Static robust optimization

Preventive decision making

Static robust optimization involves the use of uncertainty sets to model the possible variations in problem parameters. By formulating optimization models that consider the worst-case scenario within these uncertainty sets, static robust optimization provides solutions that are robust against parameter variations. We investigated various uncertainty sets and their connection to probabilistic guarantees, derived robust optimization formulations for different types of optimization models and presented numerical comparisons and real-world applications. Additionally, we studied the construction of uncertainty sets using polyhedral norms and emphasized the importance of integrating data and distributional information for better solutions.

Relevant publications:

S. Rahal, Z. Li Norm Induced Polyhedral Uncertainty Sets for Robust Linear Optimization. Optimization and Engineering. 2022, 23, 1765.

Y. Yuan, Z. Li, B. Huang. Nonlinear Robust Optimization for Process Design. AIChE Journal. 2018, 64, 481-494.

Y. Yuan, Z. Li, B. Huang. Robust optimization under correlated uncertainty: Formulations and computational study. Computers & Chemical Engineering. 2016, 85, 58-71.

Z. Li, C.A. Floudas. A comparative theoretical and computational study on robust counterpart optimization: III. Improving the Quality of Robust Solutions. Industrial & Engineering Chemistry Research. 2014, 53, 13112-13124.

Z. Li, Q. Tang, C.A. Floudas. A comparative theoretical and computational study on robust counterpart optimization: II. Probabilistic guarantees on constraint satisfaction. Industrial & Engineering Chemistry Research. 2012, 51, 6769-6788.

Z. Li, R. Ding, C.A. Floudas. A comparative theoretical and computational study on robust counterpart optimization: I. Robust linear optimization and robust mixed integer linear optimization. Industrial & Engineering Chemistry Research, 2011, 50, 10567-10603.