加权最大可满足性问题的主干逼近
Approximating the Backbone in the Weighted Maximum Satisfiability Problem
摘要：
加权最大可满足性问题（weighted Maximum Satisfiability problem，简称MAX-SAT）是一个NP难问题，在人工智能中有着广泛的应用。主干作为一种有效的启发式设计工具，已被应用于许多NP难问题的启发式设计中。本文研究了在加权MAX-SAT中检索骨干的计算复杂性，并提出了一种新的算法来解决这个问题。我们证明了在以下假设下检索完整的主干是困难的。此外，它是棘手的，以恢复一个固定的骨干部分，以及。在此基础上，提出了一种基于Walksat算子的骨干引导局部搜索算法（BGLS）。BGLS包括两个阶段：第一阶段从局部最优解中抽取骨干信息，骨干阶段在骨干的指导下进行局部搜索。在基准测试上的大量实验结果表明，BGLS在解的质量和运行时间方面都优于现有的算法。
英文摘要：
The weighted Maximum Satisfiability problem (weighted MAX-SAT) is a NP-hard problem with numerous applications arising in artificial intelligence. As an efficient tool for heuristic design, the backbone has been applied to heuristics design for many NP-hard problems. In this paper, we investigated the computational complexity for retrieving the backbone in weighted MAX-SAT and developed a new algorithm for solving this problem. We showed that it is intractable to retrieve the full backbone under the assumption that . Moreover, it is intractable to retrieve a fixed fraction of the backbone as well. And then we presented a backbone guided local search (BGLS) with Walksat operator for weighted MAX-SAT. BGLS consists of two phases: the first phase samples the backbone information from local optima and the backbone phase conducts local search under the guideline of backbone. Extensive experimental results on the benchmark showed that BGLS outperforms the existing heuristics in both solution quality and runtime.
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