2022 Optimization Days
HEC Montréal, Québec, Canada, 16 — 18 May 2022
WC8 - Derivative-free and Blackbox Optimization VI
May 18, 2022 03:30 PM – 05:10 PM
Location: METRO INC. (yellow)
Chaired by Stéphane Alarie
03:30 PM - 03:55 PM
Escaping unknown discontinuous regions in blackbox optimization
We study constrained blackbox optimization problems involving discontinuities whose positions are not known apriori. We propose a MADS algorithm, called DiscoMads, revealing and escaping these regions progressively. A convergence analysis supports the algorithm and numerical tests are conducted on analytical and engineering problems, among which a mechanical engineering problem related to the vibration of aircraft engine blades.
03:55 PM - 04:20 PM
Constrained stochastic blackbox optimization using a progressive barrier and probabilistic estimates
This work introduces StoMADS-PB, a direct-search method using a progressive barrier approach for constrained stochastic blackbox optimization. The values of the objective and constraint functions can only be computed with random noise whose distribution is unknown. Since the deterministic computable version of the blackbox is unavailable, StoMADS-PB uses estimates and introduces probabilistic bounds (for its constraint violation function), required to be accurate and reliable with high, but fixed, probabilities. Using Clarke calculus and martingale theory, Clarke stationarity convergence results for the objective and the violation function are derived with probability one.
04:20 PM - 04:45 PM
NOMAD 4: development of a new version of a blackbox optimization solver
NOMAD is an open source optimization software well suited for costly blackbox problems with inequality constraints, non-smooth and noisy design spaces. Derivative free algorithms such as mesh adaptive direct search (MADS) or Nelder Mead are available in NOMAD.
The version 3 of NOMAD is available since 2008 with several major revisions up to the current 3.9 version. However, the design of NOMAD 3 is strongly oriented by MADS and show its limits when maintenance is required or when adding new algorithms or new features. Also, the parallel evaluation capabilities of NOMAD 3 are not adapted to today's computers computational capabilities.
NOMAD 4 has been developed from scratch with a complete new architecture and design.
The presentation will describe the new design and the improvements that allow for better parallel evaluations, easier maintenance and faster addition of new features.
Benchmarking NOMAD 3 and NOMAD 4 on test suites show that the performance is maintained in the new version.
04:45 PM - 05:10 PM
Blackbox optimization with hierarchical constraints
Some complex and expensive blackbox evaluations can be structured as a sequence of constraint verifications. One can then interrupt any evaluation as soon as it appears unfeasible, especially if one already has a feasible solution in hand. By doing so, less time should be needed to solve the problem. Two different approaches are proposed here to define the hierarchical order of the constraints and to manage the interruption of the evaluations throughout the optimization process. Numerical experiments will be presented on a closed-form test problem.