On the scalability of data-parallel decomposition algorithms for stochastic programs

Abstract

This paper develops a data-parallel implementation of the L-shaped decomposition algorithm for stochastic linear programs with recourse. The algorithm decomposes the problem into independent scenario subproblems that are solved concurrently. These subproblems are structurally identical and can be solved on SIMD machines, such as the Connection Machine CM-2. The coordinating master program is a dense linear program and is solved efficiently by spreading its non-zero coefficients among multiple processors and using dense linear algebra subroutines. The parallel solution of the master program removes the serial bottleneck of the algorithm. The resulting implementation achieves good speed-ups and is scalable. Numerical results on the Connection Machine CM-2 and comparisons with a benchmark control-parallel implementation are included. © 1994 Academic Press, Inc.