Enhancing Local Search for MaxSAT with Deep Differentiation Clause Weighting

TL;DR

This paper introduces DeepDist, a novel SLS solver for (W)PMS that employs a differentiated clause weighting scheme and decimation method, significantly improving performance over existing solvers and surpassing recent MaxSAT Evaluation winners.

Contribution

It presents a new clause weighting scheme tailored for PMS and WPMS, along with an initialization method and decimation strategy, leading to a highly effective SLS solver for (W)PMS.

Findings

DeepDist outperforms state-of-the-art SLS solvers on benchmarks.

Hybrid with TT-Open-WBO-Inc surpasses MaxSAT Evaluation 2024 winners.

Distinct clause weighting improves solution quality for (W)PMS.

Abstract

Partial Maximum Satisfiability (PMS) and Weighted Partial Maximum Satisfiability (WPMS) generalize Maximum Satisfiability (MaxSAT), with broad real-world applications. Recent advances in Stochastic Local Search (SLS) algorithms for solving (W)PMS have mainly focused on designing clause weighting schemes. However, existing methods often fail to adequately distinguish between PMS and WPMS, typically employing uniform update strategies for clause weights and overlooking critical structural differences between the two problem types. In this work, we present a novel clause weighting scheme that, for the first time, updates the clause weights of PMS and WPMS instances according to distinct conditions. This scheme also introduces a new initialization method, which better accommodates the unique characteristics of both instance types. Furthermore, we propose a decimation method that prioritizes satisfying unit and hard clauses, effectively complementing our proposed clause weighting scheme. Building on these methods, we develop a new SLS solver for (W)PMS named DeepDist. Experimental results on benchmarks from the anytime tracks of recent MaxSAT Evaluations show that DeepDist outperforms state-of-the-art SLS solvers. Notably, a hybrid solver combining DeepDist with TT-Open-WBO-Inc surpasses the performance of the MaxSAT Evaluation 2024 winners, SPB-MaxSAT-c-Band and SPB-MaxSAT-c-FPS, highlighting the effectiveness of our approach. The code is available at https://github.com/jmhmaxsat/DeepDist