Anytime Cooperative Implicit Hitting Set Solving

TL;DR

This paper introduces a combined anytime cooperative implicit hitting set algorithm that integrates lower and upper bound approaches, demonstrating improved performance and anytime behavior in solving Weighted CSPs.

Contribution

It presents a novel multithreaded framework combining HS-lb and HS-ub, leading to a superior hybrid algorithm with effective anytime performance.

Findings

HS-lub outperforms HS-lb and HS-ub individually.

The combined approach reduces the optimality gap during execution.

The method sometimes surpasses state-of-the-art Toulbar2 in benchmarks.

Abstract

The Implicit Hitting Set (HS) approach has shown to be very effective for MaxSAT, Pseudo-boolean optimization and other boolean frameworks. Very recently, it has also shown its potential in the very similar Weighted CSP framework by means of the so-called cost-function merging. The original formulation of the HS approach focuses on obtaining increasingly better lower bounds (HS-lb). However, and as shown for Pseudo-Boolean Optimization, this approach can also be adapted to compute increasingly better upper bounds (HS-ub). In this paper we consider both HS approaches and show how they can be easily combined in a multithread architecture where cores discovered by either component are available by the other which, interestingly, generates synergy between them. We show that the resulting algorithm (HS-lub) is consistently superior to either HS-lb and HS-ub in isolation. Most importantly, HS-lub has an effective anytime behaviour with which the optimality gap is reduced during the execution. We tested our approach on the Weighted CSP framework and show on three different benchmarks that our very simple implementation sometimes outperforms the parallel hybrid best-first search implementation of the far more developed state-of-the-art Toulbar2.