Parallel Decomposition of Multicommodity Network Flows Using a Linear-Quadratic Penalty Algorithm

Abstract

The central theme of this paper is the design and evaluation of a parallel decomposition algorithm for multicommodity network flow problems based on the notion of piecewise linear-quadratic penalty (LQP) functions. The algorithm induces separability of both the constraint set and the objective function by commodity during the subproblem phase. Hence it is suitable for implementations on coarse grain parallel architectures. A master problem, of significantly smaller dimension than the original problem, uses dense linear algebra computations. Hence it exploits a vector architecture, but is also suited for parallel implementation and can be executed using Basic Linear Algebra (BLAS) subroutines. Computational results on a CRAY Y-MPE264 supercomputer with a set of large multicommodity network flow problems drawn from a military application are presented and analyzed. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.