Volume 57, Number 3, May-June 2023
|Page(s)||1149 - 1166|
|Published online||18 May 2023|
Branch-and-cut algorithms for the covering salesman problem
Institute of Computing, University of Campinas, Av. Albert Einstein 1251, 13083-852 Campinas, SP, Brazil
* Corresponding author: email@example.com
Accepted: 10 April 2023
The Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP is to find a minimum length Hamiltonian cycle over a subset of vertices that covers an undirected graph. In this paper, valid inequalities from the generalized traveling salesman problem are applied to the CSP in addition to new valid inequalities that explore distinct aspects of the problem. A branch-and-cut framework assembles exact and heuristic separation routines for integer and fractional CSP solutions. Computational experiments show that the proposed framework outperformed methodologies from literature with respect to optimality gaps. Moreover, optimal solutions were proven for several previously unsolved instances.
Mathematics Subject Classification: 68R05 / 90B06 / 90C10 / 90C57
Key words: Covering salesman problem / integer linear programming / branch-and-cut algorithm
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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