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<p>In this work, an original Dimensionality Reduction (DR) methodology for structural optimization is proposed, based on variable grouping combined with the Uniform Manifold Approximation and Projection (UMAP) algorithm. Instead of simply discarding the design variables with a lower impact on the responses (as performed in feature selection), the principle consists here in dividing the set of variables in groups of similar impacts on the responses, which implicitly reduces the design space size, while still allowing all variables to vary throughout the total design space. The strategy is divided in three steps: (1) assessing the relative importance of each variable with respect to the responses, using a regularized regression scheme, (2) projecting the results obtained onto a two-dimensional latent space using the UMAP technique, and (3) finding clusters of design variables based on this projection. The strategy has proved successful on structural design test cases (up to 942 variables), both to automatically constitute meaningful groups of design variables and to facilitate the evolutionary optimization process. Finally, the methodology has been applied to an industrial example, namely the dome covering the Dutch Maritime Museum in Amsterdam, showing its efficiency to address this complex 1954-variate design problem.</p>

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Dimensionality reduction combining variable grouping and UMAP for structural optimization

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • Rajan Filomeno Coelho,
  • Caroline Sainvitu,
  • Tariq Benamara

摘要

In this work, an original Dimensionality Reduction (DR) methodology for structural optimization is proposed, based on variable grouping combined with the Uniform Manifold Approximation and Projection (UMAP) algorithm. Instead of simply discarding the design variables with a lower impact on the responses (as performed in feature selection), the principle consists here in dividing the set of variables in groups of similar impacts on the responses, which implicitly reduces the design space size, while still allowing all variables to vary throughout the total design space. The strategy is divided in three steps: (1) assessing the relative importance of each variable with respect to the responses, using a regularized regression scheme, (2) projecting the results obtained onto a two-dimensional latent space using the UMAP technique, and (3) finding clusters of design variables based on this projection. The strategy has proved successful on structural design test cases (up to 942 variables), both to automatically constitute meaningful groups of design variables and to facilitate the evolutionary optimization process. Finally, the methodology has been applied to an industrial example, namely the dome covering the Dutch Maritime Museum in Amsterdam, showing its efficiency to address this complex 1954-variate design problem.