Gradient based optimization algorithms promise good performance in continuous problems. Direct methods, such as Gradient Projection (GP), deal with constraints directly, without trans- ferring the problem into an unconstrained one. As this method can lead to zig-zagging, the Relaxed Gradient Projection method (RGP) was developed. A buffer zone is created around the constraint boundaries in which projection and correction are scaled, in order to smoothen the result. This method, as well as Feasible Directions and Sequential Quadratic Programming (SQP), were tested on different analytical problems. SQP showed very promising performance, both with quadratic line search and without. Together with RGP it was implemented in the open- source framework Kratos Multiphysics. The goal was, to assess their performance for node based optimization problems, which use vertex morphing. The algorithms were tested on two different problems: the mass reduction of a hook, which is constrained by it’s strain energy, and the drag reduction of a two dimensional wing in laminar flow, which is constrained by it’s lift. After modification, RGP manages to perform well and reduce zig-zagging compared to GP, but is very sensitive to ill posed constraints. SQP fails to reproduce the promising results from the analytical problems. Using the search direction directly completely fails and using quadratic line search converges far to slow.      «

Gradient based optimization algorithms promise good performance in continuous problems. Direct methods, such as Gradient Projection (GP), deal with constraints directly, without trans- ferring the problem into an unconstrained one. As this method can lead to zig-zagging, the Relaxed Gradient Projection method (RGP) was developed. A buffer zone is created around the constraint boundaries in which projection and correction are scaled, in order to smoothen the result. This method, as well as Feasi...     »