## 1 Introduction
In contrast, if the CHNs fuse the data and transmit them towards the SN, it could greatly save energy [20]. The four advantages of data fusion technique are concluded in [21]: decreasing energy consumption, enhancing data security, improving transmission efficiency, and optimizing network resources. The data transmission by the multi-hop mechanism, has been proven in [22] more effective in energy conserving in long-distance transmissions compared to the single-hop mechanism. Thus, we need to find the optimal multi-hop paths to achieve minimized energy consumption, enhanced transmission efficiency, and reduced packet loss ratio during data transmission. In the paper, the SN is the destination node, and the CHN that has data packets to send becomes the source node. The relay node is chosen from CHNs rather than CMNs. Genetic algorithms (GAs), which imitate the natural evolution process to search for optimal solutions, have the potential to resolve the optimization problem and they are effective in finding the optimal multi-hop routing paths [23; 24]. The population initialization of the GA is usually based on a random scheme. The fitness function evaluates the individuals and the better ones are more likely to be chosen to produce the next generation [25]. Through repeated crossover, mutation, and selection operations, the population can be improved and the optimal solution can be found [26]. To our knowledge, no existing routing protocol in UWSNs combines the advantages of the clustering scheme, the data fusion technique and the GA. However, it is vital to propose an energy-efficient routing protocol that is capable of minimizing the energy dissipation and ultimately maximizing the lifecycle of UWSNs. Hence, we present an energy-efficient clustering routing protocol on the basis of a modified GA and an improved BPNN for UWSNs, which could greatly enhance network performance. The proposed protocol has three main phases: the CHN selection, the cluster formation, and the data transmission. In the CHN selection phase, the protocol introduces an optimized CHN selecting scheme. In the second phase, CMNs choose to join the CHNs according to depths of nodes and distances between nodes, and the clusters are thus formed. In the third phase, the CMNs transmit data to the CHNs through a single-hop mechanism. Once receiving the data, the CHNs fuse them by using the improved BPNN algorithm, and forward the fused data to the SN through a multi-hop scheme. Each effective multi-hop transmission path is identified through the enhanced GA. The innovations of our work are as follows:  
1. Based on a new encoding scheme, which encodes routing paths as chromosomes and sensor nodes as genes, this paper presents a modified GA to search for optimal multi-hop routing paths for CHNs to transmit data packets to the SN. 2. This paper proposes a scaling function to reallocate the range of the fitness value in the selection operator of the GA, which helps keep the population diversity and improve the convergence of the GA.
3. This paper introduces a particular crossover operator and an improved mutation operator in the GA, and also adopts an adaptive mutation probability scheme instead of using the fixed mutation probability, which helps avoid the local convergence of the GA.
4. This paper presents an improved BPNN by adopting an optimized momentum method, which is employed by CHNs to fuse data in order to reduce the energy consumption through the elimination of data redundancy and the decrease of the amount of data. 5. This paper introduces an optimized CHN selecting scheme, and improves the cluster formation process by taking into account the depth of the nodes and the distance between nodes. 6. This paper combines the clustering routing protocols, the GA, and the data fusion technique, which is an innovative application in UWSNs. Simulation results verified its effectiveness in improving network performance. The remainder of this paper is as follows. Section 2 introduces the related work.