On the relation between flexibility analysis and robust optimization for linear systems

Qi Zhang, Ignacio E. Grossmann, Ricardo M. Lima

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3109-3123
Number of pages15
JournalAIChE Journal
Issue number9
StatePublished - Sep 2016
Externally publishedYes

Bibliographical note

Funding Information:
The authors gratefully acknowledge the financial support from the National Science Foundation under Grant No. 1159443.

Publisher Copyright:
© 2016 American Institute of Chemical Engineers


  • flexibility analysis
  • optimization under uncertainty
  • robust optimization


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