In this paper we present graphical tools and parameters search algorithms for the timbre space exploration and design of complex sounds generated by physical modeling synthesis. The tools are built around a sparse representation of sounds based on Gammatone functions and provide the designer with both a graphical and an auditory insight. The auditory representation of a number of reference sounds, located as landmarks in a 2D sound design space, provides the designer with an effective aid to direct his search for new sounds. The sonic landmarks can either be synthetic sounds chosen by the user or be automatically derived by using clever parameter search and clustering algorithms. The proposed probabilistic method in this paper makes use of the sparse representations to model the distance between sparsely represented sounds. A subsequent optimization model minimizes those distances to estimate the optimal parameters, which generate the landmark sounds on the given auditory landscape.