arXiv subjects

Adrien Spagnol

Publications and source records attributed to Adrien Spagnol.

4 recordsLinked to original sources

arXiv2024

Robust Stochastic Optimal Control via variance penalization: Application to Energy Management Systems

This paper addresses a class of robust stochastic optimal control problems. Its main contribution lies in the introduction of a general optimization model with variance penalization and an associated solution algorithm that improves out-of-sample robustness while preserving numerical complexity. The proposed variance-penalized model is inspired by a well-established machine learning practice that aims to limit overfitting and extends this idea to stochastic optimal control. Using the Douglas--Rachford splitting method, the authors develop a Variance-Penalized Progressive Hedging Algorithm (VPPHA) that retains the computational complexity of the standard PHA while achieving superior out-of-sample performance. In addition, the authors propose a three-step control framework comprising (i) a random scenario generation method, (ii) a scenario reduction algorithm, and (iii) a scenario-based optimal control computation using the VPPHA. Finally, the proposed method is validated through simulations of a stationary battery Energy Management System (EMS) using ground-truth electricity consumption and production measurements from a predominantly commercial building in Solaize, France. The results demonstrate that the proposed approach outperforms a classical Model Predictive Control (MPC) strategy, which itself performs better than the standard PHA.

math.OC↗

arXiv2023

Sensitivity analysis for sets : application to pollutant concentration maps

In the context of air quality control, our objective is to quantify the impact of uncertain inputs such as meteorological conditions and traffic parameters on pollutant dispersion maps. It is worth noting that the majority of sensitivity analysis methods are designed to deal with scalar or vector outputs and are ill suited to a map-valued output space. To address this, we propose two classes of methods. The first technique focuses on pointwise indices. Sobol indices are calculated for each position on the map to obtain Sobol index maps. Additionally, aggregated Sobol indices are calculated. Another approach treats the maps as sets and proposes a sensitivity analysis of a set-valued output with three different types of sensitivity indices. The first ones are inspired by Sobol indices but are adapted to sets based on the theory of random sets. The second ones adapt universal indices defined for a general metric output space. The last set indices use kernel-based sensitivity indices adapted to sets. The proposed methodologies are implemented to carry out an uncertainty analysis for time-averaged concentration maps of pollutants in an urban environment in the Greater Paris area. This entails taking into account uncertain meteorological aspects, such as incoming wind speed and direction, and uncertain traffic factors, such as injected traffic volume, percentage of diesel vehicles, and speed limits on the road network.

math.OC↗

arXiv2023

Kernel-based sensitivity analysis for (excursion) sets

In this paper, we aim to perform sensitivity analysis of set-valued models and, in particular, to quantify the impact of uncertain inputs on feasible sets, which are key elements in solving a robust optimization problem under constraints. While most sensitivity analysis methods deal with scalar outputs, this paper introduces a novel approach for performing sensitivity analysis with set-valued outputs. Our innovative methodology is designed for excursion sets, but is versatile enough to be applied to set-valued simulators, including those found in viability fields, or when working with maps like pollutant concentration maps or flood zone maps. We propose to use the Hilbert-Schmidt Independence Criterion (HSIC) with a kernel designed for set-valued outputs. After proposing a probabilistic framework for random sets, a first contribution is the proof that this kernel is characteristic, an essential property in a kernel-based sensitivity analysis context. To measure the contribution of each input, we then propose to use HSIC-ANOVA indices. With these indices, we can identify which inputs should be neglected (screening) and we can rank the others according to their influence (ranking). The estimation of these indices is also adapted to the set-valued outputs. Finally, we test the proposed method on three test cases of excursion sets.

math.ST↗

arXiv2018

Global sensitivity analysis for optimization with variable selection

The optimization of high dimensional functions is a key issue in engineering problems but it frequently comes at a cost that is not acceptable since it usually involves a complex and expensive computer code. Engineers often overcome this limitation by first identifying which parameters drive the most the function variations: non-influential variables are set to a fixed value and the optimization procedure is carried out with the remaining influential variables. Such variable selection is performed through influence measures that are meaningful for regression problems. However it does not account for the specific structure of optimization problems where we would like to identify which variables most lead to constraints satisfaction and low values of the objective function. In this paper, we propose a new sensitivity analysis that accounts for the specific aspects of optimization problems. In particular, we introduce an influence measure based on the Hilbert-Schmidt Independence Criterion to characterize whether a design variable matters to reach low values of the objective function and to satisfy the constraints. This sensitivity measure makes it possible to sort the inputs and reduce the problem dimension. We compare a random and a greedy strategies to set the values of the non-influential variables before conducting a local optimization. Applications to several test-cases show that this variable selection and the greedy strategy significantly reduce the number of function evaluations at a limited cost in terms of solution performance.

stat.ML↗