## 1 Introduction  
### Motivation  
In recent decades, the research on wireless sensor networks (WSNs) has been a hotspot for numerous applications, such as, environment monitoring [1], smart cities [2, 3], military monitoring [4], maritime resource gathering [5] and health-care surveillance [6].  
As maritime rights and interests are paid more and more attention, underwater wireless sensor networks (UWSNs), an important extension of WSNs into ocean, is of great value in various application fields, such as, oceanographic information collection, hydrological and environmental monitoring, resources exploration, disaster forecast, underwater navigation, military defense, and etc. [7]. For UWSNs, there exist two kinds of topological structures, two dimensional network and three dimensional network. In this work, we study the three dimensional UWSNs, with which all nodes are deployed at different depths in the ocean.  
Generally, in WSNs, including UWSNs, the information from all sensor nodes, which are equipped with limited power battery, are gathered to the sink node. When the power of the node is used up, the node expires. While most nodes died, the sink node is no longer able to gain necessary information from common nodes. Considering the fact that the nodes are hard to recharge, energy consumption remains a key factor that affects the whole network lifetime. On the other hand, in underwater scenario, as the network usually occupies large area and the effective transmission semidiameter is limited, those nodes who might not transfer the signal to sink node in one hop will need relay nodes. As a result, to design an efficient data routing algorithm for UWSN, it is vital to reduce the processing complexity and traffic overhead and meanwhile ensure that the data are collected efficiently. [PERSON] et al. [8] render a layering algorithm which divides nodes to different parts according to their depth and data are forwarding based on opportunistic directional forwarding strategy. [PERSON] et al. [9] improved opportunistic routing by adding distance-vector. The algorithm uses a query mechanism to establish the distance vectors for sensor nodes, then opportunistic routing is developed to forward packet based on the distance vectors. Further studies tend to cluster all nodes in the network, and only transmit the merged message in the cluster head to the sink node. Common nodes just need to transmit their data to their cluster heads (CHs) in one hop. For instance, clustering is added as one stage in [10] to save energy better. This strategy cuts down the energy-consumption efficiently. In [11], clustering and CH transmission are introduced as well. After the formation of cluster and selection of CH, the courier nodes are deployed into the clusters to collect the aggregated data from the CHs, and the visiting tour is scheduled based on the [PERSON]'s algorithm.  
However, the works above do not consider the facts that in UWSN, while the sensor nodes are deployed to measure environmental data, for example, maritime temperatures, the signals they collect usually possess spatial correlations that induce sparsity into practical application. Based on such a fact, we comprehensively consider the routing strategy and the data sparsity to save energy even further. In such contexts, compressive sensing (CS) is adopted to reduce communication cost while also preserve information precisely. In this paper, we propose a CS based schedule which simultaneously considers routing and nodes selection for overall data reconstructions at the sink node for 3-D UWSNs. We use Particle Swarm Optimization (PSO) to optimize both the clustering and routing protocols design while the factors consisting of fitness functions consist of signal recovery quality, energy consumption, network balance and etc..