Time-Series Constraints: Improvements and Application in CP and MIP Contexts
A checker for a constraint on a variable sequence can often be compactly specified by an automaton, possibly with accumulators, that consumes the sequence of values taken by the variables; such an automaton can also be used to decompose its specified constraint into a conjunction of logical constraints. The inference achieved by this decomposition in a CP solver can be boosted by automatically generated implied constraints on the accumulators, provided the latter are updated in the automaton transitions by linear expressions. Automata with non-linear accumulator updates can be automatically synthesised for a large family of time-series constraints. In this paper, we describe and evaluate extensions to those techniques. First, we improve the automaton synthesis to generate automata with fewer accumulators. Second, we decompose a constraint specified by an automaton with accumulators into a conjunction of linear inequalities, for use by a MIP solver. Third, we generalise the implied constraint generation to cover the entire family of time-series constraints. The newly synthesised automata for time-series constraints outperform the old ones, for both the CP and MIP decompositions, and the generated implied constraints boost the inference, again for both the CP and MIP decompositions. We evaluate CP and MIP solvers on a prototypical application modelled using time-series constraints.
We thank Michel Minoux for his feedback on the integer linear programming decomposition in Sect. 4. We thank Mats Carlsson for his useful input during the early discussions of this paper. We also thank the anonymous referees for their helpful comments. The first and second authors are partially supported by the Gaspard-Monge programme. The authors at Mines Nantes are supported by project GRACeFUL, which has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement № 640954. The authors at Uppsala University are supported by grants 2011-6133 and 2012-4908 of the Swedish Research Council (VR). The last author was supported by Science Foundation Ireland under Grant Number SFI/10/IN.1/I3032. The INSIGHT Centre for Data Analytics is supported by Science Foundation Ireland under Grant Number SFI/12/RC/2289.
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