Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

defined by the user and indicate the number of designs that must be accepted or
rejected, respectively, at a given temperature. When either A = kA or R = kR the
temperature is reduced according to a user-defined cooling constant, kC:
Tk = Tk−1 (1 − kC) (2.45)
and the A and R counters are reset to zero. The search continues in this manner until
the termination conditions are met. The termination conditions are chosen by the
user based on the specific problem statement. In the PT SCI search the algorithm
terminates when kR designs are rejected at three temperatures in a row.
Equation 2.44 is called the Boltzman probability, and is the critical feature of
the SA algorithm. At high temperatures the probability of accepting a design that
increases the cost is high. By randomly accepting less favorable designs the algorithm
allows itself to climb out of areas of local minimum and more thoroughly search the
space. As the temperature decreases the acceptance probability, pA, becomes lower,
and the search eventually converges in the neighborhood of a favorable design. The
minimum cost and corresponding design variables are identified from the history of
accepted design costs. There is no guarantee that the resulting design is an optimum
in the mathematical sense, in fact it most likely is not. However, if the cooling
schedule is set appropriately for the given problem the resulting design is a good
design and in many cases is better than a locally optimal design resulting from a
gradient search.
2.5 Performance Tailoring Results
The results of the PT optimizations run on the SCI development model are presented
in the following section. Three optimization algorithms, SQP, MC SQP and SA are
compared for performance and efficiency. The SQP algorithm is part of the MATLAB
optimization toolbox, and the SA algorithm is implemented as outlined in Figure 2-4.
At each optimization or search iteration a new SCI state-space model is built
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