This a summary of the author's PhD thesis supervised by Leo Liberti, Philippe Baptiste and Daniel Krob and defended on 18 June 2009 at Ecole Polytechnique, Palaiseau, France. The thesis is written in English and is available at http://pastel.paristech.org/5275/. The computation of point-to-point shortest paths in road networks has many practical applications that require very fast solution times, meaning that Dijkstra's algorithm is not a viable option. In this work we develop an efficient algorithm to find the shortest route between two nodes of a large-scale, time-dependent graph, where we also allow the time-dependent arc cost functions to be updated at regular intervals. Furthermore, we propose a mathematical programming formulation for the shortest paths problem on time-dependent networks, that gives rise to integer programs. Within the context of solving Mixed-Integer Linear Programs through a Branch-and-Bound algorithm, we propose a new strategy for branching, mixing branching on single variables with branching on general hyperplanes. Finally, we introduce an effective heuristic for nonconvex Mixed-Integer Nonlinear Programss which combines VNS, Local Branching, NLP local search and Branch-and-Bound.
