Abstract The Traveling Salesperson Problem with Hotel Selection (TSPHS) is a realistic extension of the classic Traveling Salesperson Problem recently introduced to the literature. In the TSPHS, there is a time limit that restricts the visits that can be performed in a single day. Therefore, several days may be necessary to visit all clients. The salesperson has to spend the night in one of the available hotels. Previous works focus mainly on metaheuristics and on MIP formulations. This work presents a sophisticated exact algorithm for the TSPHS, a Branch-Cut-and-Price (BCP) algorithm that includes and adapts several features found in state-of-the-art algorithms for vehicle routing. In that algorithm, columns correspond to possible salesperson day trips; subtour elimination cuts, 2-path cuts, and limited-memory subset row cuts are separated. Computational results show that many medium-sized instances, having up to 75 clients and 20 hotels, can be solved to optimality, as well as some larger instances from the literature, with up to 225 clients.

中文翻译：

---

带酒店选择的旅行商问题的分店砍价算法

摘要 带有酒店选择的旅行推销员问题 (TSPHS) 是最近引入文献的经典旅行推销员问题的现实扩展。在 TSPHS 中，有一个时间限制，限制了一天内可以进行的访问。因此，访问所有客户可能需要几天时间。销售人员必须在可用的酒店之一过夜。以前的工作主要集中在元启发式和 MIP 公式上。这项工作为 TSPHS 提供了一种复杂的精确算法，这是一种分支切割和定价 (BCP) 算法，它包括并适应了最先进的车辆路线算法中的几个特征。在该算法中，列对应于可能的销售人员一日游；subtour消除切割、2-path切割和有限内存子集行切割是分开的。