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The Mesh Adaptive Direct Search Algorithm for Granular and Discrete Variables

Charles Audet (charles.audet***at***gerad.ca)
Sébastien Le Digabel (sebastien.le.digabel***at***gerad.ca)
Christophe Tribes (christophe.tribes***at***polymtl.ca)

Abstract: 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 calculus. This work introduces a modification to the Mads algorithm so that it handles granular variables, i.e., variables with a controlled number of decimals. This modification involves a new way of updating the underlying mesh so that the precision is progressively increased. A corollary of this new approach is the ability to treat discrete variables. Computational results are presented using the NOMAD software, the free C++ distribution of the Mads algorithm.

Keywords: blackbox optimization, derivative-free optimization, mesh adaptive direct search, granular variables, discrete variables.

Category 1: Nonlinear Optimization (Other )

Citation: SIAM Journal on Optimization, 29(2), p. 1164-1189, 2019.

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Entry Submitted: 03/15/2018
Entry Accepted: 03/15/2018
Entry Last Modified: 04/24/2019

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