Integrated intelligence of neuro-evolution with sequential quadratic programming for second-order Lane-Emden pantograph models

Abstract The present research work is to puts forth the numerical solutions of the nonlinear second-order Lane-Emden-pantograph (LEP) delay differential equation by using the approximation competency of the artificial neural networks (ANNs) trained with the combined strengths of global/local search exploitation of genetic algorithm (GA) and active-set (AS) method, i.e., ANNGAAS. In the proposed ANNGAAS, the objective function is designed by using the mean square error function with continuous mappings of ANNs for the LEP delay differential equation. The training of these constructed networks is conducted proficiently using the integrated capability of global search with GA and assisted local search along with AS approach. The performance of design computing paradigm ANNGAAS is evaluated effectively on variants of LEP delay differential models, while the statistical investigations based on different operators further validate the accuracy and convergence.

[1]  M. Raja,et al.  A Computational Analysis of Two-Phase Casson Nanofluid Passing a Stretching Sheet Using Chemical Reactions and Gyrotactic Microorganisms , 2019, Mathematical Problems in Engineering.

[2]  Abdul-Majid Wazwaz,et al.  A new algorithm for solving differential equations of Lane-Emden type , 2001, Appl. Math. Comput..

[3]  N. Shawagfeh.  Nonperturbative approximate solution for Lane–Emden equation , 1993 .

[4]  Raja Muhammad Asif Zahoor,et al.  Design of a mathematical model for the Stuxnet virus in a network of critical control infrastructure , 2019, Comput. Secur..

[5]  Robert A. Van Gorder,et al.  APPLICATION OF THE BPES TO LANE-EMDEN EQUATIONS GOVERNING POLYTROPIC AND ISOTHERMAL GAS SPHERES , 2012 .

[6]  Panos M. Pardalos,et al.  A modified active set algorithm for transportation discrete network design bi-level problem , 2017, J. Glob. Optim..

[7]  Abdul-Majid Wazwaz,et al.  Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory , 2015, Connect. Sci..

[8]  Poom Kumam,et al.  Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system , 2020 .

[9]  Yang Kuang,et al.  Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters , 2002, SIAM J. Math. Anal..

[10]  Dumitru Baleanu,et al.  A new stochastic computing paradigm for the dynamics of nonlinear singular heat conduction model of the human head , 2018, The European Physical Journal Plus.

[11]  Raja Muhammad Asif Zahoor,et al.  Bio-inspired computational heuristics for parameter estimation of nonlinear Hammerstein controlled autoregressive system , 2018, Neural Computing and Applications.

[12]  Zulqurnain Sabir,et al.  Solving a new design of nonlinear second-order Lane–Emden pantograph delay differential model via Bernoulli collocation method , 2020 .

[13]  Francesco Borrelli,et al.  A primal‐dual active‐set method for distributed model predictive control , 2017 .

[14]  Mehdi Dehghan,et al.  Variational iteration method for solving a generalized pantograph equation , 2009, Comput. Math. Appl..

[15]  Raja Muhammad Asif Zahoor,et al.  Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming , 2019, Neural Computing and Applications.

[16]  Nader Vahdat Azad,et al.  Application of nanofluids for the optimal design of shell and tube heat exchangers using genetic algorithm , 2016 .

[17]  Mehmet Sezer,et al.  Approximate solution of multi-pantograph equation with variable coefficients , 2008 .

[18]  Abdul-Majid Wazwaz,et al.  Neuro-heuristics for nonlinear singular Thomas-Fermi systems , 2018, Appl. Soft Comput..

[19]  Raja Muhammad Asif Zahoor,et al.  Intelligent computing for numerical treatment of nonlinear prey-predator models , 2019, Appl. Soft Comput..

[20]  Muhammad Awais,et al.  Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics , 2018, The European Physical Journal Plus.

[21]  A. Taghavi,et al.  A solution to the Lane–Emden equation in the theory of stellar structure utilizing the Tau method , 2013 .

[22]  W. Waseem,et al.  A study of changes in temperature profile of porous fin model using cuckoo search algorithm , 2020 .

[23]  Naveed Ishtiaq Chaudhary,et al.  Novel computing paradigms for parameter estimation in power signal models , 2019, Neural Computing and Applications.

[24]  Raja Muhammad Asif Zahoor,et al.  Bio-inspired heuristics for layer thickness optimization in multilayer piezoelectric transducer for broadband structures , 2019, Soft Comput..

[25]  Shijun Liao,et al.  A new analytic algorithm of Lane-Emden type equations , 2003, Appl. Math. Comput..

[26]  Raja Muhammad Asif Zahoor,et al.  Design of bio-inspired heuristic technique integrated with interior-point algorithm to analyze the dynamics of heartbeat model , 2017, Appl. Soft Comput..

[27]  M. A. Manzar,et al.  An efficient computational intelligence approach for solving fractional order Riccati equations using ANN and SQP , 2015 .

[28]  Z. Xin,et al.  Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem with Degenerate Density Dependent Viscosities , 2015, 1507.01069.

[29]  Juan Luis García Guirao,et al.  Stochastic numerical technique for solving HIV infection model of CD4+ T cells , 2020, The European Physical Journal Plus.

[30]  A. Wazwaz,et al.  Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method , 2013, Journal of Mathematical Chemistry.

[31]  Aydin Kurnaz,et al.  Approximate Solutions of Generalized Pantograph Equations by the Differential Transform Method , 2007 .

[32]  Wei Li,et al.  Ultrafast all-optical graphene modulator. , 2014, Nano letters.

[33]  Yigang He,et al.  Design of Fractional Swarm Intelligent Computing With Entropy Evolution for Optimal Power Flow Problems , 2020, IEEE Access.

[34]  S. Niazi,et al.  Numerical Treatments to Analyze the Nonlinear Radiative Heat Transfer in MHD Nanofluid Flow with Solar Energy , 2020 .

[35]  Zulqurnain Sabir,et al.  On a New Model Based on Third-Order Nonlinear Multisingular Functional Differential Equations , 2020 .

[36]  Shengfan Zhou,et al.  Permanence of species in nonautonomous discrete Lotka-Volterra competitive system with delays and feedback controls , 2008 .

[37]  Raja Muhammad Asif Zahoor,et al.  Novel design of Morlet wavelet neural network for solving second order Lane-Emden equation , 2020, Math. Comput. Simul..

[38]  Muhammad Tariq,et al.  Design of artificial neural network models optimized with sequential quadratic programming to study the dynamics of nonlinear Troesch’s problem arising in plasma physics , 2016, Neural Computing and Applications.

[39]  Reza Abazari,et al.  Solution of Nonlinear Second-Order Pantograph Equations via Differential Transformation Method , 2009 .

[40]  Raja Muhammad Asif Zahoor,et al.  Fractional neural network models for nonlinear Riccati systems , 2017, Neural Computing and Applications.

[41]  Raja Muhammad Asif Zahoor,et al.  Design of Epidemic Computer Virus Model with Effect of Quarantine in the Presence of Immunity , 2018, Fundam. Informaticae.

[42]  Raja Muhammad Asif Zahoor,et al.  Novel Computational Heuristics for Wireless Parameters Estimation in Bistatic Radar systems , 2020, Wirel. Pers. Commun..

[43]  Hyunsoo Kim,et al.  Nonnegative Matrix Factorization Based on Alternating Nonnegativity Constrained Least Squares and Active Set Method , 2008, SIAM J. Matrix Anal. Appl..

[44]  Raja Muhammad Asif Zahoor,et al.  Computational intelligence methodology for the analysis of RC circuit modelled with nonlinear differential order system , 2016, Neural Computing and Applications.

[45]  Poom Kumam,et al.  Fractional Neuro-Sequential ARFIMA-LSTM for Financial Market Forecasting , 2020, IEEE Access.

[46]  Raja Muhammad Asif Zahoor,et al.  Design of cascade artificial neural networks optimized with the memetic computing paradigm for solving the nonlinear Bratu system , 2019, The European Physical Journal Plus.

[47]  Muhammad Asif Zahoor Raja,et al.  A novel wavenets long short term memory paradigm for wind power prediction , 2020 .

[48]  Ayaz Hussain Bukhari,et al.  Neuro-fuzzy modeling and prediction of summer precipitation with application to different meteorological stations , 2020 .

[49]  J. A. Tenreiro Machado,et al.  An innovative fractional order LMS algorithm for power signal parameter estimation , 2020 .

[50]  Raja Muhammad Asif Zahoor,et al.  Design of fractional order epidemic model for future generation tiny hardware implants , 2020, Future Gener. Comput. Syst..

[51]  Raja Muhammad Asif Zahoor,et al.  Numerical solution of doubly singular nonlinear systems using neural networks-based integrated intelligent computing , 2017, Neural Computing and Applications.

[52]  M. Z. Liu,et al.  Properties of analytic solution and numerical solution of multi-pantograph equation , 2004, Appl. Math. Comput..