, Volume 23, Issue 4, pp 383–402 | Cite as

Translation-based approaches for solving disjunctive temporal problems with preferences

  • Enrico Giunchiglia
  • Marco MarateaEmail author
  • Luca Pulina


Disjunctive Temporal Problems (DTPs) with Preferences (DTPPs) extend DTPs with piece-wise constant preference functions associated to each constraint of the form lxyu, 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 lxyu, ⋈ ∈{<,≤}, 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).


Disjunctive temporal problems Preferences 



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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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.DIBRIS - University of GenovaGenovaItaly
  2. 2.POLCOMING - University of SassariSassariItaly

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