Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

Multiple Model
The multiple model RPT optimization is run on the SCI sample problem using both
SA, SQP and MC SQP algorithms. The optimization performance metrics and re-
sulting designs are listed in Table 3.4. The optimal costs listed in the table are much
Table 3.4: Algorithm performance: multiple model, βi =1/npv.
J ∗ iter fevals time x ∗ [m] x ∗ [kg]
Alg. [µm] # # [min] d1 d2 m1 m2
SA 273.51 64 2059 12.79 0.0440 0.0515 0.8464 19.5131
SQP 271.78 20 48 3.83 0.0432 0.0529 0.0 22.613
MC SQP 271.78 238 545 41.06 0.0432 0.0529 0.0 22.613
lower than those of the AO designs (Table 3.3), since the multiple model objective
is the weighted sum of the performance values at each of the uncertainty vertices,
and not the worst-case performance. In the results presented here the weighting βi
is the same at each vertex and equals 1/npv, so that the cost is the average of the
performance values at the uncertainty vertices.
The SQP and SA designs are nearly equivalent as the SA cost is only 0.6% higher
than SQP. The individual runs in the MC SQP algorithm result in a few different
optimal solutions with slight variations in the diameter of the inner array segments
and the design mass values. All designs, however, are at the maximum mass con-
straint, and the best design is found with either MC SQP or the combination of SA
and SQP. As seen previously with AO, using SA in conjunction with SQP finds the
global optimum much more quickly (16.62 minutes) than performing ten randomly
started MC SQP searches (41.06 minutes). The optimal cross-sectional diameters are
similar to those in the anti-optimization designs, in that the diameters of the inner
truss segments are larger than those of the outer segments. However, the MM design
has 22 kg of design mass on the positive-x arm of the interferometer while the AO
design has no lumped mass at all.
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