Version 2.0 -- cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software

TL;DR

The paper addresses efficient PDE-constrained optimization for shape optimization and optimal control. It introduces cashocs version 2.0 with a space-mapping framework, level-set topology optimization, and MPI parallelism to tackle large-scale problems. It integrates automatic handling of state constraints via quadratic penalty and augmented Lagrangian methods, automatic cost-term scaling, custom scalar products for shape gradients, and $p$-Laplace-based gradient computation, along with improved polynomial-line-search strategies. This combination broadens applicability to industrial problems and improves scalability and robustness of adjoint-based optimization workflows.

Abstract

In this paper, we present version 2.0 of cashocs. Our software automates the solution of PDE constrained optimization problems for shape optimization and optimal control. Since its inception, many new features and useful tools have been added to cashocs, making it even more flexible and efficient. The most significant additions are a framework for space mapping, the ability to solve topology optimization problems with a level-set approach, the support for parallelism via MPI, and the ability to handle additional (state) constraints. In this software update, we describe the key additions to cashocs, which is now even better-suited for solving complex PDE constrained optimization problems.

Figures (2)

• Figure 1: Example for the space mapping method for shape optimization from Blauth2023Space. The picture shows the evolution of the geometry, velocity field, and outlet flow rates over the space mapping iterations.
• Figure 2: Overview of the types of optimization problems that can be solved with cashocs. Items colored in blue are new additions to version 2.0.