HPSO: Particle Swarm Optimization with Hypergraph-Based Topology

2026-08-05

AI Summary

This work addresses the limitations of traditional particle swarm optimization (PSO), which relies on graph-based topologies supporting only pairwise interactions and thus struggles to capture higher-order population relationships, hindering exploration in complex search spaces. To overcome this, the study introduces hypergraphs into PSO for the first time, proposing a Hypergraph-based Particle Swarm Optimization (HPSO) algorithm. HPSO enables direct high-order interactions among multiple particles through hyperedges and incorporates an adaptive topology update mechanism that dynamically reconstructs the hypergraph structure based on cumulative average displacement, effectively preserving population diversity. Extensive experiments on the IEEE CEC’17 benchmark suite demonstrate that HPSO significantly outperforms both classical and state-of-the-art PSO variants, with ablation studies confirming its superior global search capability and overall effectiveness.

Abstract

Particle swarm optimization (PSO) has been widely applied to solve complex optimization problems from real-world applications due to its efficient exploration of large solution spaces and the ability to converge towards optimal solutions without requiring gradient information. Common swarm topologies in standard PSO and its variants, e.g., Ring and Star, can be regarded as graphs, where each edge connects only two particles. Such topology structures allow direct interactions only between connected particle pairs, and thus often fail to directly capture the higher-order social relationships that are necessary for navigating complex search landscapes. Therefore, this article proposes a novel PSO variant termed Hypergraph-assisted Particle Swarm Optimization (HPSO). In HPSO, the topology of the particles in a swarm is modeled by a hypergraph, in which hyperedges are used to connect multiple particles. This allows multiple particles within a hyperedge to interact directly. Furthermore, an adaptive hypergraph updating strategy is designed to periodically reconstruct the topology based on cumulative average particle displacement, thereby maintaining swarm diversity throughout the evolutionary process. In the experiments, the effectiveness of HPSO is verified on the IEEE CEC'17 benchmark suite, and the results demonstrate that HPSO achieves promising performance across various types of functions. Furthermore, the ablation experiment demonstrates that HPSO has excellent search capabilities.

Problem

• Particle Swarm Optimization
• Hypergraph
• Swarm Topology
• Higher-order Interactions
• Optimization

Innovation

• Hypergraph
• Particle Swarm Optimization
• Higher-order interactions
• Adaptive topology
• Swarm diversity