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one of the major concerns in the field structural
engineering. When structures are subjected to
sever earthquakes a huge amount of inertia loads is
imposed to the structures. In this case, considering
linear elastic behavior and ignoring the nonlinear
structural responses during the optimization pro-
cess may lead to vulnerable structural systems.
Therefore, seismic design codes suggest that,
under severe earthquake events, the structures
should be designed to deform inelastically. To
achieve structural seismic design optimization
it is necessary that the nonlinear structural time
history analysis to be performed many times. In
this case, the computational burden of the opti-
mal seismic design process is so large that could
prevent designer from comprehensively exploring
the design space, and could ultimately result in
unsuitable structures. Consequently, it is neces-
sary to employ efficient computational strategies
to achieve optimal seismic design of structures
spending low computational costs.
In the last decades, soft computing procedures
have been widely used to solve massive and
complex engineering problems. Soft computing
includes many components and the most attrac-
tive ones are meta-heuristic optimization algo-
rithms and neural networks. As meta-heuristic
or evolutionary optimization algorithms need not
gradient calculations they are more robust than
the mathematical programming based techniques
and usually present better global behavior. Be-
side the mentioned computational advantages,
the disadvantage of these methods is a slow rate
of convergence towards the global optimum.
A neural network is an interconnected network
of simple processing elements. The processing
elements interact along paths of variable con-
nection strengths which when suitably adapted
can collectively produce complex overall desired
behavior. Neural networks operate as black box,
model-free, and adaptive tools to capture and
learn significant structures in data. Their com-
puting abilities have been proven in the fields of
prediction, pattern recognition, and optimization.
They are suitable particularly for problems too
complex to be modelled and solved by classical
mathematics and traditional procedures.
The main objective of this chapter is to propose
a computationally efficient methodology to op-
timum design of structures subject to earthquake
loading considering inelastic structural behaviour.
To achieve this task, an efficient genetic algorithm
(GA) based evolutionary optimization algorithm
is employed to reduce the required analyses. Also,
a hybrid neural network system is employed to
effectively predict the nonlinear time history
responses of structures during the optimization
process.
BACKGROUND
During the last years, a number of researchers
have employed evolutionary algorithms to optimal
design of structures subject to dynamic loadings.
Kocer and Arora (1999, 2002) employed GA for
the optimal design of H-frame transition poles
and latticed towers conducting nonlinear time-
history analysis. They proposed the use of GA
and Simulated Annealing (SA) for the solution of
discrete variable problems, although the computa-
tional time required was excessive. Salajeghehand
Heidari (2005) incorporated wavelet transforms
and neural networks into the GA-based optimiza-
tion processes to predict linear structural responses
for a specific earthquake time history loading.
Lagaros
et al
. (2006) examined the influence of
various design procedures on the dynamic perfor-
mance of real-scale steel buildings. Gholizadeh
and Salajegheh (2009) employed meta-heuristic
particle swarm optimization (PSO) algorithm,
fuzzy inference systems (FIS) and radial basis
function (RBF) neural network for optimizing
linear structures subject to earthquake loading.
Gholizadeh and Salajegheh (2010a) incorporated
wavelet RBF neural network into a hybrid PSO-
GA optimization algorithm for seismic optimi-
zation of a real-scale steel building considering
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