Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

Table 5.1: Algorithm performance: RPTT, α =0.0, ∆ = 0.1.
J ∗ iter fevals time x ∗ [m] y ∗ WC [kg]
Alg. Form [µm] # # [min] d1 d2 m1 m2
SA Eq 5.3 216.03 201 8304 5.26 0.0451 0.0388 175.63 0.0774
SQP Eq 5.5 215.94 23 53 1.77 0.0451 0.0388 175.88 0.0
SQP Eq 5.3 215.97 13 1001 1.62 0.0452 0.0388 175.66 0.028
MC SQP Eq 5.5 215.94 414 906 31.47 0.0451 0.0388 175.90 0.0
MC SQP Eq 5.3 215.94 661 5843 51.82 0.0451 0.0388 175.93 0.0
Since the weighting on robustness is set to zero the optimal cost, J ∗ , is the tuned
performance at the worst-case uncertainty vertex. SA provides a starting point that
is very close to the optimal design after 201 temperature iterations and 8304 function
evaluations. The SQP algorithm performs nicely when started at the SA design
and applied to the problem of Equation 5.5. It converges to a design in only 23
iterations and 53 function evaluations. In contrast, the SQP solution obtained from
the formulation in Equation 5.3 is slightly sub-optimal. Note that the algorithm ran
for only 13 iterations, but 1001 function evaluations. The algorithm fails to properly
converge because it becomes stuck in the line search and the maximum number of
function evaluations (1000) is reached. One possible reason for this behavior is that
the objective function gradients required for the SQP algorithm are not well-posed
for this problem. The MC SQP results are equivalent to those obtained by starting
from the SA design indicating that a globally optimal design has been found. MC
SQP does find the optimal design when applied to Equation 5.3 since five out of ten
trials do converge successfully. The time results show that the combination of SA and
SQP finds the optimal design much more quickly (7 minutes) than MC SQP (31.5
minutes).
5.2.2 Comparison to PT and RPT Designs
The optimal tailoring parameters for the RPTT design and its performance in the
nominal, and worst-case (untuned) uncertainty configurations are listed in Table 5.2
along with the corresponding design variables and performances for the PT and RPT
158