Optimality-preserving Logic-Based Benders Decomposition of Answer Set Programs
TL;DR
A theoretical analysis of the conditions under which LBBD, including cuts, can preserve optimality in the context of Answer Set Programming (ASP), a prominent logic-based language in the field of Artificial Intelligence and introduces a general-purpose algorithm that preserves the optimality guarantees of Bender Decomposition.
Abstract
Bender Decomposition is a well-known solving technique in Operation Research that decomposes a problem into a master and a subproblem, which interact via “cuts". This technique has been extended to Logic-Based Bender Decomposition (LBBD), solving problems specified by logic-based languages and enabling a wider applicability. However, while Bender Decomposition guarantees optimality, LBBD does not: this property is problem-specific and depends on the defined decomposition and cuts. In this paper, we present a theoretical analysis of the conditions under which LBBD, including cuts, can preserve optimality in the context of Answer Set Programming (ASP), a prominent logic-based language in the field of Artificial Intelligence. We also introduce a general-purpose algorithm that employs both minimal unsatisfiable subsets and minimal correction subsets to define cuts in a fully automated, problem-independent way. The algorithm preserves the optimality guarantees of Bender Decomposition. An empirical evaluation on real-world scheduling instances shows that our approach can find significantly more solutions, and more optimal ones, compared to a standard direct ASP encoding, while also consistently reducing the execution time.