Aachen Dynamic Optimization Environment (ADE): Modeling and numerical methods for higher-order sensitivity analysis of differential-algebraic equation systems with optimization criteria

• Applicants: Professor Alexander Mitsos, Ph.D.; Professor Dr. Uwe Naumann
• Subject Area: Computer Architecture, Embedded and Massively Parallel Systems ; Software Engineering and Programming Languages
• Term: from 2016 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281932795

• Final Report Year: 2025

Final Report Abstract

Differential-algebraic equation systems with optimality criteria (DAEO) are a generalization of differential-algebraic equation systems. DAEOs have more algebraic variables than algebraic equations and are therefore initially underdetermined. This under-determination is resolved by formulating an optimality criterion that determines the undetermined algebraic variables. In the second funding period, dynamic optimization of DAEOs has been enabled using KKT-embedding and adjoint sensitivity analysis of the resulting nonsmooth differential algebraic equations. The coupling of the DAEO toolbox with our framework from the previous funding period enables the simulation and dynamic optimization of dynamic flux balance analysis (DFBA) models. A second-order integrator for the simulation and sensitivity analysis of DAEOs has been developed. Novel results on generalization of separability for global optimization have developed that can be used for global optimization in the context of DAEOs. Higher order adjoint sensitivities exploiting symmetry and sparsity have been developed. They have been shown to be beneficial for the deterministic global optimization using branch and bound in the context of DAEOs.

Publications

• Global Derivatives. PhD Thesis, RWTH Aachen University
  Deussen, Jens
  
• Direct single shooting for dynamic optimization of differential-algebraic equation systems with optimization criteria embedded. Computers & Chemical Engineering, 159, 107643.
  Ploch, Tobias; Deussen, Jens; Naumann, Uwe; Mitsos, Alexander & Hannemann-Tamás, Ralf
  
• Dynamic Optimization of DAEs with Embedded Optimization Problems. SciCADE, Reykjavik, July 25-29.
  T. Ploch, J. Deussen, U. Naumann, A. Mitsos & R. Hannemann-Tamás
  
• Global Derivatives. NAG Seminar Series
  Deussen, Jens
  
• Reduction of the Random Access Memory Size in Adjoint Algorithmic Differentiation by Overloading
  Naumann, Uwe
  
• Subdomain separability in global optimization. Journal of Global Optimization, 86(3), 573-588.
  Deussen, Jens & Naumann, Uwe
  
• An Efficient Local Optimizer-Tracking Solver for Differential- Algebraic Equations with Optimization Criteria. Eigth International Conference on Algorithmic Differentiation (AD2024)
  Fleming, A.
  
• An Efficient Local Optimizer-Tracking Solver for Differential-Algebraic Equations with Optimization Criteria.
  Fleming, A.; Deussen, Jens & Naumann, Uwe
  
• Differenzierbare Forschungssoftware, Seminar der GI Fachgruppe Research Software Engineering zum Umgang mit Anforderungen an Forschungs- und Innovationssoftware
  Naumann, Uwe
  
• Differenzierbare Forschungssoftware. Softwaretechnik- Trends Band 44, Heft 1, 18-19. ISSN 0720-8928.
  Naumann, Uwe
  
• Numerical simulation of differential-algebraic equations with embedded global optimization criteria. Optimization Methods and Software, 1-15.
  Deussen, Jens; Hüser, Jonathan & Naumann, Uwe