Empirical Evaluation of the Implicit Hitting Set Approach for Weighted CSPs

TL;DR

The paper investigates applying the Implicit Hitting Set (IHS) approach to Weighted CSPs (WCSPs) by evaluating 32 algorithm variants derived from four hitting-vector computation methods, four core-improvement strategies, and an option for cost-function merging. It formalizes WCSP prerequisites, introduces the key notions of hitting vectors, cores, and the termination condition tied to the optimum $w^*$ and the minimum hitting vector $MHV$. The empirical study shows no universal winner across benchmarks, but cost-function merging with maximal-core extraction provides the most robust performance, while performance is highly instance-dependent and IHS often lags behind Toulbar2 except on certain structured, small-domain problems. The results highlight significant sensitivity to problem structure and motivate future work that combines IHS with more powerful solvers or alternative search strategies, such as reduced cost fixing, PB encodings, and local search-based improvements.

Abstract

SAT technology has proven to be surprisingly effective in a large variety of domains. However, for the Weighted CSP problem dedicated algorithms have always been superior. One approach not well-studied so far is the use of SAT in conjunction with the Implicit Hitting Set approach. In this work, we explore some alternatives to the existing algorithm of reference. The alternatives, mostly borrowed from related boolean frameworks, consider trade-offs for the two main components of the IHS approach: the computation of low-cost hitting vectors, and their transformation into high-cost cores. For each one, we propose 4 levels of intensity. Since we also test the usefulness of cost function merging, our experiments consider 32 different implementations. Our empirical study shows that for WCSP it is not easy to identify the best alternative. Nevertheless, the cost-function merging encoding and extracting maximal cores seems to be a robust approach.