Numerical Solution to Troesch's Problem Using Hybrid Heuristic Computing
Suheel Abdullah Malik, Ijaz Mansoor Qureshi, Muhammad Zubaır, Muhammad Amir · 2013
In this paper an evolutionary computational technique, which is stochastic in nature, is applied for the first time to the numerical solution of the Troesch’s problem. An approximate mathematical model employing the linear combinations of log sigmoid basis functions is deduced. A fitness function (FF), containing unknown adjustable parameters and representing the trial solution along with the initial conditions, is developed. The Genetic algorithm (GA) as global optimizer is hybridized with local optimizers, such as Pattern Search (PS) and Interior Point algorithm (IPA), for achieving the unknown adjustable parameters. Comparisons of the numerical results obtained for three special cases of the Troesch’s problem are made with some important deterministic classical approximation methods, as well as, the exact solutions. The numerical results are found to be in sharp agreement with the exact solutions.