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Explainable Swarm: A Methodological Framework for Interpreting Swarm Intelligence

Nitin Gupta, Bapi Dutta, Anupam Yadav

TL;DR

This study addresses the opacity of Particle Swarm Optimization by combining Exploratory Landscape Analysis (ELA) with an explainable benchmarking framework (IOHxplainer) to reveal how topology (Star, Ring, Von Neumann) and hyperparameters drive exploration–exploitation balance across diverse landscapes. The authors integrate SHAP-based analysis, AOCC performance metrics, and data-driven configuration learning (decision trees and random forests) to map algorithm settings to problem structure, validated on 24 BBOB functions in 2D and 5D. Key contributions include a unified explainability pipeline, topology-specific performance insights, and a data-driven approach to selecting or configuring PSO settings with interpretable rules. The work advances trustworthy swarm intelligence by promoting transparent design and actionable guidelines for topology and parameter choices, with practical implications for deploying PSO in real-world optimization tasks.

Abstract

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}.

Explainable Swarm: A Methodological Framework for Interpreting Swarm Intelligence

TL;DR

This study addresses the opacity of Particle Swarm Optimization by combining Exploratory Landscape Analysis (ELA) with an explainable benchmarking framework (IOHxplainer) to reveal how topology (Star, Ring, Von Neumann) and hyperparameters drive exploration–exploitation balance across diverse landscapes. The authors integrate SHAP-based analysis, AOCC performance metrics, and data-driven configuration learning (decision trees and random forests) to map algorithm settings to problem structure, validated on 24 BBOB functions in 2D and 5D. Key contributions include a unified explainability pipeline, topology-specific performance insights, and a data-driven approach to selecting or configuring PSO settings with interpretable rules. The work advances trustworthy swarm intelligence by promoting transparent design and actionable guidelines for topology and parameter choices, with practical implications for deploying PSO in real-world optimization tasks.

Abstract

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}.

Paper Structure

This paper contains 23 sections, 3 equations, 16 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Need of Explainabilty in PSO and Current Status of Research
  3. Impact of Communication Topologies in PSO
  4. Explainable Benchmarking Frameworks for PSO
  5. Deeper Understanding Benchmark Problems
  6. Highlights of Identified Research Gaps
  7. Summary of Contributions
  8. ELA-based visualization for benchmarking
  9. Explainablity of PSO
  10. Swarm Behaviour Analysis on Population Topologies
  11. Explainer Framework for PSO
  12. IOHxplainer
  13. Experimental Setup and Results
  14. Performance Metrics
  15. Hyperparameter Impact Analysis
  16. ...and 8 more sections

Figures (16)

  • Figure 1: A Framework for Automated and Explainable Analysis of PSO Configurations.
  • Figure 2: The Impact of Hyperparameters on Performance for Benchmark Function in a 2d PSO with Star Topology
  • Figure 3: The Impact of Hyperparameters on Performance for Benchmark Function in a 2d PSO with Ring Topology
  • Figure 4: The Impact of Hyperparameters on Performance for Benchmark Function in a 2d PSO with Von Neumann Topology
  • Figure 5: The Impact of Hyperparameters on Performance for Benchmark Function in a 5d PSO with Star Topology
  • ...and 11 more figures