EURO 2024 Copenhagen
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670. A Quantile Neural Network Framework for Two-stage Stochastic Optimization: Application to Power Systems Operation

Invited abstract in session MA-19: Learning-assisted Optimization in Energy Problems, stream OR in Energy.

Monday, 8:30-10:00
Room: 44 (building: 116)

Authors (first author is the speaker)

1. Antonio Alcántara
Statistics, University Carlos III
2. Carlos Ruiz
Universidad Carlos III de Madrid
3. Calvin Tsay
Department of Computing, Imperial College London

Abstract

Two-stage stochastic programming is a popular framework for optimization under uncertainty, where decision variables are split between first-stage decisions, and second-stage (or recourse) decisions, where the latter can be adjusted after uncertainty is realized. These problems are often formulated using Sample Average Approximation (SAA), where uncertainty is modeled as a finite set of scenarios, resulting in a large deterministic problem, i.e., where the model is repeated for each scenario. The resulting problems can be challenging to solve, and several decomposition approaches have been proposed. More recently, Patel et al. (2022) approximated the expected second-stage objective value for a set of scenarios using a neural network, which can then be embedded in the first-stage problem to produce good heuristic solutions. In this work, we propose approximating the second-stage objective value with a quantile neural network, which can capture uncertainty and is not limited to expected-value optimization, e.g., to optimize the Conditional Value at Risk (CVaR). We discuss optimization formulations for embedding the quantile neural network and demonstrate the effectiveness of the proposed framework using several computational case studies including mixed-integer and nonlinear problems. Particularly, we test this novel methodology in relevant power systems’ operation problems with high renewable energy penetration.

Keywords

Status: accepted

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