blackbox optimization

Fidelity and interruption control for expensive constrained multi-fidelity blackbox optimization

  • Xavier Lebeuf
  • Sébastien Le Digabel
  • Charles Audet
  • Miguel Diago
  • Stéphane Alarie
    • Categories Constrained Nonlinear Optimization, Energy, Optimization of Simulated Systems Tags , , , , ,

    This work introduces a novel blackbox optimization algorithm for computationally expensive constrained multi-fidelity problems. When applying a direct search method to such problems, the scarcity of feasible points may lead to numerous costly evaluations spent on infeasible points. Our proposed fidelity and interruption controlled optimization algorithm addresses this issue by leveraging multi-fidelity information, allowing for … Read more

    Detecting negative eigenvalues of exact and approximate Hessian matrices in optimization

  • Warren Hare
  • Clément W. Royer
    • Categories Nonlinear Optimization Tags , , ,

    Nonconvex minimization algorithms often benefit from the use of second-order information as represented by the Hessian matrix. When the Hessian at a critical point possesses negative eigenvalues, the corresponding eigenvectors can be used to search for further improvement in the objective function value. Computing such eigenpairs can be computationally challenging, particularly if the Hessian matrix … Read more

    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

    Handling of constraints in multiobjective blackbox optimization

  • Jean Bigeon
  • Sébastien Le Digabel
  • Ludovic Salomon
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm for single-objective constrained optimization. The constraints are aggregated into a single constraint violation function which is used either in a two-phase approach, where research of a feasible … 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

    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

    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

    Determining the optimal piecewise constant approximation for the Nonhomogeneous Poisson Process rate of Emergency Department patient arrivals

  • Alberto De Santis
  • Tommaso Giovannelli
  • Stefano Lucidi
  • Mauro Messedaglia
  • Massimo Roma
    • Categories Applications - OR and Management Sciences, Integer Programming Tags , , ,

    Modeling the arrival process to an Emergency Department (ED) is the first step of all studies dealing with the patient flow within the ED. Many of them focus on the increasing phenomenon of ED overcrowding, which is afflicting hospitals all over the world. Since Discrete Event Simulation models are often adopted with the aim to … Read more

    Constrained stochastic blackbox optimization using a progressive barrier and probabilistic estimates

  • Kwassi Joseph Dzahini
  • Michael Kokkolaras
  • Sébastien Le Digabel
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Approaches Tags , , ,

    This work introduces the StoMADS-PB algorithm for constrained stochastic blackbox optimization, which is an extension of the mesh adaptive direct-search (MADS) method originally developed for deterministic blackbox optimization under general constraints. The values of the objective and constraint functions are provided by a noisy blackbox, i.e., they can only be computed with random noise whose … 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