Complex Networks Analysis of the Energy Landscape of the Low Autocorrelation Binary Sequences Problem

TL;DR

This paper analyzes the energy landscape of the NP-hard low autocorrelation binary sequences problem using network theory, revealing structural insights that inform optimization strategies.

Contribution

It applies local optima network methodology to exhaustively characterize the landscape of problem sizes up to 24, offering new quantitative insights.

Findings

Characterized the optima network structure and basins.

Identified metrics explaining problem difficulty.

Provided data to improve heuristic optimization methods.

Abstract

We provide an up-to-date view of the structure of the energy landscape of the low autocorrelation binary sequences problem, a typical representative of the $NP$-hard class. To study the landscape features of interest we use the local optima network methodology through exhaustive extraction of the optima graphs for problem sizes up to $24$. Several metrics are used to characterize the networks: number and type of optima, optima basins structure, degree and strength distributions, shortests paths to the global optima, and random walk-based centrality of optima. Taken together, these metrics provide a quantitative and coherent explanation for the difficulty of the low autocorrelation binary sequences problem and provide information that could be exploited by optimization heuristics for this problem, as well as for a number of other problems having a similar configuration space structure.