Partial MaxSAT (PMS) and Weighted PMS (WPMS) are two practical generalizations of the MaxSAT problem. In this paper, we introduce a new local search algorithm for these problems, named BandHS. It applies two multi-armed bandit (MAB) models to guide the search directions when escaping local optima. One MAB model is combined with all the soft clauses to help the algorithm select to satisfy appropriate soft clauses, while the other MAB model is combined with all the literals in hard clauses to help the algorithm select suitable literals to satisfy the hard clauses. These two models enhance the algorithm's search ability in both feasible and infeasible solution spaces. BandHS also incorporates a novel initialization method that prioritizes both unit and binary clauses when generating the initial solutions. Moreover, we apply our MAB approach to the state-of-the-art local search algorithm NuWLS and to the local search component of the incomplete solver NuWLS-c-2023. The extensive experiments conducted demonstrate the excellent performance and generalization capability of the proposed method. Additionally, we provide analyses on the type of problems where our MAB method works well or not, aiming to offer insights and suggestions for its application. Encouragingly, our MAB method has been successfully applied in core local search components in the winner of the WPMS complete track of MaxSAT Evaluation 2023, as well as the runners-up of the incomplete track of MaxSAT Evaluations 2022 and 2023.

中文翻译：

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将多手柄老虎机与 MaxSAT 的本地搜索集成


部分 MaxSAT （PMS） 和加权 PMS （WPMS） 是 MaxSAT 问题的两个实际推广。在本文中，我们介绍了一种新的本地搜索算法，用于这些问题，称为 BandHS。它应用两个多臂老虎机 （MAB） 模型来指导在逃离局部最优值时的搜索方向。一个 MAB 模型与所有软子句组合在一起，以帮助算法选择满足适当的软子句，而另一个 MAB 模型与硬子句中的所有文本组合在一起，以帮助算法选择合适的文本来满足硬子句。这两个模型增强了算法在可行和不可行解空间中的搜索能力。BandHS 还采用了一种新颖的初始化方法，在生成初始解时优先考虑 unit 子句和 binary 子句。此外，我们将 MAB 方法应用于最先进的本地搜索算法 NuWLS 和不完整求解器 NuWLS-c-2023 的本地搜索组件。进行的广泛实验证明了所提方法的优异性能和泛化能力。此外，我们还对 MAB 方法运行良好或无效的问题类型进行分析，旨在为其应用提供见解和建议。令人鼓舞的是，我们的 MAB 方法已成功应用于 2023 年 MaxSAT 评估 WPMS 完整轨道的获胜者，以及 2022 年和 2023 年 MaxSAT 评估不完整轨道的亚军的核心本地搜索组件。