Design of experiments for mixed continuous and discrete variables

Thi Thoi Tran (1, 2) , Sébastien da Veiga (3) , Delphine Sinoquet (1) , Marcel Mongeau (2, 4)

1 IFPEN - IFP Energies nouvelles
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 Safran Tech
4 ENAC - Ecole Nationale de l'Aviation Civile

Design of experiments (DoE) are used in various contexts such as optimization or uncertainty quantification when relying on a time-consuming numerical simulator. It aims to select a limited number of points at which evaluating the simulator provides maximal knowledge on the simulator outputs of interest. One motivating application is the optimal design of turbine blades in an helicopter engine, which takes as inputs mixed continuous and binary variables. This paper proposes two new approaches for space-filling design over the mixed continuous and discrete space. Numerical results for three different types of DoE problems (mixed integers, mixed binaries with cyclic symmetry, and time series) are presented. The obtained results illustrate the good performance of the proposed methods and the wide range of applications they can address.

Keywords: Design of experiments; space-filling designs; necklace distance; mixed continuous and discrete variables; super-sample kernel herding; reproducing kernel Hilbert spaces (RKHS); global alignment kernels

Domains: Statistics [math.ST]; Optimization and Control [math.OC]; Machine Learning [stat.ML]

Thi Thoi Tran, Sébastien da Veiga, Delphine Sinoquet, Marcel Mongeau. Design of experiments for mixed continuous and discrete variables. 2022. ⟨hal-03561149⟩