Regularization methods are used in microwave image reconstruction problems, which are ill-posed. Traditional regularization methods are usually problem-independent and do not take advantage of a priori information specific to any particular imaging application. In this paper, a novel problem-dependent regularization approach is introduced for the application of breast imaging. A real genetic algorithm (RGA) minimizes a cost function that is the error between the recorded and the simulated data. At each iteration of the RGA, a priori information about the shape of the breast profiles is used by a neural network classifier to reject the solutions that cannot be a map of the dielectric properties of a breast profile. The algorithm was tested against four realistic numerical breast phantoms including a mostly fatty, a scattered fibroglandular, a heterogeneously dense, and a very dense sample. The tests were also repeated where a 4 mm x 4 mm tumor was inserted in the fibroglandular tissue in each of the four breast types. The results show the effectiveness of the proposed approach, which to the best of our knowledge has the highest resolution amongst the evolutionary algorithms used for the inversion of realistic numerical breast phantoms.