Validation of algorithms for optimal routing of flow in networks

This paper presents computational results relating to solution of convex multicommodity network flow problems by using several recently developed optimization algorithms. These algorithms are based on the ideas of Gallager´s method for distributed optimization of delay in data communication networks [1], and gradient projection ideas from nonlinear programming [2], [3]. They can be used both with and without a line search. An important common feature of the algorithms which distinguishes them from other existing methods is that they utilize second derivatives and are geared towards approximating a constrained version of Newton´s method. The computational results confirm that the algorithms tend to employ good search directions as well as automatically generate a satisfactory stepsize regardless of the level and pattern of traffic input to the network. This latter advantage is of crucial importance when the algorithms are used for distributed routing of flow in data communication networks where the use of line search is nearly impossible.