Design of evolutionary computational intelligent solver for nonlinear corneal shape model by Mexican Hat and Gaussian wavelet neural networks

Abstract

In this study, an integrated computational intelligence algorithm is implemented for the numerical treatment of the two-point boundary value problems that arise in the nonlinear corneal shape (NCS) model through the exploitation of wavelet neural networks including Mexican-Hat (MHWNNs) and Gaussian-wavelet (GWNNs) through global genetic algorithms (GAs) then hybridization with local sequential quadratic programming (SQP) solvers, i.e. MHWNNs-GAs, GWNNs-GAs, MHWNNs-GA-SQP, and GWNNs-GA-SQP respectively. The GWNNs and MHWNNs are applied to calculate the mean squared error of mathematical modeling of the proposed problem through objective functions while optimization of the fitness functions is initially conducted with an efficiency of global search GAs and then the efficacy of local search technique SQP for fine-tuning. A comparison of the proposed solutions of MHWNNs-GAs, GWNNs-GAs, MHWNNs-GA-SQP, and GWNNs-GA-SQP solvers with a reference solution of Adam’s method shows that the proposed schemes have better accuracy, stability, efficiency consistency on an independent number of runs analyzed through complexity analysis and different statistical operators.

KEYWORDS:

• Gaussian-wavelets
• stochastic numerical computing
• sequential quadratic programming
• neural networks
• Mexican-Hat-wavelet
• genetic algorithms
• corneal shape model

Disclosure statement

No potential conflict of interest was reported by the author(s).