On the use of polynomial models in multiobjective directional direct search

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Abstract

Polynomial interpolation or regression models are an important tool in Derivative-free Optimization, acting as surrogates of the real function. In this work, we propose the use of these models in the multiobjective framework of directional direct search, namely the one of Direct Multisearch. Previously evaluated points are used to build quadratic polynomial models, which are minimized in an attempt of generating nondominated points of the true function, defining a search step for the algorithm. Numerical results state the competitiveness of the proposed approach.

Original languageEnglish
Pages (from-to)897-918
Number of pages22
JournalComputational Optimization And Applications
Volume77
DOIs
Publication statusPublished - 12 Oct 2020

Keywords

  • Derivative-free optimization
  • Direct search methods
  • Minimum Frobenius norm models
  • Multiobjective optimization
  • Quadratic polynomial interpolation and regression

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