Optimization and Engineering

, Volume 17, Issue 2, pp 333–358 | Cite as

Dynamic scaling in the mesh adaptive direct search algorithm for blackbox optimization

  • Charles Audet
  • Sébastien Le Digabel
  • Christophe Tribes


Blackbox optimization deals with situations in which the objective function and constraints are typically computed by launching a time-consuming computer simulation. 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 developments. This new presentation includes a nonsmooth 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.


Blackbox optimization Derivative-free optimization  Mesh adaptive direct search Dynamic scaling 

Mathematics Subject Classification

90C30 90C56 65K05 62P30 



The authors wish to thank Michael Kokkolaras for making the Supersonic Business Jet Design problem available. We also thank the referees for their constructive comments. Work of the first author was supported by NSERC Grant 239436. The second author was supported by NSERC Grant 418250. The first and second authors are supported by AFOSR FA9550-12-1-0198.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Charles Audet
    • 1
  • Sébastien Le Digabel
    • 1
  • Christophe Tribes
    • 1
  1. 1.Département de mathématiques et génie industriel, GERADÉcole Polytechnique de MontréalQuébecCanada

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