# A Study of NK Landscapes' Basins and Local Optima Networks

Abstract : We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces (Doye, 2002). We use the well-known family of $NK$ landscapes as an example. In our case the inherent network is the graph where the vertices are all the local maxima and edges mean basin adjacency between two maxima. We exhaustively extract such networks on representative small NK landscape instances, and show that they are 'small-worlds'. However, the maxima graphs are not random, since their clustering coefficients are much larger than those of corresponding random graphs. Furthermore, the degree distributions are close to exponential instead of Poissonian. We also describe the nature of the basins of attraction and their relationship with the local maxima network.
Keywords :
Type de document :
Communication dans un congrès
Genetic And Evolutionary Computation Conference, Jul 2008, Atlanta, United States. ACM New York, NY, USA, pp.555--562, 2008, 〈10.1145/1389095.1389204〉
Domaine :

https://hal.archives-ouvertes.fr/hal-00331868
Contributeur : Sébastien Verel <>
Soumis le : dimanche 19 octobre 2008 - 00:01:26
Dernière modification le : mercredi 31 janvier 2018 - 10:24:05
Document(s) archivé(s) le : lundi 7 juin 2010 - 20:45:15

### Fichiers

t07pap218-ochoa.pdf
Fichiers produits par l'(les) auteur(s)

### Citation

Gabriela Ochoa, Marco Tomassini, Sébastien Verel, Christian Darabos. A Study of NK Landscapes' Basins and Local Optima Networks. Genetic And Evolutionary Computation Conference, Jul 2008, Atlanta, United States. ACM New York, NY, USA, pp.555--562, 2008, 〈10.1145/1389095.1389204〉. 〈hal-00331868〉

### Métriques

Consultations de la notice

## 361

Téléchargements de fichiers