Nonconvex Generalized Benders Decomposition for Stochastic Separable Mixed-Integer Nonlinear Programs

TitleNonconvex Generalized Benders Decomposition for Stochastic Separable Mixed-Integer Nonlinear Programs
Publication TypeJournal Article
Year of Publication2011
AuthorsLi X, Tomasgard A, Barton PI
JournalJournal of Optimization Theory and Applications
Volume151
Pagination425-454
ISSN0022-3239
KeywordsDecomposition algorithm, global optimization, Mixed-integer nonlinear programming, stochastic programming
Abstract

This paper considers deterministic global optimization of scenario-based, two-stage stochastic mixed-integer nonlinear programs (MINLPs) in which the participating functions are nonconvex and separable in integer and continuous variables. A novel decomposition method based on generalized Benders decomposition, named nonconvex generalized Benders decomposition (NGBD), is developed to obtain ε-optimal solutions of the stochastic MINLPs of interest in finite time. The dramatic computational advantage of NGBD over state-of-the-art global optimizers is demonstrated through the computational study of several engineering problems, where a problem with almost 150,000 variables is solved by NGBD within 80 minutes of solver time.

URLhttp://dx.doi.org/10.1007/s10957-011-9888-1
DOI10.1007/s10957-011-9888-1