Restricting ambitions in global multi-objective optimization of costly functions

David Gaudrie (1, 2, 3, 4) , Rodolphe Le Riche (1, 2, 3, 4, 5) , Victor Picheny (6) , Benoît Enaux (7) , Vincent Helbert

1 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
2 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
3 FAYOL-ENSMSE - Institut Henri Fayol
4 FAYOL-ENSMSE - Département Génie mathématique et industriel
5 CNRS - Centre National de la Recherche Scientifique
6 INRA - Institut National de la Recherche Agronomique
7 PSA Peugeot Citroën

In the context of the multi-objective optimization of costly functions, it may only be possible to find specific parts of the Pareto front even with Bayesian algorithms. In this talk, we introduce a Bayesian criterion for targeted multi-objective optimization that is related to but computationally cheaper than the Expected Hypercube Improvement (EHI). We also define the Pareto front center and discuss its properties and its estimation. Finally, we propose the Centered-EHI algorithm that adapts the size of the searched Pareto region to the computational resources. These slides are a seminar version of the preprint arXiv:1809.10482 .

Mots clés: Optimization methodology; Bayesian optimization; Multiobjective Optimization; Gaussian process regression

Domaines: Optimisation et contrôle [math.OC]; Ingénierie, finance et science [cs.CE]; Génie mécanique [physics.class-ph]

David Gaudrie, Rodolphe Le Riche, Victor Picheny, Benoît Enaux, Vincent Helbert. Restricting ambitions in global multi-objective optimization of costly functions. Seminar at the ONERA: DMS/DTIS (ARF STOCHASTIQUE), Dec 2018, Châtillon, France. ⟨hal-01946450⟩