Experimental Analysis of Numeric and Symbolic Constraint Satisfaction Techniques for Temporal Reasoning

Many temporal applications like planning and scheduling can be viewed as special cases of the numeric and symbolic temporal constraint satisfaction problem. Thus we have developed a temporal model, TemPro, based on the interval Algebra, to express such applications in term 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. The constraint propagation can also be used during the backtracking to improve the performance of the search. The objective of this paper is to assess different policies for finding if a TemPro network is consistent. The main question we want to answer here is how much constraint propagation is useful for finding a single solution for a TemPro constraint graph. For this purpose, we have experimented by randomly generating large consistent networks for which either 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.