Comparison of a genetic algorithm and a gradient based optimisation technique for the detection of subsurface inclusions.

*(English)*Zbl 1106.35137Summary: An inverse problem is considered to identify the geometry of discontinuities in a conductive material \(\Omega\subset \mathbb R^2\) with anisotropic conductivity \((I+(K-I)\chi D\) from Cauchy data measurements taken on the boundary \(\partial\Omega\), where \(D\subset\Omega\), \(K\) is a symmetric and positive definite tensor not equal to the identity tensor and \(\chi D\) 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.