Memetic computing based numerical solution to Troesch problem

Article type: Research Article

Authors: Rahman, Atta^{; *}

Affiliations: Department of Computer Science, College of Computer Science and Information Technology (CCSIT), Imam Abdulrahman Bin Faisal University (IAU), Dammam, KSA

Correspondence: [*] Corresponding author. Atta Rahman, Department of Computer Science, College of Computer Science and Information Technology (CCSIT), Imam Abdulrahman Bin Faisal University (IAU), P.O. Box 1982, Dammam, KSA. E-mail: aaurrahman@iau.edu.sa.

Abstract: In this paper, a numerical solution to the Troesch problem using a memetic computing technique is proposed. In this regard, a linear combination of Gaussian radial basis functions (GRBF) as approximate mathematical framework is suggested. A set of unknown yet adaptable parameters are modeled in a cost function, representing the trial solution. Differential Evolution (DE) algorithm crossed with Interior Point algorithm (IPA) and Pattern Search (PS) are utilized to find the unknowns. Numerical results based on three special cases of proposed scheme are compared with the exact solution as well as many other numerical and classical approximation methods. Analysis reveals that the proposed scheme is promising in terms of accuracy and conformation to the exact solution.

Keywords: Troesch problem, differential evolution, gaussian radial basis function, boundary value problem, pattern search (PS), interior point algorithm (IPA), memetic computing (MC)

DOI: 10.3233/JIFS-18579

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 1, pp. 1545-1554, 2019