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CLC number: TP183; O175

On-line Access: 2017-04-12

Received: 2015-11-10

Revision Accepted: 2016-02-17

Crosschecked: 2017-03-14

Cited: 1

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Citations:  Bibtex RefMan EndNote GB/T7714


Muhammad Asif Zahoor Raja


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Frontiers of Information Technology & Electronic Engineering  2017 Vol.18 No.4 P.464-484


Neuro-heuristic computational intelligence for solving nonlinear pantograph systems

Author(s):  Muhammad Asif Zahoor Raja, Iftikhar Ahmad, Imtiaz Khan, Muhammed Ibrahem Syam, Abdul Majid Wazwaz

Affiliation(s):  Department of Electrical Engineering, COMSATs Institute of Information Technology, Attock 43200, Pakistan; more

Corresponding email(s):   rasifzahoor@yahoo.com, Muhammad.asif@ciit-attock.edu.pk

Key Words:  Neural networks, Initial value problems (IVPs), Functional differential equations (FDEs), Unsupervised learning, Genetic algorithms (GAs), Interior-point technique (IPT)

Muhammad Asif Zahoor Raja, Iftikhar Ahmad, Imtiaz Khan, Muhammed Ibrahem Syam, Abdul Majid Wazwaz. Neuro-heuristic computational intelligence for solving nonlinear pantograph systems[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(4): 464-484.

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author="Muhammad Asif Zahoor Raja, Iftikhar Ahmad, Imtiaz Khan, Muhammed Ibrahem Syam, Abdul Majid Wazwaz",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Neuro-heuristic computational intelligence for solving nonlinear pantograph systems
%A Muhammad Asif Zahoor Raja
%A Iftikhar Ahmad
%A Imtiaz Khan
%A Muhammed Ibrahem Syam
%A Abdul Majid Wazwaz
%J Frontiers of Information Technology & Electronic Engineering
%V 18
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%D 2017
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1500393

T1 - Neuro-heuristic computational intelligence for solving nonlinear pantograph systems
A1 - Muhammad Asif Zahoor Raja
A1 - Iftikhar Ahmad
A1 - Imtiaz Khan
A1 - Muhammed Ibrahem Syam
A1 - Abdul Majid Wazwaz
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 18
IS - 4
SP - 464
EP - 484
%@ 2095-9184
Y1 - 2017
PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1500393

We present a neuro-heuristic computing platform for finding the solution for initial value problems (IVPs) of nonlinear pantograph systems based on functional differential equations (P-FDEs) of different orders. In this scheme, the strengths of feed-forward artificial neural networks (ANNs), the evolutionary computing technique mainly based on genetic algorithms (GAs), and the interior-point technique (IPT) are exploited. Two types of mathematical models of the systems are constructed with the help of ANNs by defining an unsupervised error with and without exactly satisfying the initial conditions. The design parameters of ANN models are optimized with a hybrid approach GA–IPT, where GA is used as a tool for effective global search, and IPT is incorporated for rapid local convergence. The proposed scheme is tested on three different types of IVPs of P-FDE with orders 1–3. The correctness of the scheme is established by comparison with the existing exact solutions. The accuracy and convergence of the proposed scheme are further validated through a large number of numerical experiments by taking different numbers of neurons in ANN models.


概要:本文提出了一种启发式神经网络计算平台,用于解决基于不同阶数泛函微分方程的非线性受电弓系统(Pantograph systems based on functional differential equations, P-FDEs)中的初值问题(Initial value problems, IVPs)。该方案利用了前馈人工神经网络(Artificial neural networks, ANNs)、基于遗传算法(Genetical gorithms, GAs)的进化计算技术,以及内点技术(Interior-point technique, IPT)。通过设定一个无监督学习误差,针对完全和不完全满足初始条件两种情况,利用ANNs创建了系统的两种数学模型。采用GA-IPT混合算法,对ANN模型的设计参数进行了优化。在GA-IPT中,GA是有效的全局搜索工具,IPT则用于快速的局部收敛。针对三种不同类型的1-3阶P-FDEs的IVPs对该方案进行了测试。通过对比现有的精确解,确认了该方案的正确性。通过采用不同数量神经元的ANN模型进行了大量的数值实验,进一步验证了该方案的准确性和收敛性。


Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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