DSP

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DSP is an open-source and parallel package that implements decomposition methods for structured mixed-integer programming problems. These are structured optimization problems in the following form:

    minimize   c^T x + \sum_{s=1}^S q_s^T y_s
    subject to   A x                              = b
               T_s x +                    W_s y_s = h_s for s = 1, .., S
               some x, y_s are integers

where x and y_s are decision variable vectors with dimensions n_1 and n_2, respectively, A, T_s and W_s are matrices of dimensions m_1 by n_1, m_2 by n_1 and m_2 by n_2, respectively, and c, q_s, b, and h_s are vectors of appropriate dimensions.

DSP Solution Methods:

• Extensive form solver (global solver)
• Serial/parallel dual decomposition (dual bounding solver)
• Serial/parallel Dantzig-Wolfe decomposition (global solver)
• Serial/parallel Benders decomposition

Problem Types:

• Two-stage stochastic mixed-integer linear programs
• Distributionally robust stochastic mixed-integer linear programs
• Structured mixed-integer linear programs

Problem Input Formats:

• SMPS file format for stochastic programs (.dro optionally for distributionally robust)
• MPS and DEC files for generic block-structured optimization problems
• Julia modeling package DSPopt.jl

Installation

git clone --recursive https://github.com/Argonne-National-Laboratory/DSP.git

Contributors

• Kibaek Kim, Mathematics and Computer Science Division, Argonne National Laboratory.
• Victor M. Zavala, Department of Chemical and Biological Engineering, University of Wisconsin-Madison.
• Christian Tjandraatmadja, Google Research.
• Yingqiu Zhang, Industrial and Systems Engineering, Virginia Tech.

Key Publications

• Kibaek Kim. "Dual Decomposition of Two-Stage Distributionally Robust Mixed-Integer Programming under the Wasserstein Ambiguity Set" Optimization Online, 2020
• Kibaek Kim and Briand Dandurand. "Scalable Branching on Dual Decomposition of Stochastic Mixed-Integer Programming Problems" Mathematical Programming Computation (to appear), 2020
• Kibaek Kim, Cosmin Petra, and Victor Zavala. "An Asynchronous Bundle-Trust-Region Method for Dual Decomposition of Stochastic Mixed-Integer Programming" SIAM Journal on Optimization 29(1), 2019
• Kibaek Kim and Victor M. Zavala. "Algorithmic innovations and software for the dual decomposition method applied to stochastic mixed-integer programs" Mathematical Programming Computation 10(2), 2017

Acknowledgements

This material is based upon work supported by the U.S. Department of Energy, Office of Science, under contract number DE-AC02-06CH11357.