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Updated: Aug 6, 2025

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Particle swarm optimisation strategies for IOL formula constant optimisation.

Achim Langenbucher1, Nóra Szentmáry2,3, Alan Cayless4

  • 1Department of Experimental Ophthalmology, Saarland University, Homburg/Saar, Germany.

Acta Ophthalmologica
|March 22, 2023
PubMed
Summary
This summary is machine-generated.

Particle Swarm Optimization (PSO) effectively optimizes intraocular lens power calculation constants. This data-driven method achieves accurate refractive predictions comparable to traditional algorithms.

Keywords:
formula constant optimisationformula prediction errorlens power calculationnonlinear iterative algorithmparticle swarm optimisationperformance metrics

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Area of Science:

  • Ophthalmology
  • Computational Science
  • Optics

Background:

  • Intraocular lens (IOL) power calculation requires precise formula constants for accurate refractive outcomes.
  • Traditional optimization methods may face challenges with complex, non-linear formulas.

Purpose of the Study:

  • To evaluate Particle Swarm Optimization (PSO) as a data-driven iterative strategy for optimizing IOL power calculation constants.
  • To compare PSO's performance against gradient-based optimization algorithms.

Main Methods:

  • A PSO algorithm was employed to minimize the root mean squared prediction error (rmsPE) for the Castrop formula.
  • The algorithm was tested on 888 eyes implanted with Hoya Vivinex lenses.
  • PSO performance was benchmarked against Trust-Region-Reflective and Interior-Point algorithms.

Main Results:

  • PSO demonstrated rapid and stable convergence, reducing rmsPE to 0.3440 diopters.
  • The optimized constants using PSO were C/H/R = 0.2982/0.2497/0.1435.
  • PSO achieved comparable accuracy to gradient-based methods, which converged faster.

Conclusions:

  • PSO is a robust, adaptive nonlinear algorithm for optimizing multi-constant formulas.
  • It operates independently of analytical gradients, adeptly handling functions with potential local minima.
  • PSO offers a powerful alternative for refractive prediction constant optimization.