  We propose a new way of looking at local optima networks (LONs). LONs
represent fitness landscapes; the nodes are local optima, and the edges are
search transitions between them. Many metrics computed on LONs have been
proposed and shown to be linked to metaheuristic search difficulty. These have
typically considered LONs as describing static structures. In contrast to this,
Laplacian dynamics (LD) is an approach to consider the information flow across
a network as a dynamical process. We adapt and apply LD to the context of LONs.
As a testbed, we consider instances from the quadratic assignment problem (QAP)
library. Metrics related to LD are proposed and these are compared with
existing LON metrics. The results show that certain LD metrics are strong
predictors of metaheuristic performance for iterated local search and tabu
search.
