A new algorithm for the solution of the minimum cost multicommodity flow problem

The multicommodity minimum cost flow problem (MMCF) is to determine a minimum cost multicommodity flow through the constrained network. This paper considers a new barrier-penalty optimization algorithm for the solution of a general linear MMCF problem. The algorithm does not require an initial point to be feasible. This algorithm is computationally efficient and allows one to solve MMCF problems with a large number of commodities. It is also applicable to the convex MMCF problems with nonlinear constraints and/or objective function. The proof of its convergence and a new algorithm for calculating a lower bound are presented. The computer implementation of the algorithm is discussed, and computational experience is reported.