Relaxed gradient projection algorithm for constrained node-based shape optimization

Abstract

In node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

Latest developments in node-based shape optimization using Vertex Morphing parameterization

“…where BSF (i) can be adjusted by the buffer adaptation functions (Antonau et al 2021). The buffer coefficient can be separated into two components: "relaxation" and "correction" coefficient.…”

“…where x represents design parameters that define the design surface, n g and n h are numbers of inequality ( g(x) ≤ 0 ) and equality ( h(x) = 0 ) constraints. The algorithms that have been successfully used with Vertex Morphing parameterization are gradient projection (Najian Asl et al 2017;Ertl 2020), the relaxed gradient projection (RGP) method (Antonau et al 2021), and the modified search direction method (Chen et al 2019;Chen 2021). All methods are first-order direct optimization methods that (1)…”

Numerical Simulations of Vaccination and Wolbachia on Dengue Transmission Dynamics in the Nonlinear Model

“…The active set, for instance, specifies the hyperplanes that cross at the solution point while solving a linear programming issue. Here are few contributions that us ASA such that water supply model to manage the flow [58], optimal control issue based on PDE [59], node-based shape optimization [60], and for electrodynamic problems [61].…”

Aggregated Formulation of Geometric Constraints for Node-Based Shape Optimization With Vertex Morphing

“…[15] has successfully used the same projection algorithm with a constant step length for imposing the nodal non-penetration constraints, however, without the correction therm in Equation 6. [21,22] have developed alternative optimization algorithms that have proven to work well with the Vertex Morphing parametrization.…”