Abstract
As a result of the increase in industrial Internet of Things (IoT) applications, fog computing (FC) has become a major area of research. A decentralized computing system called fog computing extends cloud computing to the network’s edge. The cloud allows for real-time insights and analysis by processing and storing enormous volumes of data produced by IoT devices. Consequently, the task scheduling technique in cloud computing is crucial. A number of metrics, such as makespan, resource utilization, and energy consumption, must be optimized for FC to function efficiently. This paper proposes a novel metaheuristic optimization technique called the Gaussian Black-winged Kite Algorithm (GBKA) to address task scheduling optimization of industrial IoT applications in a fog computing environment. The proposed algorithm employs Gaussian mutation, and the migration patterns and attack style of the black-winged kite serve as the inspiration for the proposed GBKA. The algorithm is designed to balance exploration of the search space and exploitation of the best solutions, avoiding local optima and improving energy efficiency. The Google Cloud Jobs dataset (GoCJ) with varying task sizes is used to validate the proposed algorithm. An analysis has been conducted to compare the performance of the proposed algorithm with the standard Black-winged Kite Algorithm (BKA) and metaheuristic algorithms like Dragonfly Algorithm (DA), Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO). Experimental results show that GBKA reduces energy and makespan by an average of 7.26 and 9.32%, respectively. Additionally, it attains optimal resource utilization with an average overall improvement of 8.54%.
1 Introduction
The explosive growth of the industrial Internet of Things (IoT) applications has created a need for effective data processing and analysis techniques (Rathi et al., 2025; Sisinni et al., 2018). While the cloud computing scheme employs high storage and processing power, owing to the centralized nature of parties and the far distance between them, it causes high latencies in data transfer and response time, and also leads to high communication costs and security problems. Additionally, in cloud computing, bandwidth is regarded as a bottleneck (Andriulo et al., 2024). Fog computing (FC) extends traditional cloud infrastructure by providing latency-aware and highly scalable services to geographically distributed end devices (Hazra et al., 2023; Srirama, 2024). FC addresses latency and resource utilization issues that are desirable for numerous industrial IoT applications that need to analyze and respond to data instantly by placing the resources and services at the network edge, close to the IoT devices (Naha et al., 2018). This speeds up the IoT in industrial applications that require real-time data processing, particularly for the next-generation industrial IoT applications incorporated within 5G networks (Zreikat et al., 2025) such as, smart healthcare, e.g., hospitals, telemedicine, patient monitoring, treatment, etc. (Guo et al., 2024; Javaid et al., 2023; Kumar et al., 2023; Balasundaram et al., 2023; Li et al., 2024), education, e.g., distance learning, classroom, security, etc. (Li et al., 2023; Kitkowska et al., 2024; Li et al., 2024; Abd El-Sattar, 2025), smart cities (Banerjee et al., 2024), agriculture, e.g., irrigation, prediction, monitoring, etc. (Rehman et al., 2025; Bhatia et al., 2023), industries, e.g., manufacturing, maintenance, safety, etc. (Teoh et al., 2023; Xiang et al., 2024; Kabir et al., 2022; Louta et al., 2022), city development, e.g., transportation, monitoring, etc. (Modina et al., 2022; Segura-Garcia et al., 2021; Ekta and Shalli, 2025), smart grids (Saleem et al., 2024), entertainment, e.g., smart TV, virtual reality, etc. (Wu et al., 2023), among others. As the number of IoT devices grows and data usage increases exponentially, 5G-IoT industrial applications need to be optimized to manage the enormous volume of data being transmitted (Pons et al., 2023). Optimization of 5G networks in industrial IoT applications is essential to ensure reliable and efficient connectivity for IoT devices and the smooth operation of business processes. The task scheduling optimization problem is one of the biggest challenges facing IoT applications in fog computing environments. This paper addresses this issue and is organized as follows: Section 2 provides examples of earlier studies that were created to solve the task scheduling issue in fog computing environments. A number of evaluation metrics, databases, and implementations based on fog computing were examined in Section 3. Section 4 presents our methodology. Section 5 describes the experimental findings of the proposed GBKA and a comparison with cutting-edge algorithms. The paper is concluded in Section 6 with some directions for future research.
1.1 Problem statement
The rapid expansion of industrial IoT applications within 5G networks generates a large volume of real-time data for decision-making (Rathi et al., 2025; Zreikat et al., 2025; Louta et al., 2022). The International Data Corporation (IDC) estimates that there will be 125 billion connected IoT devices by 2030, while Statista, a German online platform that specializes in data collection and visualization, indicates that the global IoT market will generate over $622 billion in revenue by that time. As the volume of data produced by the IoT devices increases, service providers are finding it difficult to manage and process it. These difficulties highlight the need for efficient data processing and analysis technologies from more powerful resources such as cloud and fog computing (Andriulo et al., 2024; Hazra et al., 2023). The “pay-as-you-go” cloud computing technology in which some providers offer access to services using the pay-as-you-go formula (a payment formula in which precise billing is provided based on the time and computational capacity required), is an efficient alternative to owning and managing private data centers (DCs) for customers facing Web applications (Andriulo et al., 2024). The long transmission delay, network congestion from sensing devices to the cloud data centres, latency, and energy consumption are all increasing significantly, making cloud computing inappropriate for time-sensitive next-generation 5G-IoT applications in industries (Rathi et al., 2025; Sisinni et al., 2018; Zreikat et al., 2025; Bhatia et al., 2023; Louta et al., 2022; Ekta and Shalli, 2025). Although fog computing (FC) may be an ideal paradigm to overcome these issues, it faces significant challenges in terms of optimization problems (Pons et al., 2023). A key aspect of fog computing is the optimization of multiple metrics, including latency, bandwidth, energy usage, security concerns, node placement, resource overloading, energy consumption, task scheduling challenges, etc. The task scheduling issue is regarded as one of the most important problems in fog computing environments since the cloud processes and stores vast amounts of data produced by IoT devices. The problem refers to how to reasonably order and allocate the application tasks provided by the users to be executed on virtual machines (VMs). Furthermore, the quality of scheduling performance has a direct effect on customer satisfaction. Particularly in large-scale and high-dimensional issue settings, traditional swarm intelligence algorithms frequently fail to strike an efficient balance between global exploration and local exploitation, resulting in premature convergence or suboptimal solutions. This challenge highlights the necessity for new, enhanced optimization metaheuristic algorithms.
1.2 Motivations
Metaheuristic algorithms are optimization techniques employed to identify optimal solutions by navigating wide search spaces for complex problems that conventional methods cannot resolve. Numerous metaheuristic optimization algorithms have been developed to address complicated issues in many different domains, including computer science (e.g., machine learning, optimization problems such as task scheduling, routing, and resource allocation, etc.) such as swarm-based, physics-based, human-based, and evolutionary-based (Rajwar et al., 2023; Shriyank et al., 2025). Although metaheuristic algorithms have been applied in a variety of application domains, there is no metaheuristic algorithm superior in solving every optimization problem according to the “No Free Lunch (NFL) theorem” (Wolpert and Macready, 1997). Moreover, many algorithms have limitations, including insufficient search ability, no guarantee of optimality, computational expense, tuning parameters, and they do not provide insights into the underlying structure of the optimization problem (Pons et al., 2023). Since no algorithm can effectively and efficiently solve any optimization or instances of the same problem, the question of whether there exists a metaheuristic algorithm superior in solving every optimization problem remains unresolved despite the existence of several metaheuristic optimization algorithms (e.g., Pons et al., 2023; Prity et al., 2024; Wang et al., 2024; Behera and Sobhanayak, 2024; Al-Betar et al., 2024; Wang et al., 2022). For instance, while the authors Wang et al. (2024) were able to solve five real-world engineering design problems satisfactorily, they may be unable to solve certain types of complex problems with high-dimensional search spaces. Additionally, the method may converge prematurely or repeatedly throughout the iteration phase, which would affect the consistency of the results, particularly when dealing with large search spaces to solve optimization problems in computer science, such as task scheduling optimization of IoT applications in fog computing (TSFC). Software-defined networking (SDN) (Bera et al., 2017; Al-Shareeda et al., 2024) and software-defined-based Internet of Multimedia Things (SD-IoMT) (Nauman et al., 2020) are examples of emerging technologies that have recently shown great promise for information service innovation in the cloud and big data eras. These technologies are perfect for meeting the requirements of IoT from various networking aspects, including edge, access, core, and data center, while also offering more services to Internet users. Nauman et al. (2020) provide more comprehensive details about SDNs from the viewpoint of IoMT. SDNs are moving the IoT architecture towards network virtualization, and various studies related to SDN-based fog/edge-cloud computing to manage energy resources and reduce computing latency and overheads, among others, have been presented in (Masoumeh et al., 2025; Huang et al., 2018; Salman et al., 2018; Wood et al., 2015; Baktir and Ozgovde, 2017; Montazerolghaem, 2022). For instance, Salman et al. (2018) provide an overview of IoT from the perspective of fog and SDN technologies. Huang et al. (2017) demonstrate how SDNs are transforming IoT architecture to manage hybrid energy resources in future communication networks. Baktir and Ozgovde (2017) described the constraints and challenges of cloud-edge computing as data traffic increased and provided a vision for an SDN-based network management strategy to reduce the complexity of cloud-edge architectures. Motivated by this research works, this study demonstrates how to improve the work of Wang et al. (2024) to solve optimization problems in the field of computer science, such as TSFC using Gaussian mutation. To prevent premature convergence caused by a decrease in population diversity, the Gaussian mutation is employed. The Gaussian mutation was selected above other mutation strategies because it uses normal distribution properties to produce random changes in the population’s evolution and provides statistically controlled, small alterations around the current solution. Consequently, it avoids local optima, improves algorithm diversity, reduces oscillations in complex search environments, and enables precise local optimization during the attack phase.
1.3 Contributions
The contributions of the study are summarized as follows:
The Gaussian Black-winged Kite Algorithm (GBKA), a novel bio-inspired metaheuristic optimization algorithm using Gaussian mutation, is proposed to address task scheduling optimization in fog computing environments for IoT applications.
The black-winged kite’s attack strategy and migration behavior Wang et al. (2024) served as an inspiration for the proposed algorithm.
The algorithm is designed to balance exploration of the search space and exploitation of the best solutions.
The use of Gaussian mutation in the exploitation phase exhibits rapid convergence to optimal solutions, avoiding local optima and improving energy efficiency.
The Google Cloud Jobs dataset (GoCJ) with varying task sizes is used to validate the proposed algorithm.
GBKA shows competitive results compared with cutting-edge algorithms by minimizing makespan and energy consumption while maximizing resource utilization.
2 Prior research
This section outlines some of the prior research developed to address the task scheduling problems in fog computing environments for industrial IoT applications:
The authors in Abdel-Basset et al. (2021a) suggested an energy-aware metaheuristic algorithm based on a Harris Hawks optimization method that uses a local search strategy to enhance the quality of services offered to consumers in industrial IoT applications. The proposed algorithm is limited to scheduling the individual tasks given by the various fog computing users, and the local search strategy takes a lot of time, despite the authors’ conclusion that it works better than other cutting-edge algorithms.
Raju and Mothku (2023) introduced a method that formulates the scheduling issue as mixed-integer nonlinear programming (MINLP) to optimize energy consumption and service time while taking deadlines and resource availability into account. They used a fuzzy-based reinforcement learning (FRL) technique to deal with the dynamic and high dimensionality of the tasks. Tasks are initially prioritized using fuzzy logic and then scheduled using an on-policy reinforcement learning technique, which enhances long-term rewards compared to traditional Q-learning approaches.
To enhance the quality of services provided to users of IoT devices, Abdel-Basset et al. (2021b) presented an enhanced elitism genetic algorithm (IEGA) to solve the task scheduling problem for fog computing. By employing a modified crossover and mutation to explore a greater range of potential solutions, IEGA was enhanced in two ways, making it simpler to identify nearly optimal task scheduling configurations.
Deng et al. (2015) investigated the balance between power consumption and delay in cloud-fog systems by applying convex optimization techniques to minimize the energy consumed by the fog layer for a given workload and utilize heuristics to optimize the cloud’s energy usage. Additionally, the study addressed energy consumption associated with communications. The findings indicate that by slightly reducing computational resources, bandwidth can be conserved, and delays can be decreased.
To solve the task scheduling issue in cloud-fog environments, the authors of Potu et al. (2021) developed an extended particle swarm optimization (EPSO) algorithm with an additional gradient mechanism. Enhancing resource efficiency and reducing work completion time were the goals of the paper. Although the experimental findings showed that the proposed EPSO algorithm outperformed other algorithms, there is a trade-off between energy consumption and delay.
Karthik and Kavithamani (2021) proposed an algorithm, which integrates whale optimization and a fog computing network, aimed at enhancing the lifetime of a grid-connected network. This approach optimizes routing to prevent system malfunctions and improves communication range through selected cluster heads (CHs). The algorithm estimates energy, communication, and distance within the grid-connected network. As a result, it demonstrated improved network performance in terms of throughput, Packet Delivery Ratio (PDR), and residual energy.
To optimize the response time and energy consumption cost of fog nodes, the authors of Vakilian et al. (2021) investigated the cooperative mechanisms of fog layers using a new cuckoo evolutionary algorithm. It was discovered that greater queue lengths cause response times to increase in relation to a fog node’s workload. Nevertheless, this problem can be successfully resolved by other fog nodes running at lower processing loads, which results in notable decreases in response time and queue length. Despite the effectiveness of the results obtained, collaboration among fog nodes in wireless environments is an open issue.
By considering collaboration between fog nodes and cloud, the authors of Vakilian and Fanian (2020) proposed a framework that reveals a distinct trade-off between energy consumption and network delay in fog networks to process arrival workloads. According to simulation results, collaboration across fog nodes can greatly shorten end-user response times while increasing a fog node’s energy consumption.
The authors of Kumar et al. (2025) created a deep learning model based on Deep Reinforcement Learning (DRL) architecture to improve the workload offloading issue and power distribution across data centers inside the edge network in a multi-user Internet of Health Things (IoHT). The experimental findings demonstrate that the suggested approach works better in terms of response rate and energy savings than existing techniques. Although the proposed framewrok concentrated on IoHT in the healthcare sector, it is still difficult to expand it to other IoT domains such as smart grids, smart cities, and industrial IoT (IIoT).
An optimization framework for workload distribution in fog-cloud computing was presented by Deng et al. (2016) with the goal of reducing transmission latency and power consumption. However, rather than using a distributed approach, the optimization was carried out centrally.
3 Evaluation metrics, datasets and implementations
3.1 Evaluation metrics
A number of evaluation metrics, including resource utilization (RU), makespan, energy usage, and fitness function should be examined in order to compare the performance of the proposed algorithm with existing algorithms. The evaluation metric is a real-valued function that must be maximized or minimized among a range of possible solutions.
3.1.1 Makespan (MK) metric
The total time required to complete a certain collection of jobs or tasks in a cloud computing environment is known as the makespan. Minimizing makespan reflects the system’s performance and efficiency in handling and processing jobs. Equations 1, 2 are used to calculate it (Hazra et al., 2023):
where Etj is the total execution time of VMj and is the execution time taken by jth VM on ith task.
3.1.2 Resource utilization (RU) metric
Resource Utilization indicates the efficient management and allocation of computational resources inside cloud architecture to meet the demands of diverse workloads. Efficient utilization of servers, storage, network bandwidth, and other resources is essential for optimizing performance and minimizing waste. Equation 3 provides a mathematical method that can be used to measure it (Devi et al., 2024):
where, CTij is the completion time of the ith job on the jth VM.
3.1.3 Energy consumption (EC) metric
EC can be characterized as a cloud infrastructure’s capacity to maximize power usage without sacrificing performance. By dynamically assigning computing resources and shutting down unused servers during times of low demand, it lowers energy consumption (Hazra et al., 2023). Cloud load balancing systems ensure sustainable and environmentally friendly operations in cloud computing environments by minimizing power consumption, which helps to lower carbon footprints, operating expenses, and environmental effects. Equations 4–7 provide a mathematical method that can be used to measure it (Abdel-Basset et al., 2021c).
where bj is the energy consumed in the active state and measured in joules per minute (JPM) and sj is the processing speed of the VMj. The total energy consumed by FC is calculated by summing the energy consumed by all VMs as shown in Equation 7.
3.1.4 Fitness function
The fitness function of the proposed algorithm describes the goals that need to be optimized. Given that TSFC is a multi-objective issue, the three objectives that make up the fitness function are makespan (MK), energy consumption (EC), and resource utilization (RU) (Jain and Meena, 2019). Therefore, by giving each target a weight in relation to the other, weight variables (w1, w2, and w3) are employed to reduce this problem to a single objective. The fitness function under consideration can be defined quantitatively using Equation 8 as follows (Heirati et al., 2025):
Equation 8 describes the fitness function, which combines three objectives weighted by w1, w2, and w3, with w1 + w2 + w3 = 1 and (0 < = wi < =1). Specifically, w1 prioritizes decreasing overall energy consumed by VMs, w2 emphasizes reducing completion time (makespan), and w3 encourages increasing resource utilization (efficient resource use).
3.2 Datasets
This study uses the Google Cloud Jobs (GoCJ) dataset (Hussain and Aleem, 2018) as an open-source benchmark to compare the performance of our proposed algorithm to existing ones. The Mendeley Data repository (https://data.mendeley.com/datasets/b7bp6xhrcd/1) archives and makes the GoCJ dataset publicly accessible. Job size compositions in the GoCJ datasets are based on publicly accessible real workload traces, including Google cluster traces (https://github.com/google/cluster-data). The GoCJ dataset, which can contain any number of jobs, is created using the Monte Carlo simulation approach based on the analysis of Google cluster traces. The Monte Carlo simulation uses a sample original dataset that is created based on workload behavior in Google cluster traces. The job sizes in the original dataset are used to construct the job composition in the simulated GoCJ dataset. A Java tool generator and an Excel worksheet generator are included with the two dataset generator files, along with the GoCJ dataset as supplemental data in text and Excel file formats. The text file’s rows each specify a job’s magnitude in millions of instructions (MI). In Figure 1, the GoCJ dataset’s job distribution ratios and sizes are shown as percentages and MIs, respectively. Although GoCJ is commonly used for broad cloud and fog scheduling studies, its workload characteristics are appropriately related to Industrial IoT (IIoT) applications. The dataset includes operations of varying lengths and resource requirements, analogous to IIoT systems where short, time-sensitive sensor tasks coexist alongside more computationally intensive analytics. This variability reflects the diversity of industrial contexts that use various sensors and edge devices. As a result, while GoCJ is not particularly built for Industrial IoT, its statistical qualities make it a reasonable approximation for assessing task scheduling and resource management in Industrial IoT-oriented fog and cloud systems.
Figure 1
3.3 Implementations and parameter setups configurations
All algorithms were implemented in MATLAB (version R2022b) and executed on a machine with an Intel Core i5-8265 U CPU 1.60GHz, 8 of RAM, running the Windows 10 operating system. The number of virtual machines (VMs) is kept constant at 50, while task sizes vary across 19 values: 100, 150, 200, 250, 300, 350, 400, 450, 500, 600, 650, 700, 750, 800, 850, 900, 950 and 1,000. Each task has a heterogeneous workload from 15,000 to 900,000. Regarding the processing speed related to each VM out of 50 ones, the first half of 50 VMs is set to 2000 million instruction per second (MIPS) while the second half is set to 4,000 MIPS. To ensure a fair comparison among the algorithms, the population size and the number of iterations are set to 10 and 1,500, respectively. All the algorithms will run 20 independent times. For 15% of populations with mean μ = 0 and standard deviation σ = 0.5 and mutation factor δ = 1, we used Gaussian mutation.
4 Methodology
Our proposed algorithm, the Gaussian Black-winged Kite Algorithm (GBKA), is explained in this section. The methodology behind the proposed algorithm is based on the behavioral characteristics of biological populations inspired by the black-winged kite’s migration patterns and attack style. We will first provide a brief definition of the Black-winged Kite Algorithm (BKA) and then demonstrate how to adapt it to address task scheduling optimization in a fog computing environment for industrial IoT applications using Gaussian mutation.
4.1 The Black-winged Kite Algorithm (BKA)
The bird known as the black-winged kite has a white lower body and a blue-grey upper body. They showed powerful hovering abilities, exhibit great hunting success, and consume insects, birds, reptiles, and small mammals. The migratory and predatory behavior of the black-winged kite inspired the Black-winged Kite Algorithm (BKA), a meta-heuristic optimization method initially introduced in (
Wang et al., 2024). The primary benefits of the algorithm are:
Global Search Capability: BKA successfully navigates the solution space by leveraging the adaptive behavior of the black-winged kite, hence improving its capacity to avoid local optima.
Convergence Speed: The method exhibits rapid convergence to optimal solutions, making it appropriate for real-time applications that require rapid decision-making.
Versatility: It has been effectively evaluated on multiple benchmark functions, demonstrating flexibility in addressing complicated optimization challenges.
The pseudo code of BKA is presented in Algorithm 1. This Pseudo code clearly described the execution process of the BKA algorithm. It provides steps and operations to solve specific problems and optimizes the results through iteration and adjustment. Below is some brief information about its attack and migration behavior, along with the initialization phase.
ALGORITHM 1
4.1.1 Initialization phase
Initializing the population in BKA is to create a set of random solutions. The following matrix can be used to represent the location of every Black-winged kite (BK) as Equation 9:
where, pop represents the quantity of potential solutions, dim signifies the scale of the problem’s dimension, and is the dimension of the Black-winged kite. Each Black-winged kite’s position is equally distributed using Equation 10.
where i is an integer in the range between 1 and pop, BKlb and BKub representing the lower and upper bounds, and rand is a value selected randomly from the interval [0, 1]. During the initialization phase, BKA designates the individual with the highest fitness value as the leader within the initial population, signifying the optimal position of the black-winged kites. The mathematical expression for the initial leader, shown by the smallest value, is presented in Equations 11, 12:
4.1.2 Attacking behavior
The black-winged kite, a predator of small grassland animals and insects, adjusts its wing and tail angles in response to wind velocity while in flight. It moves carefully to identify its prey before rapidly descending to attack. This hunting strategy incorporates diverse attack characteristics, enabling comprehensive research and accurate targeting. According to (Wang et al., 2024), a mathematical model of black-winged kite attack behavior is as follows:
where, and represent the position of the ith Black-winged kites in the jth dimension in the t and (t + 1) th iteration steps, respectively.
r is a random number that ranges from 0 to 1, and p is a constant value of 0.9.
T is the total number of iterations, and t is the number of iterations that have been completed so far.
4.1.3 Migration behavior
A mathematical model for black-winged kite migratory behavior is provided as follows Equations 15, 16:
where, represents the leading scorer of the Black-winged kites in the jth dimension of the th iteration so far.
and represent the position of the ith Black-winged kites in the jth dimension in the t and (t + 1) th iteration steps, respectively.
Fr represents the current position in the jth dimension obtained by any black-winged kite in the t iteration.
Fri represents the fitness value of the random position in the jth dimension obtained from any black-winged kites in the t iteration.
C (0, 1) represents the Cauchy mutation (Jiang et al., 2023).
4.2 The proposed algorithm
This subsection presents in-depth information on our proposed algorithm, namely, the Gaussian Black-winged Kite Algorithm (GBKA) using Gaussian mutation for addressing task scheduling optimization of industrial IoT applications in a fog computing environment.
4.2.1 Gaussian mutation
Although BKA has shown promising results in solving optimization problems, it has certain drawbacks, which are as follows: It has demonstrated inadequate stability across several runs and has not produced the best results when attempting to solve particular kinds of optimization problems in industrial IoT applications like task scheduling in fog computing environment. The unequal distribution of initial parameters is the cause of inadequate stability, which causes the search strategy to vary throughout several runs. Furthermore, the algorithm may undergo early or repetitive convergence during the iteration process when handling difficult issues in high-dimensional search spaces, which would decrease the consistency of the results. To solve these problems, the initial parameters’ uneven distribution is adjusted using the Gaussian mutation as a modifier. The Gaussian mutation procedure (Lee and Yao, 2001) can be described as the insertion of a random vector that corresponds to the Gaussian or normal distribution function. It is crucial in probability theory and mathematical statistics, which can be denoted by N (μ, σ2), where μ and σ are its mean and standard deviation, respectively in Equation 17:
where x is the current solution, is the mutation strength, and N (μ, ) is a normal distribution with mean and standard deviation.
4.2.2 Gaussian Black-winged Kite Algorithm (GBKA)
BKA algorithms can be a useful tool for resolving complicated optimization issues, but when selecting an optimization algorithm for a certain problem, it’s important to take into account its limitations. Furthermore, there is no assurance that the algorithm will identify the optimal solution, particularly when dealing with large search spaces to solve optimization problems in industrial IoT applications, such as task scheduling issues in computing environments. Consequently, we should avoid keeping to the procedure where each member of the BKA transitions to a different point within the search space; alternatively, we should introduce a degree of ambiguity in development to the next generation, using the mutation technique. By enhancing BKA’s global search capabilities, the Gaussian mutation strategy helps the population maintain diversity and lowers the likelihood that the algorithm will converge to a local optimal value. The proposed GBKA incorporates a randomized mutation through the application of the mutation approach. The proposed GBKA’s primary procedure is described below and illustrated in Algorithm 2.
4.2.2.1 Initialization phase
As in BKA, the initialization of the population in GBKA begins with the creation of a set of random solutions, including the population size, maximum number of iterations, etc.
ALGORITHM 2
4.2.2.2 Attacking behavior
The same equations as the original attack behavior, as mutation are not used in this case.
4.2.2.3 Migration behavior
In order to prevent the algorithm from premature convergence, the Gaussian mutation performed on populations to generate new populations is performed in Equation 18:
Also apply Gaussian to the best solution in Equation 19.
Re-evaluate the adaptability of individuals in the new population. If the fitness of the new individual is better than that of the previous generation, replace the previous generation with the new population, otherwise the original population will not be changed.
5 Experimental results and discussion
The performance of the proposed GBKA is compared to three metaheuristic algorithms, including Ant Colony Optimization (ACO) (Dorigo and Di Caro, 1999), Particle Swarm Optimization (PSO) (Kennedy and Eberhart, 1995), and Dragonfly Algorithm (DA) (Mirjalili, 2016), in addition to the standard algorithm, BKA (Wang et al., 2024), using the GoCJ dataset as a benchmark. The evaluation metrics used are energy consumption, makespan, and resource utilization. Twenty separate runs of each algorithm were performed. The comparison is conducted with a fixed number of 50 virtual machines (VMs) and 19 task sizes (TS) of different sizes.
5.1 Energy consumption metric results
Table 1 and Figure 2 show the average energy consumed by each algorithm. According to the results in Table 1, it is found that the proposed algorithm outperforms all other algorithms in terms of energy consumption for most task size. According to the results in Figure 2, it is found that the proposed GBKA achieves lower energy consumption compared to BKA, ACO, PSO, and DA by 0.32, 8.89, 9.46, and 10.38%, respectively. By increasing the task size, the energy increases due to increasing workload on each virtual machine (see Figure 3). Therefore, the proposed GBKA is the best, as it achieves less energy for most task sizes, from 100 to 1,000, by an average total improvement of 7.26%.
Table 1
| No. of tasks | Average energy | Improvement % | ||||
|---|---|---|---|---|---|---|
| GBKA | BKA | ACO | PSO | DA | ||
| 100 | 3745004 | 3907947 | 4409084 | 4339829 | 4183297 | 10.85% |
| 4.17% | 15.06% | 13.71% | 10.48% | |||
| 150 | 5043088 | 5137943 | 6106032 | 6479173 | 5590613 | 12.8% |
| 1.85% | 17.41% | 22.16% | 9.79% | |||
| 200 | 5987854 | 5758603 | 6688760 | 7275942 | 6466912 | 7.90% |
| −3.98% | 10.48% | 17.70% | 7.41% | |||
| 250 | 5935028 | 6007888 | 7584424 | 7245443 | 6703533 | 13.13% |
| 1.21% | 21.75% | 18.09% | 11.46% | |||
| 300 | 7766288 | 7872833 | 9538392 | 8787449 | 8927539 | 11.14% |
| 1.35% | 18.58% | 11.62% | 13.01% | |||
| 350 | 8510235 | 8517489 | 9455472 | 9785169 | 9770022 | 9.00% |
| 0.09% | 10.00% | 13.03% | 12.89% | |||
| 400 | 9158199 | 9097019 | 9952132 | 10930868 | 10428462 | 8.93% |
| −0.67% | 7.98% | 16.22% | 12.18% | |||
| 450 | 9837043 | 9983644 | 10659532 | 11630409 | 11094954 | 8.99% |
| 1.47% | 7.72% | 15.42% | 11.34% | |||
| 500 | 11286446 | 11398309 | 11938412 | 12118575 | 12641015 | 6.01% |
| 0.98% | 5.46% | 6.87% | 10.72% | |||
| 550 | 12500198 | 12276050 | 13283064 | 13598372 | 13879336 | 5.52% |
| −1.83% | 5.89% | 8.08% | 9.94% | |||
| 600 | 14073747 | 14436709 | 15045984 | 14992795 | 15963663 | 6.74% |
| 2.51% | 6.46% | 6.13% | 11.84% | |||
| 650 | 15094395 | 15030931 | 16084056 | 16263473 | 16912895 | 5.92% |
| −0.42% | 6.15% | 7.19% | 10.75% | |||
| 700 | 14981668 | 14899522 | 15605004 | 16327363 | 16512875 | 5.24% |
| −0.55% | 3.99% | 8.24% | 9.27% | |||
| 750 | 17563679 | 17240672 | 19229092 | 18136374 | 19126221 | 4.53% |
| −1.87% | 8.66% | 3.16% | 8.17% | |||
| 800 | 16551700 | 16581499 | 17707968 | 17022660 | 18412100 | 4.9% |
| 0.18% | 6.53% | 2.77% | 10.10% | |||
| 850 | 17773804 | 18117006 | 18461204 | 19083432 | 19933756 | 5.8% |
| 1.89% | 3.72% | 6.86% | 10.84% | |||
| 900 | 19955973 | 19984450 | 20630948 | 20137008 | 21873038 | 3.27% |
| 0.14% | 3.27% | 0.90% | 8.76% | |||
| 950 | 19630657 | 19717084 | 20426300 | 19675705 | 21433612 | 3.24% |
| 0.44% | 3.90% | 0.23% | 8.41% | |||
| 1,000 | 21556974 | 21387346 | 22919012 | 21859938 | 23918788 | 4.10% |
| −0.79% | 5.94% | 1.39% | 9.87% | |||
| Average total improvement % | 0.32% | 8.89% | 9.46% | 10.38% | 7.26% | |
Outcomes for the energy metric.
Bold value refers to the best one.
Figure 2
Figure 3
5.2 Makespan metric results
The proposed algorithm, as shown in Table 2, achieves better makespan values for most task sizes compared to the other four algorithms, demonstrating its capability to effectively schedule and distribute tasks among the virtual machines. It is also observed that as the task size increases, the makespan on each virtual machine also increases. Additionally, Figure 4 shows that the proposed GBKA demonstrates superior performance in minimizing the average makespan with an improvement of 1.00% compared to BKA, 10.89% compared to ACO, 12.27% compared to PSO, and 13.11% compared to DA. Therefore, GBKA is the best, as it achieves a smaller makespan for most task sizes, from 100 to 1,000, with an average total improvement of 9.32%. Figure 5 shows the value of the average makespan listed in Table 2 for all algorithms.
Table 2
| No. of tasks | Average makespan | Improvement % | ||||
|---|---|---|---|---|---|---|
| GBKA | BKA | ACO | PSO | DA | ||
| 100 | 296.25 | 313.144 | 356.3 | 348.256 | 333.138 | 12.06% |
| 5.39% | 16.85% | 14.93% | 11.07% | |||
| 150 | 377.213 | 389.875 | 476.5 | 511.794 | 425.475 | 15.43% |
| 3.25% | 20.84% | 26.30% | 11.34% | |||
| 200 | 440.55 | 425.275 | 527.5 | 566.35 | 487.175 | 11.17% |
| −3.59% | 16.48% | 22.21% | 9.57% | |||
| 250 | 432.275 | 440.125 | 611 | 552.288 | 496.119 | 16.41% |
| 1.78% | 29.25% | 21.73% | 12.87% | |||
| 300 | 555.238 | 562.163 | 738 | 650.9 | 660.944 | 14.17% |
| 1.23% | 24.76% | 14.70% | 15.99% | |||
| 350 | 604.163 | 601.281 | 699.5 | 723.269 | 719.8 | 11.42% |
| −0.48% | 13.63% | 16.47% | 16.07% | |||
| 400 | 648.575 | 636.994 | 732.8 | 807.781 | 759.2 | 10.99% |
| −1.82% | 11.49% | 19.71% | 14.57% | |||
| 450 | 693.688 | 708.825 | 754.8 | 861.588 | 803 | 10.83% |
| 2.14% | 8.10% | 19.49% | 13.61% | |||
| 500 | 791.3 | 805.288 | 833.3 | 870.838 | 912.269 | 7.29% |
| 1.74% | 5.04% | 9.13% | 13.26% | |||
| 550 | 879.6 | 860.625 | 956.5 | 977.775 | 999.013 | 6.96% |
| −2.20% | 8.04% | 10.04% | 11.95% | |||
| 600 | 879.6 | 1017.4 | 1,066 | 1073.1 | 1159.53 | 18.30% |
| 13.54% | 17.49% | 18.03% | 24.14% | |||
| 650 | 1062.71 | 1051.3 | 1154.5 | 1165.23 | 1226.23 | 7.25% |
| −1.09% | 7.95% | 8.80% | 13.33% | |||
| 700 | 1064.6 | 1042.16 | 1082.3 | 1176.05 | 1184.58 | 4.77% |
| −2.15% | 1.64% | 9.48% | 10.13% | |||
| 750 | 1225.14 | 1203.94 | 1380.3 | 1290.62 | 1380.03 | 6.44% |
| −1.76% | 11.24% | 5.07% | 11.22% | |||
| 800 | 1150.73 | 1156.93 | 1,229 | 1202.27 | 1321.14 | 6.02% |
| 0.54% | 6.37% | 4.29% | 12.90% | |||
| 850 | 1238.49 | 1270.79 | 1134.1 | 1360.55 | 1431.49 | 3.95% |
| 2.54% | −9.20% | 8.97% | 13.48% | |||
| 900 | 1388.64 | 1392.59 | 1438.3 | 1407.79 | 1556.15 | 3.97% |
| 0.28% | 3.45% | 1.36% | 10.76% | |||
| 950 | 1364.79 | 1374.15 | 1445.3 | 1369.81 | 1525.46 | 4.29% |
| 0.68% | 5.57% | 0.37% | 10.53% | |||
| 1,000 | 1501.39 | 1486.73 | 1630.8 | 1533.69 | 1710.66 | 5.32% |
| −0.99% | 7.94% | 2.11% | 12.23% | |||
| Average total improvement % | 1.00% | 10.89% | 12.27% | 13.11% | 9.32% | |
Outcomes for the makespan metric.
Bold value refers to the best one.
Figure 4
Figure 5
5.3 Resource utilization metric results
The results of the various algorithms under the resource utilization measure are given in Table 3. Upon examining this table and the various values for each algorithm, it is evident that the proposed algorithm (GBKA) is thought to be the best for the majority of task sizes. This demonstrates how the proposed algorithm can improve resource utilization for this issue, supporting this analysis. GBKA outperforms BKA by 0.21%, ACO by 7.21%, and PSO by 10.77%, and DA by 15.97%, as shown in Figure 6. For most task sizes between 100 and 1,000, GBKA achieves maximum resource utilization with an average total improvement of 8.54%, making it the best. The proposed algorithm, GBKA, works well for the majority of task sizes, as seen in Figure 7, which displays the average resource utilization achieved by each algorithm on all task sizes.
Table 3
| No. of tasks | Average resource utilization | Improvement % | ||||
|---|---|---|---|---|---|---|
| GBKA | BKA | ACO | PSO | DA | ||
| 100 | 33.476 | 34.471 | 32.767 | 29.515 | 29.269 | 6.77% |
| −2.89% | 2.16% | 13.42% | 14.37% | |||
| 150 | 42.336 | 41.556 | 38.902 | 32.165 | 36.719 | 14.41% |
| 1.88% | 8.83% | 31.62% | 15.30% | |||
| 200 | 46.464 | 44.453 | 41.606 | 36.417 | 39.553 | 15.32% |
| 4.52% | 11.68% | 27.59% | 17.47% | |||
| 250 | 50.25 | 50.826 | 46.073 | 40.35 | 42.577 | 12.62% |
| −1.13% | 9.07% | 24.54% | 18.02% | |||
| 300 | 53.025 | 54.261 | 50.278 | 47.779 | 45.231 | 7.85% |
| −2.28% | 5.46% | 10.98% | 17.23% | |||
| 350 | 57.073 | 57.029 | 54.215 | 49.469 | 47.86 | 9.99% |
| 0.08% | 5.27% | 15.37% | 19.25% | |||
| 400 | 58.974 | 58.686 | 56.041 | 49.176 | 49.23 | 11.36% |
| 0.49% | 5.23% | 19.92% | 19.79% | |||
| 450 | 57.625 | 58.09 | 57.126 | 49.774 | 49.614 | 8.00% |
| −0.80% | 0.87% | 15.77% | 16.15% | |||
| 500 | 59.497 | 58.877 | 58.717 | 56.714 | 51.477 | 5.72% |
| 1.05% | 1.33% | 4.91% | 15.58% | |||
| 550 | 61.197 | 59.493 | 59.759 | 54.818 | 51.541 | 8.91% |
| 2.86% | 2.41% | 11.64% | 18.73% | |||
| 600 | 59.278 | 61.309 | 55.005 | 58.058 | 51.982 | 5.15% |
| −3.31% | 7.77% | 2.10% | 14.04% | |||
| 650 | 61.954 | 61.457 | 56.449 | 57.319 | 53.218 | 8.77% |
| 0.81% | 9.75% | 8.09% | 16.42% | |||
| 700 | 61.743 | 61.402 | 56.62 | 56.36 | 53.672 | 8.55% |
| 0.56% | 9.05% | 9.55% | 15.04% | |||
| 750 | 62.41 | 60.984 | 53.642 | 59.378 | 54.465 | 9.59% |
| 2.34% | 16.35% | 5.11% | 14.59% | |||
| 800 | 63.085 | 63.07 | 56.351 | 62.618 | 54.819 | 6.95% |
| 0.02% | 11.95% | 0.75% | 15.08% | |||
| 850 | 61.837 | 63.293 | 58.426 | 59.218 | 54.217 | 5.50% |
| −2.30% | 5.84% | 4.42% | 14.05% | |||
| 900 | 63.806 | 63.412 | 60.129 | 63.928 | 56.165 | 5.04% |
| 0.62% | 6.12% | −0.19% | 13.60% | |||
| 950 | 63.691 | 63.461 | 59.956 | 64.434 | 56.755 | 4.41% |
| 0.36% | 6.23% | −1.15% | 12.22% | |||
| 1,000 | 64.509 | 63.844 | 57.832 | 64.361 | 55.362 | 7.33% |
| 1.04% | 11.55% | 0.23% | 16.52% | |||
| Average total improvement% | 0.21% | 7.21% | 10.77% | 15.97% | 8.54% | |
Outcomes for the resource utilization metric.
Bold value refers to the best one.
Figure 6
Figure 7
5.4 Statistical results
We employed two statistical tests to compare the effectiveness of the proposed, GBKA, to that of BKA: a boxplot of fitness and nonparametric statistical analysis such as the Wilcoxon tests. Figure 8 compares the proposed, GBKA, with that of BKA by depicting a boxplot of the acquired fitness values by each within 20 independent runs on task numbers of 100, 200, 300, 400, 500, 600, 700, 700, 800, 900, and 1,000, with a virtual machine length fixed at 50. This figure clearly shows that the proposed algorithm performs better. On the other hand, we employed the Wilcoxon test to show that the proposed GBKA is statistically significant. The Wilcoxon test is a nonparametric statistical approach that compares paired samples or repeated measurements within the same group. It assesses if there is a substantial difference between two observations by measuring the absolute differences in their values. A conventional significance level of 1% or 5% is generally employed, with 5% being the prevalent criterion. At a significance level of 5%, a p-value from the Wilcoxon test < 0.05 indicates substantial differences between the two value sets; otherwise, they are believed to possess identical properties. Table 4 shows the Wilcoxon test results on the GOCJ dataset, taking into account the different task numbers, where R+ denotes the number of positive ranks where GBKA outperforms the competitive methods and R− denotes the number of negative ranks where GBKA fails to outperform the competitive methods over the 20 independent runs.
Figure 8
Table 4
| No. of tasks | GBKA vs algorithms | No. R+ | No. R− | p-value < 0.05 |
|---|---|---|---|---|
| 100 | BKA | 15 | 5 | 0.006 |
| PSO | 11 | 9 | 0.002 | |
| ACO | 17 | 3 | 0.001 | |
| DA | 17 | 3 | 0.003 | |
| 200 | BKA | 17 | 3 | 0.005 |
| PSO | 14 | 6 | 0.033 | |
| ACO | 20 | 0 | 0.000 | |
| DA | 20 | 0 | 0.000 | |
| 300 | BKA | 17 | 3 | 0.001 |
| PSO | 17 | 3 | 0.001 | |
| ACO | 20 | 0 | 0.000 | |
| DA | 20 | 0 | 0.000 | |
| 400 | BKA | 7 | 13 | 0.016 |
| PSO | 20 | 0 | 0.000 | |
| ACO | 20 | 0 | 0.000 | |
| DA | 20 | 0 | 0.000 | |
| 500 | BKA | 6 | 14 | 0.012 |
| PSO | 20 | 0 | 0.000 | |
| ACO | 20 | 0 | 0.000 | |
| DA | 19 | 1 | 0.000 | |
| 600 | BKA | 6 | 14 | 0.048 |
| PSO | 20 | 0 | 0.000 | |
| ACO | 20 | 0 | 0.000 | |
| DA | 19 | 1 | 0.000 | |
| 700 | BKA | 5 | 15 | 0.014 |
| PSO | 20 | 0 | 0.000 | |
| ACO | 20 | 0 | 0.000 | |
| DA | 20 | 0 | 0.000 | |
| 800 | BKA | 8 | 12 | 0.011 |
| PSO | 20 | 0 | 0.000 | |
| ACO | 20 | 0 | 0.000 | |
| DA | 20 | 0 | 0.000 | |
| 900 | BKA | 17 | 3 | 0.005 |
| PSO | 20 | 0 | 0.000 | |
| ACO | 20 | 0 | 0.000 | |
| DA | 20 | 0 | 0.000 | |
| 1,000 | BKA | 7 | 13 | 0.025 |
| PSO | 20 | 0 | 0.000 | |
| ACO | 20 | 0 | 0.000 | |
| DA | 20 | 0 | 0.000 |
Wilcoxon test results using a GOCJ dataset with various number of tasks.
5.5 Computational complexity
This section compares the time complexity (Big-O notation) of the proposed GBKA to the standard BKA. Integrating Gaussian mutation during GBKA’s exploitation phase has no effect on BKA’s total time complexity. The mutation procedure is performed once in linear time with respect to the problem dimension for each candidate solution, and it includes the generation of Gaussian random values for each dimension, resulting in a computing cost of O(D) per solution, where D is the dimension of the given problem. Thus, the computational complexity yields an overall time complexity of O(T × M × D), comparable to BKA, where T represents the maximum number of iterations and M represents the number of candidate solutions.
5.6 Ablation study
The proposed algorithm modified the standard Black-winged Kite Algorithm (BKA)'s uneven distribution of initial parameters by using the Gaussian mutation operator as a modifier. This operator consists of various parameters, including mutation strength, which has a significant impact on overall performance. We conducted an ablation study, as shown in Table 5, to investigate the significance of this parameter, where the outstanding values highlighted in bold. Furthermore, the GBKA algorithm’s convergence curve in comparison to BKA is presented, as seen in Figures 9, 10, to demonstrate how Gaussian mutation aids in the escape of local optima and accelerates refinement in future iterations. As demonstrated in Figures 9, 10, the convergence curves for both BKA and GBKA achieve rapid fitness decreases in the first iterations. The results in Figure 9 show that GBKA consistently converges faster and achieves lower final fitness values for all task sizes. Furthermore, while BKA has delays in subsequent iterations, GBKA shows consistent improvement, showing a better capacity to escape local optima. This behavior demonstrates how the Gaussian mutation improves solution refining and convergence stability.
Table 5
| No. of tasks | σ = 0.1 | σ = 0.3 | σ = 0.5 | σ = 0.7 | σ = 0.9 |
|---|---|---|---|---|---|
| 100 | 2910548.2 | 2461669.02 | 2449713.374 | 2586742.022 | 2466871.18 |
| 200 | 3765585.366 | 3783838.84 | 3615858.807 | 3746094.45 | 3621630.497 |
| 300 | 5001952.273 | 5107724.87 | 4748244.931 | 5055254.02 | 4842773.64 |
| 400 | 5860985.584 | 5835655.66 | 5698877.871 | 5886724.48 | 5747465.912 |
| 500 | 6879246.031 | 7000161.92 | 6834115.54 | 7252579.957 | 6900292.196 |
| 600 | 8981964.479 | 9026916.01 | 8674403.94 | 8901599.812 | 9072278.042 |
| 700 | 9348571.06 | 9374191.57 | 9196572.488 | 9330842.37 | 9355890.812 |
| 800 | 10530184.38 | 10198089.5 | 10115817.35 | 10184916.87 | 10200261.45 |
| 900 | 12549753.04 | 12164053.8 | 12099236.8 | 12177402.87 | 12370377.75 |
| 1,000 | 13041630.53 | 13193112.6 | 12931951.97 | 13896797.65 | 13222111.58 |
Effects of the standard deviation σ on the model’s performance.
Bold value refers to the best one.
Figure 9
Figure 10
5.7 Limitations
Despite the effectiveness of existing nature-inspired metaheuristic optimization algorithms, the optimization search communities continue to investigate every nature-inspired optimization phenomenon in the hope of discovering a metaheuristic algorithm that can solve all search spaces of various optimization problems. This is consistent with the no-free-lunch (NFL) theorem for optimization (Wolpert and Macready, 1997), which indicates that no single metaheuristic algorithm outperforms all others for every optimization problem under different benchmarks. As a result, some potential limitations must be addressed, one of which is that the proposed algorithm produces competitive results when compared to cutting-edge algorithms using the Google Cloud Jobs (GoCJ) dataset as a benchmark. However, when various scientific workflow performance evaluation metrics such as Sipht, Inspiral, Cybershake, Montage, and Epigenomics with varying number of tasks are used as a benchmark (Bansal and Aggarwal, 2024), the algorithm’s accuracy may vary.
6 Conclusion and future work
This paper proposed GBKA, a new energy-aware algorithm for optimizing task scheduling in fog computing environments designed for Industrial IoT. By implementing the standard Black-winged Kite Algorithm (BKA) using Gaussian mutation as a modifier; GBKA offers promising outcomes compared with other existing algorithms in terms of energy consumption, makespan and resource utilization. The algorithm is designed to balance exploration of the search space and exploitation of the best solutions. The use of Gaussian mutation in the exploitation phase exhibits rapid convergence to optimal solutions, avoiding local optima and improving energy efficiency. The proposed algorithm is validated using the Google Cloud Jobs (GoCJ) dataset and compared against BKA, ACO, PSO, and DA. Results indicate improvements in energy consumption (7.26%), makespan (9.32%), and resource utilization (8.54%). After reviewing relevant literature, this study is one of the few that attempts to address task scheduling optimization in fog computing environment for industrial IoT applications, motivated by the migratory and predatory habits of the black-winged kite. From an Industrial IoT view, the proposed GBKA provides concrete operational advantages for smart factory settings. By decreasing task execution time and consumption of energy, GBKA might decrease operational expenses linked to edge and fog infrastructure, especially in energy-intensive manufacturing processes. Enhanced task scheduling efficiency also optimizes equipment use and resource efficiency and minimizes idle time of industrial controllers and gateways, resulting in more stable and predictable system performance. In actual manufacturing environments, these enhancements result in elevated throughput, diminished energy costs, and enhanced reliability of time-sensitive industrial applications, including predictive maintenance, real-time monitoring, and automated quality control. Our future work will focus on two directions: (1) creating increasingly sophisticated algorithms that use deep learning and machine learning capabilities (e.g., Long Short-Term Memory (LSTM) networks and Deep Reinforcement Learning) to improve system performance and energy efficiency in fog computing environments for industrial IoT applications (Heirati et al., 2025; Violos et al., 2020); and (2) addressing the possibility of integrating GBKA with SDN methodology for adaptive decision-making (Masoumeh et al., 2025; Prabha et al., 2020). This integration intends to bridge the gap between metaheuristic optimization and machine learning-based prediction in fog scheduling, encouraging more research and development in emerging fields such as smart healthcare, surveillance, and industrial vision systems.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
RE: Data curation, Methodology, Software, Writing – original draft, Writing – review & editing. HuA: Conceptualization, Investigation, Methodology, Project administration, Supervision, Writing – original draft, Writing – review & editing. HF: Conceptualization, Methodology, Supervision, Writing – original draft. FA: Investigation, Methodology, Project administration, Supervision, Writing – original draft.
Funding
The author(s) declared that financial support was not received for this work and/or its publication.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that Generative AI was not used in the creation of this manuscript.
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References
1
Abdel-BassetM.MohamedR.ChakraborttyR. K.RyanM. J. (2021b). IEGA: an improved elitism-based genetic algorithm for task scheduling problem in fog computing. Int. J. Intell. Syst.36, 4592–4631. doi: 10.1002/int.22470
2
Abdel-BassetM.MohamedR.ElhosenyM.BashirA. K.JolfaeiA.KumarN. (2021c). Energy-aware marine predators algorithm for task scheduling in IoT-based fog computing applications. IEEE Trans. Ind. Inform.17, 5068–5076. doi: 10.1109/TII.2020.3001067
3
Abdel-BassetM.El-ShahatD.ElhosenyM.SongH. (2021a). Energy-aware metaheuristic algorithm for industrial-internet-of-things task scheduling problems in fog computing applications. IEEE Internet Things J.8, 12638–12649. doi: 10.1109/JIOT.2020
4
Abd El-SattarH. K. H. (2025). Future metaverse-based education to promote daily living activities in learners with autism using immersive technologies. Educ. Inf. Technol.30, 3145–3182. doi: 10.1007/s10639-024-12844-3
5
Al-BetarM. A.AwadallahM. A.BraikM. S.MakhadmehS.DoushI. A. (2024). Elk herd optimizer: a novel nature-inspired metaheuristic algorithm. Artif. Intell. Rev.57:48. doi: 10.1007/s10462-023-10680-4
6
Al-ShareedaM. A.AlsadhanA. A.QasimH. H.ManickamS. (2024). Software defined networking for internet of things: review, techniques, challenges, and future directions. Bull. Electr. Eng. Inform.13, 638–647. doi: 10.11591/EEI.V13I1.6386
7
AndriuloF. C.FioreM.MongielloM.TraversaE.ZizzoV. (2024). Edge computing and cloud computing for internet of things: a review. Informatics11:71. doi: 10.3390/informatics11040071
8
BaktirA. C.OzgovdeA. and Ersoy, C. (2017). How can edge computing benefit from software-defined networking: a survey, use cases, and future directions. IEEE Commun Surv Tutor, vol. 19, pp. 2359–2391, doi:doi: 10.1109/COMST.2017.2717482
9
BalasundaramA.RoutrayS.PrabuA. V.KrishnanP.MallaP. P.MaitiM. (2023). Internet of things (IoT)-based smart healthcare system for efficient diagnostics of health parameters of patients in emergency care. IEEE Internet Things J.10, 18563–18570. doi: 10.1109/jiot.2023.3246065
10
BanerjeeA.CostaB.ForkanA. R. M.KangY. B.MartiF.McCarthyC.et al. (2024). 5G enabled smart cities: a real-world evaluation and analysis of 5G using a pilot smart city application. Internet Things28:101326. doi: 10.1016/j.iot.2024.101326
11
BansalS.AggarwalH. (2024). An efficient workflow scheduling in cloud–fog computing environment using a hybrid particle whale optimization algorithm. Wirel. Pers. Commun.137, 441–475. doi: 10.1007/s11277-024-11421-8
12
BeheraI.SobhanayakS. (2024). Task scheduling optimization in heterogeneous cloud computing environments: a hybrid GA-GWO approach. J Parallel Distrib Comput183:104766. doi: 10.1016/j.jpdc.2023.104766
13
BeraS.MisraS.VasilakosA. V. (2017). Software-defined networking for internet of things: A survey. IEEE Internet Things J.4, 1994–2008. doi: 10.1109/JIOT.2017.2746186
14
BhatiaS.MallikarjunaB.GautamD.GuptaD.KumarS.VermaS. (2023). The future IoT: The current generation 5G and next generation 6G and 7G technologies. In proceedings of the international conference on device intelligence, computing and communication technologies, (DICCT). Dehradun, India, 212–217.
15
DengR.LuR.LaiC.LuanT. H. (2015). Towards power consumption-delay tradeoff by workload allocation in cloud fog computing. In: Proceedings of the 2015 IEEE international conference on communications (ICC). IEEE
16
DengR.LuR.LaiC.LuanT. H.LiangH. (2016). Optimal workload allocation in fog-cloud computing toward balanced delay and power consumption. IEEE Internet Things J.3, 1171–1181. doi: 10.1109/JIOT.2016.2565516
17
DeviN.DalalS.SolankiK.LilhoreU. K.SimaiyaS.NuristaniN. (2024). A systematic literature review for load balancing and task scheduling techniques in cloud computing. Artif. Intell. Rev.57:276. doi: 10.1007/s10462-024-10925-w
18
DorigoM.Di CaroG. (1999) Ant colony optimization: A new meta-heuristic. Proceedings of the 1999 congress on evolutionary computation (CEC99)
19
EktaD.ShalliR. (2025). “Integrated trends, opportunities, and challenges of 5G and internet of things” in Current and future cellular systems: Technologies, applications, and challenges. New York, NY, USA: John Wiley & Sons139–152.
20
GuoY.GantiS.WuY. (2024). Enhancing energy efficiency in telehealth internet of things systems through fog and cloud computing integration: simulation study. JMIR Biomed. Eng.9:e50175. doi: 10.2196/50175,
21
HazraA.RanaB.AdhikariM.AmgothT. (2023). Fog computing for next-generation internet of things: fundamental, state-of-the-art and research challenges. Comput Sci Rev27, 112–134. doi: 10.1016/j.cosrev.2023.100549
22
HeiratiA.FartashM.Khalily-DermanyM. (2025). Optimized task scheduling in fog-cloud computing using hybrid deep learning and metaheuristic algorithms. Neural. Process. Lett.58:5. doi: 10.1007/s11063-025-11819-w
23
HuangX.XieK.LengS.YuanT.MaM. (2018). Improving quality of experience in multimedia internet of things leveraging machine learning on big data. Futur. Gener. Comput. Syst.86, 1413–1423. doi: 10.1016/j.future.2018.02.046
24
HuangX.YuR.KangJ.GaoY.MaharjanS.GjessingS.et al. (2017). Software defined energy harvesting networking for 5G green communications. IEEE Wirel. Commun.24, 38–45. doi: 10.1109/MWC.2017.1600360
25
HussainA.AleemM. (2018). GoCJ: google cloud jobs dataset for distributed and cloud computing infrastructures. Data3, 38–46. doi: 10.3390/data3040038
26
JainS.MeenaJ. (2019). “Workflow scheduling algorithms in cloud computing: an analysis, analogy, and provocations” in Innovations in computer science and engineering. Lecture Notes in Networks and Systems. eds. SainiH.SayalR.GovardhanA.BuyyaR., vol. 74 (Singapore: Springer).
27
JavaidM.HaleemA.SinghR. P.SumanR. (2023). 5G technology for healthcare: features, serviceable pillars, and applications. Intell. Pharm.1, 2–10. doi: 10.1016/j.ipha.2023.04.001
28
JiangM. R.FengX.WangC. H.FanX.ZhangH. (2023). Robust color image watermarking algorithm based on synchronization correction with multi-layer perceptron and Cauchy distribution model. Appl. Soft Comput.140:11027. doi: 10.1016/j.asoc.2023.110271
29
KabirS.GopeP.MohantyS. P. (2022). A security-enabled safety assurance framework for IoT-based smart homes. IEEE Trans. Ind. Appl.59, 6–14. doi: 10.1109/TIA.2022.3176257
30
KarthikS.KavithamaniA. (2021). Fog computing-based deep learning model for optimization of microgrid-connected WSN with load balancing. Wirel. Netw27, 2719–2727. doi: 10.1007/s11276-021-02613-2
31
KennedyJ.EberhartR. (1995). Particle swarm optimization, Proceedings of ICNN’95 - International Conference on Neural Networks, Perth, WA, Australia. 4, 1942–1948. doi: 10.1109/ICNN.1995.488968
32
KitkowskaA.BrodénK.AbdullahL. (2024). The requirements, benefits, and barriers of IoT solutions to support well-being in elementary schools. IEEE Access12, 144965–144981. doi: 10.1109/access.2024.3469558
33
KumarA.NanthaamornphongA.SelviR.VenkateshJ.AlsharifM. H.UthansakulP.et al. (2023). Evaluation of 5G techniques affecting the deployment of smart hospital infrastructure: understanding 5G, AI and IoT role in smart hospital. Alex. Eng. J.83, 335–354. doi: 10.1016/j.aej.2023.10.065
34
KumarA.SamriyaJ. K.BhansaliA.MalikM.AryaV.AlhalabiW.et al. (2025). Energy efficient task offloading from IoHT in delay sensitive edge networks. Alex. Eng. J.128, 476–483. doi: 10.1016/j.aej.2025.05.005
35
LeeC. Y.YaoX. (2001). Evolutionary algorithms with adaptive Levy mutations. Proceedings of the 2001 Congress on Evolutionary Computation, Korea (South). 1, 568–575. doi: 10.1109/CEC.2001.934442
36
LiC.MakS. L.LeeC.C.LeeT. T.YuenN. H. Y.TangW. F. (2023) A Review of 5G building management technologies and applications in smart campus. In Proceedings of the IEEE 21st international conference. On industrial informatics (INDIN)Lemgo, Germany1–5
37
LiC.WangJ.WangS.ZhangY. (2024). A review of IoT applications in healthcare. Neurocomputing565:127017. doi: 10.1016/j.neucom.2023.127017
38
LoutaM.BantiK.KarampeliaI.MahmoodA.BeltramelliL.AbedinS. F.et al. (2022). Industrial IoT in 5G-and-beyond networks: vision, architecture and design trends. IEEE Trans. Ind. Inform.18, 4122–41378. doi: 10.1109/TII.2021.3115697
39
MasoumehM.AhmadrezaM.KamalJ. (2025). Task scheduling and load balancing in SDN based cloud computing: a review of relevant research. J. Eng. Res.13, 3132–3146. doi: 10.1016/j.jer.2024.11.002
40
MirjaliliS. (2016). Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput. & Applic.27, 1053–1073. doi: 10.1007/s00521-015-1920-1
41
ModinaN.El-AzouziR.De PellegriniF.MenascheD. S. (2022). Joint traffic offloading and aging control in 5G IoT networks. IEEE Trans. Mob. Comput.22, 4714–4728. doi: 10.1109/TMC.2022.3154089
42
MontazerolghaemA. (2022). Software-defined internet of multimedia things: energy-efficient and load-balanced resource management. IEEE Internet Things J.9, 2432–2442. doi: 10.1109/JIOT.2021.3095237
43
NahaR. K.GargS.GeorgakopoulosD.JayaramanP. P.GaoL.XiangY.et al. (2018). Fog computing: survey of trends, architectures, requirements, and research directions. IEEE Access.6, 47980–48009. doi: 10.1109/ACCESS.2018.2866491
44
NaumanA.QadriY. A.AmjadM.ZikriaY. B.AfzalM. K.KimS. W. (2020). Multimedia internet of things: a comprehensive survey. IEEE Access8, 8202–8250. doi: 10.1109/ACCESS.2020.2964280
45
PonsM.ValenzuelaE.RodríguezB.Nolazco-FloresJ. A.Del-Valle-SotoC. (2023). Utilization of 5G technologies in IoT applications: current limitations by interference and network optimization difficulties-A review. Sensors23:3876. doi: 10.3390/s23083876,
46
PotuN.JatothC.ParvataneniP. (2021). Optimizing resource scheduling based on extended particle swarm optimization in fog computing environments. Concurrency Comput. Pract. Exp.33:e6163. doi: 10.1002/cpe.6163
47
PrabhaC.GoelA.SinghJ.SinghJ. (2020). A survey on SDN controller evolution: A brief review. 2022 7th international conference on communication and electronics systems (ICCES), Coimbatore, India, pp. 569–575
48
PrityF. S.UddinK. M. A.NathN. (2024). Exploring swarm intelligence optimization techniques for task scheduling in cloud computing: algorithms, performance analysis, and future prospects. Iran J. Comput. Sci.7, 337–358. doi: 10.1007/s42044-023-00163-8
49
RajuM. R.MothkuS. K. (2023). Delay and energy aware task scheduling mechanism for fog-enabled IoT applications: a reinforcement learning approach. Comput. Netw.224:109603. doi: 10.1016/j.comnet.2023.109603
50
RajwarK.DeepK.DasS. (2023). An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges. Artif. Intell. Rev.56, 1–71. doi: 10.1007/s10462-023-10470-y,
51
RathiB.ThapaswiS.KambhampatiM.JainV.AkshayP.PandeyT. N.et al. (2025). Realizing the potential of internet of things (IoT) in industrial applications. Discov. Internet Things5:45. doi: 10.1007/s43926-025-00141-5
52
RehmanW. U.KoondharM. A.AfridiS. K.AlbashaL.SmailiI. H.ToutiE.et al. (2025). The role of 5G network in revolutionizing agriculture for sustainable development: a comprehensive review. Energy Nexus17:100368. doi: 10.1016/j.nexus.2025.100368
53
SaleemM. U.UsmanM. R.YaqubM. A.LiottaA.AsimA. (2024). Smarter grid in the 5G era: integrating the internet of things with a cyber-physical system. IEEE Access.12, 34002–34018. doi: 10.1109/ACCESS.2024.3372379
54
SalmanO.ElhajjI.ChehabA.KayssiA. (2018). IoT survey: an SDN and fog computing perspective. Comput. Netw.143, 221–246. doi: 10.1016/j.comnet.2018.07.020
55
Segura-GarciaJ.Calero JMAPastor-Aparicio AMarco-Alaez RFelici-Castell SWang Q (2021). 5G IoT system for real-time psycho-acoustic soundscape monitoring in smart cities with dynamic computational offloading to the edge. IEEE Internet Things J.8, 12467–12475. doi: 10.1109/JIOT.2021.3063520
56
ShriyankS.IslamM. M.JavedS. A.ChhetriG.et al. (2025). A review on influx of bio-inspired algorithms: critique and improvement needs. J. ACM Neural and Evolutionary Computing.37, 1–26. doi: 10.48550/arXiv.2506.04238
57
SisinniE.SaifullahA.HanS.JennehagU.GidlundM. (2018). Industrial internet of things: challenges, opportunities, and directions. IEEE Trans. Ind. Inform.14, 4724–4734. doi: 10.1109/TII.2018.2852491
58
SriramaS. N. (2024). A decade of research in fog computing: relevance, challenges, and future directions. Softw. Pract. Exper.54, 3–23. doi: 10.1002/spe.3243
59
TeohY. K.GillS. S.ParlikadA. K. (2023). IoT and fog-computing-based predictive maintenance model for effective asset management in industry 4.0 using machine learning. IEEE Internet Things J.10, 2087–2094. doi: 10.1109/jiot.2021.3050441
60
VakilianS.FanianA. (2020). Enhancing users’quality of experienced with minimum energy consumption by fog nodes cooperation in internet of things. In: Proceedings of the 2020 28th Iranian conference on electrical engineering (ICEE). IEEE
61
VakilianS.MoravvejS. V.FanianA. (2021). Using the cuckoo algorithm to optimizing the response time and energy consumption cost of fog nodes by considering collaboration in the fog layer. In: Proceedings of the 2021 5th international conference on internet of things and applications (IoT). IEEE
62
ViolosJ.PsomakelisE.DanopoulosD.TsanakasS.VarvarigouT. (2020). Using LSTM neural networks as resource utilization predictors: the case of training Deep learning models on the edge. In: DjemameK.AltmannJ.BañaresJ.Á.Agmon Ben-YehudaO.StankovskiV.TuffinB. (eds) Economics of grids, clouds, systems, and services. GECON 2020. Lecture Notes in Computer Science(), vol 12441. Springer, Cham.
63
WangF.WangX.SunS. (2022). A reinforcement learning level-based particle swarm optimization algorithm for large-scale optimization. Inf. Sci.602, 298–312. doi: 10.1016/j.ins.2022.04.053
64
WangJ.WangW. C.HuX. X.QiuL.ZangH. F. (2024). Black-winged kite algorithm: a nature-inspired meta-heuristic for solving benchmark functions and engineering problems. Artif. Intell. Rev.57:98. doi: 10.1007/s10462-024-10723-4
65
WolpertD. H.MacreadyW. G. (1997). No free lunch theorems for optimization. IEEE Trans. Evol. Comput.1, 67–82. doi: 10.1109/4235.585893
66
WoodT.HwangJ.LiuG.RamakrishnanK. K.ZhangW. (2015). Toward a software-based network: integrating software defined networking and network function virtualization. IEEE Netw.29, 36–41. doi: 10.1109/MNET.2015.7113223
67
WuD.YangZ.ZhangP.WangR.YangB.MaX. (2023). Virtual-reality inter-promotion technology for metaverse: a survey. IEEE Internet Things J.10, 15788–15809. doi: 10.1109/jiot.2023.3265848
68
XiangW.YuK.HanF.FangL.HeD.HanQ. (2024). Advanced manufacturing in industry 5.0: A survey of key enabling technologies and future trends. IEEE Trans. Industrial Inform.20, 1055–1068. doi: 10.1109/TII.2023.3274224
69
ZreikatA.ZreikatA. I.AlArnaoutZ.AbadlehA.ElbasiE.MostafaN. (2025). The integration of the internet of things (IoT) applications into 5G networks: a review and analysis. Computers14:250. doi: 10.3390/computers14070250
Summary
Keywords
fog computing, Internet of Things (IoT), task scheduling, optimization problem, metaheuristic algorithms, energy consumption, resource utilization, makespan
Citation
Eisa RM, Abd El-Sattar HK, Farouk H and Omara FA (2026) A new Gaussian Black-winged Kite Algorithm for task scheduling optimization of industrial IoT applications in fog computing environment. Front. Comput. Sci. 8:1740606. doi: 10.3389/fcomp.2026.1740606
Received
06 November 2025
Revised
31 January 2026
Accepted
02 February 2026
Published
13 April 2026
Volume
8 - 2026
Edited by
Maheswar Rajagopal, KPR Institute of Engineering and Technology, India
Reviewed by
Ahmed G. Gad, Kafrelsheikh University, Egypt
Ahmadreza Montazerolghaem, University of Isfahan, Iran
Updates
Copyright
© 2026 Eisa, Abd El-Sattar, Farouk and Omara.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Hussein Karam Abd El-Sattar, h_karam@sci.asu.edu.eg
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