## 1 Introduction  
A large number of studies have been conducted on terrestrial sensor networks concerning several aspects, and currently, the underwater wireless sensor networks (UWSNs) have attracted growing interest from researchers [1, 2]. They are different from the widely employed land-based sensor networks in terms of the cost of expensive sensors, the transmission system of acoustic signals, the dense deployment of sensors, the larger storage space to save maximal information, and the maximal power for transmission [3; 4]. An UWSN consists of movable and stationary nodes that interact via acoustic networks. UWSN is utilized in various applications which have underwater environments, such as pollution monitoring, particularly the monitoring of the population of underwater flora and fauna, chemical waste, disaster prevention, examining the health of rare marine creatures, assisted navigation, mine reconnaissance, oil leakage detection, nutrient production, oceanographic data collection [5; 6], distributed tactical surveillance, underwater military applications, target tracking, and detection. The researcher faces a lot of problems while working in UWSNs, such as longer propagation delays, narrow bandwidth, temporary loss of connectivity [7; 8], harsh geographical atmosphere, shadow zones, constrained energy, attenuation, high bit error rates, and a comparatively smaller network scale. Communication distance, energy consumption, and network life cycle are the three major considerations for designing UWSNs [9]. Topology control using the clustering model is the major solution to the problem of the UWSNs since it could balance the energy utilization, prolong the lifetime of the networks, and reduce communication interference [10]. The objective of clustering is to split the whole UWSN into different areas. In all the regions, sensors only interact with the cluster head (CH) within their own cluster. Earlier routing protocols were developed for certain layers, for example, design protocols for the transport or network layers [11]. This protocol entailed a layered protocol framework [12]. They do not take advantage of energy levels, joint optimization, and other causes, so total performance becomes insufficient [13; 14; 15]. Hence, the present study focuses on designing a protocol that could make use of data received by distinct layers, named the cross-layered routing protocol [16]. There is another issue that makes underwater transmission difficult. One of the problems is limited bandwidth. It has a direct effect on the communication rate of the network. Different sources of noise and water current lead to limited bandwidth in UWSN [17]. For longer distance transmission in UWSN, oceanic waves are utilized that could travel several kilometers at higher power and lower frequency [18]. The underwater network faces the loss of connectivity and a high bit error rate because of multi-path interference from oceanic networks. Because of the water temperature, multipath noise effect, and Doppler spread, underwater transmission is not reliable [19; 20]. Furthermore, the multi-path effect causes the incoming signal fade. As a result, routing becomes costly and challenging in UWSN [21]. This study introduces an improved metaheuristics-based clustering with a multihop routing protocol for UWSN, named the IMCMR-UWSN technique. The IMCMR-UWSN technique intends to properly arrange the nodes into clusters and determine the shortest routes for inter-cluster data transmission in the UWSN [22; 23]. To accomplish this, the IMCMR-UWSN technique designs the chaotic krill head algorithm (CKHA)-based clustering and self-adaptive glowworm swarm optimization algorithm (SA-GSO)-based multihop routing protocols [24; 25; 26]. Since multiple input parameters are used for the selection of CHs and optimum routes in UWSN, the overall network efficiency can be considerably improved. The experimental results of the IMCMR-UWSN technique are validated and the results are distinct aspects are inspected [27; 28; 29].