Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

This formulation differs from that of Sandgren and Cameron in that the standard
deviation of the objective is considered instead of that of the constraints. Also,
the weighting factor α is included to allow a trade between nominal performance
and robustness. When α =1.0 the cost function in Equation 3.11 reduces to the
PT objective (Equation 2.1), and when α = 0 nominal performance is completely
sacrificed in favor of robustness, as in AO.
3.3 RPT Designs
The RPT optimizations are run with each of the cost functions described previously
on the SCI development model with ∆ = 0.10 on both of the uncertainty parame-
ters. The design variables and constraints are equivalent to those in Equation 2.38.
Both the SQP and SA algorithms are used, and the resulting designs and algorithm
performance for each cost function are presented in the following section.
3.3.1 Algorithm comparisons
Anti-optimization
RPT through anti-optimization is applied to the two-stage optimization problem
of Equation 3.4 with SA and then with SQP. For comparison, the alternate form
(Equation 3.5) is run with SQP starting from the SA design as well as a series of
different initial guesses. The optimization performance data and resulting robust
designs are listed in Table 3.3. The “iter” column lists the number of iterations
required for convergence, and the column labelled “feval” gives the total number of
function evaluations. In the SA case, the number of iterations is equivalent to the
number of temperatures necessary to freeze the design, and in MC SQP it represents
the total number of iterations and function evaluations required by all of the individual
SQP runs.
The table shows that the SQP algorithms all find the same optimal design. Rows
two and three of the table list the results of running SQP on the two different for-
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