AI 中文总结
该研究针对标准粒子群优化（PSO）无法捕捉高阶社会关系的问题，提出基于超图拓扑的HPSO算法，通过超边实现多粒子直接交互并设计自适应拓扑更新策略，在IEEE CEC'17基准上验证了其优异搜索性能。
AI 中文摘要
粒子群优化（PSO）因能高效探索大型解空间、无需梯度信息即可收敛至最优解，已被广泛应用于解决现实世界中的复杂优化问题。标准PSO及其变体中的常见群体拓扑（如Ring和Star）可视为图，其中每条边仅连接两个粒子。这类拓扑结构仅允许相连的粒子对之间直接交互，因此往往无法直接捕捉在复杂搜索空间中导航所需的高阶社会关系。为此，本文提出一种新型PSO变体，名为超图辅助粒子群优化算法（Hypergraph-assisted Particle Swarm Optimization，HPSO）。在HPSO中，群体内粒子的拓扑由超图建模，超边用于连接多个粒子，使超边内的多个粒子可直接交互。此外，本文设计了一种自适应超图更新策略，该策略基于累积平均粒子位移定期重构拓扑，从而在进化过程中维持群体多样性。实验中，在IEEE CEC'17基准测试套件上验证了HPSO的有效性，结果表明HPSO在各类函数上均表现出良好性能；消融实验进一步证明HPSO具有优异的搜索能力。
英文摘要
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.
