We have implemented a hierarchical handling of the value selection criteria.
There are three levels of comparison. At each level a weighted sum of the
criteria described below is computed. Only solutions with the smallest sum
are considered in the next level. The weights express how quickly a complete
solution should be found. Only hard constraints are satisfied in the first
level sum. Distance from the initial solution (MPP), and a weighting of major
preferences (including time, classroom requirements and student conflicts),
are considered in the next level. In the third level, other minor criteria
are considered. In general, a criterion can be used in more than one level,
e.g., with different weights.
The above sums order the values lexicographically: the best value having the
smallest first level sum, the smallest second level sum among values with the
smallest first level sum, and the smallest third level sum among these
values. As mentioned above, this allows diversification between the
importance of individual criteria.
Furthermore, the value selection heuristics also support some limits (e.g.,
that all values with a first level sum smaller than a given percentage Pth
above the best value [typically 10%] will go to the second level comparison
and so on). This allows for the continued feasibility of a value near to the
best that may yet be much better in the next level of comparison. If there is
more than one solution after these three levels of comparison, one is
selected randomly. This approach helped us to significantly improve the
quality of the resultant solutions.
In general, there can be more than three levels of these weighted sums,
however three of them seem to be sufficient for spreading weights of various
criteria for our problem.
This library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation; either version 3 of the
License, or (at your option) any later version.
This library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.