Optimisation de fonctions coûteuses Modèles gaussiens pour une utilisation efficace du budget d'évaluations : théorie et pratique industrielle

This dissertation is driven by a question central to many industrial optimization problems : how to optimize a function when the budget for its evaluation is severely limited by either time or cost ? For example, when optimization relies on computer simulations, each taking several hours, the dimension and complexity of the optimization problem may seem irreconcilable with the evaluation budget (typically thirty parameters to be optimized with less than one hundred evaluations). This work is devoted to optimization algorithms dedicated to this context, which is out of range for most classical methods. The common principle of the methods discussed is to use Gaussian processes and Kriging to build a cheap proxy for the function to be optimized. This approximation is then used iteratively to choose the evaluation points. This choice is guided by a sampling criterion which combines local search, near promising evaluation results, and global search, in unexplored areas. Most of the criteria proposed over the years, such as the one underlying the classical EGO (for Efficient Global Optimization) algorithm, sample where the optimum is most likely to appear. By contrast, we propose an algorithm, named IAGO for Informational Approach to Global Optimization, which samples where the information gain on the optimizer location is deemed to be highest. The organisation of this dissertation is a direct consequence of the industrial concerns which drove this work. We hope it can be of use to the optimization community, but most of all to practitioners confronted with expensive-toevaluate functions. This is why we insist on the practical use of IAGO for the optimization of functions encountered in actual industrial problems. We also discuss how to handle constraints, noisy evaluation results, multi-objective problems, derivative evaluation results, or significant manufacturing uncertainties. ; Cette thèse traite d'une question centrale dans de nombreux problèmes d'optimisation, en particulier en ingénierie. Comment optimiser une ...