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On the Fractal Nature of Local Optima Networks

  • Sarah L. Thomson
  • Sébastien Verel
  • Gabriela Ochoa
  • Nadarajen Veerapen
  • Paul McMenemy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10782)

Abstract

A Local Optima Network represents fitness landscape connectivity within the space of local optima as a mathematical graph. In certain other complex networks or graphs there have been recent observations made about inherent self-similarity. An object is said to be self-similar if it shows the same patterns when measured at different scales; another word used to convey self-similarity is fractal. The fractal dimension of an object captures how the detail observed changes with the scale at which it is measured, with a high fractal dimension being associated with complexity. We conduct a detailed study on the fractal nature of the local optima networks of a benchmark combinatorial optimisation problem (NK Landscapes). The results draw connections between fractal characteristics and performance by three prominent metaheuristics: Iterated Local Search, Simulated Annealing, and Tabu Search.

Keywords

Combinatorial fitness landscapes Local optima networks Fractal analysis NK Landscapes 

Notes

Acknowledgements

This work is supported by the Leverhulme Trust (award number RPG-2015-395) and by the UK’s Engineering and Physical Sciences Research Council (grant number EP/J017515/1). We gratefully acknowledge that all network data used during this research were obtained from [2].

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Computing Science and MathematicsUniversity of StirlingStirlingUK
  2. 2.Université du Littoral Côte d’Opale, EA 4491 - LISICCalaisFrance

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