Exploring the Geometry of Swarm Intelligence: Negative Inertia and Ellipsoidal Search Space Evolution in PSO
| dc.contributor.author | Krämer, Katharina | en_US |
| dc.contributor.author | Müller, Stefan | en_US |
| dc.contributor.author | Kosterhon, Michael | en_US |
| dc.contributor.editor | Egger, Bernhard | en_US |
| dc.contributor.editor | Günther, Tobias | en_US |
| dc.date.accessioned | 2025-09-24T10:38:30Z | |
| dc.date.available | 2025-09-24T10:38:30Z | |
| dc.date.issued | 2025 | |
| dc.description.abstract | This paper introduces a geometry-aware method for analyzing swarm behavior in Particle Swarm Optimization (PSO) based on ellipsoidal modeling. Inspired by the n-ball hitting probability, we propose an abstraction of the search space covered by particles over time. Using principal component analysis (PCA), we approximate the particle distribution at each iteration with ellipsoids, enabling a visual and quantitative assessment of how well the swarm explores and concentrates its search effort. We apply this technique to investigate a PSO variant with negative inertia weights, which has shown promising performance in prior empirical analysis. While negative inertia may appear counterintuitive, our ellipsoidal analysis reveals that it introduces oscillatory search dynamics that balance exploration and exploitation more effectively than standard strategies such as constant inertia or linear decreasing inertia. Our experiments include a six-dimensional medical image registration task and an illustrative two-dimensional Rastrigin function, which serves to visually demonstrate how the swarm structure evolves. The proposed analysis framework provides new insight into swarm dynamics and offers a tool for understanding and comparing the behavior of PSO variants beyond conventional performance metrics. | en_US |
| dc.description.sectionheaders | Geometry, Simulation, and Optimization | |
| dc.description.seriesinformation | Vision, Modeling, and Visualization | |
| dc.identifier.doi | 10.2312/vmv.20251246 | |
| dc.identifier.isbn | 978-3-03868-294-3 | |
| dc.identifier.pages | 10 pages | |
| dc.identifier.uri | https://doi.org/10.2312/vmv.20251246 | |
| dc.identifier.uri | https://diglib.eg.org/handle/10.2312/vmv20251246 | |
| dc.publisher | The Eurographics Association | en_US |
| dc.rights | Attribution 4.0 International License | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | CCS Concepts: Mathematics of computing → Stochastic control and optimization; Computing methodologies → Visual analytics; Model verification and validation | |
| dc.subject | Mathematics of computing → Stochastic control and optimization | |
| dc.subject | Computing methodologies → Visual analytics | |
| dc.subject | Model verification and validation | |
| dc.title | Exploring the Geometry of Swarm Intelligence: Negative Inertia and Ellipsoidal Search Space Evolution in PSO | en_US |