A Branch-and-Cut Algorithm for Solving the Team Orienteering Problem

Abstract

This paper describes a branch-and-cut algorithm to solve the Team Orienteering Problem (TOP). TOP is a variant of the Vehicle Routing Problem (VRP) in which the aim is to maximize the total amount of collected profits from visiting customers while not exceeding the predefined travel time limit of each vehicle. In contrast to the exact solving methods in the literature, our algorithm is based on a linear formulation with a polynomial number of binary variables. The algorithm features a new set of useful dominance properties and valid inequalities. The set includes symmetric breaking inequalities, boundaries on profits, generalized subtour eliminations and clique cuts from graphs of incompatibilities. Experiments conducted on the standard benchmark for TOP clearly show that our branch-and-cut is competitive with the other methods in the literature and allows us to close 29 open instances.