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Time-Series Constraints: Improvements and Application in CP and MIP Contexts

  • Ekaterina Arafailova
  • Nicolas Beldiceanu
  • Rémi Douence
  • Pierre Flener
  • María Andreína Francisco RodríguezEmail author
  • Justin Pearson
  • Helmut Simonis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9676)

Abstract

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.

Notes

Acknowledgements

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.

References

  1. 1.
    Arafailova, E.: Reformulation of automata for time series constraints as linear programs. Master’s thesis, Université de Nantes, France (2015)Google Scholar
  2. 2.
    Beldiceanu, N., Carlsson, M., Debruyne, R., Petit, T.: Reformulation of global constraints based on constraints checkers. Constraints 10(4), 339–362 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Beldiceanu, N., Carlsson, M., Douence, R., Simonis, H.: Using finite transducers for describing and synthesising structural time-series constraints. Constraints 21(1), 22–40 (2016). http://dx.doi.org/10.1007/s10601-015-9200-3 MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Beldiceanu, N., Carlsson, M., Petit, T.: Deriving filtering algorithms from constraint checkers. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 107–122. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Beldiceanu, N., Flener, P., Pearson, J., Van Hentenryck, P.: Propagating regular counting constraints. In: AAAI 2014, pp. 2616–2622. AAAI Press (2014)Google Scholar
  6. 6.
    Berstel, J.: Transductions and Context-Free Languages. Teubner, Berlin (1979)CrossRefzbMATHGoogle Scholar
  7. 7.
    Carlsson, M., Ottosson, G., Carlson, B.: An open-ended finite domain constraint solver. In: Hartel, P.H., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, pp. 191–206. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  8. 8.
    Côté, M.-C., Gendron, B., Rousseau, L.-M.: Modeling the regular constraint with integer programming. In: Van Hentenryck, P., Wolsey, L.A. (eds.) CPAIOR 2007. LNCS, vol. 4510, pp. 29–43. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Demassey, S., Pesant, G., Rousseau, L.M.: A Cost-Regular based hybrid column generation approach. Constraints 11(4), 315–333 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    FICO: MIP formulations and linearizations. Fair Isaac Corporation, June 2009. http://www.fico.com/en/node/8140?file=5125
  11. 11.
    Francisco Rodríguez, M.A., Flener, P., Pearson, J.: Implied constraints for automaton constraints. In: GCAI 2015. EasyChair Epic Series in Computing (forthcoming), preprint at http://www.it.uu.se/research/group/astra/publications
  12. 12.
    Gurobi Optimization, Inc.: Gurobi optimizer reference manual (2015). http://www.gurobi.com
  13. 13.
    Minoux, M.: Personal communication, July 2015Google Scholar
  14. 14.
    Pesant, G.: A regular language membership constraint for finite sequences of variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Sakarovitch, J.: Elements of Language Theory. Cambridge University Press (2009)Google Scholar
  16. 16.
    Sankaranarayanan, S., Sipma, H.B., Manna, Z.: Constraint-based linear-relations analysis. In: Giacobazzi, R. (ed.) SAS 2004. LNCS, vol. 3148, pp. 53–68. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Williams, H.P.: Model Building in Mathematical Programming. Wiley, New York (2015)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ekaterina Arafailova
    • 1
  • Nicolas Beldiceanu
    • 1
  • Rémi Douence
    • 1
  • Pierre Flener
    • 2
  • María Andreína Francisco Rodríguez
    • 2
    Email author
  • Justin Pearson
    • 2
  • Helmut Simonis
    • 3
  1. 1.TASC/ASCOLA (CNRS/INRIA), Mines NantesNantesFrance
  2. 2.Department of Information TechnologyUppsala UniversityUppsalaSweden
  3. 3.Insight Centre for Data AnalyticsUniversity College CorkCorkIreland

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