Heuristic computing performances based Gudermannian neural network to solve the eye surgery corneal model

Abstract

The current work is related to present the solutions of the corneal shape-based eye surgery model (CSESM) by applying the novel procedures of Gudermannian neural network (GNN) along with the hybrid optimization of the global and local approaches of heuristic genetic algorithm (GA) and sequential quadratic programing (SQP), i.e., GNN-GASQP. An error function is constructed using the terminologies of the differential model along with the corresponding boundary conditions of the CSESM and then the optimization of the parameter is approved by the global operator GA at the start and then local refinements of SQP is implemented. Six different cases of the CSESM have been numerically treated using the GNN-GASQP and the scheme’s correctness is performed through the numerical Runge-Kutta (RK) results. The analysis based small and larger neurons is also implemented to authenticate the stability of GNN-GASQP. Moreover, the analysis through statistics using different measures of root mean square error, Theil’s inequality coefficient and variance account for is presented to check the consistency of GNN-GASQP for solving the CSESM.