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On parallelizing dual decomposition in stochastic integer programming

Miles Lubin (mlubin***at***mit.edu)
Kipp Martin (kmartin***at***chicagobooth.edu)
Cosmin Petra (petra***at***mcs.anl.gov)
Burhannedin Sandıkçı (burhan***at***chicagobooth.edu)

Abstract: For stochastic mixed-integer programs, we revisit the dual decomposition algorithm of Car\o{}e and Schultz from a computational perspective with the aim of its parallelization. We address an important bottleneck of parallel execution by identifying a formulation that permits the parallel solution of the \textit{master} program by using structure-exploiting interior-point solvers. Our results demonstrate the potential for parallel speedup and the importance of regularization (stabilization) in the dual optimization. Load imbalance is identified as a remaining barrier to parallel scalability.

Keywords: stochastic programming, mixed-integer programming, column generation, dual decomposition, parallel computing, bundle methods

Category 1: Stochastic Programming

Category 2: Optimization Software and Modeling Systems (Parallel Algorithms )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Accepted for publication in Operations Research Letters. Formerly preprint ANL/MCS-P3037-0912, Argonne National Laboratory, October 2012.

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Entry Submitted: 10/09/2012
Entry Accepted: 10/09/2012
Entry Last Modified: 02/10/2013

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