Many natural optimization problems are NP-hard, which implies that they are probably hard to solve exactly in the worst-case. However, it suffices to get reasonably good solutions for all (or even most) instances in practice. This paper presents a new algorithm for computing approximate solutions in Θ(N) for the maximum exact 3-satisfiability (MAX-E-3-SAT) problem by using supervised learning methodology. This methodology allows us to create a learning algorithm able to fix Boolean variables by using local information obtained by the Survey Propagation algorithm. By performing an accurate analysis, on random conjunctive normal form instances of the MAX-E-3-SAT with several Boolean variables, we show that this new algorithm, avoiding any decimation strategy, can build assignments better than a random one, even if the convergence of the messages is not found. Although this algorithm is not competitive with state-of-the-art maximum satisfiability solvers, it can solve substantially larger and more complicated problems than it ever saw during training.

许多自然优化问题是 NP-hard 问题，这意味着它们可能很难在最坏的情况下精确解决。然而，在实践中为所有（甚至大多数）实例获得相当好的解决方案就足够了。本文提出了一种计算 Θ( N) 使用监督学习方法解决最大精确 3-可满足性 (MAX-E-3-SAT) 问题。这种方法允许我们创建一个学习算法，该算法能够通过使用调查传播算法获得的本地信息来修复布尔变量。通过对具有多个布尔变量的 MAX-E-3-SAT 的随机连接范式实例进行准确分析，我们表明这种新算法避免了任何抽取策略，可以比随机算法更好地构建分配，即使没有发现消息的收敛。尽管该算法无法与最先进的最大可满足性求解器竞争，但它可以解决比训练期间所见过的更大、更复杂的问题。