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Fig. 13. The design history the cellular beam with 9m span
the maximum value of deflection of the beam is much smaller than its upper bound.
This indicates that the strength constraints are dominant in the design problem. The
optimum shape of the cellular beam obtained by the design algorithm under the load-
ing considered is shown in Figure 12. The design history of this run is shown in
Figure 13.
7 Conclusions
In this chapter it is shown that the optimum design problems of steel skeleton struc-
tures when formulated according to steel design codes of practice turn out to be com-
binatorial optimization problems where design variables are required to be selected
from a discrete set. This feature of the programming problems is not affected by the
code of practice adopted in the design. In the formulation of the optimum design of
moment resisting steel frames, the optimum geometry design of geodesic domes and
optimum design of cellular beams, British Code of Practice is considered while in the
mathematical modeling of the optimum design problem of grillage systems the
American steel design code is adopted. The solution of all these combinatorial struc-
tural design problems is obtained using the harmony search algorithm. In each of the
design problems considered harmony search method attained the optimum designs
without any adversity. The algorithm does not require gradient computations of the
objective function and the constraints and its computer implementation is quite easy.
It is observed that harmony search method is an effective and robust technique in
finding the solution of combinatorial structural optimization problems. It can be stated
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