10:30 AM - 10:55 AM
Parameter tuning: Runge-Kutta case study
The Runge-Kutta class of iterative methods is designed to approximate solutions of a system of ordinary differential equations (ODE). The second-order class of Runge-Kutta methods is determined by a system of 3 nonlinear equations and 4 unknowns, and includes the modified-Euler and mid-point methods. The fourth-order 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 Runge-Kutta method on a training set of ODE. Numerical experiments are conducted using the Nomad direct-search optimization solver.
10:55 AM - 11:20 AM
Order-based error for managing ensembles of surrogates in derivative-free optimization
We investigate surrogate-assisted strategies for derivative-free 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 order-based error tailored to surrogate-based 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 order-based metrics improves performance.
11:20 AM - 11:45 AM
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.
11:45 AM - 12:10 PM
A new variable selection strategy for the parallel space decomposition in derivative-free optimization.
The current parallel space decomposition of the Mesh Adaptive Direct Search algorithm (PSD-MADS) 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.