Models and algorithms for the Traveling Salesman Problem with Time-dependent Service times

Abstract

The Traveling Salesman Problem with Time-dependent Service times (TSP-TS) is a generalization of the Asymmetric TSP, in which the service time at each customer is given by a (linear or quadratic) function of the corresponding start time of service. TSP-TS calls for determining a Hamiltonian tour (i.e. a tour visiting each customer exactly once) that minimizes the total tour duration, given by the sum of travel and service times. We propose a new Mixed Integer Programming model for TSP-TS, that is enhanced by lower and upper bounds that improve previous bounds from the literature, and by incorporating exponentially many subtour elimination constraints, that are separated in a dynamic way. In addition, we develop a multi-operator genetic algorithm and two Branch-and-Cut methods, based on the proposed model. The algorithms are tested on benchmark symmetric instances from the literature, and compared with an existing approach. The computational results show that the proposed exact methods are able to prove the optimality of the solutions found for a larger set of instances in shorter computing times. We also tested the Branch-and-Cut algorithms on larger size symmetric instances with up to 58 nodes and on asymmetric instances with up to 45 nodes, demonstrating the effectiveness of the proposed algorithms. In addition, we tested the genetic algorithm on symmetric and asymmetric instances with up to 200 nodes.