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

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

Abstract: 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 on which MADS relies, so that it automatically adapts to the characteristics of the problem to solve. Another objective of the paper is to revisit the MADS method in order to ease its presentation and to reflect recent devel- opments. This new presentation includes a non smooth convergence analysis. Finally, numerical tests are conducted to illustrate the efficiency of the dynamic scaling, both on academic test problems and on a supersonic business jet design problem.

Keywords: Blackbox optimization, Derivative-Free Optimization, Mesh Adaptive Direct Search, Dynamic Scaling.

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Submitted to Optimization and Engineering

Download: [PDF]

Entry Submitted: 03/31/2014
Entry Accepted: 03/31/2014
Entry Last Modified: 03/31/2014

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