Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints


Göttlich, Simone ; Hante, Falk M. ; Potschka, Andreas ; Schewe, Lars


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DOI: https://doi.org/10.1007/s10107-021-01656-9
URL: https://madoc.bib.uni-mannheim.de/60028
Additional URL: https://link.springer.com/article/10.1007%2Fs10107...
URN: urn:nbn:de:bsz:180-madoc-600285
Document Type: Article
Year of publication: 2021
The title of a journal, publication series: Mathematical Programming : Series B
Volume: 188
Issue number: 2
Page range: 599-619
Place of publication: Berlin ; Heidelberg
Publishing house: Springer
ISSN: 0025-5610 , 1436-4646
Related URLs:
Publication language: English
Institution: School of Business Informatics and Mathematics > Wissenschaftliches Rechnen (Göttlich 2011-)
Pre-existing license: Creative Commons Attribution 4.0 International (CC BY 4.0)
Subject: 510 Mathematics
Keywords (English): mixed-integer optimization , partial differential equations , dwell-time constraints , alternating direction methods , penalty methods
Abstract: We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decom- position approach into a mixed-integer optimal control problem without combinatorial constraints and a mixed-integer problem for the combinatorial constraints in the control space. Both problems can be solved very efficiently with existing methods such as outer convexification with sum-up-rounding strategies and mixed-integer linear programming techniques. The coupling is handled using a penalty-approach. We provide an exactness result for the penalty which yields a solution approach that convergences to partial minima. We compare the quality of these dedicated points with those of other heuristics amongst an academic example and also for the optimization of electric transmission lines with switching of the network topology for flow reallocation in order to satisfy demands.
Additional information: Online-Ressource

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