We present a methodology to account for the stochastic nature of hydraulic conductivity during the design of pump-and-treat systems for aquifer cleanup. The methodology (1) uses a genetic algorithm to find the global optimal solution and (2) incorporates a neural network to model the response surface within the genetic algorithm. We apply the methodology for a real example and different optimization scenarios. The employed optimization formulation requires few hydraulic conductivity realizations. The presented approach produces a trade-off curve between reliability and treatment facility size. ¿ 1999 American Geophysical Union