This paper deals with planning of a tour for a vehicle to clear a certain set of streets in a city of snow. Our previous results on the problem contain a heuristic based on reformulation to an asymmetric traveling salesman problem (ATSP) which yields feasible solutions and upper bounds, and a relaxation of a MIP model for obtaining lower bounds. The goal now is to try to improve the solutions and bounds. In this paper we describe a branch‐and‐dive heuristic which is based on branch‐and‐bound principles. We discuss how branching can be done so that the fixations can be utilized in both the relaxation and the ATSP model, and how the search for better solutions can be done. The heuristic has been implemented and applied to real life city networks. The method is shown to outperform two other heuristics for the ATSP with precedence constraints.

中文翻译：

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单车除雪的分支潜水法

本文涉及为在雪城中清理某些街道的车辆进行旅行的计划。我们在该问题上的先前结果包括基于对不对称旅行推销员问题（ATSP）进行重新公式化的启发式方法，可得出可行的解决方案和上限，并简化了MIP模型以获得下限。现在的目标是尝试改善解决方案和界限。在本文中，我们描述了一种基于分支定界原理的分支潜求启发法。我们讨论如何进行分支，以便可以在松弛模型和ATSP模型中利用固定物，以及如何寻求更好的解决方案。启发式方法已实施并应用于现实生活中的城市网络。对于具有优先权约束的ATSP，该方法表现出优于其他两种启发式方法。