GA and ANN for Solving Fredholm Integral Equation of the First Kind

Fredholm integral equation of the first kind (FIEFK) is an example of ill-posed problem. Solving this equation using conventional methods of discretization often leads to an illconditioned linear system of equations. In this paper, we used Simpson quadrature method to discretize the problem into a system of linear equations. Then a Genetic Algorithms (GA) was used to find an initial solution to the obtained system, and a regularized Artificial Neural Network (ANN) was used to approximate the initial solution. Experimental results demonstrated the efficiency and robustness of our proposed method, in comparison with other work, by an analytically solved benchmark example.