Empirical Evaluation of the Implicit Hitting Set Approach for Weighted CSPs

TL;DR

This paper empirically evaluates various implementations of the Implicit Hitting Set approach for Weighted CSPs, finding that cost-function merging and maximal core extraction are particularly effective.

Contribution

It explores and compares multiple alternatives for the IHS approach in Weighted CSPs, highlighting robust strategies like cost-function merging.

Findings

Cost-function merging encoding is effective.

Extracting maximal cores is a robust approach.

No single best alternative was identified for WCSP.

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.