Optimal data transmission and pathfinding for WSN and decentralized IoT systems using I-GWO and Ex-GWO algorithms

Optimal data transmission and pathfinding for WSN and decentralized IoT systems using I-GWO and Ex-GWO algorithms Amir Seyyedabbasi a , Farzad Kiani a , Tofigh Allahviranloo a , Unai Fernandez-Gamiz b , Samad Noeiaghdam c,d,* a Software Engineering Department, Faculty of Engineering and Natural Science, Istinye University, Istanbul, Turkey b Nuclear Engineering and Fluid Mechanics Department, University of the Basque Country UPV/EHU, Nieves Cano 12, 01006 Vitoria-Gasteiz, Spain c Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia d Department of Applied Mathematics and Programming, South Ural State University, Lenin prospect 76, Chelyabinsk 454080, Russia Received 4 May 2022; revised 13 July 2022; accepted 7 August 2022 Available online 19 August 2022 KEYWORDS WSN; DIoT; Pathfinding; Metaheuristic algorithm; Swarm intelligence Abstract Efficient resource use is a very important issue in wireless sensor networks and decentralized IoT-based systems. In this context, a smooth pathfinding mechanism can achieve this goal. However, since this problem is a Non-deterministic Polynomial-time (NP-hard) problem type, metaheuristic algorithms can be used. This article proposes two new energy-efficient routing methods based on Incremental Grey Wolf Optimization (I-GWO) and Expanded Grey Wolf Optimization (Ex-GWO) algorithms to find optimal paths. Moreover, in this study, a general architecture has been proposed, making it possible for many different metaheuristic algorithms to work in an adaptive manner as well as these algorithms. In the proposed methods, a new fitness function is defined to determine the next hop based on some parameters such as residual energy, traffic, distance, buffer size and hop size. These parameters are important measurements in subsequent node selections. The main purpose of these methods is to minimize traffic, improve fault tolerance in related systems, and increase reliability and lifetime. The two metaheuristic algorithms mentioned above are used to find the best values for these parameters. The suggested methods find the best path of any length for the path between any source and destination node. In this study, no ready dataset was used, and the established network and system were run in the simulation environment. As a result, the optimal path has been discovered in terms of the minimum cost of the best paths obtained by the proposed methods. These methods can be very useful in decentralized peer-to- *Corresponding author at: Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk 664074, Russia. E-mail addresses: [email protected] (A. Seyyedabbasi), farzad.kian[email protected] (F. Kiani), tofigh.allahvira[email protected] (T. Allahviranloo), unai.fernand[email protected] (U. Fernandez-Gamiz), [email protected],[email protected] (S. Noeiaghdam). Peer review under responsibility of Faculty of Engineering, Alexandria University. Alexandria Engineering Journal (2023) 63, 339–357 HOSTED BY Alexandria University Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com https://doi.org/10.1016/j.aej.2022.08.009 1110-0168 Ó2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). peer and distributed systems. The metrics for performance evaluation and comparisons are i) network lifetime, ii) the alive node ratio in the network, iii) the packet delivery ratio and lost data packets, iv) routing overhead, v) throughput, and vi) convergence behavior. According to the results, the proposed methods generally choose the most suitable and efficient ways with minimum cost. These methods are compared with Genetic Algorithm Based Routing (GAR), Artificial Bee Colony Based routing (ABCbased), Multi-Agent Protocol based on Ant Colony Optimization (MAP-ACO), and Wireless Sensor Networks based on Grey Wolf optimizer. (GWO-WSN) algorithms. The simulation results show that the proposed methods outperform the others. Ó2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/). 1. Introduction Wireless Sensor Networks (WSNs) are one of the subcategories of ad-hoc networks and consist of many distributed sensor nodes. These nodes can also be used in systems comprising of the Internet of Things (IoT). One of the advantages of these nodes is their ease of assembly in difficult environments. WSNs can be used in a vast variety of application areas, such as traffic monitoring [1,2], agriculture [3,4], automobiles [5], health monitoring [6], etc. There are also many application areas in IoT, such as the Internet of Drones [7,8], Internet of Food [9], Internet of Medical-Things [10], Industrial IoT (IIoT) [11], and autonomous vehicles [12]. Moreover, WSNs and IoT systems can also collaborate as a single system [13–17]. It can be used widely, especially in decentralized IoT architectures [18,19]. In scenarios, where there are internet availability issues, or when low cost is desirable, problems can occur in an IoT system with classical centralized architectures. Furthermore, in this architecture, a large part of the load falls on the serverside cloud system. Some methods are proposed for this, such as fog/edge compute nodes. Another recommendation to troubleshoot this architecture is blockchain technology. A decentralized architectural design can be more efficient and is used extensively in application areas. Therefore, decentralized distributed architectures can be employed as a solution. We define these systems as Decentralized IoT (DIoT) systems. WSNs are generally designed in a decentralized form. Therefore, DIoT and WSN are similar in architectural aspects. One important issue in these structures is finding a suitable, optimal, and efficient path for data communication between nodes. To achieve this goal, this study proposes two efficient methods that are inspired by metaheuristic algorithms. The proposed methods can, both, find the optimal paths with efficient resource usage, and provide features such as scalability and fault tolerance. A sample system with the hybrid architecture of DIoT and WSN technologies is shown in Fig. 1. Each sensor node or IoT device can send its data packets to Base Station (BS) via single-hop or multi-hop model. In a decentralized distributed structure, multi-hop methods are frequently employed. The BS collects all data packets and transmits them to a server (possibly a cloud) for data analysis and end-user access [20]. As sensor nodes work in collaboration, it is necessary to have an efficient data transfer method. These nodes suffer from a limited power battery, bandwidth, computational capacity, and memory space. Therefore, performing the complex computations, in each sensor node, is a challenging task. Furthermore, recharging is mostly impossible due to physical constraints, such as the location of the nodes. At the same time, changing the batteries is not possible, as these sensors use one-time batteries. The main issue in WSN and IoT systems is increasing the network lifetime. It is worth noting that resource management and network topology has an important role to play in network lifetime and availability [21]. Since network lifetime deals directly with sensor nodes’ remaining battery level, energy consumption is a vital factor in these systems, making energy-one of the most important resources. However, while focusing on this goal, it is also essential to efficiently consume the other necessary resources. Therefore, the methods proposed uses the resources in a balanced manner. Unsurprisingly, efficient resource consumption, such as that of energy, increases the life of the network and, as such, the system [22,23]. In WSN and DIoT systems, one of the most important challenges is efficient resource consumption such as energy [24,25]. Techniques to find the optimal paths, in an energyefficient manner, are of vital importance. To tackle this problem, numerous multi-purpose routing solutions have been introduced in the literature but finding and proposing a general routing technique that preserves the integrity, connectivity, and inclusiveness of the network is a very costly and complicated process. In addition, finding the most efficient route among many possible paths, in a wide and complex network demands further processing. Moreover, it is not easy to find appropriate, effective coefficients for the relevant routing parameters. In addition, analytical solutions to such problems are difficult to find. In fact, these problems are categorized under Non-deterministic Polynomial-time (NP-hard) problems [26–28]. Therefore, it is fitting to use metaheuristic algorithms to solve it. However, when these algorithms are implemented in the entire routing process, they tend to cause additional overhead in the system and result in inefficient usage of some of the system’s resources. In this study, a generic system architecture is proposed, and this architecture can easily perform routing without incurring any additional cost, integrating with many different metaheuristic algorithms. Since the proposed model is comprehensive, it will be able to work well by including various algorithms for many purposes. In this study, we discussed our performance metrics as follows. i) network lifetime, ii) the alive node ratio in the network, iii) the packet delivery ratio and lost data packets, iv) routing overhead, v) throughput, and vi) convergence behavior. This paper proposes two new energy-efficient methods based on the Incremental Grey Wolf Optimization (I-GWO) and Expanded Grey Wolf Optimization (Ex-GWO) algorithms 340 A. Seyyedabbasi et al. to help find optimal paths in DIoT and WSN systems. In the GWO algorithm [29], swarming is controlled by the leader of the group, which helps to get the optimum solution for a defined problem. It can outperform other metaheuristic algorithms thanks to its hierarchy group working mechanism and balanced transitions between exploration and exploitation phases. These wolves can exhibit a successful mechanism because they have an extremely dominant hierarchy. In addition, this algorithm does not require additional cost in finding the optimal solutions in line with the simple working mechanism and parameters. In other words, the GWO algorithm works simply with a small number of parameters, preserving the random principle. Thanks to these features, it has suitable behavior in the exploration and exploitation phases which are effective in finding the optimal solution. Additionally, it only requires one vector of position, which decreases the memory demand. On the other hand, other metaheuristic methods suffer from computational overload and time inefficiency in their approach to the optimum answer. Therefore, thanks to the characteristics of the GWO algorithm, it can be used to find solutions to different complex and real problems. In this regard, the GWO algorithm may be more likely to be successful than other metaheuristic methods in this type of problem on various parameters due to its working mechanism. Therefore, the GWO variants may be more likely to be successful than other metaheuristic methods in this type of problem on various parameters due to its working mechanism. The I-GWO finds solutions much more quickly, owing to its exploitation feature and fast convergence rate in noncomplex environments, whereas Ex-GWO, due to its structure, is deemed successful in complex and large-scale systems. Hence, an appropriate choice can be made for different needs and systems. In this context, the routing methods proposed in this paper suggest the most appropriate model for various networks using these two algorithms. In these algorithms, swarming is controlled by the leader of the group, which helps to get the optimum solution for a defined problem. As a result, these algorithms are useful in decreasing network complexity and increasing the efficiency of resources used in pathfinding. Besides, these algorithms are used to present low-cost paths among the various probable paths. The proposed pathfinding methods, which use the metaheuristic algorithms, are named energy-efficient routing based on I-GWO (EERI -GWO ) and energy-efficient routing based on Ex-GWO (EER Ex-GWO ). The proposed methods try to find paths that are most suitable and most efficient with minimum costs. The other features and contributions of the proposed methods are: 1) A generic system architecture is proposed that combines the metaheuristic and network model. Due to this, the architecture is adaptable in various systems and for numerous purposes. Furthermore, many metaheuristic algorithms can be readily applied in these systems. 2) In order to increase the pathfinding efficiency, metaheuristic algorithms are used to discover the most appropriate coefficients for each parameter of the defined fitness function. 3) A novel and comprehensive fitness function is defined with an emphasis on balancing trade-offs between important parameters. This function concerns with five Fig. 1 Sample architecture for DIoT and WSN [19]. Optimal data transmission and pathfinding for WSN and decentralized IoT systems using I-GWO and Ex-GWO 341 parameters (distance between nodes, BS-hop, validtraffic, energy consumption, and buffer capacity), and a tradeoff between related parameters. 4) Finding the best routes between the nodes means that less energy is consumed in the network. This results in increased network resilience and lifetime. 5) The global knowledge and processing of the network are performed at the BS, which have abundant resources. The rest of this paper is organized as follows. In the next section, research that deals with finding a route using metaheuristic methods, present in literature, is described. In the third section, the proposed metaheuristic algorithms are briefly explained. In the fourth section, the proposed methods are detailed. In the fifth section, simulation results and analyses are provided. Conclusion and future works are given in the last section. 2. Related works In general, metaheuristic algorithms can arrive at optimal solutions for real-world problems at a low cost. In the literature, there are several widely used classifications of metaheuristicbased algorithms [30]: nature-inspired vs non-nature-inspired algorithms, population-based vs single point search algorithms, dynamic vs static objective functions, single vs various neighborhood structures, and memory-less vs memoryindependent algorithms [30]. One of the most popular discussions and classifications is the population-based and singlepoint search category. The improvement of a single-based solution is achieved by iterations, while the optimization of a population-based solution is achieved through a set of solutions. Another important area is nature-and non-natureinspired classification. Recent research shows that natureinspired algorithms are a trend and perform quite well at solving a wide variety of problems. Methods in this category are defined into four main categories [29]. They are evolutionbased, Swarm-Intelligence (SI)-based, physics-based, and human-based [31,32] approaches. This study focuses on the problem of finding the best route. Studies in lately years prefer SI methods because they generally outperform other methods in solving problems, particularly in pathfinding problems. SI methods are generally natureinspired and are based on a herd or collective social behavior and community mindset. There are many studies in this category in the literature [33–36] showcasing that SI-based methods can solve complex problems more efficiently. These algorithms consist of a group of simple particles and homogeneous members that interact with each other as well as their environment. Their agents try to find the best solutions that cooperate in the local search area and benefit from the collective effort of all the agents involved. In this study, the use of SI methods in WSN and IoT to find optimal paths is discussed [37–39]. Ant Colony Optimization (ACO) is one of the most frequent metaheuristic algorithms that is used in the systems discussed. Authors in [40] proposed a routing method for a distributed multi hop-based system using the ACO algorithm for reliable data communication. The next hops on the path are based on sensor nodes with high energy levels. However, it is not considered very successful in energy efficiency because it does not work in a fair and balanced manner. The main reason for this is that the fitness function used does not use sufficient parameters. Researchers in [41] investigated a new pheromone update mechanism in the ACO algorithm and used it to achieve energy efficiency of WSNs. The authors discuss two energy measures. In next node selection for routing, sensor nodes closer to the target are more likely to be selected. They also use four control parameters in the probabilistic decision function. Since it does not use memory efficiently, it cannot be very successful in showing efficient performance in the general analysis. Authors in [42] proposed a new routing algorithm based on ACO algorithm to achieve balanced energy consumption on each network sensor node beside the choice of the path with minimal cost. In their work, called IEMACO, they make route discovery based on a number of factors: the convergence speed of the routing algorithm, the probability of transition, and the remaining life of the nodes. Position and speed information predicts the remaining lifetime of the link. The most obvious shortcoming of this study is the usage of the memory method. In [43], the authors have proposed a dynamic energy threshold strategy different from the multipath approaches, so-called ACOHCM. It has some advantages such as network topology, searching the optimal path, and network load balancing. In the ACOHCM, initially hop counting mechanism is applied. The hop count for the sink (BS) is 0. The number of hops of other nodes is incremented by one depending on their neighbors. When the topology of the network changes, the hop counting mechanism is run again. So, the hop counts should be updated at different time intervals. Finally, an energy threshold strategy is used that is applied to each node. The authors of [44] proposed a dynamic decision-making system based on ACO algorithm for connected cars in IoT systems. They used artificial ants to control the dynamics of connected vehicles in traffic flow and for autonomous calculations. An ant colony optimization-based routing protocol for multi-agents is presented in this paper that manages network resources effectively in real-time [19]. In addition to finding the next destination of ants, the proposed method is also used to manage pheromone updates and evaporation rates. Several key parameters are taken into account when determining the next destination under various conditions, including energy remaining, buffer size, traffic rate, and distance. In terms of network lifetime and energy consumption, simulation results of the proposed method have remarkable performance. An ant colony optimization-based routing protocol for multi-agents is presented in this paper that manages network resources effectively in real-time [45]. In addition to finding the next destination of ants, the proposed method is also used to manage pheromone updates and evaporation rates. Several key parameters are taken into account when determining the next destination under various conditions, including energy remaining, buffer size, traffic rate, and distance. In terms of network lifetime and energy consumption, simulation results of the proposed method have remarkable performance. Apart from ACO, the Genetic Algorithm (GA) is another technique also recommended in such systems. In [46], it was proposed to combine simulated annealing with genetic algorithms in order to achieve optimal performance. There has been a comparison of the observed results in terms of the average residual energy, the network lifespan, and the packet transport between the BS and sink, with that of a GA-based 342 A. Seyyedabbasi et al. approach. Gupta et al [47] proposed an energy-efficient algorithm to minimize the energy consumption in each round based on GA. The proposed method attempts to reduce the total distance traveled by data in the system. In this study, a Directed Acyclic Graph (DAG) model was used and the chromosome representation, as well as a crossover method, were proposed. In their strategy, they also emphasized the minimization of the total path length. This study, which is ambitious in terms of energy efficiency, is used in comparison with the proposed methods in our study. IoT has been added to Clustered-Based Routing (CBR) for Information-Centric WSNs (ICWSNs) in a protocol known as CBR-ICWSN, which enables CBR for these networks [48]. There are two phases to this paper, which include the choice of a Cluster Head (CH) and the determination of the optimal route. Thus, by employing a Black Widow Optimization (BWO) method in order to choose an optimal set of CHs, an optimal set of CHs is selected. It is interesting to note that the authors in this paper used a different algorithm to find the optimal route. CBRICWSN is a routing protocol that is based on Oppositional ABC (OABC) and can be used to select routing routes more efficiently. The artificial Bee Colony (ABC) algorithm is yet another metaheuristic method used in such systems. Authors in [49] have proposed a new clustering routing method based on an ABC algorithm for cluster formation. Their main goal is to reduce energy consumption and exploit low-power clusters. They are concerned about the trade-off between energy consumption and the quality of the communication link within clusters. Authors in [50] propose a method based on the Grey Wolf Optimizer (GWO) algorithm to solve the energy problem in WSNs. They attempt to handle the problem of finding the correct position of unknown nodes in the network. Based on their results, their GWO-based method is better than Partial Swarm Optimization (PSO) and Modified Bat Algorithm (MBA) algorithms in the convergence and success rate. In [51] researchers have proposed a new routing algorithm in a hierarchical structure using the GWO algorithm. It avoids the energy hole by balancing the load on the nodes nearer to BS and cluster head nodes. The new fitness function, proposed in their work, takes into account the total distance and the total number of hops. This fitness function is solely used to help the wolves. One shortcoming of this study is that it does not focus sufficiently enough on the effective parameter. Without taking into account necessary and sufficient parameters, the results obtained from the fitness function can be, at best, of very limited use in real-world cases. In contrast, the fitness function proposed in our study is general and multi-purpose and can also be easily adapted to many metaheuristic algorithms. It is worth mentioning that the architecture proposed is the leading reason for this adaptability. In another study, the authors proposed a meta-heuristic artificial intelligence approach based on grey wolf social behavior to minimize the energy consumption of WSNs from the livestock industry [52]. In order to determine an algorithm’s performance, energy level, grid size, transmission range, and direction of transmission were used as factors. A metaheuristic-driven, energy-aware routing scheme (IMDEACBR) is proposed in [53]. The IMD-EACBR model aims for maximum energy usage and lifetime. IMD-EACBR employs an improved Archimedes optimization algorithmbased clustering (IAOAC) technique to cluster head selection. Furthermore, the TLBO-MHR technique is applied for optimum route selection using teaching–learning-based optimization (TLBO). Simulated outcomes reveal improvements in dead node proportions, network lifespan, energy consumption, packet delivery ratio (PDR), and latency. A novel clustering and routing method is presented in this paper in an effort to enhance system efficiency [54]. In order to optimize it, it relies mostly on genetic algorithms as well as equilibrium optimization. Using genetic algorithms, a first phase is carried out that clusters the sensor nodes based on their features. As a result, the best cluster heads are selected to improve system stability. The purpose of this work is to reduce the energy consumption of WSN networks by improving the clustering algorithm and the equilibrium optimization algorithm used for selecting the optimal path between cluster heads and base stations. Consequently, the proposed method has been obtained to be the most energy-efficient, have a longer network lifespan, and deliver more packages than other methods. This study aims to develop an energy-efficient cluster routing protocol that can be applied to wireless sensor networks [55]. In the first step of the cluster head selection process, we used the Honey Badger Algorithm to select cluster heads. In order to find the optimal cluster head among all sensors, the Honey Badger Algorithm is used. This algorithm takes into account factors including distance to the base station, residual energy, distance to its neighbors, node degree, and centrality. It then selects the optimal cluster head. A fuzzy Firebug Swarm Optimization algorithm is used to perform the routing between the cluster heads and the base stations. This method offers a reduction in the amount of end-to-end delay, an increase in the number of packets that are delivered, a higher throughput, and a reduction in the number of packets lost, which are all factors that affect how much energy is consumed by the network. In another study in the literature, a hybrid optimization algorithm is proposed to propose a new energy-aware CH selection framework in WSNs through hierarchical routing [56]. As well as energy and distance, delay, and Quality of Service (QoS) are considered when selecting the CH. It is proposed to develop a hybrid algorithm that combines the principles of Sea Lion Optimization (SLnO) and Particle Swarm Optimization (PSO) to select the optimal CH. The performance of the adopted method is compared with other traditional models using a variety of metrics. Compared to other conventional methods, the proposed algorithm has higher normalized energy. In this paper, the chaotic fuzzy grasshopper is applied to optimizing routing on the Internet of Things, focusing in particular on the sleep-wake schedules of nodes, which are an essential part of the routing [57]. During the evaluation of the efficiency of the proposed method, the following three criteria were utilized: the remaining energy, the network life, and the coverage rate of the network. It has been determined that the results are based on two different scenarios that have been analyzed. Consequently, the proposed method performs better than the base method in all scenarios and is more effective for all criteria of comparison than the base method. The use of metaheuristic methods has become very popular in IoT and WSN systems, especially in recent years. In this paper, two methods to find optimal paths in DIoT and WSN applications are provided using two metaheuristic algorithms (I-GWO and Ex-GWO). These methods can be applied in both DIoT and WSNs. Optimal data transmission and pathfinding for WSN and decentralized IoT systems using I-GWO and Ex-GWO 343 3. I-GWO and Ex-GWO algorithms This section briefly describes two metaheuristic algorithms used in the methods proposed in this paper. The Grey wolf optimizer (GWO) algorithm is inspired by grey wolves in their natural habitat [29]. Alpha (a), beta (b), delta (d), and omega (x) are the four types of wolves found in a pack. These wolves have different responsibilities in the pack. Alpha Wolf is the leader of the pack. Beta wolves are the co-leaders of the alpha wolf. The third level of hierarchy in the pack is that of delta wolves. The remaining wolves which are not part of the upper level of the hierarchy are omega wolves. Encircling, hunting, and attacking are the three main attributes of the wolves. Incremental Grey Wolf Optimizer (I-GWO) algorithm, used in the first pathfinding method of this paper, is an upgraded version of the GWO [36]. In the I-GWO algorithm, the leader encircles the prey (Eq. (1)), hunts it and finally (Eq. (2)), attacks the prey based on the A !value. If |A|less than1, a wolf is attacking its prey, otherwise, it’s busy finding other prey. The second wolf on the pack follows the leaders’ position and updates its own position to attack the prey. Generally, the n th wolf in the pack updates its own position based on the n-1 wolf before it (Eq. (3)). Eq. (4), 5, and 6 are the control mechanisms to avoid trapping in local optima and to balance movements between exploration and exploitation phases. Da !¼Ca !Xa !X ! ð1Þ X1 !¼X ! aA1 !Da !ð2Þ Xn !tþ1ðÞ¼ 1 n1Xn1 i¼1XitðÞ;n¼2;3; mð3Þ A !¼2a !r1 !a !ð4Þ C !¼2r2 !ð5Þ a !¼21t2 T2  ð6Þ Additionally, in both I-GWO and Ex-GWO, a !is linearly decreased from 2 to 0 over the course of iterations, and is obtained using Eq. (6) and (12), respectively. The effect of a ! is on the range of motion, directing the algorithm in finding the solution and is used to get closer to the solution range. Random vectors r1 !and r2 !lie in the range [0, 1]. A !, and C ! are coefficient vectors that lead to encircling the prey [29,33– 35]. These parameters control the tradeoff between exploration and exploitation phases. Due to this, wolves do not always go in the same direction. In all variants, whenever A * is less than 1, the wolves in the pack attack to hunt, otherwise, they try to find the prey. X !is the position vector of the prey, whereas Xi !is the position vector of the grey wolf, and Di !is a vector that depends on the location of the target. Where i{a,b, d}. Moreover, tis current iteration and Tis maximum iteration numbers. The other metaheuristic algorithm used in this paper is the Expanded Grey Wolf Optimizer (Ex-GWO) [36] algorithm. The hunting mechanism of the Ex-GWO is uses a technique dissimilar to one used in I-GWO and GWO algorithms. Encircling of the prey is performed using the first wolf in the pack (Eq. (7)). The fourth wolf in the pack updates its position based on the first three wolves before it. Generally, the n th wolf in the pack updates its own position based on the first wolf in the pack as well as the wolves before it (Eq. (8) and (9)). In ExGWO the attacking mechanism ensures that the prey does not escape. The coefficients a, A, and Care calculated using Eq. (10), 11, and 12. Da !¼Ca !Xa !X !  Db !¼Cb !Xb !X !  Dd !¼Cd !Xd !X ! ð7Þ X1 !¼X ! aA1 !Da ! X2 !¼X ! bA2 !Db ! X3 !¼X ! dA3 !Dd !ð8Þ Xn !tþ1ðÞ¼ 1 n1Xn1 i¼1XitðÞ;n¼4;5; mð9Þ A !¼2a !r1 !a !ð10Þ C !¼2r2 !ð11Þ a !¼21t T  ð12Þ I-GWO algorithm is based on the leader wolfs’ behavior. Other wolves in the pack update their own position based on all the wolves selected afore themselves. In the Ex-GWO algorithm, the n th wolf updates its own position relevant to the prey according to their immediate successor and the first three wolves. In [36], it is proved that the performance of I-GWO and Ex-GWO algorithms is better than GWO. On the other hand, I-GWO tries to find solutions much quickly due to its exploitation feature and its fast convergence rate, and ExGWO, owing to its structure, is likely to be successful in complex and large-scale systems. 4. Proposed pathfinding methods The used metaheuristic algorithms are a natural match for the problem suit and exhibit a balanced behavior, as such, they have been used in this paper as the problem-solving methodology. As explained in the literature section, many metaheuristicbased algorithms have been used for similar systems. It is known that metaheuristic-based methods do not guarantee to find optimal solutions, but they try to find the solutions close to the optima, providing more efficient execution time and CPU power consumption in time and space complexities. Each of the proposed metaheuristic methods in the literature has its advantages along with its shortcomings. This study focuses on broader parameters in proposing comprehensive and accurate methods to be used in WSN and DIoT. Accordingly, a new fitness function has been defined. The defined fitness function is used to calculate the cost of each path in the network and 344 A. Seyyedabbasi et al. includes residual energy, traffic status, buffer rate, BS-hop, and neighbor list of each node as formulated in Eq. (13). BS-hop indicates the hop counts of each node to BS. In this study, BS is assumed to be the destination node. The BS node does not look only at the distance or number of hops of each node relative to itself to find the most suitable path (between each node and itself) but also focuses on other effective parameters that are defined in the new fitness function. It takes into account the dynamic resources of the nodes in the system and the variable parameters of the network. For this purpose, a new fitness function is defined. The paths between the source and destination nodes are selected according to hop values and passed through the fitness function. The sum of the best fitness values for each hop will be the candidate for the best route (Eq.14.). Subsequently, the minimum value among candidates is chosen as the best path between the two relevant nodes for each hop count (Eq.15). At this stage, the lowest-cost path is chosen for each hop count (step 2). Step 3 selects the best path with the minimum cost among all hop sizes (Eq.16). At the same time, as mentioned before, one of the most important issues discussed in these systems is energy saving. In this section, the new energy-efficient routing methods based on the two metaheuristic algorithms, EER I-GWO and EER Ex-GWO , are introduced. They can aid in modeling useful solution models in the pathfinding of wide and complex networks (especially in decentralized architecture). These methods focus on the critical features of sensor nodes in pathfinding. As aforementioned, pathfinding and routing are NP-hard problems in the complex distributed and Peer-to-Peer (P2P) structures such as WSN and DIoT. Therefore, these proposed methods can provide a good solution for finding optimal paths in the entire search space. In short, they find the optimal path from the sets of possible paths in multiple hops. 4.1. Proposed architecture In this subsection, some definitions and design factors of the proposed methods have been summarized along with the description of the proposed methods. Sensor nodes (IoT devices) are deployed randomly in the network, and different paths are created between any pair of source and destination nodes. The metaheuristic algorithms used in this paper belong to the SI category and are population-based. A general architecture is suggested for the relevant metaheuristic algorithms to work harmoniously with the proposed methods. Thanks to this architecture, the algorithms used can be easily adapted to the relevant system. Furthermore, it should be noted that other metaheuristic methods are also able to easily use such systems. The conceptual schema of the proposed architecture is presented in Fig. 2. In this architecture, the search space is considered as a matrix where the rows represent the number of search agents, and the columns signify the coefficient numbers. In the simulation of I-GWO and Ex-GWO, the number of search agents is assumed to be equal to the number of grey wolves in the pack. Moreover, the coefficient numbers, which are used as the dimension of the problem, are assumed to be four and their values are obtained using Eq. (13). The fitness function, defined earlier, is used to calculate the cost of each path. In addition, all the coefficients used in the proposed methods are updated at every round of the network based on metaheuristic algorithms. When the number of hops between two nodes is one, they are already single-hop and are direct neighbors, so there is no need to specify a route. The problem arises with multi-hop structures. In these cases, there may be paths of various lengths between the two nodes. There may be intermediate nodes between source and destination when the hop counts are more than one. In the proposed architecture, best route for any hops of paths is found considering Eq. (14) and (15), and the best among them is chosen using Eq. (16). Therefore, the best path between two intermediate nodes is obtained, along with the calculation of the final best path cost between source and destination. The fitness function is given by Eq. (13), which calculates the cost between two nodes i and j. Costi;j¼c1di;j  þc2Hj  þc2 ValidTraffic Ti;j  þc3 Einitial Ej : Buffer Capacity Bj  ð13Þ Where d i,j is distance between nodes iand j.E j indicates the residual energy of the node j, and H j is hops count of node jto BS. T i,j is the traffic status between nodes iand j.B j indicates the buffer rate of the nodes j.ValidTraffic,BufferCapacity, and E initial are common variables that are used for each node. The values of these three variables are their maximum values at each node and they are related to node hardware properties. Furthermore, c 1 ,c 2 ,c 3 ,c 4 are three control parameters, with values between 0 and 1 where c 1 +c 2 +c 3 +c 4 = 1 and c 1 <c 2 <c 3 <c 4 . These control parameters are calculated by metaheuristic algorithms (I-GWO and Ex-GWO). The coefficients updates are done at each round of the network. It is worth mentioning that the network rounds term is different with metaheuristic iterations. This difference is described in the subsequent subsection. 4.2. The network rounds and metaheuristic iterations In the actual application of sensor networks and IoT, the network round and metaheuristic algorithms iteration work separately. In the network considerations, the rounds and iterations should be handled separately. Each round of the network occurs in certain time periods. In the proposed methods, a time interval between each round of the network is considered. If the round and iterations work together, it causes an overload on the network. Metaheuristic algorithms try to find the best solutions. At the same time, there is no specific time to reach the solution, as such, the pathfinding operation is done in the BS. After that, over a period of time, data packet transfer is completed between the target (destination) and the source. The concept of iteration is an expression used widely in metaheuristic methods. Each iteration tries to approach the solution based on the results obtained in the previous iteration. Both the number of iterations and the number of network rounds depend on the system design. In this paper, these parameters are defined and quantified. Furthermore, they are described in the simulation section. 4.3. Pathfinding mechanism In the proposed methods, the metaheuristic algorithms used help in finding the best path with a minimum cost between Optimal data transmission and pathfinding for WSN and decentralized IoT systems using I-GWO and Ex-GWO 345 the source and destination (BS) node. There are paths with various numbers of hops as seen in the first step of Fig. 2.In this step, the cost of the path for all intermediate nodes between the source and destination nodes is calculated utilizing Eq. (13). The most optimized coefficient values of each parameter in this equation are obtained from metaheuristic algorithms, as described in the previous subsection. In the second step, the algorithm calculates costs for the candidate path applying Eq. (14) and then selects the path with the minimum cost as the best path for each hop count using Eq. (15). This procedure is applied for all hop counts. Indeed, this process is performed for all paths with different sizes. Naturally, the best candidate path is chosen among the paths of the same length. In the end, as indicated in step 3 of Fig. 2, the algorithm selects the minimum cost path from the obtained candidate paths, as an optimal solution between these nodes (source and destination) based on Eq. (16). In other words, the optimal path is chosen among the best paths of different lengths. The proposed methods attempt to select the paths that are the most convenient and efficient routes with the minimum costs. CostCondidate S;D¼X j¼n i¼1 costi;jð14Þ Costh S;D¼MinðCostCondidate S;DÞ8hHopCount ð15Þ CostS;D¼Min Costh S;D  ð16Þ Where CostCondidate S;Dis shows the total cost between nodes i and j. This process is calculated separately for each hop count. The shortest path found for each hop is considered Costh S;D. After finding the shortest path for all hops, one shortest path among all is accepted as the final answer and it is called CostS;D. This process is described in Fig. 3 with a schematic example. For instance, the hop size in the first round of the network may be different from hop sizes in subsequent rounds. At the same time, the hop sizes in different rounds may vary from each other. In this study, the destination node is assumed to be the BS, and therefore, the costs between each sensor node and BS are calculated. Here, in the path, the packet is also passed just once from each sensor node. In the end, BS chooses the minimum cost path using Eq. (16). Finally, the BS broadcasts selected optimal paths to source nodes. For example, if the candidate path between node 4 and BS is N4, N61, N98, N43, and BS, then, first of all, the cost of tuples (N4, N61), (N61, N98), (N98, N43), and (N43, BS) is calculated from Eq.13. An example of candidate paths with sample costs are represented in Table 1. The sum of each tuple value is calculated through Eq.14, which is the cost of each individual path. After all candidate paths for each hop count have been calcuFig. 2 Conceptual schema of the proposed architecture in finding optimal paths. 346 A. Seyyedabbasi et al. lated, their minimum is selected as best, by means of Eq.15. In the end, only one of the best paths for all hops is obtained according to Eq.16. This example is schematically represented in Fig. 3. A hand-shaking method for checking the availability of next-hop is performed. On a default network, each node’s information is considered to be recorded in the BS, as outlined in Table 2. This information is obtained by a request data packet that is sent to sensor nodes via BS in the initialization phase of the network. Residual energy, traffic status, buffer size, distance to the BS, and neighbor list are stored in the BS. The decisions in finding the optimum path are made using metaheuristic algorithms by BS, which have unlimited energy sources. Note that balanced behavior is required between these five parameters. The remaining energy level and the remaining buffer size are desired to be high, whereas the network traffic and the distances are desired to be low. The methods proposed and detailed earlier, handle the balancing requirement. As mentioned, the optimal paths are obtained in the BS. For this, as previously emphasized, I-GWO and Ex-GWO methods are used to find the optimized coefficients of the defined parameters. The BS node has a table regarding nodes’ information. In this table, some basic information such as residual energy, traffic status, buffer rate, BS-hop and neighbor list of each node is stored. Each sensor node also holds a table, which is called the routing table, that includes a neighbors list, distance to neighbors, distance to BS, and BS-hop. The relevant routing table is presented in Table 3. 4.4. Definition of data packet frames Data packets are used for communication between system nodes. These packets have various suitable formats that are defined in these devices. However, they can be customized to optimize the use of resources. Efficient system resource utilization can be ensured with the definition of the appropriate packet template and dynamic structure, according to the system needs. The use of custom data packets is also helpful in finding paths. In this study, two general types of data packet frames are defined. As mentioned before, in the initialization phase of the network, BS broadcasts a message to request global information about the sensor devices. This information is obtained by a request data packet broadcasted to nodes via BS, as depicted in Fig. 4(a). In response, the sensor nodes transmit the relevant information (residual energy, traffic situation, buffer rate, BS-hop, and neighbor list) to BS. The formats of the sensor node’s response packet are also shown in Fig. 4(b) along with different fields defined in these packets. The TTL field is intended to prevent the occupation of network traffic. A deadline value is defined for each packet. Each node reduces the TTL value by one for each packet received. The initial value of this field varies depending on the type of application. Owing to the source and destination addresses filed, each node can be applied to multiple sources and destination scenarios at the same time as parallel and concurrent models because it knows which nodes are source and which is destination. Due to the nature of the proposed methods, parallel and concurrent models are naturally supported. This feature is very important in the proposed methods, and it offers the opportunity to work in many parallel and concurrent application areas. Fig. 3 A working mechanism of proposed method in pathfinding. Table 1 Template candidate paths cost at the end of each iteration. Candidate paths Sample values Path 1 0.78 Path 2 1.36 . . .. . . Path n n Optimal data transmission and pathfinding for WSN and decentralized IoT systems using I-GWO and Ex-GWO 347 5.8. General comparison and discussion In this study, simulations were investigated on 6 different parameters and the results of each were shown. In addition, in line with the results obtained, the methods used in each parameter have their performances ranked from the best to the worst (Table 6). As can be seen from the results obtained, both of the proposed methods perform better. I-GWO tries to find solutions more quickly thanks to its exploitation feature and fast convergence rate, and Ex-GWO, due to its structure, is likely to be successful in complex and large-scale systems. In these algorithms, swarming is controlled by the leader of the group, which helps to get the optimum solution for a defined problem. Besides, benefiting from the defined fitness functions and comprehensive architecture, these algorithms were made easier to adapt to the proposed pathfinding methods and exhibit efficient behavior. The third place, MAP-ACO, has performed well, but because of the use of a metaheuristic algorithm in all operations in its method, the performance in the network, naturally, was limited. The main reason for this is that the devices used have limited resources. However, in the architecture of this study, metaheuristic algorithms used were run only in the first part of the method and this causes increased efficiency. In fourth place, GWO-WSN is listed. GWO-WSN has not been very successful due to its noncomprehensive fitness function. However, this method could have had a more stable working mechanism due to its GWO structure. When the performance analysis of the other two methods is done, it is seen that they are not very successful. 6. Conclusion and future works This work solved one of the main challenges in wireless sensor networks and decentralized IoT systems by improving the Fig. 12 Throughput analysis. Fig. 13 Convergence speed analysis. 354 A. Seyyedabbasi et al. energy consumption of the network. It finds the best route by examining all available paths between any two nodes with a proposed general architecture. Finding the best routes between nodes results in less energy being consumed in the network, thus efficient use of resources and increasing the overall lifetime of the system. Thanks to this architecture, many metaheuristic algorithms can work in an adaptive way, so it takes the role of a multi-purpose general model and will provide convenience to researchers working in this field. In this study, EERI -GWO and EER Ex-GWO routing methods are proposed using I-GWO and Ex-GWO algorithms as metaheuristic algorithms. These two methods are energy efficient routing methods that try to find optimum paths. These methods provide more efficient execution time and CPU power in time and space complexities. The search space is considered as a matrix, where the rows represent the number of search agents, and the column signifies the coefficient numbers. These coefficients are updated by the metaheuristics used. This study focuses on broader parameters in proposing more comprehensive and accurate methods in WSN and DIoT. Accordingly, a new fitness function has been defined. The defined fitness function is used to calculate the cost of each path in the network and includes residual energy, traffic status, buffer rate, BS-hop, and neighbor list of each node. The paths between the two source and destination nodes are selected according to hop values and passed through the fitness function. The sum of the best fitness values for each hop will be the candidate for the best route. Subsequently, the minimum value among candidates is chosen as the best path between the two competing nodes. Each node acquires its best neighbor from its routing table. Related network equations were mapped in accordance with metaheuristic algorithms. The performances of two metaheuristic algorithms used in the proposed routing methods were evaluated on various parameters. After iterations of metaheuristic algorithms, the best solution is found as an optimal path for the network in the current rounds. The routing operations are performed in the BS. The results have displayed those proposed methods have better performance than ABCbased, GAR, GWOWSN, and MAP-ACO methods. Furthermore, results show that these two methods are more successful in finding the most appropriate paths in these systems. According to the results of this study, and other studies in the literature, it can be said with confidence that swarm intelligence is stronger than particle intelligence in similar systems. The proposed methods in this paper may be more suitable for a network of any scale. In these methods, the most appropriate and efficient path can be found between multiple sources and destination nodes concurrently or in parallel (depending on the needs of the problem and application area). In addition, the proposed methods have better performance in terms of robustness and fault tolerance factors. Apart from the pros and strengths of the study, the shortcomings can be summarized as follows. The shortcomings of this study are planned to be continued and completed in future studies. In this study, no tests were performed on a real system covering big data. In this study, simulations were made using homogeneous sensor nodes. However, heterogeneous sensor nodes were not used. This study did not focus on the multi-objective and Pareto-based problem. In future work, the proposed methods will be tested on real testbeds with a large density of various devices for the generation and analysis of big data. Similarly, the proposed approach can perform more efficiently in multi-objective and Pareto-based problems. Especially in parameters that have trade-offs with each other (e.g., network connectivity and energy consumption) can be applied. The proposed methods will be used for solving many complex problems such as feature selection, complex electrical circuits, 3D path planning in mobile robotics or connected vehicle networks, and optimized node localization in the systems. It should be noted that with the growth in IoT technology, most of the proposed path planning methods focus on homogeneous sensor networks, but IoT devices can greatly benefit from heterogeneous sensor nodes. In this way, this work can help use heterogeneous sensor nodes to support different IoT devices. Accordingly, the proposed method can be easily applied to the wearable sensor network, which has become extremely popular in the last decade. Funding The work of U.F.-G. was supported by the government of the Basque Country for the ELKARTEK21/10 KK-2021/00014 and ELKARTEK22/85 research programs, respectively. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] M. Bottero, B.D. Chiara, F.P. Deflorio, Wireless sensor networks for traffic monitoring in a logistic centre, Transportation Research Part C: Emerging Technologies 26 (2013) 99–124. Table 6 Rank of algorithms performance (Summary). Parameters EER I-GWO EER Ex-GWO MAP-ACO GAR ABCbased GWO-WSN Packet Delivery Rate 2 13645 Alive Nodes Number 2 13564 Network Lifetime Rate 2 13564 Overhead 124563 Throughput 2 13564 Convergence 2 13564 Optimal data transmission and pathfinding for WSN and decentralized IoT systems using I-GWO and Ex-GWO 355 [2] A.S. Ibrahim, K.Y. Youssef, A.H. Eldeeb, M. Abouelatta, H. 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