A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs

This paper proposes a joint decomposition method that combines Lagrangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global optimality, without the need for explicit branch and bound search...

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Bibliographic Details
Published in:Journal of global optimization 2019-11, Vol.75 (3), p.595-629
Main Authors: Ogbe, Emmanuel, Li, Xiang
Format: Article
Language:English
Subjects:
Benders decomposition
Computer Science
Decomposition
Dependent variables
Global optimization
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Real Functions
Solvers
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Summary:This paper proposes a joint decomposition method that combines Lagrangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global optimality, without the need for explicit branch and bound search. In this approach, we view the variables coupling the scenario dependent variables and those causing nonconvexity as complicating variables. We systematically solve the Lagrangian decomposition subproblems and the generalized Benders decomposition subproblems in a unified framework. The method requires the solution of a difficult relaxed master problem, but the problem is only solved when necessary. Enhancements to the method are made to reduce the number of the relaxed master problems to be solved and ease the solution of each relaxed master problem. We consider two scenario-based, two-stage stochastic nonconvex MINLP problems that arise from integrated design and operation of process networks in the case study, and we show that the proposed method can solve the two problems significantly faster than state-of-the-art global optimization solvers.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-019-00786-x