Charles Audet

A general mathematical framework for constrained mixed-variable blackbox optimization problems with meta and categorical variables

  • Charles Audet
  • Edward Hallé-Hannan
  • Sébastien Le Digabel
    • Categories Nonlinear Optimization Tags , , , ,

    A mathematical framework for modelling constrained mixed-variable optimization problems is presented in a blackbox optimization context. The framework introduces a new notation and allows solution strategies. The notation framework allows meta and categorical variables to be explicitly and efficiently modelled, which facilitates the solution of such problems. The new term meta variables is used to … Read more

    Hierarchically constrained blackbox optimization

  • Stéphane Alarie
  • Charles Audet
  • Paulin Jacquot
  • Sébastien Le Digabel
    • Categories Nonlinear Optimization Tags , ,

    In blackbox optimization, evaluation of the objective and constraint functions is time consuming. In some situations, constraint values may be evaluated independently or sequentially. The present work proposes and compares two strategies to define a hierarchical ordering of the constraints and to interrupt the evaluation process at a trial point when it is detected that … Read more

    The equilateral small octagon of maximal width

  • Christian Bingane
  • Charles Audet
    • Categories Combinatorial Optimization, Global Optimization, Nonlinear Optimization Tags , , ,

    A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with $n=2^s$ vertices is not known when $s \ge 3$. This paper solves the first open case and finds the optimal equilateral small octagon. Its width is approximately $3.24\%$ larger than the width of the regular octagon: $\cos(\pi/8)$. … Read more

    Quantifying uncertainty with ensembles of surrogates for blackbox optimization

  • Charles Audet
  • Sébastien Le Digabel
  • Renaud Saltet
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    This work is in the context of blackbox optimization where the functions defining the problem are expensive to evaluate and where no derivatives are available. A tried and tested technique is to build surrogates of the objective and the constraints in order to conduct the optimization at a cheaper computational cost. This work proposes different … Read more

    Tight bounds on the maximal perimeter of convex equilateral small polygons

  • Christian Bingane
  • Charles Audet
    • Categories Combinatorial Optimization, Global Optimization, Nonlinear Optimization Tags , , ,

    A small polygon is a polygon of unit diameter. The maximal perimeter of a convex equilateral small polygon with $n=2^s$ vertices is not known when $s \ge 4$. In this paper, we construct a family of convex equilateral small $n$-gons, $n=2^s$ and $s \ge 4$, and show that their perimeters are within $\pi^4/n^4 + O(1/n^5)$ … Read more

    NOMAD version 4: Nonlinear optimization with the MADS algorithm

  • Charles Audet
  • Sébastien Le Digabel
  • Viviane Rochon Montplaisir
  • Christophe Tribes
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems Tags , , ,

    NOMAD is software for optimizing blackbox problems. In continuous development since 2001, it constantly evolved with the integration of new algorithmic features published in scientific publications. These features are motivated by real applications encountered by industrial partners. The latest major release of NOMAD, version 3, dates from 2008. Minor releases are produced as new features … Read more

    Two decades of blackbox optimization applications

  • Stéphane Alarie
  • Charles Audet
  • Aïmen E. Gheribi
  • Michael Kokkolaras
  • Sébastien Le Digabel
    • Categories Applications - Science and Engineering, Chemical Engineering, Mechanical Engineering Tags , , ,

    This work reviews blackbox optimization applications over the last twenty years, addressed using direct search optimization methods. Emphasis is placed on the Mesh Adaptive Direct Search (MADS) derivative-free optimization algorithm. The core of the document describes applications in three specific fields: Energy, materials science, and computational engineering design. Other applications in science and engineering as … Read more

    Optimization of noisy blackboxes with adaptive precision

  • Stéphane Alarie
  • Charles Audet
  • Pierre-Yves Bouchet
  • Sébastien Le Digabel
    • Categories Nonlinear Optimization Tags , , , , , , ,

    In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It can be noisy, in the sense that its outputs are contaminated by random errors. Sometimes, the source of these errors is identified and controllable, in the sense that it is possible to … Read more

    Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates

  • Charles Audet
  • Kwassi Joseph Dzahini
  • Michael Kokkolaras
  • Sébastien Le Digabel
    • Categories Nonlinear Optimization, Other Topics, Unconstrained Optimization Tags , , , ,

    We present a stochastic extension of the mesh adaptive direct search (MADS) algorithm originally developed for deterministic blackbox optimization. The algorithm, called StoMADS, considers the unconstrained optimization of an objective function f whose values can be computed only through a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based … Read more

    Performance indicators in multiobjective optimization

  • Charles Audet
  • Jean Bigeon
  • Dominique Cartier
  • Sébastien Le Digabel
  • Ludovic Salomon
    • Categories Multi-Criteria Optimization, Nonsmooth Optimization

    In recent years, the development of new algorithms for multiobjective optimization has considerably grown. A large number of performance indicators has been introduced to measure the quality of Pareto front approximations produced by these algorithms. In this work, we propose a review of a total of 63 performance indicators partitioned into four groups according to … Read more