Journées de l'optimisation 2017
HEC Montréal, 810 mai 2017
1^{er} Atelier Canadien sur l'optimisation des soins de santé (CHOW)
HEC Montréal, 1011 mai 2017
JOPT2017
HEC Montréal, 8 — 11 mai 2017
TB2 Optimization sans dérivées / DerivativeFree Optimization
9 mai 2017 10h30 – 12h10
Salle: GérardParizeau
Présidée par Nadir Amaioua
4 présentations

10h30  10h55
Parameter tuning: RungeKutta case study
The RungeKutta class of iterative methods is designed to approximate solutions of a system of ordinary differential equations (ODE). The secondorder class of RungeKutta methods is determined by a system of 3 nonlinear equations and 4 unknowns, and includes the modifiedEuler and midpoint methods. The fourthorder class is determined by a system of 8 nonlinear equations and 10 unknowns. This work formulates the question of identifying good values of these 8 parameters for a given family of ODE as a blackbox optimization problem. The objective is to determine the parameter values that minimize the overall error produced by a RungeKutta method on a training set of ODE. Numerical experiments are conducted using the Nomad directsearch optimization solver.

10h55  11h20
Orderbased error for managing ensembles of surrogates in derivativefree optimization
We investigate surrogateassisted strategies for derivativefree optimization using the mesh adaptive direct search (MADS) blackbox optimization algorithm. In particular, we build an ensemble of surrogate models to be used within the search step of MADS, and examine different methods for selecting the best model for a given problem at hand. To do so, we introduce an orderbased error tailored to surrogatebased search. We report computational experiments for analytical benchmark problems and engineering design applications. Results demonstrate that different metrics may result in different model choices and that the use of orderbased metrics improves performance.

11h20  11h45
Handling infeasibility in blackbox optimization using supervised classification
Blackbox optimization problems, where the objective function and the constraints have unknown analytic expressions, lead to multiple difficulties such as no access to the gradient and long CPU time. Moreover, since the functions can sometimes be given by simulations or experiments, some of the computations can crash and give unreliable results. The MADS is algorithm deals with constrained blackbox optimization problems. Since its introduction in 2006, it has known severals improvements to manage constraints. However, binary constraints are currently managed the same way as the other constraints. Considering the lack of information given by binary constraints, they would benefit from a specific treatment.
That presentation proposes a way to manage binary constraints using tools from supervised classification. Our work includes the case with a single constraint, which will be binary, since it offers a way to manage the case when simulations or experiments crash. 
11h45  12h10
A new variable selection strategy for the parallel space decomposition in derivativefree optimization.
The current parallel space decomposition of the Mesh Adaptive Direct Search algorithm (PSDMADS) is an asynchronous parallel method that uses a simple generic strategy to decompose a problem into smaller dimension subproblems. The present work explores new strategies for selecting the subset of variables defining subproblems to be explored in parallel. These strategies are based on ranking the variables using statistical tools to determine the most influential ones. The statistical approach improves the decomposition of the problem into smaller more relevant subproblems. This work aims to improve the use of available processors.