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The critical state in particle swarm optimisation

The critical state in particle swarm optimisation

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Particle swarm optimisation (PSO) is a widely used meta-heuristic algorithm, which has been successfully applied to a large variety of problems in optimisation, prediction, classification, visualisation and robotics. However, the underlying mechanism that leads to good solutions in these domains is not well understood. A number of parameters influence the algorithm mainly by determining the balance between exploration and exploitation. In this chapter, we describe the behaviour of PSO as a product of random matrices, and use a Lyapunov exponent to precisely characterise the critical parameters for PSO. The theoretical results are discussed based on numerical experiments for standard benchmark problems.

Chapter Contents:

  • Abstract
  • 10.1 Introduction
  • 10.1.1 Particle swarm optimisation
  • 10.1.1.1 PSO parameter selection and resultant behaviours
  • 10.1.1.2 Alternative meta-heuristics
  • 10.1.1.3 The problem of making comparisons between algorithms
  • 10.1.2 On criticality
  • 10.1.3 The dynamics of PSO
  • 10.1.4 Matrix formulation
  • 10.2 Critical swarm conditions for a single particle
  • 10.2.1 PSO as a random dynamical system
  • 10.2.2 Stability
  • 10.2.3 Personal best vs. global best
  • 10.3 Simulations
  • 10.3.1 Combining the results from multiple cost functions
  • 10.4 Discussion
  • 10.4.1 Relevance of criticality
  • 10.4.2 Comparison with earlier explanations
  • 10.4.2.1 Lines of stability when viewed against average cost function results
  • 10.4.2.2 Lines of stability when viewed against individual cost function results
  • 10.4.2.3 Lines of stability when viewed against detailed cost function results
  • 10.4.3 Switching dynamics at discovery of better solutions
  • 10.4.4 The role of personal best, present best and best ever
  • 10.5 Conclusion
  • Acknowledgement
  • References

Inspec keywords: particle swarm optimisation

Other keywords: PSO; meta-heuristic algorithm; particle swarm optimisation; critical parameters

Subjects: Optimisation; Optimisation techniques; Optimisation techniques

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