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Shift-and-Propagate

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Abstract

In recent years, there has been a growing interest in the design of general purpose primal heuristics for use inside complete mixed integer programming solvers. Many of these heuristics rely on an optimal LP solution, which may take a significant amount of time to find. In this paper, we address this issue by introducing a pre-root primal heuristic that does not require a previously found LP solution. This heuristic, named Shift-and-Propagate , applies domain propagation techniques to quickly drive a variable assignment towards feasibility. Computational experiments indicate that this heuristic is a powerful supplement to existing rounding and propagation heuristics.

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Notes

  1. In principle, Shift-and-Propagate could be started from any solution within the variable bounds. We decided for the zero assignment since for many MIP s, in particular those which model combinatorial problems and those with many set packing and covering constraints, all feasible solutions have the majority of integer variables set to zero.

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Acknowledgments

Many thanks to Christina Burt and two anonymous reviewers for their valuable comments. This research has been supported by the DFG Research Center Matheon Mathematics for key technologies in Berlin, http://www.matheon.de.

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Authors and Affiliations

  1. Fair Isaac Europe Ltd, c/o Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Timo Berthold

  2. Department of Optimization, Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Gregor Hendel

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  1. Timo Berthold
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  2. Gregor Hendel
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Correspondence to Timo Berthold.

Appendix

Appendix

We present the instance-wise experimental outcome in Tables 4 and 5.

Table 4 Results of different variable sortings w.r.t. to the primal bound and the heuristic time
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Table 5 Results of the root experiment for all three settings in terms of heuristic/root solving time and objective value for all 163 instances
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Berthold, T., Hendel, G. Shift-and-Propagate. J Heuristics 21, 73–106 (2015). https://doi.org/10.1007/s10732-014-9271-0

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