Improved wild horse optimization with levy flight algorithm for effective task scheduling in cloud computing

Cloud Computing, the efficiency of task scheduling is proportional to the effectiveness of users. The improved scheduling efficiency algorithm (also known as the improved Wild Horse Optimization, or IWHO) is proposed to address the problems of lengthy scheduling time, high-cost consumption, and high virtual machine load in cloud computing task scheduling. First, a cloud computing task scheduling and distribution model is built, with time, cost, and virtual machines as the primary factors. Second, a feasible plan for each whale individual corresponding to cloud computing task scheduling is to find the best whale individual, which is the best feasible plan; to better find the optimal individual, we use the inertial weight strategy for the Improved whale optimization algorithm to improve the local search ability and effectively prevent the algorithm from reaching premature convergence. To deliver services and access to shared resources, Cloud Computing (CC) employs a cloud service provider (CSP). In a CC context, task scheduling has a significant impact on resource utilization and overall system performance. It is a Nondeterministic Polynomial (NP)-hard problem that is solved using metaheuristic optimization techniques to improve the effectiveness of job scheduling in a CC environment. This incentive is used in this study to provide the Improved Wild Horse Optimization with Levy Flight Algorithm for Task Scheduling in cloud computing (IWHOLF-TSC) approach, which is an improved wild horse optimization with levy flight algorithm for cloud task scheduling. Task scheduling can be addressed in the cloud computing environment by utilizing some form of symmetry, which can achieve better resource optimization, such as load balancing and energy efficiency. The proposed IWHOLF-TSC technique constructs a multi-objective fitness function by reducing Makespan and maximizing resource utilization in the CC platform. The IWHOLF-TSC technique proposed combines the wild horse optimization (WHO) algorithm and the Levy flight theory (LF). The WHO algorithm is inspired by the social behaviours of wild horses. The IWHOLF-TSC approach's performance can be validated, and the results evaluated using a variety of methods. The simulation results revealed that the IWHOLF-TSC technique outperformed others in a variety of situations.


Introduction
Customers' access to diverse administrations and assets can be transformed using cloud computing. Clients can use the cloud to rapidly extend their capabilities without having to invest in licensing or foundations [1]. As time has passed, cloud computing has grown in popularity among clients as a means of obtaining administrations. Several task scheduling strategies have been proposed Page 2 of 14 Saravanan et al. Journal of Cloud Computing (2023) 12:24 to enhance system performance by optimizing resource utilization. However, symmetry-based strategies have received little consideration. Given the widespread adoption of cloud computing technology, it is anticipated that symmetry will be employed to enhance cloud computing performance. Cloud computing has the advantages of flexibility, constant quality, and less maintenance because the administrations and products are maintained by the outsider organization. These are the hypotheses that explain why the cloud is so prominent. Simplified terms for these cloud administrations include Software on Demand, Platform on Demand, and Infrastructure on Demand (IaaS) [2][3][4]. With cloud computing, multiple tasks can be carried out in the background at the same time. Server farm and board costs can be kept in check through the innovative use of virtualization and board robotization. In the age of cloud computing, making a reservation seems like a contradiction in terms. Ad-lobbing the asset utilization rate has the purpose of arriving at a perfect booking calculation Allocating diverse resources to the required errands is an NP-complete issue. Some Grid and Cloud system techniques have been implemented because of this factor. By employing meta-heuristics based on populations, it is possible to expand the size of the search area and yet achieve better outcomes [5][6][7]. Single-based meta-heuristic computations, rather than doing a thorough search, use different methods to arrive at the optimum answer for a random wellness task. As a result, utilizing population-based meta-heuristics to identify the best arrangement requires far less effort than using single-based meta-heuristics. Both calculations presented above have advantages and disadvantages. After then, a combination of meta-heuristics calculations is created by merging the two computations, which eliminates the negative marks in the separate calculations. With each recreation, the combined meta-heuristics calculation provides the best outcomes [8]. An alternative business model that is rapidly gaining traction around the world is the Internet-enabled business (e-Company). Internetenabled businesses are transforming computing into a paradigm that consists of services that are commoditized and distributed in the same way that water, electricity, or gas are traditionally delivered. It doesn't matter where services are located or offered; users can use them according to their needs. Several computer paradigms have claimed to be able to deliver utility computing.
A cloud computing environment's fundamental purpose is to make the most efficient use of available computing resources. In the optimization process, scheduling methods are critical. As a result, user tasks must be scheduled using an efficient scheduling technique [9]. To reduce the total execution time, scheduling algorithms aim to distribute the workload across the available processors and maximize their efficiency. Many firms are migrating their infrastructure and operations to the cloud rather than retaining them on-premises, emphasizing the significance of installing a new CC solution. Cloud-based apps and services are becoming increasingly important [10]. As a result, the services' quality needed to be carefully addressed. Furthermore, the CC platform allows us to use many virtual resources for all the required tasks, rendering traditional and manual scheduling methods ineffective and demanding the creation of unique effective scheduling solutions.
However, task scheduling remains one of the major issues, potentially affecting performance, QoS, and user experience. As a result, the critical technical contribution in this paper, based on the idea is to introduce an enhanced solution with a novel genetic algorithm to exploit the collaboration between thin-thick clients and cloud network to optimise task scheduling of the processing system to deal with the issues, thereby improving QoS, user experience, and system reliability. Our proposal considers not only network contention but also the cost charged to cloud customers (CCs), as these two factors play important roles in meeting user expectations. Furthermore, the approach is experimentally evaluated and compared to others. The results show that our method is more efficient at task scheduling and more cost-effective than other approaches.
For cloud job scheduling, this study introduces the IWHOLF-TSC technique, which is an enhanced wild horse optimization with levy flight algorithm. The proposed IWHOLF-TSC technique reduces the CC platform's makespan and maximizes the utilization of the CC platform's resources to construct a multi-objective fitness function [11]. The suggested IWHOLF-TSC technique combines the wild horse optimization (WHO) algorithm with the Levy flight theory (LF). The social living traits of wild horses inspire the WHO algorithm. The performance validation of the IWHOLF-TSC approach can be done and the outcomes evaluated using a variety of methods. This paper's contributions are as follows: (1) A metaheuristic optimization techniques for task scheduling is proposed, and IWHO is used to solve the entire problem; (2) an IWHO algorithm is proposed, which improves the convergence and accuracy of the WOA-based method, which improves the efficiency of task scheduling; and (3) describes the implementation process of the IWHOLF-TSC algorithm and compares it with the ACO, PSO, and WOA algorithms. The results of the experiments show that the algorithm works under a variety of task quantity conditions. The scheduling effect of down is superior.
The rest of this article is structured as follows. The related work is introduced in the second section. IWHOLF-TSC is introduced in the third section. The fourth section

Related work
In Pradeep, K., et al. [1], the Lion Advancement (LOA) and Opposition Based Learning (OBL) calculations are used in Crossbreed Oppositional Lion Enhancement Calculation (OLOA) With Cloud sim programming conditions, the given arrangement is recreated and displayed, and the obtained results show a significant improvement in execution over existing calculations such as Particle Swarm Optimization (PSO), Oppositional Dark Wolf Streamlining Agent (OGWO), and Genetic calculations (GA).
In Natesan, G. et al. [2], when compared to three recent planning calculations, GA-ETI reduced the time it took to execute work processes by 11-85 percent without increasing the cost. For a tough test and to integrate several upgrade objectives, GA-ETI shows the most efficient technique to building the optimal layer-scheduler for the framework of a work process supervisor. In Gobalakrishnan, N, et al. [3], an alternative to this approach is Particle Swarm Optimization (PSO), which makes use of both artificial and simulated ringing organisms in a symbiotic search (SASOS). Time spent by the executive team, implementation costs, communication costs, energy and resource consumption, epsilon restraint, and penalty characteristics are all comparable objectives.
In Casas, I., et al. [4], the multi-take interlace peak scheduling method (MIPSM) has been presented as a planning technique for quickly altering the content of resource loads. Three queues are created for CPU, CPUintensive I/O memory capacity, and memory-intensive I/O. During the execution of planned operations, resource load peaks are dispersed. Using as minimal CPU, I/O, and memory as feasible is the purpose of each of the three queues in this system. In Zhou, J., et al. [5], to consider, the budget, budget, and performance optimization, I developed a resource cost model. To improve the quality of the solution, the augmented ant colony algorithm and feedback were utilized in a certain order. A check-up to reduce both runtime and fitness expenses, a hybrid glowworm swarm optimization technique was created.
Nanjappan et al. [6] the proposed algorithm uses an ANFIS-BWO (Adaptive-Neuro-Fuzzy-Inference System-Black-Widow-Optimization) technique to allocate a proper VM for each task to reduce time delay. Another important goal for optimum consumption of cloud properties is resource scheduling. The BWO algorithm is used to generate an ideal solution set. The presented technique can allocate the VMs present on the cloud using the best scheduler schemes. The introduced technique's primary goal is to reduce computation time and cost while also minimising energy consumption for various tasks. Tong Zhou et al. [7] To design new reward functions to enhance the decision-making abilities of multiple reinforcement learning-based AI schedulers (RL). Using real-world case studies, the proposed methodology is evaluated and validated in a smart factory. Experiment results demonstrate that the new architecture for smart factories not only improves the learning and scheduling efficiency of multiple AI schedulers, but also effectively manages unanticipated events such as rush orders and machine breakdowns.
Mohammad Hasani Zade et al. [8] The suggested algorithm has two stages (i.e., meta-scheduler and local scheduler). The tasks are assigned to hosts in the meta-scheduler stage based on their priorities, completion dates, and host power. With the suggested Parallel Reinforcement Learning Caledonian Crow, the best mapping between tasks and virtual machines is discovered in the local-scheduler stage (PRLCC). The New Caledonian Crow Learning Algorithm (NCCLA), Reinforcement Learning (RL), and parallel strategy are all combined in the proposed PRLCC.
Kaur & Kaur et al. [9]. To save cost and time developed a hybrid algorithm that combines heuristic and metaheuristic algorithms. To address the problem of task scheduling in cloud computing, which necessitates non-traditional optimization attitudes to achieve the optimal solution, the current paper proposes a hybrid multiple-objective approach called hybrid grey wolf and whale optimization (HGWWO) algorithms, which integrates two algorithms, namely, the grey wolf optimizer (GWO) and the whale optimization algorithm (WOA), with the goal of combining the advantages of each algorithm for miniaturisation.
Thekkepuryil et al. [10] the authors propose an improved version of the ant-lion optimization (ALO) algorithm that is crossbred with the popular particle swarm optimization (PSO) algorithm to improve system scheduling precision for cloud computing. A new security technique known as Data Encryption Standard (DES) is used, which encodes the information present in the cloud while scheduling is performed. The research's goal is to contribute an improved system scheduling framework that is more secure than existing frameworks. Improvement parameters are evaluated in terms of time, load, and cost. Shiau et al. [11] Cloud computing has been used to create cloud computing classrooms. Cloud computing student BI is unclear. Most researchers have compared few users' BI theories. This study tested, compared, and unified six theories: service quality (SQ), self-efficacy (SE), the motivational model (MM), the technology acceptance model (TAM), and extension of the Theory of Reasoned Action/ Theory of planned behavior (TRA/TPB) in cloud computing classrooms.
Palos-Sanchez, et al. [12]. studied Data Replication and Management, two important technologies for managing Researcher's analyses data replication techniques and cloud deployment of data-intensive apps. The paper's knowledge can be used to design and model cloud-based mechanisms and approaches. Medara et al. [13] The energy-efficient and reliability aware workflow task scheduling in cloud environment (EERS) algorithm is introduced in this paper, which conserves energy while making the most of the system's reliability. To begin, use a task-rank calculation programme to keep task dependencies intact. Following that, a task clustering algorithm is used to reduce communication costs, resulting in lower energy consumption. T. Dillon et al. [14] presented the problems and difficulties with cloud computing. We explained how Cloud computing, Service-Oriented Computing, and Grid computing are related. We examined a few difficulties encountered when adopting cloud computing. After highlighting the interoperability problem, various solutions are discussed for various cloud service deployment models. Fan et al. [15] This study examines the short-and long-term competition between SaaS and SWS using a game theoretical approach. We examine both the longterm quality competition between the two firms as well as a model of price competition over one period. Software-as-a-service businesses can effectively differentiate their products by reducing the cost of system implementation by bundling software with services.
Agrawal et al. [16]. Cloud computing is a rapidly expanding and evolving platform. It offers its customers excellent services. Cloud computing development is significantly improving in terms of security in educational use. It provides numerous methods for accessing various resources' platform applications via on-demand web pages. This paper demonstrates various trending technologies, cloud computing features, and cloud computing security, as well as their application in education. Duraipandian. 2022 [17] Artificial Intelligence (AI) modernises today's society and paves the way for many digital applications to flourish. AI is important in everything from agriculture to space science. Improvements to electronic processors and other chips are also assisting AI in gaining computational efficiency. The design of micro electronic devices is allowing sensors to be moved to specific locations via Internet of Things (IoT) communication. The goal of this author is to examine the performance of AI methodologies in various applications to identify research gaps.
Palos-Sanchez et al., [18] examine the state of this technology from two angles: that of the European Union and, specifically, that of SMEs. The European Commission's strategic positions will then be evaluated considering the effects of adopting the cloud paradigm. Haag et al., [19] Identify five new research areas, including theoretical and practical phenomena, that describe the factors that influence the adoption of cloud services in organizations. These areas include information technology (IT)-related public threat appeals, trust in technology versus vendor trust, bring your own cloud, organizational identity transformation, and intelligent clusters of IT initiatives.
Ramezani et al., [20] an interval many-objective evolutionary algorithm (InMaOEA) is proposed for solving the cloud computing task scheduling problem. An interval many-objective cloud task scheduling optimization (I-MCTSO) model is developed by transforming uncertain factors into interval parameters. This model considers four optimization objectives: task completion rate, task make time, scheduling cost, and load balance. Mohammad Hasani et al., [21] a presentation designed to improve the performance of the Red Fox Optimization (RFO) algorithm. Initially, a Quasi-Opposition Based Learning method is used to generate the initial population, and a Levy flight method is employed to improve the exploratory ability of newly generated foxes. Two fuzzy control systems are used to achieve a balance between exploration and exploitation. Table 1 summarizes and compares the existing approaches.
In [5] the authors propose an improved version of the ant-lion optimization (ALO) algorithm that is crossbred with the popular particle swarm optimization (PSO) algorithm to improve system scheduling precision for cloud computing. A new security technique known as Data Encryption Standard (DES) is used, which encodes the information present in the cloud while scheduling is performed. The research's goal is to contribute an improved system scheduling framework that is more secure than existing frameworks. Improvement parameters are evaluated in terms of time, load, and cost.
Nanjappan et al. [6] The energy-efficient and reliability aware workflow task scheduling in cloud environment (EERS) algorithm is introduced in this paper, which conserves energy while making the most of the system's reliability. To begin, use a task-rank calculation programme to keep task dependencies intact. Following that, a task clustering algorithm is used to reduce communication costs, resulting in lower energy consumption.
Agrawal et al. [16]. Cloud computing is a rapidly expanding and evolving platform. It offers its customers excellent services. Cloud computing development is significantly improving in terms of security in educational use. It provides numerous methods for accessing various resources' platform applications via on-demand web pages. This paper demonstrates various trending technologies, cloud computing features, and cloud computing security, as well as their application in education. Artificial Intelligence (AI) modernises today's society and paves the way for many digital applications to flourish. AI is important in everything from agriculture to space science. The advancement of cloud storage and wireless communication systems is assisting AI in achieving certain goals in the digital world. Improvements to electronic processors and other chips are also assisting AI in gaining computational efficiency. The design of micro electronic devices is allowing sensors to be moved to specific locations via Internet of Things (IoT) communication. The goal of this author is to examine the performance of AI methodologies in various applications in order to identify research gaps.

The proposed model
In this research, a new IWHOLF-TSC technique has been developed to effectually schedule tasks in CC environment. The proposed IWHOLF-TSC technique has derived a fitness function by minimizing make span and maximizing resource usage in the CC platform. The proposed IWHOLF-TSC technique integrates the concepts of WHO algorithm, which is stimulated from the social living characteristics of wild horses with LF. Figure 1 illustrates the system architecture of TS in CC.

Problem Formulation
The problem of TS from the cloud was determined as for scheduling, distributing, and assigning several various tasks to several VM efficiently and for performing every task that is able from minimum execution time [33]. The cloud system (CS) contains (N pm ) physical machines (PM), and all machines contain (N vm ) VM as demonstrated in Eq. (1).
where PM i , (i = 1, 2, . . . , N pm ) refers the PM carried out from the cloud and it could be written as: where VM k , (k = 1, 2, . . . , N vm ) defines the k th VM. N vm signifies the amount of VM and VM k refers the k th VM devices from the cloud. The feature of VM k was defined as: where id signifies the identifier amount of VM and MIPS k refers the report processing acceleration of VM by millions of instructions-per-seconds.
where N tsk defines the number of tasks i projected by users. Task i implies the i th task from the task series that is defined as:  where SIDT i represents the identification number of j th task and task − length i signifies the length of tasks [34]. Time ECT i defines the predicted completion time to i th task; LI i refers the task preference from the number of tasks N tsk . The Expected Complete Time (ECT) measure of size N tsk × N vm signifies the execution time required that carry out the tasks on all computing devices VM which is resolved by the subsequent matrix:

Design of IWHOLF Algorithm
The WHO approach mathematically simulates and duplicates the social life performance of these wild horses naturally [35]. The horse usually lives from herd with stallion and several foals as well as mares. It can be demonstrated that variations of performances are containing mate and graze, pursue, dominate, command. In the 5 steps for WHO techniques are listed under Primary, an initial population was separated as to several groups. N refers the number of populations and G signifies the number of groups from this technique [36]. All groups have a (5) leader (stallion), thus the number of stallions from this technique is equivalent G , and (NG) denotes the residual population (Foal and mare) were distributed similarly amongst these groups. The subsequent formula is presented for simulating the grazing performance: where X j i,G signifies the present place of foal/mare group members, Stallion defines the stallion place, R refers the uniform stochastic number in the range of -2 and 2, and Z implies the adaptive process computed in the subsequent formula: where P refers the vector containing zero to one, − → R 1 and − → R 3 implies the arbitrary number from the range of zero and one, R 2 represents the uniform arbitrary number from the range of zero and one, TDR stands for the adaptive parameter which begins with 1 and reduces still it attains 0 finally, the execution of technique based on subsequent formula: where it implies the existing iteration and maxit stands for the maximal number of iterations. For implementing the mate performance of horses, the foal (7) drives in group i to temporary group but foal drives in group j to temporary group [37]. For simulating the mate performance of horses, the Crossover function of mean form is presented as: During the WHO technique, Stallions (group leaders) lead the group to water hole [38]. The Stallions compete to this water hole thus the domination group utilizes this water hole primarily afterward another group utilizes the water hole. The subsequent formula is mentioned that step of technique: where Stalllion G i refers the next place of leaders. WH signifies the place of water hole. During the subsequent stage, leader is selected based on fitness. The leader place and relevant member are modifying dependent upon this formula: The IWHOLF was dependent upon cuckoo search (CS) technique [39]. In the iteration of presented technique a novel solution was created utilizing the Levy flight as the subsequent formula: where X i,G implies the i th place of group member, γ represents the step scaling size, X g stands for the global optimum solutions, ⊕ stands for the procedure of element-wise multiplication, denotes the Levy flight (LF) exponents, but u and v are determined as: The standard deviations σ u and σ v are formulated as: where Ŵ refers the Gamma function, a novel candidate solution was created and was executed. The principal benefit of this enhancement was capability of the presented method for balancing global exploration and local exploitation.

Application of IWHOLF Algorithm for Task Scheduling
A major objective function of the IWHOLF technique is to reduce the makespan value by ordering the appropriate collection of tasks to be executed on VMs [40].
Since resource usage is related to makespan value, a higher usage value indicated that the CSP receives huge profit as shown in Algorithm.1.

Algorithm. 1 Task Scheduling
where k = 1, 2, 3,…, N VM , i = 1, 2, 3,…, N tsk , and ECT ik means required execution time of ith tasks on kth VM. N VM represents the total VM count and N tsk represents task count. The integrated fitness value with multi-objective function of all collections is determined by the use (16)  of Eq. (13) that represents the evolution power of the organisms.
Generally, the demanded tasks are planned to free VMs and the tasks are attended depending upon the order. The major intention of task scheduling over VMs is the way of attaining high usage of VMs along with minimal makespan values [41]. The Expected Time to Compute (ETC) of provide task to be listed on every VM can be used by the IWHOLF-TSC technique for scheduling process.

Experimental validation
To further validate the algorithm's task scheduling effect in cloud computing, the IWC algorithm is compared to the ACO, PSO, and WOA algorithms. Table 1 lists the parameters required by the algorithm. Choose a CPU Core i3, memory 4 G DDR3, a hard disc capacity of 1000 G, Windows 7, and MATLAB 2012. The experiment is divided into small-scale and large-scale cloud computing tasks. The comparison indicators are cost value, time value, and memory load value. To explain the effect of better scheduling, this paper sets the number of smallscale tasks to [0, 1000] and the number of large-scale tasks to [1000, 10000].
To demonstrate the algorithm's efficiency in cloud computing task scheduling, the ant colony algorithm (ACO), particle swarm optimization (PSO), and whale optimization algorithm (WOA) were chosen from the classical algorithms and compared with the algorithm proposed herein for cloud computing task scheduling. The Cloud-Sim simulation platform was then used to simulate the cloud computing environment. Table 2 shows the main parameters required by the algorithm in this case. When combined with the characteristics of the tasks in cloud computing, the tasks were divided into small-scale tasks and large-scale tasks, which were compared in the QoS indicators based on time and cost.
A brief makespan (MKS) analysis of the IWHOLF-TSC technique is compared with recent methods under small tasks are provided in Table 3 and Fig. 2 A detailed MKS analysis of the IWHOLF-TSC approach is compared with recent algorithms under large tasks are given in Table 4  A degree of imbalance (DOI) analysis of the IWHOLF-TSC method is compared with recent methods under numerous tasks in Table 5 and Fig. 4. The results indicated that the IWHOLF-TSC method has offered reduced DOI under all tasks [78][79][80][81][82]. For instance, with 100 tasks, the IWHOLF-TSC method has provided       Figure 7 and Table 8 illustrate a comparative success rate examination of the IWHOLF-TSC approach with other existing methods. The figure shows that the cloud computing approach has resulted in higher performance with success rate. For example, with no of tasks 100, the success rate value is 85.478% for IWHOLF-TSC, whereas the WOA, MSA, ALO, and MALO models have obtained success rate of 77.345%, 73.768%, 61.526%, and 65.026%, respectively. However, the IWHOLF-TSC model has shown maximum performance with different data set size. Similarly, under 1000 tasks, the success rate value of IWHOLF-TSC is 93.775%, while it is 83.879%, 75.943%, 64.837%, and 68.937% for WOA, MSA, ALO, and MALO models, respectively.

Conclusion
In this article, a new IWHOLF-TSC technique for effectively scheduling tasks in a CC environment is presented. The purpose of this article is to introduce an IWHOLF-TSC based task scheduling method in cloud computing task scheduling, with the goal of improving the effect of cloud computing task scheduling. Two optimization strategies based on the IWHOLF-TSC algorithm are proposed to further improve scheduling   In the simulation experiment, IWHOLF-TSC was pitted against the ant colony algorithm, the particle swarm algorithm, and the whale optimization algorithm across a variety of tasks. According to the results, the IWHOLF-TSC algorithm performs well in terms of task scheduling time, scheduling cost, and virtual machine. The application is used to schedule cloud computing tasks. Resource allocation and clustering processes for IoT assisted cloud environments can be designed as part of the future scope.