Towards Simulation Based Mixed-Integer Optimization with Differential Equations

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autor(en): Gugat M, Leugering G, Martin A, Schmidt M, Sirvent M, Wintergerst D
Zeitschrift: Networks
Jahr der Veröffentlichung: 2018
Band: 72
Heftnummer: 1
Seitenbereich: 60-83
ISSN: 0028-3045
eISSN: 1097-0037
Sprache: Englisch


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-Autoren / FAU-Herausgeber

Gugat, Martin apl. Prof. Dr.
Lehrstuhl für Angewandte Mathematik
Leugering, Günter Prof. Dr.
Lehrstuhl für Angewandte Mathematik
Martin, Alexander Prof. Dr.
Lehrstuhl für Wirtschaftsmathematik
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen
Sirvent, Mathias
Lehrstuhl für Wirtschaftsmathematik
Wintergerst, David
Lehrstuhl für Angewandte Mathematik


Zitierweisen

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: 

Zuletzt aktualisiert 2018-30-07 um 10:38