A coordinate transformation based finite element method is presented for detecting contours of breast cancer tissues in the context of microwave imaging. The geometry and location of a single or multiple cancerous tumors inside a breast tissue are identified by constructing an inverse problem based on the genetic optimization algorithm. The expensive forward solution phase during repeated cost function evaluations is accelerated by placing a transformation medium inside the finite element mesh. This allows using a uniform or rectangular mesh even when irregular tumor geometries are considered. Therefore, the computational load is reduced. The algorithm is implemented in MATLAB using parallel programming tools. A realistic numerical breast phantom repository, which is available in the University of Wisconsin-Madison webpage, is used to test the algorithm. The performance of the algorithm is also tested by utilizing the Monte Carlo approach, where the inverse problem is run several times and the statistical parameters of the runs are determined. Various simulation results are demonstrated.