Article Dans Une Revue Optimization and Engineering Année : 2024

Scalable Enforcement of Geometric Non-interference Constraints for Gradient-Based Optimization

Résumé

Many design optimization problems include constraints to prevent intersection of the geometric shape being optimized with other objects or with domain boundaries. When applying gradient-based optimization to such problems, the constraint function must provide an accurate representation of an object's boundary and be smooth, amenable to numerical differentiation, and fast-to-evaluate for a large number of points. We propose the use of tensor product Bsplines to generate an efficient-to-evaluate implicit level set function that locally approximates the signed distance function for representing geometric non-interference constraints. Adapting ideas from the field of surface reconstruction, we formulate an energy minimization problem to compute the implicit function values at B-spline control points given an oriented point set sampled over a geometric shape. Unlike previous non-interference constraint formulations, our method requires an initial setup, but results in a more efficient and scalable representation of geometric non-interference constraints. This paper presents the results of accuracy and scaling studies performed on our formulation. We demonstrate our method by solving a medical robot design optimization problem with non-interference constraints. We achieve constraint evaluation times on the order of 10 −6 seconds per point on a modern desktop workstation, and a maximum on-surface error of less than 1.0% of the minimum bounding box diagonal for all examples studied. Overall, our method provides an effective formulation for non-interference constraint enforcement with high computational efficiency for gradient-based design optimization problems whose solutions may require hundreds of evaluations of constraints and their derivatives.

Fichier principal
Vignette du fichier
PaperSubmission.pdf (9.75 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04312659 , version 1 (28-11-2023)

Licence

Identifiants

Citer

Ryan C. Dunn, Anugrah Jo Joshy, Jui-Te Lin, Cédric Girerd, Tania K. Morimoto, et al.. Scalable Enforcement of Geometric Non-interference Constraints for Gradient-Based Optimization. Optimization and Engineering, 2024, 25, pp.1849-1882. ⟨10.1007/s11081-023-09864-2⟩. ⟨hal-04312659⟩
106 Consultations
138 Téléchargements

Altmetric

Partager

  • More