Border-search and jump reduction method for size optimization of spatial truss structures

doi:10.1007/s11709-018-0478-2

Frontiers of Structural and Civil Engineering

2019, Vol. 13

Issue (1): 123-134 https://doi.org/10.1007/s11709-018-0478-2

本期目录

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

全文: PDF(1340 KB) HTML

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.

Key words： optimum design sensitivity analysis reduction method spatial trusses OpenSees

收稿日期: 2017-10-04 出版日期: 2019-01-04

Corresponding Author(s): Babak DIZANGIAN

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2019, 13(1): 123-134.
Babak DIZANGIAN, Mohammad Reza GHASEMI. Border-search and jump reduction method for size optimization of spatial truss structures. Front. Struct. Civ. Eng., 2019, 13(1): 123-134.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-018-0478-2
https://academic.hep.com.cn/fsce/CN/Y2019/V13/I1/123

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Tab.1

Tab.2

Fig.8

variable group	bar areas	optimal cross-sectional area (in²)
variable group	bar areas	Ref. [³¹]^a)	Ref. [³²]^b)	Ref. [³³]^c)	Ref. [³⁴]^d)	$X start p 1$	$X s t e p p 1$	$X L p 1$	$X G$
1	A_1–4	2.563	2.629	2.588	2.6320	10	2.5	2.500	2.5738
2	A_5,6	1.553	1.162	1.083	1.1952	10	2.5	0.500	1.2406
3	A_7,8	0.281	0.343	0.363	0.3541	10	2.5	0.100	0.3426
4	A_9,10	0.512	0.423	0.422	0.4145	10	2.5	1.300	0.4212
5	A_11–14	2.626	2.782	2.827	2.7644	10	2.5	2.500	2.7828
6	A_15–18	2.131	2.173	2.055	2.0297	10	2.5	2.500	2.0142
7	A_19–22	2.213	1.952	2.044	2.0909	10	2.5	2.500	2.1491

Tab.3

source	weight (lb)	No. of analyses^a)
Ref. [³¹]	1034.740	N/A
Ref. [³²]	1024.800^b)	15000
Ref. [³³]	1022.230^b)	200000
Ref. [³⁴]	1024.000^b)	12500
$X s t e p p 1$	1213.421	5
$X L p 1$	1089.208	45
$X G$	1025.802	1800

Tab.4

Fig.9

Fig.10

Fig.11

Fig.12

variable group	bar areas	optimal cross-sectional area (in²)			cross-sectional area in current work (in²)
variable group	bar areas	Ref. [³⁵]^a)	Ref. [³⁶]^b)	Ref. [³⁷]^c)	$X start p1$	$X s t e p p1$	$X L p1$	$X G$
1	A_1–4	1.743	1.860	1.94459	10	0.7692	0.7500	1.65344
2	A₅_–₁₂	0.518	0.521	0.5026	10	0.7692	0.7500	0.50681
3	A₁₃_–₁₆	0.100	0.100	0.10000	10	0.7692	0.1000	0.10000
4	A_17,18	0.100	0.100	0.10000	10	0.7692	0.1000	0.10000
5	A₁₉_–₂₂	1.308	1.271	1.26757	10	0.7692	0.7500	1.14299
6	A_23–30	0.519	0.509	0.50990	10	0.7692	0.8333	0.57423
7	A₃₁_–₃₄	0.100	0.100	0.10000	10	0.7692	0.1000	0.10000
8	A_35,36	0.100	0.100	0.10000	10	0.7692	0.1000	0.10000
9	A₃₇_–₄₀	0.514	0.485	0.50674	10	0.7692	0.8333	0.34987
10	A₄₁_–₄₈	0.546	0.501	0.51651	10	0.7692	0.8333	0.52909
11	A₄₉_–₅₂	0.100	0.100	0.10752	10	0.7692	0.1000	0.10000
12	A_53,54	0.109	0.100	0.10000	10	0.7692	0.8333	0.10000
13	A₅₅_–₅₈	0.161	0.168	0.15618	10	0.7692	0.1000	0.10000
14	A₅₉_–₆₆	0.509	0.584	0.54022	10	0.7692	0.8333	0.67830
15	A₆₇_–₇₀	0.497	0.433	0.42229	10	0.7692	0.8333	0.26164
16	A_71,72	0.562	0.520	0.57941	10	0.7692	0.8333	0.52311

Tab.5

source	weight (lb)	No. of analyses^a)
Ref. [³⁵]	381.7790	N/A
Ref. [³⁶]	380.8370^b)	13742
Ref. [³⁷]	379.9740	10500
$X start p1$	8530.9000	1
$X s t e p p1$	710.9080	13
$X L p1$	524.9800	100
$X G$	378.4304	1250

Tab.6

Fig.13

variable group	optimal cross-sectional area (in²)
variable group	Ref. [³⁹]^a)	Ref. [⁴⁰]^b)	$X start p1$	$X s t e p p1$	$X L p1$	$X G$
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

source	weight (lb)	no. of analyses
Ref. [³¹]	20125.350	15000
Ref. [³²]	19908.030	20000
$X start p1$	70920.994	1
$X s t e p p1$	35460.497	3
$X L p1$	23358.880	78
$X G$	19905.450	1100

Tab.8

Fig.14

Fig.15

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

Viewed

Full text

Abstract

Cited

Shared

Discussed