Hyperparameter-free minimum-lengthscale constraints for topology optimization
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Author(s)
Arrieta, Rodrigo
Romano, Giuseppe
Johnson, Steven
Date Issued
September 3, 2026
Journal
Structural and Multidisciplinary Optimization
Publisher
Springer Science and Business Media LLC
Citation
Arrieta, R., Romano, G. & Johnson, S.G. Hyperparameter-free minimum-lengthscale constraints for topology optimization. Struct Multidisc Optim 69, 210 (2026).
Version
Author's final manuscript
Abstract
The geometric constraints of Zhou et al. (2015) are a widely used technique in topology/freeform optimization to impose minimum lengthscales for manufacturability. However, its efficiency degrades as design binarization is increased, and it requires heuristic tuning of multiple hyperparameters. In this work, we derive analytical hyperparameters from first principles, depending only on the target lengthscale. We present results for both conic and PDE-based filtering schemes, showing that the latter is less robust due to the singularity of its underlying Green's function. To address this, we also introduce a double-filtering approach to obtain a well-behaved PDE-based filter. Combined with our derived hyperparameters, we obtain a straightforward strategy for enforcing lengthscales using geometric constraints, with minimal hyperparameter tuning. A key enabling factor is the recent subpixel-smoothed projection (SSP) method (Hammond et al. 2025), which facilitates the rapidlyconverging optimization of almost-everywhere binary designs. The effectiveness of our method is demonstrated for several photonics and heat-transfer inverse-design problems.
Subjects
Topology optimization
Geometric constraints
Minimum lengthscales
Density filters
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://doi.org/10.1007/s00158-026-04388-6
