ABSTRACT This paper introduces the Selective Generalized Traveling Salesman Problem (SGTSP). In SGTSP, the goal is to determine the maximum profitable tour within the given threshold of the tour’s duration, which consists of a subset of clusters and a subset of nodes in each cluster visited on the tour. This problem is a combination of cluster and node selection and determining the shortest path between the selected nodes. We propose eight mixed integer programming (MIP) formulations for SGTSP. All of the given MIP formulations are completely new, which is one of the major novelties of the study. The performance of the proposed formulations is evaluated on a set of test instances by conducting 4608 experimental runs. Overall, 4138 out of 4608 (~90%) test instances were solved optimally by using all formulations.

中文翻译：

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选择性广义旅行商问题

摘要 本文介绍了选择性广义旅行商问题（SGTSP）。在 SGTSP 中，目标是在给定的旅行持续时间阈值内确定最大的盈利旅行，该阈值由集群子集和旅行中访问的每个集群中的节点子集组成。这个问题是集群和节点选择的组合以及确定所选节点之间的最短路径。我们为 SGTSP 提出了八种混合整数规划 (MIP) 公式。所有给定的 MIP 配方都是全新的，这是该研究的主要创新之一。通过进行 4608 次实验运行，在一组测试实例上评估了所提出配方的性能。总体而言，通过使用所有公式，4608 个 (~90%) 测试实例中的 4138 个得到了最佳解决。