Shaping and Sizing-Shaping Optimization of Truss Structures via Triangular Optimizer Algorithm (TOA) Optimization Method

Authors

Abstract

In this article, triangular optimizer algorithm optimization method is presented for minimizing the weight of the truss structures. Triangular optimizer algorithm is a new metaheuristic method which is inspired of triangle. In this method, the initial vector of design variables is considered as the base of the triangle (first row). Then the objective functions are calculated and the best and the worst response are identified. The worst response is removed from the current population and the remaining population after some modifications is defined the second row. This process continues till reaching the apex of triangle, the optimal solution of this triangle. In the second iteration (second triangle), a certain number of the initial design variables are retrieved by the optimal solution of the previous triangle and the remaining of this population are created in the initial interval for escape from local optimums. So base of the second optimal triangle is formed. Then the mentioned algorithm is performed until optimum response of second triangle is achieved. These operations are continued until the convergence condition being satisfied. To prove the capabilities of the proposed algorithm shaping and sizing-shaping optimization of four truss structures are considered. The obtained statistical results of truss structures optimization show that the TOA is able to managed to achieve better optimal solutions compared to different optimization techniques.

Keywords


م
م
[1]
AlRashidi, M. R., El
-
Hawary, M. E.
(2007).
Hybrid
Particle
Swarm Optimization Approach for Solving the
Discrete OPF Problem
Considering the Valve Loading Effects
.
IEEE Transactions on Power
Systems, Vol. 22
, No. 4, pp. 2030
-
2038
.
[
2
]
Rao, S. S. (2009).
Engineering Optimization: Theory and Practice
”.
4
th
Edition, John Wiley and Sons
.
[
3
]
Prugel
-
Bennett, A. (2010).
Benefits of a Population: Five Mechanisms that Advantage Population
-
Based
Algorithms
”.
Evolutionary Computation, IEEE Transactions on, Vol. 14, No. 4, pp. 500
-
517
.
[
4
]
S. Kirkpat
rick, C.D. Gela
tto, M.P. Vecchi.
(1983). “
Optimization by simulated annealing
”.
Science 220, pp.
671
680
.
[
5
]
J. Kennedy, R.C. Eberhart.
(1995).
Particle swarm optimization
”.
i
n: Proceedings of IEEE International
Conference on Neural Networks,
vol. 4
, pp. 1942
1948
.
[
6
]
M. Melanie.
(1999).
An Introduction to Genetic Algorithms
”.
Massachusetts: MIT Press
.
[
7
]
M. Dorigo and C. Blum,
(2005).
“Ant colony
optimization theory: A survey”.
Theoretical Computer
Science, 344,
pp. 243
278
.
[
8
]
Pham DT, Ghanbarzadeh A, Koc E, Ot
ri S, Rahim S and Zaidi M.
(2005).
The Bees Algorithm
. Technical
Note, Manufacturing Engineering Centre, Cardiff University,
UK
.
[
9
]
Kang Seok Lee, Zong Woo Geem,
(2005).
A new meta
-
heuristic algorithm for continuous engineering
optimization: harmony se
arch theory and practice
”.
Comput. Methods Appl. Mech. Engrg. 194,
pp.
3902
3933
.
[
10
]
Esmat Rashedi, Hossein
Nezamabadi
-
pour, Saeid Saryazdi. (2009).
GSA: A Gravitational Search
Algorithm
”.
Information Sciences 179,
pp 2232
2248
.
[
11
]
Yang, X. S. (2009).
Firefly Algorithms for Multimodal Optimization
”.
Stochastic Algorithms:
Foundations and Applications, Vol. 5792, pp. 169
-
178
.
[
12
]
Kaveh, A., Talatahari, S. (2010).
A Novel Heuristic Optimization Method: Charged System Search
”.
Acta
Mech, Vol. 213, pp.
267
289
.
[
13
]
Eskandar, H., Sadollah, A
., Bahreininejad, A., Hamdi, M. (2012).
Water Cycle Algorithm
A novel
Metaheuristic Optimization Method for Solving Constrained Engineering Optimization Problems
”.
Computers and Structures, Vol. 110, pp. 151
166
.
[
14
]
Kaveh, A., Khayatazad, M. (2012).
A New Meta
-
Heuristic Method: Ray Optimization
”.
Computers and
Structures, Vol. 112, pp. 283
-
294
.
[
15
]
Kaveh, A., Farhodi, N. (2013).
A New Optimization Method: Dolphin Echolocation
”.
Advances in
Engineering Software, V
ol. 59, pp. 53
-
70
.
[
16
]
Kaveh A, Talatahari S.
(2009).
Size optimization of space trusses using Big Bang
Big Crunch algorithm
”.
Comput Struct; 87:
pp.
1129
-
40
.
[
17
]
Rahami H, Kaveh A, Gholipour Y.
(2008).
Sizing, geometry and topology optimization of
trusses via
force method and genetic algorithm
”.
Eng Struct; 30:
pp.
2360
-
9
.
[
18
]
Rasmussen MH, Stolpe M.
(2008).
Global optimization of discrete truss topology design problems using a
parallel cut
-
and
-
branch method
”.
Comput Struct; 86:
pp.
1527
-
38
.
[
19
]
G.I.N. Rozvany, M. Zhou. (1996).
Advances in overcoming computational pitfalls in topology
optimization
”.
in: Proc. of the Sixth AIAA/NASA/ISSMO Symp. on Multi
-
disc. Anal. and Optim
.
,
pp. 1122
1132
.
[
20
]
L. Gil, A. Andreu. (2001).
Shape and cross
-
section
optimization of a truss structure
”.
Comput. Struct. 79,
pp. 681
689
.
[
21
]
N.L. Pedersen, A.K. Nielsen. (2001).
Optimization of practical trusses with constraints on
eigenfrequencies, displacements, stresses and buckling
”.
report
no. 664, Technical University of
Denmark
.
[
22
]
W.H. Z
hang, M. Domaszewski, C. Fleury. (1998).
A new mixed convex approximation method with
applications for truss configuration optimization
”.
Struct. Optim. 15, pp. 237
241
.
[
23
]
Goldberg DE, Samtani MP.
(
1986).
Engineering optimization via genetic algorithm
”.
electronic
computation. New York: ASCE
;
p
p. 471
6
.
[
24
]
Jenkins WM.
(1991).
Towards structural optimization via the Genetic algorithm
. Comput Struct
;40:
pp.
1321
7
.
[
25
]
Adeli H, Cheng NT.
(1993)
.
Integrated genetic algorithm for optimization of space structures
. J
Aerospace Eng, ASCE;
6:
pp.
315
28
.
[
26
]
Rajeev S, Krishnamoorthy
. (1992).
CS. Discrete optimization of structures using genetic algorithms
. J
Struct Eng, ASCE;
118:
pp.
1233
50
.
[
27
]
Wu S
-
J, Chow P
-
T.
(1995).
Integrated discrete and configuration optimization of trusses using genetic
algorithms
. Comput Struct;
55(4):
pp.
695
702
.
[
28
]
Hwang S
-
F, He R
-
S.
(2006).
A hybrid real
-
parameter genetic algorithm for function optimization
. Adv
Eng Infor;
20:
pp.
7
21
.
[
29
]
Tang W, Tong L, Gu Y.
(2005).
Improved genetic algorithm for design optimization of truss structures
with sizing, shape and topology variables
. Internat J Numer Methods Engrg;
62:
pp.
1737
62
.
[
30
]
Hasanc ̧ebi O, Erbatu
r F.
(2001).
Layout optimization of trusses using improved GA methodologies
.
Acta Mech;
146:
pp.
87
107
.
[
31
]
Kaveh A, Kalatjari V.
(2004). “
Size/geometry optimization of trusses by the force method and genetic
algorithm
. Z Angew Math Mech;
84(5):
pp.
347
57
.
[
32
]
Li LJ, Huang ZB, Liu F.
(2009).
A heuristic particle swarm optimization method for truss structures with
discrete variables
”.
Comput Struct;
87:
pp.
435
-
43
.
[
33
]
Y.M. Xie
, G.P. Steven. (1997).
Evolutionary Structural Optimization
”.
Springer,
Berlin
.
[
34
]
D.N. Chu. (1997).
Evolutionary structural optimization method for systems with stiffness and
displacement constraints
. Ph.D. Thesis, Department of Civil and Building Engineering, Victoria
University of Technology, Melbourne, Australia
.
[
35
]
D. Wang, W.H. Zhang, J.S. Jiang. (2002).
Truss shape optimization with multiple displacement
constraints
”.
Comput. Methods Appl. Mech. Engrg.
191, pp.
3597
3612
.
[
36
]
H. Rahami, A. Kaveh, Y. Gholipour
. (2008).
Sizing, geometry and topology optimization
of trusses via
force method and genetic algorithm
”.
Engineering Structures