Conference Proceeding

On the Fractal Nature of Local Optima Networks



Thomson SL, Verel S, Ochoa G, Veerapen N & McMenemy P (2018) On the Fractal Nature of Local Optima Networks. In: Liefooghe A & López-Ibáñez M (eds.) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2018.. Lecture Notes in Computer Science, 10782. EvoCOP 2018 - The 18th European Conference on Evolutionary Computation in Combinatorial Optimisation, Parma, Italy, 04.04.2018-06.04.2018. Cham, Switzerland: Springer, pp. 18-33.

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

FundersThe Leverhulme Trust and Engineering and Physical Sciences Research Council
Title of seriesLecture Notes in Computer Science
Number in series10782
Publication date31/12/2018
Publication date online03/03/2018
Place of publicationCham, Switzerland
ISSN of series0302-9743
ConferenceEvoCOP 2018 - The 18th European Conference on Evolutionary Computation in Combinatorial Optimisation
Conference locationParma, Italy

People (2)


Professor Gabriela Ochoa
Professor Gabriela Ochoa

Professor, Computing Science

Dr Sarah Thomson
Dr Sarah Thomson

Lecturer in Computing Science, Computing Science and Mathematics - Division

Research centres/groups