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Exponential size neighborhoods for makespan minimization scheduling

Author

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  • Tobias Brueggemann
  • Johann L. Hurink
  • Tjark Vredeveld
  • Gerhard J. Woeginger

Abstract

We investigate the quality of local search heuristics for the scheduling problem of minimizing the makespan on identical parallel machines. We study exponential size neighborhoods (whose size grows exponentially with the input length) that can be searched in polynomial time, and we derive worst‐case approximation guarantees for the local optima of such neighborhoods. The so‐called split neighborhood splits a feasible schedule into two layers, and then recombines the two layers by finding a perfect matching. We show that the makespan of every local optimum for split is at most a factor of 2 away from the globally optimal makespan. We then combine the split neighborhood with two neighborhoods from the literature. The combination of split with the jump neighborhood only marginally improves the approximation guarantee, whereas the combination with the lexicographic‐jump neighborhood decreases the approximation guarantee from 2 to 3/2. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Suggested Citation

  • Tobias Brueggemann & Johann L. Hurink & Tjark Vredeveld & Gerhard J. Woeginger, 2011. "Exponential size neighborhoods for makespan minimization scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 795-803, December.
    • Handle: RePEc:wly:navres:v:58:y:2011:i:8:p:795-803
    DOI: 10.1002/nav.20485
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    References listed on IDEAS

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    1. Petra Schuurman & Tjark Vredeveld, 2007. "Performance Guarantees of Local Search for Multiprocessor Scheduling," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 52-63, February.
    2. Recalde, D. & Rutten, C. & Schuurman, P. & Vredeveld, T., 2009. "Local search performance guarantees for restricted related parallel machine scheduling," Research Memorandum 061, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Antonio Frangioni & Emiliano Necciari & Maria Grazia Scutellà, 2004. "A Multi-Exchange Neighborhood for Minimum Makespan Parallel Machine Scheduling Problems," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 195-220, June.
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