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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.

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Acknowledgements

The authors would like to thank the two anonymous referees, whose comments and suggestions improved the quality of the paper.

Funding

Support for both authors was provided by national funds through FCT – Fundação para a Ciência e a Tecnologia I. P., under the scope of Projects PTDC/MAT-APL/28400/2017 and UIDB/00297/2020.

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  1. Department of Mathematics, FCT-UNL-CMA, Campus de Caparica, 2829-516, Caparica, Portugal

    C. P. Brás & A. L. Custódio

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  1. C. P. Brás
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  2. A. L. Custódio
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Correspondence to A. L. Custódio.

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Brás, C.P., Custódio, A.L. On the use of polynomial models in multiobjective directional direct search. Comput Optim Appl 77, 897–918 (2020). https://doi.org/10.1007/s10589-020-00233-8

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