The Undirected m-Peripatetic Salesman Problem: Polyhedral Results and New Algorithms

In the m-peripatetic salesman problem (m-PSP), the aim is to determine m edge disjoint Hamiltonian cycles of minimum total cost on a graph. This article introduces new valid inequalities and polyhedral results for the m-PSP. An improved 2-index branch-and-cut algorithm is developed. Tests performed on randomly generated and TSPLIB Euclidean instances indicate that this algorithm can solve instances with more than double the size of what was previously achievable.