Branch-and-cut algorithms for the covering salesman problem

TL;DR

This paper introduces a branch-and-cut framework for the Covering Salesman Problem, applying new and existing inequalities to improve solution quality and computational efficiency, leading to optimal solutions for previously unsolved instances.

Contribution

It develops a novel branch-and-cut approach incorporating new valid inequalities for CSP, enhancing solution accuracy and computational performance.

Findings

Outperformed existing methods in optimality gaps

Proven optimal solutions for several previously unsolved instances

Effective integration of inequalities from related problems

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.