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Data-fitted constraint aggregation schemes
Publikationstyp
Conference Presentation
Date Issued
2022-06
Sprache
English
Author(s)
Ambrozkiewicz, Olaf
Institut
Citation
8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2022)
Contribution to Conference
Peer Reviewed
true
Constraint aggregation is a way to reduce the size of the dual problem of a constrained optimization problem by replacing nc similar constraints with a single, aggregated con-straint. In this contribution, especially the local volume constraints by Wu et al. [1] are
studied, since employing them in a topology optimization (TO) problem usually leads to one constraint per finite element of the model.
Commonly used constraint aggregation functions, like e.g. the p-norm, p-mean, or Kreisselmeier-Steinhauser (KS) [2] function, include a tunable aggregation parameter p. Increasing p also increases the accuracy of the approximation of the maximum (worst) value
of all nc original constraints by the aggregated constraint. On the downside, an increase of p also increases the nonlinearity of the aggregated constraint, possibly leading to convergence issues. Therefore, it is desirable to keep p as low as possible without compromising the quality of the approximation by the aggregated constraint.
However, the choice of a speci c aggregation parameter p is often not justi ed in the literature. Local volume constraints are used in the context of TO e.g. to enforce redundant designs [1], for which the robustness to partial failure is implicitly increased, or to enforce
a maximum feature size [3]. Although the same constraint equations can be used for both cases, a value of p = 16 is sufficient in [1], and, depending on the studied geometry, values up to p = 300 are used in [3]. In this contribution, very high values of p are seen
as an indication, that the chosen aggregation function is not well suited for the studied problem. Therefore, alternative aggregation functions based on the p-norm are introduced, that offer an additional parameter to adapt the aggregation characteristics to the expected
distribution of the data being aggregated. This results in higher accuracy also for very low p values when compared to known aggregation functions.
REFERENCES
[1] Wu, J., Aage, N.,Westermann, R., and Sigmund, O., Infi ll Optimization for Additive Manu-
facturing -- Approaching Bone-like Porous Structures. IEEE Transactions on Visualization
and Computer Graphics, Vol. 24(2), pp. 1127--1140, 2018.
[2] Kreisselmeier, G. and Steinhauser, R., Systematic Control Design by Optimizing a Vector
Performance Index. IFAC Proceedings Volumes, Vol. 12(7), pp. 113--117, 1979.
[3] Fernández, E., Collet, M., Alarcón, P., Bauduin, S. and Duysinx, P., An aggregation strat-
egy of maximum size constraints in density-based topology optimization. Structural and
Multidisciplinary Optimization, Vol. 60(5), pp. 2113--2130, 2019.
studied, since employing them in a topology optimization (TO) problem usually leads to one constraint per finite element of the model.
Commonly used constraint aggregation functions, like e.g. the p-norm, p-mean, or Kreisselmeier-Steinhauser (KS) [2] function, include a tunable aggregation parameter p. Increasing p also increases the accuracy of the approximation of the maximum (worst) value
of all nc original constraints by the aggregated constraint. On the downside, an increase of p also increases the nonlinearity of the aggregated constraint, possibly leading to convergence issues. Therefore, it is desirable to keep p as low as possible without compromising the quality of the approximation by the aggregated constraint.
However, the choice of a speci c aggregation parameter p is often not justi ed in the literature. Local volume constraints are used in the context of TO e.g. to enforce redundant designs [1], for which the robustness to partial failure is implicitly increased, or to enforce
a maximum feature size [3]. Although the same constraint equations can be used for both cases, a value of p = 16 is sufficient in [1], and, depending on the studied geometry, values up to p = 300 are used in [3]. In this contribution, very high values of p are seen
as an indication, that the chosen aggregation function is not well suited for the studied problem. Therefore, alternative aggregation functions based on the p-norm are introduced, that offer an additional parameter to adapt the aggregation characteristics to the expected
distribution of the data being aggregated. This results in higher accuracy also for very low p values when compared to known aggregation functions.
REFERENCES
[1] Wu, J., Aage, N.,Westermann, R., and Sigmund, O., Infi ll Optimization for Additive Manu-
facturing -- Approaching Bone-like Porous Structures. IEEE Transactions on Visualization
and Computer Graphics, Vol. 24(2), pp. 1127--1140, 2018.
[2] Kreisselmeier, G. and Steinhauser, R., Systematic Control Design by Optimizing a Vector
Performance Index. IFAC Proceedings Volumes, Vol. 12(7), pp. 113--117, 1979.
[3] Fernández, E., Collet, M., Alarcón, P., Bauduin, S. and Duysinx, P., An aggregation strat-
egy of maximum size constraints in density-based topology optimization. Structural and
Multidisciplinary Optimization, Vol. 60(5), pp. 2113--2130, 2019.
Subjects
constraint aggregation
local volume constraints
topology optimization
DDC Class
600: Technik
620: Ingenieurwissenschaften
Funding Organisations