In this study, bio-inspired computational techniques have been exploited to get the numerical solution of a nonlinear two-point boundary value problem arising in the modelling of the corneal shape. The computational process of modelling and optimization makes enormously straightforward to obtain accurate approximate solutions of the corneal shape models through artificial neural networks, pattern search (PS), genetic algorithms (GAs), simulated annealing (SA), active-set technique (AST), interior-point technique, sequential quadratic programming and their hybrid forms based on GA–AST, PS–AST and SA–AST. Numerical results show that the designed solvers provide a reasonable precision and efficiency with minimal computational cost. The efficacy of the proposed computing strategies is also investigated through a descriptive statistical analysis by means of histogram illustrations, probability plots and one-way analysis of variance.

在这项研究中，已利用生物启发性的计算技术来获取在角膜形状建模中出现的非线性两点边值问题的数值解。通过人工神经网络，模式搜索（PS），遗传算法（GA），模拟退火（SA），有效集技术（AST），建模和优化的计算过程使获得角膜形状模型的精确近似解变得非常简单，内点技术，顺序二次规划及其基于GA–AST，PS–AST和SA–AST的混合形式。数值结果表明，所设计的求解器以最小的计算成本提供了合理的精度和效率。