An end-to-end data-driven optimisation framework for constrained trajectories

Florent Dewez (1) , Benjamin Guedj (2, 3, 4, 1, 5, 6, 7, 8) , Arthur Talpaert (1) , Vincent Vandewalle (9, 1, 10)

1 MODAL - MOdel for Data Analysis and Learning
2 UCL - University College of London [London]
3 UCL-CS - Department of Computer science [University College of London]
4 Inria-CWI - Inria-CWI
5 Inria-London - The Inria London Programme
6 Inria - Institut National de Recherche en Informatique et en Automatique
7 Inria Lille - Nord Europe
8 The Alan Turing Institute
9 Université de Lille
10 METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694

Many real-world problems require to optimise trajectories under constraints. Classical approaches are based on optimal control methods but require an exact knowledge of the underlying dynamics, which could be challenging or even out of reach. In this paper, we leverage data-driven approaches to design a new end-to-end framework which is dynamics-free for optimised and realistic trajectories. We first decompose the trajectories on function basis, trading the initial infinite dimension problem on a multivariate functional space for a parameter optimisation problem. A maximum \emph{a posteriori} approach which incorporates information from data is used to obtain a new optimisation problem which is regularised. The penalised term focuses the search on a region centered on data and includes estimated linear constraints in the problem. We apply our data-driven approach to two settings in aeronautics and sailing routes optimisation, yielding commanding results. The developed approach has been implemented in the Python library PyRotor.

Mots clés: Statistical modelling; Functional data; Constrained optimisation Contents

Domaines: Applications [stat.AP]; Apprentissage [cs.LG]; Optimisation et contrôle [math.OC]; Machine Learning [stat.ML]

Florent Dewez, Benjamin Guedj, Arthur Talpaert, Vincent Vandewalle. An end-to-end data-driven optimisation framework for constrained trajectories. Data-Centric Engineering, 2022, 3, pp.e6. ⟨10.1017/dce.2022.6⟩. ⟨hal-03024720⟩