Lifting Symmetry Breaking Constraints with Inductive Logic Programming

TL;DR

This paper presents a novel approach using Inductive Logic Programming to lift symmetry breaking constraints from small instances into interpretable first-order constraints, enabling transferability and improving efficiency in solving large-scale combinatorial problems.

Contribution

It introduces a model-oriented method for ASP that generalizes SBCs via ILP, outperforming existing instance-specific and direct solver approaches.

Findings

Framework learns general constraints from small instances.

Significantly outperforms state-of-the-art instance-specific methods.

Enables transfer of symmetry constraints to larger problem instances.

Abstract

Efficient omission of symmetric solution candidates is essential for combinatorial problem-solving. 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 the Inductive Logic Programming paradigm. Experiments demonstrate the ability of our framework to learn general constraints from instance-specific SBCs for a collection of combinatorial problems. The obtained results indicate that our approach significantly outperforms a state-of-the-art instance-specific method as well as the direct application of a solver.