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172 results on '"Homem-de-Mello, Tito"'

2. Effective Scenarios in Multistage Distributionally Robust Optimization with a Focus on Total Variation Distance

Author

Rahimian, Hamed, Bayraksan, Guzin, and Homem-de-Mello, Tito

Subjects
Mathematics - Optimization and Control, 90C15, 90C39, 90C47
Abstract

We study multistage distributionally robust optimization (DRO) to hedge against ambiguity in quantifying the underlying uncertainty of a problem. Recognizing that not all the realizations and scenario paths might have an "effect" on the optimal value, we investigate the question of how to define and identify critical scenarios for nested multistage DRO problems. Our analysis extends the work of Rahimian, Bayraksan, and Homem-de-Mello [Math. Program. 173(1--2): 393--430, 2019], which was in the context of a static/two-stage setting, to the multistage setting. To this end, we define the notions of effectiveness of scenario paths and the conditional effectiveness of realizations along a scenario path for a general class of multistage DRO problems. We then propose easy-to-check conditions to identify the effectiveness of scenario paths in the multistage setting when the distributional ambiguity is modeled via the total variation distance. Numerical results show that these notions provide useful insight on the underlying uncertainty of the problem.

Published
2021

4. Application-Driven Learning: A Closed-Loop Prediction and Optimization Approach Applied to Dynamic Reserves and Demand Forecasting

Author

Garcia, Joaquim Dias, Street, Alexandre, Homem-de-Mello, Tito, and Muñoz, Francisco D.

Subjects
Mathematics - Optimization and Control, Computer Science - Machine Learning, Electrical Engineering and Systems Science - Systems and Control, Statistics - Methodology, Statistics - Machine Learning
Abstract

Forecasting and decision-making are generally modeled as two sequential steps with no feedback, following an open-loop approach. In this paper, we present application-driven learning, a new closed-loop framework in which the processes of forecasting and decision-making are merged and co-optimized through a bilevel optimization problem. We present our methodology in a general format and prove that the solution converges to the best estimator in terms of the expected cost of the selected application. Then, we propose two solution methods: an exact method based on the KKT conditions of the second-level problem and a scalable heuristic approach suitable for decomposition methods. The proposed methodology is applied to the relevant problem of defining dynamic reserve requirements and conditional load forecasts, offering an alternative approach to current ad hoc procedures implemented in industry practices. We benchmark our methodology with the standard sequential least-squares forecast and dispatch planning process. We apply the proposed methodology to an illustrative system and to a wide range of instances, from dozens of buses to large-scale realistic systems with thousands of buses. Our results show that the proposed methodology is scalable and yields consistently better performance than the standard open-loop approach.

Published
2021

31. Modeling uncertainty processes in strategic energy planning optimization

Author

Babonneau, Frédéric, Guevara, Esnil, Homem-De-Mello, Tito, and Sciencesconf.org, CCSD

Subjects
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-RO] Computer Science [cs]/Operations Research [cs.RO], Strategic energy planning, Stochastic Dual Dynamic Programming, regressive process, Markov chain, Auto
Abstract

Modeling uncertainty processes in strategic energy planning optimization

Published
2022

48. A study on the cross-entropy method for rare-event probability estimation

Author

Homem-de-Mello, Tito

Subjects
Algorithm, Information theory -- Evaluation -- Methods -- Analysis, Mathematical optimization -- Evaluation -- Methods -- Analysis, Sampling (Sound engineering) -- Methods -- Evaluation -- Analysis, Algorithms -- Analysis -- Methods
Abstract

We discuss the problem of estimating probabilities of rare events in static simulation models using the recently proposed cross-entropy method, which is a type of importance-sampling technique in which the […]

Published
2007

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