On the Fractal Nature of Local Optima Networks

Sarah Thomson (1) , Sébastien Verel (2) , Gabriela Ochoa (1) , Nadarajen Veerapen (1) , Paul Mcmenemy (1)

1 University of Stirling
2 LISIC - Laboratoire d'Informatique Signal et Image de la Côte d'Opale

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.

Mots clés: Combinatorial Fitness Landscapes; Local Optima Networks; Fractal Analysis; NK Landscapes

Domaines: Intelligence artificielle [cs.AI]

Sarah Thomson, Sébastien Verel, Gabriela Ochoa, Nadarajen Veerapen, Paul Mcmenemy. On the Fractal Nature of Local Optima Networks. EvoCOP 2018 - The 18th European Conference on Evolutionary Computation in Combinatorial Optimisation, Apr 2018, Parma, Italy. pp.18-33, ⟨10.1007/978-3-319-77449-7_2⟩. ⟨hal-01824984⟩