Efficient lifting of symmetry breaking constraints for complex combinatorial problems
This work addresses the problem of scaling symmetry breaking for complex combinatorial problems in industrial applications, representing an incremental improvement over existing methods.
The paper tackles the challenge of efficiently eliminating symmetric solution candidates in combinatorial problems by extending a model-based approach for Answer Set Programming, incorporating a new conflict analysis algorithm, redefining the learning task, and suggesting a new example generation method, with experiments on Partner Units Problem instances showing computational benefits from learned first-order constraints.
Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based approaches for symmetry breaking are limited to problems for which a set of representative and easily-solvable instances is available, which is often not the case in practical applications. This work extends the learning framework and implementation of a model-based approach for Answer Set Programming to overcome these limitations and address challenging problems, such as the Partner Units Problem. In particular, we incorporate a new conflict analysis algorithm in the Inductive Logic Programming system ILASP, redefine the learning task, and suggest a new example generation method to scale up the approach. The experiments conducted for different kinds of Partner Units Problem instances demonstrate the applicability of our approach and the computational benefits due to the first-order constraints learned.