2025-09-10 –, 202
Direct collocation-based dynamic optimization plays an important role in the optimization of equation-based models. With this approach, continuous problems are transcribed into sparse nonlinear programs (NLPs) that can be solved efficiently. The open-source Modelica environment OpenModelica provides an implementation using Radau IIA collocation, but has major limitations, such as the lack of parameter optimization, no adaptive mesh refinement, and no support for higher-order integration schemes. This paper presents (1) a comprehensive reimplementation that addresses these limitations and (2) a novel $h$-method mesh refinement algorithm. Implemented in the custom Python / C++ optimization framework GDOPT, the approach demonstrates significant performance improvements, solving typical problems 2 to 3 times faster than OpenModelica under equivalent conditions. Using the proposed mesh refinement algorithm, the framework correctly identifies non-smooth regions and increases resolution accordingly, requiring only a small increase in computation time. The implementation lays the foundation for a future integration into the OpenModelica toolchain.
Linus Langenkamp is a research associate in the Department of Engineering Sciences and Mathematics at Hochschule Bielefeld (Bielefeld University of Applied Sciences). He earned his Master of Science degree from Hochschule Bielefeld and joined the department in January 2025. His work on the OpenModelica project focuses on dynamic optimization, efficient numerical methods for differential equation systems, and physics-enhanced neural ordinary differential equations.
- Professor of Mathematics and Technical Applications, Bielefeld University of Applied Sciences (HSBI, since 1999)
- Research focus: numerical mathematics, nonlinear optimization, symbolic and numerical methods for large hybrid differential-algebraic systems
- Founding member of the Modelica Association (1996) and Open Source Modelica Consortium (2004)
- Key contributions to the BackEnd and C-Runtime of the OpenModelica Compiler
- Co-Author of the Modelica Petri Net Library and Modelica Neural Network Library
- Research stays at ABB Research Center (Switzerland, USA, Sweden), Linköping University (Sweden), and Politecnico di Milano (Italy)
- Member, Promotionskolleg NRW (since 2022)
- Founding board member, Institute for Data Science Solutions (IDaS), HSBI (since 2022)