Invited Session Tue.3.MA 004

Tuesday, 15:15 - 16:45 h, Room: MA 004

Cluster 20: Robust optimization [...]

Applications of robust optimization II


Chair: Allison Kelly O'Hair



Tuesday, 15:15 - 15:40 h, Room: MA 004, Talk 1

Allison Kelly O'Hair
Adaptive, dynamic and robust optimization to learn human preferences

Coauthor: Dimitris Bertsimas


In 1944, in one of the most influential works of the twentieth century, John von Neumann and Oskar Morgenstern developed the idea of expected utility theory to make decisions under uncertainty. In 1979, Daniel Kahneman and Amos Tversky, in their Nobel prize winning work, presented a critique of expected utility theory by observing that some of its axioms violate human behavior. Specifically, people are loss averse, are inconsistent and evaluate outcomes with respect to deviations from a reference point. However, they did not propose a constructive method to learn preferences that adhere to the new principles. In this work, we use robust and integer optimization in an adaptive and dynamic way to determine preferences that are consistent with human behavior in agreement with the critique of Kahneman and Tversky. We use robust linear optimization to model loss averse behavior, integer optimization to correct for inconsistent behavior and choice-based conjoint analysis in an adaptive questionnaire to dynamically select pairwise questions. We have implemented an online software that uses the proposed approach and report empirical evidence of its strength.



Tuesday, 15:45 - 16:10 h, Room: MA 004, Talk 2

Andy Sun
Adaptive robust optimization for the security constrained unit commitment problem

Coauthors: Dimitris Bertsimas, Eugene Litvinov, Jinye Zhao, Tongxin Zheng


Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet these challenges, we propose a two-stage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty. Compared to the conventional stochastic programming approach, the proposed model is more practical in that it only requires a deterministic uncertainty set, rather than a hard-to-obtain probability distribution on the uncertain data. The unit commitment solutions of the proposed model are robust against all possible realizations of the modeled uncertainty. We develop a practical solution methodology based on a combination of Benders decomposition type algorithm and the outer approximation technique. We present an extensive numerical study on the real-world large scale power system operated by the ISO New England, which demonstrates the economic and operational advantages of our model over the current practice.



Tuesday, 16:15 - 16:40 h, Room: MA 004, Talk 3

Nathan Kallus
The power of optimization over randomization in designing controlled trials

Coauthors: Dimitris Bertsimas, Mac A. Johnson


The purpose of a controlled trial is to compare the effects of a proposed drug and a null treatment. Random assignment has long been the standard and aims to make groups statistically equivalent before treatment. By the law of large numbers, as the sample grows, randomized groups grow similar almost surely. However, with a small sample, which is practical reality in many disciplines, randomized groups are often too dissimilar to be useful for any inference at all. To remedy this situation, investigators faced with difficult or expensive sampling usually employ specious assignment schemes to achieve better-matched groups, and without theoretical motivation they then employ probabilistic significance tests, whose validity is questionable. Supplanting probabilistic hypothesis testing with a new theory based on robust optimization, we propose a method we call robust hypothesis testing that assigns subjects optimally and allows for mathematically rigorous inference that does not use probability theory and which is notable for allowing inference with small samples. We provide empirical evidence that suggests that optimization leads to significant advantages over randomization.


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