###### Abstract
Pressure routing can achieve high delivery ratios and low end-to-end delay, but it consumes more energy because of the use of opportunistic routing and the repeated transmission of the copies of same packets. The cluster sleep-wake scheduling algorithm in UWSNs was proposed by [PERSON] et al. in [30], which shows the rotating temporary control nodes that control the sleep-wake scheduling, thus minimizing the energy dissipation. The energy optimization clustering algorithm (EOCA) was put forward by [PERSON] et al. in [11], where the number of neighboring nodes, the remaining energy of nodes, the motion of nodes, and the distance factor are taken into account. Additionally, the EOCA provides a maximum effective communication range based on the remaining energy of nodes, thereby controlling the energy dissipation for packet delivery. However, the EOCA does not optimize the multi-hop paths for data transmission to the SN. Greedy algorithms have shown great strength in addressing combinational optimization problems, which make local optimal choices at every step [31; 32]. They are effective in finding global optimal solutions in specific circumstances [33], and we take [PERSON]'s algorithm and [PERSON]'s algorithm as examples [34; 35]. [PERSON]'s algorithm, which was proposed by [PERSON] in 1959, has been widely used to look for the shortest paths between network nodes. It can thus be employed in routing algorithms to find the shortest path to the destination node [36]. [PERSON]'s algorithm constructs minimum spanning trees and can usually find the best solutions [37]. Nevertheless, the greedy algorithms are considered short-sighted because they only make the best choice at every step and do not consider the overall condition. That is the reason why they cannot obtain the optimal solution sometimes. Hence, researchers proposed many metaheuristics extending greedy algorithms, which can be applied to a wide range of different problems [38; 39; 40; 41]. The greedy randomized adaptive search procedure (GRASP) was presented by [PERSON] et al. in [38], where the present problem can be solved in every iteration. Each iteration has two stages: stage one provides the initial solution and stage two aims to find the improved solution by applying the local search procedure to the solution provided by stage one. The fixed set search (FSS) was proposed by [PERSON] et al. in [39], which adds the learning method to the GRASP and is thus more effective than the GRASP in the solution quality as well as the computational cost. In the work of [PERSON] in [40], the worm optimization (WO), on the basis of the worm behaviors, was proposed to solve unrelated parallel machine schedule problems, which can find the optimal solution as well as reduce the makespan. In [41], the particle swarm optimization (PSO) and the fuzzy algorithm are used in a clustering scheme for UWSNs, which can find the optimal number of clusters and select the optimal CHNs, thereby reducing the energy dissipation and prolonging the lifespan of UWSNs. The ant colony optimization (ACO) algorithm is also a population-based metaheuristic that extends the greedy algorithm, which has been widely used to optimize routing paths [42; 43; 44]. The ACOcan find optimal paths from source nodes to destination nodes so that the energy consumption can be reduced and the network lifetime can be prolonged. ACO algorithms simulate ant behavior, as ants could usually find the optimal paths to foods [45]. Ants release pheromones on the path that they make. Other ants are more likely to choose the path with higher pheromone concentration, and the following ants will also release pheromones on the path, which increases the pheromone concentration [46]. The higher pheromone concentration will attract more ants, which forms a positive feedback loop. After a period of time, the ant colony will find the shortest path to the food source. So far, many researchers have applied ACO algorithms to routing algorithms. [PERSON] et al.