A hybrid Harris hawks-Nelder-Mead optimization for practical nonlinear ordinary differential equations
A hybrid Harris hawks-Nelder-Mead optimization for practical nonlinear ordinary differential equations
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DOI：
10.1007/s12065-020-00497-3
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发表时间：
2020-10-11
影响因子：
2.6
通讯作者：
Hassanien, Aboul Ella
中科院分区：
文献类型：
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作者：
Rizk-Allah, Rizk M.;Hassanien, Aboul Ella
微分方程经常出现在科学研究和工程的许多领域。通常，就计算工作量而言，找到分析（精确）解是一项昂贵的任务，并且对于某些复杂任务来说可能不是一项可实现的任务。为了有效地处理各种线性和非线性微分方程，本文提出了一种基于混合Harris hawks-Nelder-Mead优化算法的近似方法，目的是获得精确可靠的解。该方法基于傅里叶级数展开和Harris hawks-Nelder-Mead优化算法。在这个意义上，微分方程被表示为一个优化模型的加权残差函数（成本函数），需要被最小化，其中微分方程的边界和初始条件被认为是优化模型的约束。通过六个不同性质的微分方程和四个机械工程微分方程的算例，验证了该算法的实用性和有效性。通过世代距离度量和Wilcoxon符号秩检验对不同算法进行比较，验证了该算法的有效性。
Differential equations can often be seen in many fields of scientific research and engineering. Typically, finding the analytical (exact) solution is expensive task in terms of computational effort and may not an attainable task for some complex tasks. To effectively handle a wide variety of linear and nonlinear differential equations, this paper presents an approximate methodology based on hybrid Harris hawks-Nelder-Mead optimization algorithm with the aim to achieve accurate and reliable solution. The proposed methodology is introduced on basis of Fourier series expansion and Harris hawks-Nelder-Mead optimization algorithm. In this sense, the differential equation is represented as an optimization model by the means of the weighted residual function (cost function) that needed to be minimized, where the boundary and initial conditions of the differential equation are considered as the constraints of the optimization model. The practicality and efficiency of the proposed algorithm are demonstrated through six differential equations with different nature as well as four mechanical engineering differential equations. The comparison against different algorithms, by using the generational distance metric and Wilcoxon sign rank test, showed the effectiveness of the proposed algorithm.