Implementation of an optimal multicommodity network flow algorithm based on gradient projection and a path flow formulation

Abstract : The implementation of a multicommodity flow algorithm into a FORTRAN code is discussed. The algorithm is based on a gradient projection method with diagonal scaling based on Hessian or Jacobian information. The flows carried by the active paths of each origin-destination (OD) pair are iterated upon one OD pair, per iteration. The data structures and memory requirements of the algorithm are discussed and are compared with those of other formulation based on link flows associated with each origin, and aggregate link flows.

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