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Solution Enumeration by Optimality in Answer Set Programming

Published online by Cambridge University Press:  10 September 2021

JUKKA PAJUNEN  and
TOMI JANHUNEN Open the ORCID record for TOMI JANHUNEN [Opens in a new window]
JUKKA PAJUNEN
Affiliation:
Department of Computer Science, Aalto University, P.O. Box 15400, FI-00076 Aalto, Finland (e-mail: jukka.m.pajunen@gmail.com)
TOMI JANHUNEN
Affiliation:
Computing Sciences, Tampere University, FI-33014 Tampere, Finland and Department of Computer Science, Aalto University, P.O. Box 15400, FI-00076 Aalto, Finland (e-mails: tomi.janhunen@tuni.fi, tomi.janhunen@aalto.fi)
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Abstract

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Given a combinatorial search problem, it may be highly useful to enumerate its (all) solutions besides just finding one solution, or showing that none exists. The same can be stated about optimal solutions if an objective function is provided. This work goes beyond the bare enumeration of optimal solutions and addresses the computational task of solution enumeration by optimality (SEO). This task is studied in the context of answer set programming (ASP) where (optimal) solutions of a problem are captured with the answer sets of a logic program encoding the problem. Existing answer set solvers already support the enumeration of all (optimal) answer sets. However, in this work, we generalize the enumeration of optimal answer sets beyond strictly optimal ones, giving rise to the idea of answer set enumeration in the order of optimality (ASEO). This approach is applicable up to the best k answer sets or in an unlimited setting, which amounts to a process of sorting answer sets based on the objective function. As the main contribution of this work, we present the first general algorithms for the aforementioned tasks of answer set enumeration. Moreover, we illustrate the potential use cases of ASEO. First, we study how efficiently access to the next-best solutions can be achieved in a number of optimization problems that have been formalized and solved in ASP. Second, we show that ASEO provides us with an effective sampling technique for Bayesian networks.

Keywords

answer set programmingoptimization problemssolution enumerationsamplingBayesian networks
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Special Issue 6: 37th International Conference on Logic Programming Special Issue II , November 2021 , pp. 750 - 767
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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