This work introduces a combinatorial optimization problem called Mars Express Memory Dumping Problem (Mex-Mdp), which arises in the European Space Agency program Mars Express. It concerns the generation of high quality schedules for the spacecraft memory downlink problem. Mex-Mdp is an NP-hard combinatorial problem characterized by several kinds of constraints, such as on-board memory capacity, limited communication windows over the downlink channel, deadlines and ready times on the observation activities. The contribution of this paper is twofold: on one hand it provides a CSP model of a real problem, and on the other it presents a set of metaheuristic strategies based on local and randomized search which are built around the constraint-based model of the problem. The algorithms are evaluated on a benchmark set distilled from ESA documentation and the results are compared against a lower bound of the objective function.