Abstract
On the one hand, constraint satisfaction problems allow one to expressively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to expressively model set constraint problems and to encode them automatically into SAT instances. We apply our technique to the social golfer problem and we also use it to break symmetries of the problem. Our technique is simpler, more expressive, and less error-prone than direct modeling. The SAT instances that we automatically generate contain less clauses than improved direct instances such as in Triska and Musliu (Ann Oper Res 194(1):427–438, 2012), and with unit propagation they also contain less variables. Moreover, they are well-suited for SAT solvers and they are solved faster as shown when solving difficult instances of the social golfer problem.
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Notes
Indeed, we did it with MiniZinc (http://www.minizinc.org/) but did not obtain good results in terms of running time and instances that could be solved.
This technique which consists in increasing the number of symmetries in order to obtain more solutions, sometimes gives even better results, especially with incomplete solvers such as local search.
We have tested the incomplete solver Sparrow Balint and Fröhlich (2010) and no solution was found with a time out of one hour.
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Lardeux, F., Monfroy, E., Crawford, B. et al. Set constraint model and automated encoding into SAT: application to the social golfer problem. Ann Oper Res 235, 423–452 (2015). https://doi.org/10.1007/s10479-015-1914-5
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DOI: https://doi.org/10.1007/s10479-015-1914-5