arXiv:2507.10119v1 Announce Type: new Abstract: Application migration in edge-cloud system enables high QoS and cost effective service delivery. However, automatically orchestrating such migration is typically solved with heuristic approaches. Starting from the Markov Decision Process (MDP), in this paper, we identify, analyze and compare selected state-of-the-art Artificial Intelligence (AI) planning and Reinforcement Learning (RL) approaches for solving the class of edge-cloud application migration problems that can be modeled as Towers of Hanoi (ToH) problems. We introduce a new classification based on state space definition and analyze the compared models also through this lense. The aim is to understand available techniques capable of orchestrating such application migration in emerging computing continuum environments.