Hougardy and Schroeder (WG 2014) proposed a combinatorial technique for pruning the search space in the traveling salesman problem, establishing that, for a given instance, certain edges cannot be present in any optimal tour. We describe an implementation of their technique, employing an exact TSP solver to locate k-opt moves in the elimination process. In our computational study, we combine LP reduced-cost elimination together with the new combinatorial algorithm. We report results on a set of geometric instances, with the number of points n ranging from 3,038 up to 115,475. The test set includes all TSPLIB instances having at least 3,000 points, together with 250 randomly generated instances, each with 10,000 points, and three currently unsolved instances having 100,000 or more points. In all but two of the test instances, the complete-graph edge sets were reduced to under 3n edges. For the three large unsolved instances, repeated runs of the elimination process reduced the graphs to under 2.5n edges.

翻译：Hougardy与Schroeder（WG 2014）提出了一种组合技术，用于在旅行商问题中剪枝搜索空间，证明对于给定实例，某些边不可能出现在任何最优环游中。我们描述了他们技术的实现，采用精确TSP求解器在消除过程中定位k-opt移动。在我们的计算研究中，将LP约简成本消除与新的组合算法相结合。我们报告了一组几何实例的结果，其中点数n从3,038到115,475不等。测试集包括所有至少含3,000个点的TSPLIB实例，以及250个随机生成的各含10,000个点的实例，还有三个当前未解的、含100,000个或更多点的实例。除两个测试实例外，所有实例的完全图边集均被约简至低于3n条边。对于三个大型未解实例，重复运行消除过程后，图被约简至低于2.5n条边。