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Communities of minima in local optima networks of combinatorial spaces

Author

Listed:
  • Daolio, Fabio
  • Tomassini, Marco
  • Vérel, Sébastien
  • Ochoa, Gabriela

Abstract

In this work, we present a new methodology to study the structure of the configuration spaces of hard combinatorial problems. It consists in building the network that has as nodes the locally optimal configurations and as edges the weighted oriented transitions between their basins of attraction. We apply the approach to the detection of communities in the optima networks produced by two different classes of instances of a hard combinatorial optimization problem: the quadratic assignment problem (QAP). We provide evidence indicating that the two problem instance classes give rise to very different configuration spaces. For the so-called real-like class, the networks possess a clear modular structure, while the optima networks belonging to the class of random uniform instances are less well partitionable into clusters. This is convincingly supported by using several statistical tests. Finally, we briefly discuss the consequences of the findings for heuristically searching the corresponding problem spaces.

Suggested Citation

  • Daolio, Fabio & Tomassini, Marco & Vérel, Sébastien & Ochoa, Gabriela, 2011. "Communities of minima in local optima networks of combinatorial spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1684-1694.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:9:p:1684-1694
    DOI: 10.1016/j.physa.2011.01.005
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    Citations

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    Cited by:

    1. Sebastian Herrmann & Gabriela Ochoa & Franz Rothlauf, 2016. "Communities of Local Optima as Funnels in Fitness Landscapes," Working Papers 1609, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    2. Tomassini, Marco, 2021. "Complex networks analysis of the energy landscape of the low autocorrelation binary sequences problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    3. Sun, Yixiang & Du, Haifeng & Gong, Maoguo & Ma, Lijia & Wang, Shanfeng, 2014. "Fast computing global structural balance in signed networks based on memetic algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 261-272.
    4. Tamás Vinkó & Kitti Gelle, 2017. "Basin Hopping Networks of continuous global optimization problems," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(4), pages 985-1006, December.
    5. Gabriela Ochoa & Nadarajen Veerapen, 2018. "Mapping the global structure of TSP fitness landscapes," Journal of Heuristics, Springer, vol. 24(3), pages 265-294, June.

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