Meta-heuristic Hypergraph-Assisted Robustness Optimization for Higher-order Complex Systems

TL;DR

This paper introduces a hypergraph-based robustness optimization method for complex systems using genetic algorithms, achieving significant improvements and revealing new topological structures that enhance system resilience.

Contribution

It systematically investigates hypergraph modeling for robustness optimization and proposes a novel genetic algorithm approach with topology insights for higher-order systems.

Findings

Robustness improved by 16.6% to 205.2% in experiments

Identified Lotus and Cactus topologies influencing robustness

Proposed a hypergraph generation method with controllable robustness

Abstract

In complex systems (e.g., communication, transportation, and biological networks), high robustness ensures sustained functionality and stability even when resisting attacks. However, the inherent structure complexity and the unpredictability of attacks make robustness optimization challenging. Hypergraphs provide a framework for modeling complicated higher-order interactions in complex systems naturally, but their potential has not been systematically investigated. Therefore, we propose an effective method based on genetic algorithms from Artificial Intelligence to optimize the robustness of complex systems modeled by hypergraphs. By integrating percolation-based metrics with adaptive computational techniques, our method achieves improved accuracy and efficiency. Experiments on both synthetic and real-world hypergraphs demonstrate the effectiveness of the proposed method in mitigating malicious attacks, with robustness improvements ranging from 16.6% to 205.2%. Further in-depth analysis reveals that optimized hypergraph-based systems exhibit a preferential connection mechanism in which high-hyperdegree nodes preferentially connect to lower-cardinality hyperedges, forming a distinctive Lotus topology that significantly improves robustness. Based on this finding, we propose a robust hypergraph generation method that allows robustness to be controlled via a single parameter rb. Notably, for rb<-1, a distinct Cactus topology emerges as an alternative to the Lotus topology observed for rb>1. The discovery of the Lotus and Cactus topologies offers valuable insights for designing robust higher-order networks while providing a useful foundation for investigating cascading failure dynamics in complex systems.