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had to abandon the conventional gradient-based
approaches. Heuristic optimization algorithms
progressively became popular in structural opti-
mization (Foley & Schinler, 2003; M. Fragiadakis,
Lagaros, & Papadrakakis, 2006b; N. D. Lagaros
& Papadrakakis, 2007; Min Liu, et al., 2006). The
most commonly used approaches include genetic
algorithms (GA), simulated annealing (SA), taboo
search (TS), and shuffled complex evolution. A
further advantage of the heuristic algorithms is
that they are very effective in terms of finding
the global minimum of highly nonlinear and/or
discontinuous problems where the gradient-based
algorithms are usually trapped at a local minimum.
provisions were followed to determine the validity
of design alternatives. Static pushover analysis
was used to derive an equivalent SDOF system
which was utilized in computing the maximum
interstory drift ratios. Liu et al. (2004) studied
the PBSD of steel moment-resisting frames us-
ing GA. Three merit functions were defined: the
initial material and lifetime seismic damage costs,
and the number of different steel section types.
Maximum interstory drift was used for the per-
formance assessment of the frames through static
pushover analysis. Code provisions were taken
into account in design. Different sources of uncer-
tainty in estimating seismic demand and capacity
were incorporated into analysis using the SAC/
FEMA guidelines (Cornell, Jalayer, Hamburger,
& Foutch, 2002). The results were presented as
Pareto-fronts for competing merit functions. Final
designs obtained from the optimization algorithm
were assessed using inelastic dynamic time his-
tory analysis. Liu (2005) formulated an optimal
design framework for steel structures based on the
PBSD. The considered objectives were the mate-
rial usage, initial construction expenses, degree
of design complexity, seismic structural perfor-
mance and lifetime seismic damage cost. Design
variables were section types for members of the
frames. The validity of designs was performed
based on the existing code provisions. A lumped
plasticity model was used for structural modeling.
Both static pushover and inelastic dynamic (only
when structural response parameters were directly
taken as objective functions) analysis were used.
Fragiadakis et al. (2006b) used evolutionary strate-
gies for optimal design of steel structures. Initial
construction and life cycle costs were considered
as the two merit functions. The constraints were
based on the provisions of the European design
codes. A fiber-based finite element model was used
to conduct static pushover analysis to determine
the inelastic response of structures. Deterministic
structural damage states based on the maximum
interstory drift was employed; however, probabi-
listic formulations were adopted for calculating
Review of Studies on LCC
Optimization of Structures
LCC analysis of structures has gained importance
in the recent years due to concerns related to
the civil infrastructure sustainability; therefore,
studies on LCC optimization of structures are
relatively new compared to the rest of the lit-
erature on structural optimization. Below, a brief
review of existing studies on LCC optimization
is provided. The section is not intended to be
comprehensive; the goal is to highlight some of
the critical components of seismic LCC analysis
that are addressed in more detail in this chapter.
Wen and Kang (2001a) developed an analyti-
cal formulation to evaluate the LCC of structures
under multiple hazards. The methodology is then
applied to a 9-story steel building to find the
minimum LCC under earthquake, wind and both
hazards (Wen & Kang, 2001b). In this study, the
simplified method based on an equivalent single-
degree-of-freedom (SDOF) system developed by
Collins et al. (1996) was used for structural assess-
ment. Liu et al. (2003) investigated the optimal
performance-based seismic design (PBSD) of
steel moment frame structures. Merit functions
were selected as the initial material and lifetime
seismic damage costs. Reducing design complex-
ity was also incorporated in the algorithm. Code
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