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首页> 美国卫生研究院文献>SpringerPlus >A new numerical approach to solve Thomas–Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming
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A new numerical approach to solve Thomas–Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming

机译：一种新的数值方法使用结合顺序二次规划的生物启发式启发法来求解原子的Thomas-Fermi模型

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In this study, a novel bio-inspired computing approach is developed to analyze the dynamics of nonlinear singular Thomas–Fermi equation (TFE) arising in potential and charge density models of an atom by exploiting the strength of finite difference scheme (FDS) for discretization and optimization through genetic algorithms (GAs) hybrid with sequential quadratic programming. The FDS procedures are used to transform the TFE differential equations into a system of nonlinear equations. A fitness function is constructed based on the residual error of constituent equations in the mean square sense and is formulated as the minimization problem. Optimization of parameters for the system is carried out with GAs, used as a tool for viable global search integrated with SQP algorithm for rapid refinement of the results. The design scheme is applied to solve TFE for five different scenarios by taking various step sizes and different input intervals. Comparison of the proposed results with the state of the art numerical and analytical solutions reveals that the worth of our scheme in terms of accuracy and convergence. The reliability and effectiveness of the proposed scheme are validated through consistently getting optimal values of statistical performance indices calculated for a sufficiently large number of independent runs to establish its significance.
机译：在这项研究中，开发了一种新颖的受生物启发的计算方法，以通过利用有限差分方案（FDS）的强度离散化来分析在原子势能和电荷密度模型中出现的非线性奇异Thomas-Fermi方程（TFE）的动力学。并通过遗传算法（GA）与顺序二次规划混合进行优化。 FDS程序用于将TFE微分方程转换为非线性方程组。根据均方意义上组成方程式的残差构建适应度函数，并将其表示为最小化问题。系统参数的优化是使用GA进行的，GA是与SQP算法集成的可行的全局搜索工具，用于快速优化结果。通过采用不同的步长和不同的输入间隔，将设计方案应用于解决五种不同情况下的TFE。将拟议的结果与最新的数值和解析解进行比较，可以发现我们的方案在准确性和收敛性方面的价值。通过持续获取统计性能指标的最优值（为足够多的独立运行计算得出其性能）来验证所提出方案的可靠性和有效性。

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