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Global optimization for mixed categorical-continuous variables based on Gaussian process models with a randomized categorical space exploration step

Abstract : Real industrial studies often give rise to complex optimization problems involving mixed variables and time consuming simula-tors. To deal with these difficulties we propose the use of a Gaussian process regression surrogate with a suitable kernel able to capture simultaneously the output correlations with respect to continuous and categorical/discrete inputs without relaxation of the categorical variables. The surrogate is integrated into the Efficient Global Optimization method based on the maximization of the Expected Improvement criterion. This maximization is a Mixed Integer Non-Linear problem which is solved by means of an adequate optimizer: the Mesh Adaptive Direct Search, integrated into the NOMAD library. We introduce a random exploration of the categorical space with a data-based probability distribution and we illustrate the full strategy accuracy on a toy problem. Finally we compare our approach with other optimizers on a benchmark of functions. ARTICLE HISTORY
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Submitted on : Thursday, April 9, 2020 - 6:18:47 PM
Last modification on : Friday, February 12, 2021 - 12:01:09 PM

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Miguel Zuniga, Delphine Sinoquet. Global optimization for mixed categorical-continuous variables based on Gaussian process models with a randomized categorical space exploration step. INFOR: Information Systems and Operational Research , Taylor & Francis, 2020, ⟨10.1080/03155986.2020.1730677⟩. ⟨hal-02512185⟩

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