10h30 - 10h55
Formulations for Surrogate-Based Constrained Blackbox Optimization
This presentation introduces different ways of using statistical surrogate tools within the Mesh Adaptive Direct Search (MADS) framework for constrained blackbox optimization. The surrogates that we consider are global models, providing capabilities for diversification in order to escape local optima. In addition, we focus on different formulations of the subproblem that is considered at each search step of MADS, and in practice, the dynaTree package is used. The formulations exploit different tools such as interpolation, classification, expected improvement and feasible expected improvement. Numerical examples are presented both on academic problems and on realistic applications.
10h55 - 11h20
The Mesh Adaptive Direct Search Algorithm for Blackbox Optimization with Linear Equalities
The Mesh Adaptive Direct Search (MADS) algorithm is designed to solve blackbox optimization problems under general inequality constraints. Currently, MADS does not support equality constraints, both in theory and practice. The present work proposes extensions to solve problems with linear equality constraints. The main idea consists in reformulating the optimization problem into an equivalent one without equality constraints, with possibly fewer optimization variables. Our reformulations involve orthogonal projections, QR and SVD decompositions as well as Simplex decompositions into basic and nonbasic variables. All of our proposed strategies are studied in a unified convergence analysis, guaranteeing Clarke stationarity under mild conditions. Numerical results on a subset of CUTEr collection are reported.
11h20 - 11h45
Robust Optimization of Noisy Blackbox Problems using the Mesh Adaptive Direct Search algorithm.
Mesh adaptive direct search (MADS) is an algorithm designed to solve blackbox optimization problems where the objective function typically corresponds to a computer simulation. In this talk, we are interested in problems contaminated with stochastic noise, as often observed in practice. We propose a smoothing technique for the elimination of noise, directly incorporated within the MADS framework. The objective of this new method is to obtain a solution that is stable relative to small perturbations in the solution space, as commonly desired by engineers. Numerical results illustrate the efficiency of this approach.