Sampling local optima networks of large combinatorial search spaces: The qap case

Abstract

Local Optima Networks (LON) model combinatorial landscapes as graphs, where nodes are local optima and edges transitions among them according to given move operators. Modelling landscapes as networks brings a new rich set of metrics to characterize them. Most of the previous works on LONs fully enumerate the underlying landscapes to extract all local optima, which limits their use to small instances. This article proposes a sound sampling procedure to extract LONs of larger instances and estimate their metrics. The results obtained on two classes of Quadratic Assignment Problem (QAP) benchmark instances show that the method produces reliable results.