The Covering Tour Problem.

The Covering Tour Problem (CTP) is defined on a graph G = (V ∪ W, E), where W is a set of vertices that must be covered. The CTP consists of determining a minimum length Hamiltonian cycle on a subset of V such that every vertex of W is within a prespecified distance from the cycle. The problem is first formulated as an integer linear program, polyhedral properties of several classes of constraints are investigated, and an exact branch-and-cut algorithm is developed. A heuristic is also described. Extensive computational results are presented. [ABSTRACT FROM AUTHOR]