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Handling precedence constraints in scheduling problems by the sequence pair representation

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  • Andrzej Kozik

    (Opole University)

Abstract

In this paper, we show that sequence pair (SP) representation, primarily applied to the rectangle packing problems appearing in the VLSI industry, can be a solution representation of precedence constrained scheduling. We present three interpretations of sequence pair, which differ in complexity of schedule evaluation and size of a corresponding solution space. For each interpretation we construct an incremental precedence constrained SP neighborhood evaluation algorithm, computing feasibility of each solution in the insert neighborhood in an amortized constant time per examined solution, and prove the connectivity property of the considered neighborhoods. To compare proposed interpretations of SP, we construct heuristic and metaheuristic algorithms for the multiprocessor job scheduling problem, and verify their efficiency in the numerical experiment.

Suggested Citation

  • Andrzej Kozik, 2017. "Handling precedence constraints in scheduling problems by the sequence pair representation," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 445-472, February.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:2:d:10.1007_s10878-015-9973-8
    DOI: 10.1007/s10878-015-9973-8
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    References listed on IDEAS

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    1. Elisabeth Günther & Felix G. König & Nicole Megow, 2014. "Scheduling and packing malleable and parallel tasks with precedence constraints of bounded width," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 164-181, January.
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    5. Agnetis, Alessandro & Kellerer, Hans & Nicosia, Gaia & Pacifici, Andrea, 2012. "Parallel dedicated machines scheduling with chain precedence constraints," European Journal of Operational Research, Elsevier, vol. 221(2), pages 296-305.
    6. Kolisch, R. & Padman, R., 2001. "An integrated survey of deterministic project scheduling," Omega, Elsevier, vol. 29(3), pages 249-272, June.
    7. Adam Janiak & Andrzej Kozik & Maciej Lichtenstein, 2010. "New perspectives in VLSI design automation: deterministic packing by Sequence Pair," Annals of Operations Research, Springer, vol. 179(1), pages 35-56, September.
    8. Edmund K Burke & Michel Gendreau & Matthew Hyde & Graham Kendall & Gabriela Ochoa & Ender Özcan & Rong Qu, 2013. "Hyper-heuristics: a survey of the state of the art," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(12), pages 1695-1724, December.
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