Efficient Cluster-Based Heuristics for the Team Orienteering Problem with Time Windows.

In the Team Orienteering Problem with Time Windows (TOPTW), a variant of the Vehicle Routing Problem with Profits, a set of locations is given, each associated with a profit, a visiting time and a time window. The aim is to maximize the overall profit collected by a number of routes, while the duration of each route must not exceed a given time budget. TOPTW is NP-hard and is typically used to model the Tourist Trip Design Problem. The latter deals with deriving near optimal multiple-day tours for tourists visiting a destination with several points of interest (POIs). The most efficient known heuristic approach to TOPTW which yields the best solution quality versus execution time, is based on Iterated Local Search (ILS). However, the ILS algorithm treats each node separately, hence it tends to overlook highly profitable areas of nodes situated far from the current solution, considering them too time-expensive to visit. We propose two cluster-based extensions to ILS addressing the aforementioned weakness by grouping nodes on separate clusters (based on geographical criteria), thereby making visits to such nodes more attractive. Our approaches improve ILS with respect to solutions quality and execution time as evidenced by experimental tests exercised on both existing and new TTDP-oriented benchmark instances.