Experimental Analysis of Numeric and Symbolic Constraint Satisfaction Techniques for Temporal Reasoning
Résumé
Many temporal applications like planning and scheduling can be viewed as special cases of numeric and symbolic temporal constraint satisfaction problem. We have developed a temporal model, TemPro, based on the interval algebra, to express such applications in terms of qualitative and quantitative temporal constraints. TemPro extends the interval algebra relations of Allen to handle numeric information. To solve a constraint satisfaction problem, different approaches have been developed. These approaches generally use constraint propagation to simplify the original problem, and backtracking to directly search for possible solutions. Constraint propagation can also be used during backtracking to improve the performance of the search. The objective of this paper is to assess different policies for checking if a TemPro network is consistent. The main question we want to answer is how much constraint propagation is useful for finding a single solution for a TemPro constraint graph. For this purpose, we have randomly generated large consistent networks for which arc and/or path consistency algorithms (AC-3, AC-7 and PC-2) were applied. The main result of this study is an optimal policy combining these algorithms either at the symbolic (Allen relation propagation) or at the numerical level.