A Local Search Approach to Modelling and Solving Interval Algebra Problems

Local search techniques have attracted considerable interest in the artificial intelligence community since the development of GSAT and the minconflicts heuristic for solving propositional satisfiability (SAT) problems and binary constraint satisfaction problems (CSPs) respectively. Newer techniques, such as the discrete Langrangian method (DLM), have significantly ∗The authors gratefully acknowledge the financial support of the Australian Research Council, grant A00000118, in the conduct of this research improved on GSAT and can also be applied to general constraint satisfaction and optimisation. However, local search has yet to be successfully employed in solving temporal constraint satisfaction problems (TCSPs). In this paper we argue that current formalisms for representing TCSPs are inappropriate for a local search approach, and we propose an alternative CSPbased end-point ordering model for temporal reasoning. In particular we look at modelling and solving problems formulated using Allen’s interval algebra (IA) and propose a new constraint weighting algorithm derived from DLM. Using a set of randomly generated IA problems, we show that our local search outperforms existing consistency-enforcing algorithms on those problems that the existing techniques find most difficult.