Lifting Symmetry Breaking Constraints with Inductive Logic Programming
This addresses the issue of time-consuming recomputation of SBCs for large-scale instances or advanced encodings in combinatorial problem-solving, particularly for Answer Set Programming, though it is incremental as it builds on existing SBC methods.
The paper tackles the problem of efficiently omitting symmetric solution candidates in combinatorial problem-solving by introducing a model-oriented approach that lifts instance-specific Symmetry Breaking Constraints (SBCs) into interpretable first-order constraints using Inductive Logic Programming, significantly outperforming a state-of-the-art instance-specific method and direct solver application.
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.