NOMAD version 4: Nonlinear optimization with the MADS algorithm

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

HyperNOMAD: Hyperparameter optimization of deep neural networks using mesh adaptive direct search

The performance of deep neural networks is highly sensitive to the choice of the hyperparameters that define the structure of the network and the learning process. When facing a new application, tuning a deep neural network is a tedious and time consuming process that is often described as a “dark art”. This explains the necessity … Read more

The Mesh Adaptive Direct Search Algorithm for Granular and Discrete Variables

The mesh adaptive direct search (Mads) algorithm is designed for blackbox optimization problems for which the functions defining the objective and the constraints are typically the outputs of a simulation seen as a blackbox. It is a derivative-free optimization method designed for continuous variables and is supported by a convergence analysis based on the Clarke … Read more

Robust optimization of noisy blackbox problems using the Mesh Adaptive Direct Search algorithm

Blackbox optimization problems are often contaminated with numerical noise, and direct search methods such as the Mesh Adaptive Direct Search (MADS) algorithm may get stuck at solutions artificially created by the noise. We propose a way to smooth out the objective function of an unconstrained problem using previously evaluated function evaluations, rather than resampling points. … Read more

Dynamic scaling in the Mesh Adaptive Direct Search algorithm for blackbox optimization

Blackbox optimization deals with situations in which the objective function and constraints are typically computed by launching a time-consuming computer sim- ulation. The subject of this work is the Mesh Adaptive Direct Search (MADS) class of algorithms for blackbox optimization. We propose a way to dynamically scale the mesh, which is the discrete spatial structure … Read more

Reducing the Number of Function Evaluations in Mesh Adaptive Direct Search Algorithms

The mesh adaptive direct search (MADS) class of algorithms is designed for nonsmooth optimization, where the objective function and constraints are typically computed by launching a time-consuming computer simulation. Each iteration of a MADS algorithm attempts to improve the current best-known solution by launching the simulation at a finite number of trial points. Common implementations … Read more