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 benchmarks from the most recent PB Competition, as well as 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，近年来通过多种精妙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种途径：首先，单元传播等机制此前仅用于求解MaxSAT问题，可推广至伪布尔优化问题；其次，现有局部搜索算法主要利用变量层面的启发式信息（即得分）引导搜索，而子句作为连接变量与给定公式的中间桥梁，其作用值得深入探究。为此，我们首先将基于单元传播的简化算法扩展至伪布尔优化问题，对伪布尔优化问题的单元子句给出更广义的定义，并将其应用于现有求解器LS-PBO构建初始赋值；随后，我们引入一种新的子句级启发式因子"care"，为当前迭代中满足程度较低的谓词设置更高优先级。在最新PB竞赛基准测试及最小宽度置信区间、无线传感器网络优化、座位安排等三个实际应用基准问题上的实验表明，与当前最优算法相比，我们的算法DeciLS-PBO展现出优越性能。