On the use of Genetic Algorithms for Solving Ill-Posed Problems

In this article we investigate the use of genetic algorithms for regularizing ill-posed problems. Various approaches of genetic algorithms are considered in order to deal with the numerical problems caused by the instability of the solution of ill-posed problems. Two test examples, a simple one-dimensional ill-posed problem and the Cauchy problem for the Laplace equation are considered in order to illustrate the performance and limitations of genetic algorithms when applied to inverse and ill-posed problems. The combination of genetic algorithms with other regularization methods such as the function specification method is also investigated.