Resource prioritization and allocation in fog computing using hybrid optimization

Abstract

With the rapid proliferation of IoT devices, the volume of data generated has reached unprecedented levels, necessitating efficient management strategies. Fog computing, complemented by 5G technologies, offers promising solutions to reduce service latency and enhance Quality of Service (QoS). However, allocating resources effectively remains challenging due to factors such as uncertainty, mobility, heterogeneity, and limited resources in fog computing environments. Traditional resource allocation (RA) algorithms often fall short of addressing these complexities. This study proposes a novel approach to RA in fog computing, utilizing a non-linear function to optimize resource allocation. An objective function is introduced, incorporating multi constraints such as resource utilization, service response rate, makespan, migration cost, and communication cost. The methodology emphasizes efficient resource allocation in crucial scenarios, facilitating rapid resource distribution where needed. The novel Coati Integrated Beluga Whale Optimization (CI-BWO) strategy is proposed to achieve optimal resource allocation in fog computing environments. By leveraging CI-BWO, this research aims to overcome the limitations of traditional RA methods and enhance the performance and scalability of fog computing applications. Finally, the superiority of the suggested strategy is assessed by comparison with many existing methods. When the task count is 200, the developed CI-BWO attained less migration cost of around 1.287, while existing models have acquired higher migration costs.

Keywords

Heterogeneity inFog computing optimal resource allocation migration cost resource prioritization hybrid optimization algorithm

1. Introduction

Due to IoT technology, everyday objects may now be connected to the Internet, enabling beneficial machine-human interaction. It linked various actuators, sensors, and controls for devices [26,33,36]. It is now widely used in many industries, including healthcare, retail, industrial automation, transportation, etc. IoT applications may generate a lot of data by utilizing numerous smartphones and sensors, which can cause problems with network capacity, latency, and security in typical cloud computing settings [11,19,39]. To tackle the problems of conventional cloud computing, new distributed computing technologies were introduced nowadays [16] and [10].

Fog computing [15,35] has arisen as a viable alternative to address the rising need for extension of the process, network, and storage resources close to end users to complement the unstable nature of cloud computing. As an option to support applications and services in the cloud in the future, FC, also identified as the cloud on the edge, is emerging [5,21,25]. Fog technology helps address the computational demands of sensitive applications by serving as a bridge between IoT devices and cloud servers. In order to bring computational services closer to IoT devices, the fog computing environment consists of processor components, network devices, and storage devices [22,38]. In comparison to direct cloud interaction, it aids in lowering latency, energy usage, and network bandwidth. It is a paradigm for operating a highly virtualized and distributed environment that connects devices and CDC to deliver network, storage, and computational services. Nonetheless, fog nodes often have limited processing and storage capacity [13,17,31]. Thus, it is not possible to consider these nodes as dedicated servers.

Moreover, computing nodes also struggle with managing workload fluctuations, effective resource allocation, and power consumption. In the FC environment, these problems necessitate efficient management of computer resources [7,20,23]. The hybrid heuristic-based list scheduling algorithm provides scheduling tasks efficiently across diverse cloud resources to minimize the overall makespan of computational workflows [27]. Resource allocation and scheduling are among the most important issues to consider in order to adapt to both cloud and fog settings because of resource constraints, heterogeneity, geographical restrictions, environmental requirements, and the fluctuating nature of resource needs. The objective of scheduling and resource allocation [24,40] is to improve resource usage efficiency, meet users’ QoS demands, and maximize profit for both fog suppliers and users, among other difficult issues. Nevertheless, there is hardly any in-depth study on the technology and just a cursory review and investigation of the topic in the literature when it comes to fog computing resource allocation [4,32]. The literature has not provided much study of the particular technological issues. Furthermore, as this is a new paradigm, there are a number of unanswered research problems and difficulties to be solved. Computing resource allocation is one of these problems; its goal is to deliver the computing resources in a suitable way.

Fog computing involves distributing computing resources and services closer to the edge of the network, which introduces challenges such as dynamic workload variations, resource constraints, and the need for efficient resource allocation to optimize system performance. Many existing approaches for resource allocation in fog computing may rely on simplistic linear models that do not adequately capture the complex interactions and non-linearities inherent in fog computing environments. Some existing algorithms may not scale well with increasing numbers of IoT devices and edge nodes, leading to inefficiencies in resource utilization and allocation. In order to overcome these drawbacks, this work proposes a novel resource prioritization and allocation in Fog computing using hybrid optimization. The proposed methodology aims to overcome the limitations of existing approaches by introducing a non-linear optimization framework with a comprehensive objective function and leveraging hybrid optimization techniques through CI-BWO. This initiative is motivated by the growing complexity and criticality of fog computing applications, where efficient resource allocation is crucial for achieving optimal performance and meeting diverse operational requirements.

The contributions of the proposed work are given below:

–
Introduces a new RA approach that efficiently aids in directing two processes namely Resource prioritization and Resource allocation. This focuses on RA in fog computing, which is done by demonstrating a non-linear function.
–
Considers parameters like resource utilization, service response rate, makespan, migration cost and communication cost for optimal RA.
–
Proposes a novel CI-BWO for performing optimal resource allocation in fog computing.

The proposed research is organized as follows: The existing works on RA are provided in Section 2. Novel strategy for RA in fog computing is given in Section 3. Section 4 explains resource prioritization. The optimal allocation of resources via the CI-BWO algorithm is explained in Section 5. The experimental analysis and conclusions are given in Sections 6 and 7.
2. Literature review

2.1. Related works

In 2023, Hu et al. [14] suggested an F-RAN of ERRH for edge computing with numerous antennas and capabilities. The F-RAN facilitated energy harvesting for EUs and task offloading for CUs at the same time. Full collaboration between eRRHs in both the computation and communication sectors has significantly increased the SWOPT performance, owing to the worldwide control of a central server. In particular, optimizing the beam resources and bandwidth in the communiquérealm, along with the computing frequencies and offload method in the computation domain, maximized the energy harvest performance of EUs. Extensive simulation results illustrated that suggested resource scheduling scheme’s superiority over existing competitors.

In 2023, Abdulazeez and Askar [1] provided a methodical examination of applying RL or DRL algorithms to fog computing problems pertaining to offloading. Initially, three main groups were identified in the classification of FC offload methods depending on DRL and RL algorithms: “value-based, policy-based, and hybrid-based algorithms”. Important features, such as the formulation of the offloading issue, the techniques used, performance indicators, tools for assessment, case scenarios, their benefits and downsides, offloading paths, offload type, and SDN design were then compared between these categories. Lastly, a full discussion of future problems and potential research paths is provided.

By integrating vehicles with idle resources as F-UEs, Zhang et al. [41] in 2022 established an end edge cloud cooperation model for offload in FVNETs. A 2-TRRA paradigm was suggested to enable adaptive orchestration of end-to-cloud resources in various load conditions. To reach the SE of the computing resource price and reservation, an iterative technique was suggested. The challenge of allocating computation and communication resources on a limited timeframe was converted into a multiagent random game, and a distributed solution based on lenient multiagent DRL was generated to reduce the total delay. F-UE-motivated tuning was incorporated to reserve more F-UE resources as latency performance deteriorates. According to simulation findings, the anticipated end edge cloud coordinated compute offloading approach in FVNETs beats baselines with regard to average latency.

Liu et al. [18] in 2022 focused on the association of user, RA (which includes power and bandwidth), and cache distribution in varied fog-RAN. The presented work takes energy and cross-tier interference mitigation into consideration, The optimization problem pertaining to user association, caching and RA technique was initially described as non-convex. Subsequently, it was changed into a convex issue that may be resolved by a suggested process that utilized the ADMM idea. Next, a method based on ADMM was suggested to improve the Fog-RAN’s energy efficiency. Simulation results showed the convergence and efficacy of the suggested algorithm over the existing solutions.

For the fog computing platform, Feng et al. [8] presented a unique game-based method for cyber risk management. The idea of cyber-insurance was used to shift the cyber risks associated with the fog computing system to an outside entity. The three primary components of the network model were the “cyber-insurer, the attacker, and the provider of fog computing”. To increase the integrity of the FC paradigm that was made up of several fog nodes, the FC provider constantly improves the distribution of its defensive computation resources. In the meantime, the attacker modifies its attack computer resource allocation dynamically to raise the likelihood of an effective attack. Additionally, the provider decides dynamically whether to subscribe each fog node to cyber insurance in order to guard against any losses brought on by assaults. At the subordinate level, an evolutionary game was created to examine the attack strategy of the attacker and the provider’s defensive and cyber insurance contribution plans. When optimizing its premium strategy at the higher level, the cyber guarantor considered the EE at the next level. Using methods from optimal control theory, the SE was analyzed and analytically it was proven that the EE was distinctive and stable.

In 2023 Tong et al. [34] created a collaborative FC model to accomplish widespread cooperative execution of computational tasks by data forwarding and offloading on the fog layer. Next, using this model, an integrated optimization issue was suggested to reduce the UE’s job execution latency. An HCCCA was provided to determine the best job offload and RA choices for FNs, taking into account the trade-off between lower latency and equality of cooperation. In conclusion, the outcomes showed that HCCCA was far more efficient than traditional systems.

To increase the dependability of fog-based IoT systems, Roozbeh et al. [30] in 2023 presented a new major backup RA technique called ReLIEF that depends upon ML. ReLIEF is an RL technique to choose good nodes for main and backup job execution. RL performed exceptionally well in dynamic contexts by finding a balance between workload and communiqué latency on individual fog devices. According to the analysis, this suggested method has the potential to cut task-dropping rates by as much as 84% when related to the existing works. In addition, it has the potential to distribute workload evenly and boost system dependability by around 72% when compared to its competitors.

Gai et al. [9] tackled the problem of resource management by putting out a new strategy for fog computing resource optimization called the EFRO model. A heuristic method was created that minimized time usage and energy costs simultaneously. One key component of EFRO was its ability to combine smart shift operations with standardization, driven by an HC process, to generate RA solutions that were almost ideal. The outcomes of the experiments show that the EFRO was skilled at controlling resources in fog computing settings close to optimally. Specifically, EFRO increased the energy of extant RR and MESF schemes by 71 and 55 per cent, correspondingly. Moreover, EFRO reduced the assignment time of DECM.

In 2022, Sing et al. [29] examined a fog system with constrained resources in which real-time jobs with diverse resource configurations must be allocated within the given execution deadline. The jobs involved were divided into two parts. TCB, the first module, categorized the task heterogeneity using upgraded least squares and dynamic FCM. TOORA was the second module. It determined whether to send the work to cloud or fog and allocated the fog nodes’ resources as efficiently as possible by utilizing the high throughput WOA method.

In 2023, Shahid et al. [12] introduced SMO’s use in fog computing. For resource allocation and scheduling in an FC network, an SMO technique was suggested based on heuristic initialization. The algorithm reduced the overall expense (service by selecting the best fog nodes for the jobs (in terms of both time and cost).

In 2023, Yakubu et al. [37] has presented a study on optimizing resource allocation in a complex computing environment that integrates the Internet of Things (IoT), fog computing, and cloud computing. The paper focuses on developing an efficient meta-heuristic approach to manage resource allocation while ensuring load balancing across these interconnected layers. The authors identify the challenges posed by the dynamic and heterogeneous nature of IoT devices, the variability in workload demands, and the need for efficient utilization of fog and cloud resources. They propose a meta-heuristic algorithm Modified Harris-Hawks Optimization (MHHO) designed to dynamically allocate resources based on real-time workload characteristics and resource availability. The algorithm aims to optimize performance metrics such as response time, energy consumption, and resource utilization efficiency.

In 2024, Afzali et al. [2] has explored efficient resource allocation strategies for handling Internet of Things (IoT) requests within a hybrid fog-cloud computing environment. The study addresses the challenges posed by the heterogeneous nature of IoT devices, varying workload demands, and the need for optimized utilization of fog computing and cloud resources. The authors propose a novel resource allocation scheme designed to dynamically manage IoT requests by leveraging both fog computing at the edge and cloud resources with the aid of the Improved Binary Particle Swarm Optimization (IBPSO) algorithm. The scheme aims to optimize performance metrics such as response time, energy efficiency, and resource utilization while ensuring scalability and reliability in processing IoT data.

In 2023, Asghari Alaieet al. [3] has established a hybrid bi-objective scheduling algorithm tailored for scientific workflows, where the goal is to minimize both the execution time of workflows and maximize their reliability. Scientific workflows often consist of complex sequences of computational tasks with dependencies, making efficient scheduling crucial for achieving timely and dependable results. This paper addresses the critical challenge of efficiently scheduling scientific workflows on cloud platforms, focusing on optimizing two key objectives: execution time and reliability. The algorithm employs advanced task scheduling techniques to optimize the sequence and allocation of tasks across cloud resources, aiming to minimize overall execution time.

In 2022, Hosseini Shirvani et al. [28] has developed a bi-objective scheduling algorithm designed specifically for scientific workflows in cloud computing environments. The primary objectives are to optimize the makespan of workflow executions and minimize the monetary costs associated with utilizing cloud resources efficiently. This paper addresses the challenge of scheduling scientific workflows on cloud platforms to minimize both makespan (completion time) and monetary costs. It integrates cost-aware scheduling strategies to minimize the financial expenses incurred by executing workflows on cloud platforms. This includes optimizing resource provisioning, workload distribution, and scheduling decisions to mitigate unnecessary expenditures.

2.2. Review

In both academia and business, a great deal of investigation was done on solving the scheduling and resource allocation issue in the cloud. Fog resource scheduling and allocation should take into account parameters like the task’s makespan (or completing time), cost of user, and application performances for efficient computational resource allocation. Furthermore, because several users share diverse resources with little to no visibility into the resource itself, the fog environment is very unpredictable and volatile. Providers attempt to oversubscribe numerous users for a shared resource in an effort to maximize resource usage; this leads to interference and resource contention.

Moreover, it is quite challenging to forecast the variations in RAS performance. However, despite the abundance of resource scheduling techniques, there is still a shortage of task models for cloud and fog computing. The different FRAS solutions can only have increased practicability through the evaluation of appropriate task models. As a result, creating a workable task pattern in a fog atmosphere has emerged as a persistent issue. However, most researchers still use basic mathematical models in the present distributed cloud environment, including queue and process, DAG, and certain types of workflows, or they use the job model in the prevailing corresponding framework for the resource allocation approach [20].

Furthermore, a complicated job can be broken down into several cooperative subtasks in numerous fog applications and data-storing services. Within these subtasks, varied intricate relationships and communications, including interdependence, conflicts, concurrency, and replacement occur. These subtasks also take pricing, execution time and cost into consideration. The conventional methods now in use are inadequate for representing the dynamic nature of tasks.

3. Novel strategy for resource allocation in fog computing

A new concept termed fog computing, often known as “clouds at the edge” distributes services close to the devices to enhance QoS. In the framework of cloud computing, the IoT, big data, and fog computing are becoming increasingly prevalent. This makes it very difficult to explore fog and cloud resource scheduling strategies in order to increase profit for both resource providers and users, improve resource utilization efficiency, and satisfy users’ QoS demand.

This work develops a new RA approach that efficiently aids in directing two processes namely,

(a)
Resource prioritization and
(b)
Resource allocation.

In fog computing, a non-linear feature is formed for assigning resources in the cloud during RA by considering specific constraints such as resource utilization, service response rate, makespan, migration cost and communication cost. Particularly, for optimal RA, a new CI-BWO model is proposed that determines the optimal allocation of resources. Figure 1 displays the working system of the developed RA scheme in fog settings.

Fig. 1.
Architecture of the working system of the proposed RA scheme.
3.1. Dataset creation

Numerous fog applications could be divided into multiple jobs and occupations that include the use of fog resources. Fog computing applications are complex and involve various tasks that utilize fog resources like computing power, storage, and networking. These tasks require collaboration among professionals with different skills to design, implement, and maintain robust fog computing solutions. This approach helps in optimizing the use of resources and improving the overall efficiency and effectiveness of fog computing applications in diverse domains. The user’s job can also be broken down into several smaller jobs. The task is assigned to VMs so they may effectively exploit the resources and carry out the jobs. The cost and duration of each subtask may vary based on available resources. It is vital to allocate the tasks on resources appropriately to gratify the user’s need for an immediate response with a minimal amount of user effort.

4. Resource prioritization

4.1. Prioritization

The resources are arranged based on resource size and specific service types. Among the service types, urgent services include health care, entertainment, vehicle security, and weather predictions. After obtaining an initial request from the user for a service, the cloud server distributor locates and distributes services. The developed model prioritizes health care, with traffic security following in second, entertaining in third, and climate in fourth place. Because of this, the size of jobs in the fields of medicine and entertainment are higher, whereas those in the fields of environmental and road safety are low and medium in size. Table 1 displays the priority strategy for different services.

Table 1
Prioritization of diverse services.

Type Size Priority Deadline

Climate type Lower 4 Higher

Entertaining Higher 3 Higher

Road security Medium 2 Shorter

Medical Higher 1 Shorter

Type	Size	Priority	Deadline
Climate type	Lower	4	Higher
Entertaining	Higher	3	Higher
Road security	Medium	2	Shorter
Medical	Higher	1	Shorter

5. Optimal allocation of resources via CI-BWO algorithm

5.1. Muti-constraints

For optimal allocation of resources, the optimal parameters considered are

Resource utilization

Service response rate

Makespan

Migration cost and

Communication cost

1. Resource utilization $(R U)$

This parameter shows how efficiently resources are being exploited in every process or system. $R U$ is represented in Eq. (1), here, $A R U$ and $T R C$ points out actual resource usage and total resource capacity.

R U = (\frac{A R U}{T R C}) \times 100

(1)

2. Service Response rate $(S R R)$

To perform a job, the response rate of resources is measured via the time of response of a fog resource providing a service [20]. The $S R R$ is represented in Eq. (2).

S R R = \sum_{i = 1}^{U} \frac{r t_{c u_{i}} - r t_{min}}{r t_{max} - r t_{min}} / U

(2)

Here, $r t_{c u_{i}}$ refers to the current response time, $r t_{min}$ and $r t_{max}$ points out the minimum and maximal response time and U points out how many times a user applies a resource.

3. Makespan $(M S)$

A makespan is the period to complete a task. It displays the quantity of time that is utilized from the start of the prior activity and its finishing time.

4. Migration Cost $(M G)$

The $M G$ is a noteworthy feature to assess the scheduling procedure. The MG of VM is evaluated from $N \times N$ matrix, wherein the rows and columns refer to the migrating cost of PM. The matrix with equal columns and rows (i.e. $(1, 1)$ , $(2, 2)$ ) determinesless migration cost, whereas, the others have larger migration cost. It is exactly shown in Eq. (3), where, $T a$ denotes task and m points out task count.

M G = \sum_{T a_{i} = 1}^{m} M G (T a_{i; i = 1, 2, \dots, m})

(3)

5. Communication Cost $(C C)$

Here, communication costs $C C$ amongst tasks i and j are provided to diverse VMs. $C C$ is modelled as in Eq. (4).

C C = \sum_{T a_{i} = 1}^{n} C C (T a_{i}, i = 1, 2, \dots, n)

(4)

5.2. Objectives

The objective function based on the considered constraints for RA in FC is determined as per Eq. (5) and Eq. (6). The considered constraints for RA in FC are service response rate, resource utilization, makespan, migration cost and communication cost. Here, the service response rate and resource utilization should be high, while, other constraints like make span, migration cost and communication cost should be low as possible. Based on this property, we define the objective function in two sets. The service response rate and resource utilization to be high is given in Eq. (5). The makespan, migration cost and communication cost to be less is given in Eq. (6). Here, resource utilization maximizing efficient use of available computing, storage, and networking resources. Service response rate responds faster to user requests, leading to enhanced user satisfaction and productivity. Makespan minimizing the overall completion time of tasks across fog nodes. Migration Cost minimizing the cost associated with migrating tasks between fog nodes. Communication Cost minimizing communication overhead and latency between fog nodes and end-users.

\begin{aligned} O b j (F_{1}) & = min [(1 - ϖ_{1}) S R R + (1 - ϖ_{2}) R U] \end{aligned}

(5)

\begin{aligned} O b j (F_{2}) & = min [ϖ_{3} * M S + ϖ_{4} * C C + ϖ_{5} * M G] \end{aligned}

(6)

Here, $S R R$ refers to the service response rate, $R U$ defines resource utilization, $M S$ denotes the makespan, $C C$ signifies the communication cost, and $M G$ represents the migration cost.

The final objective function is computed by combining Eq. (5) and Eq. (6) as exposed in Eq. (7), wherein, μ implies a weight parameter that lies between 0 and 1, i.e., $0 < μ < 1$ . Here, $ϖ_{1}$ , $ϖ_{2}$ , $ϖ_{3}$ , $ϖ_{4}$ and $ϖ_{5}$ are computed as shown in Eq. (8).

\begin{aligned} O b j (F) & = μ \times F_{1} + (1 - μ) F_{2}, 0 < μ < 1 \end{aligned}

(7)

\begin{aligned} ϖ_{i} & = \frac{P a r a m e t e r s o f i}{S u m o f P a r a m e t e r s} \end{aligned}

(8)

5.3. Proposed CI-BWO algorithm

Solution encoding: The VMs are provided as inputs for optimal RA. The lower and upper limits for the solution are assigned as zero and ten respectively.

The BWO [42] technique improves learning strategies and expedites the search process. Nevertheless, we combine the idea of COA [6] in BWO which is thereafter called CI-BWO, to prevent being stuck in local optima. COA and BWO typically exhibit different search strategies. COA, inspired by coati behaviour, emphasizes exploration through random walks and social behavior mimicking, while BWO, inspired by the social behavior of beluga whales, emphasizes exploitation through a cooperative search strategy. By integrating these approaches, CI-BWO can achieve a balanced exploration-exploitation trade-off, effectively navigating search spaces to find optimal solutions. CI-BWO benefits from both algorithms’ convergence mechanisms, potentially accelerating convergence speed compared to using either algorithm individually. One common challenge in optimization is getting trapped in local optima. CI-BWO mitigates this by combining COA’s ability to explore diverse regions of the search space with BWO’s ability to exploit promising regions efficiently. This robustness improves the likelihood of finding globally optimal solutions or high-quality solutions in complex, multimodal optimization landscapes.

BWO operates in two different phases: exploration and exploitation. The BWO algorithm chooses beluga whales at random to undertake a worldwide search across the specified region during the exploration phase. On the other hand, the exploitation stage limits the search to the immediate neighbourhood inside the allocated region. The possibility of whale fall is also taken into consideration by the BWO, which affects how beluga whale positions are adjusted. The BWO’s theoretical framework represents how beluga whales, acting as search agents, move around the assigned region by shifting positions. The BWO functions as a population-level system in which a single beluga whale represents a possible solution and the word “beluga whale” implies a search agent. Throughout the optimization process, both of these entities get constant updates. As per Eq. (9), the initial position of belugas is arbitrarily determined, which, d points out the size of implementation variables and n indicates the size of the population.

A = [\begin{matrix} a_{1, 1} & \dots & a_{1, 2} & \dots & a_{1, d} \\ : & ⋱ & : & . . . & : \\ a_{i, 1} & \dots & a_{2, 2} & \dots & a_{2, d} \\ : & . . . & : & ⋱ & : \\ a_{n, 1} & \dots & a_{n, 2} & \dots & a_{n, d} \end{matrix}]

(9)

Moreover, Eq. (10) determines the fitness value of entire belugas.

F = [\begin{matrix} f (a_{1, 1}, a_{1, 2}, \dots \dots \dots, a_{1, d}) \\ f (a_{2, 1}, a_{2, 2}, \dots \dots \dots, a_{2, d}) \\ ⋮ \\ f (a_{n, 1}, a_{n, 2}, \dots \dots \dots, a_{n, d}) \end{matrix}]

(10)

The CI-BWO travels from one phase to other phases by using the balance factor $b f b f$ shown in Eq. (11), where, $Γ_{max}$ and Γ points out maximal as well as current iterations. If $b f > 0.5$ , the exploration phase is done; if, $b f ⩽ 0.5$ defines the exploitation phase as done.

b f = B_{0} (1 - Γ / 2 Γ_{max})

(11)

Exploration phase: At this point, the BWO approach mimics the swimming movements of beluga whales. Furthermore, according to the records, belugas’ social and mating behaviors may be seen in a variety of contexts, particularly when they swim in pairs. Therefore, the typical configuration of search agents that take this position is represented as follows in Eq. (12).

{\begin{matrix} A_{i, j}^{T + 1} = A_{i, P j}^{T} + (A_{r, P 1}^{T} - A_{i, P j}^{T}) (1 + r_{1}) \sin (2 \prod r_{2}), j = even \\ A_{i, j}^{T + 1} = A_{i, P j}^{T} + (A_{r, P 1}^{T} - A_{i, P j}^{T}) (1 + r_{1}) \cos (2 \prod r_{2}), j = odd \end{matrix}

(12)

Where, $P_{j}$ ( $j = 1, 2, \dots, d$ ) points out arbitrary number chosen from d-dimension; $A_{r, P 1}^{T}$ points out present position of rth beluga; $r_{1}$ , $r_{2}$ les among (0, 1); $A_{i, P j}^{T}$ points out ith position of beluga on $P_{j}$ dimension; $\sin (2 \prod r_{2})$ , $\cos (2 \prod r_{2})$ points out positions of beluga whales fins at the surface; and $A_{i, j}^{T + 1}$ points out novel position of ith beluga jth dimension.

Exploitation phase: In this stage, the BWO algorithm incorporates the beluga whales’ hunting habits. These aquatic animals are able to cooperate in their pursuit of prey and modify their course in response to the whereabouts of adjacent whales. As a result, the beluga whales communicate with each other in order to maximize their hunting efforts and determine which one is the most likely. The updated location of Beluga is shown in Eq. (13).

A_{i}^{T + 1} = r_{3} A_{b e s t}^{T} - r_{4} A_{i}^{T} + c_{1} \cdot L f \cdot (A_{r}^{T} - A_{i}^{T})

(13)

In Eq. (13), $A_{i}^{T + 1}$ points out the updated position, and $c_{1} = 2 r_{4} (1 - Γ / Γ_{max})$ points out the strength of random jump and levy flight $L f$ is given in Eq. (14).

L f = 0.05 \times \frac{u \times σ}{| v |^{1 / ϑ}}

(14)

In Eq. (14), $σ = (\frac{Υ (1 + ϑ) \times \sin (\prod ϑ / 2)}{Υ ((1 + ϑ) / 2) \times ϑ \times 2^{(ϑ - 1) / 2}})$ ; v, u points out arbitrary numbers and $ϑ = 1.5$ .

Whale fall:

In order to replicate the behaviour of whale falls, specific Beluga whales from the entire group are chosen based on a probability function that indicates the chance of their unintentional drop. The magnitude and location of the whale falls are continuously updated to ensure a consistent census of the population as the whales migrate to new places and occasionally reach this destination. As demonstrated by Eq. (15), this updating process may be calculated theoretically, here, $r_{5}$ , $r_{6}$ , $r_{7}$ points out arbitrary integer amid $[0, 1]$ ; and $A_{s t e p}$ points out the step size of whale fall as given in Eq. (24).

A_{i}^{T + 1} = r_{5} A_{i}^{T} - r_{6} A_{r}^{T} + r_{7} A_{s t e p}

(15)

As per CI-BWO, the whale fall is modelled based on the COA [42] update. The COA update is shown in Eq. (16).

A_{i, j}^{p 2} = A_{i, j} + (1 - 2 r) . (L b_{l}^{L O} + r . (U b_{l}^{L O} - L b_{l}^{L O}))

(16)

On deriving $A_{i, j}$ from Eq. (16), we get Eq. (17).

A_{i, j} = A_{i, j}^{p 2} - (1 - 2 r) . (L b_{l}^{L O} + r . (U b_{l}^{L O} - L b_{l}^{L O}))

(17)

Substituting COA update Eq. (17) in Eq. (15), we get Eq. (22).

\begin{aligned} A_{i}^{T + 1} & = r_{5} (A_{i, j}^{p 2} - (1 - 2 r) . (L b_{l}^{L O} + r . (U b_{l}^{L O} - L b_{l}^{L O}))) \\ - r_{6} A_{r}^{T} + r_{7} A_{s t e p} \end{aligned}

(18)

\begin{aligned} A_{i}^{T + 1} & = r_{5} A_{i, j}^{p 2} - r_{5} ((1 - 2 r) . (U b_{l}^{L O} + r . (U b_{l}^{L O} - L b_{l}^{L O}))) - r_{6} A_{r}^{T} + r_{7} A_{s t e p} \\ - r_{6} A_{r}^{T} + r_{7} A_{s t e p} \end{aligned}

(19)

\begin{aligned} A_{i}^{T + 1} - r_{5} A_{i, j}^{p 2} & = - r_{5} ((1 - 2 r) . (U b_{l}^{L O} + r . (U b_{l}^{L O} - L b_{l}^{L O}))) \\ - r_{6} A_{r}^{T} + r_{7} A_{s t e p} \end{aligned}

(20)

\begin{aligned} A_{i}^{T + 1} (1 - r_{5}) & = - r_{5} ((1 - 2 r) . (U b_{l}^{L O} + r . (U b_{l}^{L O} - L b_{l}^{L O}))) \\ - r_{6} A_{r}^{T} + r_{7} A_{s t e p} \end{aligned}

(21)

Finally, Eq. (22) is used to update the whale fall.

\begin{aligned} A_{i}^{T + 1} = \frac{- r_{5} ((1 - 2 r) . (U b_{l}^{L O} + r . (U b_{l}^{L O} - L b_{l}^{L O}))) - r_{6} A_{r}^{T} + r_{7} A_{s t e p}}{(1 - r_{5})} \end{aligned}

(22)

In Eq. (22), the random values are replaced by a chaotic cubic map as shown in Eq. (23), where, r is a positive integer between 0 and 4, $x_{n}$ lies between 0 and 1.

\begin{aligned} x_{n + 1} & = r . x_{n} (1 - x_{n}^{2}) \end{aligned}

(23)

\begin{aligned} A_{s t e p} & = (U b - L b) \exp (- c_{2} Γ / Γ_{max}) \end{aligned}

(24)

In Eq. (24), $L b$ and $U b$ points out the lower and upper bound; and $c_{2} = 2 W f \times n$ points out the step factor. The possibility of whale fall is specified in Eq. (25).

\begin{aligned} W f = 0.1 - 0.05 Γ / Γ_{max} \end{aligned}

(25)

The flowchart of CI-BWO is given in Figure 2.

Fig. 2.

Flowchart of proposed CI-BWOmodel.

Pseudocode of CI-BWO (Algorithm 1):

Table 2

System configuration.

	Device specifications
Processor	11th Gen Intel(R) Core (TM) i5-1135G7 @ 2.40 GHz 2.42 GHz
Installed RAM	16.0 GB (15.7 GB usable)
System type	64-bit operating system, x64-based processor

6. Results and discussion

6.1. Simulation procedure

The proposed model for RA in fog computing using CI-BWO was done in MATLAB. The experimental analysis was done by varying the count of tasks from 50 to 200. The counts of PMs considered were two and the counts of VMs considered were five.The system configuration is described in Table 2.

The considered metrics for analysis were resource utilization, service response rate, makespan, communication and migration costs. The analysis of adopted CI-BWO was established over existing methods like BWO, COA, JSO, HGS and EHO, MHHO [37], IBPSO [2], WORA [29] and SMO [12]. Moreover, statistical assessment on adopted CI-BWO over BWO, COA, JSO, HGS EHO, MHHO [37], IBPSO [2], WORA [29] and SMO [12] was carried outbase on the most common performance metrics resource utilization, service response rate, makespan, migration cost and communication cost. These performance metrics are the most widely used in the resource allocation process in order to evaluate the credibility of the proposed system. Moreover, these metrics are used in the objective function also. The parameters of the algorithms used for analysis are shown in Table 3.

Table 3
Parameter of the optimization algorithms.

CI-BWO parameter, ϑ 1.5

BWO parameter, ϑ 1.5

EHO parameters

ϑ 0.5

β 0.5

$n - c l a n$ 5

HGS parameters

A 5

Speed 1

$T 1$ 3

e 4

$L H$ 10000

L 0.5

JSO parameters

a 4

SMO parameters

Members 10

$p r$ 0.1

Global Limit Count 0

WOA parameters

b 1

p 0.5

Fig. 3.

Analysis of CI-BWO over varied existing models on (a) service response rate and (b) resource utilization for varied task count.

Fig. 4.

Analysis of CI-BWO over varied existing models on (a) makespan (b) communication cost (c) migration cost and (d) latency for varied task count.

6.2. Performance analysis

The service response rate and resource utilization analysis for RA in FC with respect to varied task count is exposed in Figure 3(a) and (b). In addition, the service response rate and resource utilization analysis for RA in FC with respect to varied VM count is exposed in Figure 4(a), (b), (c) and (d) shows the makespan, communication cost and latency. The service response rate and resource utilization have to be higher for better RA in FC. For all counts of tasks, it is observed that the service response rate and resource utilization are higher for theCI-BWO scheme over MHHO [37], IBPSO [2], BWO, COA, JSO, HGS, EHO, WORA [29] and SMO [12]. Likewise, for all counts of VMs, the service response rate and resource utilization are higher for the CI-BWO scheme over MHHO [37], IBPSO [2], BWO, COA, JSO, HGS, EHO, WORA [29] and SMO [12]. Compared to other methods, the service response rate is high for CI-BWO when the task count is 50. Nevertheless, our developed CI-BWO has shown a high service response rate for all tasks. Next to a task count of 50, the service response rate is higher for CI-BWO when the task count is 100. These results demonstrate the CI-BWO’s ability to allocate resources optimally ensures that VMs are not overburdened or underutilized, contributing to consistent and predictable service response times. Applications running on fog computing systems respond faster to user requests, leading to enhanced user satisfaction and productivity. Likewise, resource utilization is high for CI-BWO when the task count is 50. At all task counts, extant MHHO [37], IBPSO [2], BWO, COA, JSO, HGS and EHO, WORA [29] and SMO [12] show less resource utilization than CI-BWO. CI-BWO’s higher resource utilization indicates that it effectively utilizes computing resources (CPU cycles, memory, storage) across fog nodes to handle VMs’ tasks efficiently. It balances the load dynamically, preventing resource wastage and ensuring that fog nodes operate close to their capacity without overload. Efficient resource utilization is essential for maximizing the utilization of fog nodes while minimizing operational costs. This shows that high service response rate and resource utilization are attained for developed CI-BWO over MHHO [37], IBPSO [2], BWO, COA, JSO, HGS and EHO, WORA [29] and SMO [12].

Fig. 5.

Analysis of CI-BWO over varied existing models on (a) service response rate and (b) resource utilization for varied VM.

Fig. 6.

Analysis of CI-BWO over varied existing models on (a) makespan (b) communication cost (c) migration cost and (d) latency for varied VM.

Similarly, the makespan, migration cost, communication cost and latency analysis for varied task counts are exposed in Figure 4(a), (b), (c) and (d). Moreover, the makespan, migration cost, communication cost and latency. analysis for varied VM counts are exposed in Figure 5(a) and (b). This shows the service response rate and resource utilization. In Figure 4(a), the makespan seems to be less for our developed CI-BWO, while, extant MHHO [37], IBPSO [2], BWO, COA, JSO, HGS and EHO, WORA [29] and SMO [12] models attained higher makespan. Specifically, makespan is less when the task count is 200. When the task count is 50, the makespan of developed CI-BWO is less when compared to existing MHHO [37], IBPSO [2], BWO, COA, JSO, HGS and EHO, WORA [29] and SMO [12] methods. Lower makespan signifies better resource utilization efficiency, ensuring that fog nodes handle tasks effectively without idle resources. CI-BWO aims to minimize makespan by optimizing the allocation of resources to VMs. By strategically assigning tasks and managing workload distribution, CI-BWO reduces the time taken to complete tasks, thus minimizing makespan. The minimal migration cost, communication cost and latency obtained by developed CI-BWO for varied tasks are shown in Figure 6(b), (c) and (d). When the task count is 200, the developed CI-BWO attained less migration cost of around 1.287, while, MHHO [37], IBPSO [2], BWO, COA, JSO, HGS and EHO, WORA [29] and SMO [12] models attained higher migration cost of about 3.2672, 3.8561,4.2879,1.999, 2.478, 5.2989, 3.809, 1.587 and 4.878 respectively. Reduced migration costs translate into lower operational expenses for managing fog computing infrastructure. CI-BWO optimizes VM placement and resource allocation, reducing the need for frequent migrations. By intelligently allocating resources based on workload demands and node capacities, CI-BWO minimizes VM migrations, thus lowering migration costs. In all the task counts, the proposed CI-BWO model achieves less communication costs when compared to existing schemes like MHHO [37], IBPSO [2], BWO, COA, JSO, HGS and EHO, WORA [29] and SMO [12]. Lower communication costs mean less bandwidth is consumed, optimizing network resources for other critical tasks. CI-BWO optimizes VM placement and resource allocation to minimize data movement and reduce inter-fog communication. By strategically placing VMs closer to data sources or users, CI-BWO minimizes communication distances and associated costs. Moreover, in all the task counts, the proposed CI-BWO model achieves lower latency rates when compared to existing schemes like MHHO [37], IBPSO [2], BWO, COA, JSO, HGS and EHO, WORA [29] and SMO [12]. Low latency supports real-time data processing and decision-making in IoT, healthcare monitoring, and industrial automation. Fog nodes operate efficiently with reduced latency, maximizing the utilization of computing resources for critical tasks. CI-BWO aims to minimize latency by optimizing resource allocation and reducing task processing times. By placing VMs strategically and managing workload distribution, CI-BWO decreases latency associated with task execution and data processing. The minimal latency, migration cost and communication cost obtained by developed CI-BWO is due to the introduction of CI-BWO for performing optimal RA in FC.

6.3. Statistical analysis

The statistics related to the objective of the CI-BWO method over BWO, COA, JSO, HGS and EHO are given in Table 4. The considered scenarios are “minimum, maximum, mean, median and SD”. The cost incurred for RA in FC should be less for effective computation. Particularly, a less cost of 101.84is achieved by CI-BWO for the mean case, while, costs attained using MHHO [37], IBPSO [2], BWO, COA, JSO, HGS and EHOare highat104.32, 105.46, 104.455, 106.039, 106.29, 104.556 and 103.957. Moreover, a less cost of 46.4715 is achieved by CI-BWO for the SD case, while, the cost attained using MHHO [37], IBPSO [2], BWO, COA, JSO, HGS and EHOare high at 47.32, 48.63, 47.9431, 49.91, 50.6877, 48.3224 and 47.9241. This minimal cost for RA in FC is owing to the introduction of the new CI-BWO algorithm, which considered the objective parameters like make span, migration cost and communication cost, service response rate and resource utilization.

Table 4
Statistical analysis on optimal RA in fog computing.

Methods Mean Median SD Minimum Maximum

BWO 104.455 108.104 47.9431 36.2803 165.329

COA 106.039 107.338 49.91 37.0929 172.388

JSO 106.29 106.938 50.6877 36.6288 174.656

HGS 104.556 107.593 48.3224 36.729 166.309

EHO 103.957 106.819 47.9241 36.3091 165.88

MHHO [37] 104.32 106.32 47.32 37.92 164.32

IBPSO [2] 105.46 106.42 48.63 35.41 166.2

CI-BWO 101.84 105.089 46.4715 35.9029 161.28

Methods	Mean	Median	SD	Minimum	Maximum
BWO	104.455	108.104	47.9431	36.2803	165.329
COA	106.039	107.338	49.91	37.0929	172.388
JSO	106.29	106.938	50.6877	36.6288	174.656
HGS	104.556	107.593	48.3224	36.729	166.309
EHO	103.957	106.819	47.9241	36.3091	165.88
MHHO [37]	104.32	106.32	47.32	37.92	164.32
IBPSO [2]	105.46	106.42	48.63	35.41	166.2
CI-BWO	101.84	105.089	46.4715	35.9029	161.28

6.4. Computation time analysis

The computation time analysis of the CI-BWO model over MHHO [37], IBPSO [2], BWO, COA, JSO, HGS and EHO, WORA [29] and SMO [12] techniques is exposed in Table 5. The proposed CI-BWO model has attained a lower computation time of 0.065, while, compared methods have got a high computation time.

Table 5
Computation time analysis on optimal RA in fog computing.

Methods Time (sec)

BWO 0.203379

COA 0.129898

WORA [29] 0.188293

SMO [12] 0.07951

JSO 0.092878

HGS 0.177313

EHO 0.108768

MHHO [37] 0.10732

IBPSO [2] 0.10525

CI-BWO 0.065325

Methods	Time (sec)
BWO	0.203379
COA	0.129898
WORA [29]	0.188293
SMO [12]	0.07951
JSO	0.092878
HGS	0.177313
EHO	0.108768
MHHO [37]	0.10732
IBPSO [2]	0.10525
CI-BWO	0.065325

6.5. Convergence analysis

The cost-convergence analysis of theCI-BWO model over BWO, COA, JSO, HGS, and EHO optimization techniques is exposed in Figure 7. The examination is carried out throughout a range of 0 to 50 iterations. When compared to the MHHO [37], IBPSO [2], BWO, COA, JSO, HGS, WORA [29], SMO [12], and EHO schemes, the CI-BWO model has attained the lowest cost values for every iteration. Looking at the graph, it appears that the generated model’s cost function reached a minimal cost value between the 40th and 50th iterations, in comparison to other models. In this case, during the 40th to 50th iterations, HGS has achieved greater cost values over MHHO [37], IBPSO [2], BWO, COA, JSO and EHO. A lower cost of 125 was achieved by the CI-BWO, compared to MHHO [37], IBPSO [2], BWO, COA, JSO, HGS, WORA [29], SMO [12], and EHO. Hence, the overall valuation shows the impact of the established CI-BWO model on better RA in fog computing.

Fig. 7.

Convergence analysis of CI-BWO over varied existing models.

Table 6

Friedman test and Wilcoxon test.

Methods	p value
Friedman test
BWO	0.0657669
COA	0.0573879
WORA [29]	0.0459985
SMO [12]	0.0374898
JSO	0.0428979
HGS	0.0348787
EHO	0.0482784
MHHO [37]	0.057298
IBPSO [2]	0.0478779
CI-BWO	0.0732989
Wilcoxon test
BWO	0.043909
COA	0.0390479
WORA [29]	0.032089
SMO [12]	0.040376
JSO	0.0472989
HGS	0.037498
EHO	0.0468279
MHHO [37]	0.036479
IBPSO [2]	0.050399
CI-BWO	0.0265768

6.6. Friedman and Wilcoxon test

Table 6 describes the analysis of the Friedman test and Wilcoxon test for the proposed CI-BWO model over conventional algorithms. The Friedman test is a non-parametric test used to determine if there are statistically significant differences between multiple related groups. CI-BWO’s p-value (0.0732989) is marginally higher than 0.05, suggesting better performance against the null hypothesis compared to other methods like MHHO [37], IBPSO [2], BWO, COA, JSO, HGS, WORA [29], SMO [12], and EHO schemes. The Wilcoxon signed-rank test is another non-parametric test used to compare paired data (in this case, CI-BWO against each of the other methods like MHHO [37], IBPSO [2], BWO, COA, JSO, HGS, WORA [29], SMO [12], and EHO schemes). It assesses whether the difference in performance between the two methods is consistent across all pairs. CI-BWO has p-values ranging from 0.0265768 to 0.050399 in the Wilcoxon test against different methods such as MHHO [37], IBPSO [2], BWO, COA, JSO, HGS, WORA [29], SMO [12], and EHO schemes. Both tests together suggest that CI-BWO has shown varying performance compared to existing methods in fog computing resource prioritization and allocation.

6.7. Practical applications

The research on resource prioritization and allocation in fog computing using hybrid optimization has numerous practical applications across various domains and industries. Fog computing can prioritize resources in healthcare settings to ensure timely delivery of critical patient monitoring data, optimize the allocation of computing resources for medical imaging processing, and support telemedicine applications with low-latency communication. In industrial IoT (IIoT) environments, fog computing can optimize resource allocation for predictive maintenance tasks, manage real-time data analytics for quality control in manufacturing processes, and enhance overall operational efficiency by prioritizing resource-intensive tasks. Fog computing can prioritize resources for real-time traffic management systems, optimize fleet management operations by allocating resources for route optimization and vehicle tracking, and improve logistics operations with efficient inventory management and supply chain monitoring. In disaster management scenarios, fog computing can prioritize resources for emergency response systems, enabling real-time data collection, analysis, and coordination among responders to improve decision-making and rescue operations efficiency. Fog computing can optimize resource allocation in precision agriculture applications by analyzing sensor data from farms, optimizing irrigation schedules based on soil moisture levels, and facilitating precision pest management strategies. These practical applications demonstrate the versatility and impact of resource prioritization and allocation in fog computing using hybrid optimization techniques across diverse sectors, enhancing operational efficiency, real-time decision-making capabilities, and overall user experience in decentralized computing environments.

7. Conclusion and future directions

The proposed work focused on RA in fog computing, which was done by demonstrating a non-linear function. An objective function was incorporated that considered parameters like resource utilization, service response rate, makespan, migration cost and communication cost. Moreover, the suggested work on RA focused on allocating the resources in crucial scenarios, which enabled for quicker distribution of resources. Here, a strategy named CI-BWO was introduced, which aided in the optimal allocation of resources in fog computing. From analysis, when the task count was 50, the makespan of developed CI-BWO was less when compared to existing MHHO, IBPSO, BWO, COA, JSO, HGS, EHO, WORA and SMO methods. When the task count is 200, the developed CI-BWO attained less migration cost of around 1.287, while, MHHO, IBPSO, BWO, COA, JSO, HGS and EHO, WORA and SMO models attained higher migration cost of about 3.2672, 3.8561, 4.2879,1.999, 2.478, 5.2989, 3.809, 1.587 and 4.878 respectively. Moreover, a less cost of 46.4715 is achieved by CI-BWO for the SD case, while, the cost attained using MHHO, IBPSO, BWO, COA, JSO, HGS and EHO are high at 47.32, 48.63, 47.9431, 49.91, 50.6877, 48.3224 and 47.9241.The advantages of resource prioritization and allocation in fog computing using hybrid optimization lie in its ability to optimize resource usage, enhance performance, reduce costs, support diverse applications, and adapt to dynamic operational conditions. Fog computing can optimize resource allocation for environmental monitoring systems, such as air quality monitoring stations, by analyzing sensor data, predicting pollution patterns, and facilitating timely interventions for pollution control. These benefits collectively contribute to making fog computing systems more efficient, resilient, and capable of meeting the demands of modern decentralized computing environments. However, this work does not address alternative metrics such as security, scalability, node stability, and reliability of task completion. Additionally, it lacks adequate focus on the heterogeneity of devices in fog computing environments. In future, this work will be integrating energy-aware optimization strategies into hybrid algorithms to minimize energy consumption in fog computing environments. This is crucial for sustainability and cost-effectiveness, especially in IoT deployments where devices may have limited energy resources. Additionally, it will explore adaptive SLA metrics that can dynamically adjust based on workload variations, network congestion, and user demand fluctuations and develop more sophisticated models to accurately predict resource dissipation across different fog nodes and devices.

Footnotes

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CI-BWO parameter, ϑ	1.5
BWO parameter, ϑ	1.5
EHO parameters
ϑ	0.5
β	0.5
$n - c l a n$	5
HGS parameters
A	5
Speed	1
$T 1$	3
e	4
$L H$	10000
L	0.5
JSO parameters
a	4
SMO parameters
Members	10
$p r$	0.1
Global Limit Count	0
WOA parameters
b	1
p	0.5

Resource prioritization and allocation in fog computing using hybrid optimization

Abstract

Keywords

1. Introduction

2.1. Related works

2.2. Review

3. Novel strategy for resource allocation in fog computing

4. Resource prioritization

4.1. Prioritization

Table 1 Prioritization of diverse services. Type Size Priority Deadline Climate type Lower 4 Higher Entertaining Higher 3 Higher Road security Medium 2 Shorter Medical Higher 1 Shorter

5.1. Muti-constraints

6.1. Simulation procedure

Table 3 Parameter of the optimization algorithms. CI-BWO parameter, ϑ 1.5 BWO parameter, ϑ 1.5 EHO parameters ϑ 0.5 β 0.5 n − c l a n 5 HGS parameters A 5 Speed 1 T 1 3 e 4 L H 10000 L 0.5 JSO parameters a 4 SMO parameters Members 10 p r 0.1 Global Limit Count 0 WOA parameters b 1 p 0.5

Table 5 Computation time analysis on optimal RA in fog computing. Methods Time (sec) BWO 0.203379 COA 0.129898 WORA [29] 0.188293 SMO [12] 0.07951 JSO 0.092878 HGS 0.177313 EHO 0.108768 MHHO [37] 0.10732 IBPSO [2] 0.10525 CI-BWO 0.065325

6.7. Practical applications

7. Conclusion and future directions

Footnotes

Nomenclature

References

Table 1
Prioritization of diverse services.

Type Size Priority Deadline

Climate type Lower 4 Higher

Entertaining Higher 3 Higher

Road security Medium 2 Shorter

Medical Higher 1 Shorter

Table 5
Computation time analysis on optimal RA in fog computing.

Methods Time (sec)

BWO 0.203379

COA 0.129898

WORA [29] 0.188293

SMO [12] 0.07951

JSO 0.092878

HGS 0.177313

EHO 0.108768

MHHO [37] 0.10732

IBPSO [2] 0.10525

CI-BWO 0.065325