Biomedical Engineering Reference
In-Depth Information
time.
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There is no universal answer to these questions. They have to
be answered in the context of the problem being solved. When
dealing with an optimization scheme for radiotherapy, one hopes that
these decisions can be made once and for all and be embedded in the
algorithm so that they do not need to be revisited, but this may not
always be the case.
Search Parameters
Even if, for our problem, scale issues do not need to be continually
readdressed, there are parameters of the search process which may
well need to be adjusted to make it work well for a particular case.
For example, in the simulated annealing algorithm the behavior of the
search is quite strongly affected by the initial size of the cooling and
throw parameters and by the schedule for their modification as the
search proceeds. These may need to be adjusted if the search does not
appear to be converging to a solution.
When is an iterative search over? I have made several references to
ending a search when the score is no longer significantly improving.
But, what does the term significant mean in this context? Is a change
of, say, 0.1 in the score large or small? Of course, one cannot answer
this question without an understanding of what the score represents;
there will be quite different answers for different score functions, or
for the same score function with different importance weighting
factors. This question requires the user's expert understanding of the
nature of the score function, largely gained from making numerous
similar searches in the past.
When many different starting points are tried, or different score
functions are used, it is a common experience that the solutions are
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The importance of understanding the scale of step sizes used in a search can
be seen by analogy with the following scenario. Imagine that Figure 9.6
represents a countryside landscape, and that the distance between the starting
point, S, and the location of the low-point, M, is some hundreds of meters. If a
hiker starts walking down-hill from S, taking normal meter-long strides, he or
she will have an excellent chance of locating M. Imagine, on the other hand, an
ant starting out from the same point, but taking millimeter-sized steps. The ant
is very likely soon to find him or herself in a very small indentation in the earth
and, since he or she measures slopes over very small dimensions, may conclude
that the minimum has been found. Yes, it's a minimum, but not the global one.
And even if we assume the surface is without small indentations, the hapless ant
will take an extraordinarily long time to get to the bottom.
