joint work with Gavin Smith
An important consistency check in aerospace design is to ensure that no two distinct parts occupy the same space. Discretization of geometry models often introduces small interferences not present in the fully detailed model. We focus on the efficient computation of penetration depth between two 3-D convex polytopes, a well-studied computer graphics problem, to distinguish between real interference and discretization error. We reformulate a 5-variable constrained global optimization problem into a 2-variable nonsmooth problem to more easily find global solutions with a direct search method.
joint work with Delphine Sinoquet
Real industrial studies often boils down to complex optimization problems involving mixed variables and time consuming simulators. To deal with these difficulties we propose the use of a Gaussian process regression surrogate with a suitable kernel able to capture simultaneously the output correlations with respect to continuous and categorical/discrete inputs without relaxation of the categorical variables. The surrogate is integrated in the Efficient Global Optimization method based on the maximization of the Expected Improvement criterion. This maximization is a Mixed Integer Non-Linear problem which we tackle with an adequate optimizer : the Mesh Adaptive Direct Search, integrated in the NOMAD library. We introduce a random exploration of the categorical space with a data-based probability distribution and we illustrate the full strategy accuracy on a toy problem. Finally we compare our approach with other optimizers on a benchmark of functions.
joint work with Gabriela Naves Maschietto, Stephane Couturier, Thomas Lecomte, David Mouquet, Vincent Martin
District heating networks (DHN) are a driving force for decarbonization and energy efficiency. A DHN produces thermal energy and delivers it over distribution networks to buildings. We propose a production scheduling optimization tool that considers heat production and distribution. We use mixed-integer nonlinear models where heat-only and cogeneration units are handled. The network dynamics is addressed by a black-box simulation model. We employ RBF models for time series forecasting that replace the black-box function to obtain an approximate solution. Results on a real case study are shown.