4 Presentations

• 
  10:30 AM - 10:55 AM

  A graph-structured distance for heterogeneous datasets with meta variables

  • Edward Hallé-Hannan, presenter, Polytechnique
  • Charles Audet, GERAD - Polytechnique Montréal
  • Sébastien Le Digabel, GERAD, Polytechnique Montréal
  • Youssef Diouane, Polytechnique Montréal

  Heterogeneous datasets emerge in various machine learning or optimization applications that feature different data sources, various data types and complex interrelationships between variables. In practice, heterogeneous datasets are often partitioned into smaller well-behaved ones that are easier to process. However, some applications involve expensive-to-generate or limited size datasets, which motivates methods that utilize heterogeneous datasets in their entirety. This last remark is particularly important for blackbox (or simulation-based) optimization that tackles objective functions and constraints that may require hours, or even days, to evaluate. The first main contribution of this work is a modelling graph-structured framework that generalizes state-of-the-art hierarchical, tree-structured, or variable-size frameworks. This framework models domains that involve heterogeneous datasets in which variables may be continuous, integer, or categorical, with some identified as meta if their values determine the inclusion/exclusion or affect constraints of other so-called decreed variables. Excluded variables are introduced to manage variables that are included in some points, but excluded in others. The second main contribution is the graph-structured distance that compares extended points with any combination of included and excluded variables: any pair of points can be compared, allowing to work directly in heterogeneous datasets with meta variables. The contributions are illustrated with some regression experiments, in which the performance of a multilayer perceptron w.r.t. to its hyperparameters is modeled with inverse distance weighting and K-nearest neighbors models.

• 
  10:55 AM - 11:20 AM

  Parallel versions of the mesh adaptive direct search algorithm

  • Samuel Mendoza, presenter, Polytechnique Montréal
  • Sébastien Le Digabel, GERAD, Polytechnique Montréal
  • Antoine Lesage-Landry, Polytechnique Montréal

  This presentation surveys the different parallel variants of the mesh adaptive direct search (mads) algorithm for constrained blackbox optimization. These problems can inherently imply high computational costs due to the possible large number of variables and multi-modality of the search space. In addition, the potential time-intensive nature and time heterogeneity of the blackboxes defining the problem prompts the need for efficient implementations. With the increasing use of high-performance computing, parallelism emerges as a actionable solution to mitigate computation time. The reviewed methods employ diverse levels of parallelism and distinct parallel strategies to effectively tackle each aspect outlined above. The presentation details the practical implementations, provides computational results, and offers insights into the advantages and limitations of each mads parallel method.

• 
  11:20 AM - 11:45 AM

  Adapting the DMulti-MADS algorithm to mixed-integer multiobjective derivative-free optimization

  • Ludovic Salomon, presenter, Polytechnique Montreal
  • Christophe Tribes, Polytechnique Montreal
  • Sébastien Le Digabel, GERAD, Polytechnique Montréal

  The DMulti-MADS method is an extension of the Mesh Adaptive Direct Search (MADS) algorithm for multiobjective derivative-free optimization. It is convergence-based and at the same time has shown good experimental performance. DMulti-MADS was originally designed for continuous variables only. However, many "real-world" engineering applications also have integer variables that need to be considered. In this talk, we describe a simple adaptation of the DMulti-MADS algorithm to consider both continuous and integer variables. Numerical experiments on artificial benchmarks and real-world problems are performed against state-of-the-art algorithms.

• 
  11:45 AM - 12:10 PM

  Optimizing a cellular solid compression problem via the NOMAD blackbox optimizer

  • Paul Patience, presenter, Polytechnique Montréal
  • Charles Audet, GERAD - Polytechnique Montréal
  • Bruno Blais, Polytechnique Montréal

  Cellular solids are porous materials used in sandwich panels, heat
  exchangers, tissue engineering scaffolds and catalysts.
  Advances in additive manufacturing have permitted the production of
  triply periodic minimal surface (TPMS)–like cellular solids, which have
  properties uniquely suited to these applications and have thus been the
  focus of recent research.
  Alas, the field of cellular solid design trails behind that of
  mathematical optimization — much of the literature relies on variants of
  grid search.
  We are the first to apply the MADS blackbox optimization algorithm, as
  implemented by the NOMAD optimizer, to cellular solid design.
  We have developed a cellular solid generator suitable for use as input
  to NOMAD, and a blackbox mimicking a problem in the literature
  consisting of the compression of a block composed of a cellular solid,
  with the goal of maximizing the cellular solid's relative Young's
  modulus.
  We will present the cellular solid generator as well as the results we
  obtained from applying NOMAD to the compression problem and a comparison
  with those from the literature.
  It is our hope that this will pave the way for researchers in cellular
  solid design to employ more advanced methods of mathematical
  optimization.