A Dynamic Parametrization Scheme for Shape Optimization Using Quasi-Newton Methods

Abstract

A variable parametrization scheme is developed and demonstrated for shape optimization using quasi-Newton methods. The scheme performs adaptive parametrization refinement while preserving the approximate Hessian of the shape optimization problem and enables free-form shape design using quasi-Newton optimization methods. Using a Bspline parametrization, the scheme is validated using a 1-D shape approximation problem and is shown to improve efficiency and optimal solution quality compared to the traditional quasi-Newton method. The scheme is also applied to a 3-D test problem, demonstrating the feasibility of free-form shape optimization using parametrization refinement and a method for partially constraining the degrees of freedom.

Adaptive Shape Control for Aerodynamic Design

“…Rather the important shape parameters are discovered as a natural consequence of optimization, and are clearly visible to the designer in the emergent pattern of shape parameters. In addition, a growing body of evidence indicates that substantial design acceleration can be achieved by using variable shape control, [1][2][3][4][5][6] an observation we corroborate in this study.…”

“…Hwang and Martins developed a conceptually reversed approach that starts from an initial fine parameterization, and then uses coarsened search spaces to accelerate design improvement, analogous to grid sequencing in PDE solvers. 4 Their major achievement is an exact transfer of the Hessian information when switching between search spaces, avoiding the initial Hessian build-up time. The disadvantage of this approach is that the sequence of search spaces must be provided a priori.…”