Solving Over-Constrained Temporal Reasoning Problems Using Local Search

Temporal reasoning is an important task in many areas of computer science including planning, scheduling, temporal databases and instruction optimisation for compilers. Given a knowledge-base consisting of temporal relations, the main reasoning problem is to determine whether the knowledge-base is satisfiable, i.e., is there a scenario which is consistent with the information provided. However, many real world problems are over-constrained (i.e. unsatisfiable). To date, there has been little research aimed at solving over-constrained temporal reasoning problems. Recently, we developed standard backtracking algorithms to compute partial scenarios, in the spirit of Freuder and Wallace's notion of partial satisfaction. While these algorithms were capable of obtaining optimal partial solutions, they were viable only for small problem sizes. In this paper, we apply local search methods to overcome the deficiencies of the standard approach to solving over-constrained temporal reasoning problems. Inspired by our recent success in efficiently handling reasonably large satisfiable temporal reasoning problems using local search, we have developed two new local search algorithms using a random restart strategy and a TABU search. Further, we extend our previous constraint weighting algorithm to handle over-constrained problems. An empirical study of these new algorithms was performed using randomly generated under- and over-constrained temporal reasoning problems. We conclude that 1) local search significantly outperforms standard backtracking approaches on over-constrained temporal reasoning problems; and 2) the random restart strategy and TABU search have a superior performance to constraint weighting for the over-constrained problems. We also conjecture that the poorer performance of constraint weighting is due to distortions of non-zero global minima caused by the weighting process.