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Stabilized column generation for the temporal knapsack problem using dual-optimal inequalities

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  • Timo Gschwind

    (Johannes Gutenberg University Mainz)

  • Stefan Irnich

    (Johannes Gutenberg University Mainz)

Abstract

We present two new methods to stabilize column-generation algorithms for the temporal knapsack problem (TKP). Caprara et al. (INFORMS J Comp 25(3):560–571, 2013] were the first to suggest the use of branch-and-price algorithms for Dantzig–Wolfe reformulations of the TKP. Herein, the respective pricing problems are smaller-sized TKP that can be solved with a general-purpose MIP solver or by dynamic programming. Our stabilization methods are tailored to the TKP as they use (deep) dual-optimal inequalities, that is, inequalities known to be fulfilled by all (at least some) optimal dual solutions to the linear relaxation. Extensive computational tests reveal that both new stabilization techniques are helpful. Several previously unsolved instances are now solved to proven optimality.

Suggested Citation

  • Timo Gschwind & Stefan Irnich, 2017. "Stabilized column generation for the temporal knapsack problem using dual-optimal inequalities," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 541-556, March.
    • Handle: RePEc:spr:orspec:v:39:y:2017:i:2:d:10.1007_s00291-016-0463-x
    DOI: 10.1007/s00291-016-0463-x
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    References listed on IDEAS

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    Cited by:

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    3. Martinovic, J. & Strasdat, N. & Valério de Carvalho, J. & Furini, F., 2023. "A combinatorial flow-based formulation for temporal bin packing problems," European Journal of Operational Research, Elsevier, vol. 307(2), pages 554-574.
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