A Textured Decomposition based Algorithm for Large-Scale Multicommodity Network Flow Problems

Abstract

In this paper, we propose a textured decomposition based algorithm with parallel processing capability for solving large scale multicommodity network flow problem (MFP), which is popular in communication networks and transportation systems. We show that the algorithm will always converge to one of the stationary points characterized by the textured decomposition. Moreover, a modification over the MFP and sufficient conditions are developed to guarantee that the convergent stationary point is the unique minimum solution of the modified MFP; and it is the global minimum solution of the MFP in its limit. To avoid ill-condition, a practical two-stage textured decomposition based algorithm is proposed to get a more elaborate approximate global minimum solution. A simulation example for this two-stage algorithm was given in which only few iterations are needed to converge. Assume two processors available, a speed up ratio around 10:1 is estimated based on a projected Newton method if it is incorporated with this two-stage algorithm.