RRT-AFIR-based searches follow a two-stage selection process: the initial selection of a cluster and the subsequent selection of a node within the chosen cluster. In the context of a reinforcement learning algorithm, this approach should be referred to as a hierarchical search. Therefore, a hierarchical node selection policy is also examined. The score (S J,t ) of the cluster J is defined as an average of a set of scores sampled hypothetically from the score distributions estimated at the iteration step t for the candidate nodes attributed to that cluster, expressed as S J,t = 1/N J,t k∈C J,t x k . Here, the score x k is sampled from a normal distribution associated with a candidate node k whose mean and variance are s k,t and σ 2 k,t (n s k,t ) -1 , respectively, depending on the iteration step t. C J,t represents the set of candidate nodes in cluster J at iteration step t, and N J,t is the number of elements in that set. By statistically averaging of S J,t over their normal distributions of all the candidate nodes in that cluster J, the average score (S J,t ) and corresponding standard deviation (Σ J,t ) of cluster J are respectively given as,