We consider the customary formulation of non-cyclic train timetabling, calling for a maximum-profit collection of compatible paths in a suitable acyclic network. The associated ILP models look for a maximum-weight clique in a(n exponentially-large) compatibility graph. By taking a close look at the structure of this graph, we analyze the existing ILP models and propose some new stronger ones, all having the essential property that both separation and column generation can be carried out efficiently. Computational results show that the LP relaxations of the new formulations can lead to much stronger upper bounds on highly-congested instances.
V. Cacchiani, A. Caprara, P. Toth (2009). Non-cyclic Train Timetabling and Comparability Graphs. PISA : s.n.
Non-cyclic Train Timetabling and Comparability Graphs
CACCHIANI, VALENTINA;CAPRARA, ALBERTO;TOTH, PAOLO
2009
Abstract
We consider the customary formulation of non-cyclic train timetabling, calling for a maximum-profit collection of compatible paths in a suitable acyclic network. The associated ILP models look for a maximum-weight clique in a(n exponentially-large) compatibility graph. By taking a close look at the structure of this graph, we analyze the existing ILP models and propose some new stronger ones, all having the essential property that both separation and column generation can be carried out efficiently. Computational results show that the LP relaxations of the new formulations can lead to much stronger upper bounds on highly-congested instances.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
