To investigate surrogate optimisation (SO) as a modern, purely data-driven, nonlinear
adaptive iterative strategy for lens formula constant optimisation in intraocular
lens power calculation.A 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.The 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.The 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.
