PSOAnalysis

Numerical analysis of Particle Swarm Optimization

PSO is a multi-agent metaheuristic derivative-free optimization method capable of globally minimizing nonconvex and nonsmooth functions in high dimensions. It was initially introduced by Kennedy and Eberhart in the 1990s.

Version 1.2

Date 31.05.2023

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R e f e r e n c e

On the Global Convergence of Particle Swarm Optimization Methods

https://link.springer.com/article/10.1007/s00245-023-09983-3

by

• Hui   H u a n g   (University of Graz),
• Jinniao   Q i u   (University of Calgary),
• Konstantin   R i e d l   (Technical University of Munich & Munich Center for Machine Learning)

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D e s c r i p t i o n

MATLAB implementation, which illustrates PSO and the influence of its parameters, and tests the method on a competitive high-dimensional and well understood benchmark problem in the machine learning literature.

For the reader's convenience we describe the folder structure in what follows:

BenchmarkFunctions

• objective_function.m: objective function generator
• ObjectiveFunctionPlot1/2d.m: plotting routine for objective function

VarianceandEnergyBasedCBOAnalysis

• analyses: convergence and parameter analyses of PSO
  • PSONumericalExample.m: testing script
  • PSOParameters_PhaseTransition.m: Phase transition diagrams for parameter analysis
• results: folder to save numerical results
  • plot_phasetransitiondiagram: plotting routine for phase diagrams
  • PhaseTransitionDiagrams_msigma2: folder for phase transition diagrams for m and sigma2
• PSO: code of PSO optimizer
  • compute_yalpha.m: computation of consensus point
  • S_beta.m: function to compare current with in-time best position
  • PSO_update: one PSO step
  • PSO.m: PSO optimizer
  • PSOmachinelearning.m: PSO optimizer for machine learning applications
• visualizations: visualization of the CBO dynamics
  • PSODynamicsIllustration.m: Illustration of the PSO dynamics
  • PSOIllustrative.m: Illustration of the PSO at work

NN: machine learning experiments with PSO as optimization method for training

• architecture
  • NN.m: forward pass of NN
  • eval_accuracy.m: evaluate training or test accuracy
  • comp_performance.m: compute and display loss and training or test accuracy
• data: data and function to load data
• Scripts_for_PSO
  • MNISTClassificationPSO.m: script training the NN for MNIST with PSO
• results/PSO: folder to save numerical results
  • plot_training_testing_accuracy: plotting routine for performance plots
  • CNN: folder for CNN results
  • ShallowNN: folder for shallow NN results
  • plot_loss_and_testing_accuracy_PSON100/1000: plotting routine for performance plots

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C i t a t i o n

@article{huang2023global,
  title={On the global convergence of particle swarm optimization methods},
  author={Huang, Hui and Qiu, Jinniao and Riedl, Konstantin},
  journal={Applied Mathematics \& Optimization},
  volume={88},
  number={2},
  pages={30},
  year={2023},
  publisher={Springer}
}