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An improved clustering-based multi-swarm PSO using local diversification and topology information

Yves Matanga, Yanxia Sun, Zenghui Wang

TL;DR

This paper addresses two core limitations of clustering-based multiswarm PSO: insufficient local exploration during the preliminary search and limited clustering resolution that can miss sub-niches. It introduces two enhancements—pervasive-cognitive preliminary scouting using Halton sampling and concavity-based sub-niching via Hill-Valley tests—embedded in the TImPSO framework, which also uses silhouette-based k selection and Halton initialisation. Empirical results on the IEEE CEC2013 niching benchmarks show that TImPSO achieves higher peak ratios than kPSO, EDHC-PSO, and NichePSO, and remains superior after SQP post-optimisation, demonstrating the value of geometry/topology-aware clustering for multimodal optimization. The work also discusses scalability challenges in parallel niching and suggests a hybrid path integrating sequential niching to handle many peaks, with future tests on practical problems.

Abstract

Multi-swarm particle optimisation algorithms are gaining popularity due to their ability to locate multiple optimum points concurrently. In this family of algorithms, clustering-based multi-swarm algorithms are among the most effective techniques that join the closest particles together to form independent niche swarms that exploit potential promising regions. However, most clustering-based multi-swarms are Euclidean distance-based and only inquire about the potential of one peak within a cluster and thus can lose multiple peaks due to poor resolution. In a bid to improve the peak detection ratio, the current study proposes two enhancements. First, a preliminary local search across initial particles is proposed to ensure that each local region is sufficiently scouted prior to particle collaboration. Secondly, an investigative clustering approach that performs concavity analysis is proposed to evaluate the potential for several sub-niches within a single cluster. An improved clustering-based multi-swarm PSO (TImPSO) has resulted from these enhancements and has been tested against three competing algorithms in the same family using the IEEE CEC2013 niching datasets, resulting in an improved peak ratio for almost all the test functions.

An improved clustering-based multi-swarm PSO using local diversification and topology information

TL;DR

This paper addresses two core limitations of clustering-based multiswarm PSO: insufficient local exploration during the preliminary search and limited clustering resolution that can miss sub-niches. It introduces two enhancements—pervasive-cognitive preliminary scouting using Halton sampling and concavity-based sub-niching via Hill-Valley tests—embedded in the TImPSO framework, which also uses silhouette-based k selection and Halton initialisation. Empirical results on the IEEE CEC2013 niching benchmarks show that TImPSO achieves higher peak ratios than kPSO, EDHC-PSO, and NichePSO, and remains superior after SQP post-optimisation, demonstrating the value of geometry/topology-aware clustering for multimodal optimization. The work also discusses scalability challenges in parallel niching and suggests a hybrid path integrating sequential niching to handle many peaks, with future tests on practical problems.

Abstract

Multi-swarm particle optimisation algorithms are gaining popularity due to their ability to locate multiple optimum points concurrently. In this family of algorithms, clustering-based multi-swarm algorithms are among the most effective techniques that join the closest particles together to form independent niche swarms that exploit potential promising regions. However, most clustering-based multi-swarms are Euclidean distance-based and only inquire about the potential of one peak within a cluster and thus can lose multiple peaks due to poor resolution. In a bid to improve the peak detection ratio, the current study proposes two enhancements. First, a preliminary local search across initial particles is proposed to ensure that each local region is sufficiently scouted prior to particle collaboration. Secondly, an investigative clustering approach that performs concavity analysis is proposed to evaluate the potential for several sub-niches within a single cluster. An improved clustering-based multi-swarm PSO (TImPSO) has resulted from these enhancements and has been tested against three competing algorithms in the same family using the IEEE CEC2013 niching datasets, resulting in an improved peak ratio for almost all the test functions.

Paper Structure

This paper contains 21 sections, 21 equations, 5 figures, 7 tables, 8 algorithms.

Table of Contents

  1. Introduction
  2. Classical particle swarm optimisation
  3. Neighbourhood topologies
  4. Clustering-based multiswarm PSO algorithms
  5. kPSO
  6. EDHC-PSO
  7. NichePSO
  8. Proposed Enhancements
  9. k-means clustering
  10. Estimating the number of clusters using Silhouette analysis
  11. Contribution analysis of loosely connected topologies in CMPSO algorithms
  12. The Clustering defect of CMPSO algorithms
  13. Proposed algorithm
  14. Computational experiments
  15. Performance measure
  16. ...and 6 more sections

Figures (5)

  • Figure 1: Spatial illustration of a particle movement in PSO Bansal2019
  • Figure 2: PSO neighbourhood topologies: (a) Cognitive model (b) lbest topology (c) gbest topology (d) small-world topology (e) Von Neumann topology (f) Wheel topology
  • Figure 3: Halton-sequence based particle scouting (2D space)
  • Figure 4: Distance-based Clustering Defect Illustration
  • Figure 5: Proposed algorithm framework