On the Fractal Nature of Local Optima Networks

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


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.


Combinatorial fitness landscapes Local optima networks Fractal analysis NK Landscapes 



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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