Dynamic Shortest Paths Methods for the Time-Dependent TSP

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in directed graph where (asymmetric) arc-costs depend on the time arc is entered. With traffic data abundantly available, methods to optimize routes with respect travel times are widely desired. This holds particular problem, which corner stone of logistic planning. In this paper, we devise column-generation-based IP solve TDTSP full generality, both arc- and path-based formulations. algorithmic key path arises from pricing column generation independent interest—namely, find paths time-expanded that acyclic underlying (non-expanded) graph. As computationally too costly, price over set contain no cycles length k. addition, devise—tailored TDTSP—several families valid inequalities, primal heuristics, propagation method, branching rule. Combining these provide—to our knowledge—the first elaborate method general fully time-dependence. We also provide results complexity approximability TDTSP. computational experiments randomly generated instances, able large majority small instances (20 nodes) optimality, while closing about two thirds remaining gap (40 after one hour computation.