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Translation-based approaches for solving disjunctive temporal problems with preferences

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Abstract

Disjunctive Temporal Problems (DTPs) with Preferences (DTPPs) extend DTPs with piece-wise constant preference functions associated to each constraint of the form l ≤ x − y ≤ u, where x,y are (real or integer) variables, and l,u are numeric constants. The goal is to find an assignment to the variables of the problem that maximizes the sum of the preference values of satisfied DTP constraints, where such values are obtained by aggregating the preference functions of the satisfied constraints in it under a “max” semantic. The state-of-the-art approach in the field, implemented in the native DTPP solver Maxilitis, extends the approach of the native DTP solver Epilitis. In this paper we present alternative approaches that translate DTPPs to Maximum Satisfiability of a set of Boolean combination of constraints of the form l⋈x − y⋈u, ⋈ ∈{<,≤}, that extend previous work dealing with constant preference functions only. We prove correctness and completeness of the approaches. Results obtained with the Satisfiability Modulo Theories (SMT) solvers Yices and MathSAT on randomly generated DTPPs and DTPPs built from real-world benchmarks, show that one of our translation is competitive to, and can be faster than, Maxilitis (This is an extended and revised version of Bourguet et al. 2013).

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Notes

  1. Note that in the case of the second reduction this corresponds to a model, while for the first reduction, where the constraints are mutually exclusive, this is according to the semantic of a Max-SAT solution.

  2. These benchmarks have been generated using the program provided by Michael D. Moffitt, author of Maxilitis.

  3. We have tested our solvers on the biggest formulas we could solve but employing real-valued variables, and results are very similar to those when variables are integers.

  4. We consider number of conflicts yices outputs by running it in verbose mode; MathSAT does not look to output such number.

References

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Acknowledgments

The authors would like to thank the reviewers for useful comments and criticisms. They would like to thank also Michael D. Moffitt for providing his solvers and the program for generating random benchmarks, and Bruno Dutertre for his support about Yices.

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Authors and Affiliations

  1. DIBRIS - University of Genova, Viale F. Causa 15, Genova, Italy

    Enrico Giunchiglia & Marco Maratea

  2. POLCOMING - University of Sassari, Viale Mancini 5, 07100, Sassari, Italy

    Luca Pulina

Authors
  1. Enrico Giunchiglia
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  2. Marco Maratea
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  3. Luca Pulina
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Correspondence to Marco Maratea.

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Appendix

Appendix

Table 3 Performance of the selected solvers on random DTPPs with k = 2 with different sizes
Full size table
Table 4 Performance of the selected solvers on random DTPPs having k = 2, with different levels
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Table 5 Performance of the selected solvers on random DTPPs with k = 3 with different sizes. The table is organized as Table 3
Full size table
Table 6 Performance of the selected solvers on random DTPPs with k = 3 with different levels. The table is organized as Table 4
Full size table

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Giunchiglia, E., Maratea, M. & Pulina, L. Translation-based approaches for solving disjunctive temporal problems with preferences. Constraints 23, 383–402 (2018). https://doi.org/10.1007/s10601-018-9293-6

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