Local search is an effective method for solving large-scale combinatorial optimization problems, and it has made remarkable progress in recent years through several subtle mechanisms. In this paper, we found two ways to improve the local search algorithms in solving Pseudo-Boolean Optimization(PBO): Firstly, some of those mechanisms such as unit propagation are merely used in solving MaxSAT before, which can be generalized to solve PBO as well; Secondly, the existing local search algorithms utilize the heuristic on variables, so-called score, to mainly guide the search. We attempt to gain more insights into the clause, as it plays the role of a middleman who builds a bridge between variables and the given formula. Hence, we first extended the combination of unit propagation-based decimation algorithm to PBO problem, giving a further generalized definition of unit clause for PBO problem, and apply it to the existing solver LS-PBO for constructing an initial assignment; then, we introduced a new heuristic on clauses, dubbed care, to set a higher priority for the clauses that are less satisfied in current iterations. Experiments on three real-world application benchmarks including minimum-width confidence band, wireless sensor network optimization, and seating arrangement problems show that our algorithm DeciLS-PBO has a promising performance compared to the state-of-the-art algorithms.

翻译：局部搜索是解决大规模组合优化问题的有效方法，近年来通过若干精巧机制取得了显著进展。本文发现了改进局部搜索算法求解伪布尔优化问题的两条路径：首先，某些机制（如单元传播）此前仅用于求解MaxSAT问题，可将其泛化至PBO问题；其次，现有局部搜索算法利用变量上的启发式信息（即分值）主导搜索过程。我们尝试从子句层面获取更深入见解，因为子句作为连接变量与给定公式的中间媒介。因此，我们首先将基于单元传播的消减算法扩展至PBO问题，给出了PBO问题中单元子句的进一步泛化定义，并将其应用于现有求解器LS-PBO以构建初始赋值；随后，我们引入了一种新的子句启发式信息——关注度，用于为当前迭代中满足程度较低的子句赋予更高优先级。在三个真实世界应用基准（最小宽度置信带、无线传感器网络优化及座位安排问题）上的实验表明，与当前最优算法相比，我们的DeciLS-PBO算法具有优越性能。