Risk Minimization of Disjunctive Temporal Problem with Uncertainty

The Disjunctive Temporal Problem with Uncertainty (DTPU) is a fundamental problem that expresses temporal reasoning with both disjunctive constraints and contingency. A recent work (Peintner et al, 2007) develops a complete algorithm for determining Strong Controllability of a DTPU. Such a notion that guarantees 100% confidence of execution may be too conservative in practice. In this paper, following the idea of (Tsamardinos 2002), we are interested to find a schedule that minimizes the risk (i.e. probability of failure) of executing a DTPU. We present a problem decomposition scheme that enables us to compute the probability of failure efficiently, followed by a hill-climbing local search to search among feasible solutions. We show experimentally that our approach effectively produces solutions which are near-optimal.