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Variable ordering for decision diagrams: A portfolio approach

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Abstract

Relaxed decision diagrams have been successfully applied to solve combinatorial optimization problems, but their performance is known to strongly depend on the variable ordering. We propose a portfolio approach to selecting the best ordering among a set of alternatives. We consider several different portfolio mechanisms: a static uniform time-sharing portfolio, an offline predictive model of the single best algorithm using classifiers, a low-knowledge algorithm selection, and a dynamic online time allocator. As a case study, we compare and contrast their performance on the graph coloring problem. We find that on this problem domain, the dynamic online time allocator provides the best overall performance.

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Notes

  1. The code has been downloaded from https://github.com/heldstephan/exactcolors.

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  1. Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    Anthony Karahalios & Willem-Jan van Hoeve

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  1. Anthony Karahalios
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  2. Willem-Jan van Hoeve
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Correspondence to Anthony Karahalios.

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Partially supported by Office of Naval Research Grants No. N00014-18-1-2129 and N00014-21-1-2240 and National Science Foundation Award #1918102.

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Karahalios, A., van Hoeve, WJ. Variable ordering for decision diagrams: A portfolio approach. Constraints 27, 116–133 (2022). https://doi.org/10.1007/s10601-021-09325-6

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