Solving disjunctive temporal problems with preferences using maximum satisfiability

The Disjunctive Temporal Problem (DTP) involves conjunction of DTP constraints, each DTP constraint being a disjunction of difference constraints of the form x−y≤c, where x and y range over a domain of interpretation, and c is a numeric constant. The DTP is recognized to be an expressive framework for constraints modeling and processing. The addition of preferences, in the form of weights associated to difference constraints for their satisfaction, needs methods for aggregating preferences among and within DTP constraints to compute meaningful and high quality solutions, while further enhancing DTP expressivity and applicability. In this paper we consider an utilitarian aggregation of DTP constraints weights, and a prominent semantic for aggregating such weights from its difference constraints weights that considers the maximum among the weights associated to satisfied difference constraints in it. We present a novel approach that reduces the problem to Maximum Satisfiability of DTPs (Max-DTPs). In this way, we can employ off-the-shelf Max-DTP solvers with different solution methods, ranging from Satisfiability Modulo Theories (SMT), to interval-based and Boolean optimization-based solvers. We then compare the performance of our approach with different back-end solvers on both randomly generated and real-world benchmarks, in comparison with MAXILITIS, the best solver that can deal with DTPs with preferences using the aggregation methods considered. Results show that the YICES SMT solver is the best, and that YICES and the TSAT# solver based on Boolean optimization can be orders of magnitude faster than MAXILITIS.

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