Applying local search to temporal reasoning

Local search techniques have attracted considerable interest in the artificial intelligence (AI) community since the development of GSAT (Selman et al., 1992) and the min-conflicts heuristic (Minton et al., 1992) for solving large propositional satisfiability (SAT) problems and binary constraint satisfaction problems (CSPs) respectively. Newer SAT techniques, such as the Discrete Langrangian Method (DLM) (Shang and Wah, 1998), have significantly 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). We argue that current formalisms for representing TCSPs are inappropriate for a local search approach, and we propose an alternative CSP-based end-point ordering model for temporal reasoning. In particular we look at modelling and solving problems formulated using Allen's (1983) 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 Nebel's (1997) backtracking algorithm on larger and more difficult consistent problems.