Towards Simulation Based Mixed-Integer Optimization with Differential Equations

Journal article


Publication Details

Author(s): Gugat M, Leugering G, Martin A, Schmidt M, Sirvent M, Wintergerst D
Journal: Networks
Publication year: 2018
Volume: 72
Journal issue: 1
Pages range: 60-83
ISSN: 0028-3045
eISSN: 1097-0037
Language: English


Abstract


We propose a decomposition based method for solving mixed-integer nonlinear optimization problems with "black-box" nonlinearities, where the latter, e.g., may arise due to differential equations or expensive simulation runs. The method alternatingly solves a mixed-integer linear master problem and a separation problem for iteratively refining the mixed-integer linear relaxation of the nonlinearity. We prove that our algorithm finitely terminates with an approximate feasible global optimal solution of the mixed-integer nonlinear problem. Additionally, we show the applicability of our approach by three case studies from mixed-integer optimal control, from the field of pressurized flows in pipes with elastic walls, and from steady-state gas transport. For the latter we also present promising numerical results of our method applied to real-world instances.


FAU Authors / FAU Editors

Gugat, Martin apl. Prof. Dr.
Lehrstuhl für Angewandte Mathematik
Leugering, Günter Prof. Dr.
Lehrstuhl für Angewandte Mathematik
Martin, Alexander Prof. Dr.
Economics - Discrete Optimization - Mathematics (EDOM)
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen
Sirvent, Mathias
Economics - Discrete Optimization - Mathematics (EDOM)
Wintergerst, David
Lehrstuhl für Angewandte Mathematik


How to cite

APA:
Gugat, M., Leugering, G., Martin, A., Schmidt, M., Sirvent, M., & Wintergerst, D. (2018). Towards Simulation Based Mixed-Integer Optimization with Differential Equations. Networks, 72(1), 60-83. https://dx.doi.org/10.1002/net.21812

MLA:
Gugat, Martin, et al. "Towards Simulation Based Mixed-Integer Optimization with Differential Equations." Networks 72.1 (2018): 60-83.

BibTeX: 

Last updated on 2018-30-07 at 10:38