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A bi-level methodology for solving large-scale mixed categorical structural optimization

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In this work, large-scale structural optimization problems involving non-ordinal categorical design variables and continuous variables are investigated. The aim is to minimize the weight of a structure with respect to cross-section areas, with materials and stiffening principles selection. First, the problem is formulated using a bi-level decomposition involving master and slave problems. The master problem is given by a first-order-like approximation that helps to drastically reduce the combinatorial explosion raised by the categorical variables. Continuous variables are handled in a slave problem solved using a gradient-based approach, where the categorical variables are driven by the master problem. The proposed algorithm is tested on three different structural optimization test cases. A comparison to state-of-the-art algorithms emphasize efficiency of the proposed algorithm in terms of the optimum quality, the computation cost, and the scaling with respect to the problem dimension.

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This work is part of the MDA-MDO project of the French Institute of Technology IRT Saint Exupery. We wish to acknowledge the PIA framework (CGI, ANR) and the project industrial members for their support, financial backing and/or own knowledge: Airbus, Airbus Group Innovations, SOGETI High Tech, Altran Technologies, CERFACS.

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Correspondence to Pierre-Jean Barjhoux.

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Replication of results

This section is intended to help readers to replicate the results provided in this paper. A supplementary material allows to replicate the 3-bar truss example detailed in section 4.2. In order to replicate the scalable 2D cantilever (Section 4.4) and 120-bar truss (Section 4.5), the reader needs to adapt the 3-bar truss physical model consequently. The geometries are depicted on Fig. 6 and Fig. 8, material data is provided in Table 4, and the solution of the 120-bar truss is given in Table 5.

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Responsible Editor: Seonho Cho

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1.1 Materials definition

Table 4 Numerical details on materials attributes

1.2 120-bar solution

Table 5 Solution of 120-bar truss mixed categorical-continuous optimization

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Barjhoux, PJ., Diouane, Y., Grihon, S. et al. A bi-level methodology for solving large-scale mixed categorical structural optimization. Struct Multidisc Optim 62, 337–351 (2020).

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