Scalable branching on dual decomposition of stochastic mixed-integer programming problems

Kim, Kibaek; Dandurand, Brian

doi:10.1007/s12532-021-00212-y

Title: Scalable branching on dual decomposition of stochastic mixed-integer programming problems

Journal Article · 03 January 2022 · Mathematical Programming Computation

DOI: https://doi.org/10.1007/s12532-021-00212-y · OSTI ID:1883196

Kim, Kibaek ^[1]; Dandurand, Brian ^[1]

Argonne National Lab. (ANL), Argonne, IL (United States)

In this work, we present a scalable branching method for the dual decomposition of stochastic mixed-integer programming. Our new branching method is based on the branching method proposed by Caroe and Schultz that creates branching disjunctions on first-stage variables only. We propose improvements to the process for creating branching disjunctions, including (1) branching on the optimal solutions of the Dantzig-Wolfe reformulation of the restricted master problem and (2) using a more comprehensive (yet simple) measure for the dispersions associated with subproblem solution infeasibility. We prove that the proposed branching process leads to an algorithm that terminates finitely, and we provide conditions under which globally optimal solutions can be identified after termination. We have implemented our new branching method, as well as the Caroe-Schultz method and a branch-and-price method, in the open-source software package DSP. Using SIPLIB test instances, we present extensive numerical results to demonstrate that the proposed branching method significantly reduces the number of node subproblems and solution times.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1883196

Journal Information:: Mathematical Programming Computation, Journal Name: Mathematical Programming Computation Journal Issue: 1 Vol. 14; ISSN 1867-2949

Publisher:: Mathematical Optimization Society, Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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