The increasing complexity of fog computing 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 in
fog computing, within an increasing degree of distribution. The designs
leverage the execution of the GA in the fog devices themselves by dealing with
the specific features of this domain: constrained resources and widely
geographical distribution of the devices. For their evaluation, we implemented
a benchmark case using the NSGA-II for the specific problem of optimizing the
fog service placement, according to the guidelines of our three distributed
designs. These three experimental scenarios were compared with a control case,
a traditional centralized version of this GA algorithm, considering 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. Finally, the proposal with a distributed population and
that only interchanges solution between the workers' neighbors achieves the
lowest network load but with compromised solution quality.

在本文中，我们提出并评估了三种分布式遗传算法（GA）设计，用于雾计算中的资源优化问题，其设计基于 GA 在雾设备本身中的执行，以应对约束资源和设备广泛地理分布等特定问题。通过利用 NSGA-II 实施了基准案例，在优化雾服务部署问题的特定领域指导下，对这三种分布式设计进行了比较评估。结果表明，最低分布度的设计在保持目标空间集中存储的同时，实现了与传统方法相当的解决方案质量但产生了更高的网络负载。第二种设计完全分配了种群给工作节点，减少了网络开销，但在解决方案多样性方面表现较差，同时在优化目标最小化方面仍具有足够好的结果。最后，使用分布式种群且仅在相邻工作节点之间交换解决方案的提议实现了最低的网络负载，但解决方案质量受到了影响。