The Robust Traveling Salesman Problem with Interval Data

The traveling salesman problem is one of the most famous combinatorial optimization problems, and has been intensively studied in the last decades. Many extensions to the basic problem have been also proposed, with the aim of making the resulting mathematical models as much realistic as possible. We present a new extension to the basic problem, where travel times are specified as a range of possible values. This model reflects the intrinsic difficulties to estimate travel times exactly in reality. We apply the robust deviation criterion to drive optimization over the interval data problem so obtained. Some interesting theoretical properties of the new optimization problems are identified and presented, together a new mathematical formulation and some exact algorithms. The exact methods are compared from an experimental point of view. The methodology we propose can be used to attack the robust counterpart of other NP-hard combinatorial optimization problems.