Local Optima Networks: A New Model of Combinatorial Fitness Landscapes

Gabriela Ochoa (1) , Sébastien Verel (2) , Fabio Daolio (3) , Marco Tomassini (3)

1 Computing Science and Mathematics
2 LISIC - Laboratoire d'Informatique Signal et Image de la Côte d'Opale
3 ISI - Institut des systèmes d'information

This chapter overviews a recently introduced network-based model of combinatorial landscapes: Local Optima Networks (LON). The model compresses the information given by the whole search space into a smaller mathematical object that is a graph having as vertices the local optima and as edges the possible weighted transitions between them. Two definitions of edges have been proposed: basin-transition and escape-edges, which capture relevant topological features of the underlying search spaces. This network model brings a new set of metrics to characterize the structure of combinatorial landscapes, those associated with the science of complex networks. These metrics are described, and results are presented of local optima network extraction and analysis for two selected combinatorial landscapes: NK landscapes and the quadratic assignment problem. Network features are found to correlate with and even predict the performance of heuristic search algorithms operating on these problems.

Domaines: Intelligence artificielle [cs.AI]

Gabriela Ochoa, Sébastien Verel, Fabio Daolio, Marco Tomassini. Local Optima Networks: A New Model of Combinatorial Fitness Landscapes. Hendrik Richter, Andries Engelbrecht. Recent Advances in the Theory and Application of Fitness Landscapes, Springer Berlin Heidelberg, pp.233-262, 2014, Emergence, Complexity and Computation, 978-3-642-41887-7. ⟨10.1007/978-3-642-41888-4_9⟩. ⟨hal-00945508⟩