Surrogate optimisation strategies for intraocular lens formula constant optimisation

被引:0
|
作者
Langenbucher, Achim [1 ,7 ]
Wendelstein, Jascha [1 ,2 ]
Cayless, Alan [3 ]
Hoffmann, Peter [4 ]
Szentmary, Nora [5 ,6 ]
机构
[1] Saarland Univ, Dept Expt Ophthalmol, Homburg, Saar, Germany
[2] Inst Refrakt & Ophthalmo Chirurg IROC, Zurich, Switzerland
[3] Open Univ, Sch Phys Sci, Milton Keynes, England
[4] Augen & Laserklin Castrop Rauxel, Castrop Rauxel, Germany
[5] Saarland Univ, Dr Rolf M Schwiete Ctr Limbal Stem Cell & Aniridia, Homburg, Saar, Germany
[6] Semmelweis Univ, Dept Ophthalmol, Budapest, Hungary
[7] Saarland Univ, Dept Expt Ophthalmol, Kirrberger Str 100 Bldg 22, D-66424 Homburg, Germany
关键词
formula constant optimisation; formula prediction error; lens power calculation; nonlinear iterative algorithm; performance metrics; surrogate optimisation; PARTIAL COHERENCE INTERFEROMETRY; BIOMETRY;
D O I
10.1111/aos.16670
中图分类号
R77 [眼科学];
学科分类号
100212 ;
摘要
PurposeTo investigate surrogate optimisation (SO) as a modern, purely data-driven, nonlinear adaptive iterative strategy for lens formula constant optimisation in intraocular lens power calculation.MethodsA SO algorithm was implemented for optimising the root mean squared formula prediction error (rmsPE, defined as predicted refraction minus achieved refraction) for the SRKT, Hoffer Q, Holladay, Haigis and Castrop formulae in a dataset of N = 888 cataractous eyes with implantation of the Hoya Vivinex hydrophobic acrylic aspheric lens. A Gaussian Process estimator was used as the model, and the SO was initialised with equidistant datapoints within box constraints, and the number of iterations restricted to either 200 (SRKT, Hoffer Q, Holladay) or 700 (Haigis, Castrop). The performance of the algorithm was compared to the classical gradient-based Levenberg-Marquardt algorithm.ResultsThe SO algorithm showed stable convergence after fewer than 50/150 iterations (SRKT, HofferQ, Holladay, Haigis, Castrop). The rmsPE was reduced systematically to 0.4407/0.4288/0.4265/0.3711/0.3449 dioptres. The final constants were A = 119.2709, pACD = 5.7359, SF = 1.9688, -a0 = 0.5914/a1 = 0.3570/a2 = 0.1970, C = 0.3171/H = 0.2053/R = 0.0947 for the SRKT, Hoffer Q, Holladay, Haigis and Castrop formula and matched the respective constants optimised in previous studies.ConclusionThe SO proves to be a powerful adaptive nonlinear iteration algorithm for formula constant optimisation, even in formulae with one or more constants. It acts independently of a gradient and is in general able to search within a (box) constrained parameter space for the best solution, even where there are multiple local minima of the target function.
引用
收藏
页码:e915 / e925
页数:11
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