Maintaining and Scanning the Pool

The cut manager's primary job is to receive a solution from an NP module and return cuts from the pool that are violated by it. The cuts are stored along with two pieces of information--the level of the tree on which the cut was generated, known simply as the level of the cut, and the number of times it has been checked for violation since the last time it was actually found to be violated, known as the number of touches. The number of touches can be used as a simplistic measure of its effectiveness. Since the pool can get quite large, the user can choose to scan only cuts whose number of touches is below a specified threshold and/or cuts that were generated on a level at or above the current one in the tree. The idea behind this second criterion is to try to avoid checking cuts that were not generated ``nearby'' in the tree, as they are less likely to be effective. Any cut generated at a level in the tree below the level of the current node must have been generated in a different part of the tree. Although this is admittedly a naive method, it does seem to work reasonably well.

On the other hand, the user may define a specific measure of quality for each cut to be used instead. For example, the degree of violation is an obvious candidate. This measure of quality must be computed by the user, since the cut pool module has no knowledge of the cut data structures. The quality is recomputed every time the user checks the cut for violation and a running average is used as the global quality measure. The cuts in the pool are periodically sorted by this measure and only the highest quality cuts are checked each time. All duplicate cuts, as well as all cuts whose number of touches exceeds or whose quality falls below specified thresholds, are periodically purged from the pool to keep it as small as possible.

Ted Ralphs