On a Time-Dependent Formulation and an Updated Classification of ATSP Formulations

Maria Teresa Godinho (1) , Luís Gouveia (2) , Pierre Pesneau (3, 4)

1 Departemento de Matematica [Beja]
2 CIO - Centro de Investigação Operacional
3 IMB - Institut de Mathématiques de Bordeaux
4 Realopt - Reformulations based algorithms for Combinatorial Optimization

In this chapter we contextualize, in terms of the ATSP, a recent compact formulation presented in Godinho et al [11] for the time-dependent traveling salesman problem (TDTSP). The previous paper provides one way of viewing the new model, the time-dependent TSP point of view where it is put in evidence how to obtain the new model by tightening the linear programming relaxation of a well known formulation for the TDTSP. In this chapter, we will present the ATSP point of view and will show how to obtain the model by i) enhancing the subproblem arising in the standard multicommodity ow (MCF) model for the ATSP and then ii) by using modelling enhancement techniques. We will compare the linear programming relaxation of the new formulation with the linear programming relaxation of the three compact and non-dominated formulations presented in Oncan et al. [19]. As a result of this comparison we present an updated classication of formulations for the asymmetric traveling salesman problem (ATSP).

Domaines: Recherche opérationnelle [math.OC]

Maria Teresa Godinho, Luís Gouveia, Pierre Pesneau. On a Time-Dependent Formulation and an Updated Classification of ATSP Formulations. Ali Ridha Mahjoub. Progress in Combinatorial Optimization, Wiley, 2011, 9781848212060. ⟨hal-00648457⟩