Large Neighborhood Prioritized Search for Combinatorial Optimization with Answer Set Programming

TL;DR

This work tackles combinatorial optimization within Answer Set Programming by proposing Large Neighborhood Prioritized Search (LNPS), a metaheuristic that alternates destruction of parts of a solution with prioritized reconstruction, implemented in ASP as the heulingo solver. LNPS maintains explicit notions of $x^{*}$, $x$, and $x^{t}$ and uses configurable destruction plus a prioritized search to explore large neighborhoods while aiming for optimality through suitable stop criteria. The main contributions are the design and ASP-based implementation of LNPS, the flexible, heuristic-driven heulingo framework, and extensive empirical evaluations showing improved bounds and competitiveness with adaptive LNS on a challenging benchmark suite. The results demonstrate the practical impact of combining domain-informed prioritization with large-neighborhood exploration in ASP, with potential extensions to adaptive LNPS and broader optimization settings.

Abstract

We propose Large Neighborhood Prioritized Search (LNPS) for solving combinatorial optimization problems in Answer Set Programming (ASP). LNPS is a metaheuristic that starts with an initial solution and then iteratively tries to find better solutions by alternately destroying and prioritized searching for a current solution. Due to the variability of neighborhoods, LNPS allows for flexible search without strongly depending on the destroy operators. We present an implementation of LNPS based on ASP. The resulting heulingo solver demonstrates that LNPS can significantly enhance the solving performance of ASP for optimization. Furthermore, we establish the competitiveness of our LNPS approach by empirically contrasting it to (adaptive) large neighborhood search.

Figures (1)

• Figure 1: The architecture of heulingo