Generalized Partition Crossover (GPX) is a deterministic recombination operator developed for the Traveling Salesman Problem. Partition crossover operators return the best of 2k reachable offspring, where k is the number of recombining components. This article introduces a new GPX2 operator, which finds more recombining components than GPX or Iterative Partial Transcription (IPT). We also show that GPX2 has O(n) runtime complexity, while also introducing new enhancements to reduce the execution time of GPX2. Finally, we experimentally demonstrate the efficiency of GPX2 when it is used to improve solutions found by the multitrial Lin-Kernighan-Helsgaum (LKH) algorithm. Significant improvements in performance are documented on large (n>5000) and very large (n=100,000) instances of the Traveling Salesman Problem.

中文翻译：

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旅行商问题的新广义分区交叉：局部最优之间的隧道

广义分区交叉 (GPX) 是为旅行商问题开发的确定性重组算子。分区交叉算子返回 2k 个可达后代中最好的，其中 k 是重组组件的数量。本文介绍了一个新的 GPX2 算子，它发现了比 GPX 或迭代部分转录（IPT）更多的重组组件。我们还展示了 GPX2 的运行时间复杂度为 O(n)，同时还引入了新的增强功能以​​减少 GPX2 的执行时间。最后，我们通过实验证明了 GPX2 在用于改进由多次试验 Lin-Kernighan-Helsgaum (LKH) 算法找到的解决方案时的效率。在旅行商问题的大型 (n>5000) 和非常大 (n=100,000) 实例上记录了性能的显着改进。