Multicommodity flow problems with a bounded number of paths: A flow deviation approach

We propose a modified version of the Flow Deviation method of Fratta, Gerla and Kleinrock to solve multicommodity problems with minimal congestion and a bounded number of active paths. We discuss the approximation of the min-max objective function by a separable convex potential function and give a mixed-integer non linear model for the constrained routing problem. A heuristic control of the path generation is then embedded in the original algorithm based on the concepts of cleaning the quasi inactive paths and the reduction of the flow width for each commodity. Numerical experiments show the validity of the approach for realistic medium-size networks associated with routing problems in broadband communication networks with multiple protocols and label-switched paths (MPLS).