Enhancing Collocation-Based Dynamic Optimization through Adaptive Mesh Refinement

Abstract

Direct collocation-based dynamic optimization plays animportant role in the optimization of equation-basedmodels. With this approach, continuous problems aretranscribed into sparse nonlinear programs (NLPs) that canbe solved efficiently. The open-source Modelica environmentOpenModelica provides an implementation using Radau IIAcollocation, but has major limitations, such as the lack ofparameter optimization, no adaptive mesh refinement, and nosupport for higher-order integration schemes. This paperpresents (1) a comprehensive reimplementation thataddresses these limitations and (2) a novel $h$-method meshrefinement algorithm. Implemented in the custom Python /C++ optimization framework GDOPT, the approach demonstratessignificant performance improvements, solving typicalproblems 2 to 3 times faster than OpenModelica underequivalent conditions. Using the proposed mesh refinementalgorithm, the framework correctly identifies non-smoothregions and increases resolution accordingly, requiringonly a small increase in computation time. Theimplementation lays the foundation for a future integrationinto the OpenModelica toolchain.