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 ( ) 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 associated with the room size:
In our experiments, the parameters and
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 as follows:
such that
, let
denote class(i),
the starting time of
,
the end time of
,
the duration
of
,
is some chosen constant, and
is
the relative length between
and
as defined below.
MEDIUM