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

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

Document Type: Working paper
Year of publication: 2019
Place of publication: Mannheim
Publication language: English
Institution: School of Business Informatics and Mathematics > Wissenschaftliches Rechnen (Göttlich 2011-)
Subject: 510 Mathematics
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 decomposition 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.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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