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linear behavior. Computational performance of
GA and PSO examined by Gholizadeh (2010)
for dynamic design optimization of structures
considering nonlinear responses while a sur-
rogate model employed to predict the structural
responses during the optimization process. Also,
Gholizadeh and Samavati (2011) designed struc-
tures subject to earthquake for optimum weight
considering linear responses by a combination
of wavelet transforms, RBF neural networks
and an improved GA. Lagaros and Papadrakakis
(2011) employed back-propagation (BP) neural
network to predict nonlinear seismic responses
of 3D frame structures. They specified that the
predicted responses may be used in the frame
work of performance based design of structures
to reduce the computational effort. The proposed
methodology in this chapter consists of two main
computational strategies outlined as follows:
In the first strategy, an efficient evolutionary
optimization algorithm is employed. The main
drawback of the evolutionary algorithms, espe-
cially GA, is a slow rate of convergence. In the
present chapter, a GA based structural optimiza-
tion algorithm that can increase the probability of
achieving the global optimum with accelerated
convergence emphasizing on structural nonlinear
time history analysis reduction is employed. For
this purpose, the concepts of cellular automata
(CA) (Von Neumann, 1966) and GA are hybrid-
ized and the resulted hybrid algorithm is called
cellular genetic algorithm (CGA). In the CGA, a
small dimensioned grid is selected and the arti-
ficial evolution is evolved by a novel crossover
and traditional mutation operations. In each itera-
tion, cellular crossover operation produces a new
design at each site according to the fitness index
of neighboring cells of each site. As the size of
the population is small, the optimization process
converges to a pre-mature solution. In each pro-
cess, the best solution is saved. For creating a new
population the saved best solution is transformed
to the new population and the remaining ones are
randomly selected. Thereafter, the optimization
process is repeated to achieve a new solution. The
process of creating the new population with elite
sites is continued until the method converges.
However, employing the CGA the number of the
required generations is considerably reduced dur-
ing the optimization process, but due to this fact
that the seismic optimization process requires a
great number of nonlinear time history analyses
the overall time of the optimization process is
still very long.
In the second strategy, in order to reduce the
computational burden of the nonlinear time history
analysis, a hybrid neural network system (HNNS)
based on generalized regression neural network
(GRNN) (Wasserman, 1993) is employed. In this
case, instead of performing nonlinear dynamic
analysis by finite element method (FEM) a neural
network model is used to predict the necessary
nonlinear time history responses during the
optimization process. By employing the natural
frequencies as the inputs of neural networks,
better performance generality can be obtained.
As the natural frequencies are required during
the optimization process, evaluating of these by
analytic methods can impose additional compu-
tational burden to the process. In order to prevent
from this difficulty, another GRNN is employed
to effectively predict the frequencies. During the
optimization process many designs are examined
and due to considering nonlinear response analysis
it is probable that some of them lose their stabil-
ity during the ground motion and the nonlinear
dynamic analysis fails to converge. It is evident
that such designs should be rejected. As during
the optimization process, GRNN is employed
to evaluate the responses instead of the exact
nonlinear time history analysis, it is necessary to
detect such instable structures. For this purpose, a
probabilistic neural network (PNN) (Wasserman,
1993) is used. Using the PNN, evaluating the
time history responses of the instable structures is
ignored during the optimization process and this
makes the optimization process more efficient.
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