## 1 Introduction  
The underwater acoustic sensor network (UWASN) has recently attracted considerable attention because of its potential for use in a variety of military and civilian applications, such as ocean environmental monitoring, ocean exploration, target detection, surveillance systems, and communication among underwater sensor nodes [1; 2; 3; 4]. In the UWASN, a number of sensor nodes are deployed in the ocean to collect data, which must be successfully exchanged among adjacent sensor nodes. For this reason, each sensor node must be positioned to be able to perform collaborative communication tasks over a targeted area. The deployment efficiency of sensor nodes in the UWASN is evaluated in terms of their connectivity and the area covered by the limited number of sensor nodes in the targeted area, because underwater sensor devices are more expensive and more difficult to deploy at precise positions compared to sensor nodes on land [5]. Most attempts to find an optimal deployment scheme for sensor nodes have assumed that every sensor node has the same sensing range [6; 7; 8; 9], which is reasonable in the case of terrestrial wireless communication systems. However, underwater communication performance is significantly influenced by temporal and spatial variations in the ocean environment [10; 11]. Underwater acoustic communication presents a challenging problem in that the underwater acoustic communication channel is a time-varying multipath channel formed by multiple interactions of sound with the sea surface and bottom of the ocean, particularly in shallow water. This multipath channel causes significant delay in spreading, often covering hundreds of symbols, thereby causing inter-symbol interference (ISI). This happens because the underwater sound propagates with relatively low sound speed (mean sound speed in water is around 1500 m/s, which is approximately 200,000 times lower than that of an electromagnetic wave) [12]. The ISI results in a significant degradation in communication performance [13]. In addition, a time-varying channel produces a short coherence time or a large Doppler spread resulting from the temporal and spatial variations in the sea surface [14]. Therefore, if all sensor nodes are deployed at equal distances from each other in the targeted area under the assumption that each sensor node has the same communication radius, performance degradation of the UWASN may occur. It is necessary to develop an optimal deployment algorithm for underwater sensor nodes, which must be able to reflect performance variations in the sensor network due to environmental fluctuations. One of the methods to improve the performance of the UWASN is to use array processing. Array processing techniques using an array of spatially separated receivers have been reported to decrease communication error rates by eliminating the ISI caused by multipath channels in the ocean and to have better communication performance than single receivers that only use the equalizer technique [15; 16; 17]. In this paper, a multi-channel combining technique using a vertical line array is applied to the UWASN. The performance of the communication system is then estimated over the targeted area, which is converted to the communication performance surface (PS). The PS is a projection of the geospatial information of the performance of a system. In general, the PS in a sonar system is used to provide insight into the relative performance for the detection range of the system, demonstrating the impact of the ocean environment on the system capability [18]. Here, a communication PS is predicted based on the communication radius estimated on each grid within the targeted area. On the basis of the estimated communication PS, the optimal deployment of sensor nodes is obtained using a hybrid optimization method combining the advantages of a virtual force algorithm [19; 20] and a particle swarm optimization [21; 22], called virtual force-particle swarm optimization (VFPSO) [23].