Local Optima Networks: A New Model of Combinatorial Fitness Landscapes
This provides a novel modeling approach for researchers in optimization and combinatorial search to analyze and predict algorithm behavior, though it is incremental in applying existing network science to known problems.
The paper introduces Local Optima Networks (LON) as a network-based model to compress combinatorial fitness landscapes into graphs of local optima and transitions, enabling new metrics from complex network science to characterize landscape structure. It applies this model to NK landscapes and the quadratic assignment problem, finding that network features correlate with and predict heuristic search algorithm performance.
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.