Benchmark for Euclidean Single-Depot Bounded Multiple Travelling Salesman Problem instances

Published: 6 November 2023| Version 2 | DOI: 10.17632/z6rwf28682.2
Víctor Hugo Pacheco Valencia


This repository introduces 168 novel instances (file: instances-168.csv) designed for solving the Euclidean Single-Depot Bounded Multiple Traveling Salesman Problem (Bounded MTSP). These instances are adapted from the TSP library, with city '1' designated as the depot, and the remaining 'n-1' cities representing destinations to be visited by 'k' salespeople. To define the tour constraints, we establish 'm_{\min}' (minimum) and 'm_{\max}' (maximum) bounded values, informed by real-world surveys reflecting client visits ranging from 15 to 60. Our repository provides three sets of 'm_{\min}' and 'm_{\max}' pairs: 30, 50; 24, 40; and 18, 30. Additionally, the value for 'k' is calculated using the formula: $$k= \left \lceil \frac{1.3 \times |V|}{m_{\max}} \right \rceil$$. In addition to the 168 new instances, we have included 6 instances proposed by (Junjie & Dingwei, 2006) (file instances-6.csv)and 16 instances proposed by (Necula et al. 2015) (instances-16.csv), bringing the total to 190 instances. For each instance, we provide the best solution delivered by our 3-phase algorithm (Pacheco-Valencia et al., 2023, folder: code) in (folders: solutions-22 and solutions-163) and their corresponding solution graph (folder: graphs), along with a table detailing the minimum, average, and maximum costs, as well as the average processing time (file: results.xlsx). These instances serve as valuable benchmarks for researchers exploring MTSP variants. R. Necula, M. Breaban, and M. Raschip, ``Performance evaluation of ant colony systems for the single-depot multiple traveling salesman problem,'' In International Conference on Hybrid Artificial Intelligence Systems, Springer, Cham. pp. 257--268, 2015. Available:\_22 P. Junjie and W. Dingwei, ``An ant colony optimization algorithm for multiple travelling salesman problem,'' In First International Conference on Innovative Computing, Information and Control-Volume I (ICICIC'06), Vol. 1, pp. 210--213, IEEE, 2006 Available: V. H. Pacheco-Valencia, N. Vakhania and J. A. Hernández-Aguilar, "An Algorithm to Solve the Euclidean Single-Depot Bounded Multiple Traveling Salesman Problem," In 2023 IEEE World Conference on Applied Intelligence and Computing (AIC), Sonbhadra, India, 2023, pp. 7-12, Available: TSPLIB Available: Last consulted 30 sep 2023



Universidad Autonoma del Estado de Morelos Facultad de Ciencias


Combinatorial Optimization, Traveling Salesman Problem, Euclidean Space