MWaOA: A Bio-Inspired Metaheuristic Algorithm for Resource Allocation in Internet of Things

1  Introduction

In modern Internet of Things (IoT) systems, resource management is a key component for ensuring a pleasant and seamless end-user experience [1]. The end-user level in such IoT systems comprises devices with limited communication and computational capabilities [2]. In this scenario, improper utilization of available resources burdens the system and results in a poor Quality of Service (QoS). The careful allocation and utilization of processing power, storage, and bandwidth directly influences the overall performance of IoT systems [3,4]. Resource management also addresses critical aspects, such as scalability and network performance in IoT environments [5]. Organizations achieve cost optimization by efficiently managing the available resources. Furthermore, effective resource management upholds QoS and security in IoT applications, thereby ensuring the reliability and integrity of data transmission [6,7]. Recently times, metaheuristic optimization algorithms have played a crucial role in addressing resource management challenges in IoT systems [8]. Typically, these algorithms mimic natural phenomena to resolve nondeterministic polynomial-time hardness issues [9,10]. These algorithms have demonstrated greater efficiency in handling problems that cannot be resolved within polynomial time [11]. Employing a suitable optimization algorithm leads to faster convergence towards optimal solutions with a limited computational time [12]. However, conventional optimization techniques [13,14] often struggle to effectively handle resource allocation in gateway management, leading to suboptimal performance. Similarly, traditional metaheuristic methods tend to converge prematurely, become trapped in local optima, or demand extensive computational resources [15]. To fulfill various user demands while enhancing overall system performance, restricted network resources are dynamically allocated based on the magnitude and position of the base stations. The problem is then divided into four constrained subproblems that are resolved using a constrained reinforcement-learning model. Moreover, a reward mechanism is designed to encourage agent cooperation in distributed training settings [16]. However, these algorithms fail to sufficiently balance diversification and intensification, leading to inefficient exploration of the solution space [17]. Among the available optimization algorithms, only a few are efficient in solving both global optimization and resource-allocation problems [18]. To overcome this resource allocation problem, a Modified Walrus Optimization Algorithm (MWaOA) is proposed in this article, which maintains a balanced trade-off between diversification and intensification. Particularly in this context, the proposed MWaOA supports the allocation of multiple resources to the gateway.

The key contributions of this study are defined below:

•   The inclusion of the crowding process in the MWaOA improves the trade-off between the exploration and exploitation phases by preventing premature convergence and introducing diversity in the search space.

•   The MWaOA is proposed with improved tendencies of extensification and intensification, with a primary focus on reducing the energy consumption and latency during resource allocation.

•   After allocating resources to a gateway in IoT systems, the proposed MWaOA consistently achieves near-optimal solutions compared to other optimization algorithms. Furthermore, the fitness function of MWaOA is based on the communication costs incurred during resource allocation to the gateway.

•   Six evaluation metrics such as delay, throughput, energy consumption, response time, execution time, and resource utilization are used to analyze the efficacy of MWaOA and the comparative optimization algorithms.

The remainder of this article is structured as follows. Section 2 provides an account of the existing research models designed for resource allocation and management, along with their advantages and setbacks, and Section 3 details the proposed methodology. The empirical analysis of the proposed MWaOA model, its future scope, and the conclusion of this study are provided in Sections 4 and 5, respectively.

2  Related Works

Rafique et al. [19] introduced a hybrid optimization approach combining Modified Cat Swarm Optimization (MCSO) and Modified Particle Swarm Optimization (MPSO) algorithms for resource management in fog computing environments. In this study, the MCSO and MPSO algorithms were used to manage the resources and schedule tasks among fog devices. The primary objective of this model was to optimize resource usage and reduce the response time through efficient task scheduling and resource allocation. Three performance metrics were utilized to evaluate the effectiveness of the hybrid optimization algorithm within fog-IoT systems. However, the incorporation of this hybrid approach resulted in a poor trade-off between the total operating cost and execution time, proving its application in complex fog systems.

Arunkumar Reddy and Venkata Krishna [20] presented a Feedback-based Fuzzy Algorithm (FFA) for resource management in fog-computing environments. The presented algorithm effectively minimized the makespan by stabilizing computational tasks. The IoT-based cloud system’s efficacy was improved through FFA by reducing the load redistribution and communication costs and minimizing the energy consumption, latency, and network bandwidth. However, fuzzy logic-based models are ineffective in adapting to new scenarios or unforeseen circumstances, requiring manual intervention. Furthermore, Liu et al. [21] and Sangaiah et al. [22] employed a Whale Optimization Algorithm (WOA) in the cloud edge paradigm for resource management. The empirical evaluation demonstrated that the WOA improved the allocation cost and minimized response time in cloud-edge computing environments in contrast to other optimization algorithms. However, despite the allocation of resources before processing, the absence of runtime resource allocation remains a key issue in this model. Vakili et al. [23] presented a Grey Wolf Optimization (GWO) and MapReduce framework to combine services with optimized QoS. The GWO select the appropriate candidate composite service which ensures to aggregate four QoS constraints such as cost, energy savings, availability, and response time. The MapReduce framework include services based on parallel execution and fitness value for selecting relevant services. The simulation result provides cost availability, energy-saving improvement and response time through GWO and MapReduce framework. However, it affects the performance as it utilized GWO without adaptive tuning thereby declining complexity.

Zhang et al. [24] developed an orchestration framework based on a Deep Neural Network (DNN) for resource management in industrial IoT systems. The DNN model was trained, pre-stored, and placed for performing inference. This model efficiently managed resource management to enable effective inference. However, resolving the associated challenges was taxing on the model due to the presence of mixed-integer variables. Therefore, a novel deep reinforcement learning was integrated with the Markov decision process for optimal resource allocation in industrial IoT systems. Nonetheless, this process was computationally expensive and requires increased processing time. Additionally, Maddikunta et al. [25] developed a hybrid algorithm with a WOA and Moth Flame Optimization (MFO) for green communication in IoT systems. The obtained empirical outcomes prove that the developed hybrid algorithm outperformed existing optimization algorithms. Regardless, this algorithm needs to be further extended to consider other factors, such as link lifetime and network density.

Iwendi et al. [26] presented a hybrid algorithm that integrates the WOA and Simulated Annealing (SA) for the selection of optimal Cluster Heads (CHs) in IoT systems to optimize energy consumption. The evaluation measures considered for CH selection were the cost function, residual energy, temperature, load, and alive nodes. This hybrid algorithm demanded multiple, frequent communications between cloud and fog nodes for decision-making. This led to a communication overhead and increased bandwidth consumption with latency. Janakiraman [27] introduced a hybrid algorithm using Artificial Bee Colony (ABC) and Ant Colony Optimization (ACO) algorithms for resource management in IoT systems. The appropriate CHs in IoT systems were selected using the ACO-ABC algorithm, which demonstrated superior resource management in terms of throughput, residual energy, and percentage of dead nodes and alive nodes. However, the reduced scalability with an increased number of IoT devices was a key drawback of this model.

Sharma et al. [28] presented a hybrid algorithm combining the Firefly Algorithm (FA) and Grey Wolf Optimization (GWO) algorithm for load balancing in IoT systems. Similarly, Nematollahi et al. [29] suggested an MFO algorithm with opposition-based learning to effectively distribute resources in IoT systems. Afzali et al. [30] introduced an improved binary Particle Swarm Optimization (PSO) algorithm for effective resource allocation in IoT-fog cloud computing environments. The improved binary PSO algorithm reduced latency and offered better load balancing between fog nodes. Yakubu and Murali [31] implemented a modified Harris Hawk Optimization (HHO) algorithm for effective task distribution between cloud and fog environments through task prioritization. This enhanced resource utilization and reduced power consumption, task execution cost, and makespan time in the cloud as well as in the fog layer. However, the incorporation of optimization algorithms (FA, GWO, MFO, PSO, and HHO) in IoT-fog-cloud computing environments often demands frequent communication among IoT devices, cloud servers, and fog nodes for timely decision-making, which led to communication overhead and increased the risk of potential bottlenecks with bandwidth utilization.

Mirmohseni et al. [32] utilized a Markov model for resource allocation in IoT systems. The Markov model efficiently maximized network usage and reduced latency in the fog layer. However, the static probability of the Markov model led to suboptimal resource allocation, particularly in a dynamic IoT environment. Abbasi et al. [33] introduced a multi-objective genetic algorithm for workload allocation in IoT-fog cloud computing environments. The performance of this multi-objective genetic algorithm was validated in four computing environments: only cloud, fog cloud, and IoT-fog cloud, in terms of delay and energy consumption. Karthick and Gomathi [34] integrated WOA with the Galactic Swarm Optimization Algorithm (GSOA) for efficient resource management in IoT systems. However, the use of multi-objective and hybrid optimization algorithms raised two key concerns of high communication overhead and integration complexity in IoT-fog cloud environments.

By analyzing the aforementioned models, it was noted that the majority of optimization algorithms struggled to manage exploitation and exploration rates for resource management. Furthermore, a few existing studies leave room for enhancement in terms of delay, energy consumption, and resource usage. Simultaneously, research on modifying current metaheuristics or combining them with alternative approaches is just as essential as developing entirely new ones. Modification or hybridization is necessary to preserve the performance consistency in established metaheuristics, paving the way for further advancements. Another concern arising from the rapid development of metaheuristics is the lack of personalized search evaluations. Despite being based on multiple search techniques, many modern metaheuristics are still evaluated using the same comparative frameworks as their predecessors. This is akin to the pattern of newer approaches outperforming older approaches. This situation is related to the pattern of younger people outperforming older ones. Paradoxically, there has been little effort to investigate the methods used to create the metaheuristic. Several studies have evaluated the suggested metaheuristic as a complete set rather than employing a modular evaluation method. Therefore, the MWaOA is proposed in this study to efficiently manage the balance between exploration and exploitation for effective resource management in IoT environments.

3  Methodology

This research proposes MWaOA [35] for effective resource management, which includes two types of nodes: gateway nodes and resource nodes. Gateway nodes are interconnected with resources, and resource nodes are utilized to facilitate service instances. In this scenario, the gateway nodes are considered anchor nodes that are used to connect the diversified entities of modern IoT systems. Every gateway controls the traffic generated by IoT data for the entire array of resources. Furthermore, the resources are connected to distinct gateways. Additionally, the communication costs between the gateway and resources are predefined. This helps to reduce communication costs by focusing on effective resource distribution [36,37]. In modern IoT systems, communication costs are significantly influenced by the adopted model. Addressing this challenge involves identifying resource allocation patterns [38] that minimize communication costs. Communication cost is considered the primary factor as it significantly impacts the feasibility and long-term sustainability of IoT systems. It also plays a critical role in guiding decisions related to resource allocation and infrastructure development. The following equations describe the mathematical framework for modeling the transmission cost of resource allocation in an IoT environment. Accordingly, the objective function (Objfunction) is defined in terms of transmission cost, as mathematically expressed in Eq. (1).

Objfunction=MinimizeTrcost(1)

where, the transmission cost is represented as Trcost, and is mathematically defined in Eq. (2).

Trcost=∑j=1|NVg|Trcost(j)r×Trcost(BG)PNfactor(2)

where, the transmission cost of a gateway with respect to the resources is denoted as Trcost(j)r, and the transmission cost of all gateways is represented as Trcost(BG). The number of gateways in the considered system is indicated as |NVg|. The mathematical expression for Trcost(BG) is given in Eq. (3).

Trcost(BG)=∑i=1|NVg|∑j=1,j≠i|NVg|Trcost−BG(ij)(3)

where, transmission cost incurred between the ith and jth gateways is denoted as Trcost−BG(ij), and the term Trcost(j)r is computed using Eq. (4).

Trcost(j)r=∑r=1|NVgr|TRcost(j)r(4)

where, the transmission cost between the jth gateway and the rth IoT resource is represented as TRcost(j)r, and the set of IoT resources inter-connected to the jth gateway is denoted as NVgr. The costs of gateways and their associated IoT resources are analytically combined to provide an accurate assessment of the communication overhead, as given in Eq. (4). Furthermore, PNfactor is used to balance the resource allocation to the gateway, and it is computed using Eq. (5). The term PNfactor(i) is defined in Eq. (6).

PNfactor=1+∑i|NVg|PNfactor(i)×α(5)

PNfactor(i)={1,if|NVgr|≤ϵ||NVgr||NVg||0,if|NVgr|>ϵ||NVgr||NVg||(6)

where, the resources allocated to the jth gateway are represented as |NVgr|, and α refers to the constant scaling factor with a value of 1.4, which is determined by implementing the MWaOA. This constant value s analytically determined through a series of controlled trials using the MWaOA framework to optimize the trade-off between resource utilization and communication efficiency. The selected value (α=1.4) yields minimum transmission costs and an effective balance, while preventing resource overload on specific gateways. A detailed explanation of the MWaOA is provided in Section 3.1, and the corresponding system model is visually illustrated in Fig. 1.

Figure 1: Detailed visual illustration of system model with IoT resources, service instances and gateways

Resource management remains a critical concern in the IoT. This study focuses on the discovery and identification of all available resources, selection of optimal resources, and their efficient distribution to achieve effective resource management. The system performance is enhanced through a comprehensive evaluation of key parameters, such as energy efficiency, cost, data precision, responsiveness, and reliability. Several advancements in resource management across various computing domains are systematically reviewed. However, resource management in the IoT continues to pose significant challenges, demanding the development of more advanced and effective methods.

The primary objective of this study is to develop a generic and, extendable resource management system for IoT settings. The proposed resource management system enhances the overall performance of IoT by managing resource sharing among applications with varying degrees of criticality. Fig. 2 displays the resource management approach, which comprises the following components.

•   Applications

•   Application Descriptions

•   Resources

•   Resource Descriptions

•   Resource Management components

•   Applications are deliberated as software processes which offer various types of services to consumers. To process these services, the proposed application requires access to resources generated by the devices.

•   Resource and application represent the data necessary for managing resource content.

•   Resource description comprises both functional and non-functional attributes of the resource. The characteristics and modules utilized depend on the domain and specific ontology applied to describe the resource. The resource management process is not bound to a particular ontology; the only requirement is that the application designer uses the same ontology when specifying resources.

•   The application description includes two primary constraints: criticality and resource specification. Criticality defines the importance of an application within an IoT model. It is defined either at the application design time by the designer or at run time by the system manager, while resource specifications define the types of resources required by the requester (applicant).

Figure 2: Overall flow diagram of resource management process and its application in IoT domain

From the detailed review of existing models, it is observed that no metaheuristic procedure has been developed based on the replication of walrus activities and behaviors. However, the distinctive behaviors of walruses, such as nutrition exploration, relocation, outflow, and defensive aggression towards predators, are well-suited for the development of an optimization algorithm. In the following section, the mathematical equations of a new metaheuristic procedure, referred to as the Modified Walrus Optimization Algorithm (MWaOA), are developed to address this research gap and solve complex optimization problems, as explained in the following subsections.

3.1 Inspiration of MWaOA

Generally, the walrus is considered one of the largest deep-sea creatures after whales. Walruses mostly live in regions with moderate seawater temperatures, or near colder regions. Many herds of walruses consist of hundreds to thousands of individuals, with their bodies being tube-shaped, sturdy, and overweight, featuring flattened skulls and rounded snouts. Along the upper lip, they have approximately 400 long and firm whiskers composed of blood vessels and nerve endings which provide them with an acute sense of touch. Among these features, the most distinctive trait is the white pair of prominent upper canine teeth, which grow continuously throughout life and eventually form tusks. These tusks are used for self-defense, digging through sludge and gravel to find food, such as clams, prawns, and crabs, and to help climb onto ice surfaces. Despite their massive appearance, walruses are generally agile in aquatic environments. Compared to other aquatic animals, walruses are considered exceptional divers, capable of staying underwater for up to 20 min at a depth of approximately 500 m. Additionally, walruses remained near the subsurface for up to two hours before needing to resurface air within three minutes. This research introduces a novel metaheuristic process called the Walrus Optimization Algorithm. The behavior of walruses is modeled through migration, breeding, roosting, and foraging activities. At this point, two objectives are intended to be addressed.

(1)   The performance of the walrus population is evaluated based on peril and shelter indicators.

(2)   Communication and characteristic distinctions within the population are explicitly modeled in the Walrus procedure. Specifically, the model accounts for social structures and interactions among males, females, and young walruses.

In arithmetic terms, the search space refers to the domain within which the procedure attempts to identify the optimal solution. It is typically a multidimensional space composed of decision variables, while the solution space consists of all possible outcomes. An optimal result corresponds to the position of the walrus in the search space, representing a potential solution to the stated issue. The identified solution is expressed in vector form, with all elements constrained within the decision-parameter ranges defined by the problem. The walrus algorithm aims to identify optimal results to enhance the efficiency of the problem’s objective function of the problem.

3.2 Initialization of MWaOA

WaOA is an efficient population-based meta-heuristic optimization algorithm inspired by the natural behavior of walruses [24,30]. In the context of resource management problems in IoT systems, each walrus represents a candidate solution, with its position in the search space defining candidate values [12]. In the proposed MWaOA, a crowding mechanism is incorporated into the conventional WaOA to prevent premature convergence and to maintain population diversity. The introduction of the crowding factor C enables the algorithm to efficiently balance the exploitation and exploration phases. Accordingly, the fitness of a solution, denoted by Fi is modified and expressed mathematically in Eq. (7).

Fi′=Fi+C×perturbation(7)

where, C refers to the crowding factor, Fi′ is the adjusted fitness, and Fi is the original fitness of solution i. Perturbation is introduced to enhance both the exploitation and exploration phases; it represents a controlled variation of candidate solutions aimed at improving the local search capabilities and preventing stagnation. This controlled randomness helps escape local minima and promotes the exploration of new areas within the solution space. The crowding mechanism plays a significant role in balancing exploration and exploitation during the search process. Exploration predominates in the early iterations, maintaining diversity to avoid premature convergence, while exploitation intensifies in later iterations by focusing on the search for promising regions. Performance evaluation employs key metrics such as the diversity index and convergence rate, with diversity values ranging from 0.4 to 0.8 during initial stages and narrowing to 0.1 to 0.3 as convergence progresses. In certain test cases, particularly those involving complex, multimodal environments, the crowding mechanism preserves multiple candidate solutions, thereby enhancing solution quality and convergence reliability.

Initially, the population is divided into sub-swarms with available resources allocated to each gateway. The total message cost Tcost serves as the objective function, and the proposed MWaOA aims to minimize this objective function, as expressed in Eq. (8).

Tcost=∑j=1GN(djr1×dg)(8)

where, the number of gateways is denoted as GN, the total cost endured during intergateway communication is represented as dg, and the total cost endured during data distribution between the resources and gateways is denoted as djr1. In the proposed MWaOA, the walrus position is updated in three distinct steps by mimicking their natural behaviors, which are given below:

•   Feeding process (exploration phase)

•   Migration

•   Fighting and escaping against predators (exploitation phase)

3.2.1 Feeding Process (Exploration Phase)

Walruses consume a diverse range of over 60 marine species including shrimp, sea cucumbers, tunicates, soft corals, tube worms, and various mollusks. However, they primarily prefer benthic bivalve mollusks, especially clams, which forage by grazing along the seafloor. Walruses locate food using sensitive vibrissae and vigorous flipper motion. The strongest walrus, identified by its tall tusks, leads and guides smaller walruses to food sources. The strongest walrus is considered as the candidate solution with the best fitness value in the current iteration. This increases the convergence speed towards near-optimal solutions, while maintaining an adaptive exploration mechanism to preserve solution diversity. Consequently, the strongest walrus in the group represents the best candidate solution with the optimal objective function value. Walruses’ search behavior covers various regions of the search space, enhancing the WaOA’s global exploration capability. This unique behavior improves the exploration power of the MWaOA during a global search. The position-updating process is mathematically modeled using Eqs. (9) and (10), respectively. In this phase, the position of the walrus is updated based on Eq. (9). The objective function value improves when the newly generated position is better than the previous one, as mathematically expressed in Eq. (10).

xi,jP1=xi,j+randi,j×(SWj−Ii,j×xi,j)(9)

Xi={XiP1,FiP1<Fi,Xi,else,(10)

When the strongest walrus with the best objective function is denoted as SW, integers are denoted as Ii,j which randomly range between one and two, random numbers are represented as randi,j ε [0,1], the objective function is denoted as FiP1, the new position of the ith walrus in the exploration phase is represented as XiP1, and the jth dimension is denoted as xi,jP1.

3.2.2 Migration

Migration is a common activity among walruses who move to crags or stony beaches, especially when the air becomes too hot during late summer. In the MWaOA, the migration process guides walruses through the search space to explore suitable regions. This process is mathematically described by Eqs. (11) and (12), respectively. During migration, each walrus was randomly moved to the position of another walrus within the search space. The new position is initially generated using Eq. (11). According to Eq. (12), if this new position improves the objective function value compared with the previous position, the position of the walrus is updated accordingly.

xi,jP2={xi,j+randi,j×(xk,j−Ii,j×xi,j),Fk<Fixi,j+randi,j×(xi,j−xk,j),else(11)

Xi={XiP2,FiP2<Fi,Xi,else,(12)

where, the value of the objective function is denoted as Fk and FiP2, the walrus’s jth dimension positions of the walrus are denoted as xk,j and XiP2, k∈{1,2,…,N}, and k≠i is the position of the selected walrus to which the ith walrus migrates. The position newly generated in this phase is denoted as XiP2.

3.2.3 Fighting and Escaping against Predators (Exploitation Phase)

Walruses are frequently attacked by polar bears and killer whales as they are often visible. During the exploitation phase, the fighting and escaping strategies of walruses against predators lead to changes in their positions. These natural behaviors enhance the exploitation capability of the MWaOA within the local search space. A neighborhood is defined around each walrus to simulate this phenomenon. First, a random position within the neighborhood is generated using Eqs. (13) and (14), respectively. The newly generated position replaces the previous position of the walrus if it improves the objective function value, as mathematically expressed in Eq. (15).

xi,jP3=xi,j+(lblocal,jt+(ublocal,jt−rand×lblocal,jt))(13)

Localbounds={lblocal,jt=lbjiterublocal,jt=ubjiter(14)

Xi={XiP3,FiP3<Fi,Xi,else,(15)

where, the local upper and local lower bounds of the jth variable are denoted as ublocal,jt and lblocal,jt, the upper and lower bounds of the jth variable are represented as ubj and lbj, iteration is denoted as iter, the value of the objective function is denoted as FiP3, xi,jP3 is denoted as the walrus jth dimension, and the newly generated position of the ith walrus in the exploitation phase is denoted as XiP3. The configuration parameters of the MWaOA are as follows: the population size is 100, the upper bound size is 8, the lower bound size is 2, and the total number of iterations is 100. After reaching the maximum number of iterations, the MWaOA is terminated.

In the initial stage, once the iteration of the MWaOA is completed, the positions of all walruses are updated based on the implementation of the first, second, and third phases, after which newer values are calculated for the walruses’ positions and objective functions. The candidate solutions are consistently updated and enhanced through the MWaOA stages until the final iteration, as described in Eqs. (9) and (15), respectively. The convergence process of the MWaOA is maintained by the adaptive balance between exploration and exploitation achieved through crowding-based diversity preservation. Furthermore, reliable experimental results across multiple datasets demonstrated stable and consistent convergence behavior. The complexity of MWaOA is approximately O(N×I×D), where N refers to the population size, I is the number of iterations, and D represents the problem dimensionality. Thus, the MWaOA exhibits strong performance reliability across diverse problem settings and effectively avoids premature convergence. Optimal candidate solutions are obtained during the execution of the method, as provided by the MWaOA upon completion. A flowchart of the proposed MWaOA method is shown in Fig. 3. The pseudocode of the proposed MWaOA is as follows.

Figure 3: Systematic flowchart of modified walrus optimization algorithm for efficient resource management in smart IoT systems

Pseudocode of the proposed MWaOA

Initially, set the optimization parameters.

Initialization of walrus’s positions.

For iter=1:Maximum number of iteration

Strongest walrus position is updated based on the value of objective function

For i=1:N

Feeding process (exploration phase)

Compute the new position of the walrus utilizing Eq. (9).

Update the position of walrus utilizing Eq. (10).

Migration process

Select a walrus immigration destination.

Compute the new position of the walrus utilizing Eq. (11).

Update the position of walrus utilizing Eq. (12).

Fighting and escaping against predators (exploitation phase)

Compute the new random location of the walrus in the neighborhood using Eqs. (13) and (14), respectively.

Update the location of walrus utilizing Eq. (15).

End

Preserve the best candidate solution.

End

Output: optimal solution achieved using MWaOA.

End MWaOA

While addressing optimization problems, analyzing the computational complexity is essential for evaluating the efficiency of a procedure. This analysis typically focuses on three key stages: initialization, fitness evaluation, and update. The amount of temporary memory space used during execution is estimated based on space complexity. Specifically, the maximum memory utilized at any given time during the initialization phase is referred to as the spatial complexity of the MWaOA.

4  Simulation Results

The MWaOA is simulated using Python software (version 3.10.0) on the Keras, SciPy, and Theano libraries. The model’s performance is evaluated on a system running a 64-bit Windows operating system equipped with 8 GB of RAM and an Intel® Core™ i5 processor, representing a modest computational setup. However, the proposed MWaOA effectively handles large datasets, including those containing up to 800 resources and 100 iterations. This demonstrates the practical feasibility of the MWaOA for non-specialized hardware. For further analysis, as the dataset size or iteration count increases, the computational time may become more demanding. Therefore, additional optimization of more powerful hardware will be considered in future work. In this study, datasets of varying sizes (small, medium, and large) are created to evaluate the performance of MWaOA against other algorithms, namely FA, GWO, MFO, HHO, Galactic Swarm Improved-WOA (GSIWOA) [34], and WaOA. In the generated datasets, the number of gateways ranges from four to 100, while the number of resources increases from ten to 800. Eight test samples are generated during the experimentation to assess the performance of the MWaOA and the comparative algorithms. The generated test samples are listed in Table 1.

The first three datasets, DS-1, DS-2, and DS-3, are smaller datasets, while DS-4, DS-5, and DS-6 are medium datasets, and DS-7 and DS-8 are larger datasets. The communication costs between resources and gateways range from one to 20, and the communication costs between gateways range from 20 to 40. In this study, the empirical analysis of the proposed MWaOA and comparative algorithms (FA, GWO, MFO, HHO, GSIWOA [34], and WaOA) is carried out three-folds. In the first fold, four performance metrics: delay, throughput, energy consumption, and response time are considered. These are used to evaluate the performance of MWaOA in comparison with the other algorithms under different service arrival rates. In the second fold, the performance of the proposed and comparative algorithms is validated for different simulation epochs using the same four metrics. Finally, in the third-fold, the performance of MWaOA and the comparative algorithms are evaluated for different service arrival rates based on execution time and resource utilization.

4.1 Performance Metrics

Six performance metrics, namely, delay, throughput, energy consumption, response time, execution time, and resource utilization, are utilized to validate the efficacy of the MWaOA against that of the comparative optimization algorithms. In a smart IoT system, delay is defined as the time taken to process a transaction or any task, including processing time and queuing delays. Furthermore, the throughput is defined as the number of tasks or operations that are successfully completed within a given period. The performance metric throughput is directly proportional to the processing capacity of IoT systems. The formulas used to compute the delay and throughput are given in Eqs. (16) and (17), respectively.

Delay=Completion time−Initiation time(16)

Throughput=Number of completed tasksTime−period(17)

Furthermore, in the context of IoT systems, the energy consumption is measured as the total energy used for communication and task execution. Response time is defined as the time taken by the IoT system to respond to a user request. The energy consumption and response time are mathematically expressed in Eqs. (18) and (19), respectively. Additionally, in a smart IoT system, execution time is measured as the time taken by the MWaOA to complete a specific task or operation. Performance metric resource utilization evaluates the usage of system resources, including memory, central processing units, and other components. Eqs. (20) and (21) are used to compute the execution time and resource utilization in the context of resource management in smart IoT systems.

Energy consumption=Power×Time(18)

Response time=Request completion time−Request submission time(19)

Execution time=Finish time−Start time(20)

Resource utilization=Time resources are busyTotal time(21)

4.2 Empirical Evaluation of the MWaOA with Distinct Service Arrival Rates

In this analysis, Tables 2 and 3 present the delay and throughput of the proposed MWaOA and the comparative optimization algorithms (FA, GWO, MFO, HHO, GSIWOA [34], and WaOA) under distinct service arrival rates. The optimal adaptation of resource allocations and assignment of gateways reduce the delay in MWaOA to meet end-user requirements. Furthermore, compared to existing optimization algorithms, the throughput achieved by MWaOA shows a significant improvement. Based on the results in Tables 2 and 3, it is evident that MWaOA reduces delay more effectively and improves throughput than benchmark algorithms under varying service arrival rates.

Furthermore, the values for the energy consumption and response time of MWaOA and the comparative algorithms (FA, GWO, MFO, HHO, GSIWOA [34], and WaOA) are presented in Tables 4 and 5. As shown in Table 4, the energy consumption of MWaOA is significantly lower than that of the other algorithms. The proposed MWaOA efficiently assigns resources under varying service arrival rates, leading to a reduced energy usage in IoT environments. In addition, Table 5 shows that the response time of MWaOA is comparatively lower than that of the baseline algorithms. The optimal allocation of multiple resources by the MWaOA minimizes unnecessary task-processing delays.

A graphical comparison of MWaOA and existing optimization algorithms for distinct service arrival rates in terms of delay and throughput is illustrated in Figs. 4 and 5. These figures clearly show that MWaOA consistently achieved the lowest delay across all arrival rates and outperformed the comparative models in terms of throughput. Figs. 6 and 7 present a graphical comparison of MWaOA and existing algorithms in terms of energy consumption and response time. Fig. 6 demonstrates that the proposed MWaOA results in lower energy consumption while maintaining the resource efficiency. Fig. 7 shows that the MWaOA achieves the fastest response time under high-load conditions.

Figure 4: Graphical representation of delay using MWaOA and existing optimization algorithms for distinct service arrival rates

Figure 5: Graphical analysis of throughput using MWaOA and comparative optimization algorithms [34]

Figure 6: Energy consumption of MWaOA and existing optimization algorithms for distinct service arrival rates [34]

Figure 7: Response time of MWaOA and comparative optimization algorithms for distinct service arrival rates

4.3 Empirical Evaluation of the MWaOA with Distinct Simulation Epochs

The empirical results of the MWaOA and the comparative algorithms (FA, GWO, MFO, HHO, GSIWOA [34], and WaOA) for distinct simulation epochs in terms of delay and throughput are presented in Tables 6 and 7. In this analysis, the simulation epochs vary from one to ten to evaluate the performance of the proposed model. By examining Tables 6 and 7, it is observed that GSIWOA achieves minimal delay and maximum throughput among the existing algorithms, namely, FA, GWO, MFO, HHO, GSIWOA [34], and WaOA. The common parameters considered in FA, GWO, MFO, HHO, GSIWOA [34], and WaOA are outlined as follows: population size is 100, maximum iterations is 100, alpha is 0.25, lower boundary is 0, beta is 0.80, upper boundary is 8, and gamma is 1. The specific parameters of FA and GWO are the absorption coefficient is 1, attractiveness is 0.2, number of appliances is 12, coefficient vector ranging between 0 and 2; and random vectors ranging between 0 and 1. The specific parameter configurations of MFO, HHO, and GSIWOA [34] are as follows: rabbit energy ranged between 0 and 2, shrinking encircling coefficient is 0.5, spiral updating probability is 0.5, and random search capability is 0.1. A graphical comparison of MWaOA and the existing optimization algorithms for distinct simulation epochs in terms of delay and throughput is shown in Figs. 8 and 9. The graphical representation in Fig. 8 clearly shows that the proposed MWaOA consistently reduced the delay as the number of simulation epochs increased. Similarly, Fig. 9 demonstrates that the MWaOA maintains a stable throughput advantage across all epochs.

Figure 8: Delay of MWaOA and comparative optimization algorithms for distinct simulation epochs [34]

Figure 9: Throughput of MWaOA and existing optimization algorithms for distinct simulation epochs

Correspondingly, the energy consumption and response time of MWaOA also decrease as the number of simulation epochs increases, due to effective decision-making and improved QoS that sustain the network performance. Tables 8 and 9, along with Figs. 10 and 11, present the energy consumption and response time of the MWaOA and the baseline algorithms for varying simulation epochs. Fig. 10 shows that the MWaOA maintained a lower energy consumption throughout the simulation epochs. Similarly, Fig. 11 indicates that the MWaOA achieves faster response times as the number of epochs increases. By examining Tables 8 and 9, it is observed that MWaOA reduces the energy consumption by approximately 5% to 30%, which is lower than that of the other existing algorithms. Additionally, MWaOA reduced the response time by 4% to 28%, outperforming the baseline algorithms FA, GWO, MFO, HHO, GSIWOA [34], and WaOA, particularly across different simulation epochs.

Figure 10: Energy consumption of MWaOA and comparative optimization algorithms for distinct simulation epochs [34]

Figure 11: Response time of MWaOA and existing optimization algorithms for distinct simulation epochs [34]

4.4 Empirical Evaluation of the MWaOA by Means of Execution Time and Resource Usage

Tables 10 and 11, along with Figs. 12 and 13, present the execution time and resource usage of MWaOA and the comparative algorithms FA, GWO, MFO, HHO, GSIWOA [34], and WaOA under distinct service arrival rates. The execution time of MWaOA is comparatively lower, which is achieved by effectively balancing the diversification and intensification processes. Furthermore, resource usage in MWaOA increases with higher service arrival rates. This improvement is primarily due to the ability of the algorithm to maintain diversity within the population, enabling broader exploration of the search space.

Figure 12: Execution time of MWaOA and comparative optimization algorithms for distinct service arrival rates [34]

Figure 13: Resource usage of MWaOA and comparative optimization algorithms for distinct service arrival rates

Fig. 12 shows that the proposed MWaOA exhibits a higher execution time due to its advanced adaptive mechanism. Meanwhile, Fig. 13 clearly demonstrates that MWaOA achieves efficient resource usage despite the increased optimization complexity. The comparative analysis initially focused on models such as FA, GWO, and MFO because of their widespread use and proven effectiveness in solving similar optimization problems, as highlighted in the survey. These models are well-established benchmarks for evaluating the performance of the proposed algorithm. However, including state-of-the-art algorithms, such as DE, CMA-ES, and recent deep reinforcement learning methods, would provide a broader and more comprehensive evaluation. This will be considered in future work to strengthen the comparative analysis.

4.5 Discussion

In the current decade, the IoT has emerged as a vital network technology aimed at achieving higher performance through improved system control, resource allocation, and data exchange. Traditional IoT systems often face challenges in resource allocation, which is crucial for delivering a satisfactory user experience. This paper proposes a novel intelligent metaheuristic optimization algorithm, MWaOA, designed for the effective allocation of multiple resources to gateways in IoT systems. In the context of resource management, the MWaOA introduces adaptive cycles during the exploration and exploitation phases of resource allocation. This approach overcomes the early convergence issues by effectively balancing exploration and exploitation. The overall analysis clearly demonstrates that MWaOA achieves superior results across all performance metrics to its multilevel adaptive search scheme combined with crowding-based diversity preservation. These mechanisms allow the MWaOA to maintain a robust balance between exploration and exploitation. Furthermore, the integration of perturbation and adaptive position updating helps the model avoid local optima, thereby ensuring effective convergence. The incorporation of the strongest walrus mechanism guides the search towards optimal regions, enhancing the delay, throughput, energy consumption, and response time. The effectiveness of MWaOA is further evaluated by comparing its results with those of recent optimization algorithms, such as GSIWOA [34] and WaOA, as well as classical approaches, including Genetic Algorithm (GA), Tabu Search (TS), Simulated Annealing (SA), and Particle Swarm Optimization (PSO), based on the total message cost during resource allocation, as shown in Table 12.

Eight diverse test samples are utilized to evaluate the performance of the MWaOA and comparative algorithms. Algorithms such as GA, TS, SA, PSO, WaOA, and GSIWOA [34] often face issues with local optima, which negatively affect their search process during resource management. In contrast, MWaOA counters this issue through its crowding process, enabling it to achieve significantly better optimization results than other algorithms. From Table 12, it is clear that MWaOA incurs a higher total message cost than existing algorithms such as GA, TS, SA, and PSO. This is due to its multilevel adaptive mechanism and iterative resource allocation models, which introduce additional computational and communication overheads. However, these mechanisms enhance the optimization capability and ensure better convergence, resulting in increased overall message exchange during allocation. Accordingly, the MWaOA did not marginally outperform models such as GA, TS, SA, and PSO in scenarios where communication efficiency or low overhead is critical to maintaining minimal message costs by design. Hence, the MWaOA is especially suitable for applications that prioritize optimization accuracy over communication efficiency.

For the statistical test analysis, message cost was selected as it directly represents communication overhead, which is a critical factor in IoT environments, where devices operate under constrained bandwidth and limited energy resources. Efficient management of message cost is essential for minimizing network congestion and extending node lifespan. One-way ANOVA is conducted to assess whether there are statistically significant differences in the mean message cost among the seven approaches (GA, TS, SA, PSO, GSIWOA, WaOA, and MWaOA). Despite using similar datasets, an independent-samples assumption is utilized for approximate analysis, following common practice in comparative studies. The ANOVA test demonstrated a statistically significant variation in message costs among the approaches (p ≈ 0.00234), indicating significant differences in communication efficiency. Specifically, the proposed MWaOA records the highest average message cost, signifying that its resource allocation policy experiences higher messaging overhead due to adaptive decision-making. In addition, this test strongly supports the efficiency of the proposed MWaOA and highlights its advantages over other approaches. Due to various limitations, such as scalability, dataset dependency, and high communication overhead in accessing suitable real-world IoT datasets within the current scope of this study, this study relies on simulated datasets designed to closely reflect the characteristics of real-world IoT environments, including dynamic resource demands, heterogeneous device interactions, and varying network conditions. These datasets effectively capture the complexities and variabilities frequently encountered in real-world IoT applications.

5  Conclusion

In this article, MWaOA is proposed and implemented in IoT systems to assign multiple resources to a gateway and achieve auto-workload prediction and auto-scaling. Compared with existing optimization algorithms, the proposed MWaOA better sustains global optimization advantages and overcomes early convergence concerns in both the exploration and exploitation phases. The mitigation of early convergence using a crowding process in MWaOA facilitates a balance between exploration and exploitation phases, which benefits effective resource management in smart IoT systems. In the context of resource management, MWaOA’s performance is analyzed using six metrics: delay, throughput, energy consumption, response time, execution time, and resource utilization. The performance of the MWaOA and comparative algorithms (FA, GWO, MFO, HHO, GSIWOA, and WaOA) is validated for different service arrival rates and simulation epochs. Specifically, extensive empirical analysis demonstrates that MWaOA reduces energy consumption by approximately 5% to 30% and minimizes response time by 4% to 28% compared with existing optimization algorithms across varying simulation epochs. Furthermore, the integration of MWaOA in IoT systems significantly improves throughput and resource utilization under both scenarios (different service arrival rates and simulation epochs). Examining the results, the MWaOA demands limited resource allocation, even as the number of gateways increases. However, the performance of the MWaOA degrades as the problem size increases, indicating the need for a more efficient model. The major limitation of MWaOA is scalability; the computational complexity increases with larger dataset sizes and dimensions, and the memory requirements increase significantly, which affects execution. These challenges stem from the multilevel adaptive operations and iterative resource allocation policies in MWaOA that require substantial computational resources to maintain solution diversity and ensure global convergence. Additionally, the MWaOA cannot provide better results when applied to unstructured data because its adaptive mechanisms cannot simplify it efficiently. Therefore, future work can focus on hybrid models, such as integrating MWaOA with Long Short-Term Memory (LSTM), to forecast resource requirements at different phases of IoT systems and achieve better performance, particularly under conditions of increased gateways.

Acknowledgement: The authors acknowledge Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R409), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

Funding Statement: This research was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R409), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

Author Contributions: The paper investigation, resources, data curation, writing—original draft preparation, writing—review and editing, and visualization were conducted by Rekha Phadke and Abdul Lateef Haroon Phulara Shaik; The paper conceptualization and software were conducted by Dayanidhi Mohapatra and N. Sathyanarayana; The validation, formal analysis, methodology, supervision, project administration, and funding acquisition of the version to be published were conducted by Doaa Sami Khafaga and Eman Abdullah Aldakheel. All authors reviewed the results and approved the final version of the manuscript.

Availability of Data and Materials: The authors confirm that the data supporting the findings of this study are available within the article.

Ethics Approval: Not applicable.

Conflicts of Interest: The authors declare no conflicts of interest to report regarding the present study.

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