The onset of complexity in many combinatorial optimization problems can be connected to the existence of phases of in which the ground states of the corresponding diluted spin statistical model form an exponential number of disconnected clusters. Typically, local search algorithms like Simulated Annealing are unable to find even a single one optimal configuration, due to the presence of an exponentially larger number of metastable states and local minima. In our work we show how the Survey Propagation algorithm can be generalized to include external forcing messages, and used to address selectively an exponential number of glassy ground states. These capabilities are used to provide a direct experimental evidence of replica symmetry breaking in large-size problems and to realize a new lossy data compressor, exploiting as a computational resource the clustered nature of the space of addressable states.