A variable neighborhood search method for the orienteering problem with hotel selection

In this paper, we present the orienteering problem with hotel selection (OPHS), an extension of the orienteering problem (OP). In the OPHS, a set of vertices with a score and a set of hotels are given. The goal is to determine a fixed number of connected trips that visits some vertices and maximizes the sum of the collected scores. Each trip is limited in length and should start and end in one of the hotels. We formulate the problem mathematically, explain the differences with related optimization problems and indicate what makes this problem inherently more difficult.