Parallel distributed-memory simplex for large-scale stochastic LP problems

Miles Lubin (), J. Hall (), Cosmin Petra () and Mihai Anitescu ()

Computational Optimization and Applications, 2013, vol. 55, issue 3, 596 pages

Abstract: We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal basic solutions, which allow for efficient hot-starts (e.g., in a branch-and-bound context) and can provide important sensitivity information. Our approach exploits the dual block-angular structure of these problems inside the linear algebra of the revised simplex method in a manner suitable for high-performance distributed-memory clusters or supercomputers. While this paper focuses on stochastic LPs, the work is applicable to all problems with a dual block-angular structure. Our implementation is competitive in serial with highly efficient sparsity-exploiting simplex codes and achieves significant relative speed-ups when run in parallel. Additionally, very large problems with hundreds of millions of variables have been successfully solved to optimality. This is the largest-scale parallel sparsity-exploiting revised simplex implementation that has been developed to date and the first truly distributed solver. It is built on novel analysis of the linear algebra for dual block-angular LP problems when solved by using the revised simplex method and a novel parallel scheme for applying product-form updates. Copyright Springer Science+Business Media New York (outside the USA) 2013

Keywords: Simplex method; Parallel computing; Stochastic optimization; Block-angular (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10589-013-9542-y

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