Solution methods for the Time-Dependent Orienteering Problem

The orienteering problem (OP) is defined on a graph in which scores are assigned to the vertices and a travel time is assigned to each edge linking two vertices. The objective of the OP is to select a subset of vertices and determine the order in which they are visited so that the total collected score is maximized while the maximum total travel time is not exceeded. In addition, a feasible OP solution should start and end at a predetermined vertex. Orienteering problems are typically used in logistic planning tools and they serve as the basic problem formulation of personalized touristic trip planners. This research focuses on developing metaheuristics to obtain solutions within a few seconds of computation time for time-dependent orienteering problems (TD-OP) which means that the travel time between two vertices depends on the departure time at the first vertex. This specific problem formulation allows us to tackle congestion related issues in routing problems. To the best of our knowledge, a solution method for this problem is only provided in journal papers by Abbaspour et al. (2011) and Garcia et al. (2013).