Acta Universitatis Apulensis Comparison of a Genetic Algorithm and a Gradient Based Optimisation Technique for the Detection of Subsurface Inclusions

An inverse problem is considered to identify the geometry of discontinuities in a conductive material Ω 2 R ⊂ with anisotropic conductivity (I+(K-I)χD from Cauchy data measurements taken on the boundary ∂Ω, where Ω ⊂ D , K is a symmetric and positive definite tensor not equal to the identity tensor and χD is the characteristic function of the domain D. In this study we use a real coded genetic algorithm in conjunction with a boundary element method to detect an anisotropic inclusion D, such as a circle, by a single boundary measurement. Numerical results are presented for both isotropic and anisotropic inclusions. The results obtained using the genetic algorithm are compared with the results obtained using a gradient based method. The genetic algorithm based method developed in this paper is found to be a robust, efficient method for detecting the size and location of subsurface inclusions.