We consider a large-scale multi-depot multi-commodity Inventory Routing Problem (IRP) to model the packaging return logistics of a major European car manufacturer. No algorithm is known to properly scale to our context. We propose a Large Neighborhood Search (LNS) based on common routing neighborhoods and two new ones: the reinsertion of a customer and a commodity in the IRP solution. We also try to bypass the heavy computations of the LNS leveraging recent ideas in Machine Learning for Operations Research in structured prediction.
In large railway networks, real-time traffic management is essential to minimize disruptions and maximize punctuality. We propose a novel approach to tackle the Multi-Agent Path Finding problem, using the AIcrowd Flatland challenge as a testing ground. By leveraging machine learning inside simple combinatorial procedures such as prioritized planning, we provide a principled way to make better heuristic decisions and anticipate delay propagation.
High-dimensional time series are a core ingredient of the statistical modeling toolkit, for which numerous estimation methods are known. But when observations are scarce or corrupted, the learning task becomes much harder. The question is: how much harder? In this paper, we study the properties of a partially-observed Vector AutoRegressive process, which is a state-space model endowed with a stochastic observation mechanism. Our goal is to estimate its sparse transition matrix, but we only have access to a small and noisy subsample of the state components. Interestingly, the sampling process itself is random and can exhibit temporal correlations, a feature shared by many realistic data acquisition scenarios. We start by describing an estimator based on the Yule-Walker equation and the Dantzig selector, and we give an upper bound on its non-asymptotic error. Then, we provide a matching minimax lower bound, thus proving near-optimality of our estimator. The convergence rate we obtain sheds light on the role of several key parameters such as the sampling ratio, the amount of noise and the number of non-zero coefficients in the transition matrix. These theoretical findings are commented and illustrated by numerical experiments on simulated data.
@unpublished{dalleMinimaxEstimationPartiallyObserved2022,title={Minimax {{Estimation}} of {{Partially-Observed Vector AutoRegressions}}},author={Dalle, Guillaume and De Castro, Yohann},date={2022-05-05},number={arXiv:2106.09327},eprint={2106.09327},eprinttype={arxiv},primaryclass={eess, math, stat},publisher={{arXiv}},doi={10.48550/arXiv.2106.09327},url={http://arxiv.org/abs/2106.09327},abbr={Talk},archiveprefix={arXiv},bibtex_show={true},html={https://easychair.org/publications/preprint/9CGf},selected={true}}
Understanding and predicting delays is a central task for any railway system, but it is made much more difficult by interactions between trains. We propose a new model for the delay propagation phenomenon, which takes into account infrastructure constraints without assuming knowledge of the resource conflicts linking trains with one another. Our approach relies on a set of hidden variables called the network jam, structured as a Dynamic Bayesian Network to enable spatial propagation. We also present a statistical analysis of the minimax estimation error, a variational inference method and numerical tests on simulated and real data.
The invention relates to a method for determining a soiling speed of a photovoltaic generation unit, in which, on the basis of values of an electrical variable generated by the photovoltaic generation unit at a plurality of moments in a time series and corresponding values of meteorological parameters, and on the basis of a relationship between an electrical variable generated by said generation unit at one moment, the values taken with the meteorological parameters at the same moment, and the occurrence of cleaning events, wherein said relationship comprises multiple relational parameters including the speed of soiling and the occurrence of a cleaning event is modelled by a probability law involving a relational parameter, the soiling speed is determined in iterations in which vectors that are representative of the occurrence of cleaning events are simulated.
@patent{stephanMethodDeterminingSoiling2020,type={patent},title={Method for Determining a Soiling Speed of a Photovoltaic Generation Unit},author={Stephan, Pierre and Dalle, Guillaume},holder={{Electricite De France}},date={2020-06-11},number={WO2020115431A1},location={{WO}},url={https://patents.google.com/patent/WO2020115431A1/en},abbr={Patent},bibtex_show={true},html={https://patents.google.com/patent/WO2020115431A1/en}}
Train delays are a frequent feature of many large railway networks. Anticipating their consequences requires real-time delay prediction systems, which can be deployed to assist passenger information or traffic regulation. A major challenge for delay prediction is the amount of interactions between trains: since they must share the same resources, one train’s delay can affect many others by blocking the track or monopolizing a driver. Working on a dataset of recorded event times provided by the French railway company SNCF, we construct a delay propagation model that exploits the limited information available. Identifying infrastructure constraints as the main interaction vector leads to the definition of a hidden "network delay", which expresses the amount of congestion on the network’s edges. Its probabilistic evolution is structured as a Dynamic Bayesian Network. To learn parameters and predict future delays, we use Stochastic Variational Inference, as implemented in the Pyro library. We first analyze our model from a theoretical point of view, giving a lower bound on the minimax estimation risk. We then perform numerical tests, both on a simulated dataset and on actual event logs from the Paris suburban network. While these tests do underline the limitations of our approach, they also show that delay propagation deserves to be taken into account when designing a delay prediction system.
A new method is introduced to predict train delays on a suburban railway network. Delay propagation is accounted for using a Dynamic Bayesian Network related to the underlying infrastructure graph. We analyze a simplified model from a statistical point of view, and obtain a lower bound on the minimax estimation risk. We propose a generic implementation using Stochastic Variational Inference and the Pyro library to separate estimation from modeling. We present numerical tests on both simulated data and real event logs from the Paris RER network.
@unpublished{dalleDelayPropagationSuburban2019a,title={Delay Propagation on a Suburban Railway Network},author={Dalle, Guillaume and De Castro, Yohann and Parmentier, Axel},date={2019-12-04},url={https://www.easychair.org/smart-program/PGMODAYS2019/2019-12-04.html#talk:136943},abbr={Talk},bibtex_show={true},eventtitle={{{PGMO Days}}},html={https://www.easychair.org/smart-program/PGMODAYS2019/2019-12-04.html\#talk:136943},venue={{Saclay, France}}}