Structural and Multidisciplinary Optimization

, Volume 44, Issue 2, pp 259–275 | Cite as

A modified Benders decomposition method for efficient robust optimization under interval uncertainty

  • Sauleh SiddiquiEmail author
  • Shapour Azarm
  • Steven Gabriel
Research Paper


The goal of robust optimization problems is to find an optimal solution that is minimally sensitive to uncertain factors. Uncertain factors can include inputs to the problem such as parameters, decision variables, or both. Given any combination of possible uncertain factors, a solution is said to be robust if it is feasible and the variation in its objective function value is acceptable within a given user-specified range. Previous approaches for general nonlinear robust optimization problems under interval uncertainty involve nested optimization and are not computationally tractable. The overall objective in this paper is to develop an efficient robust optimization method that is scalable and does not contain nested optimization. The proposed method is applied to a variety of numerical and engineering examples to test its applicability. Current results show that the approach is able to numerically obtain a locally optimal robust solution to problems with quasi-convex constraints (≤ type) and an approximate locally optimal robust solution to general nonlinear optimization problems.


Robust optimization Nonlinear optimization Benders decomposition Interval uncertainty Quasi-convex function 



The authors wish to thank Dr. Mian Li and Mr. Amir Mortazavi for their constructive ideas to improve the paper. The work presented in this paper was supported in part by the Office of Naval Research Contract N000140810384. Such support does not constitute an endorsement by the funding agency of the opinions expressed in this paper.


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Sauleh Siddiqui
    • 1
    Email author
  • Shapour Azarm
    • 2
  • Steven Gabriel
    • 3
  1. 1.Department of Applied MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of Mechanical EngineeringUniversity of MarylandCollege ParkUSA
  3. 3.Department of Civil EngineeringUniversity of MarylandCollege ParkUSA

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