On the Fine-Grain Decomposition of Multicommodity Transportation Problems
Author(s)Zenios, Stavros A.
We develop algorithms for nonlinear problems with multicommodity transportation constraints. The algorithms are of the row-action type and, when properly applied,decompose the underlying graph alternatingly by nodes and edges. Hence, a fine-grain decomposition scheme is developed that is suitable for massively parallel computer architectures of the SIMD (i.e., single instruction stream, multiple data stream) class. Implementations on the Connection Machine CM-2 are discussed for both dense and sparse transportation problems. The dense implementation achieves computing rate of 1.6-3 GFLOPS. Several aspects of the algorithm are investigated empirically. Computational results are reported for the solution of quadratic programs with approximately 10 million columns and 100 thousand rows.
Massachusetts Institute of Technology, Operations Research Center
Operations Research Center Working Paper;OR 236-90