Life Cycle Cost Considerations in Seismic Design Optimization of Structures - Structural Seismic Design Optimization and Earthquake Engineering - page 2

and location of structural members are determined
and formation of new boundaries are allowed. The
number of joints in the structure, the joint support
locations, and number of members connected to
each joint are unknown. In other words, topology
and shape of the structure are optimized in addi-
tion to the shape of individual elements. Figure
1 illustrates the sizing and topology optimization
problems for a structural frame. The structure
being optimized may vary significantly from a
component of a mechanical device to a member
of a full-scale structure depending on the problem.
Most problems in structural earthquake engineer-
ing fall into the category of sizing optimization
and deal with full-scale structures.
The problems in structural optimization may
also be classified based on the number of objec-
tives, i.e. single- and multi-objective. For single-
objective seismic design optimization problems,
the objective is usually selected as the initial cost
for reinforced concrete (RC) and total weight for
steel structures; and the performance is determined
based on the conformance to the requirements of
a seismic design code. The code provisions are
usually introduced to the problem as constraints.
Some example studies include Moharrami and
Grierson (1993), Adamu et al. (1994), Memari
and Madhkhan (1999), Zou and Chan (2005) and

Sahab et al. (2005). As a consequence of the
formulation of the problem, the majority of the
single-objective optimization methods provide a
single optimal solution (which minimizes the
objective and satisfies the constraints). However,
the decision maker does not have a broad view
of to what extend the constraints are satisfied.
Thus, she has to either accept or reject the optimal
solution. On the other hand, since more than one
objective is considered in multi-objective optimi-
zation problems, commonly a set of equivalently
optimal solutions are obtained which provides the
decision maker the flexibility to tradeoff between
the solutions and she may base her selection on
rather transparent results. Some example multi-
objective studies include Li et al. (1999) and Liu
et al. (2006).
It is natural to include multiple objectives (e.g.
structural performance, initial and life-cycle costs)
in the LCC optimization of structures; however,
the number of objectives is not usually the only
difference between LCC and initial cost optimiza-
tion problems. The former necessitates the use of
probabilistic formulations to evaluate the failure
probability at different limit states in addition to
the derivation of the probabilistic seismic hazard
at different intensities. Whereas, in the latter
the evaluation of the structural performance at

Figure 1. Example illustration of (a) sizing, and (b) topology optimization problems