Estimating the Tour Length for the Close Enough Traveling Salesman Problem

• Main Authors: Debdatta Sinha Roy, Bruce Golden, Xingyin Wang, Edward Wasil
• Format: Article
• Language: English
• Published: MDPI AG 2021-04-01
• Series: Algorithms
• Subjects: close enough traveling salesman problem; tour-length estimation; regression models
• Online Access: https://www.mdpi.com/1999-4893/14/4/123

We construct empirically based regression models for estimating the tour length in the Close Enough Traveling Salesman Problem (CETSP). In the CETSP, a customer is considered visited when the salesman visits any point in the customer’s service region. We build our models using as many as 14 independent variables on a set of 780 benchmark instances of the CETSP and compare the estimated tour lengths to the results from a Steiner zone heuristic. We validate our results on a new set of 234 instances that are similar to the 780 benchmark instances. We also generate results for a new set of 72 larger instances. Overall, our models fit the data well and do a very good job of estimating the tour length. In addition, we show that our modeling approach can be used to accurately estimate the optimal tour lengths for the CETSP.