Chin. Phys. B ›› 2014, Vol. 23 ›› Issue (1): 18903-018903.doi: 10.1088/1674-1056/23/1/018903

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇    下一篇

Unsupervised neural networks for solving Troesch’s problem

Muhammad Asif Zahoor Raja   

  1. Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan
  • 收稿日期:2013-02-23 修回日期:2013-05-18 出版日期:2013-11-12 发布日期:2013-11-12

Unsupervised neural networks for solving Troesch’s problem

Muhammad Asif Zahoor Raja   

  1. Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan
  • Received:2013-02-23 Revised:2013-05-18 Online:2013-11-12 Published:2013-11-12
  • Contact: Muhammad Asif Zahoor Raja E-mail:Muhammad.asif@ciit-attock.edu.pk, rasifzahoor@yahoo.com

摘要: In this study, stochastic computational intelligence techniques are presented for the solution of Troesch’s boundary value problem. The proposed stochastic solvers use the competency of a feed-forward artificial neural network for mathematical modeling of the problem in an unsupervised manner, whereas the learning of unknown parameters is made with local and global optimization methods as well as their combinations. Genetic algorithm (GA) and pattern search (PS) techniques are used as the global search methods and the interior point method (IPM) is used for an efficient local search. The combination of techniques like GA hybridized with IPM (GA-IPM) and PS hybridized with IPM (PS-IPM) are also applied to solve different forms of the equation. A comparison of the proposed results obtained from GA, PS, IPM, PS-IPM and GA-IPM has been made with the standard solutions including well known analytic techniques of the Adomian decomposition method, the variational iterational method and the homotopy perturbation method. The reliability and effectiveness of the proposed schemes, in term of accuracy and convergence, are evaluated from the results of statistical analysis based on sufficiently large independent runs.

关键词: Troesch’, s problem, artificial neural network, genetic algorithm, hybrid methods

Abstract: In this study, stochastic computational intelligence techniques are presented for the solution of Troesch’s boundary value problem. The proposed stochastic solvers use the competency of a feed-forward artificial neural network for mathematical modeling of the problem in an unsupervised manner, whereas the learning of unknown parameters is made with local and global optimization methods as well as their combinations. Genetic algorithm (GA) and pattern search (PS) techniques are used as the global search methods and the interior point method (IPM) is used for an efficient local search. The combination of techniques like GA hybridized with IPM (GA-IPM) and PS hybridized with IPM (PS-IPM) are also applied to solve different forms of the equation. A comparison of the proposed results obtained from GA, PS, IPM, PS-IPM and GA-IPM has been made with the standard solutions including well known analytic techniques of the Adomian decomposition method, the variational iterational method and the homotopy perturbation method. The reliability and effectiveness of the proposed schemes, in term of accuracy and convergence, are evaluated from the results of statistical analysis based on sufficiently large independent runs.

Key words: Troesch’s problem, artificial neural network, genetic algorithm, hybrid methods

中图分类号:  (Interdisciplinary applications of physics)

  • 89.20.-a
89.20.Ff (Computer science and technology) 89.20.Kk (Engineering)