A Model-Oriented Approach for Lifting Symmetries in Answer Set Programming

TL;DR

This paper introduces a model-oriented method using Inductive Logic Programming to lift symmetry-breaking constraints in Answer Set Programming, enabling transferability and interpretability across problem instances.

Contribution

It proposes a novel approach that lifts SBCs into first-order constraints, addressing limitations of instance-specific methods and enhancing applicability to large-scale problems.

Findings

Successfully applied to simple combinatorial problems

Enables transfer of symmetry constraints across instances

Lays groundwork for extension to complex decision problems

Abstract

When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for each given problem instance. However, the application of such approaches to large-scale instances or advanced problem encodings might be problematic since the computed SBCs are propositional and, therefore, can neither be meaningfully interpreted nor transferred to other instances. As a result, a time-consuming recomputation of SBCs must be done before every invocation of a solver. To overcome these limitations, we introduce a new model-oriented approach for Answer Set Programming that lifts the SBCs of small problem instances into a set of interpretable first-order constraints using a form of machine learning called Inductive Logic Programming. After targeting simple combinatorial problems, we aim to extend our method to be applied also for advanced decision and optimization problems.