from topology optimization. Eng Comput 33(1):95–106
Cheng MY, Prayogo D (2016) A novel fuzzy adaptive teaching–learning-based optimization (FATLBO) for solving structural optimization problems. Eng Comput 33(1):55–69
Kaintura A, Spina D, Couckuyt I, Knockaert L, Bogaerts W, Dhaene T (2017) A kriging and stochastic collocation ensemble for uncertainty quantification in engineering applications. Eng Comput 33(4):935–949
Shobeir V (2016) The optimal design of structures using ACO and EFG. Eng Comput 32(4):645–653
Shi J, Cao J, Cai K, Wang Z, Qin QH (2016) Layout optimization for multi-bi-modulus materials system under multiple load cases. Eng Comput 32(4):745–753
Ho-Huu V, Nguyen-Thoi T, Vo-Duy T, Nguyen-Trang T (2016) An adaptive elitist differential evolution for optimization of truss structures with discrete design variables. Comput Struct 165:59–75
Deb K, Gulati S (2001) Design of truss-structures for minimum weight using genetic algorithms. Finite Elem Anal Des 37(5):447–465
Kaveh A, Laknejadi K (2012) A hybrid evolutionary graph-based multi-objective algorithm for layout optimization of truss structures. Acta Mech 224(2):343–364
Veldhuizen DAV, Lamont G (2000) Multiobjective evolutionary algorithms: analyzing the state-of-the-art. Evol Comput 8(2):125–147
Zhou A, Qu BY, Li H, Zhao SZ, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evolut Comput 1(1):32–49
Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3:257–271
Srisomporn S, Bureerat S (2008) Geometrical design of plate-fin heat sinks using hybridization of MOEA and RSM. IEEE Trans Compon Packag Technol 31(2):351–360
Pholdee N, Bureerat S (2013) Hybridisation of real-code population-based incremental learning and differential evolution for multiobjective design of trusses. Inf Sci 223:136–152
Santawy MFE, Ahmed AN (2012) A multi-objective chaotic harmony search technique for structural optimization. Comput Sci 1:9–12
Gholizadeh S, Baghchevan A (2017) Multi-objective seismic design optimization of steel frames by a chaotic meta-heuristic algorithm. Eng Comput 33(4):1045–1060
Nasrollahi A (2017) Optimum shape of large-span trusses according to AISC-LRFD using ranked particles optimization. J Constr Steel Res 134:92–101
Lim J, Lee B (2015) A semi-single-loop method using approximation of most probable point for reliability-based design optimization. Struct Multidiscip Optim 53:745–757
Coletti G, Petturiti D, Vantaggi B (2017) Fuzzy memberships as likelihood functions in a possibilistic framework. Int J Approx Reas 88:547–566
Komal (2018) Fuzzy reliability analysis of DFSMC system in LNG carriers for components with different membership function. Ocean Eng 155:278–294
Kharmanda G, Sharabatey S, Ibrahim H, Makhloufi A, Elhami A (2009) Reliability-based design optimization using semi-numerical strategies for structural engineering applications. Int J CAD/CAM 9:1–16
Lombardi M, Haftka RT (1998) Anti-optimization technique for structural design under load uncertainties. Comput Methods Appl Mech Eng 157(1–2):19–31
Pholdee N, Bureerat S (2012) Performance enhancement of multiobjective evolutionary optimisers for truss design using an approximate gradient. Comput Struct 106–107:115–124
Noilublao N, Bureerat S (2013) Simultaneous topology, shape, and sizing optimisation of plane trusses with adaptive ground finite elements using MOEAs. Math Probl Eng 2013:1–9
Park S, Choi S, Sikorsky C, Stubbs N (2004) Efficient method for calculation of system reliability of a complex structure. Int J Solids Struct 41(18–19):5035–5050
Greiner D, Hajela P (2011) Truss topology optimization for mass and reliability considerations—co-evolutionary multiobjective formulations. Struct Multid Optim 45(4):589–613
Ho-Huu V, Nguyen-Thoi T, Le-Anh L, Nguyen-Trang T (2016) An effective reliability-based improved constrained differential evolution for reliability-based design optimization of truss structures. Adv Eng Softw 92:48–56
Kroetz HM, Tessari RK, Beck AT (2017) Performance of global metamodeling techniques in solution of structural reliability problems. Adv Eng Softw 114:394–404
Zhao Y, Zhang X, Lu Z (2018) Complete monotonic expression of the fourth-moment normal transformation for structural reliability. Comput Struct 196:186–199
Ma X, Liu F, Qi Y, Li L, Jiao L, Liu M, Wu J (2014) MOEA/D with Baldwinian learning inspired by the regularity property of continuous multiobjective problem. Neurocomputing 145:336–352
Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731
Sivasubramani KS, Swarup S (2011) Environmental/economic dispatch using multi-objective harmony search algorithm. Electr Power Syst Res 81:1778–1785
Aittokoski T, Miettinen K (2010) Efficient evolutionary approach to approximate the Pareto-optimal set in multiobjective optimization, UPS-EMOA. Optim Methods Softw 25(6):841–858
Bureerat S, Sriworamas K (2013) Simultaneous topology and sizing optimization of a water distribution network using a hybrid multiobjective evolutionary algorithm. Appl Soft Comput 13(8):3693–3702
Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31
Mlakar M, Petelin D, Tušar T, Filipič B (2015) GP-DEMO: differential evolution for multiobjective optimization based on Gaussian process models. Eur J Oper Res 243(2):347–361
Robič T, Filipič B (2005) DEMO: differential evolution for multiobjective optimization. Lect Notes Comput Sci 3410:520–533
Coello Coello CA, Reyes-Sierra M (2006) Multi-objective particle swarm optimizers: a survey of the state-of the-art. Int J Comput Intell Res 2(3):287–308
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95 proceedings of the sixth international symposium on micro machine and human science, pp 39–43
Ahrari A, Deb K (2016) An improved fully stressed design evolution strategy for layout optimization of truss structures. Comput Struct 164:127–144
Techasen T, Wansasueb K, Panagant N, Pholdee N, Bureerat S (2018) Multiobjective simultaneous topology, shape and sizing optimization of trusses using evolutionary optimizers. IOP Conf Ser Mater Sci Eng 370:012029
Acknowledgements
This work was supported by the Graduate Engineering Camp Fund, Faculty of Engineering, Khon Kaen University, Thailand, and the Thailand Research Fund (TRF).
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Techasen, T., Wansasueb, K., Panagant, N. et al. Simultaneous topology, shape, and size optimization of trusses, taking account of uncertainties using multi-objective evolutionary algorithms. Engineering with Computers 35, 721–740 (2019). https://doi.org/10.1007/s00366-018-0629-z
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DOI: https://doi.org/10.1007/s00366-018-0629-z