Welcome to LSDO GeNIe

The LSDO Lab’s Gemoetric Non-Interference (GeNIe) constraint formulation is an efficient and scalable method to enforce non-interference constraints in gradient-based optimization. We define geometric non-interference as a constraint to enforce such that the design body does not interfere with any other geometric shape in the environment. Non-interference constraints appear in layout optimization, optimal path planning optimization, and shape optimization problems.

In the diagram below, geometric non-interference is enforced between the design body and the infeasible space outside of the grey geometric shape. In gradient-based optimization, a constraint function \(\phi(\mathbf{x})\geq0\), where \(\mathbf{x}\) is the design variables, must be enforced to prevent the design body from interfering with the infeasible region. It is required that \(\phi\) is continuous and differentiable for gradient-based optimization and desired that it is fast-to-evaluate, scalable, and an accurate representation of the boundary \(\Gamma\) between the feasible \(\phi(\mathbf{x})>0\) and infeasible \(\phi(\mathbf{x})<0\) spaces. The focus of this package is on generating the geometric non-interferencee constraint function \(\phi\).

This package is more efficient formulation to the original energy minimization formulation presented in a previous paper. As an unconstrained quadratic programming problem, the solution to this formulation reduces to a solution to a sparse linear system; however, the original implementation was done using a BFGS approximation using a gradient-based optimizer. The original implementation, lsdo_noninterference, can be found here, but we recommend this package.

Cite the original work

Pending review and revisions…

"Scalable Enforcement of Geometric Non-interference Constraints for Gradient-Based Optimization"
Ryan C. Dunn, Anugrah Jo Joshy, Jui-Te Lin, Cedric Girerd, Tania K. Morimoto, John T. Hwang 
Springer Nature's Structural and Multidisciplinary Optimization Journal