The Travelling Salesperson Problem (TSP) is one of the best-studied NP-hard problems. Over the years, many different solution approaches and solvers have been developed. For the first time, we directly compare five state-of-the-art inexact solvers—namely, LKH, EAX, restart variants of those, and MAOS—on a large set of well-known benchmark instances and demonstrate complementary performance, in that different instances may be solved most effectively by different algorithms. We leverage this complementarity to build an algorithm selector, which selects the best TSP solver on a per-instance basis and thus achieves significantly improved performance compared to the single best solver, representing an advance in the state of the art in solving the Euclidean TSP. Our in-depth analysis of the selectors provides insight into what drives this performance improvement.

中文翻译：

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通过机器学习利用 TSP 求解器互补性

旅行商问题 (TSP) 是研究最深入的 NP 难题之一。多年来，已经开发了许多不同的解决方法和求解器。我们第一次在大量著名的基准实例上直接比较了五个最先进的不精确求解器——即 LKH、EAX、它们的重启变体和 MAOS，并展示了互补的性能，因为不同的实例可以通过不同的算法最有效地解决。我们利用这种互补性来构建一个算法选择器，它在每个实例的基础上选择最佳 TSP 求解器，因此与单个最佳求解器相比，性能显着提高，代表了求解欧几里得 TSP 的最新技术进步。