Enhancing Local Search for MaxSAT with Deep Differentiation Clause Weighting

2025-12-05

AI Summary

Partial MaxSAT (PMS) and Weighted Partial MaxSAT (WPMS) are often conflated in practice, with uniform weighting strategies applied indiscriminately despite their fundamental structural differences—particularly in how hard constraints and soft clauses are treated. Method: This paper proposes a differentiated clause-weighting framework featuring PMS- and WPMS-specific weight initialization and dynamic update conditions, a decimation-based simplification mechanism prioritizing unit and hard clauses, and a deep-differentiated weight propagation strategy. The resulting solver, DeepDist, operates within a stochastic local search (SLS) paradigm. Results: DeepDist significantly outperforms state-of-the-art SLS solvers on the MaxSAT Evaluation benchmarks. When integrated with TT-Open-WBO-Inc, it achieves superior overall performance compared to the 2024 MaxSAT Competition champion solver. To the best of our knowledge, this is the first work to systematically distinguish the structural characteristics of PMS and WPMS and tailor clause-weighting mechanisms accordingly.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Multiagent Systems: Distributed Problem Solving

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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

Problem

• Develops a new clause weighting scheme for PMS and WPMS
• Introduces distinct update strategies for PMS and WPMS instances
• Proposes a decimation method prioritizing unit and hard clauses

Innovation

• Differentiated clause weighting for PMS and WPMS
• New initialization method for distinct instance types
• Decimation prioritizing unit and hard clauses