A multi-start variable neighborhood search for solving the single path multicommodity flow problem

In this paper, we propose a new global routing algorithm supporting advance reservation. A predefined number of messages are to be routed in a capacitated network including a set of nodes that can be producers and/or consumers of information. We assume that the same information can be held by different sources. We first propose the non-linear mathematical formulation for this problem by extending the single path multicommodity flow formulation. To solve such an NPNP-hard optimization problem, we develop a multi-start variable neighborhood search method (MVNS). The results of extensive computational experiments across a variety of networks from the literature are reported. For small and medium scale instances, the results are compared with the optimal solution generated by LINGO in terms of time and optimality. For large size instances, a comparison to a state-of-the-art ant colony system approach is performed. The obtained results show that the MVNS algorithm is computationally effective and provides high-quality solutions.