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

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...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization 2018-07, Vol.58 (1), p.215-228
Main Authors: Gao, Huanhuan, Breitkopf, Piotr, Coelho, Rajan Filomeno, Xiao, Manyu
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Crossovers
Dijkstra's algorithm
Engineering
Engineering Design
Engineering Sciences
Frame structures
Machine learning
Manifolds (mathematics)
Model reduction
Mutation
Operators
Optimization
Research Paper
Shortest-path problems
Theoretical and Applied Mechanics
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Summary: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.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-017-1890-2