In this paper, we consider the \({{\mathcal{N}\mathcal{P}}}\)-hard problem of determining fixed-length cycles in undirected edge-weighted graphs. Two solution methods are proposed, one based on integer programming (IP) and one that uses bespoke local search operators. These methods are executed under a common algorithmic framework that seeks to partition problem instances into a series of smaller sub-problems. Large-scale empirical tests indicate that the local search algorithm is generally preferable to IP, even with short run times. However, it can still produce suboptimal solutions, even with relatively small graphs.

中文翻译：

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确定具有边权的无向图中特定长度的循环的方法

在本文中，我们考虑了在无向边加权图中确定固定长度循环的难题。提出了两种解决方法，一种基于整数规划（IP），另一种使用定制的本地搜索算子。这些方法在通用算法框架下执行，该框架旨在将问题实例划分为一系列较小的子问题。大规模的实证测试表明，即使运行时间很短，本地搜索算法通常也优于 IP 算法。然而，即使图形相对较小，它仍然可以产生次优的解决方案。