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Global Landscape Structure and the Random MAX-SAT Phase Transition

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Parallel Problem Solving from Nature – PPSN XVI (PPSN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12270))

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Abstract

We revisit the fitness landscape structure of random MAX-SAT instances, and address the question: what structural features change when we go from easy underconstrained instances to hard overconstrained ones? Some standard techniques such as autocorrelation analysis fail to explain what makes instances hard to solve for stochastic local search algorithms, indicating that deeper landscape features are required to explain the observed performance differences. We address this question by means of local optima network (LON) analysis and visualisation. Our results reveal that the number, size, and, most importantly, the connectivity pattern of local and global optima change significantly over the easy-hard transition. Our empirical results suggests that the landscape of hard MAX-SAT instances may feature sub-optimal funnels, that is, clusters of sub-optimal solutions where stochastic local search methods can get trapped.

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Notes

  1. 1.

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Acknowledgements

This research has been partially funded by the Spanish Ministry of Economy and Competitiveness (MINECO) and the European Regional Development Fund (FEDER) under contract TIN2017-88213-R (6city project), the University of Málaga, Consejería de Economía y Conocimiento de la Junta de Andalucía and FEDER under contract UMA18-FEDERJA-003 (PRECOG project), the Ministry of Science, Innovation and Universities and FEDER under contract RTC-2017-6714-5 (ECOIoT project), and the University of Málaga under contract PPIT.UMA.B1.2017/07 (EXHAURO Project).

Author information

Authors and Affiliations

  1. Computing Science and Mathematics, University of Stirling, Stirling, Scotland, UK

    Gabriela Ochoa

  2. ITIS Software, University of Malaga, Malaga, Spain

    Francisco Chicano

  3. Faculty of Business and Economics, Information Systems Department, University of Lausanne, Lausanne, Switzerland

    Marco Tomassini

Authors
  1. Gabriela Ochoa
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  2. Francisco Chicano
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  3. Marco Tomassini
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Corresponding author

Correspondence to Francisco Chicano .

Editor information

Editors and Affiliations

  1. Leiden University, Leiden, The Netherlands

    Thomas Bäck

  2. Leiden University, Leiden, The Netherlands

    Mike Preuss

  3. Leiden University, Leiden, The Netherlands

    André Deutz

  4. Sorbonne University, Paris, France

    Hao Wang

  5. Sorbonne University, Paris, France

    Carola Doerr

  6. Leiden University, Leiden, The Netherlands

    Michael Emmerich

  7. University of Münster, Münster, Germany

    Heike Trautmann

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Ochoa, G., Chicano, F., Tomassini, M. (2020). Global Landscape Structure and the Random MAX-SAT Phase Transition. In: Bäck, T., et al. Parallel Problem Solving from Nature – PPSN XVI. PPSN 2020. Lecture Notes in Computer Science(), vol 12270. Springer, Cham. https://doi.org/10.1007/978-3-030-58115-2_9

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  • DOI: https://doi.org/10.1007/978-3-030-58115-2_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58114-5

  • Online ISBN: 978-3-030-58115-2

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