The travelling salesman problem (TSP) is one of the well-studied NP-hard problems in the literature. The state-of-the art inexact TSP solvers are the Lin-Kernighan-Helsgaun (LKH) heuristic and Edge Assembly crossover (EAX). A recent study suggests that EAX with restart mechanisms perform well on a wide range of TSP instances. However, this study is limited to 2,000 city problems. We study for problems ranging from 2,000 to 85,900. We see that the performance of the solver varies with the type of the problem. However, combining these solvers in an ensemble setup, we are able to outperform the individual solver's performance. We see the ensemble setup as an efficient way to make use of the abundance of compute resources. In addition to EAX and LKH, we use several versions of the hybrid of EAX and Mixing Genetic Algorithm (MGA). A hybrid of MGA and EAX is known to solve some hard problems. We see that the ensemble of the hybrid version outperforms the state-of-the-art solvers on problems larger than 10,000 cities.

翻译：旅行商问题（TSP）是文献中研究充分的NP难问题之一。目前最先进的不精确TSP求解器包括Lin-Kernighan-Helsgaun（LKH）启发式算法和边缘装配交叉（EAX）算法。近期研究表明，具有重启机制的EAX算法在各类TSP实例上表现优异，但该研究仅限于2000个城市的问题。本研究针对2000至85900个城市的问题展开分析，发现求解器的性能随问题类型而变化。然而，通过集成方式组合这些求解器，我们能够超越单个求解器的性能。我们认为集成方法是充分利用富余计算资源的有效途径。除EAX和LKH外，我们还采用了EAX与混合遗传算法（MGA）的多种混合版本。已知MGA与EAX的混合算法能够解决部分难题，实验表明，对于超过10000个城市的问题，混合算法集成方法的性能优于现有最先进求解器。