Orthogonalization of Linear Representations for Efficient Evolutionary Design Optimization
Repräsentations-agnostische Optimierung linearer Deformationsmodelle: Eine Orthogonalisierung der Deformationsmatrix verkürzt die Konvergenz evolutionärer Designoptimierung um bis zu einer Größenordnung.
Andreas Richter
Nicole Dresselhaus 
Stefan Menzel
Mario Botsch
Hernan Aguirre
Real-world evolutionary design optimization of complex shapes is usually solved with linear deformation representations — and how well that works depends almost entirely on the initial deformation setup. With radial basis functions (RBF), for example, convergence speed is governed by the condition number of the kernel matrix, which earlier work tried to improve by carefully placing RBF kernels.
The paper shows that such representation-specific techniques are inherently limited, and proposes a generic, representation-agnostic alternative: orthogonalize the deformation matrix. This black-box optimization projects any given linear deformation setup onto an optimal condition number without changing its design space — and, as the numerical experiments show, boosts the convergence speed of evolutionary optimizations by up to an order of magnitude.
Citation
@online{richter2018,
author = {Richter, Andreas and Dresselhaus, Nicole and Menzel, Stefan
and Botsch, Mario and Aguirre, Hernan},
publisher = {ACM},
title = {Orthogonalization of {Linear} {Representations} for
{Efficient} {Evolutionary} {Design} {Optimization}},
date = {2018-07-15},
url = {https://drezil.de/Papers/gecco-2018-orthogonalization.html},
doi = {10.1145/3205455.3205568},
isbn = {978-1-4503-5618-3},
langid = {en}
}