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On heuristic search for the single machine total weighted tardiness problem - Some theoretical insights and their empirical verification

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  • Geiger, Martin Josef

Abstract

The article presents theoretical and experimental investigations of computational intelligence techniques for machine sequencing problems. Contrary to other approaches, which are experimentally driven only, our work is motivated by gaining insights in the underlying principles of heuristic search for this particular problem. We therefore first theoretically analyze local search neighborhoods, deriving expectations about their relative performance. An empirical study on benchmark data follows, verifying the initial propositions. In result, we may conclude theoretically and empirically on the relative performance of neighborhood search operators for the single machine total weighted tardiness problem. The results are useful for the proposition of heuristic search procedures based on local search, as they lead to an order of neighborhood structures with respect to their relative performance. The obtained insights are verified by investigating the effectiveness of a (multi-operator) Variable Neighborhood Search approach for the problem at hand. We are able to show that most known benchmark instances are reliably solved to optimality, leaving an overall average gap of around 1% above the optimum.

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  • Geiger, Martin Josef, 2010. "On heuristic search for the single machine total weighted tardiness problem - Some theoretical insights and their empirical verification," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1235-1243, December.
  • Handle: RePEc:eee:ejores:v:207:y:2010:i:3:p:1235-1243
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    References listed on IDEAS

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    1. C.R. Reeves, 1999. "Landscapes, operators and heuristic search," Annals of Operations Research, Springer, vol. 86(0), pages 473-490, January.
    2. Bilge, Umit & Kurtulan, Mujde & Kirac, Furkan, 2007. "A tabu search algorithm for the single machine total weighted tardiness problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1423-1435, February.
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    Cited by:

    1. Huber, Sandra & Geiger, Martin Josef, 2017. "Order matters – A Variable Neighborhood Search for the Swap-Body Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 263(2), pages 419-445.
    2. Lang, Fabian & Fink, Andreas & Brandt, Tobias, 2016. "Design of automated negotiation mechanisms for decentralized heterogeneous machine scheduling," European Journal of Operational Research, Elsevier, vol. 248(1), pages 192-203.
    3. Arthur Kramer & Anand Subramanian, 2019. "A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems," Journal of Scheduling, Springer, vol. 22(1), pages 21-57, February.
    4. Geiger, Martin Josef, 2017. "A multi-threaded local search algorithm and computer implementation for the multi-mode, resource-constrained multi-project scheduling problem," European Journal of Operational Research, Elsevier, vol. 256(3), pages 729-741.

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