A Benchmark Test Suite for Multiple Traveling Salesmen Problem with Pivot Cities

Abstract

Multiple Traveling Salesmen Problem with Pivot Cities (PCMTSP) extends the Multiple Traveling Salesmen Problem (MTSP) by introducing pivot cities, which are allowed to be visited by multiple traveling salesmen. The difficulty of this problem lies in the repeatable visits of pivot cities and the efficient construction of legal solutions. Besides, the number of pivot cities and the visiting times of the pivot cities directly enlarge the solution space exponentially. Though a few studies have made attempts to solve this problem, there is no common benchmark to fairly evaluate the performance of the proposed methods in these studies. To fill this gap, this paper constructs a PCMTSP generator and then establishes a benchmark test suite consisting of PCMTSP instances with three different scales, namely small-scale, medium-scale, and large-scale, and three different visit types, namely intensive, sparse, and normal. Finally, this paper adapts five classical ant colony optimization (ACO) algorithms to solve the constructed PCMTSP instances. Experimental results demonstrate that the five ACOs are capable of solving PCMTSP. Hopefully, with this benchmark set, the research on PCMTSP can be boosted. In particular, the constructed benchmark set can be downloaded from https://gitee.com/bzy1999/pcmtsp. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.