Papers for
architectural engineers
Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.
Hybrid metaheuristics improve architectural design under tight evaluation limits
Hybrid metaheuristics for architectural design optimization under small evaluation and wall-clock budgets
Abstract: Architectural and structural design optimization in parametric software affords about a thousand evaluations of an expensive model for problems with tens of variables, a regime for which most metaheuristics were not designed. On the side of artificial intelligence, two hybrid metaheuristics are proposed: a covariance matrix adaptation evolution strategy (CMA-ES) whose sampling is enriched with differential-evolution trial vectors, and a particle swarm with success-history parameter adaptation, differential-evolution injection and local refinement. A budget-aware delay of population-size reduction in adaptive differential evolution is also proposed. Under a hard cap of 1,200 evaluations, all counted, the CMA-ES hybrid ranks first on seven shifted and rotated functions at 10 and 30 variables and beats CMA-ES on six of seven functions at 30 variables. Ablations attribute this gain to the injection and show that a local search pays off only when its result re-enters the population. The delayed schedule improves three adaptive differential-evolution variants in 40 of 51 comparisons, with no loss. On the side of engineering application, in Grasshopper the CMA-ES hybrid and plain CMA-ES are never significantly worse than the optimizers of Galapagos, SilverEye, Opossum and Tunny on travelling-salesman instances and on a built 85-variable free-form shell, where they end 48 % below the best external tool in 15 minutes. On a 22-variable building-performance problem with binary choices, differential evolution leads instead. Shifting and rotating the functions reverses the rank of Harris hawks optimization. Solvers should therefore be selected by problem structure and stopping time, not by a single ranking.
Flexible geometric surfaces classified and new structures discovered
Flexible discrete translational surfaces
Abstract: We give a full list of translational nets which flex within their class of discrete surfaces of translation, by reducing the classification problem to the one of flexible complete bipartite frameworks on the sphere, for which the solution is known. We also obtained two novel classes which correspond to Bottema's spherical 16-bar mechanisms and the constant diagonal angle frameworks. Based on an algorithm for the construction of all flexible translational nets, we also discuss flexible translational tubes and toroids. Furthermore, we present novel results for both topologies which are implied by Bottema's spherical 16-bar mechanisms.
Neural models speed up optimizing shapes for vibration frequencies
Neural networks for spectral optimization
Abstract: Given a functional dependent on the spectrum of a differential operator, we address the problem of finding a domain which optimizes this functional. PDE solvers might be used to tackle this optimization. It is however computationally expensive. We propose two neural network models which learn the spectrum directly from the geometry of the domain and can be used to optimize the domain from one or more eigenvalues. We investigate two representations. The first encodes the domain through Fourier coefficients and a light MLP, which is efficient on star-shaped geometries, achieving a precision of 0.2\%. Through a rescaling of the coefficients the designed models satisfy the scaling law of the eigenvalues. Additionally, averaging the outputs of the trained surrogates over rotations and reflections induces invariance for these transformations. The second is a model that takes the landscape function, the indicator function and the gradient of the landscape function. A Gram-Schmidt process produces orthogonal eigenfunctions as output of the model along with the associated eigenvalues. The landscape model reaches 1\% mean relative error on the first ten eigenvalues, compared with 4\% for an FNO model. Replacing the landscape by an SDF worsened both prediction and optimization errors. The trained model also generalizes from synthetic shapes to domains given as classical image dataset. The resulting surrogates of both approaches recover classical spectral optima such as the disk for the first eigenvalue or the conjectured minima of higher eigenvalues. This confirms that our models produce accurate differentiable estimates of eigenvalues, which can be used in shape optimization problems involving spectral quantities.