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Hard Constraints

The most common and important hard constraint is what is sometimes referred to as an edge constraint between two events, which simply states that a given pair of events ( tex2html_wrap_inline2143 ) must not overlap in time. The name is due to the similarity of any simple timetabling problem with vertex coloring in graph theory [9, 10].

Events that must not overlap in time include:

Other examples are space or room constraints:

A cost is associated with any violation of these constraints. The room constraint is implemented using a non-linear function for the cost tex2html_wrap_inline2149 associated with the room size:

  equation1497

In our experiments, the parameters tex2html_wrap_inline2151 and tex2html_wrap_inline2153 were set to 0.5 and 0.8, respectively.

There is also a cost assigned to any violation to the constraint that if it is all possible certain classes not be scheduled at the same time or have any overlap in their scheduled times. For example, many of the mathematics and physics departments classes are taken by roughly the same pool of students majoring in those two fields or other closely related fields. Therefore, scheduling those classes in overalapping timeslots ought be avoided if all possible. From this constraint we obtain what we refer to as the exclusion cost tex2html_wrap_inline2159 as follows:

tex2html_wrap_inline2161 such that tex2html_wrap_inline2163 , let tex2html_wrap_inline2165 denote class(i), tex2html_wrap_inline2167 the starting time of tex2html_wrap_inline2165 , tex2html_wrap_inline2171 the end time of tex2html_wrap_inline2165 , tex2html_wrap_inline2175 the duration of tex2html_wrap_inline2165 , tex2html_wrap_inline2179 is some chosen constant, and tex2html_wrap_inline2181 is the relative length between tex2html_wrap_inline2165 and tex2html_wrap_inline2185 as defined below.

  equation1508

  equation1530

MEDIUM


next up previous
Next: Medium Constraints Up: Constraints of the Timetabling Previous: Constraints of the Timetabling

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