gn-miqp-mwe - A minimum working example for the Gauss-Newton-based decomposition algorithm for nonlinear mixed-integer optimal control problems
This repository provides a minimum working example to illustrate potential advantages of the Gauss-Newton-based decomposition approach presented in [1] for a numerical case study of Mixed-Integer Optimal Control (MIOC) of a simple nonlinear and unstable system, cf. [2], Example 8.17, pp. 577-579.
We describe the problem setup and implementation and compare the results of the proposed approach to results obtained using the Combinatorial Integral Approximation (CIA) problem [3].
Python version >= 3.6 is required. The Python packages required for running the algorithms are listed in the file requirements.txt, such as casadi [4] and gurobipy [5]. In addition to these packages, pycombina [6] is required.
While the GN-MIQP in this example is sufficiently small so that it can be solved using the restricted trial license of Gurobi included in the pip-version of gurobipy, note that a different license might be required for larger problems or production use, cf. [5].
The source code for the examples provided in this repository is released under the BSD 3-clause license. The provided PDF documentation is licensed under CC-BY 4.0.
[1] A Bürger, C Zeile, A Altmann-Dieses, S Sager, and M Diehl. A Gauss-Newton-based decomposition algorithm for nonlinear mixed-integer optimal control problems. Automatica 152, 110967, 2023. Available as an open access article at https://doi.org/10.1016/j.automatica.2023.110967
[2] J B Rawlings, D Q Mayne, and M M Diehl. Model Predictive Control: Theory, Computation, and Design. Nob Hill, 2nd edition, 2020. 3rd printing. Available at https://sites.engineering.ucsb.edu/~jbraw/mpc/.
[3] S Sager, M Jung, and C Kirches. Combinatorial integral approximation. Mathematical Methods of Operations Research, 73(3):363, 2011.
[4] J A E Andersson, J Gillis, G Horn, J B Rawlings, and M Diehl. CasADi – A software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 11(1):1-36, 2019.
[5] Gurobi Optimization, LLC. Gurobi optimizer reference manual. https://www.gurobi.com, 2022. Last accessed September 18, 2022.
[6] A Bürger, C Zeile, M Hahn, A Altmann-Dieses, S Sager, and M Diehl. pycombina: An open-source tool for solving combinatorial approximation problems arising in mixed-integer optimal control. In IFAC-PapersOnLine, volume 53, pages 6502-6508, 2020. 21st IFAC World Congress.