2.1. Nature/bio inspired methods & metaheuristic approaches

EPSO, a resource scheduling technique proposed by Narayana et al. [6], was implemented in a Fog environment. Authors used the PSO method in conjunction with the proximal gradient method to ease the convex problems. To converge the local and global solutions, the developed method employs additional gradient parameters. To demonstrate the effectiveness of the developed method, total cost and makespan metrics were compared. The developed method shortens the execution time of many tasks at the expense of increased energy consumption.

Yadav et al. [7] proposed a service distribution method in Fog environment that is a blend of PSO and GA methods to achieve ideal service distribution. The proposed technique lays services on Fog nodes to attain the appropriate feasible execution while minimizing the time and energy consumption for applications of IoT.

The fireworks algorithm task scheduling technique was introduced in [8]. Authors demonstrated a mechanism for detecting fireworks explosions. This paper also used the task clustering method. Memory and CPU utilization metrics were used in their load utilization model without regard for cost. Aburukba et al. [9] presented a model scheduling application in IoT via integer programming, with the goal of minimizing service request latency. Authors made use of the genetic algorithm to schedule IoT applications and compared the method to priority-strict queuing, round-robin, and waited-fair queuing in terms of latency parameter. It is observed that the proposed method also demonstrated substantial progress in achieving query deadlines by up to 31%.

In their work [10], Yang et al. proposed Fog simulator and a task scheduling method that considers execution time and resource costs. The work proposes a multi-objective evolutionary method that changes the neighborhood based on the present Fog computing scenario of the task scheduling group to distribute the current job scheduling group more efficiently. The authors demonstrated how their approach reduces load, job execution time, and resource cost. However, unlike other analyzed scheduling systems, the availability of Fog suppliers was not considered in this work.

Authors in [11] presented Hidden Morkov Model and Harris Hawk Optimization algorithms for predicting each Fog provider’s availability and scheduling of tasks respectively. Proposed work reduces offloaded tasks, SLA violation and deadline-missed workflows.

Yadav et al. [12] proposed fireworks algorithm to design scheduling algorithm in Fog environment. Authors have also considered immediate finish time, which is a heuristic approach. The hybrid method intended to speed up the search by utilizing both solution space exploitation and exploration. The aim of this work is to reduce cost and makespan and increase throughput. Cuckoo search was proposed [13] to address placement in IoT service. This multi objective work focuses on various metrics like energy consumption, response time, throughput, and delay. Both Quality of Service and optimization resource utilization in Fog environment is addressed in this work.

A multi objective grey wolf optimization algorithm is presented by Faten A. Saif et al. [14]. The proposed work plays a vital role in distributing tasks in Fog-cloud system. Evaluation result shows the effectiveness of grey wolf algorithm in reducing energy consumption and delay. In [15], authors propose an autonomic IoT service placement technique based on the grey wolf optimisation scheme to deploy IoT applications on Fog nodes, improving system performance while taking execution costs into account. Furthermore, the autonomic ideas aid in the development of an auto management system that better matches the dynamic behaviour of the Fog environment.

2.2. Machine learning/deep learning techniques

The learning automata approach is proposed by the authors in [16] as an effective dynamic service provisioning mechanism to decide whether to release or deploy IoT applications across the heterogeneous and dynamic Fog infrastructure. Additionally, to install the IoT applications on the Fog infrastructure, the authors created an autonomous dynamic service provisioning manager (DSPM) that adheres to a self-management control loop.

In [17], a Deep Reinforcement Learning-based IoT application scheduling method named DRLIS is presented to balance the load on the Edge/Fog servers and adaptively and efficiently optimize the response time of heterogeneous IoT applications. The authors developed an Edge-Fog-cloud integrated serverless computing system using the FogBus2 function-as-a-service architecture and DRLIS as a workable scheduler. Comprehensive experiment results demonstrate that DRLIS dramatically lowers the execution cost of Internet of Things applications. Load balancing, energy conservation, and scheduling demands have an impact on the Edge-Fog-cloud computing architecture’s performance and dependability. To overcome these difficulties, a reinforcement learning Fog scheduling technique is put out in [18]. Comparing the suggested approach to the current scheduling techniques, the testing findings show that it improves load balancing and reduces response time.

Zhang et al., [19] proposed a method for MTCN’s multi-target-aware dynamic resource scheduling that increases resource flexibility. The authors established multi-target-aware embedded limitations and considered differentiable QoS needs such as computing, storage, bandwidth, latency, and so forth. The authors also describe a scheduling network based on Deep Reinforcement Learning (DRL) that can effectively and scientifically interact with the MTCN environment.

Authors in [20] investigated resource auto-scaling in the Fog environment to prevent issues with over- and under-provisioning of Fog resources for time-varying demands from IoT devices. Deep learning was used as a solution to this issue. Additionally, to explain the interactions between the intended modules, IoT, Fog, and cloud devices for automatic resource scaling, a framework for resource auto-scaling based on the three-tier Fog architecture was suggested. In [21], authors suggest a resource allocation strategy using collaborative machine learning (CML) for SDN-enabled Fog computing. The resource allocation strategy for the SDN-enabled Fog computing environment is linked with the suggested CML model. The outcomes of the suggested approach are tested using FogBus and iFogSim, utilizing a variety of performance assessment measures such execution time, power consumption, latency, and bandwidth utilization.

Fuzzy logic with the K-Means clustering algorithm to efficiently arrange Fog nodes according to their workload patterns and resource attributes is presented in [22]. The suggested technique assigns jobs to Fog nodes dynamically by fusing fuzzy logic’s flexibility with Keans’ clustering powers. It describes how jobs may be intelligently assigned to Fog nodes by utilizing machine learning techniques, which will reduce execution time, response time, and network utilization.

To summarize, the survey reported in this section aims at scheduling/load balancing in Fog and Edge computing environments. However, most of them focus on optimization without considering resource utilization, energy and the number of tasks completed. The proposed work in this article focuses on multi-objective task scheduling algorithm using hybrid approach to improve overall performance in Fog-Edge computing.

3.1. Initialization of ANN for resource allocation

To initialize the artificial neural network for resource allocation in a Fog-Edge environment first, the problem needs to be solved using the ANN should be clearly defined. In this case, the problem is resource allocation in a Fog-Edge environment. This involves deciding which resources (e.g., CPU, memory, network bandwidth) should be allocated to which tasks or applications running on the Fog or Edge nodes. Next, the input and output variables of the ANN should be determined. The selection of input variables for resource allocation in a Fog-Edge environment may include workload on each Fog or Edge node, available resources on each node, and QoS requirements of each task or application. The output variable is the allocation of resources to each task or application.

3.2. Training dataset preparation using Antlion intelligent orchestration technique

The Antlion Intelligent Orchestration Technique (AIOT) is a swarm intelligence-based optimization algorithm that is suitable for resource allocation in a Fog-Edge environment. In this phase, a dataset is generated using Antlion optimization for task scheduling. Here the process has resources and a list of tasks which are fed to the Antlion optimizer to generate an optimal schedule with the least power and makespan. This outcome consists of a list of tasks and the resources allocated to them which can be Fog, Edge, or cloud resource. Each run generates an output representing the optimal allocation of resources for each task or application. The resulting input-output pairs can be saved as data points in the training dataset.

3.3. Antlion optimization algorithm

The proposed optimization model is a nature-inspired model. This model is chosen for optimization because this model is better optimized than other swarm-based models like ACO, PSO, Butterfly and many more in terms of optimization time and finding the global best solution. This model allows us to find the best optimal solution without sticking in local optimal solution which has least probability.

The mathematical model corresponding to each step is described in the paragraph that follows.

1. Position of each ants and Antlions in A_ant and A_Antlion matrices respectively. For modeling ant’s movement, Eq (1) is used: (1)
   Where c_sum denotes the cumulative sum, max and s represent maximum number of iterations and steps of random walk respectively.
   c_sum and stochastic function rn(s) are expressed as: (2) (3)
   To keep ants’ movement within the search space, normalization of ant’s random walk is performed as: (4) where represents the j^th ant position at iteration t, l_j and h_j denotes smallest and largest random walk of j^th variable, and are the lowest and highest of j^th variable in iteration t.
2. Ant entrapment:
   Ant entrapment in the Antlion pit is achieved by changing the random walks of ants. (5) (6) where δ^t and α^t denotes the lowest and highest values of all variables in iteration t, and represents the lowest and highest of j^th ant, denotes position of j^th Antlion selected at t^th iteration.
3. Trap construction:
   ALO employs the Roulette Wheel selection method to find better Antlions with higher fitness values. These fittest Antlions attract more ants. To simulate ant sliding the random walk of ants should be reduced as (7) where I is the ratio mentioned in [23].
4. Catching prey and rebuilding the trap:
   The fitness function is calculated. Eq (8) is adopted for this process: (8)
   When the ants leave the search space, the boundary checking mechanism is applied. The ant must return to the search domain after leaving it.
5. Elitism:
   Elitism is performed to store or retain the fittest Antlion for the subsequent generations. The retained Antlions are considered elite. Elite affects the manoeuvre of all the ants through iterations along with the Antlion chosen by roulette wheel selection. (9) where represents the random number to represent ant path, denotes random path the elite at t^th iteration, and is the ant lion position.

3.3.1 Pseudo code: Ant lion algorithm.

1. Initialization: Population of ants = P, Number of Antlions = N, maximum epoch, or iteration = max, current iteration = t, Random walk = R. Initialize the solutions randomly (of both Antlions and ants)

2. Compute the fitness function of Antlions and ants.

3. Identify the best Antlion and consider it to be optimal or the Elite

4. While t<max do

5.  for each Antlion solution

6.   use Roulette Wheel to select an Antlion

7.   Slide ant towards selected Antlion using Eq (7)

8.   The position of the ant is updated using Eq (9)

9.  end for

10.  Compute the fitness of all ants

11.  Use Eq 8 to substitute Antlion

12.  If an Antlion fitness> elite, then update elite

13. End While

Return Elite

The proposed Antlion algorithm process is described in Pseudo code and the workflow is described in Fig 3. Here, the population of solutions is initially seeded as ants on a search space. The position of ants and Antlions are stored as matrices. Fitness of Antlions, ants are computed, and the best Antlion is identified as Elite. Next, till the termination condition is met, for each Antlion solution, an Antlion is selected using roulette wheel selection. Subsequently, ants are made slide towards Antlion using the trap constructed and then position of the ant is updated. Fitness of all the ants is computed the Antlion will be replaced by ants if its fitness is higher and update the elite. Finally, once the termination condition is met, elite is returned as fittest Antlion.

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Fig 3. Antlion algorithm workflow.

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Once the data has been generated, it should be preprocessed to ensure that it is in a suitable format for training the ANN. This could involve scaling the input variables to a common range, one-hot encoding categorical variables, and normalizing the output variables. The training dataset should be split into a training set and a validation set. To train the ANN, the training set is used to minimize the error between the actual and desired outputs, while the validation set is used to evaluate its performance. A suitable algorithm, such as backpropagation, can be used for this purpose. After training the ANN using the training dataset, it can then be used to allocate resources in a Fog-Edge environment based on the input variables. The output of the ANN represents the optimal allocation of resources for each task or application.

Fig 4 shows the flow diagram of the proposed orchestration model for Fog-Edge computing environment. The key steps are defined properly using Input sequence of the Fog nodes and Edge nodes with optimal fitness function using Antlion technique. The offspring is used to train the neural network which provides the better results of the orchestration in a cloud and Edge computing environment.

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Fig 4. Flow of orchestration model.

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3.4 Neural model designing

Fig 5 shows the architecture of the proposed ANN design, which consists of two input variables fed into the first hidden layer, comprised of four neurons. The outputs of the first hidden layer are then forwarded to the second hidden layer, which also consists of four neurons. Next, the outputs of the second hidden layer are passed to the third hidden layer, consisting of four neurons as well. Finally, the output of the third hidden layer is fed into the output layer, containing a single neuron. Each neuron in the hidden and output layers is associated with an activation function that transforms the sum of its weighted inputs into an output. The proposed ANN design includes several activation functions, such as the sigmoid, ReLU, and Leaky ReLU functions. The ANN model consists of an Input layer, 3 dense layers with activation function ReLu, Leaky ReLU and Softmax and the last layer being the output layer as shown in Table 2. Where ADAM is used as an optimizer to optimize the ANN model.

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Fig 5. System architecture of feedforward neural network.

https://doi.org/10.1371/journal.pone.0304067.g005

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Table 2. Configuration of proposed neural network.

https://doi.org/10.1371/journal.pone.0304067.t002

3.5. Neural model training

During training, the neural model iteratively adjusts the weights of the connections between neurons to improve its ability to predict the output given the input. This phase adjusts the weights of interconnected neurons in the network to predict the expected output using activation function. Once the model is trained, it can be used to make predictions on new input data that it has not seen before.

3.6. Error back propagation and correction

The process involves propagating the error backwards through the network from the output layer to the input layer. The correction of the weights during the backpropagation process is done to minimize the error. The optimization algorithm used during training ensures that the weights are updated in a way that is efficient and effective at minimizing the loss function.

The basic equation for the error backpropagation algorithm is: (10) where δ_j is the error term for neuron j in the network shown in Fig 5, f’(z_j) is the derivative of the activation function of neuron j with respect to its input, w_jk is the weight of the connection between neuron j and neuron k in the network, δ_k is the error term for neuron k in the network, ∑_k w_jk δ_k is the sum of the weighted error terms for all neurons k that are connected to neuron j.

Once the error terms have been calculated for each neuron in the network, the weights are adjusted using the following equation: (11)

Where, Δw_jk is the change in weight of the connection between neuron j and neuron k, α is the learning rate which determines the step size of the weight update, δ_k is the error term for neuron k, a_j is the activation of neuron j which is the output of neuron j after applying its activation function to its input. The weights are updated iteratively using this equation until the error of the network is minimized.

4.1. Steps in proposed model

For an optimal utilization of the resources in Fog-Edge computing environment, following key step are followed in ANN inspired Antlion based orchestration in a Fog-Edge computing environment. The high-level block diagram of an ANN inspired Antlion-based Orchestration Algorithm for Fog-Edge Environment includes:

Input: Fog-Edge Environment Parameters

1: Initialize the Antlion population with random positions and velocities.

2: For each Antlion, encode its position and velocity using a neural network.

3: Evaluate the fitness of each Antlion based on its position and velocity using the fitness function.

4: Select the Antlion with the highest fitness score as the leader.

5: Update the position and velocity of each Antlion based on the leader’s position and velocity using the Antlion-inspired update rules.

6: For each Antlion, decode its new position and velocity using a neural network.

7: Evaluate the fitness of each Antlion again using the fitness function.

8: Check if the termination condition is met. If so, stop the algorithm and return the solution. If not, go to step 4.

9: Orchestrate the Fog-Edge environment based on the solution obtained from the Antlion-inspired algorithm.

The time complexity of proposed model is divided into two parts training and prediction. The time complexity of prediction is constant “C” as the trained neural network takes constant time to predict the resource (Node where the request will be processed). The proposed model takes most time in dataset preparation and model training which is a one-time process. Dataset preparation using Ant Lion algorithm takes time complexity of O(N) where N is the problem size which is the number of tasks to be scheduled. Where as compared to other existing metaheuristic models inspired from Fuzzy logic O(N²), Genetic algorithm O(g(nm + nm + n)) where “g” is the number of generations, “n” is the number of population and “m” ins the population size. and particle swarm optimization is O(nmd) where “n” is the population size, “m” is the number of iteration and “d” is the parameters dimensions. In general existing models are dependent of the number of iteration/evolution taking place or have complexity much higher like N² on the other hand proposed model takes constant time to predict the resource for the schedule.

The over head of the proposed model is the retraining of the trained model in order to overcome the decay of the trained neural network. Decay of the trained model is a phase where the accuracy of the trained model changes with changes in the environment i.e. input. This require retraining training and error back propagation to improve the accuracy of the model. Where the training time complexity is O(Ne * L * E), Ne is the number of neurons, L is number of layers neural architecture and E is the number of samples used for training.

5.1 Energy consumption

We first analyze the energy consumption at various levels. Energy Consumption is the total quantity of energy used at various levels. The energy consumption model of the Edge device is framed as follows: Consider the task T_k placed on the Edge device for execution. The time taken to execute the task is calculated through the load of task T_k and processing power of the Edge device. (12) where LD_j is the load of the task j, P_E is the processing power of Edge device. The total execution time of all tasks in the Edge device is represented as ET_A. Eq (13) represent the energy consumption of an Edge device. (13) where Pow_edge denotes the power while executing the tasks for Edge device. E_edge represents the energy consumption of the Edge device.

Fig 8 shows the evaluation result of energy consumption in cloud layer. Average energy consumption via the proposed algorithm is less by 90% compared to fuzzy logic and 60% compared to round robin respectively. Similarly, as shown in Fig 9 average energy consumption in Edge layer less by 30% compared to fuzzy logic and 14% compared to round robin algorithm.

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Fig 8. Average energy consumption in cloud.

https://doi.org/10.1371/journal.pone.0304067.g008

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Fig 9. Average energy consumption in Edge.

https://doi.org/10.1371/journal.pone.0304067.g009

5.2 CPU utilization

CPU utilization is another key parameter we have considered to evaluate the algorithms. Fig 10 shows the average CPU utilization in cloud layer, it is observed that the average CPU utilization rate of the proposed method is higher by 89% compared to fuzzy logic and 50% compared to round robin respectively. Fig 11 depicts the average CPU utilization in Edge layer, here average CPU utilization of the proposed method is higher by 91% compared to fuzzy logic and 85% compared to round robin respectively.

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Fig 10. Average CPU utilization in cloud.

https://doi.org/10.1371/journal.pone.0304067.g010

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Fig 11. Average CPU utilization in Edge.

https://doi.org/10.1371/journal.pone.0304067.g011

5.3 Network utilization

Another parameter incorporated to evaluate the algorithms is network usage. Fig 12 shows the WAN utilization by all the algorithms in the Edge layer. As shown in the figure, average WAN usage of the proposed method is higher by 90% compared to fuzzy logic and 93% compared to round robin respectively.

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Fig 12. WAN utilization in Edge.

https://doi.org/10.1371/journal.pone.0304067.g012

5.4 Waiting time

Since the users’ requests are processed at the Edge level, the amount of waiting time required is very much less compared to waiting time at the cloud level. Average waiting time in Edge layer is depicted in Fig 13. As observed, the average waiting time decreases by 96% compared to fuzzy logic and 1.4% compared to round robin respectively.

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Fig 13. Average waiting time in Edge.

https://doi.org/10.1371/journal.pone.0304067.g013

5.5 Tasks completion

Number of tasks successfully executed at cloud and Edge layer is depicted in Figs 14 and 15 Since the Edge is closer to the users, more number of tasks can be completed in a shorter time. As observed, the total number of tasks successfully executed at Edge level is very high compared to number of tasks executed at cloud level, thus the proposed algorithm results in high throughput.

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Fig 14. Number of tasks executed in cloud.

https://doi.org/10.1371/journal.pone.0304067.g014

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Fig 15. Number of tasks executed in Edge.

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Further the experiment is been conducted over 500–3000 Edge devices to study the performance in real work scenarios of healthcare application where the node definition is showcase in Table 4. The experiments are performed to evaluate energy efficiency, CPU utilization and number of task completed over cloud and edge. The main aim is to study the computational load that is transferred from cloud to Edge servers because the main aim of Edge computing is to compute majority of tasks over the Edge servers with high performance.

Figs 16 and 17 showcases the average energy consumption (Wh/Datacenter) where the energy consumed at the cloud datacenter is least because less number of task load is diverted over cloud datacenter. On the other hand the energy consumption of the Edge server is least for proposed algorithm because the average load over the Edge server is high with evenly distributed tasks with no hotspots and under utilized server where as compare to lated Fuzzy logic and genetic approaches are good in balancing the load over the cloud and Edge but fails to evenly distribute the tasks over Edge servers which leads to high energy consumption under over loaded condition. The figure also shows competing performance of Round robin but that is because most of the tasks are not completed due to deadline failure resulting in least energy consumption.

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Fig 16. Average energy consumption in cloud.

https://doi.org/10.1371/journal.pone.0304067.g016

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Fig 17. Average energy consumption in Edge.

https://doi.org/10.1371/journal.pone.0304067.g017

Figs 18 and 19 showcases the average CPU utilization in cloud and Edge servers. The results shows the CPU utilization of cloud is least for the proposed algorithm and for Edge servers the average CPU utilization increases to 99% under heavy loaded condition. Similar performance is showcased in Figs 20 and 21 where a study of number of tasks completed over cloud and Edge servers is showcased. Figure shows that majority of tasks are completed over Edge servers as compared to other existing algorithm and to avoid task failure in over loaded condition the tasks are also diverted to cloud servers which increases the number of task completed on cloud when the task load increases.

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Fig 18. Average CPU utilization in cloud.

https://doi.org/10.1371/journal.pone.0304067.g018

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Fig 19. Average CPU utilization in Edge.

https://doi.org/10.1371/journal.pone.0304067.g019

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Fig 20. Number of tasks executed in cloud.

https://doi.org/10.1371/journal.pone.0304067.g020

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Fig 21. Number of tasks executed in Edge.

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