A Quick-and-Dirty Approach to Robustness in Linear Optimization

Linear Optimization;Robust Optimization;Weighted Analytic Center;Combinatorics and Optimization

Karimi, Mehdi

University of Waterloo

关键词: Linear Optimization;    Robust Optimization;    Weighted Analytic Center;    Combinatorics and Optimization;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/7178/1/Karimi_Mehdi.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

We introduce methods for dealing with linear programming (LP) problems with uncertain data, using the notion of weighted analytic centers. Our methods are based on high interaction with the decision maker (DM) and try tofind solutions which satisfy most of his/her important criteria/goals. Starting with the drawbacks of different methods for dealing with uncertainty in LP, we explain how our methods improve most of them. We prove that, besides many practical advantages, our approach is theoretically as strong as robust optimization. Interactive cutting-plane algorithms are developed for concave and quasi-concave utility functions. We present some probabilistic bounds for feasibility and evaluate our approach by means of computational experiments.