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This paper sought to investigate the performance of multi-hop underwater acoustic sensor networks (UW-ASNs) when they deploy cooperative routing algorithms combining the cooperative communication and routing methods. Taking into account energy efficiency, the studied schemes are discriminated by different policies of selecting next hop nodes as well as relay nodes of one-hop cooperative communications such that the transmission energy of routing paths is minimized. In order to take full advantage of broadcast nature in wireless communication, we propose to use a node exploited as a joint relay for two-hop cooperative communication. In addition, the unreliable communication of acoustic channels is addressed by the incorporated channel-aware mechanism which updates the links by exploiting packet receptions. On the bases of communication, two cooperative routing protocols are developed. The simulation results show that the network employing the proposed schemes achieves improved performance in terms of energy efficiency, throughput, and end-to-end delay as compared to the related works.