For a few decades the family of Local Search methods and Metaheuristics has been quite successful in solving large real-life problems. Applying Local Search to Constraint Satisfaction Problems (CSPs) has also been attracting some interest as it can tackle CSPs instances far beyond the reach of classical propagation-based solvers. In this research we address the issue of parallelizing constraint solvers for massively parallel architectures, with the aim of tackling platforms with several thousands of CPUs. A design principle implied by this goal is to abandon the classical model of shared data structures which have been developed for shared-memory architectures or tightly controlled master-slave communication in cluster-based architectures and to first consider either purely independent parallelism or very limited communication between parallel processes, and then to see if we can improve runtime performance using some form of communication.