The problem of reconstructing the support of an imaged object from the support of its autocorrelation is addressed within the framework of genetic algorithms. First, we propose a method of coding binary sets into chromosomes that is both efficient and general, producing reasonably short chromosomes and being able to represent convex objects, as well as some non-convex and even clustered ones. Furthermore, in order to compensate for the computational costs normally incurred when genetic algorithms are applied, a novel multiresolution version of the algorithm was introduced and tested. The multiresolution genetic algorithm consists of a superposition of multiple algorithms evolving at different resolutions, sequentially. Upon occurrence of some convergence criteria at the current scale, the genetic population was mapped at a superior scale by a coarse-to-fine mapping that preserved the progress registered previously. This mapping is implemented in a genetic algorithm framework by a new genetic operator called cloning. A number of experiments of object support reconstruction were performed and the best results from different genetic generations were depicted in chronological sequence. While both versions of genetic algorithms achieved good results, the multiresolution approach was also able to substantially improve the convergence speed of the process. The effectiveness of the method can be extended even further if a parallel implementation of the genetic algorithm is employed. Finally, alternate coding methods could be readily used in both the standard and the multiresolution approaches, with no need for further adaptations of the basic structure of the genetic algorithm.