A Lagrangian dual method for two-stage robust optimization with binary uncertainties

Subramanyam, Anirudh

doi:10.1007/s11081-022-09710-x

A Lagrangian dual method for two-stage robust optimization with binary uncertainties

Journal Article · Tue Mar 29 00:00:00 EDT 2022 · Optimization and Engineering

DOI:https://doi.org/10.1007/s11081-022-09710-x· OSTI ID:1969127

Subramanyam, Anirudh ^[1]

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

This report presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably Benders decomposition and column-and-constraint generation, compute worst-case parameter realizations by solving mixed-integer bilinear optimization subproblems. However, their numerical solution can be computationally expensive not only due to their resulting large size after reformulating the bilinear terms, but also because decision-independent bounds on their variables are typically unknown. We propose an alternative Lagrangian dual method that circumvents these difficulties and is readily integrated in either algorithm. We specialize the method to problems where the binary parameters switch on or off constraints as these are commonly encountered in applications, and discuss extensions to problems that lack relatively complete recourse and to those with integer recourse. Numerical experiments provide evidence of significant computational improvements over existing methods.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1969127

Journal Information:: Optimization and Engineering, Journal Name: Optimization and Engineering Journal Issue: 4 Vol. 23; ISSN 1389-4420

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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42 ENGINEERING
Lagrangian dual
binary uncertainty
robust optimization
two-stage problems

A Lagrangian dual method for two-stage robust optimization with binary uncertainties

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