The relevant concept is the Ordered Performance Curve (OPC). Imagine a thought
experiment in which we evaluate the performances of all possible designs in
the search space and order them according to #1 design (best), #2 design
(second best), . . ., etc. By definition this curve represented by these
performance values must be monotonically increasing (assuming we are
minimizing). Of course, we can only imagine such a curve. In practice, we
can only estimate the performances even if we have time to evaluate all of
them. Thus, the observed order may in fact be different from the true order.
The overlap between the actual top-g and the observed top-g may
not be perfect. In fact it is precisely the probability of this overlap,
called alignment probability, that we are interested in. It is clear
that this probability depends not only on the errors of the estimation but
also on the shape of the OPCs. We submit that there are only five general
possible shapes for OPC of all problem types. We illustrate them in the next
transparency.