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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (1) : 123-134     https://doi.org/10.1007/s11709-018-0478-2
RESEARCH ARTICLE |
Border-search and jump reduction method for size optimization of spatial truss structures
Babak DIZANGIAN1(), Mohammad Reza GHASEMI2
1. Department of Civil Engineering, Velayat University, Iranshahr 9911131311, Iran
2. Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan 9816745845, Iran
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Abstract

This paper proposes a sensitivity-based border-search and jump reduction method for optimum design of spatial trusses. It is considered as a two-phase optimization approach, where at the first phase, the first local optimum is found by few analyses, after the whole searching space is limited employing an efficient random strategy, and the second phase involves finding a sequence of local optimum points using the variables sensitivity with respect to corresponding values of constraints violation. To reach the global solution at phase two, a sequence of two sensitivity-based operators of border-search operator and jump operator are introduced until convergence is occurred. Sensitivity analysis is performed using numerical finite difference method. To do structural analysis, a link between open source software of OpenSees and MATLAB was developed. Spatial truss problems were attempted for optimization in order to show the fastness and efficiency of proposed technique. Results were compared with those reported in the literature. It shows that the proposed method is competitive with the other optimization methods with a significant reduction in number of analyses carried.

Keywords optimum design      sensitivity analysis      reduction method      spatial trusses      OpenSees     
Corresponding Authors: Babak DIZANGIAN   
Just Accepted Date: 24 April 2018   Online First Date: 29 May 2018    Issue Date: 04 January 2019
 Cite this article:   
Babak DIZANGIAN,Mohammad Reza GHASEMI. Border-search and jump reduction method for size optimization of spatial truss structures[J]. Front. Struct. Civ. Eng., 2019, 13(1): 123-134.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-018-0478-2
http://journal.hep.com.cn/fsce/EN/Y2019/V13/I1/123
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Babak DIZANGIAN
Mohammad Reza GHASEMI
Fig.1  An efficient random strategy
Fig.2  The flow chart of border-search operator (BSO)
Fig.3  Flow chart of proposed optimization method. MSV: Most sensitive variables
Fig.4  Space degradation strategy (SDS)
Fig.5  Stair-wise step-by-step formulation
Fig.6  Sequential BSOs and JOs to find local optimums, Phase 2
Fig.7  22-bar space truss, Example 1 [33] (unit: in, 1 in=2.54 cm)
condition node x (kips) y (kips) z (kips)
1 1 –20 0 –5
2 –20 0 –5
3 –20 0 –30
4 –20 0 –30
2 1 –20 –5 0
2 –20 –50 0
3 –20 –5 0
4 –20 –50 0
3 1 –20 0 35
2 –20 0 0
3 –20 0 0
4 –20 0 –50
Tab.1  Loading conditions for 22-bar space truss
design variables members compression (ksi) tension (ksi)
1 A1–4 24 36
2 A5,6 30 36
3 A7,8 28 36
4 A9,10 26 36
5 A11–14 22 36
6 A15–18 20 36
7 A19–22 18 36
Tab.2  Allowable stresses and member grouping data for the 22-bar space truss
Fig.8  First sensitivity analysis at Xstepp1 for the 22-bar space truss
variable group bar areas optimal cross-sectional area (in2) cross-sectional area in current work (in2)
Ref. [31]a) Ref. [32]b) Ref. [33]c) Ref. [34]d) Xstartp1 Xstepp1 XLp1 XG
1 A1–4 2.563 2.629 2.588 2.6320 10 2.5 2.500 2.5738
2 A5,6 1.553 1.162 1.083 1.1952 10 2.5 0.500 1.2406
3 A7,8 0.281 0.343 0.363 0.3541 10 2.5 0.100 0.3426
4 A9,10 0.512 0.423 0.422 0.4145 10 2.5 1.300 0.4212
5 A11–14 2.626 2.782 2.827 2.7644 10 2.5 2.500 2.7828
6 A15–18 2.131 2.173 2.055 2.0297 10 2.5 2.500 2.0142
7 A19–22 2.213 1.952 2.044 2.0909 10 2.5 2.500 2.1491
Tab.3  Comparing optimal designs for the 22-bar space truss
source weight (lb) No. of analysesa)
Ref. [31] 1034.740 N/A
Ref. [32] 1024.800b) 15000
Ref. [33] 1022.230b) 200000
Ref. [34] 1024.000b) 12500
Xstepp1 1213.421 5
XLp1 1089.208 45
XG 1025.802 1800
Tab.4  Weights and the number of analyses
Fig.9  Convergence history of best weight for 22-bar space truss
Fig.10  72-bar space truss [33] (unit: in, 1 in=2.54 cm)
Fig.11  First sensitivity analysis at Xste pp1 for the 72-bar truss
Fig.12  Convergence history of best weight of 72-bar space truss
variable group bar areas optimal cross-sectional area (in2) cross-sectional area in current work (in2)
Ref. [35]a) Ref. [36]b) Ref. [37]c) Xstartp1 Xs tepp1 XLp1 XG
1 A1–4 1.743 1.860 1.94459 10 0.7692 0.7500 1.65344
2 A512 0.518 0.521 0.5026 10 0.7692 0.7500 0.50681
3 A1316 0.100 0.100 0.10000 10 0.7692 0.1000 0.10000
4 A17,18 0.100 0.100 0.10000 10 0.7692 0.1000 0.10000
5 A1922 1.308 1.271 1.26757 10 0.7692 0.7500 1.14299
6 A23–30 0.519 0.509 0.50990 10 0.7692 0.8333 0.57423
7 A3134 0.100 0.100 0.10000 10 0.7692 0.1000 0.10000
8 A35,36 0.100 0.100 0.10000 10 0.7692 0.1000 0.10000
9 A3740 0.514 0.485 0.50674 10 0.7692 0.8333 0.34987
10 A4148 0.546 0.501 0.51651 10 0.7692 0.8333 0.52909
11 A4952 0.100 0.100 0.10752 10 0.7692 0.1000 0.10000
12 A53,54 0.109 0.100 0.10000 10 0.7692 0.8333 0.10000
13 A5558 0.161 0.168 0.15618 10 0.7692 0.1000 0.10000
14 A5966 0.509 0.584 0.54022 10 0.7692 0.8333 0.67830
15 A6770 0.497 0.433 0.42229 10 0.7692 0.8333 0.26164
16 A71,72 0.562 0.520 0.57941 10 0.7692 0.8333 0.52311
Tab.5  Comparing optimal designs for the 72-bar space truss
source weight (lb) No. of analysesa)
Ref. [35] 381.7790 N/A
Ref. [36] 380.8370b) 13742
Ref. [37] 379.9740 10500
Xstartp1 8530.9000 1
Xs tepp1 710.9080 13
XLp1 524.9800 100
XG 378.4304 1250
Tab.6  Weights and the number of analyses
Fig.13  120-bar dome truss [33]
variable group optimal cross-sectional area (in2) cross-sectional area in current work (in2)
Ref. [39]a) Ref. [40]b) Xstartp1 Xs tepp1 XLp1 XG
1 3.3005 3.2984 10 5 3.60 3.303
2 2.7481 2.7894 10 5 2.25 2.127
3 3.9036 3.8743 10 5 3.20 2.910
4 2.5713 2.5719 10 5 3.20 2.820
5 1.2889 1.1549 10 5 2.25 1.950
6 3.4089 3.3341 10 5 3.60 3.337
7 2.8150 2.7860 10 5 3.95 3.680
Tab.7  Comparing optimal designs for the 120-bar dome truss
source weight (lb) no. of analyses
Ref. [31] 20125.350 15000
Ref. [32] 19908.030 20000
Xstartp1 70920.994 1
Xs tepp1 35460.497 3
XLp1 23358.880 78
XG 19905.450 1100
Tab.8  Weights and the number of analyses
Fig.14  First sensitivity analysis at Xs tepp1 for the 120-bar dome truss
Fig.15  Convergence history of best weight of 120-bar dome truss
1 R MKling, P Banerjee. ESP: Placement by simulated evolution. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1989, 8(3): 245–256
https://doi.org/10.1109/43.21844
2 D EGoldberg, J H Holland. Genetic algorithms and machine learning. Machine Learning, 1988, 3(2–3): 95–99
https://doi.org/10.1023/A:1022602019183
3 RBattiti, G Tecchiolli. The reactive Tabu search. ORSA Journal on Computing, 1994, 6(2): 126–140
https://doi.org/10.1287/ijoc.6.2.126
4 MDorigo, V Maniezzo, AColorni. Ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics, 1996, 26(1): 29–41
https://doi.org/10.1109/3477.484436
5 JKennedy. Particle swarm optimization. In: Sammut C, Webb G I, eds. Encyclopedia of Machine Learning. Boston: Springer, 2011, 760–766
6 XYang, S Deb. Cuckoo search via levy flight. In: Proceedings of World Congress on Nature and Biologically Inspired Algorithms. IEEE, 2009, 210–214
7 MEusuff, K Lansey, FPasha. Shuffled frog-leaping algorithm: A memetic meta-heuristic for discrete optimization. Engineering Optimization, 2006, 38(2): 129–154
https://doi.org/10.1080/03052150500384759
8 X SYang, M Karamanoglu, XHe. Flower pollination algorithm: A novel approach for multiobjective optimization. Engineering Optimization, 2014, 46(9): 1222–1237
https://doi.org/10.1080/0305215X.2013.832237
9 BXing, W J Gao. Fruit fly optimization algorithm. In: Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms. Cham: Springer, 2014, 167–170
10 HVaraee, M R Ghasemi. Engineering optimization based on ideal gas molecular movement algorithm. Engineering with Computers, 2017, 33(1): 71–93
https://doi.org/10.1007/s00366-016-0457-y
11 JPark, M Ryu. Optimal design of truss structures by rescaled simulated annealing. KSME International Journal, 2004, 18(9): 1512–1518
https://doi.org/10.1007/BF02990365
12 AEl Dor, M Clerc, PSiarry. A multi-swarm PSO using charged particles in a partitioned search space for continuous optimization. Computational Optimization and Applications, 2012, 53(1): 271–295
https://doi.org/10.1007/s10589-011-9449-4
13 M KDhadwal, S N Jung, C J Kim. Advanced particle swarm assisted genetic algorithm for constrained optimization problems. Computational Optimization and Applications, 2014, 58(3): 781–806
https://doi.org/10.1007/s10589-014-9637-0
14 M SHayalioglu. Optimum load and resistance factor design of steel space frames using genetic algorithm. Structural and Multidiscip-linary Optimization, 2001, 21(4): 292–299
https://doi.org/10.1007/s001580100106
15 PShahnazari-Shahrezaei, RTavakkoli-Moghaddam, HKazemipoor. Solving a new fuzzy multi-objective model for a multi-skilled manpower scheduling problem by particle swarm optimization and elite Tabu search. International Journal of Advanced Manufacturing Technology, 2013, 64: 1517
16 C VCamp, B J Bichon, S P Stovall. Design of steel frames using ant colony optimization. Journal of Structural Engineering, 2005, 131(3): 369–379
https://doi.org/10.1061/(ASCE)0733-9445(2005)131:3(369)
17 AKaveh, S Talatahari. Optimum design of skeletal structures using imperialist competitive algorithm. Computers & Structures, 2010, 88(21): 1220–1229
https://doi.org/10.1016/j.compstruc.2010.06.011
18 A HGandomi, X S Yang, A H Alavi. Cuckoo search algorithm: A metaheuristic approach to solve structural optimization problems. Engineering with Computers, 2013, 29(1): 17–35
https://doi.org/10.1007/s00366-011-0241-y
19 MSheikhi, A Ghoddosian. A hybrid imperialist competitive ant colony algorithm for optimum geometry design of frame structures. Structural Engineering and Mechanics, 2013, 46(3): 403–416
https://doi.org/10.12989/sem.2013.46.3.403
20 TDede, V Togan. A teaching learning based optimization for truss structures with frequency constraints. Structural Engineering and Mechanics, 2015, 53(4): 833–845
https://doi.org/10.12989/sem.2015.53.4.833
21 MSalar, M R Ghasemi, B Dizangian. A fast GA-based method for solving truss optimization problems. International Journal of Optimization in Civil Engineering, 2015, 6(1): 101–114
22 MFarshchin, C V Camp, M Maniat. Multi-class teaching-learning-based optimization for truss design with frequency constraints. Engineering Structures, 2016, 106: 355–369
https://doi.org/10.1016/j.engstruct.2015.10.039
23 MArtar. A comparative study on optimum design of multi-element truss structures. Steel and Composite Structures, 2016, 22(3): 521–535
https://doi.org/10.12989/scs.2016.22.3.521
24 GBekdaş, S M Nigdeli, X S Yang. Sizing optimization of truss structures using flower pollination algorithm. Applied Soft Computing, 2015, 37: 322–331
https://doi.org/10.1016/j.asoc.2015.08.037
25 SKanarachos, J Griffin, M EFitzpatrick. Efficient truss optimization using the contrast-based fruit fly optimization algorithm. Computers & Structures, 2017, 182: 137–148
https://doi.org/10.1016/j.compstruc.2016.11.005
26 HGhasemi, H S Park, T Rabczuk. A level-set based IGA formulation for topology optimization of flexoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 239–258
https://doi.org/10.1016/j.cma.2016.09.029
27 K MHamdia, M Silani, XZhuang, PHe, T Rabczuk. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227
https://doi.org/10.1007/s10704-017-0210-6
28 NVu-Bac, T Lahmer, XZhuang, TNguyen-Thoi, TRabczuk. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31
https://doi.org/10.1016/j.advengsoft.2016.06.005
29 BDizangian, M R Ghasemi. Ranked-based sensitivity analysis for size optimization of structures. Journal of Mechanical Design, 2015, 137(12): 121402
https://doi.org/10.1115/1.4031295
30 A DBelegundu, T RChandrupatla. Optimization Concepts and Applications in Engineering. Cambridge: Cambridge University Press, 2011
31 M RKhan, K D Willmert, W A Thornton. A new optimality criterion method for large scale structures. In: Proceedings of 19th Structures, Structural Dynamics and Materials Conference, Structures, Structural Dynamics, and Materials and Co-located Conferences. Bethesda, 1979
32 L JLi, Z B Huang, F Liu, Q HWu. A heuristic particle swarm optimizer for optimization of pin connected structures. Computers & Structures, 2007, 85(7–8): 340–349
https://doi.org/10.1016/j.compstruc.2006.11.020
33 K SLee, Z W Geem. A new structural optimization method based on the harmony search algorithm. Computers & Structures, 2004, 82(9–10): 781–798
https://doi.org/10.1016/j.compstruc.2004.01.002
34 STalatahari, M Kheirollahi, CFarahmandpour, A HGandomi. A multi-stage particle swarm for optimum design of truss structures. Neural Computing & Applications, 2013, 23(5): 1297–1309
https://doi.org/10.1007/s00521-012-1072-5
35 R EPerez, K Behdinan. Particle swarm approach for structural design optimization. Computers & Structures, 2007, 85(19–20): 1579–1588
https://doi.org/10.1016/j.compstruc.2006.10.013
36 S ODegertekin. Improved harmony search algorithms for sizing optimization of truss structures. Computers & Structures, 2012, 92–93: 229–241
https://doi.org/10.1016/j.compstruc.2011.10.022
37 AKaveh, R Sheikholeslami, STalatahari, MKeshvari-Ilkhichi. Chaotic swarming of particles: A new method for size optimization of truss structures. Advances in Engineering Software, 2014, 67: 136–147
https://doi.org/10.1016/j.advengsoft.2013.09.006
38 C KSoh, J Yang. Fuzzy controlled genetic algorithm search for shape optimization. Journal of Computing in Civil Engineering, 1996, 10(2): 143–150
https://doi.org/10.1061/(ASCE)0887-3801(1996)10:2(143)
39 S.Kazemzadeh Azad Optimum design of structures using an improved firefly algorithm. International Journal of Optimization in Civil Engineering, 2011, 1(2): 327–340
40 AHadidi, S K Azad, S K Azad. Structural optimization using artificial bee colony algorithm. In: Proceedings of 2nd International Conference on Engineering Optimization. 2010, 6–9
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