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Categorical structural optimization using discrete manifold learning approach and custom-built evolutionary operators

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Abstract

In present work, we address the non-ordinal categorical design variables, such as different beam/bar cross-section types, various materials or components available within a catalog. We interpret the admissible values of categorical variables as discrete points in multi-dimensional space of physical attributes, which allows computing distances but has no ordering property. Then we propose to use the Isomap manifold learning approach to eliminate the possibly redundant dimensionality and obtain a reduced-order design space in which the geodesic distances are preserved in a low-dimensional graph. Then, taking advantage of the shortest path and the neighbors provided by Dijkstra algorithm, we propose graph-based crossover and mutation operators to be used in evolutionary optimization. The method is applied to the optimal design of truss and frame structures.

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Acknowledgements

This research is supported by the China Scholarship Council (201406290021), the National Natural Science Foundation of China (No.11302173 and No. 11620101002) and the Natural Science Foundation of Shaanxi Province (No. 2017JQ1037).

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Authors and Affiliations

  1. Building, Architecture and Town Planning Department, Université Libre de Bruxelles, Brussels, Belgium

    Huanhuan Gao

  2. Laboratoire Roberval UMR 7337 UTC-CNRS, Sorbonne Universités, Université de Technologie de Compiègne, Compiègne, France

    Huanhuan Gao, Piotr Breitkopf & Rajan Filomeno Coelho

  3. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, People’s Republic of China

    Manyu Xiao

Authors
  1. Huanhuan Gao
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  2. Piotr Breitkopf
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  3. Rajan Filomeno Coelho
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  4. Manyu Xiao
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Corresponding author

Correspondence to Huanhuan Gao.

Appendices

Appendix A

Table 4 The attribute catalog of bar cross-sections for test 1 and test 2
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Appendix B

Table 5 The attribute catalog of beam cross-sections for test 3
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Gao, H., Breitkopf, P., Coelho, R.F. et al. Categorical structural optimization using discrete manifold learning approach and custom-built evolutionary operators. Struct Multidisc Optim 58, 215–228 (2018). https://doi.org/10.1007/s00158-017-1890-2

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  • DOI: https://doi.org/10.1007/s00158-017-1890-2

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