In this paper the problem of minimization of pumping cost in a polluted fractured aquifer is studied, taking into account the use of additional wells that will retard or pump the pollution plumes, in order to maintain water quality of the existing production wells for a given period of time. Genetic Algorithms (GAs) have been selected as optimization tool, while advective mass transport is simulated by means of a moving point technique. Computational details on pollution arrival to fractures and wells are discussed and some optimal results are presented.