In water networks characterized by a significant variation in ground elevations the necessity of pumping water in some areas is complicated by a conflicting requirement to reduce excess pressures in other areas. This and the increasing cost of electricity has led to the use of Pumps-operating-As-Turbines (PATs) devices that can reduce pressure (and leakage) whilst harvesting energy. This paper presents a methodology for optimal water distribution system (WDS) management, driving the optimization by minimizing the surplus pressure at network nodes and the operational pumping costs and maximizing the income generated through energy recovery. The method is based on a highly parallelized Evolutionary Algorithm, employing an hydraulic solver to evaluate hydraulic constraints. Water demands at network nodes are considered as uncertain variables modelled by using a probabilistic approach in order to take into account unknown future demands. The approach is demonstrated in different case studies. Results obtained highlight that the economic benefits of installing PATs for energy recovery in conjunction with a combined pump-scheduling and pressure management regime is especially related to the input network characteristics. Further analysis of the importance of the probabilistic approach and of the influence of the interval time step adopted for the optimization has been evaluated.