Application of NSGA-II framework to the travel planning problem using real-world travel data

In this paper we assess the performance of the classic NSGA-II algorithm when applied to a broad and realistic formulation of a bi-objective travel planning problem. Given a set of destinations and a travel time window, our goal is to find a Pareto set of detailed travel itineraries, which are both cost and time efficient. When the sequence of cities is fixed, the travel planning problem is commonly modeled in literature as a time-dependent network and the best itinerary is computed using shortest path algorithms. However, in our formulation, finding the order of cities that produces a good trade-off solution is also a goal. Additionally, a set of nondominated solutions must be provided to the tourist so that he/she can choose the best option based on his/her own preferences. Then, our formulation is built as a bi-objective Time Dependent Shortest Path Problem (TDSPP) embedded in a bi-objective Travel Salesman Problem (TSP). For managing the process of creation and evolving a population of routes, we apply a parallelized version of the NSGA-II framework. We present experimental results on 180 real-world instances, and show that, given 1 minute of execution, our approach is able to reach an approximated solution in average up to 10% divergent from an exact implementation.