Enhancing Collocation-Based Dynamic Optimization through Adaptive Mesh Refinement

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.