Complex-network analysis of combinatorial spaces: The NK landscape case

TL;DR

This paper introduces a network-based approach to analyze combinatorial fitness landscapes, specifically NK landscapes, by modeling local maxima and their transition probabilities to understand search difficulty.

Contribution

It adapts the inherent network concept to NK landscapes, providing a new way to characterize landscape complexity through network properties.

Findings

Network properties correlate with search difficulty

Most NK landscape instances exhibit similar network structures

Transition probabilities influence landscape ruggedness

Abstract

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent network is the graph whose vertices represent the local maxima in the landscape, and the edges account for the transition probabilities between their corresponding basins of attraction. We exhaustively extracted such networks on representative NK landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties are related to the search difficulty on the underlying NK landscapes with varying values of K.