Abstract
Many real world cyclic scheduling problems involve applications that need to be repeated with different periodicity. For example, multirate control systems present multiple control loops that are organized hierarchically: the higher-level loop responds to the slower system dynamics and typically its period can be a few orders of magnitude longer than the lowest level. Cyclic scheduling problems can be cast into classical RCPSP instances via a technique called unfolding [4, 6], which causes graph expansion. In the case of multirate applications, this expansion can be significantly large. In this context, finding a high-quality allocation and schedule could be very challenging. In this paper, we propose a new Multirate Resource Constraint, modeling unary resources, that avoids graph expansion by exploiting the multirate nature of the schedule in its filtering algorithm. In an experimentation on synthetic and real-world instances, we show that our method drastically outperforms approaches based on state-of-the-art unfolding and constraint based scheduling.
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Notes
- 1.
In the whole paper we assume that the durations and the periods are positive values.
- 2.
The generator and the synthetic instances solved in this work can be found at https://github.com/alessioBonfietti/Multirate-Resource-Constraint-Repo.
- 3.
The time limit value refers to the limit we use for the subproblem of the last application (the hardest). The previous subproblems were solved with a time limit halved at each step (e.g. if we have three applications, the limits would be 75,150,300, respectively).
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Acknowledgements
We would like to show our gratitude to William Aeby for his assistance in extracting the industrial instances.
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Bonfietti, A., Zanarini, A., Lombardi, M., Milano, M. (2016). The Multirate Resource Constraint. In: Rueher, M. (eds) Principles and Practice of Constraint Programming. CP 2016. Lecture Notes in Computer Science(), vol 9892. Springer, Cham. https://doi.org/10.1007/978-3-319-44953-1_8
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