## 1 Introduction  
An underwater wireless sensor network (UWSN) consists of several underwater wireless sensors distributed within the marine environment that assist wide-ranging applications, including navigation, surveillance, disaster prevention, data acquisition, and resource exploration [1; 2; 3]. All the sensors of a UWSN are armed with an acoustic modem since they employ acoustic signals to interact with one another [4; 5; 6]. This node is able to form a network without any architecture. The sensors are responsible for monitoring the underwater environments, namely the temperature, and transmit the gathered information to a sink node (SN) via a single hop or many hops [7; 8; 9]. The SN, placed on the aquatic surface, is capable of receiving the information from underwater sensors via acoustic signal and transmitting the collected information to terrestrial network devices via radio signal [10; 11; 12]. In underwater environments, the radio signal attenuates quickly and faces the absorption problem. Therefore, they are unsuitable for longer-distance underwater communication. The complete upsurge is adapted at the time of submerged communication since it is lesser affected by scattering, absorption loss, and attenuation [13; 14]. The acoustic signal propagates slowly causing higher propagation delay. Furthermore, there is another drawback of the underwater acoustic network, namely the high error rate, and the low bandwidth. Hence, it uses lot of energy to effectively transfer information packs in a UWSN and keeps the better presentation of a UWSN. Moreover, the sensors have constrained energy, and it is not easier to redistribute or recharge them [15; 16; 17]. Thus, the network lifetime and energy consumption are primary concerns in a UWSN. The routing protocol for a UWSN deals with the path selection to transmit data packets to the surface destination in an effective and efficient manner [18; 19]. In recent times, engineers, researchers, and scientists have employed the routing protocol to examine the underwater medium for various applications. The proposal of the routing protocol for UWSNs is of great significance. This protocol identifies a path from the bottom to the top of the water surface for ensuring system efficiency, based on the desired parameter [20; 21]. Especially, the problems related to the underwater medium and at the time of packet forwarding are taken into account by this protocol for achieving the optimum efficiency of the network based on the intended purpose. For example, this protocol deals with the shadow zones, high propagation delay, constrained battery power, movement of the sensors with water current, reliable transmission of data packet at the time of unfavorable channel condition, severe noise, and interference [22]. The transmission of information through the multi-hop method was proved in [23] to be efficient in energy preservation in longer-distance transmission than the single-hop method. Therefore, it was necessary to discover the optimum multi-hop paths for achieving improved transmission efficacy, reduced packet loss ratio (PLR), and minimized energy consumption at the time of data transmission [24; 25]. This article develops an effective chaotic search-and-rescue-optimization-based multi-hop data transmission (CSRO-MHDT) protocol for UWSNs to optimize energy efficiency and lifetime. At the initial stage, the CSRO-MHDT protocol involves the design of a weighted clustering approach (WCA) for the effectual selection of cluster heads (CHs) and cluster construction. In addition, the CSRO algorithm is presented by integrating the chaotic concepts into the traditional search and rescue optimization (SRO) algorithm. Moreover, the CSRO-MHDT technique has a suitability purpose, connecting remaining energy, reserves, and node degrees. For assessing the better outcomes of the CSRO-MHDT technique, a wide-ranging experimental analysis was carried out and the results were assessed under several aspects. The following is the outline for the remainder of the paper.