This paper deals with the Close-Enough Traveling Salesman Problem (CETSP). In the CETSP, rather than visiting the vertex (customer) itself, the salesman must visit a specific region containing such vertex. To solve this problem, we propose a simple yet effective exact algorithm, based on Branch-and-Bound and Second Order Cone Programming (SOCP). The proposed algorithm was tested in 824 instances suggested in the literature. Optimal solutions are obtained for open problems with up to a thousand vertices. We consider both instances in the two- and three-dimensional space.
Submitted to INFORMS Transportation Science