Global optimization of general non-convex problems with intermediate bilinear substructures

This work considers the global optimization of general non-convex nonlinear and mixed-integer nonlinear programming (MINLP) problems with underlying bilinear substructures. We combine reformulation-linearization techniques and advanced convex envelope construction techniques to produce tight subprob...

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Bibliographic Details
Published in:Optimization methods & software Vol. 29; no. 3; pp. 442 - 462
Main Authors: Zorn, Keith, Sahinidis, Nikolaos V.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.05.2014
Taylor & Francis Ltd
Subjects:
Algorithms
branch-and-bound global optimization
Cutting
factorable polyhedral relaxation
Filtering
Filtration
Mathematical analysis
Mathematical models
mixed-integer nonlinear programming
Optimization
reformulation-linearization techniques
Substructures
ISSN:1055-6788, 1029-4937
Online Access:Get full text
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Summary:This work considers the global optimization of general non-convex nonlinear and mixed-integer nonlinear programming (MINLP) problems with underlying bilinear substructures. We combine reformulation-linearization techniques and advanced convex envelope construction techniques to produce tight subproblem formulations for these underlying structures. When incorporated as linear cutting planes, these relaxation strengthening strategies are highly effective at tightening standard linear programming relaxations generated by factorable programming techniques. Because the size of these augmented linear relaxations increases exponentially with the number of variables, we employ cut filtering and selection strategies to ensure that the tightened subproblems are solved efficiently. We introduce algorithms for bilinear substructure detection, cutting plane identification, cut filtering, and cut selection and embed the proposed implementation in Branch-and-Reduce Optimization Navigator at every node in the branch-and-bound tree. A computational study including problem instances from standard literature test libraries is included to assess the performance of the proposed implementation. Results show that underlying bilinear substructures are identified in 30% of the problems in GLOBALLib and MINLPLib and that the exploitation of these structures significantly reduces computational time, branch-and-bound tree size, and required memory.
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ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2013.783032