The increasing complexity of Compute Continuum environments calls for efficient resource optimization techniques. In this paper, we propose and evaluate three distributed designs of a genetic algorithm (GA) for resource optimization, within an increasing degree of distribution. The designs leverage the execution of the GA in the infrastructure devices themselves by dealing with the specific features of this domain: constrained resources and wide geographical distribution of the devices. For their evaluation, we implemented a benchmark case using the NSGA-II for the specific problem of optimizing the application placement, according to the guidelines of our three distributed designs. These three experimental scenarios were compared against a control case, representing a traditional centralized version of this GA algorithm, evaluating solution quality and network overhead. The results show that the design with the lowest distribution degree, which keeps centralized storage of the objective space, achieves comparable solution quality to the traditional approach but incurs a higher network load. The second design, which completely distributes the population between the workers, reduces network overhead but exhibits lower solution diversity while keeping enough good results in terms of optimization objective minimization. The second design demonstrates the highest overall efficiency in optimization performance and network cost. Finally, the proposal with a distributed population that only interchanges solutions between the workers’ neighbors achieves the lowest network load but with compromised solution quality.