The ability to verify critical software is a key issue in embedded and cyber physical systems typical of automotive, aeronautics or aerospace industries. Bounded model checking and constraint programming approaches search for counter-examples that exemplify a property violation. The search of such counter-examples is a long, tedious and costly task especially for programs performing floating point computations. Indeed, available search strategies are dedicated to finite domains and, to a lesser extent, to continuous domains. In this paper, we introduce new strategies dedicated to floating point constraints. They take advantage of the properties of floating point domains (e.g., domain density) and of floating point constraints (e.g., floating point arithmetic) to improve the search for floating point constraint problems. First experiments on a set of realistic benchmarks show that such dedicated strategies outperform standard search and splitting strategies.