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arXiv · 2104.01173

Branch-and-cut algorithms for the covering salesman problem

Lucas Porto Maziero·Fábio Luiz Usberti·Celso Cavellucci
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Abstract

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.

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Lucas Porto Maziero, Fábio Luiz Usberti, Celso Cavellucci. 2021-04-02. Branch-and-cut algorithms for the covering salesman problem. https://arxiv.org/abs/2104.01173

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