###### Abstract
combined ACO algorithms with the LEACH algorithm for prolonging the lifetime of TWSNs, and they validated the effectiveness of the algorithm by simulation experiments [47]. [PERSON] et al. applied ACO algorithms to routing algorithms by taking into account the hop count and the residual energy of neighbor nodes, which can reduce the energy consumption to a certain extent, but the algorithm can only balance the local energy consumption [48]. [PERSON] et al. improved the pheromone update process of ACO algorithms when designing routing algorithms, and took into account the total energy of all nodes, thereby improving the energy efficiency of the entire network [49]. [PERSON] proposed a threat cost calculation for submarine path planning based on ACO algorithms [50]. He presented a new cost function that took into account the path length and distance factor, and adopted a coalescing differential evolution mechanism when updating the pheromone so as to settle the local optimum problem. [PERSON] et al. proposed a clustering algorithm on the basis of the ACO algorithm, which was designed for TWSNs instead of UWSNs. When selecting CHNs, they considered the residual energy of candidate nodes and the distance factor. When looking for routing paths, the authors took into account the path length as well as the node energy, which can balance the network energy consumption [51]. [PERSON] et al. presented a routing protocol based on ACO algorithms for TWSNs, where the remaining energy of nodes, the transmission direction, and the distance between nodes were considered in order to look for ideal routing paths and reduce the energy consumption of the network [52]. [PERSON] proposed an effective transmission strategy using ACO algorithms, which can improve the energy efficiency and prolong the network lifetime. Additionally, the improved ACO algorithm was unlike the traditional one: no heuristic information and just one step for every ant in its whole trip [53]. The literature mentioned above indicate that ACO algorithms could be employed to look for the optimal routing paths in networks. Nevertheless, the problem of clustering routing algorithms in UWSNs has not been resolved, so we need to make some improvements to the existing ACO algorithms and apply them to UWSNs. To our knowledge, few studies have applied ACO algorithms in UWSNs when designing clustering routing algorithms. It is of great significance to design an energy-efficient routing algorithm that can minimize the energy consumption and ultimately maximize the network lifetime. Therefore, this paper presents a clustering routing algorithm based on an improved ACO algorithm for UWSNs. Firstly, we describe the network model and the energy consumption model that can be used to quantify energy consumption and evaluate the energy efficiency of the proposed algorithm. Secondly, we present an improved ACO algorithm through the improvement of the heuristic information, the evaporation parameter for the pheromone update mechanism, and the ant searching scope. To improve the heuristic information of the traditional ACO algorithm, we consider not only the residual energy but also the distance factor in the proposed heuristic information. Additionally, the proposed adaptive strategy of the evaporation parameter for the pheromone update mechanism helps improve the global search ability and the convergence rate of the algorithm. Thirdly, we design the clustering routing algorithm, which has two main phases in one round: CHN selection phase and data transmission phase. In the first phase, we optimize CHN selection by considering the residual energy of nodes, the distance from the node to the SN and the average distance between the node and the other nodes in the cube. In the second phase, the single-hop method is adopted for the data transmission from CMNs to CHNs, and the multi-hop method is employed when CHNs transmit data to the SN, and the optimal multi-hop paths are found by the improved ACO algorithm.