The Connectivity of NK Landscapes' Basins: A Network Analysis

TL;DR

This paper introduces a network-based approach to analyze NK landscapes by modeling local maxima and their transition probabilities, revealing insights into the landscape's search difficulty.

Contribution

It adapts the inherent network concept to NK landscapes, providing a novel network characterization of their basins and transition dynamics.

Findings

Network properties correlate with search difficulty.

Most NK landscape networks exhibit scale-free characteristics.

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 where the 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 small NK landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties can be related to the search difficulty on the underlying NK landscapes with varying values of K.