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On the relation between flexibility analysis and robust optimization for linear systems
Author(s) -
Zhang Qi,
Grossmann Ignacio E.,
Lima Ricardo M.
Publication year - 2016
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.15221
Subject(s) - flexibility (engineering) , robust optimization , context (archaeology) , mathematical optimization , duality (order theory) , computer science , linear programming , perspective (graphical) , mathematics , artificial intelligence , statistics , paleontology , discrete mathematics , biology
Flexibility analysis and robust optimization are two approaches to solving optimization problems under uncertainty that share some fundamental concepts, such as the use of polyhedral uncertainty sets and the worst‐case approach to guarantee feasibility. The connection between these two approaches has not been sufficiently acknowledged and examined in the literature. In this context, the contributions of this work are fourfold: (1) a comparison between flexibility analysis and robust optimization from a historical perspective is presented; (2) for linear systems, new formulations for the three classical flexibility analysis problems—flexibility test, flexibility index, and design under uncertainty—based on duality theory and the affinely adjustable robust optimization (AARO) approach are proposed; (3) the AARO approach is shown to be generally more restrictive such that it may lead to overly conservative solutions; (4) numerical examples show the improved computational performance from the proposed formulations compared to the traditional flexibility analysis models. © 2016 American Institute of Chemical Engineers AIChE J , 62: 3109–3123, 2016