Life Cycle Cost Considerations in Seismic Design Optimization of Structures - Structural Seismic Design Optimization and Earthquake Engineering - page 15

Figure 8. Curve fitting to obtain the (a) mean and (b) standard deviation of earthquake demand in
continuous form

TS algorithm has also been applied to structural
optimization problems. Bland (1998) applied TS
algorithm to weight minimization of a space truss
structure with various local minima and showed
that TS algorithm was very effective in finding
the global minimum when both reliability and
displacement constraints were applied. Mano-
haran and Shanmuganathan (1999) investigated
the efficiency of TS, SA, GA and branch-and-
bound in solving the cost minimization steel truss
structures. It was concluded that TS produced
solutions better than or as good as both SA and
GA and it arrives at the optimal solution quicker
than both methods. In a more recent study, Ohsaki
et al. (2007) explored the applicability of SA and
TS algorithms for optimal seismic design of steel
frames with standard sections. It was concluded
that TS was more advantageous over SA in terms
of the diversity of the Pareto solutions and the
ability of the algorithm to search the solutions
near the Pareto front.
To describe the modified TS algorithm used
here, first, it is required to make the following
definitions. The taboo list includes points in the
design space for which the objective functions are
evaluated for. Since inelastic dynamic time history
analysis is computationally costly, this list is used

to avoid multiple runs with the same combination
of design variables. That is, a point in the taboo
list is not evaluated again. The Pareto list includes
the points that are not dominated by other points
within the set for which the evaluation of objective
functions is performed (i.e. the taboo list). The
seed list includes the points around which optimal
solutions are looked for. The latter are called as
the neighboring points and they are basically the
adjacent elements of the multidimensional array,
that defines the decision (or design) variables,
around the given seed point. The modified TS
algorithm works as follows:

A. Start with the minimum cost combination
(or initial design), evaluate the objective
function and add this point into taboo, seed
and Pareto lists. Use this point as the initial
seed point.
B. Find the neighboring points around the cur-
rent seed. Here the number of neighboring
points is chosen equal to the number of
design variables and selected randomly
amongst all the adjacent elements of the
multidimensional array that defines the
design variables.