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Soft Constraints

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 tex2html_wrap_inline2187 between all the academic departments I and all the buildings involved in scheduling J. Using tex2html_wrap_inline2187 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 tex2html_wrap_inline2205 where tex2html_wrap_inline2207 the distance to all buildings B is a vector denoted by tex2html_wrap_inline2211 where tex2html_wrap_inline2213 and tex2html_wrap_inline2215 . At each step of the scheduling process and according to tex2html_wrap_inline2205 space preferences, tex2html_wrap_inline2205 courses would be scheduled into buildings tex2html_wrap_inline2221 where tex2html_wrap_inline2223 and the distance is denoted by the vector tex2html_wrap_inline2225 where tex2html_wrap_inline2227 . In addition, let tex2html_wrap_inline2229 .

Now the cost associated with the distance of department tex2html_wrap_inline2205 is computed as follows:

  equation1540

Note that throughout the scheduling process, the denominator of equation 4 stays fixed while the numerator may change. SOFT

 


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

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