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Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints
- Source :
- Mathematical Programming. 188:599-619
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
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.
- Subjects :
- 0209 industrial biotechnology
Mathematical optimization
021103 operations research
Linear programming
General Mathematics
Numerical analysis
0211 other engineering and technologies
02 engineering and technology
Optimal control
Network topology
Maxima and minima
020901 industrial engineering & automation
Flow (mathematics)
Optimization and Control (math.OC)
FOS: Mathematics
49J15, 49J20, 65K05, 90C11
Heuristics
Mathematics - Optimization and Control
Software
Integer (computer science)
Mathematics
Subjects
Details
- ISSN :
- 14364646 and 00255610
- Volume :
- 188
- Database :
- OpenAIRE
- Journal :
- Mathematical Programming
- Accession number :
- edsair.doi.dedup.....cf482a23b4ac1885582dcfe4a5784ec6