Enhancing Local Search for MaxSAT with Deep Differentiation Clause Weighting

TL;DR

The paper tackles Partial and Weighted Partial MaxSAT (PMS/WPMS) by introducing DeepDist, a stochastic local search solver that differentiates clause weighting for PMS and WPMS through a Deep-Weighting scheme with tailored initialization and a decimation method (UnH-Decimation). This combination enables more effective exploration of the search space and faster attainment of feasible solutions, followed by improved optimization of soft clauses. Empirical results on MaxSAT Evaluations benchmarks show DeepDist consistently outperforms state-of-the-art SLS solvers and enhances hybrid solvers, with particularly strong performance in WPMS scenarios. The work highlights the importance of problem-structure-aware weighting and initialization, and points to future work on balancing hard/soft increments for further gains.

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

Figures (2)

• Figure 1: Comparison of DeepDist and baseline SLS solvers within 60s based on the "#score" metric
• Figure 2: Comparison of DeepDist and baseline SLS solvers within 300s based on the "#score" metric