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Journal of Global Optimization

, Volume 70, Issue 4, pp 811–842 | Cite as

A Utility Theory Based Interactive Approach to Robustness in Linear Optimization

  • Mehdi Karimi
  • Somayeh Moazeni
  • Levent Tunçel
Article

Abstract

We treat uncertain linear programming problems by utilizing the notion of weighted analytic centers and notions from the area of multi-criteria decision making. After introducing our approach, we develop interactive cutting-plane algorithms for robust optimization, based on concave and quasi-concave utility functions. In addition to practical advantages, due to the flexibility of our approach, we prove that under a theoretical framework proposed by Bertsimas and Sim (Oper Res 52:35–53, 2004), which establishes the existence of certain convex formulation of robust optimization problems, the robust optimal solutions generated by our algorithms are at least as desirable to the decision maker as any solution generated by many other robust optimization algorithms in the theoretical framework. We present some probabilistic bounds for feasibility of robust solutions and evaluate our approach by means of computational experiments.

Keywords

Linear optimization Uncertainty in data Robust optimization Cutting-plane algorithms Weighted analytic centers Interactive decision making 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.School of Business, Stevens Institute of TechnologyHobokenUSA
  3. 3.Department of Combinatorics and Optimization, Faculty of MathematicsUniversity of WaterlooWaterlooCanada

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