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

The Team Orienteering Problem with Time Windows (TOPTW) deals with deriving a number of tours comprising a subset of candidate nodes (each associated with a “profit” value and a visiting time window) so as to maximize the overall “profit”, while respecting a specified time span. TOPTW has been used as a reference model for the Tourist Trip Design Problem (TTDP) in order to derive near-optimal multiple-day tours for tourists visiting a destination featuring several points of interest (POIs), taking into account a multitude of POI attributes. TOPTW is an NP-hard problem and the most efficient known heuristic is based on Iterated Local Search (ILS). However, ILS treats each POI separately; hence it tends to overlook highly profitable areas of POIs situated far from the current location, considering them too time-expensive to visit. We propose two cluster-based extensions to ILS addressing the aforementioned weakness by grouping POIs on disjoint clusters (based on geographical criteria), thereby making visits to such POIs more attractive. Our approaches improve on ILS with respect to solutions quality, while executing at comparable time and reducing the frequency of overly long transfers among POIs.