The priority-based traveling backpacker problem: Formulations and heuristics

The Traveling Backpacker Problem (TBP) has been recently proposed to address the growing use of air transportation for tourism. It aims to identify routes with the minimum air ticket costs of a predefined set of destinations. Nevertheless, this problem may not be as flexible as the backpacker's profile. Backpackers usually have a limited budget and wish to get good deals. To better address this type of traveler, this paper introduces priority-based variants for the TBP, where not necessarily all destinations are visited. For such, prizes are assigned to the places according to the user's preferences for the destinations. The first model here proposed is the Prize Collecting Traveling Backpacker Problem (PCTBP). It minimizes the air ticket costs plus the penalties for unvisited destinations. Besides, we introduce the Time-Dependent Orienteering Problem (TDOP), which maximizes the prizes associated with the destinations but limits the budget according to a predefined value. Computational experiments involved real data and prizes following different distributions. Efficient multi-start randomized heuristics were developed for the problems. The results indicated that, depending on how the user assigns the prizes, the pattern of the routes differs significantly.