Dynamic Discretization Discovery for Solving the Time-Dependent Traveling Salesman Problem with Time Windows

We present a new solution approach for the time-dependent traveling salesman problem with time windows. This problem considers a salesman who departs from his home, has to visit a number of cities within a predetermined period of time, and then, returns home. The problem allows for travel times that can depend on the time of departure. We consider two objectives for the problem: (1) a makespan objective that seeks to return the salesman to his home as early as possible and (2) a duration objective that seeks to minimize the amount of time that he is away from his home. The solution approach is based on an integer programming formulation of the problem on a time-expanded network, because doing so enables time dependencies to be embedded in the definition of the network. However, because such a time-expanded network (and thus, the integer programming formulation) can rapidly become prohibitively large, the solution approach uses a dynamic discretization discovery framework, which has been effective in other contexts. Our computational results indicate that the solution approach outperforms the best-known methods on benchmark instances and is robust with respect to instance parameters.