Nitin Gupta, Bapi Dutta, Anupam Yadav
Swarm based optimization algorithms have demonstrated remarkable success in solving complex optimization problems. However, their widespread adoption remains sceptical due to limited transparency in how different algorithmic components influence the overall performance of the algorithm. This work presents a multi-faceted interpretability related investigations of one of the popular swarm algorithms, Particle Swarm Optimization. Through this work, we provide a framework that makes the role of different topologies and parameters in PSO interpretable and explainable using novel machine learning approach. We first developed a comprehensive landscape characterization framework using Exploratory Landscape Analysis to quantify problem difficulty and identify critical features in the problem that affects the optimization performance of PSO. Secondly, we rigorously compare three topologies - Ring, Star, and Von Neumann analyzing their distinct impacts on exploration-exploitation balance, convergence behavior, and solution quality and eventually develop an explainable benchmarking framework for PSO. The work successfully decodes how swarm topologies affect information flow, diversity, and convergence. Through systematic experimentation across 24 benchmark functions in multiple dimensions, we establish practical guidelines for topology selection and parameter configuration. These findings uncover the black-box nature of PSO, providing more transparency and interpretability to swarm intelligence systems. The source code is available at \textcolor{blue}{https://github.com/GitNitin02/ioh_pso}.