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The Timetabling Data Set

Our study case involved real scheduling data covering three semesters at Syracuse University. The size and type of the three-semester data set is shown in Table 1. Nine types of rooms were used: auditoriums, classrooms, computer clusters, conference rooms, seminar rooms, studios, laboratories, theaters, and unspecified types. Staff and teaching assistants are considered part of the set of professors. Third semester (summer) data was much smaller than other semesters, however there were additional space and time constraints and fewer available rooms.

Our data set is quite large in comparison to data used by other researchers. For example, high school data used by Peterson and colleagues [20, 21] consists of approximately 1000 students, 20 different possible majors, and an overall periodic school schedule (over weeks). In the case of Abramson et al. [2], their data set was created randomly and was relatively small, and they stated that problems involving more than 300 tuples were very difficult to solve.

Timetabling problems can be characterized by their sparseness. After all the required lessons have been scheduled, there will be tex2html_wrap_inline2431 spare space-time slots, and the sparseness ratio of the problem is defined as tex2html_wrap_inline2433 . Dense problems have a low sparseness ratio, since they have relatively few spare space-time slots, and are thus harder to solve than sparse problems with many slots to spare. Table 2 shows the sparseness ratio (see section 3) of the data for each of the three semesters. For university scheduling, the sparseness ratio generally decreases as the data size (particularly the number of classes) increases, so the problem becomes more difficult. The first two semesters are of similar difficulty, whereas the third semester has fewer classes, and is sparser and relatively easier to solve.

Including student preferences makes the problem much harder, but these are viewed as medium constraints and thus are not necessarily satisfied in a valid solution.


next up previous
Next: Analysis of the Cooling Up: Experimental Results Previous: Experimental Results

Saleh Elmohamed
Thu Sep 4 11:43:55 EDT 1997