Abstract
In optimal control problems with binary switches varying over time, it often arises as a subproblem to optimize a linear function over the set of binary vectors of a given finite length satisfying certain practical constraints, such as a minimum dwell time or a bound on the number of changes over the entire time horizon. While the former constraint has been investigated polyhedrally, no results seem to exist for the latter, although it arises naturally when discretizing binary optimal control problems subject to a bounded total variation. We investigate two variants of the problem, depending on whether the number of changes in a switch is penalized in the objective function or whether it is bounded by a hard constraint. We show that, while the former variant is easy to deal with, the latter is more complex, but still tractable. We present a full polyhedral description of the set of feasible switchings for this case.
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Buchheim, C., Hügging, M. (2022). Bounded Variation in Binary Sequences. In: Ljubić, I., Barahona, F., Dey, S.S., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2022. Lecture Notes in Computer Science, vol 13526. Springer, Cham. https://doi.org/10.1007/978-3-031-18530-4_5
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DOI: https://doi.org/10.1007/978-3-031-18530-4_5
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