Local optima networks and the performance of iterated local search

TL;DR

This paper investigates how features of Local Optima Networks (LONs) can predict the performance of local search algorithms on combinatorial landscapes, validating LONs as effective models.

Contribution

It introduces a statistical analysis linking LON metrics to heuristic performance, demonstrating their predictive power.

Findings

LON features significantly influence heuristic success

Certain network metrics can partly predict search performance

LONs effectively model the structure of fitness landscapes

Abstract

Local Optima Networks (LONs) have been recently proposed as an alternative model of combinatorial fitness landscapes. The model compresses the information given by the whole search space into a smaller mathematical object that is the graph having as vertices the local optima and as edges the possible weighted transitions between them. A new set of metrics can be derived from this model that capture the distribution and connectivity of the local optima in the underlying configuration space. This paper departs from the descriptive analysis of local optima networks, and actively studies the correlation between network features and the performance of a local search heuristic. The NK family of landscapes and the Iterated Local Search metaheuristic are considered. With a statistically-sound approach based on multiple linear regression, it is shown that some LONs' features strongly influence and can even partly predict the performance of a heuristic search algorithm. This study validates the expressive power of LONs as a model of combinatorial fitness landscapes.