A Hybrid Many-Objective Optimization Algorithm for Job Scheduling in Cloud Computing Based on Merge-and-Split Theory

Abstract

Scheduling jobs within a cloud environment is a critical area of research that necessitates meticulous analysis. It entails the challenge of optimally assigning jobs to various cloud servers, each with different capabilities, and is classified as a non-deterministic polynomial (NP) problem. Many conventional methods have been suggested to tackle this difficulty, but they often struggle to find nearly perfect solutions within a reasonable timeframe. As a result, researchers have turned to evolutionary algorithms to tackle this problem. However, relying on a single metaheuristic approach can be problematic as it may become trapped in local optima, resulting in slow convergence. Therefore, combining different metaheuristic strategies to improve the overall system enactment is essential. This paper presents a novel approach that integrates three methods to enhance exploration and exploitation, increasing search process efficiency and optimizing many-objective functions. In the initial phase, we adopt cooperative game theory with merge-and-split techniques to train computing hosts at different utilization load levels, determining the ideal utilization for each server. This approach ensures that servers operate at their highest utilization range, maximizing their profitability. In the second stage, we incorporate the mean variation of the grey wolf optimization algorithm, making significant adjustments to the encircling and hunting phases to enhance the exploitation of the search space. In the final phase, we introduce an innovative pollination operator inspired by the sunflower optimization algorithm to enrich the exploration of the search domain. By skillfully balancing exploration and exploitation, we effectively address many-objective optimization problems. To validate the performance of our proposed method, we conducted experiments using both real-world and synthesized datasets, employing CloudSim software version 5.0. The evaluation involved two sets of experiments to measure different evaluation metrics. In the first experiment, we focused on minimizing factors such as energy costs, completion time, latency, and SLA violations. The second experiment, in contrast, aimed at maximizing metrics such as service quality, bandwidth utilization, asset utilization ratio, and service provider outcomes. The results from these experiments unequivocally demonstrate the outstanding performance of our algorithm, surpassing existing state-of-the-art approaches.

1. Introduction

Cloud computing provides users convenient Internet access to software, storage, networks, and databases as needed [1,2,3]. Scheduling user jobs in cloud computing poses a challenge, as effective job scheduling aims to minimize scheduling latency and maximize bandwidth utilization while also preventing network congestion and avoiding single points of resource failure resulting from overload situations [4]. One of the most challenging aspects in this context involves directing jobs to appropriate destinations, which can lead to resource fragmentation and overcrowding. To address this issue, the optimal pairing of jobs and hosts, known as the job–host combination (JHC), presents a straightforward solution [5].

Recently, researchers have been focusing on the challenge of efficiently scheduling jobs in response to frequent user requests directed at the CCS. Users submit their requests with specific requirements, and the CCS’s responsibility is to match these requests with suitable computing machine architectures, considering the availability and capabilities of resources. The CCS then uses a job scheduling algorithm to distribute the incoming jobs among virtual machines (VMs). However, the problem arises when the number of requests increases significantly due to the exponential growth of active processing servers. This leads to the creation of additional resource fragments. As job scheduling problems fall within the non-deterministic polynomial (NP) category [6,7,8], several efficient methods have been suggested to attain optimal or near-optimal solutions. This is essential since conventional techniques, such as SJF, FCFS, and RR, are not effective in solving NP-hard optimization problems.

Game theory techniques that excel in job allocation on cloud hosts, ensuring fair distribution, have been uncovered. These approaches are known for their low time complexity compared to alternative heuristics [9], making them efficient in selecting appropriate destination hosts. Considerable efforts have been devoted to categorizing these hosts based on their capabilities, a crucial aspect in task scheduling management using game theoretical methods. This involves grouping them into clusters, each characterized by specific parameters, such as extensive use of CPU, memory, or I/O. In recent times, researchers have introduced swarm intelligence optimization algorithms, like ant colonies [10], bat algorithms [11], and sparrow search [12], to achieve workload balancing across virtual machines (VMs) by efficiently assigning tasks to appropriate VMs. However, some of these cutting-edge metaheuristic approaches encounter difficulties such as slow convergence [13,14,15,16]. Consequently, grey wolf and sunflower optimization algorithms have garnered increased interest from scholars due to their superior optimization performance compared to other swarm intelligence optimization algorithms.

1.1. Research Motivation and Objectives

Cloud computing facilitates the distant execution of various applications, catering to a diverse range of clients. These applications cover a broad spectrum of fields, including IoE, data science analytics, and biomedical. As an example, data center traffic surged from 6 ZB to approximately 20 ZB between 2016 and 2021 [17,18]. The recent COVID-19 pandemic has also led to a significant surge in the utilization of cloud-based healthcare applications. These applications encompass various functions such as patient health monitoring, bill payment, online patient oxygen level data collection, access to patients’ historical medical records, and more [19]. As a result, data centers are scaling up and increasing in size to meet the escalating demands of user-oriented requests. This expansion has caused a substantial increase in resource fragmentation, exacerbating challenges related to scheduling latency, data loss, and the consumption of energy and carbon emissions.

According to a recent study, cloud data centers rank among the highest energy consumers globally. They are projected to contribute around four and a half percent of global energy expenses by 2025. Moreover, energy expenditures of these centers are expected to double roughly every five years [20,21]. The study suggests that by 2025, cloud data centers could be responsible for nearly three and a half percent of global CO${}_2$, equal to approximately 100 Mmt of CO${}_2$ decay annually [21]. Therefore, it is imperative to tackle the continuously increasing problem of user requests.

The scheduling of user jobs must adhere to specific constraints, including latency, completion time, SLA violations, energy consumption, service quality, asset utilization ratio, bandwidth utilization, and service provider considerations. Thus, there is a pressing need for a many-objective task scheduling approach that effectively balances the tradeoffs among the mentioned objectives.

This research paper introduces a novel hybrid many-objective optimization algorithm, named SGWO, for job scheduling. In the past, various approaches have been explored to address the task scheduling problem, including queuing theory, heuristic methods, game theory techniques, and metaheuristic solutions. However, queuing and heuristic models often fell short in achieving global optimum results, particularly for more complex scheduling problems [21,22,23]. On the other hand, metaheuristics and game theory have demonstrated effective placement solutions in polynomial time [24,25]. Significantly, GWO and SFO are indisputably superior swarm-intelligence-based metaheuristic approaches that have exhibited outstanding performance in addressing diverse optimization challenges across various domains, such as vehicular sensor networks, data sciences, mechanical engineering, and academia [26,27,28]. However, despite their competitive solutions, both GWO and SFO struggle to maintain robust exploration and exploitation and may get stuck in local optima, impacting the quality of scheduling solutions. According to the findings of [22], no single metaheuristic approach can universally manage all types of optimization concerns. These considerations and shortcomings serve as strong motivations for this research, leading to the proposal of a hybrid optimization scheduling approach. This approach aims to overcome the limitations of standard GWO and SFO by making significant adjustments to the encircling and hunting phases of GWO to enhance search space exploitation. Additionally, a novel pollination operation based on SFO is introduced to improve exploration.

1.2. Research Highlights

The challenges mentioned earlier have compelled us to carry out this research. Our proposed solution has the following main objectives:

• To prevent job overloading by employing resource monitoring to distribute jobs across virtual machines evenly. This approach aids in predicting the cloud resource load, facilitating improved task placement and reduced scheduling latency.
• To avoid resource fragmentation, the merge-and-split theory is employed to train hosts at their optimal utilization loads and determine the most efficient destination for tasks. This ensures efficient resource allocation and utilization.
• To improve the precision of the search space and avoid being confined to a local best solution, enhanced versions of the GWO and SFO algorithms are utilized. These improved algorithms, based on the behavior of grey wolves and sunflowers, yield more effective solutions.

1.3. Research Contributions

The primary contributions of this research can be summarized as follows:

• We utilize the merge-and-split theory to establish the performance-SLA tradeoff of hosts. Our approach involves rigorous training of hosts at diverse utilization tiers, spanning from 0% to 100%. The ultimate goal is to effectively distinguish between hosts capable of meeting the tradeoff and those with low-performance utilization.
• The mean variation in the GWO paradigm is enhanced by integrating the SGWO model to improve the formulation model for encircling and hunting, as well as the exploitation of the search space.
• The SGWO approach incorporates a novel pollination operator from the enhanced sunflower optimization technique. This integration achieves a balanced tradeoff between the exploration and exploitation phases, leading to improved scheduling solutions of higher quality.
• For performance evaluation, distinct datasets are chosen as the workloads. Thorough experiments are carried out, wherein the simulation results of the proposed SGWO are compared with those of state-of-the-art mapping paradigms. The findings and observations undeniably establish the superiority of SGWO over the baseline algorithms.

1.4. Research Outline

The remaining parts of this work are arranged as follows: Section 2 provides an overview of the traditional differential evolution method. Section 3 presents the framework of the SGWO system. Section 4 outlines the formulation of the many-objective functions. Section 5 elaborates on the steps utilized in the proposed algorithm. Section 6 presents the experimental results and a performance comparison. Finally, Section 7 offers the conclusions and observations of the study, along with potential avenues for future research.

2. Literature Survey

Mishra et al. [29] introduced a load balance workload scheme to distribute incoming tasks evenly among cloud machines. Their system’s design was uplifted by the collective conduct of a flock of birds and incorporated the binary variant of the BSO-LB approach. In their approach, jobs were represented as birds, while VMs were likened to food particles. The tasks were considered distinct and not subject to interruption. To validate the efficacy of their proposed solution, they conducted experiments on the GoCJ dataset from Google. During the evaluation, their approach was compared against MAX-MIN, RASA, Improved PSO, FCFS, SJF, and RR algorithms.

Junaid et al. [30] presented a methodology for workload classification by employing a support vector machine. Their classification process relied on file type formatting, encompassing various multimedia file formats. To enhance load balancing, they devised an innovative hybrid approach that combined ACO with FTF. According to their research, this hybrid paradigm outperformed other comparable methods, such as ACOPS, CPSO, QMPSO, CSO, and D-ACOELB. Their approach is superior, as demonstrated by consistently outperforming others based on critical evaluation metrics. These metrics include QoS, transfer time, provider profit, and optimization time.

Abdel-Basset et al. [3] introduced a novel task scheduler called HDE with the aim of tackling the issue of job mapping in cloud environments. They introduced two enhancements in their solution. They began by adjusting the scaling factor to balance exploring new and exploiting existing options. They accomplished this by dynamically incorporating numerical values based on the current iteration. Furthermore, they improved the exploitation operator of differential evolution to produce more favorable outcomes during periodic iterations. They created random datasets to gauge their system’s effectiveness and rigorously compared their algorithm to SMA, EO, SCA, WOA, RR, and SJF. The outcome indicated that HDE outperformed the others in terms of makespan.

Mangalampalli et al. [31] developed a nature-inspired multi-objective job placement method employing the GWO algorithm. Their primary goal was to dynamically make job dispatching decisions considering the current state of cloud resources and future workload demands. Furthermore, their proposed approach considered users’ budget constraints and task priorities while allocating resources. The algorithm’s performance was assessed using four datasets named da01, da02, da03, and da04. The results revealed that the MOTSGWO algorithm surpassed other evaluated performance metrics in terms of effectiveness.

Pirozmand et al. [32] proposed a paradigm that employed an improved PSO model to tackle task dispatching challenges in cloud environments. To reduce the execution time compared to the conventional PSO, they incorporated a multi-adaptive learning technique. In the initial population stage, they introduced two types of particles: regular particles and locally best particles. This step aimed to enhance the population’s diversity and increase the likelihood of achieving the local optimum. Compared to similar algorithms, their approach demonstrated superior optimization of evaluation metrics, including processing time, fair distribution, and productivity.

Chandrashekar and Krishnadoss [33] introduced the opposition-based sunflower optimization (OSFO) algorithm as a means to enhance the service provider throughput of task schedulers in cloud computing environments. The algorithm aimed to optimize operational costs, energy consumption, and makespan while allocating tasks.

Essam H et al. [34] focused on the concept of cloud job dispatching and conducted an investigation that encompassed various swarm evolutionary and hybrid meta-heuristic scheduling techniques. The authors recognized that task scheduling, particularly job mapping, is a challenging optimization problem known as NP-hard. To address this, they extensively reviewed the relevant literature and aimed to overcome the limitations of existing techniques by developing novel scheduling approaches that would enhance system productivity.

Wanneng et al. [35] introduced a robust agile response job mapping optimization technique. The study aimed to enhance cloud service center energy efficiency and scheduling speed. Agile response optimization methods were used to achieve this goal. The researchers analyzed the probability density function of job requests. They implemented a timeout mechanism to prevent network congestion due to job failures—the proposed solution aimed to ensure scheduling stability and effectiveness.

K. Devi et al. [36] developed a robust security model that utilizes deep learning techniques to allocate tasks to reliable cloud resources. This model’s core objectives were to thwart resource exhaustion and ensure all resource users were treated equitably. The proposed algorithm’s efficacy was measured using various metrics, including running process time, functioning expenses, and memory usage. The algorithm’s performance was compared to the RR and WRR algorithms.

Saravanan et al. [37] introduced an enhanced paradigm for scheduling efficiency, utilizing the wild horse optimization (WHO) algorithm to address challenges related to task scheduling duration, operation expenditures, and virtual machine overloading. The paradigm begins by constructing a job mapping and distribution model, optimizing various constraints such as time, cost, and virtual machines. Subsequently, the proposed solution incorporates a weighting strategy to enhance the whale optimization algorithms, thereby improving the local search capability and preventing premature convergence. Moreover, the algorithm combines the WHO algorithm with the LF to further enhance the effectiveness of task scheduling.

Jena et al. [38] introduced a hybrid approach for achieving a balanced distribution of cloud resources. Their method utilizes an enhanced Q-learning technique alongside improved PSO to dynamically balance workloads among virtual machines. Through this approach, the algorithm effectively enhances the throughput of virtual machines (VMs) and optimizes task prioritization by adjusting task waiting times. The algorithm’s efficiency was put to the test through rigorous evaluations using both simulated scenarios and actual implementation on a real platform. The results demonstrate that their algorithm outperforms competitors, showcasing its superiority in resource management and task allocation.

Kumar et al. [39] introduced a novel approach for task mapping on virtual machines using the standard PSO algorithm. The main objective of this algorithm was to minimize the overall costs associated with task placement. The proposed PSO algorithm underwent assessment using various metric measurements through the CloudSim simulator to evaluate its performance. The proposed PSO algorithm was compared against existing scheduling methods, such as FCFS and round robin, to demonstrate its effectiveness. The aim was to highlight the superiority of the new approach over these conventional methods. Additionally, the PSO model was pitted against the Min–Min scheduling technique to examine the outcomes of simulated scientific workflows. The results indicated that the PSO method exhibited remarkable performance, particularly when compared to similar algorithms, by effectively optimizing the task completion time and reducing operational expenses.

Yuan et al. [40] introduced a unique crossover operator called “two-part chromosome crossover” in their study to tackle the MTSP using GA for optimal outcomes. The approach employs a dual chromosome expression technique to reduce the search space and enhance overall solution quality by incorporating TCX. Compared to three other crossover methods, the proposed algorithm outperformed them by achieving superior results in minimizing the total travel distance and length of the most extended tours. The study’s findings conclusively demonstrate the effectiveness of this approach in significantly improving solution quality.

Table 1. A synopsis of the papers applied to the topic.

Ref.	Evaluation Measurements				Algorithms	Limitations
	Latency Time	SLA Missing	AUR Weights	Bandwidth Usage
[29]	✗	✓	✗	✗	Bird swarm optimization for load balancing (BSO-LB)	Slow convergence rate Increase iteration number
[30]	✗	✓	✗	✓	Hybrid model for load balance (HMLB) in cloud	Higher execution time System scalability Latency problem
[3]	✗	✗	✗	✓	Hybrid differential evolution (HDE)	Lack of data security during placement Increased latency Resource utilization deficiency
[31]	✗	✓	✗	✗	Multi-objective task scheduling grey wolf optimization (MOTSGWO)	High resource fragments High overhead consumption among VMs
[32]	✗	✓	✗	✓	Improved particle swarm optimization (IPSO)	Task failure arising from neglecting the characteristics of the tasks High scheduling latency
[33]	✓	✓	✗	✗	Opposition-based sunflower optimization (OSFO)	Lack of bandwidth utilization consideration Revoke AUR constraints Throughput affected by various task scheduling
[34]	✓	✗	✗	✓	Hybrid angles-based multi-objective algorithm approach	Lack of task deadline increased failure rate SLA violation and high processing time Throughput affected by various task scheduling
[35]	✗	✓	✗	✗	A strong agile response task model optimization algorithm	High latency overhead due to lack of region aware Lack of resource destination failure
[36]	✗	✓	✗	✓	A security model utilizing deep learning techniques to map jobs in cloud platforms	Asset utilization ratio is not considered High latency due to overloading
[37]	✓	✓	✗	✓	Improved wild horse optimization (IWHO) algorithm	Seeking optimal task-VM combination pairs is difficult High iteration numbers
[38]	✓	✓	✗	✓	Q-learning with modified particle swarm optimization (QMPSO)	High convergence speed High computation and latency High SLA violations and execution processing time
[39]	✓	✓	✗	✗	Particle swarm optimization (PSO) algorithm	High bandwidth fragments Discovering optimal task-VM pair is difficult High searching process time
[40]	✗	✓	✗	✗	Genetic model algorithm for optimal and efficient outcomes	Viewing the minimum parameter numbers Selecting optimal resource is difficult High latency overhead
Our	✓	✓	✓	✓	Merge-and-split theory, SFO, and GWO algorithms	The evaluation metrics are assessed using CPU-intensive tasks

presents an overview of the relevant research covered within this paper.

3. The SGWO Framework

The main goal of the SGWO paradigm is to attain the best possible job scheduling outcome by integrating three distinct methodologies. This section commences with an introduction to the system’s design. Following this, we elucidate the evaluation criteria, the problem at hand, and the objective function. Lastly, we offer a comprehensive account of how each individual method influences job scheduling in its own capacity.

3.1. System Architecture

The SGWO is structured with the following layers in its system architecture, as shown in Figure 1.

• Cloud Users (Step 1): Jobs are being submitted to the cloud by users located in different geographical regions.
• Workload Assessment (Step 2): The workloads, which refer to independent jobs, are assessed based on their deadlines, requirements, and architecture.
• Central Cloud Scheduler (Step 3): The CCS serves as a crucial intermediary between users and the underlying cloud platform. It fulfills several important responsibilities, such as initiating negotiation sessions between users and providers, imposing penalties for user violations, and making decisions regarding the acceptance or rejection of assigned jobs based on resource availability and stability. Additionally, it utilizes metaheuristic algorithms to attain harmony between exploring and exploiting the search space domain, ultimately finding the most profitable destination, among other tasks. Within this layer, various evaluation metrics such as energy consumption, completion time, SLA violations, latency, bandwidth utilization, service quality, service provider profit, and asset utilization ratio are enhanced. To improve the search efficiency for optimal resource destinations, this involves collaborative efforts among the mean variation in GWO, improved SFOA, and the application of merge-and-split-based cooperative game theory.
• Cloud Data Center (Step 4): Within this layer, a set of resilient processing servers is implemented, where each server has the capability to host a particular group of virtual machine instance types, subject to specific constraints.

3.2. Mathematical Formulation

This subsection establishes the evaluation metrics within a mathematical context, serving as the foundation for the proposed SGWO strategy.

3.2.1. Energy Expenditure Model

Instead of concentrating on a particular utilization level, this model takes into account the server’s desired utilization range. As a result, it evaluates the power consumption of a server across different utilization loads [41].

$${\mathcal{P}}_j\left(u\right)=\xi \times {\mathcal{P}}_j^{mx}+(1-\xi ){\mathcal{P}}_j^{mn}\times u$$

(1)

The symbols ${\mathcal{P}}_j^{mn}$ and ${\mathcal{P}}_j^{mx}$ unequivocally represent the power consumption of a host server when it is inactive and active, respectively. The variable u represents the server utilization. By utilizing the power model, we can define the energy cost in the following manner. In order to obtain the complete energy consumption of all the servers in a data center, it is imperative to assess Equation (3).

$$E_j={\int }_{\tau }^{\Delta \tau }{\mathcal{P}}_j\left(u\right)dt$$

(2)

$$E^{ToT}=\sum _{i=1}^{\mathcal{K}}{E}_j$$

(3)

3.2.2. Service Provider Profit

The provider is highly motivated to maximize this metric since it signifies an improved equilibrium between the service charge and operational costs. The formula for calculating this metric is outlined as follows [42].

$$\mathcal{S}pro={\alpha }_{\mathcal{K}}\times \sum _{i=1}^n\sum _{j=1}^m\left(\frac{{\displaystyle \sum _{i=1}^m}\xi \times \zeta (.)}{{\mathcal{P}}_j\left(u\right)}\right)-{\beta }_{\mathcal{K}}$$

(4)

where ${\alpha }_{\mathcal{K}}$ corresponds to the operational cost of servers denoted by $\mathcal{K}$, and ${\beta }_{\mathcal{K}}$ represents the electricity cost measured in kilowatts per hour for server ${\mathcal{S}}_j$.

3.2.3. Asset Utilization Ratio

This metric quantifies the resource utilization efficiency for completed jobs. The calculation is achieved by dividing the total cost, which accounts for the overhead time during startup, idle periods, and shutdown, by the actual processing fee.

$$AUR=\frac{{\mathcal{P}}_j\left(u\right)\times \left[\tau {\mathcal{O}}_j\right]}{{\mathcal{P}}_j\left(u\right)\times \left[\tau {\mathcal{O}}_j+{\displaystyle \sum _{i=1}^m}\xi \times \zeta (.)\right]}\times 100\%$$

(5)

where $\tau {\mathcal{O}}_j=({\tau }_s+{\tau }_i+{\tau }_e$), ${\tau }_s$ is the initiate time of VM, ${\tau }_i$ is the idle and suspend time when two adjacent VMs are allocated, and ${\tau }_e$ represents the reduced time of the virtual machine, while $\xi$ and $\zeta (.)$ denote the combined size of the input data for task $m_i$. Here, $\zeta (.)$ is a normalization function that accounts for the complexity of the input data size.

3.2.4. VM Length Time

This metric refers to the overall duration required for a VM to complete its tasks, covering both the execution and completion of the assigned operations.

$$\mathcal{L}oT=\sum _{i=1}^v\frac{\mathcal{L}(\xi \times \zeta (.\left)\right)}{{\mathcal{P}}_j\left(v{m}_i\right)\times mips\left(v{m}_i\right)}$$

(6)

Here, v represents the combined count of virtual machines and allocated jobs that are capable of being executed.

3.2.5. Quality of Service of Scheduled Tasks

To compute this metric, the process involves comparing the number of tasks that fulfill the QoS requirements with the total number of planned tasks, thereby determining the percentage. This metric’s increased value signifies greater efficiency in the task mapping model [43].

$$\mathcal{Q}o\mathcal{S}=\left(\frac{{\tau }_j}{\mathcal{Y}}\right)\times 100\%,\mathrm{S}.\mathrm{t}.d\left({\tau }_j\right)<d\left(ToT\right)$$

(7)

In the given context, ${\tau }_j$ represents the task that has been assigned; $\mathcal{Y}$ signifies the total accumulated tasks in the queue; $d\left({\tau }_j\right)$ denotes the specific deadline allocated to the task, ${\tau }_j$; and $d\left(ToT\right)$ refers to the collective deadlines permitted for all tasks.

3.2.6. Latency Overhead

This metric pertains to the extra time taken by a job to complete its execution, impacting both the SLA and the proposed SGWO model. In simpler terms, it signifies the disparity between a job’s anticipated and actual completion time. The calculation for this metric is as follows.

$$\mathcal{L}a=d\left({\tau }_i\right)-\left({\xi }_i\times {\zeta }_i(.)\right)$$

(8)

3.2.7. Bandwidth Utilization

This metric assesses the assigned bandwidth throughout the job scheduling and allocation process. It quantifies the variance between the overall aggregated bandwidth and the remaining bandwidth, calculated in the following manner.

$$\mathcal{B}and=((\mathcal{B}an{d}^{ToT}-\mathcal{B}an{d}_{j,v}^i)\times \mathcal{D}{e}_{j,v}^i)$$

(9)

3.3. Using Merge-and-Split Theory to Train Hosts

During this phase, we conduct training on computing hosts at various utilization levels in order to determine the desired (i.e., preferred) utilization. The preferred utilization refers to the rate at which hosts perform most efficiently, taking into account related constraints. Subsequently, we split and merge the preferred utilization levels from each host, forming a consolidated and effective dataset called optimal utilization. Once we have the preferred utilization collation, we can select the preferred utilization for each individual host. To ensure that hosts operate at their highest efficiency and achieve a greater utilization rate, we specifically focus on splitting the utilization levels with higher asset utilization ratios (AURs) to form an effective collation. This approach guarantees that hosts work at their best utilization, thereby maximizing the overall utilization rate. The range of optimal utilization can be represented as [$\varpi ,\varpi +\psi$], with $\psi$ indicating the predefined range of utilization. The value of $\varpi$ can be calculated using the following method [44].

$$\varpi =argmax{\int }_{\alpha }^{\alpha +1}{f}_{\mathcal{PU}}^{\mathcal{U}}du,\mathrm{S}.\mathrm{t}.0\le \varpi \le \varpi +1\le 1$$

(10)

The function model, $f_{\mathcal{PU}}^{\mathcal{U}}$, represents the optimal utilization derived from the preferred utilization, where $\mathcal{U}$ is a value ranging from 0 to 1.

Illustrative Scenario

Figure 2 provides an illustrative example to demonstrate the functioning of the merge-and-split-based procedure. Let us suppose we have a cloud network comprising three servers: the alpha server, the beta server, and the delta server. During this process, it is imperative that hosts are trained to operate at various utilization levels spanning from 0% to 100%. The ultimate objective is pinpointing the utilization rank resulting in each server’s highest average utilization rate (AUR).

Based on Figure 2, we can observe that the alpha server exhibits preferred utilization at 40%, 60%, and 80%. The beta server, on the other hand, demonstrates preferred utilization at 30% and 50%. Lastly, the delta server shows preferred utilization at 20%, 30%, 70%, and 90%. To begin, we employ a split-based collational game theory to separate the preferred utilization values from the non-preferred ones for each server. This ensures that we focus on the most efficient utilization levels.

Following the split-based procedure, we create a collection called the preferred utilization group. Next, we utilize a merge-based cooperative game theory to combine the highest utilization values within the preferred utilization collection. This process results in the formation of the final effective collection known as the optimal group. The virtual machines are then assigned tasks based on the utilization values within the optimal group.

In our scenario, the optimal group comprises the following utilization levels: 60%, 80%, 50%, 30%, 70%, and 90%. These utilization values have been identified as the most efficient for operating virtual machines and executing assigned tasks.

3.4. Using Mean Variation in GWO to Improve Exploitation

Our proposed solution aims to reduce the extent of search domain exploitation as one of its essential goals. To achieve this, we have employed the mean variation in the grey wolf optimization technique proposed by [45]. The adjustments to both the encircling and hunting phases are made based on the model presented in [45]. In these adjustments, the primary reliance is on the coefficient vectors parameter to emphasize exploitation. These changes allow our algorithm to effectively search both local and global domains, enabling it to explore the most suitable combinations of tasks and destinations.

3.4.1. Encircling the Bait

During this particular phase, the hunting process relies on the positions denoted as $\alpha$, $\beta$, and $\gamma$ [45]. To enhance the effectiveness of the bait, we have included the following improved equations, which are used in the computation [46].

$$\overrightarrow{\mathcal{D}}=|\overrightarrow{\mathcal{Q}}\times {\overrightarrow{\xi }}_{\mathcal{K}}\left(\tau \right)-\theta \times \left[\overrightarrow{\xi }\left(\tau \right)\right]|$$

(11)

$$\overrightarrow{\xi }(\tau +1)=\overrightarrow{{\xi }_{\mathcal{K}}}\left(\tau \right)-\overrightarrow{\mathcal{V}}\times \overrightarrow{\mathcal{L}}$$

(12)

The notation $\tau$ and $\tau +1$ are used to represent the current and upcoming iterations, respectively. The vectors $\overrightarrow{\mathcal{V}}$ and $\overrightarrow{\mathcal{L}}$ represent coefficients, while $\xi$ represents the location vector of a grey wolf, and ${\overrightarrow{\xi }}_{\mathcal{K}}$ represents the location vector of the prey. The vectors $\overrightarrow{\mathcal{V}}$ and $\overrightarrow{\mathcal{Q}}$ are represented as follows.

$$\overrightarrow{\mathcal{V}}=2\overrightarrow{\alpha }\times {\overrightarrow{\beta }}_1-\overrightarrow{\alpha }$$

(13)

$$\overrightarrow{\mathcal{Q}}=2\times {\overrightarrow{\beta }}_2$$

(14)

During the iterations, the values of the vector $\overrightarrow{\alpha }$ are gradually reduced from 2 to 0 in a linear fashion. The vectors ${\overrightarrow{\beta }}_1$ and ${\overrightarrow{\beta }}_2$ are random and have values within the range of 0 to 1.

3.4.2. Hunting the Bait

In this phase, the most influential wolf is denoted as $\alpha$ as it consistently achieves successful hunts. Nevertheless, the wolves denoted as $\beta$ and $\gamma$ also contribute to the hunting process. It is crucial for all wolves to be aware of the position of the prey. Once they initially locate the bait, their starting positions are recorded. Subsequently, their positions are updated using information from other search agents. The improved equations for this process are provided below [46].

$$\overrightarrow{{\mathcal{D}}_{\alpha }}=|\overrightarrow{{\mathcal{Q}}_1}\times {\overrightarrow{\xi }}_{\alpha }-\theta \times \left[\overrightarrow{\xi }\left(\tau \right)\right]|$$

(15)

$$\overrightarrow{{\mathcal{D}}_{\beta }}=|\overrightarrow{{\mathcal{Q}}_2}\times {\overrightarrow{\xi }}_{\beta }-\theta \times \left[\overrightarrow{\xi }\left(\tau \right)\right]|$$

(16)

$$\overrightarrow{{\mathcal{D}}_{\delta }}=|\overrightarrow{{\mathcal{Q}}_3}\times {\overrightarrow{\xi }}_{\delta }-\theta \times \left[\overrightarrow{\xi }\left(\tau \right)\right]|$$

(17)

$${\overrightarrow{\xi }}_1={\overrightarrow{\xi }}_{\alpha }-{\overrightarrow{\mathcal{V}}}_1\times \left({\overrightarrow{\mathcal{D}}}_{\alpha }\right)$$

(18)

$${\overrightarrow{\xi }}_2={\overrightarrow{\xi }}_{\beta }-{\overrightarrow{\mathcal{V}}}_2\times \left({\overrightarrow{\mathcal{D}}}_{\beta }\right)$$

(19)

$${\overrightarrow{\xi }}_3={\overrightarrow{\xi }}_{\delta }-{\overrightarrow{\mathcal{V}}}_3\times \left({\overrightarrow{\mathcal{D}}}_{\delta }\right)$$

(20)

$$\overrightarrow{\xi }(\tau +1)=\frac{{\overrightarrow{\xi }}_1+{\overrightarrow{\xi }}_2+{\overrightarrow{\xi }}_3}{3}$$

(21)

3.5. Using ISFOA to Enhance Exploration

The methodology of sunflower optimization operates through two key stages. The initial stage, known as pollination, involves sunflowers collaborating to create a pollen gamete. The subsequent stage, termed movement, entails the sunflowers executing random motions toward the sun. The primary factor that greatly influences the attainment of an effective solution for our given problem is the thorough exploration of the domain search space. Therefore, we integrate an improved version of the sunflower optimization algorithm, as suggested by [47], which introduces a novel pollination operator. This operator aims to balance the exploitation and exploration capabilities. Drawing inspiration from [47], our proposed algorithm incorporates the following sections.

3.5.1. Initial Population

In our scenario, we consider a collection of computing servers referred to as sunflowers. Each individual sunflower, which represents a server, possesses a restricted number of items in the form of virtual machines (VMs). These VMs are responsible for carrying out scheduling tasks, either individually or concurrently. To express this concept mathematically, we can propose the following statement.

$$\mathcal{GP}=\left\{{\mathcal{S}}_1,{\mathcal{S}}_2,\cdots ,{\mathcal{S}}_i\right\}$$

(22)

$${\mathcal{S}}_i=\left\{{\mathcal{V}}_1,{\mathcal{V}}_2,\cdots ,{\mathcal{V}}_j\right\}$$

(23)

$${\mathcal{V}}_j^i={\mathcal{V}}_{j,min}+{\zeta }_{i,j}\left({\mathcal{V}}_{j,max}-{\mathcal{V}}_{j,min}\right)$$

(24)

In the given context, ${\zeta }_{i,j}$ represents a randomly generated number within the range of [0,1]. The lower bound of ${\zeta }_{i,j}$ is denoted as ${\mathcal{V}}_{j,min}$, while the upper bound is represented as ${\mathcal{V}}_{j,max}$.

3.5.2. Pollination Strategy

A vector with n dimensions represents the pollen strategy. Each element, denoted as $\mathcal{Y}$, within this n-dimensional vector is assigned a random value between 0 and 1, where $0<{\mathcal{Y}}_{i,j}<1$. Drawing inspiration from [47], the mapping scheme is established in the following manner.

$${\mathcal{K}}_{i,j}=\left({\mathcal{Y}}_{i,j}\times \mathcal{V}\right)+1$$

(25)

In this context, ${\mathcal{Y}}_{i,j}$ refers to a random value associated with the i-th element in the n-dimensional vector. This value is generated within the range of 0 and 1. Furthermore, $\mathcal{V}$ denotes the count of VMs responsible for hosting the assigned jobs. The sunflowers are updated according to the following equation.

$${\mathcal{K}}_i^{\tau +1}={\mathcal{Y}}_{i,j}\times \left({\mathcal{K}}_i^{\tau }-{\mathcal{K}}_j^{\tau }\right)+{\mathcal{K}}_j^{\tau }$$

(26)

where ${\mathcal{K}}_i^{\tau }$ and ${\mathcal{K}}_j^{\tau }$ are the sunflower’s positions at iteration $\tau$. In our solution, we have integrated the model suggested by [47] to improve the algorithm’s population rate as follows.

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill {\mathcal{K}}_i^{\tau +1}& ={\delta }^{\tau }\times \mathcal{O}+\left(1-{\delta }^{\tau }\right)\times \mathcal{L}\hfill \\ \hfill \mathcal{O}& ={\mathcal{K}}_j^{\tau }+\mathcal{G}\left(-1,+1\right)\times \left({\mathcal{K}}_i^{\tau }-{\mathcal{K}}_j^{\tau }\right)\hfill \\ \hfill \mathcal{L}& ={\mathcal{K}}_j^{\tau }+\gamma \times \left({\mathcal{K}}^{★}-{\mathcal{K}}_i^{\tau }\right)\hfill \end{array}\end{array}$$

(27)

The control parameter that regulates the switching probability during iteration $\tau$ is represented by ${\delta }^{\tau }$. The sunflower with the best outcome is denoted as ${\mathcal{K}}^{★}$. $\mathcal{G}\left(-1,+1\right)$ produces a uniformly distributed random number between −1 and 1. The scaling factor, $\gamma$, determines the search direction’s magnitude, which is assigned a value of $3\times \lambda$, where $\lambda$ ranges from 0 to 1. The procedure outlined in [47] calculates ${\delta }^{\tau }$.

$${\delta }^{\tau }=\delta (max)-\frac{\tau }{m}(\delta (max)-\delta (min))$$

(28)

Here, m represents the absolute most significant number of iterations. The values of $\delta (max)$ and $\delta (min)$ are specifically set to 0.6 and 0.4, respectively.

3.5.3. Movement Strategy

During the movement phase, the selection of sunflowers is determined according to Equation (29) in the following manner [47].

$${\mathcal{K}}_i^{\tau +1}={\mathcal{K}}_i^{\tau }+{\mathcal{Y}}_{i,j}\times \frac{{\mathcal{K}}^{★}-{\mathcal{K}}_i^{\tau }}{\left|\right|{\mathcal{K}}^{★}-{\mathcal{K}}_i^{\tau }\left|\right|}$$

(29)

This equation assists the sunflowers in adjusting their directions toward the most suitable position to be replaced by the sun.

$${\mathcal{K}}^{★}={\mathcal{K}}_{\mathcal{V}}|\mathcal{GP}\left({\mathcal{K}}_{\mathcal{V}}\right)>\mathcal{GP}\left({\mathcal{K}}_j\right)$$

(30)

4. Many-Objective Problem Analysis

To ensure profitable job scheduling, a balance must be struck between resource utilization and energy consumption, creating a tradeoff between the two.

4.1. Problem Definition

The job allocation for a heterogeneous faulty computer network and complex independent jobs is represented by a binary decision variable. This variable determines the mapping of jobs to processing servers, specifically the allocated virtual machines (VMs). The definition of this binary decision variable is as follows.

A mapping function, $\mathbb{F}:j_i\to ({\mathcal{S}}_i,{\mathcal{V}}_{\mathcal{K}})$, is an optimal solution in case of the following:

$${\xi }_{j,v}^i=\left\{\begin{array}{cc}1:\hfill & \mathrm{If}i\mathrm{th}\mathrm{job}\mathrm{is}\mathrm{placed}\mathrm{on}\mathrm{the}j\mathrm{th}\mathrm{server}\hfill \\ \hfill & \mathrm{allocating}\mathrm{the}\mathcal{V}\mathrm{th}\mathrm{virtual}\mathrm{machine}\hfill \\ \\ 0:\hfill & \mathrm{Otherwise}.\hfill \end{array}\right.$$

(31)

4.2. Problem Objective

Our proposed solution aims to optimize the placement of a batch of jobs on cloud servers that offer the highest profitability. To achieve this objective, our focus lies in addressing the following optimization problem.

$$\forall possiblemapping\sum _{j=1}^{\mathcal{N}}(\mathcal{S}ch.({\tau }_i))$$

(32)

Subject to the following constraints,

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill & minimize\left(E^{ToT},\mathcal{L}oT,\mathcal{L}a,\mathcal{B}and\right)\hfill \\ \hfill & maximize\left({\mathcal{S}}_{pro},AUR,\mathcal{Q}o\mathcal{S}\right)\hfill \end{array}\end{array}$$

5. The SGWO Algorithm Design

This section aims to elucidate our suggested technique for enhancing the effectiveness of the proposed SGWO algorithm in cloud systems through the implementation of hybridization metaheuristic strategies.

5.1. Executable Server Selection

The first step involves setting up the initial phase, during which the cloud network establishes a group of diverse processing servers with varying capabilities. These servers are equipped with a limited number of virtual machines, each with a predefined level of processing power. A productive cycle, consisting of Steps 2 to 24, ensures the optimal utilization of each server. In Step 3, servers are trained at specific levels of utilization to determine their efficiency. Step 4 involves assigning multiple tasks of varying input sizes to each server in order to assess its computational capacity. In Step 5, a preferred utilization group is created for each server. Finally, in Step 6, the optimal utilization is chosen based on the preferred utilization groups, selecting the one with the highest asset utilization ratio.

Starting from Step 7 and continuing until Step 23, an internal loop is initiated to examine the virtual machines assigned to each server. Since each virtual machine operates within distinct time slots, a secondary loop from Steps 8 to 22 is responsible for updating a matrix called the window matrix (WM) that keeps track of the latest and completed time slots. The WM provides information about available time slots and helps determine the most efficient ones for hosting scheduled jobs, as indicated in Steps 9 and 10. In Step 11, the current and projected costs of execution and power consumption are calculated using Equations (1) and (6).

The Algorithm 1 in Steps 12–21 continuously monitors the workload status of the server and makes predictions regarding the utilization of virtual machines (VMs). This forecast aids the algorithm in predicting the level of utilization following the allocation of incoming jobs. The designated destination machine will only be chosen if the CPU usage of the newly assigned server falls within the desired range or is within 3% of it, as noted in [44] study.

Algorithm 1: Executable Server Selection.

5.2. Hybridize Metaheuristic Approaches to Improve Exploration and Exploitation

The second algorithm, Algorithm 2, incorporates enhanced versions of the sunflower optimization and the mean variation of the grey wolf optimization algorithms. The main aim is to attain improved results by finding a middle ground between exploration and exploitation. This ensures a more efficient search process within the domain space. Modifications have been made to the traditional sunflower optimization algorithm, as well as the encircling and hunting phases in the mean grey wolf optimization algorithm. The key steps of Algorithm 2 can be summarized as follows.

Algorithm 2: Exploration and Exploitation Tradeoff.

In the first two steps, the grey wolves, sunflower optimization algorithm, coefficient vectors (n and m), and populations are initialized. Step 3 involves calculating the energy and power costs. Steps 4–7 encompass the establishment of a new measurement termed $ma{x}_i$ for determining the maximum iteration count. This involves the creation of an environment comprising solely AUR-aware servers, the computation of object fitness functions for GWO and SPO, and the subsequent sorting of fitness weights using their respective index values. The primary objective of the while loop in Steps 8–12 is to ensure the depreciation in the fitness operation during population initialization. On the other hand, the for loop in Steps 14–21 adjusts the coefficient values of m and n exclusively for AUR-aware processing servers. The positions of each grey wolf are updated in Step 16, while the scores for the alpha, beta, and gamma wolves are updated in Step 19.

In Step 24, the power and energy costs for each sunflower object are re-evaluated. Step 25 performs the computation of pollination for the sunflower objects. Sunflower movement is determined in Step 26, and the position of the sun is adjusted based on the provided equation in Step 27.

5.3. SGWO Time Complexity Analysis

It is essential to comprehend that the time complexity of the SGWO algorithm relies on three key parameters. The first parameter is the population size, denoted as $\mathcal{PS}$. The second parameter is the problem dimensionality, represented as $\mathcal{PD}$. Finally, the third parameter is the maximum number of iterations, depicted as $max\mathcal{ITR}$. As a result, the overall time complexity of the proposed SGWO model can be mathematically expressed as $\mathcal{O}\left(\mathcal{PS}\times \mathcal{PD}\times max\mathcal{ITR}\right)$.

6. Experimental Results and Analysis

This section covers three key areas. Firstly, it provides a description of the simulation set environment. Secondly, it presents the results obtained from the analysis of numerical data. Furthermore, thirdly, it explains the findings from the statistical analysis.

6.1. SGWO Case Study

Presently, cloud systems play a crucial role in the healthcare sector, particularly with the significant rise in chronic diseases. Patient self-checking (PSC) has become a daily necessity, and many patients require remote access to cloud services through their smartphones or smart cards for timely assistance with emerging issues. Additionally, doctors are increasingly using cloud-based networks to send prescriptions and conduct remote telemedicine sessions.

However, this increase in data generation from both patients and doctors can overload the system and lead to network congestion. To address this, efficient task scheduling is imperative for real-time health monitoring systems. When patients submit their requests, the cloud scheduler must distinguish between static and dynamic requests. Static requests involve resource allocation at compile time, with all task attributes and destination resources known beforehand. In contrast, dynamic requests occur during runtime without prior information about the submitted tasks. Separating and prioritizing tasks are crucial in the healthcare system to ensure effective and timely patient monitoring.

Building on a previous case study, we propose a job scheduling paradigm for cloud systems that can be applied to remotely schedule healthcare tasks and monitor patients in real-world scenarios. Our objective is to consider various completion time goals, ensuring critical tasks are mapped and processed first to prevent any life-threatening situations for patients. Additionally, we aim to optimize scheduling delays and avoid violations of service-level agreements (SLAs) to reduce response time duration. Moreover, we take into account energy and bandwidth utilization optimization to prevent resource fragmentation and network congestion, further enhancing the efficiency of the healthcare cloud system.

6.2. Simulation Setup

The simulation employed CloudSim toolkit [48,49] on a Windows 11 operating system equipped with 8 GB of RAM. Within the simulation environment, 100 autonomous servers were utilized, each with a restricted number VMs. To assess the suggested algorithm’s effectiveness, a meticulously chosen set of 500 tasks was selected. The memory capacity assigned was 1 Gb, with a power capacity of 10,000 MIPS and a bandwidth allocation of 1 Gb/s. The simulation was executed for approximately 100 iterations. The dataset utilized in this research study was collected from two distinct sources.

To assess the effectiveness of the proposed algorithm, a comparative evaluation is conducted against existing approaches, namely, HMLB [30], QMPSO [38], PSO [39], and GA [40]. The evaluation encompasses several performance metrics, including load energy consumption, asset utilization ratio, service provider profit, completion time, service quality, latency, and service-level agreement (SLA). These metrics are utilized to assess and gauge the effectiveness of the SGWO model compared to the previously mentioned existing methods. Moreover,

Table 2. Processing servers and virtual machines configuration.

Operating systems	Microsoft Windows 11 Education
	(×86)–32-bit processor
Programmed language	Java-based language
CPU processor	Intel${}^{\circledR }$ Five Core™ Processor
Simulation running	≈100 iterations
Applicable round mapping	0.167–0.341 s
Mapped memory size	8 GB of RAM
Job appearance frequency	35–102 requests per sec.
Processing server quantity	100 computing servers
Computational ability	10,000 MIPS
Initiating time service	≈180 s
Terminating time	≈21 s
Applied software	CloudSim v. 3.0.2
Number of iterations	100 iterations
Duration of simulation	6870 s
Time of service delivery	0.280–0.612 s
Virtual machine quantity	1000 virtual machines
Computational ability	430–1680 MIPS
Number of elements	Two items
Starting time	100 s
Ending time	8 s
Allocation size	2 GB
Memory capacity	1 Gb/s
Network bandwidth	1 Gb/s

outlines the setup details for simulation settings, processing servers, and virtual machines.

6.3. Numerical Analysis

Numerical analysis is carried out using both a minimization function and a maximization function. The minimization function comprises evaluation metrics that are targeted for reduction to enhance system productivity. On the other hand, the maximization function involves metrics that are aimed to be increased for improved system efficiency.

Figure 3a demonstrates that the SGWO algorithm outperforms other algorithms regarding energy consumption. Compared to HMLB, QMPSO, PSO, and GA, the SGWO algorithm improves energy costs by approximately 5.12%, 9.41%, 11.02%, and 13.52%, respectively. The inferior performance of the current algorithms can be attributed to inadequate parallelism management, latency control, and VM time slot handling. As evidenced by the data presented in Figure 3a, it is clear that all approaches exhibit a rise in energy consumption as the workload expands, mainly due to the larger input data sizes. Still, the SGWO algorithm maintains a consistent energy cost rate by dynamically reallocating allocated VMs to accommodate incoming tasks, eliminating the need for initiating new resource executions. As the quantity of tasks grows, the SGWO algorithm leads to an approximate 4.08% decrease in energy expenses. In contrast, the HMLB, QMPSO, PSO, and GA approaches can only optimize energy costs by 3.39%, 2.11%, 2.01%, and 1.15%, respectively, when assigning the same number of tasks.

Figure 3b illustrates a comparison between the SGWO algorithm and other methods in terms of completion time. The SGWO algorithm surpasses different algorithms in terms of completion time preservation, particularly as the number of jobs increases. SGWO achieves this by assigning tasks to the appropriate destinations for faster execution. By reusing allocated VMs, the fragmentation of resources decreases, thereby eliminating idle time. The numerical data indicate that SGWO saves time by 47.20%, while HMLB, QMPSO, PSO, and GA achieve time savings of 35.64%, 28.15%, 21.73%, and 16.80%, respectively. Additionally, SGWO minimizes idle times and effectively switches idle servers, enabling task execution solely on powerful active servers. This enhancement in the functionality of SGWO persists even with an increasing number of input data sizes. The results clearly indicate that SGWO achieved significant time savings of 17.64% to 31.52% for 75 jobs and an impressive 31.23% to 42.67% for 430 jobs. It is evident that SGWO is the most efficient solution.

Figure 3c clearly indicates that the SGWO algorithm surpasses all other algorithms in meeting the service-level agreement (SLA) requirements. The success of SGWO can be attributed to its emphasis on efficiently mapping jobs onto more effective and proficient servers. In contrast, other approaches encounter issues like VM overlapping due to time slot conflicts, leading to a decline in SLA performance. Additionally, SGWO excels at handling VM repacking, enabling the consolidation of jobs onto a smaller number of servers and minimizing resource wastage. This, in turn, aids in meeting the quality of service requirements, which plays a crucial role in enhancing the SLA. The numerical results show that SGWO improves the SLA by 47.25%. In comparison, the HMLB, QMPSO, PSO, and GA approaches achieve improvements of 32.54%, 29.31%, and 21.85%, respectively.

Figure 3d presents a comparison of algorithms in terms of latency, which is determined by the number of assigned tasks. The evaluation takes into account various metrics, such as energy costs, completion time, and SLA, all of which have an impact on this measure. The SGWO algorithm stands out from the rest because of its ability to intelligently direct jobs to the most advantageous resources, ensuring timely completion within deadlines. SGWO’s effectiveness in estimating the time required to assign a specific job based on virtual machine (VM) availability leads to improved latency and enhanced scheduling efficiency. On the contrary, alternative approaches show a decrease in performance as the portion of scheduled jobs increases. This is principally attributed to their method of controlling the quality of service by adding and overloading cloud resources with too many tasks, ultimately negatively affecting scheduling latency.

Figure 4a presents a comparison of algorithms concerning service quality, which is influenced by the number of tasks and VM instance types. Additionally, various evaluation metrics, such as asset utilization ratio, bandwidth, and service throughput, directly impact this measure. The standout feature of the SGWO algorithm lies in its capability to accurately predict the earliest and latest running times of jobs, ensuring timely completion within specified deadlines. By efficiently managing approximately 237 jobs while adhering to the quality of service requirements, SGWO surpasses similar algorithms in performance. Another contributing factor to the enhanced quality of service provided by SGWO is its efficient user charge management. As part of the evaluation, the quality of service is assessed with different numbers of VMs. SGWO showcases its ability to accurately estimate job sizes based on the allocated VMs, resulting in improved quality of service and increased profitability for the service provider. Conversely, as the numeral of scheduled jobs enlarges, other approaches experience a decline in performance. This is primarily due to their approach of attempting to control the quality of service by adding more processing servers, ultimately leading to a deterioration in system performance.

Figure 4b illustrates the superior performance of the SGWO algorithm in efficiently utilizing allocated bandwidth compared to other algorithms. Unlike MOTSGWO, IPSO, and OSFO, the SGWO algorithm effectively directs tasks to their designated destinations, mitigating the risk of bandwidth congestion. Additionally, the algorithm achieves balance in distributing the workload across cloud virtual machines. As user workloads increase due to diverse requests, bandwidth utilization tends to rise exponentially. However, the SGWO algorithm manages to maintain a consistent bandwidth cost rate by allocating only powerful servers and avoiding resource fragmentation. This prevents bandwidth exhaustion and failures, ensuring a stable and reliable system operation.

Figure 4c illustrates the dominance of the SGWO algorithm compared to other algorithms concerning the asset utilization ratio. The success of SGWO can be attributed to its focus on mapping jobs onto more efficient and effective servers. In contrast, other approaches suffer from VM overlapping caused by time slot conflicts, leading to a degradation in AUR. SGWO efficiently manages the repacking of virtual machines, consolidating jobs onto fewer servers and drastically reducing resource waste. The figures speak for themselves—SGWO increases AUR by an impressive 21.76%. In comparison, MOTSGWO, IPSO, and OSFO approaches fall short, with AUR improvements of only 19.02%, 14.23%, and 9.13%, respectively.

Figure 4d presents a comparison between the SGWO algorithm and other algorithms regarding provider profit. The SGWO algorithm achieves the highest profit rates, leading to increased profitability of processing servers. For instance, when considering a server with 176 VMs, the SGWO algorithm improves the profit rate by approximately 12%, 15%, and 21% compared to the MOTSGWO, IPSO, and OSFO algorithms, respectively. This advancement highlights the SGWO algorithm’s effective ability to balance conflicting objectives.

6.4. Statistical Analysis

In order to ensure a comprehensive statistical assessment of the suggested solution, the algorithm was executed several times on average. Two significant datasets were used to evaluate eight key metrics, which include energy consumption, completion time, SLA violations, latency overhead, service quality, asset utilization ratio, and service quality.

The results in

Table 3. The energy consumption rate by processing datasets on computing servers.

	Workload
Algorithms	${\mathcal{W}}_{\mathbf{1}}$	${\mathcal{W}}_{\mathbf{2}}$	${\mathcal{W}}_{\mathbf{3}}$	${\mathcal{W}}_{\mathbf{4}}$	${\mathcal{W}}_{\mathbf{5}}$
SGWO	07	08	15	19	24
HMLB	08	13	19	24	29
QMPSO	12	17	23	29	36
PSO	17	21	26	34	41
GA	21	25	32	39	47

provide a comprehensive assessment of how the proposed solution enhances energy consumption costs in comparison to similar algorithms. The data in Table 3 unambiguously demonstrate that the proposed approach significantly reduces energy expenses for all input dataset sizes, outperforming alternative algorithms. This is attributed to the proposed approach’s optimal utilization, which ensures minimized energy costs and enhanced system efficiency. On average, the SGWO algorithm surpasses HMLB, QMPSO, PSO, and GA across all workload sizes in terms of energy efficiency.

The presented data in

Table 4. The completion time by processing datasets on computing servers.

	Workload
Algorithms	${\mathcal{W}}_{\mathbf{1}}$	${\mathcal{W}}_{\mathbf{2}}$	${\mathcal{W}}_{\mathbf{3}}$	${\mathcal{W}}_{\mathbf{4}}$	${\mathcal{W}}_{\mathbf{5}}$
SGWO	065	077	104	148	165
HMLB	077	095	115	162	184
QMPSO	094	115	127	182	196
PSO	112	124	139	192	205
GA	121	132	148	207	237

clearly demonstrate the superior performance of the SGWO model over HMLB, QMPSO, PSO, and GA in terms of task execution times. By efficiently managing virtual machines, this algorithm allows for the execution of more jobs with fewer VMs, thereby reducing the unnecessary time overhead caused by deploying too many virtual machines.

Table 5. The SLA by processing datasets on computing servers.

	Workload
Algorithms	${\mathcal{W}}_{\mathbf{1}}$	${\mathcal{W}}_{\mathbf{2}}$	${\mathcal{W}}_{\mathbf{3}}$	${\mathcal{W}}_{\mathbf{4}}$	${\mathcal{W}}_{\mathbf{5}}$
SGWO	12	21	35	42	51
HMLB	14	25	37	53	62
QMPSO	17	32	45	59	69
PSO	22	37	51	64	76
GA	27	41	57	71	84

presents a thorough evaluation of the SGWO algorithm in comparison to other algorithms across various workload sizes. The results demonstrate that the SGWO algorithm surpasses HMLB, QMPSO, PSO, and GA in terms of minimizing SLA violations, indicating its superior performance in meeting service-level agreements. The findings reveal that when the number of tasks reaches 500, the proposed SGWO algorithm optimizes the SLA violations value to 51, while HMLB, QMPSO, PSO, and GA achieve values of 62, 69, 76, and 84, respectively.

Table 6. The latency time by processing datasets on computing servers.

	Workload
Algorithms	${\mathcal{W}}_{\mathbf{1}}$	${\mathcal{W}}_{\mathbf{2}}$	${\mathcal{W}}_{\mathbf{3}}$	${\mathcal{W}}_{\mathbf{4}}$	${\mathcal{W}}_{\mathbf{5}}$
SGWO	20	26	32	45	57
HMLB	27	32	39	49	64
QMPSO	29	38	46	56	72
PSO	31	44	53	67	78
GA	35	51	59	77	85

outlines an evaluation of the proposed SGWO algorithm in relation to HMLB, QMPSO, PSO, and GA, focusing on the latency overhead metric and the varying number of tasks. The numerical analysis clearly indicates that the proposed SGWO algorithm exhibits lower latency in comparison to its competitors, demonstrating its efficiency in minimizing delays. The findings demonstrate that as the number of tasks reaches 500, the proposed SGWO algorithm achieves an optimized latency value of 57. In contrast, the competing algorithms HMLB, QMPSO, PSO, and GA yield latency values of 64, 72, 78, and 85, respectively. This highlights the superior performance of the SGWO algorithm in minimizing latency compared to the other approaches.

Table 7. The service quality rate by processing datasets on computing servers.

	Workload
Algorithms	${\mathcal{W}}_{\mathbf{1}}$	${\mathcal{W}}_{\mathbf{2}}$	${\mathcal{W}}_{\mathbf{3}}$	${\mathcal{W}}_{\mathbf{4}}$	${\mathcal{W}}_{\mathbf{5}}$
SGWO	81,125	86,785	91,247	123,012	149,201
HMLB	62,782	66,014	85,782	100,032	121,078
QMPSO	58,785	63,143	70,778	81,453	105,045
PSO	50,205	60,017	64,125	77,728	87,078
GA	40,445	50,182	54,574	67,804	77,907

elucidates how the proposed algorithm surpasses the performance of HMLB, QMPSO, PSO, and GA algorithms. The results obtained from the simulation environment reveal that several tasks in the other algorithms, particularly PSO and GA, fail to meet their deadlines due to limited resource allocation for a restricted number of workloads, resulting in a decline in their offered quality of service. Moreover, the interdependency between parent and child tasks significantly influences the progress of the proposed algorithm. For instance, in ${\mathcal{W}}_3$, approximately 83% of tasks successfully fulfill their quality of service requirements, while HMLB, QMPSO, PSO, and GA achieve percentages of around 57%, 41%, and 23%, respectively.

The numerical examination presented in

Table 8. The bandwidth utilization by processing datasets on computing servers.

	Workload
Algorithms	${\mathcal{W}}_{\mathbf{1}}$	${\mathcal{W}}_{\mathbf{2}}$	${\mathcal{W}}_{\mathbf{3}}$	${\mathcal{W}}_{\mathbf{4}}$	${\mathcal{W}}_{\mathbf{5}}$
SGWO	112	152	159	182	191
HMLB	119	164	169	189	215
QMPSO	126	171	182	194	229
PSO	142	179	191	210	237
GA	156	186	198	221	248

emphasizes the supremacy of the proposed SGWO algorithm compared to HMLB, QMPSO, PSO, and GA across different workload sizes. According to the table, it is imperative to note that once the number of jobs hits 500, the proposed SGWO model achieves a bandwidth rate of 191, while the competing algorithms, including HMLB, QMPSO, PSO, and GA, achieve bandwidth rates of 215, 229, 237, and 248, respectively.

Table 9. The asset utilization rate by processing datasets on computing servers.

	Workload
Algorithms	${\mathcal{W}}_{\mathbf{1}}$	${\mathcal{W}}_{\mathbf{2}}$	${\mathcal{W}}_{\mathbf{3}}$	${\mathcal{W}}_{\mathbf{4}}$	${\mathcal{W}}_{\mathbf{5}}$
SGWO	0.71	0.75	0.83	0.87	0.96
HMLB	0.64	0.69	0.76	0.81	0.88
QMPSO	0.56	0.61	0.69	0.78	0.83
PSO	0.51	0.57	0.66	0.73	0.80
GA	0.48	0.52	0.61	0.68	0.78

clearly shows that the SGWO algorithm has significantly improved the utilization ratio of assets. This improvement surpasses HMLB, QMPSO, PSO, and GA methods. The SGWO algorithm consistently outperforms the other approaches across all evaluated datasets, demonstrating higher efficiency in terms of asset utilization ratio. As the task size increases, the asset utilization ratio improves, and the SGWO algorithm shows even more significant progress in this regard. Particularly, when the workload size reaches 500, the proposed SGWO algorithm achieves an approximate rate of 96%, while HMLB, QMPSO, PSO, and GA approaches achieve rates of 88%, 83%, 80%, and 78%, respectively.

Table 10. The service provider profit by processing datasets on computing servers.

	Workload
Algorithms	${\mathcal{W}}_{\mathbf{1}}$	${\mathcal{W}}_{\mathbf{2}}$	${\mathcal{W}}_{\mathbf{3}}$	${\mathcal{W}}_{\mathbf{4}}$	${\mathcal{W}}_{\mathbf{5}}$
SGWO	66	78	88	95	117
HMLB	61	69	76	84	95
QMPSO	56	64	69	76	87
PSO	48	52	57	63	74
GA	42	48	51	59	67

investigates the influence of different datasets on the profit of the service provider. The analysis involves the assessment of workloads ${\mathcal{W}}_1$, ${\mathcal{W}}_2$, ${\mathcal{W}}_3$, ${\mathcal{W}}_4$, and ${\mathcal{W}}_5$ using the SGWO, HMLB, QMPSO, PSO, and GA algorithms. An interesting discovery is that as the input sizes increase from ${\mathcal{W}}_3$ to ${\mathcal{W}}_5$, the profit ratio for the SGWO algorithm experiences a substantial increase from 88 to 117. Conversely, in the other algorithms, such as HMLB, QMPSO, PSO, and GA, the rates increase from 76 to 95, 69 to 87, 57 to 74, and 51 to 67, respectively. Based on the observation, it can be stated with certainty that the cloud environment boasts highly efficient resource allocation. It is worth noting that the number of tasks assigned profoundly impacts the provider’s profit and overall output efficiency, which cannot be overlooked.

7. Conclusions

The SGWO algorithm is the primary focus of this research paper. It was specifically developed to tackle the crucial task of job scheduling in the cloud paradigm. The SGWO algorithm incorporates modifications to the encircling and hunting phases of the GWO algorithm, utilizing the mean variation technique. Additionally, it enhances exploration capabilities by modifying the pollination operator found in the traditional SFO algorithm. In the SGWO approach, servers undergo training at various utilization levels using the merge-and-split theory, allowing for the identification of their preferred utilization. The results of this study demonstrate that the SGWO algorithm outperforms comparable algorithms, leading to significant performance improvements. The evaluation process includes the utilization of both real-world and simulated datasets. When compared with other metaheuristics like HMLB, QMPSO, PSO, and GA, the SGWO algorithm shows superior performance across various performance metrics, including energy consumption, completion time, asset utilization ratio, service provider profit, and quality of service.