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On the use of polynomial models in multiobjective directional direct search

A. L. Custódio (alcustodio***at***fct.unl.pt)
C. P. Bras (mb***at***fct.unl.pt)

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.

Keywords: Multiobjective optimization, derivative-free optimization, direct search methods, quadratic polynomial interpolation and regression, minimum Frobenius norm models.

Category 1: Nonlinear Optimization


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Entry Submitted: 08/02/2019
Entry Accepted: 08/02/2019
Entry Last Modified: 08/04/2020

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