Abstract
Periodic scheduling problems (PSP) are frequently found in a wide range of applications. In these problems, we schedule a set of tasks on a set of machines in time, where each task is to be executed repeatedly with a given period. The tasks are assigned to machines, and at any moment, at most one task can be processed by a given machine. Since no existing works address the complexity of PSPs with precedence relations, we consider the most basic PSP with chains and end-to-end latency constraints given in the number of periods. We define a degeneracy of a chain as the number of broken precedence relations within the time window of one period. We address the general problem of finding a schedule with the minimum total degeneracy of all chains. We prove that this PSP is strongly NP-hard even when restricted to unit processing times, a common period, and 16 machines, by a reduction from the job shop scheduling problem. Finally, we propose a local search heuristic to solve the general PSP and present its experimental evaluation.
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Notes
- 1.
On the other hand, two tasks with equal period are not necessarily in the same \(C_{c}\).
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Acknowledgements
Research leading to these results has received funding from the EU ECSEL Joint Undertaking and the Ministry of Education of the Czech Republic under grant agreement 826452 (project Arrowhead Tools).
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Hladík, R., Minaeva, A., Hanzálek, Z. (2020). On the Complexity of a Periodic Scheduling Problem with Precedence Relations. In: Wu, W., Zhang, Z. (eds) Combinatorial Optimization and Applications. COCOA 2020. Lecture Notes in Computer Science(), vol 12577. Springer, Cham. https://doi.org/10.1007/978-3-030-64843-5_8
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