<BODY bgcolor="#aaeebb"> <H3><CENTER>Ordered Performance Curve (OPC)</CENTER></H3> <P><CENTER><IMG SRC="Lect2_2.gif" WIDTH="578" HEIGHT= "264" ALIGN="BOTTOM" NATURALSIZEFLAG="3"></CENTER> <UL> <LI><B>Actual performances ordered by value (minimum is best)<BR> <BR> </B> <LI><B>Observed performance order may be different due to error </B> </UL> <BR> <tt> <A HREF="Slide05.html" target="_parent">To Next Slide</A> / <A HREF="Slide03.html" target="_parent">To Previous Slide</A> / <A HREF="../OOTOC.html" target="_parent">Table of Content</A> </tt> <BR> <hr> <hr> <P> 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-<i>g</i> and the observed top-<i>g</i> may not be perfect. In fact it is precisely the probability of this overlap, called <b>alignment probability</b>, 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.<BR> </BODY> </HTML>