Soft constraints are preferences that do not deal with time conflicts, and have a lower penalty (or cost) associated with them. We aim to minimize the cost, but do not expect to be able to reduce it to zero. Some examples are:
Some soft constraints may have higher priority (and thus higher cost) than others. For example, balancing classes over the week will have a higher priority than students preferences.
We have dealt with the distance minimization constraint in the following way.
Given the various building preferences of the departments, we
have constructed a matrix between all the academic
departments I and all the buildings involved in scheduling
J. Using
in conjunction with the (appropriately scaled)
distance between all buildings involved in the process,
a final distance matrix Q is derived and
directly used in the scheduling process. Also, unless otherwise
stated, a department's home building is always the first
preference for the department classes to be assigned.
Let B denote the set of all k buildings,
D denote the set of all n departments. Also for department
where
the distance to all buildings B is a vector
denoted by
where
and
.
At each step of the scheduling process and according to
space preferences,
courses would be scheduled into buildings
where
and the distance is denoted by the
vector
where
. In addition,
let
.
Now the cost associated with the distance of department is
computed as follows:
Note that throughout the scheduling process, the denominator of equation 4 stays fixed while the numerator may change. SOFT