Metaheuristics are a class of approximate methods, which are designed to attack hard combinatorial optimization problems. In metaheuristics, a neighborhood is defined by the specified move operation for a solution. The neighborhood plays an essential role in the performance of its algorithms. It is important to capture the statistical properties of neighborhoods. In this paper, we present a theoretical analysis of neighborhoods for a wide class of combinatorial optimization problems, instead of just for restricted instances. First, we give a probabilistic model which allows us to compute statistics for various types of neighborhoods. Here we introduce an approach in which the solution space (the landscape) for a wide class of combinatorial optimization problems can be approximated to AR(1), which can be used to capture the statistics of the solution space. The theoretical results obtained from our proposed model closely match empirically observed behavior. Second, we present an application in which we use our probabilistic model of neighborhoods.

元启发法是一类近似方法，旨在解决困难的组合优化问题。在元启发法中，邻域由解决方案的指定移动操作定义。邻域对其算法的性能起着至关重要的作用。捕获邻域的统计特性非常重要。在本文中，我们提出了针对各种组合优化问题的邻域的理论分析，而不仅仅是针对受限实例。首先，我们给出一个概率模型，它允许我们计算各种类型社区的统计数据。在这里，我们介绍一种方法，其中一类广泛的组合优化问题的解空间（景观）可以近似为 AR(1)，它可用于捕获解空间的统计数据。从我们提出的模型中获得的理论结果与经验观察到的行为非常吻合。其次，我们提出了一个使用邻域概率模型的应用程序。