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Cost Function

The cost function measures the quality of the current schedule and generally involves the weighted sum of penalties associated with different types of constraint violations. Summing these penalties or costs is not strictly necessary, provided that the components (individual costs) can be combined in some fashion to reflect the overall quality of the schedule. The aim of the optimization technique is to minimize the cost function. We consider the following as part of the cost function:

Each of the terms in the cost function are assigned different weights [46], in order to quantify the relative importance of the corresponding constraints. For example, hard constraints should be weighted so that their cost is much greater than the medium constraints, which should similarly be weighted to have higher costs than the soft constraints. The values of each of the terms for the constraint costs need to be taken into account when specifying the weights. For example, soft constraints involving the students require summing the cost over all students, which will usually be much larger than the equivalent sum over all professors, since the number of professors is much smaller than the number of students. However, constraints involving professors are usually given a higher cost than constraints involving students, in which case the weights for the professor costs will need to be much larger than the weights for the student costs.

What we have done is to select individual weights based on the relative importance of the various constraints of a particular type (hard, medium, and soft), and then included an additional overall weighting factor for each type of constraint, with the weighting factor for hard constraints being much larger than for medium constraints, which in turn is much larger than for soft constraints.


next up previous
Next: Methods for Tackling the Up: The Timetabling Problem Previous: Soft Constraints

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