Offre en lien avec l’Action/le Réseau : – — –/Doctorants

Laboratoire/Entreprise : EDF labs / Mines St-Etienne
Durée : 3 ans
Contact : leriche@emse.fr
Date limite de publication : 2021-06-15

Contexte :
The design of complex industrial systems such as wind turbines or solar power plants can be formulated as an optimization problem where some of the variables are continuous while others are discrete. Moreover, the objective function is costly in the sense that it involves the use of computationally intensive codes. Such problems are also frequent in machine learning: the optimization problem is inherent to the training of a neural network, the discrete variables describe the architecture of the network while the weights of the network and other hyper-parameters are continuous.
To tackle the cost issue in the optimization problem, it is customary to use a metamodel, i.e., optimize a running model of the true (costly) function.

Sujet :
The main ambition of the thesis is to propose the most generic solution possible to the problem of costly mixed optimization, overcoming in particular the following difficulties:

Combinatorial explosion and computational cost: the presence of discrete variables (ordinal or nominal) in the absence of any notion of convexity leads to a number of possible combinations for the discrete variables that increases exponentially with the search space dimension. This is particularly problematic when the associated problem functions (objectives and constraints) are costly to evaluate. The development of Gaussian process surrogate models and strategies for refining numerical designs of experiments adapted to mixed variables seems at present a very promising prospect ;

Genericity: Mixed optimization problems have long been studied by the operations research community, and have led to the creation of a large number of specialized approaches, adapted to various cases. The emergence of mixed surrogate models and adapted refining criteria enables the possibility of developing more generic methods. The demonstration of this genericity requires in particular the possibility of testing the new methods on different industrial applications; this is why four main test cases, coming from different industrial sectors, are considered for this thesis: design of a wind power plant, a turbo-machine, and offshore wind turbine floats, as well as the dimensioning of an electrical network.

Profil du candidat :
Good knwoledge of the foundations of statistical learning and optimization
Ease in scientific programming, with a good knowledge of R, Python.

Formation et compétences requises :
Student with a master degree or equivalent in probability/statistics/operational research.

Adresse d’emploi :
Either Paris Ile-de-France or St-Etienne.

Document attaché : 202101181338_phd_EMSE-EDF_metamodeling_optim_mixed_var.pdf