Uncertain Traveling Salesman Problem

This paper mainly investigates the traveling salesman problem under uncertain environment, in which not all the edge weights are deterministically present, but are present with uncertain variables. As a result, five types optimal route models for the uncertain traveling salesman problem, i.e., expected optimal route, α-optimal route, distribution optimal route, expected approximation optimal route, and α-approximation optimal route, are constructed on the basis of uncertainty theory. Taking advantage of some properties of uncertainty theory, these models can be transformed to responding deterministic form. Finally, some numerical examples are performed to show the applications of the models.