In recent years, the use of computing, control, and data storage through cloud computing has aimed to take advantage of abundant computing resources to handle these applications. In this regard, tasks with high computational load are offloaded to remote cloud centers, which is known as computational offloading, to reduce the computational pressure on the terminal device [1], reducing the energy consumption for local processing and thus extending battery life. However, these centers are usually far from the end devices, and this relocation may not be a suitable solution for delay-constrained applications and increases bandwidth usage, cost, and energy consumption. To overcome these challenges, edge computing [2] and fog computing have been proposed as an extension of the cloud that can process data at the edge of the network and close to the end devices [3]. Fog computing introduces an edge layer by deploying fog servers between the end devices and remote cloud centers, which is mainly composed of terminals such as wireless access points, routers, base stations, etc. Since fog servers have network communication, computing, and storage functions and are close to terminal devices, they can improve the real-time processing response speed, reduce network congestion, and enhance data privacy protection capabilities.

Computational offloading is a multi-objective, NP-hard optimization problem [4] that cannot be solved in polynomial time using traditional deterministic algorithms and can only obtain an approximate solution. Previous research can be classified into the categories of mathematical optimization algorithms such as Mixed Integer Programming (MIP), heuristic, metaheuristic, and game theory; artificial intelligence-based optimization algorithms such as Machine Learning (ML); and control theory-based algorithms such as the Lyapunov optimization approach, or a combination of them.

Some of the main contributions that illustrate the innovations of the current paper are mentioned below:

I. A classification of the works done in the field of computational offloading using metaheuristic algorithms is presented.

II. Metaheuristic algorithms are discussed in terms of the methods used. Solving the computational offloading problem in resource-constrained environments requires the use of appropriate and efficient metaheuristic algorithms.

III. Challenges and unsolved issues regarding computational offloading using metaheuristic algorithms are enumerated and suggested for future research areas.

The rest of the paper is as follows. Section 2 describes the basic concepts, including metaheuristic algorithms and computational offloading. Section 3 shows how the relevant research was collected. Also, Section 4 describes the metaheuristic algorithms used for computational offloading. Section 5 analyzes and reviews the relevant research. Section 6 discusses the challenges and unsolved issues, and Section 7 describes the conclusions of the current paper.

In this section, the main concepts of the research, including metaheuristic algorithms and computational offloading, are described. A detailed understanding of the aforementioned concepts can highlight the importance of the present work and facilitate a more detailed examination of related research and a better comparison of them in terms of various indicators.

In this article, we are looking for a comprehensive review of metaheuristic algorithms for computation offloading. Collecting relevant research and subsequently reviewing them should follow a specific order, which is done by modeling articles [15], [16].

In [17], task offloading is presented as a multi-objective optimization problem focusing on reducing the total system power consumption and task execution delay. Then, according to the NP-hard nature of the problem, it has been solved using two metaheuristic methods, i.e., the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and the Bees Algorithm. The simulation results support the robustness of both metaheuristic algorithms in terms of energy consumption and delay reduction. The proposed method achieves a better trade-off regarding the probability of discharge and the power required for data transmission.

In [18], a metaheuristic scheduler, Smart Ant Colony Optimization task offloading algorithm inspired by nature, is proposed to offload the Internet of Things (IoT)-sensor applications tasks in a fog environment. Numerical results show a significant improvement in delay in task offloading of IoT-sensor applications. In [19], an improved metaheuristic optimization algorithm called particle swarm optimization based on genetic learning is designed, which integrates the strong local search capacity of a particle swarm optimizer and the genetic operation of a genetic algorithm. The proposed method jointly optimizes the offloading of tasks, transmission power, and bandwidth allocation of existing channels. Simulations with real-world data show that the proposed method significantly outperforms other existing methods in energy consumption of a whole system.

In [20], an attempt has been made to investigate the profitability of computational offloading from the service provider's perspective. Initially, near-optimal evacuation decisions are determined using evolutionary algorithms such as genetic algorithms and binary particle swarm optimization algorithms. After several iterations of the evolutionary process for the evacuation decision, the optimal solution is finally obtained, which allocates the resources based on the exact calculation of the profit value. According to the performed simulations, the proposed evolutionary algorithms perform better than the spectral efficiency-based evacuation algorithm, with shorter times in terms of profitability.

In [21], an offload decision-making framework based on the binary cuckoo search algorithm is proposed for mobile edge computing. Simulation results show that offload decisions depend on several parameters, including the number of mobile devices managed by the edge server, bandwidth, and number of tasks. The decisions made also depend on the priority assigned to each target. The proposed method significantly reduces the execution time when a large number of mobile devices are involved. In [22], a layered fitting algorithm is proposed that distributes tasks equally between the fog and the cloud, based on priority levels. Also, a metaheuristic approach based on modified Harris-Hawks optimization is proposed to allocate the best available resource to a task in a layer. The main goal is to reduce task completion time, task execution cost, and power consumption and increase resource utilization in both the fog and cloud layers. Based on the results, the system performance is improved in terms of task completion time, execution cost, and power consumption.

In [23], a new metaheuristic approach based on a modified genetic algorithm with directed search operators is presented to optimize overall execution time and energy consumption. A comparison of the efficiency of the proposed approach with alternatives shows improvements in solution quality and convergence speed to the solution. In [24], a partial computational offloading technique with minimum energy is proposed. A constrained optimization problem is formulated to minimize the cost for the system, and then an improved hybrid metaheuristic algorithm is developed that synergistically combines the Metropolis acceptance criterion from annealing simulation and genetic operations. Experiments with real tasks have shown that the proposed approach has significantly lower system cost and faster convergence speed than benchmarks.

In [25], an improved Aquila multi-objective optimizer equipped with a Pareto front is proposed to offload tasks from IoT devices to fog nodes with the aim of reducing response time. To improve the algorithm, contrast-based learning is used to diversify the population and discover optimal solutions. The proposed algorithm is evaluated with the number of tasks and fog nodes to reduce the response time. The results show that the average response time and failure rate obtained by the proposed algorithm are improved compared to other algorithms. In [26], a hybrid genetic algorithm is proposed to solve the task offloading problem. The speed of simulated annealing and the accuracy of the genetic algorithm are used to develop a fast and accurate Hybrid algorithm. Experimental results show that the proposed approach achieves significantly lower scheduling time compared to other schemes.

In [27], a hybrid metaheuristic algorithm for task offloading in edge computing is proposed, which is based on the simulated annealing algorithm and the red deer algorithm to generate an optimal task offloading schedule that minimizes system completion time and transfer time. Simulation results prove that the proposed approach can significantly reduce system completion time and transfer time. In [28], a hybrid metaheuristic algorithm combined with a greedy rule, hybrid mutation, and the whale optimization algorithm is proposed to realize partial computational offloading. Also, a partial offloading architecture of heterogeneous edge intelligence is proposed to validate the model and algorithm with real-world hardware and software. Experimental results show that the proposed approach outperforms several classical optimization algorithms in minimizing energy consumption.

In [29], the joint optimization of task offloading, communication, and computational resource allocation in edge computing is investigated, aiming to minimize energy consumption under deadline constraints and capacity constraints. The decision space is divided into several decision regions based on the characteristics of the problem under study, and a task offloading and resource allocation algorithm based on particle swarm optimization is designed to manage each decision region separately. The simulation and testbed-based experimental results show that the proposed algorithm can save energy consumption and improve efficiency compared to existing algorithms.

In [30], binary particle swarm optimization is used to make workload offloading decisions that consider both system cost and quality of service. Experimental results show that the proposed approach significantly outperforms existing benchmark algorithms in balancing system cost and quality of service in shared cloud-edge-end scenarios. In [31], a hybrid computational offload framework is presented that integrates edge and cloud resources to facilitate efficient and scalable data processing. The proposed system integrates a genetic algorithm and particle swarm optimization to enhance task offload, reduce delay, and optimize resource utilization. Experimental findings show that this approach significantly enhances system performance, minimizes energy consumption, and ensures stable connectivity between different devices.

In this section, we analyze and review related research to provide an overview for those interested in computational offloading using metaheuristic algorithms. This helps researchers make the right choice of improvement criteria, the paradigm under discussion, the simulator used, and other important research parameters.

Figure 4 shows the number of uses of each metaheuristic algorithm in the relevant papers. As we can see, the popular metaheuristic algorithms such as the genetic algorithm and particle swarm optimizer have been the most used, each of which has been used by 6 and 5 papers, respectively.

As we can see in Fig. 5, today, reducing execution time delay, reducing energy consumption, and reducing execution cost are the criteria that have received more attention from researchers than other criteria. A review of the relevant articles shows that 38%, 21%, and 13% of previous articles focused on reducing execution time delay, reducing energy consumption, and reducing execution cost, respectively. Delay-sensitive and real-time applications have made the delay criterion very important, and the limitation of users' battery life has also made energy consumption one of the important criteria. On the other hand, system developers want to implement at the lowest cost, so cost will also be one of the criteria of interest.

As we can see in Fig. 6, edge computing is the most popular paradigm in research related to computational offloading using metaheuristic algorithms. The importance of accelerating the processing of user-requested services and the need for processing resources to be close to users will further increase the use of edge computing. Also, user mobility and addressing this challenge will cause the use of the mobile edge computing paradigm to increase further.

As shown in Fig. 7, 53% of the research on computational offloading using metaheuristic algorithms used the MATLAB environment to evaluate the results. Also, about 40% of the simulation studies were conducted using the iFogSim tool. iFogSim brings ease in evaluating fog and edge networks due to its ready-made modules and classes.

With the expansion of delay- and energy-sensitive programs, optimization of computational load unloading to increase service quality criteria, including reducing delay and energy consumption, has been a hot topic of interest in recent years, and many studies have been presented in this regard with different approaches and in different computing environments. However, it has always faced challenges due to the dynamism and uncertainty of computing environments in real-world scenarios. In this section, we point out some of the main challenges of the previous approaches in computation offloading:

I. Getting stuck in local optima and setting too many hyperparameters:

Some of the unloading research, despite their achievements, have their own shortcomings. The biggest problem of metaheuristic methods is getting stuck in local optima. To obtain a global optimal solution, they must make a trade-off between exploration and exploitation. In addition, metaheuristic algorithms have many meta-parameters that are often difficult to tune. These are parameters that are manually set by the researcher. For example, in a genetic algorithm, crossover rate and mutation rate must be carefully adjusted. In contrast, the development of newer algorithms can require providing fewer parameters and better global search capabilities to be used to model more complex high-dimensional real-world scenarios such as offloading in fog computing.

II. Failure to consider the dynamics of the environment and lack of interaction with the environment:

Some of the unloading research, despite their achievements, often considers the environment static for convenience. This unrealistic assumption cannot include real-world requirements with dynamic environment conditions such as time-varying transmission channel conditions, bandwidth limitations, computing capabilities of servers, energy available in user devices, and random arrival rates of tasks. Considering that system dynamics play an important role in long-term performance, these methods may fail to achieve long-term computing discharge performance in dynamic, variable environments. The variety of tasks and the dynamics of the fog computing environment make the problem of offloading complex and difficult. In such a dynamic and complex system, traditional optimization methods may not be able to converge to an optimal solution in a reasonable time.

III. Exponential increase in search space and high computational load:

Existing algorithms usually suffer from an exponential increase in search space and heavy computational load, especially in large-scale scenarios. In most real-world scenarios, system dynamics are difficult to measure or model. This difficulty is especially true when the dimensions of the search spaces are large. The use of ML methods, especially deep reinforcement learning, can lead to the improvement of the situation during evacuation operations by gathering new experiences. As a result, the needs of delay-sensitive applications can be met by increasing adaptability to environmental changes.

With the development of computing paradigms such as edge computing, fog computing, and cloud computing, and the need for users to process their requested services, deciding which services should be processed locally and which ones should be processed non-locally has become a challenge. This issue is addressed by the concept of computation offloading. Computation offloading is a process in which heavy computational tasks are transferred from resource-constrained devices, such as IoT devices, smartphones, and sensors, to remote computing servers with significant computational capacity. Due to the existence of numerous conditions, including environmental dynamics, user mobility, etc., and the existence of various criteria such as latency, energy consumption, cost, etc., the computation offloading problem is classified as NP-Hard. To address these problems and reach a near-optimal solution in a reasonable time, we can use metaheuristic algorithms. In this study, we reviewed and analyzed related research in the field of computational offloading using metaheuristic algorithms. This article can provide a perspective for researchers interested in this field and inform them about the challenges and open issues in this field.

All authors contributed to the ideation and design of the study. A. M. wrote the initial draft and collected and analyzed the data. Project supervision and validation of the results were performed by B. Gh. All authors read and approved the final version.

This research did not receive any specific grant from funding agencies.

All the data are available in this paper.

The authors declare no conflict of interest.

The author confirms consent for the publication of this work.

This article does not contain any studies with human participants performed by the author.