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}.

翻译：基于群体智能的优化算法在解决复杂优化问题方面已展现出显著成效。然而，由于算法各组件如何影响整体性能的透明度有限，其广泛应用仍受到质疑。本研究针对一种流行的群体算法——粒子群优化（PSO），开展了多方面的可解释性相关探究。通过这项工作，我们提出了一个框架，利用新颖的机器学习方法，使PSO中不同拓扑结构和参数的作用变得可解释与可说明。首先，我们基于探索性景观分析（Exploratory Landscape Analysis）构建了全面的景观特征刻画框架，以量化问题难度并识别影响PSO优化性能的关键问题特征。其次，我们系统比较了三种拓扑结构——环形（Ring）、星形（Star）和冯·诺依曼（Von Neumann）拓扑，分析它们对探索-利用平衡、收敛行为和解质量的差异化影响，并最终建立了一个可解释的PSO基准测试框架。该工作成功揭示了群体拓扑如何影响信息流、多样性和收敛性。通过对24个多维基准函数进行系统实验，我们为拓扑选择和参数配置提出了实用指南。这些发现揭开了PSO的黑箱特性，为群体智能系统提供了更高的透明度和可解释性。源代码可在 \textcolor{blue}{https://github.com/GitNitin02/ioh_pso} 获取。