Observations and Analysis

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.