Solving Over-constrained Disjunctive Temporal Problems with Preferences

We present an algorithm and pruning techniques for efficiently finding optimal solutions to over-constrained instances of the Disjunctive Temporal Problem with Preferences (DTPP). Our goal is to remove the burden from the knowledge engineer who normally must reason about an inherent trade-off: including more events and tighter constraints in a DTP leads to higher-quality solutions, but decreases the chances that a solution will exist. Our method solves a potentially over-constrained DTPP by searching through the space of induced DTPPs, which are DTPPs that include a subset of the events in the original problem. The method incrementally builds an induced DTPP and uses a known DTPP algorithm to find the value of its optimal solution. Optimality is defined using an objective function that combines the value of a set of included events with the value of a DTPP induced by those events. The key element in our approach is the use of powerful pruning techniques that dramatically lower the time required to find an optimal solution. We present empirical results that show their effectiveness.