The Multiconstraint Team Orienteering Problem with Multiple Time Windows

The Orienteering Problem (OP) is a combinatorial routing problem of which the goal is to find a tour that maximises the total score earned by visiting vertices. A set of vertices is given, determined by their coordinates and a score. The pairwise travel times between the vertices are known. The total travel time should not exceed a predetermined time budget. Each vertex can be visited at most once. The OP serves as the starting point for modelling tourist trip design problems [2, 4]: a tourist who wants to visit a city or region is limited in time, and cannot visit every tourist attraction. Therefore, the tourist has to make a selection of the most interesting places to visit, within the limited time frame. The score represents the estimated personal interest of the tourist in the location. The time budget obviously represents the maximal amount of time the tourist has available. Solving the OP results in a personal trip for the tourist. However, while executing the planned trip, unexpected events often make the solution infeasible. Therefore, a fast algorithm is needed in order to dynamically recalculate the plan. Well known OP extensions are the Team OP (TOP), and the OP with Time Windows (TW). The former allows modelling trip planning problems for multiple days, the latter allows defining a period for each vertex in which the visit has to take place.