I don't want to give the impression that OO has solved all problems if we are just willing to soften our goals. First of all, getting within 1% of the top design in order DOES NOT mean we are within 1% of the performance value. OO does not promise anything with respect to the performance value. A needle in a haystack problem will be inherently hard. And OO cannot help there.
Secondly, the (Thurston) additive noise model we use may not be appropriate. In particular, we may have noise/error that are design dependent, i.e.,
This is a problem of control strategy design for a well known optimal control
problem involving linear dynamic systems and quadratic performance criterion.
While the optimal solution to this problem is well known, we shall pretend no
knowledge of this and see how an iterative search procedure using ordinal
optimization might work in this case. The following self explanatory
transparency defines this problem which has an optimal control solution of
J*= 40.45 and u(t) = 0.618x(t) --- a linear
feedback strategy! If we quantize the scalar output variable
x(t) into n values and control variable
u(t) to m values, then the strategy search space,
Q, is nm --- a very large number for n = 100,
m > 5. We shall denote the search space defined by different
m values as Qm. We can randomly sample a
strategy in Qm by randomly picking one of the
m control values for every one of the 100 output values of x.
We randomly sample 5,000 such strategies in Qm and
then approximately evaluate the J values for each strategy sampled.
The approximation comes from not evaluating the J value in steady state
t -> Inf. but only for t = 100.