Abstract
Fredholm Integral Equation of the First Kind (FIEFK) is an example of ill-posed problems. Solving this type of equation using conventional methods of discretization often leads to an ill-conditioned system of linear equations. This paper deals with the numerical solution for the FIEFK occurring in the synthesis of the electromagnetic fields. To tackle this problem, we propose a hybrid method based on Genetic Algorithms (GAs) and Artificial Neural Networks. The method consists of two major steps. The first step is to find an initial solution by utilizing a GA, and the second is to refine the solution using a regularized neural network. Experimental results prove the efficiency of our proposed method in comparison with a previous work.
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Sammany, M., Pelican, E. & Harak, T.A. Hybrid neuro-genetic based method for solving ill-posed inverse problem occurring in synthesis of electromagnetic fields. Computing 91, 353–364 (2011). https://doi.org/10.1007/s00607-010-0123-y
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DOI: https://doi.org/10.1007/s00607-010-0123-y
Keywords
- Fredholm integral equation of the first kind
- Ill-posed problems
- Genetic algorithms
- Regularized neural networks