Efficient Robust Optimization of Structures Subjected to Earthquake Load and Characterized by Uncertain Bounded System Parameters - Structural Seismic Design Optimization and Earthquake Engineering - page 122

Figure 5. The variation of optimal weight of the beam with increasing range of uncertainty

Figure 6. The optimal weight of the frame with varying upcrossing level

robustness. If one desires more robustness, the
design will be further away from its ideal optimal
value. The situation can be studied further in terms
of Pareto-front. The Pareto-front is one where any
improvement in one objective can only achieve
through worsening of at least one other objective.
If one chooses a design that is not Pareto-optimal,
one essentially forfeits improvements that would
otherwise entail no compromise. The Pareto fronts
obtained by the proposed and the conventional

RDO approaches are plotted in Figure 8. The
uncertainty ranges of the DVs and DPs are taken
as per Table 1 and kj is considered to be 1.0 to
develop this figure. The Pareto front is determined
by evaluating the optimal solutions (the objective
function and its associated dispersion) for differ-
ent settings of α . Maximum robust solution is
obtained when α is1.0. The designer puts maxi-
mum emphasis on optimal objective, not on its
robustness, if α is zero. Thus, the designer can