Johnson et al. [#51##1#] noted in their SA implementation for the TSP
that the number of steps at each temperature (or the size of the Markov
chain) needed to be at least proportional to the ``neighborhood'' size
if they were to obtain worthwhile tour quality. From our experiments
we found that the above hypothesis raised in [#51##1#] to also hold
eventhough the nature of our problem is different than
TSP. Furthermore, in few tests for one semester we fixed number of
classes and professors but varied number of rooms and time slots and
found that the final result improved as the size of Markov chain becomes
more proportional to a combination of number of classes, number of
rooms and number of time slots. In other words, as the ratio
of Markov chain to the combined number of classes, rooms, and
timeslots approaches 1.0 a more improved final result is obtained. We
also observed the same behavior when we fixed the number of rooms and
time slots but varied number of classes. In regard to the relation
between the initial temperature and number of iterations per
temperature, in few runs not involving the preprocessing phase, we
observed that as the number of iterations per temperature decreases it
is more preferable to start with a lower initial temperature, and this
is more so when using the geometric cooling schedule than adaptive
annealing.
Also, we observed that the efficacy of starting annealing (using either
adaptive or non-adaptive schedules) from a good solution depends not
only on the energy (or cost) of that solution, but also on how it was
obtained, that is, on its structure and the configuration of the
search space. This observation deserves a bit more analysis which be
the subject of another paper.