CAP Research Roulette
Seminars run by PhD students and postdocs with the Control and Power Group
Every week, an invited speaker gives a talk on a relevant topic (preferably in control and power) consisting of a 20-minute presentation followed by a 10-minute discussion. The content of talks can be
- conference contributions,
- initial research proposals,
- preparation for Early Stage Assessment/Late Stage Review, or
- tutorials on topics of the speaker's expertise.
After the talk, the participants can enjoy coffee and snacks (funded by the group) together in the Faraday Cage on EEE Level 6 and continue the discussion.
The CAP Research Roulette is open to everyone in the Control and Power Group. MSc students from Control Systems and Future Power Network Courses, who are willing to continue pursuing an academic career, are also strongly encouraged to participate.
Talk of the week
Title: A hybrid SDDP Machine Learning approach to represent non-convexities in the hydrothermal operation problem
Speaker: Joaquim Garcia
Venue: EEE 1109B
Date and Time: Friday 26/07/2019 15:00-16:00
Abstract: The Stochastic Dual Dynamic Programming (SDDP) algorithm allows to uncouple in time the multistage stochastic operation of hydrothermal systems. In this framework, any stage’s future cost of the operation, conditioned the decision of the current stage, can be approximated by means of hyperplane constructed iteratively in the backward phase of the algorithm. If the future cost (cost to-go) function is convex in relation to the state variables, the approximation determined by this hyperplane is guaranteed a lower bound for the real future cost function and the algorithm it is guaranteed to converge to the optimal solution, under mild conditions. However, if the future cost function is not convex, the optimality of the algorithm cannot be guaranteed.
The treatment of non-convexities of the future cost function in the SDDP algorithm is a recurrent theme in the literature. In this work, a new alternative based on machine learning is proposed: we apply support vector machine (SVM) as a classification approach to recognize and delimit the validity regions of the hyperplanes generated by the SDDP algorithm. This allows the algorithm for stochastic dynamic operation to evaluate solutions that were not feasible, considering only the convex envelope constructed by the original cuts.
The SVM method is well suited for the classification of cuts employed, because of its robustness to solve large problems, which is something desired in the scope of this proposal, given the real dimensions of the problem of operation of hydrothermal systems. Moreover, the ability of the method to do classification even when classes are not linearly separable and the fact that the classification function is differentiable are key requirement for the proposed algorithm. Finally, the model selection step (optimization of SVM model hyperparameters) is fully parallelizable, just like many steps in the SDDP algorithm.
The classification of cuts employed and the proposed algorithm also do not guarantee the optimality of the solution, since they do not necessarily construct lower bounds for the nonconvex future cost functions. However, the results of the application of the method demonstrate that this approach is able to better approximate of these functions, making possible to obtain better solutions to the hydrothermal system operation problem.
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