key: cord-0030319-o1avkndx
authors: Anuradha, Durairaj; Subramani, Neelakandan; Khalaf, Osamah Ibrahim; Alotaibi, Youseef; Alghamdi, Saleh; Rajagopal, Manjula
title: Chaotic Search-and-Rescue-Optimization-Based Multi-Hop Data Transmission Protocol for Underwater Wireless Sensor Networks
date: 2022-04-08
journal: Sensors (Basel)
DOI: 10.3390/s22082867
sha: 31571aa4eee0a802086b7215b994ae34952eaaee
doc_id: 30319
cord_uid: o1avkndx

Underwater wireless sensor networks (UWSNs) have applications in several fields, such as disaster management, underwater navigation, and environment monitoring. Since the nodes in UWSNs are restricted to inbuilt batteries, the effective utilization of available energy becomes essential. Clustering and routing approaches can be employed as energy-efficient solutions for UWSNs. However, the cluster-based routing techniques developed for conventional wireless networks cannot be employed for a UWSN because of the low bandwidth, spread stay, underwater current, and error probability. To resolve these issues, this article introduces a novel chaotic search-and-rescue-optimization-based multi-hop data transmission (CSRO-MHDT) protocol for UWSNs. When using the CSRO-MHDT technique, cluster headers (CHs) are selected and clusters are prearranged, rendering a range of features, including remaining energy, intracluster distance, and intercluster detachment. Additionally, the chaotic search and rescue optimization (CSRO) algorithm is discussed, which is created by incorporating chaotic notions into the classic search and rescue optimization (SRO) algorithm. In addition, the CSRO-MHDT approach calculates a fitness function that takes residual energy, distance, and node degree into account, among other factors. A distinctive aspect of the paper is demonstrated by the development of the CSRO algorithm for route optimization, which was developed in-house. To validate the success of the CSRO-MHDT method, a sequence of tests were carried out, and the results showed the CSRO-MHDT method to have a packet delivery ratio (PDR) of 88%, whereas the energy-efficient clustering routing protocol (EECRP), the fuzzy C-means and moth–flame optimization (FCMMFO), the fuzzy scheme and particle swarm optimization (FBCPSO), the energy-efficient grid routing based on 3D cubes (EGRC), and the low-energy adaptive clustering hierarchy based on expected residual energy (LEACH-ERE) methods have reached lesser PDRs of 83%, 81%, 78%, 77%, and 75%, respectively, for 1000 rounds. The CSRO-MHDT technique resulted in higher values of number of packets received (NPR) under all rounds. For instance, with 50 rounds, the CSRO-MHDT technique attained a higher NPR of 3792%.

According to Durrani and colleagues [26] , an adoptive, clustered-node routing method for a smart ocean underwater sensor network has been presented (SOSNET). The described approach makes use of a moth-flame optimizer (MFO) to calculate the near-optimal number of clusters that are required for routing to be effective. Moth migration toward the light is taken into consideration while using the MFO, a biologically inspired optimization technique.

NR et al. [27] introduced the lion optimized cognitive acoustic network (LOCAN) for reducing packet delay and packet loss at the time of transmitting packets in a UWASN; these are caused by water column variation, including the Doppler effect and geometric spreading (GS). Doppler effects form because of sensor node movement and sea surface variations, including temperature and salinity.

The authors in [28] developed a protocol-inspired method called the beckoning penguin swarm optimization protocol (BPSOP), which was inspired by the natural features of penguins. The foraging features of penguins are employed for finding the optimal route in a UWSN.

The authors in [29] designed an energy-effectual and void-region-avoidance routing method. The idea of the GWO approach is utilized for selecting an optimal forwarder node. The presented method expands the lifetime of the network by balancing the network energy and preventing the void region.

In [30] , a new approach, called improved energy-balanced routing (IEBR), was developed for UWSNs. The presented method consists of two phases: data broadcast and routing establishment. To begin, a precise method for determining the transmission distance is developed in order to locate the neighbor at the optimal distance and to determine the submerged net connections [31] [32] [33] . Additionally, IEBR selects relays based on neighbor depth, minimizes hops in a connection-based depth threshold, and eliminates the data communication loop issue [34, 35] .

Rajeswari et al. [36] developed a cooperative ray optimization approach (CoROA), which assists in minimizing the packet loss and delay, which rise because of the geometric spreading and Doppler environments in underwater acoustic networks. The presented method is recognized for its effective performance in distinct environments, including spatial and temporal variations, where the throughput, battery life, and network lifetime are improved.

To improve the overall efficiency of a system, Fei et al. [37] suggested a hybrid clustering technique based on FCM and MFO with the goal of boosting system efficiency (FCMMFO) [38, 39] . In order to achieve this, the researchers first used FCM to generate energy-efficient clusters, and then applied an optimization approach known as MFO to select the ideal CH for each cluster [40, 41] .

Yuhan Su et al. investigated the impacts of transmission-obliging broadcast and radio channel circumstances on submerged acoustic communication, and we calculated the best transmit power setting factor. No prior knowledge of the IoUT model was required to implement the proposed technique. The suggested technique can increase IoUT transmission performance according to the findings of the simulation. Compared with Q-learning, the DQN-based approach upsurges the joint information by 3% and decreases the outage likelihood by 40%. We plan to examine cooperative communications in IoUT in greater detail in the future. To increase cooperative communication in relay-assisted IoUT systems, novel reinforcement learning algorithms with low computational and communication overheads need to be developed.

Zhigang Jin et al. proposed a mobbing-avoidance routing protocol for UASNs based on strengthening knowledge. Through exploration, the RCAR protocol finds the best route to minimize congestion and save energy. The RCAR protocol extends reinforcement learning's reward function with congestion and energy. To speed up the meeting process and to ensure the best routing decision, we used a simulated steering tube with changeable radius based on neighboring average residual energy. Yougan Chen et al. offered the PB-ACR protocol for multi-hop UASNs, which includes node payload balancing as well as DCC. The energy consumption of each system node can be lowered by grouping packets based on the importance of the data included in them. While maintaining an appropriate balance between node payload and cooperative gain, the proposed PB-ACR protocol has the potential to improve system life and throughput when compared with the existing ACAR protocol.

In a study by Jianying Zhu et al., the proposed algorithm's advantages diminish with the node count. This technique is also well-matched with the noncooperative ACOA-AFSA fusion algorithm, and it has a reasonable level of difficulty in time-variant marine surroundings. Therefore, the suggested ACOA-AFSA fusion DCC technique is more ideal for medium-sized networks, where it can boost data transmission reliability, while extending the life of a system. In future study, we will simplify the suggested algorithm's hardware implementation to make it appropriate for other underwater acoustic networking applications. Table 1 shows the current state of wireless sensor networks (WSNs) using clustering and multi-hop routing. 

In this study, a novel CSRO-MHDT method was developed for the optimal choice of routes for data transmission in a UWSN. Clustering is a well-known energy-saving strategy in sensor networks. The least-cost-clustering steering procedure (MCCP) is one of the clustering-based routing protocols (UWSNs). This parameter is composed of three important values: the total energy consumed by member nodes during data transfer to the CH, the total energy residual on the bunch head node and its associate bulges, and the distance between the cluster head node and the originating base station. The major intention of the CSRO-MHDT technique is to the reduce energy dissipation and enhance the lifetime of a UWSN. Primarily, the CSRO-MHDT technique involves WCA for the effectual choice of CHs. In addition, the CSRO-MHDT technique derives a fitness function and can effectually select the set of routes in a UWSN. Figure 1 presents the general procedure of the CSRO-MHDT method. 

The system contains dynamic bulges, which are sparse and arbitrarily dispersed during an × × process. The data source is water-medium-sensed data. The data were gathered utilizing an underwater sensor. The current flow, pressure, and temperature are the identified parameters. The underwater sensor was prepared with an acoustic modem, which enables them to communicate with other nodes in the aquatic environment [42] [43] [44] [45] . An SN is equipped with both a radio frequency (RF) and an acoustic modem for communication with the base station (BS) on the surface landmass; the SN's acoustic modem receives data from underwater sensors, while the RF modem communicates with the base station (BS) by transmitting data through the base station. Despite the fact that it has a short transmission distance, the BS is capable of traversing a sensing field and collecting data from sensor nodes on the field. Each sensor node's power consumption is lowered, since fewer relays are required to transmit the sensor's message to the BS. It can be considered that the network condition is related to the networks. The topology varies rapidly due to the fact that underwater sensors are transferable, depending on water current velocities of around 1-3 m/s [46] [47] [48] [49] [50] . The network condition can be considered as follows:

•

The bulges identify their place and the place of the SN in a primary situation.

The node can develop the and the CM/relay.

The CH rotates amongst the sensors to conserve energy.

Acoustic waves in an underwater broadcast medium have distinct characteristics from radio waves; hence, a WSN cannot be employed for underwater broadcasting networks. For the present study, we used the power consumption strategy of an underwater acoustic channel [51] [52] [53] [54] [55] [56] . The energy required to transport k bits of information across a reserve, d, at an information amount, R, is computed as follows:

where implies the power utilization for routing 1 bit of information and stands for the transmitted power. 

The system contains N dynamic bulges, which are sparse and arbitrarily dispersed during an L × L × L process. The data source is water-medium-sensed data. The data were gathered utilizing an underwater sensor. The current flow, pressure, and temperature are the identified parameters. The underwater sensor was prepared with an acoustic modem, which enables them to communicate with other nodes in the aquatic environment [42] [43] [44] [45] . An SN is equipped with both a radio frequency (RF) and an acoustic modem for communication with the base station (BS) on the surface landmass; the SN's acoustic modem receives data from underwater sensors, while the RF modem communicates with the base station (BS) by transmitting data through the base station. Despite the fact that it has a short transmission distance, the BS is capable of traversing a sensing field and collecting data from sensor nodes on the field. Each sensor node's power consumption is lowered, since fewer relays are required to transmit the sensor's message to the BS. It can be considered that the network condition is related to the networks. The topology varies rapidly due to the fact that underwater sensors are transferable, depending on water current velocities of around 1-3 m/s [46] [47] [48] [49] [50] . The network condition can be considered as follows:

The bulges identify their place and the place of the SN in a primary situation.

The node can develop the CH and the CM/relay.

The CH rotates amongst the sensors to conserve energy.

Acoustic waves in an underwater broadcast medium have distinct characteristics from radio waves; hence, a WSN cannot be employed for underwater broadcasting networks. For the present study, we used the power consumption strategy of an underwater acoustic channel [51] [52] [53] [54] [55] [56] . The energy required to transport k bits of information across a reserve, d, at an information amount, R, is computed as follows: where E elec implies the power utilization for routing 1 bit of information and P Tx stands for the transmitted power. In order to received k bits of information, the receiver radio power utilization is provided under the following:

Assume that P r refers the constants dependent upon the devices. In order to fuse k bits of data, the power utilization is formulated as:

where E DA0 refers the energy used for fusing 1 bit of data, for instance, in use, as 5 nJ/bit. Fusing data is a frequent and successful method for removing data redundancy, shrinking data size, and lowering energy consumption. The data fusion is implemented in this research using an upgraded back propagation neural network (BPNN). Sensor nodes in UWSNs may collect information with great dismissal. When superfluous information is directed to the SN, wasteful energy ingesting occurs, resulting in the node's premature death and the network's lifespan being shortened. In comparison, if the CHNs integrate the data and send it to the SN, then significant energy savings may be realized [57, 58] . While the node is mobile, caused by the water current, it can be located according to the random motion of the node under the functioning time. The current velocity is 1-3 m s .

The weight clustering technique defines the CH and utilized cluster infrastructure utilizing three measures: node degree (ND i ), (RES i ), and distance (DIS i ). For all the nodes, the weight, P i , was computed as:

However, w 1 , w 2 , and w 3 signify the coefficient of model state, as follows:

The SN(x) for transmitting k bits of data to the receiver at distance, d, is calculated as follows:

where E and E T demonstrate the present energy level of the SN and the energy spent on data distributing, respectively.

where E e stands for the electron energy, E a implies the energy has been utilized in implication, and E R(k) defines the energy transmitted on the received data.

In addition, the mean value of the distance between neighboring nodes, which exist as single-hop neighbors, can be calculated as follows:

Although dist i, nb j describes distance of the SN from the neighboring jth SN, eventually, the NDEG implies the quantity of neighboring nodes, which have a transmitting radius, as follows: dist(x,y) < trans range x = y, and dist(x, y) defines the distance between two nodes, n x and n y , and trans range stands for the transmission range of the nodes.

The position of the lost human is the primary motivation of the search and rescue optimization method for optimization problems, and the significance of the clue originating in this position defines the cost of the solution. Now, the best method discloses a good position with additional hints [59] . When leaving certain clues, people seek the best option across the search method. However, the search position for the individual is kept in a situation matrix (matrix X), with the equivalent size of the memory matrix, and the left clue can be saved in a memory matrix (matrix M). n × d shows the problem parameter and n determines the individual quantity in the group.

From the above equation, assuming there are random clues amongst the obtained clues, the search direction can be attained by the following:

where C k denotes a random value among 1 and 2N, X i , and C k defines the position of the i th human and the k th clue, respectively. sd i indicates the search direction of the clues. It is noticed that C k equals X j , k = i. For avoiding repetitive position searches, the parameter of X i will not be modified by moving in the indicated direction [60] [61] [62] [63] [64] . The SAR approach uses a binomial crossover operator for applying to the limitations. Moreover, when the clue has greater significance compared with the current clue, a region was searched for the sp i direction. Otherwise, a search for the location of the existing position in the sp i is continuous. Therefore, the novel position of the j th variable is expressed by the ith human, as follows:

where c k,j denotes the position of variable j and the clue k. j r , r 1 , and r 2 represent three uniform random numbers within [1, d] , [−1, 1], and [0, 1], respectively. The second stage is about the individual. Here, an exploitation term has been performed regarding the human's current location [65] [66] [67] [68] . This stage employs the distinct clues connection concept from the social stage. The position, upgraded by the human, i, can be attained as follows:

where r 3 denotes a uniformly distributed number between 0 and 1, C m and C k define two arbitrary numbers between 1 and 2 N, respectively, and i = k = m. They could testify that they are in the solution space afterward, solving the solution from the preceding stages. This phase is named the boundary. In such cases, the following formula is utilized when the solution is placed outside the border:

where j = 1, 2, . . . , d, X min j , and X max j represent the minimal and maximal thresholds for the parameter j, respectively. According to this stage, the lost human candidate is searched for on the basis of the previously elucidated technique. When the sum of the cost function in a given scenario, X i f X i , is superior to the existing one, ( f (X i )), then the preceding location (X) would be saved in an accidental position in the memory matrix (M), and would be described as novel situation. If not, then the situation would be left, and the memory would not be upgraded.

where n determines a random integer among 1 and N, and M n defines the location of clue number, n, in the memory matrix. Time is critical in locating lost individuals due to threat of injury, and any delay that occurs at the time of searching could lead to death [69] [70] [71] [72] . Hence, when a person does not discover a notable clue during their search, it leaves the next person with the existing position.

where usn determines the unproductive searching number. When usn is superior to MU for a person, it moves towards the other location in the space solution. Figure 2 portrays the flow chart of SRO method. function in a given scenario, , is superior to the existing one, , then the preceding location (X) would be saved in an accidental position in the memory matrix (M), and would be described as novel situation. If not, then the situation would be left, and the memory would not be upgraded.

where determines a random integer among 1 and , and defines the location of clue number, , in the memory matrix.

Time is critical in locating lost individuals due to threat of injury, and any delay that occurs at the time of searching could lead to death [69] [70] [71] [72] . Hence, when a person does not discover a notable clue during their search, it leaves the next person with the existing position.

where determines the unproductive searching number. When is superior to for a person, it moves towards the other location in the space solution. Figure 2 portrays the flow chart of SRO method. Search and rescue optimization (SRO), when searching for people, typically takes place in two distinct phases: social and individual. Collection followers search for clues founded in their location, and focus on areas that are more likely to yield clues in the social phase. There is no regard for where or how many clues have been found by others during the individual search phase. In general, clues fall into two categories, as follows: Search and rescue optimization (SRO), when searching for people, typically takes place in two distinct phases: social and individual. Collection followers search for clues founded in their location, and focus on areas that are more likely to yield clues in the social phase. There is no regard for where or how many clues have been found by others during the individual search phase. In general, clues fall into two categories, as follows:

Remember to save a clue: A member of the exploration group is present and searching the surrounding area.

Forgotten clue: Members of the group discovered the clue, but no one is in the location to solve it. To put it another way, the person who discovered the hint has abandoned it in search of further potentially relevant information. Members of the group, on the other hand, have access to the information about that clue.

To increase exploration competence and ensure that the ideal answer is reached, the chaotic approach is combined with the krill head algorithm (KHA). Because Chebyshev maps are the most utilized chaotic behavioral maps, chaotic sequences are likely to be created efficiently and fast. Furthermore, longer sequences are not necessary Therefore, the existing solution has been switched to an accidental resolution in the solution space, according to Equation (7) for a possible solution, when usn > MU (Multi − User). In addition, for an unfeasible solution, usn is superior to MU, the memory matrix solution using the minimum number of limitation violations is selected, and the current solution is switched through the solution, so that the current solution substitutes the memory matrix.

where r 4 shows a frequently distributed random number within the range of 0-1. Under instruction to recover the worldwide optimization capability of an SRO algorithm, the chaotic concept is integrated into it. The chaotic state is an unstable state, which is extremely sensitive to initial conditions, which can be utilized for avoiding the local optimum problem and improving the quality of the solution. It is applied for achieving improved exploration and exploitation in every searching region, thereby enhancing the outcome in determining optimum global solutions [46] [47] [48] . The chaotic map was used in this study to indicate human searches around their current location in the individual phase, and the concept of linking different hints is used in the communal stage for exploration. In contrast to the social stage, the separation stage changed every dimension of X ij . Time is an important factor in the search-and-rescue procedure, because missing individuals may be hurt, and search-and-rescue parties arriving late may result in death. As a result, these processes should be designed in such a way that a huge amount of data is examined in as short a period of time as possible. As a result, if a human did not find the best hints after running a specific search count in their location, they would leave and go to a different site.

where x k i and x k+1 i denote positions at iterations k and k + 1 and C map represents a chaotic map. In this work, ten chaotic maps were used to determine the random values involved in the SRO algorithm.

The main function of the CSRO algorithm is maximizing the lifespan of networks and minimizing energy utilization of all sensor nodes. Assume that h 1 is the most objective function, such that CH is selected as the next hop, CH, with a superior RE, to route the data; such that, for maximizing the network lifespan, for instance, h 1 is maximization. Assume that h 2 is another main function that has a minimal distance among the CHs to the next hop CH, and the next hop CH, to the base station (BS). This procedure occurs under the instruction to decrease the energy utilization of the network as required for minimizing h 2 . Assume that h 3 is the third main function; thus, CHs is selected as the next hop among the CHs with a lesser node degree. In order to improve the lifespan of the network, h 3 must be minimized. Assume that b ij is a Boolean variable, determined as follows:

which is subject to the following:

The constraint in (23) means that the next hop node of CH i will be in the range of CH i , and that the next hop node is CH j . β 1, β 2 , β 3 indicate the anchor nodes with the target distance. The constraint in (25) declares that the next hop node of CH i is unique, for instance, CH j , and the constraint makes sure that there could not be 0 or 100% weight on either of the objectives.

This section analyzes the CSRO-MHDT method in comparison with recent methods of effective data transmission processes in a UWSN. The consequences are reviewed under variable rounds of execution. Table 2 0  300  300  300  300  300  300  40  300  300  300  300  300  300  80  300  300  300  300  300  300  120  300  300  300  300  300  300  160  300  300  300  300  300  300  200  300  300  300  300  300  300  240  300  300  300  300  300  300  280  300  300  300  300  300  299  320  300  300  300  300  299  297  360  300  300  300  297  298  295  400  300  300  298  298  297  290  440  300  296  290  299  298  287  480  296  294  287  290  290  285  520  294  288  279  284  281  271  560  287  276  268  262  264  254  600  279  264  253  240  243  238  640  269  234  230  202  228  218  680  253  217  211  188  187  179  720  226  183  172  169  160  152  760  214  142  132  130  140  50  800  183  113  121  89  95  3  840  139  72  94  56  20  0  880  116  28  37  12  0  0  920  68 300  296  290  299  298  287  480  296  294  287  290  290  285  520  294  288  279  284  281  271  560  287  276  268  262  264  254  600  279  264  253  240  243  238  640  269  234  230  202  228  218  680  253  217  211  188  187  179  720  226  183  172  169  160  152  760  214  142  132  130  140  50  800  183  113  121  89  95  3  840  139  72  94  56  20  0  880  116  28  37  12  0  0  920  68 Table 3 and Figure 4 , respectively (LND). The results indicated that the CSRO-MHDT technique has resulted in lengthened lifetime over the existing methods. With respect to FND, the CSRO-MHDT method reached FND at 476 rounds, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models attained FND at earlier rounds of 440, 403, 361, 323, and 280, respectively. In addition, in terms of HND, the CSRO-MHDT FND  476  440  403  361  323  280  HND  838  754  749  730  753  722  LND  998  940  921  903 874 840 Next, a brief TEC investigation of the CSRO-MHDT method in comparison with existing approaches is provided in Table 4 and Figure 5 . The results indicated that the CSRO-MHDT technique had the lowest TEC under all rounds compared with existing methods. For example, with 50 rounds, the CSRO-MHDT method obtained lower TEC of 2.22%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models achieved higher TEC of 2.46%, 2.71%, 5.39%, 5.15%, and 7.59%, respectively. With 500 rounds, the CSRO-MHDT system had the lowest TEC of 34.16%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models achieved higher TEC of 39.29%, 39.29%, 56.84%, 46.60%, and 65.87%, respectively. Finally, with 1000 rounds, the CSRO-MHDT technique had the lowest TEC of 99%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE methodologies attained higher TEC of 99.55%, 99.52%, 99.61%, 100%, and 100%, respectively. Next, a brief TEC investigation of the CSRO-MHDT method in comparison with existing approaches is provided in Table 4 and Figure 5 . The results indicated that the CSRO-MHDT technique had the lowest TEC under all rounds compared with existing methods. For example, with 50 rounds, the CSRO-MHDT method obtained lower TEC of 2.22%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models achieved higher TEC of 2.46%, 2.71%, 5.39%, 5.15%, and 7.59%, respectively. With 500 rounds, the CSRO-MHDT system had the lowest TEC of 34.16%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models achieved higher TEC of 39.29%, 39.29%, 56.84%, 46.60%, and 65.87%, respectively. Finally, with 1000 rounds, the CSRO-MHDT technique had the lowest TEC of 99%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE methodologies attained higher TEC of 99.55%, 99.52%, 99.61%, 100%, and 100%, respectively.

A detailed PLR analysis of the CSRO-MHDT approach in comparison with recent methods is offered in Table 5 and Figure 6 . The outcomes showed that the CSRO-MHDT technique had the lowest PLR under all rounds compared with existing approaches. For instance, with 50 rounds, the CSRO-MHDT algorithm had decreased PLR of 1%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE systems obtained higher PLR of 1%, 1%, 1%, 1%, and 1%, respectively. Next, with 500 rounds, the CSRO-MHDT technique had a low PLR of 2%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models had higher PLR results of 5%, 7%, 8%, 9%, and 10%, respectively. Finally, with 1000 rounds, the CSRO-MHDT technique had a low PLR of 12%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models had increased PLR of 17%, 19%, 22%, 23%, and 25%, respectively. A detailed PLR analysis of the CSRO-MHDT approach in comparison with recent methods is offered in Table 5 and Figure 6 . The outcomes showed that the CSRO-MHDT technique had the lowest PLR under all rounds compared with existing approaches. For instance, with 50 rounds, the CSRO-MHDT algorithm had decreased PLR of 1%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE systems obtained higher PLR of 1%, 1%, 1%, 1%, and 1%, respectively. Next, with 500 rounds, the CSRO-MHDT technique had a low PLR of 2%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models had higher PLR results of 5%, 7%, 8%, 9%, and 10%, respectively. Finally, with 1000 rounds, the CSRO-MHDT technique had a low PLR of 12%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models had increased PLR of 17%, 19%, 22%, 23%, and 25%, respectively. 0  0  0  0  0  0  0  50  1  1  1  1  1  1  100  1  1  1  1  1  2  150  1  1  1  2  3  3  200  1  1  2  3  4  3  250  1  2  3  3  4  4  300  1  2  3  4  5  5  350  2  3  4  5  6  6  400  2  3  5  6  7  7  450  2  4  6  7  8  9  500  2  5  7  8  9  10  550  3  6  8  9  10  11  600  4  7  9  10  11  12  650  5  8  10  11 12 14 Table 7 and Figure 8 depict the PDR analysis of the CSRO-MHDT algorithm under varying rounds in comparison with existing approaches. The outcomes revealed that the CSRO-MHDT technique resulted in increased values of PDR under all rounds. For instance, with 150 rounds, the CSRO-MHDT technique attained superior PDR of 99%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models reached lower PDR results of 99%, 99%, 98%, 97%, and 97%, respectively. Moreover, with 500 rounds, the CSRO-MHDT approach had an increased PDR of 98%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE models obtained lower PDR results of 95%, 93%, 92%, 91%, and 90%, respectively. Finally, with 1000 rounds, the CSRO-MHDT technique accomplished a higher PDR of 88%, whereas the EECRP, FCMMFO, FBCPSO, EGRC, and LEACH-ERE techniques exhibited reduced PDR of 83%, 81%, 78%, 77%, and 75%, respectively. 0  100  100  100  100  100  100  50  99  99  99  99  99  99  100  99  99  99  99  99  98  150  99  99  99  98  97  97  200  99  99  98  97  96  97  250  99  98  97  97  96  96  300  99  98  97  96  95  95  350  98  97  96  95  94  94  400  98  97  95  94  93  93  450  98  96  94  93  92  91  500  98  95  93  92  91  90  550  97  94  92  91  90  89  600  96  93  91  90  89  88  650  95  92  90  89  88  86  700  94  92  89  89  86  85  750  93  91  88  86  85  84  800  93  90  87  85  82  83  850  92  88  85  83  81  81  900  91  87  84  83  80  79  950  90  85  82  79  78  77  1000  88  83  81  78  77  75 By examining the above results and discussion, it can be confirmed that the CSRO-MHDT technique can accomplish effective data transmission in a UWSN .  750  93  91  88  86  85  84  800  93  90  87  85  82  83  850  92  88  85  83  81  81  900  91  87  84  83  80  79  950  90  85  82  79  78  77  1000  88  83  81  78 By examining the above results and discussion, it can be confirmed that the CSRO-MHDT technique can accomplish effective data transmission in a UWSN. 

In this study, a novel CSRO-MHDT method was developed for the optimal choice of routes for data transmission in a UWSN. The primary intention of the CSRO-MHDT technique is to reduce energy dissipation and enhance the lifetime of the UWSN. Primarily, the CSRO-MHDT technique involves WCA for effective choice of CHs. In addition, the CSRO-MHDT technique derived a fitness function and effectively selected a set of routes in a UWSN. For assessing the outcomes of the CSRO-MHDT technique, a wide-ranging experimental examination was carried out and the results were assessed under several aspects. The extensive comparative analysis highlighted the superior performance of the CSRO-MHDT technique over recent state-of-the-art approaches. Therefore, the CSRO-MHDT method can be used in application for optimal data transmission in UWSNs. In the future, delay-aware data aggregation schemes can be designed to improve the efficiency of UWSNs. 

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The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (22UQU4281768DSR03).

The Authors declare no conflict of interest.

No. of Rounds CSRO-MHDT  EECRP  FBCPSO  FCMMFO  EGRC  LEACH-ERE   0  0  0  0  0  0  0  50  1  1  1  1  1  1  100  1  1  1  1  1  2  150  1  1  1  2  3  3  200  1  1  2  3  4  3  250  1  2  3  3  4  4  300  1  2  3  4  5  5  350  2  3  4  5  6  6  400  2  3  5  6  7  7  450  2  4  6  7  8  9  500  2  5  7  8  9  10  550  3  6  8  9  10  11  600  4  7  9  10  11  12  650  5  8  10  11  12  14  700  6  8  11  11  14  15  750  7  9  12  14  15  16  800  7  10  13  15  18  17  850  8  12  15  17  19  19  900  9  13  16  17  20  21  950  10  15  18  21  22  23  1000  12  17  19  22  23  25 Sensors