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A Novel Application for Game Tree Search - Exploiting Pruning Mechanisms for Quantified Integer Programs

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Advances in Computer Games (ACG 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12516))

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Abstract

We investigate pruning in search trees of so-called quantified integer (linear) programs (QIPs). QIPs consist of a set of linear inequalities and a minimax objective function, where some variables are existentially and others are universally quantified. A good way to solve a QIP is to apply game tree search, enhanced with non-chronological back-jumping. We develop and theoretically substantiate tree pruning techniques based upon algebraic properties. The presented Strategic Copy-Pruning mechanism allows to implicitly deduce the existence of a strategy in linear time (by static examination of the QIP-matrix) without explicitly traversing the strategy itself. We show that the implementation of our findings can massively speed up the search process.

This research is partially supported by the German Research Foundation (DFG) project “Advanced algorithms and heuristics for solving quantified mixed - integer linear programs”.

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Notes

  1. 1.

    \(\mathbb {Z}\), \(\mathbb {N}\) and \(\mathbb {Q}\) denote the set of integers, natural numbers, and rational numbers, respectively.

  2. 2.

    This is only a matter of interpretation and consequences are not discussed further.

  3. 3.

    Future means variable blocks with index \(\ge k\).

  4. 4.

    Sources are available at http://www.q-mip.org.

  5. 5.

    The studied benchmark instances and a brief explanation can be found at http://www.q-mip.org/index.php?id=41.

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Authors and Affiliations

  1. Chair of Technology Management, University of Siegen, Siegen, Germany

    Michael Hartisch & Ulf Lorenz

Authors
  1. Michael Hartisch
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  2. Ulf Lorenz
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Correspondence to Michael Hartisch .

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Editors and Affiliations

  1. Université Paris-Dauphine, Paris, France

    Tristan Cazenave

  2. Leiden University, The Hague, The Netherlands

    Jaap van den Herik

  3. The University of New South Wales, Sydney, NSW, Australia

    Abdallah Saffidine

  4. National Chiao-Tung University, Hsin-Chu, Taiwan

    I-Chen Wu

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Hartisch, M., Lorenz, U. (2020). A Novel Application for Game Tree Search - Exploiting Pruning Mechanisms for Quantified Integer Programs. In: Cazenave, T., van den Herik, J., Saffidine, A., Wu, IC. (eds) Advances in Computer Games. ACG 2019. Lecture Notes in Computer Science(), vol 12516. Springer, Cham. https://doi.org/10.1007/978-3-030-65883-0_6

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  • DOI: https://doi.org/10.1007/978-3-030-65883-0_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-65882-3

  • Online ISBN: 978-3-030-65883-0

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