Multi objective task scheduling based on hybrid metaheuristic algorithm for cloud environment

Abstract

Cloud computing is gaining a huge popularity for on-demand services on a pay-per-use basis. However, single data centre is restricted in offering the services, as it does not have unlimited resource capacity mostly in the peak demand time. Generally, the count of Virtual Machines (VM) is more in public cloud; still, the security is not ensured. In contrast, the VMs are limited in private cloud with high security. So, the consideration of security levels in task scheduling is remains to be more critical for secured processing. This works intends to afford the optimization strategies for optimal task scheduling with multi-objective constraints in cloud environment. Accordingly, the proposed optimal task allocation framework considers the objectives such as execution time, risk probability, and task priority. For this, a new hybrid optimization algorithm known as Clan Updated Seagull Optimization (CUSO) algorithm is introduced in this work, which is the conceptual blending of Elephant Herding Optimization (EHO) and Seagull Optimization Algorithm (SOA). Finally, the performance of proposed work is evaluated over other conventional models with respect to certain performance measures.

Keywords

Cloud computing virtual machine task scheduling optimization execution time

1. Introduction

‘Cloud computing is a large-scale distributed computing concept, which includes the development of traditional grid computing and distributed computing’. Task scheduling exists as a remarkable issue in cloud environment [6, 14]. It is the process of scheduling the tasks to use the resources in a timely and secured manner. Thereby, the tasks are allocated to the specific resources that makethe better scheduling of the jobs [26, 8]. The major objective of task scheduling is to improve the Quality of Service (QoS) by maintaining the efficacy of task completion, henceminimizing the cost. This strategy can be attained only if the available virtual resources are deployed in an optimal manner to schedule the tasks [23, 34, 22]. With effective scheduling of resources, a better cloud computing environment can be created. In general, the constraints that are regarded in scheduling methods are task completion cost, execution and allocation time, resource utilization and so on [20, 37].

Moreover, the traditional task-scheduling approaches concern more on Central Processing Unit (CPU) memory, task-resource needs, execution cost and execution time [9, 17, 24]. The task scheduling in the cloud computing is regarded as a Non-deterministic Polynomial-time hardness (NP-hard problem), which can be computed by means of certain heuristic schemes. The traditional works have used Particle Swarm Optimization (PSO) algorithm for scheduling the task in cloud [10, 29, 7]. Furthermore, the scheduling models in conventional distributed computing could not employ in an efficient way as it is dynamic and large-scale.

To date, evolutionary algorithms like Genetic Algorithm (GA) and Estimation of Distribution Algorithm (EDA) were introduced for solving many scheduling and mapping problems [27, 5]. Moreover, the optimization algorithms [39, 16] based on single-objective would apply the traditional algorithms including Max-Min, Suffrage, and Min-Min models. However, the existing algorithms related to scheduling provides less extensibility and adaptability. Some other traditional schemes [21, 35, 11] would not consider the security factors endeavored while decreasing the completion time of task [28, 12, 38]. Hence, it is necessary to develop a new task scheduling model [25, 1] that should take account of the security constraints as well. The main contribution of this adopted method is given as follows:

•
Implements a multi-objective task scheduling model including the constraint like execution time, risk probability, and task priority that ensures secured scheduling process.
•
Proposes a new hybrid optimization algorithm known as Clan Updated Seagull Optimization (CUSO), which is a conceptual blending of Elephant Herding Optimization (EHO) and Seagull Optimization Algorithm (SOA).
•
The proposed method overcomes the drawbacks of the traditional SOA, like high computational cost and easily falling into the local optima and enhances its performance.

In this paper, the review on tasks scheduling in cloud environment is determined in Section 2. Proposed task scheduling scheme: an overview is portrayed in Section 3. Cloud setup and multi-objectives for scheduling the task is portrayed in Section 4. Proposed hybrid task scheduling algorithm: combined elephant herding and seagull optimization is depicted in Section 5. The result and discussion are specified in Section 6. At the end, the conclusion of this paper is depicted in Section 7.
2. Literature review

In 2017, Liu et al. [6] has established a multi-task scheduling model, which incorporated task workload model by considering service quantity and service coefficient. Subsequently, the impacts of diverse workload-oriented task scheduling techniques were analyzed in terms of utilization and total completion time. Scenario without or with time parameters were separately analysed thoroughly. Finally, the simulated outcomes have indicated that the large workload tasks with high priority shortened the make span and increased the utilization without affecting the quality.

In 2019, Abazari et al. [33] have designed a novel efficient technique that considered both interaction and tasks security while scheduling the tasks in cloud. Moreover, a heuristic model was used for task scheduling on the basics of task’s completion time and security requirements for improving the security. In addition, a novel attack response method was presented for reducing the definite security risks in the cloud. Furthermore, the outcomes demonstrated that the designed algorithm has reduced the threats, thus enhancing the security of the network.

In 2019, Panda et al. [36] have developed multi-cloud network, where several clouds were integrated mutually for providing a combined service in a mutual manner. On the other hand, the scheduling of task in multi-cloud was highly difficult when compared to single cloud. Three algorithms have been proposed for a multi-cloud network. The presented model depends on the conventional Min-Min and Max-Min algorithm. Finally, the developed model was evaluated with respect to average cloud consumption, throughput, and make span over other approaches.

In 2019, Pang et al. [2] have developed an EDA-GA and GA based hybrid algorithm for task scheduling. Initially, the sampling and probability models of EDA were exploited for generating specific viable solutions. As the final step, the optimum scheduling approach for allocating tasks to VM’s were realized. This model has benefits of stronger searching capability and faster convergence speed. The investigational results illustrated that the presented scheme has efficiently improved the load balancing capability and reduced the completion time.

In 2019, Sanaj and Joe [13] has explored Chaotic Squirrel Search Algorithm (CSSA) for optimal multitask scheduling in an IaaS cloud environment. The technique has generated job plans continuously, which make the present schemes more cost-efficient. To guarantee global convergence, the network was generated with chaotic optimization for well-organized task allocation. Finally, the developed CSSA model has revealed better outcomes when compared over the traditional Squirrel Search Algorithm (SSA) model.

In 2020, Wilczyński and Joanna [26] has introduced a novel method for scheduling the tasks depending on block chain mechanism. In contrast to traditional schemes, the execution of block chain modules was offloaded. In addition, a new proof-of-schedule consensus algorithm (instead of ‘proof-of-work’) was developed and have used Stackelberg games to enhance the authorization of the created schedules. The experimentations has revealed that the presented method significantly enhanced the effectiveness of created schedules with improved make span.

In 2020, Lavanya et al. [8] has explored two allocation models termed asThreshold based Task scheduling algorithm (TBTS) algorithm and Service level agreement-based Load Balancing (SLA-LB) models. TBTS scheduled the tasks in batches and it aids the scheduling of tasks in virtual machines with diverse configurations. SLA-LB scheduled the tasks in a dynamic manner depending on the necessity of users, like budget and deadline. Experimental outcomes revealed that the outcome of the developed approach outperformed the traditional models regarding utilization factor, penalty, gain cost and make span.

In 2020, Ismayilov and Haluk [23] have investigated a prediction-oriented approach named as Neural Network Dominated Sorted Genetic Algorithm (DNN-DNSGA-II) that incorporated Non-Dominated Sorted Genetic Algorithm (NSGA-II) with ANN framework. In addition, five foremost non-prediction oriented dynamic approaches were adopted for solving the workflow scheduling issue. The proposed work concerned on six objectives namely, enhancement of utilization and reliability reduction of energy, cost, make span and level of imbalance.

Table 1
Review on conventional task scheduling models in cloud environment: Features and challenges

Author [citation]	Adopted scheme	Features	Challenges
Liu et al. [6]	SAW model	Reduced make span	Continuous arrival of task is not considered
		Highly reliable
Abazari et al. [33]	MOWS	Reduces security threats	Have to analyse the dynamic work flow
		High make span
Panda et al. [36]	Min-Min and	Minimal complexity	No consideration on fault tolerance
	Max-Min model	High utilization of cloud
Pang et al. [2]	EDA-GA	Improved load balance	Need consideration on real cloud environments
		Minimal execution time
Sanaj and Joe [5]	CSSA algorithm	Cost effective	Analysis on real time has to be focused
		Increased throughput
Wilczyński and Joanna [26]	Stackelberg Game	Higher make span	Real scenario has to be focused more
		Highly secure
Lavanya et al. [8]	SLA-LB model	Minimal execution time	Energy utilization is not taken into account
		Reduced penalty cost
Ismayilov and Haluk [23]	NN model	Highly reliable	Requires concern on machine learning models
		Reduced make span

Table 1 demonstrate the review on task scheduling in cloud environment and the works are arranged in a year wise manner. The years are arranged as per the ascending order.

Initially, SAW model was deployed in [6] that offer high reliability with reduced make span. MOWS was developed in [33] that offers improved make span with minimal security threats, but it have to analyze the dynamic work flow. In addition, Min-Min and Max-Min model was used in [36], which provides minimal complexity with high utilization of cloud; nevertheless, it needs deliberation on fault tolerance. Likewise, EDA-GA was presented in [2] that enhance the load balance and it concerns on the minimal execution time. However, it needs consideration on real cloud environments. Nevertheless, continuous arrival of task is not considered. CSSA algorithm was deployed in [13] that are cost effective and it also increased the throughput, however, analysis on real time has to be concentrated more. In addition, Stackelberg Game was presented in [26] that offers improved make span and it is highly secure. Nevertheless, real scenario has to be focused more. Also, SLA-LB model were employed in [8] that provides minimal execution time with reduced penalty cost. However, it requires consideration on energy utilization. Finally, NN model was presented in [23] that offers reduced make span with higher reliability; but, machine learning models are not considered. There, these limitations have to be considered for improving the performance of scheduling the task in cloud effectively in the current research work.

The issue of user communication and task scheduling in a device-to-device (D2D) network is a costly method and the dynamic workflow scheduling was not taken into account. A pair-wise comparison matrix technique is used to allocate the resources. It is not possible to find a solution if the matrix size is too large. However, the majority of these works were not considered for publication of environment with multiple clouds [36]. Reduce the makespan and balance the workload in the network while having no effect on the other fundamental parameters. A meta-heuristic method consists of a task sequencing method and a virtual machine searching strategy. The similarity function, task type, dependency relationship between the tasks and the input and output data size are not considered. Moreover, the study does not provide detailed examination of convergence rate [36].

3. Proposed task scheduling scheme: An overview

The major components of cloud environment are listed below:

•
Cloud Manager: This is a central entity that handles the customers’ service requests and collects the significance of cloud providers’ VMs.
•
Customer ( $C U$ ): This is the client of cloud’s service. The CU can create their requests through the cloud manager’s help.
•
CSP: It is a cloud distributor and it deploys the VMs on the physical server. The CSP provide on-demand services. Each cloud has a management server to direct the peak demands that interrelates with other manager servers to pass the customer requests. Moreover, the demands of customer are often extended in the clouds, and the requests are controlled through a distributed scheme.

The following connections occur among the components of the cloud approach are as follows: “(a) CU-cloud manager, (b) cloud manager-CSP, (c) CSP-CSP, (d) CSP-cloud manager, and (e) cloud manager-CU”. Additionally, the overhead will occurred for making a decision on the individual part. However, the flexibility of the cloud model creates these marginal overheads. Figure 1 illustrates the adopted task scheduling model in cloud.

The manager locates the task in a waiting queue while the cloud manager get a task, and an active VM is identified for assigning the task depending on the objectives. Moreover, the defined objectives in this proposed work are execution time, risk probability, and task priority. The adopted model has concerned on optimal allocation of tasks through the optimization model. Further, the tasks are allocated concurrently in the VMs and the scheduling has occurred in parallel. A new hybrid algorithm referred to CUSO model is introduced for optimal scheduling. In addition, the risk probability is the major consideration, as the parameter ensures secured scheduling of task. The VM allocation is done for each task based on the risk probability (along with other metrics).

Figure 1.
Cloud task scheduling architecture.

4. Cloud setup and multi-objectives for scheduling the task

4.1 Cloud setup

Consider a cloud $C_{J}$ with cloud service provider denoted by CSP. The scheduling strategy $S_{J}$ , and the count of VMs $|{V_{J}}|$ is allocated by the CSP. The CSP allows the cloud to process requests from the user. The PM with large count of VMs resides within the cloud. Moreover, the request from the users is regarded as the tasks [19]. Further, the task set $T=T_{1},T_{2},T_{3},\ldots,T_{L}$ is a dependent tasks in which $T_{J},1\leqslant J\leqslant L$ are $J^{\text{th}}$ tasks with an instruction set $\textit{ins}_{J}$ (in MI). For processing these tasks, a set of VM is regarded $V=V_{1},V_{2},V_{3},\ldots,V_{N}$ , in which the VMs set is $V_{J},1\leqslant J\leqslant N$ and it is deployed under $C_{J}$ . Moreover, a virtual machine $VM_{I}\in V_{J};1\leqslant J\leqslant N;1\leqslant I\leqslant|{V_{J}}|$ has the processing speed in MIPS $P_{I}$ . The total VM in all the clouds is indicated as $N^{\prime}=\sum\limits_{J=1}^{m}{|{V_{J}}|}$ . The task execution time on $VM_{I}$ is $T_{J},1\leqslant J\leqslant L$ . Additionally, $J\leqslant I\leqslant N$ is depicted in the form of the matrix and it is known as ETC matrix. Further, the ETC matrix is indicated in Eq. (1).

$\displaystyle\textit{ETC}=\left\{\begin{array}[]{*{20}c}&{T_{1}}&{T_{2}}&{% \ldots}&{T_{L}}\\ {VM_{1}}&{\textit{ETC}_{11}}&{\textit{ETC}_{21}}&{\ldots}&{\textit{ETC}_{11}}% \\ \vdots&\vdots&\vdots&\vdots&\vdots\\ {VM_{|{V_{1}}|}}&{\textit{ETC}_{1|{V_{1}}|}}&{\textit{ETC}_{11|{V_{1}}|}}&{% \ldots}&{\textit{ETC}_{L|{V_{1}}|}}\\ \vdots&\vdots&\vdots&\vdots&\vdots\\ {VM_{\gamma+1}}&{\textit{ETC}_{1(\gamma+1)}}&{\textit{ETC}_{2(\gamma+1)}}&{% \ldots}&{\textit{ETC}_{1(\gamma+1)}}\\ \vdots&\vdots&\vdots&\vdots&\vdots\\ {VM_{\gamma+1}|{V_{N}}|}&{\textit{ETC}_{1(\gamma+|{V_{N}}|)}}&{\textit{ETC}_{2% (\gamma+|{V_{N}}|)}}&{\ldots}&{\textit{ETC}_{L(\gamma+|{V_{N}}|)}}\\ \end{array}\right.$ (1)

Figure 2.

Workflow model.

In Eq. (1), $\gamma=\sum\limits_{K=1}^{N-1}|{V_{K}}|$ . Moreover, $\textit{ETC}_{JI},1\leqslant J\leqslant L;1\leqslant I\leqslant N^{\prime}$ represents the ratio of the instruction set (in MI) to the processing speed. Moreover, $\textit{ETC}_{IJ}$ is shown in Eq. (2) [19].

$\displaystyle\textit{ETC}_{JI}=\frac{\textit{INS}_{J}}{P_{I}}$ (2)

The mapping is performed in terms of allocating, scheduling, and matching tasks. The mapping function $F$ attains the request set $R=\{{R_{1},R_{2}^{,}R_{3},\ldots R_{r}}\}$ from the $C U$ , $CU=\{{CU_{1},CU_{2}^{,}CU_{3},\ldots CU_{r}}\}$ . The request $R=\{{T_{1},T_{2}^{,}T_{3},\ldots T_{L^{\prime}}}\};1\leqslant J\leqslant r;L^{% \prime}<<L$ is assumed to the group of VM’s $V=\{{V_{1},V_{2},V_{3},\ldots,V_{N}}\}$ . Further, $|T|=\sum\limits_{K=1}^{r}{|{R_{K}}|}$ . The VM set as $V(F:T\to V)$ for secure mapping of the task onto the cloud. This work intends to schedule the optimal task by considering the objectives like (a) lower execution time of VM, (b) lower risk probability, and (c) high task priority. The work flow model is depicted in Fig. 2.

4.2 Cloud parameters

The parameters are given in the Table 2. Only one physical machine is considered and the 20 virtual machine are considered.

Table 2
Cloud parameters

S. No	Parameters
1.	Cloud $=$ 1
2.	PM $=$ 1
3.	VM $=$ 20
4.	Task $=$ [200, 400, 600, 800, 1000]

4.3 Objective function

As per the proposed work using optimization logic, the multi-objective functions are defined as the single-objective function during the scheduling process, and the defined objective function of this proposed work is given in Eq. (3), in which, the weight $W$ ranges from [0, 1].

$\displaystyle\textit{obj}=\min\{({1-W})ET^{\textit{task}}+({1-W})RP+(W)*% \textit{Rank}\}$ (3)

The VM and tasks are the input solution to the proposed CUSO model for optimal scheduling regarding its objectives. The solution encoding of the adopted work is given in Fig. 3.

Figure 3.

Solution encoding of proposed work.

Execution time of VM ( $ET^{VM}$ ): The sequence of tasks gets executed and appears in queues. The execution time is known as the time spent through the VM for processing a task. The task’s execution time tends to vary on the basis of its application. The missing deadline problems are solved while a task is executed in minimum amount of time. Moreover, $E T$ is evaluated by Eq. (4).

$\displaystyle ET^{VM}=\left({\frac{1}{3}}\right).G\times\left\{{\frac{\textit{% MIPS of VM}}{\textit{Max}(\textit{MIPS})}+\frac{\textit{Z of VM}}{\textit{Max}% (\textit{Z})}+\frac{\textit{A of VM}}{\textit{Max}(\textit{A})}}\right\}$ (4)

In Eq. (4), $Z$ , $A$ indicates the processor and the memory of VM, correspondingly, and $G$ is set constantly as 1.

Execution time for all tasks $ET^{\textit{task}}$ : Mathematically, the formula for $ET^{\textit{task}}$ is given in Eq. (5).

$\displaystyle ET^{\textit{task}}=\frac{1}{\max(ET^{\textit{task}}\times H)% \times M}\times\sum\limits_{J=1}^{T_{J}}{({H\times ET^{\textit{task}}})}$ (5)

Risk Probability $R P$ : While scheduling, the risk probability [33] of tasks $T_{J}$ , $VM_{J}$ for a particular task is given in Eq. (6).

$\displaystyle\Pr ob^{q}({T_{J}^{q},VM_{J}^{q}})=\left\{{{\begin{array}[]{*{20}% c}0&{\text{if }SD_{J}^{q}\leqslant SS_{I}^{q}}\\ {1-e^{-({SD_{J}^{q}\leqslant SS_{I}^{q}})}}&\text{otherwise}\\ \end{array}}}\right.$ (6)

In Eq. (6), $SD_{J}^{q}$ , $SS_{I}^{q}$ indicates the security demand and security services $t_{i}$ . Further, the task risk probability is the joint probability of all risk probability of the task for each security service. If $SD_{J}^{q}<SS_{I}^{q}$ , then the risk probability of scheduling $T_{J}$ on $VM_{J}$ is zero. Here, $\Pr ob({T_{J},VM_{I}})$ indicates the probability of task $T_{J}$ attacked during the execution, and it is specified in Eq. (7).

$\displaystyle\Pr ob({T_{J},VM_{I}})=1-\prod\limits_{q}{\left({1-\Pr ob^{q}({T_% {J}^{q},VM_{I}^{q}})}\right)}$ (7)

The risk probability of workflow is an average of the probabilities of all tasks. The average probability of composed tasks being attacked in a workflow is determined in Eq. (8).

$\displaystyle RP=\frac{\sum\limits_{T_{J}\in T}{\Pr ob({T_{J},VM_{I}})}}{N}$ (8)

Task Priority: Assume the following scheduling approaches [33].

•

Certain tasks are scheduled on the similar VM; still, they work in a specific way.

•

The task would not start till all the input data is obtained.

•

The task would not begin until all predecessor tasks are performed.

Here, the rank is assigned to each task through DAG’s bottom-up traversal. The security to the task rank is added unlike other scheduling approaches. Similarly, if two tasks have the identical communication cost and complexity, the high security task defines high rank because it schedules faster. Moreover, the task with more security demand would program on highly secure VM.

$\displaystyle\textit{Rank}_{u}({T_{J}})=w_{J}+\mathop{\max}\limits_{T_{I}\in% \textit{succ}({T_{J}})}({c_{J,I}+\textit{Rank}_{u}({T_{I}})})+\sum\nolimits_{K% }{{SD_{i}}\mathord{\left/{\vphantom{{SD_{i}}K}}\right.\kern-1.2pt}K}$ (9)

In Eq. (9), $c_{J,I}$ specifies the average communication time among $T_{J}$ and $T_{I},w_{J}$ denotes the average of task $T_{J}$ execution time of VMs, and $\textit{succ}({T_{J}})$ indicates the group of sudden successor tasks of $T_{J}$ .

5. Proposed hybrid task scheduling algorithm: Combined elephant herding and seagull optimization

5.1 Proposed CUSO model

Even though, the existing SOA [3] model solves the complex large-scale constrained issues, the constraints provide high computational complexity. In this work, SOA is combined with EHO [18] to propose the hybrid model termed as CUSO scheme. Generally, the hybrid optimization schemes are said to be more appropriate for specific search issues [40]. Accuracy is improved by employing the hybridization concept.In the meta-heuristic approach, the hybridization concept means merging the algorithms in order to provide a new powerful algorithm based on the features of the merged ones. In the adopted model EHO is merged with SOA. The main disadvantage of SOA is that it relies on local optima and has a high computational complexity. To overcome the certain drawback the SOA is hybridized with EHO. The EHO will provide low computational complexity and it escapes from the local optima.

Seagull is a sea bird found all over the world and its scientific name is Laridae. Seagulls are the large range of species with various lengths and masses. It is an intelligent bird and they use bread crumbs to catch the attention of the fish. Generally, the seagulls exist in colonies and they use their intelligence to attack and find the prey. Two phases of seagull behaviour includes like migration and attacking behaviours. The seasonal moments of seagulls is Migration that moves from one place to other for finding the most abundant and richest food sources that provides more adequate energy.

Seagulls move towards the best survival fittest seagull direction in a group (i.e.), the seagull’s fitness value is less than others. In addition, other seagulls updated their early locations on the basis of fittest seagull. The seagulls often attack the other migrating birds in the sea. The seagulls generate the spiral shape moment in the attacking phase. Moreover, the seagulls travel in a group throughout the migration phase. The seagull’s prior locations are dissimilar that avoids the collision among each other.

(i) Migration (exploration): The SOA stimulates the group of seagulls’ moment from one location to other during the migration phase. Further, the seagull must assure 3 conditions in this phase:

Collision avoidance: An extra variable $D$ is used for calculating the new search agent location to avoid the collision among the neighbours.

$\displaystyle\vec{B}_{u}=D\times\mathord{\buildrel\lower 3.0pt\hbox{$% \scriptscriptstyle\leftarrow$}\over{Z}}_{u}(d)$ (10)

In Eq. (10), $\vec{B}_{u}$ specifies the search agent’s position that would not mixed with other search agent, $D$ denotes the search agent’s moment behaviour, $\mathord{\buildrel\lower 3.0pt\hbox{$\scriptscriptstyle\leftarrow$}\over{Z}}_{u}$ specifies the search agent’s current position, and $d$ refers to the current iteration.

$\displaystyle D=g_{f}-({d\times({{g_{f}}\mathord{\left/{\vphantom{{g_{f}}{Max_% {iteration}}}}\right.\kern-1.2pt}{\textit{Max}_{\textit{iteration}}}})})$ (11)

In Eq. (11), $d=0,1,2,\ldots,\textit{Max}_{\textit{iteration}}$ , $g_{f}$ is used for controlling the frequency of deploying variable $D$ that is reduced linearly from $g_{f}$ to 0. Here, the $g_{f}$ value is set as 2.

Movement towards best direction of neighbors: Conventionally, in SOA, the search agents are moved towards the best direction of nearby search agent onceit neglects the collision among the neighbors. However, as per the proposed CUSO method, the positions are updated based on the clan update of EHO, and it is given in Eq. (12).

$\displaystyle Z_{\textit{new},ci,j}=Z_{ci,j}+\alpha*({Z_{\textit{best}}-Z_{ci,% j}})\times\mathord{\buildrel\lower 3.0pt\hbox{$\scriptscriptstyle\frown$}\over% {r}}+\textit{Levy}(\beta)$ (12)

In Eq. (12), $Z_{\textit{new},ci,j}$ indicates the newly updated clan of EHO, $Z_{ci,j}$ refers to the old position for elephant $j$ in clan $c i$ , and $\mathord{\buildrel\lower 3.0pt\hbox{$\scriptscriptstyle\frown$}\over{r}}\in[{0% ,1}]$ .

Further, the behavior of $G$ is randomized and used to balance the exploitation and exploration. Moreover, $G$ is computed using Eq. (13).

$\displaystyle G=2\times D^{2}\times\textit{rand}$ (13)

In Eq. (13), rand is the random number within [0, 1].

Remain close to the best search agent: Further, the position of search agent is updated based on the best search agent, and it is specified in Eq. (14).

$\displaystyle\vec{Q}_{u}=|{\vec{B}_{u}+\vec{A}_{u}}|$ (14)

In Eq. (14), $\vec{Q}_{u}$ indicates the distance among the best fit search agent and other search agent.

(ii) Attacking or exploitation: This phase aims to develop the experience and history of the search process. In addition, the Seagulls continuously alter the angle of attack and its speed during the migration. The seagulls maintain their altitude by their weight and wings. The spiral movement behavior occurred in the air during the prey attack. This behavior in ${d}^{\prime}$ , ${l}^{\prime}$ , and ${n}^{\prime}$ planes is determined in Eqs (15)–(17).

$\displaystyle{d}^{\prime}=x\times\cos(y)$ (15) $\displaystyle{l}^{\prime}=x\times\sin(y)$ (16) $\displaystyle{n}^{\prime}=x\times y$ (17)

where

$\displaystyle x=h\times e^{ij}$ (18)

In Eq. (18), $x$ indicates the radius of spiral’s each turn, $e$ specifies the base of the natural logarithm, $h$ and $j$ denotes the constants for defining the spiral shape. Conventionally, $i$ indicates the random number within $[{0\leqslant i\leqslant 2\pi}]$ . As per the proposed CUSO model, $i$ is calculated using $\frac{\textit{Chaotic map}}{\textit{Sine map}}$ as per Eq. (19), where $a$ is the control parameter ranges from 0.4.

$\displaystyle i=\frac{a}{4}\sin(\vec{Z}_{u})$ (19)

In the attacking phase, the search agent could sustain the positions based on the best solution. However, as per the proposed CUSO method, the positions of search agent are updated as given in Eq. (20).

$\displaystyle\vec{Z}_{u}(d)=({\vec{Q}_{u}\times{d}^{\prime}\times{l}^{\prime}% \times{n}^{\prime}})+Z_{\textit{best}}(d)+({\vec{Z}_{\textit{best}}(d)-\vec{Z}% _{u}(d)})\times\omega$ (20)

In Eq. (20), $\vec{Z}_{\textit{best}}$ saved the best solution and updated the another search agents location, $\omega$ denotes the inertia weight (i.e.), $\omega=0.95$ .

The SOA begins with a random created population. During the iteration process, the search agents could update their positions in terms of best search agent. $D$ is linearly minimized from $g_{f}$ to 0. Further, the variable $G$ is responsible for smooth transition among exploitation and exploration. Algorithm 1 shows the pseudo code of the adopted CUSO scheme.

Algorithm 1: Pseudo code of adopted CUSO model
1. Initialize seagull population with position $\vec{Z}_{u}$
2. Optimal search agent $\vec{Z}_{\textit{best}}$
3. Initialize the parameters $D$ , $G$ and $\textit{Max}_{\textit{iteration}}$
4. Set $g_{f}\leftarrow 2$
5. Set $h\leftarrow 1$
6. Set $j\leftarrow 1$
7. While ( $d<\textit{Max}_{\textit{iteration}}$ ) do
8. $\vec{Z}_{\textit{best}}\leftarrow$ Compute fitness $({\vec{Z}_{u}})$
9. $\textit{rand}\leftarrow\textit{Rand}({0,1})$
10. $y\leftarrow\textit{Rand}({0,2\pi})$
11. $x\leftarrow h\times e^{ij}$
12. Calculate the distance $\vec{Q}_{u}$ using Eq. (14).
13. $Z\leftarrow{d}^{\prime}\times{l}^{\prime}\times{n}^{\prime}$
14. Compute ${d}^{\prime},{l}^{\prime},{n}^{\prime}$ planes using Eqs (15) to (17).
15. The proposed position update of search agent is given in Eq. (20).
16. $d\leftarrow d+1$
17. Return $\vec{Z}_{\textit{best}}$
18. End

6. Results and discussions

6.1 Simulation environment

The adopted task scheduling in cloud environment with CUSO model was implemented in PYTHON. The performance of proposed CUSO model for optimal task scheduling is validated over other models with respect toexecution time, makespan, response time, resource utilization, and risk probability as well. It consists of only one physical machine and 20 virtual machines are considered. The overall count of the task to be accomplished is varied as 200, 400, 600, 800, and 1000, respectively. This evaluation is done with a varying count of VMs. Further, the proposed CUSO model is evaluated over the existing works like PSO [31], Whale Optimization Algorithm (WOA) [4], Modified Mean Grey Wolf Optimization MGWO [30], Grey Wolf Optimization (GWO) [32], Grasshopper Optimization Algorithm (GOA) [15], EHO [18], and SOA [3], respectively.

6.2 Convergence graph

The convergence of the adopted CUSO model and the traditional models is assessed by varying the count of iterations from 0, 20, 40, 60, 80, and 100, correspondingly. Figure 4 represents the convergence analysis of adopted approach over other existing approaches like PSO, WOA, MGWO, GWO, GOA, EHO, SOA, CSSA and NN, respectively. The proposed approach attains the minimum cost function as per the defined objectives in Eq. (3). Initially, the cost function at 0 ${}^{\text{th}}$ iteration attained by both the proposed CUSO model and existing models is high. As the count of iteration increases, the cost function of CUSO algorithm gets decreased. This indicates that the proposed work ensures better or optimal task scheduling. Moreover, the hybrid concept solves the given problem with better convergence to minimization function.

In particular, the cost function of proposed CUSO model had a fall in between the range 0 to 45 count of iterations and then it remains constant till 100 ${}^{\text{th}}$ iteration. The cost function of the adopted CUSO scheme provides lower value ( $\sim$ 112) at the 80 ${}^{\text{th}}$ iteration than other existing models. Further, the cost function of the proposed CUSO model attains reduced cost values with better performance at the 100 ${}^{\text{th}}$ iteration when compared to the other techniques like PSO, WOA, MGWO, GWO, GOA, EHO, SOA, CSSA and NN, respectively in Fig. 4. Till the 30 ${}^{\text{th}}$ iterations, the cost function of the proposed CUSO model seems little poorer than the existing method like MGWO. After the 45 ${}^{\text{th}}$ iteration, the adopted CUSO model had attained the minimum value. Consequently, it is shown clearly that the adopted CUSO approach had recorded the least cost function that indicates the tasks are scheduled more optimally.

Figure 4.

Convergence graph of proposed Clan Updated Seagull Optimization model and existing approaches.

6.3 Evaluationon execution time

The analysis of execution time for each task is not the similar, as it varies on the basis of the application used. Nevertheless, the VMs should execute the tasks with minimal execution time. Figure 5 illustrates the execution time analysis of the proposed work over conventional model. From the graph, the adopted CUSO model is 51.578%, 54%, and 11.53% better with minimum execution time than the traditional models like WOA, MGWO, and SOA, respectively for task count $=$ 1000 in Fig. 5. This is the impact of proposed hybrid concept to reach the objective of execution time minimization. Additionally, the proposed CUSO model had achieved the value of ( $\sim$ 0.5 secs) at task count $=$ 400 that is considered to be the least execution time when compared to the existing works like PSO, MGWO, GWO, CSSA and NN, respectively. When compared to the task count 200, the proposed model attains lower execution time for task count 600. Though, the execution time of the adopted CUSO scheme is varied for certain task counts, the overall outcomes of the proposed algorithm are capable for task scheduling.

Figure 5.

Analysis on execution time of proposed Clan Updated Seagull Optimization model and existing approaches.

6.4 Evaluation on makespan

The Evaluation on makespan of the adopted CUSO scheme and existing schemes for various task counts is shown in Fig. 6. In graph, the proposed CUSO model had achieved the least makespan while scheduling task count 200 than other task counts. The proposed CUSO model attains better outcomes with less makespan value than the existing works like PSO, WOA, MGWO, GWO, GOA, EHO, SOA, CSSA and NN,respectively while scheduling 400 counts of tasks. On observing the figure, the proposed CUSO model had recorded the least makespan value ( $\sim$ 240 secs) for 100 tasks count than other existing works. Therefore, the improvement of the adopted CUSO scheme has attained effectively when compared to other existing techniques.

Figure 6.

Evaluationon makespan of proposed Clan Updated Seagull Optimization model and existing approaches.

6.5 Evaluationon resource utilization

Figure 7 represents the resource utilization of both the adopted CUSO scheme and the traditional approaches. As per the objectives of the proposed model in Eq. (3), the resource utilization is less to execute more tasks. On observing the graph, the proposed CUSO model had utilized less resource to execute the 800 task when compared to other traditional models like PSO, WOA, MGWO, GWO, GOA, EHO, SOA, CSSA and NN, respectively. Moreover, the presented CUSO model is 5.17% better than the extant approaches like PSO for task count $=$ 200. This impact is due to the logical modification of hybrid algorithm combining clan update of EHO in sea gull. The proposed work had recorded the minimum resource usage ( $\sim$ 4.2) that is found to be better outcomes than other existing models. Thus, the analysis has shown the improvement with minimal resource utilization of proposed work for task scheduling.

Figure 7.

Evaluationon resource utilization of proposed Clan Updated Seagull Optimization model and existing approaches.

Figure 8.

Analysis on risk probability of adopted Clan Updated Seagull Optimizationschemes and existing approaches.

6.6 Analysis on risk probability

Figure 8 represents the analysis on risk probability of adopted CUSO scheme over other existing algorithms. On observing the graph, it is proved that the proposed CUSO model ensures lower risk probability for scheduling and executing the task counts. Nevertheless, the traditional model portrays more risk. From the graph, the proposed CUSO model had attained minimum risk probability for task count 600 while scheduling the tasks when compared to other traditional models like PSO, WOA, MGWO, GWO, GOA, EHO, SOA, CSSA and NN, respectively. Moreover, the risk probability acquired by the proposed CUSO model while scheduling the task 800 that is the least value ( $\sim$ 200) when compared to PSO $=\sim$ 205, WOA $=\sim$ 215, GWO $=\sim$ 225, GOA $=\sim$ 235, EHO $=\sim$ 210, CSSA $=\sim$ 248 and NN $=\sim$ 202, respectively. Further, the risk probability of the proposed seems to be minimal than the conventional schemes for all other tasks. Finally, the analysis has proven that the proposed CUSO model has the ability to process the tasks scheduling in a secured manner than other schemes.

6.7 Overall performance examination

Tables 6 to 7 represents the overall performance Examination of the adopted CUSO scheme over other existing models for task count 200, 400, 600, 800, and 1000, respectively. From the Table 6, the presented CUSO model provides better outcomes with lower execution time, risk probability, makespan, and resource utilization at task count 200 than other traditional models like PSO, WOA, MGWO, GWO, GOA, EHO, SOA, CSSA and NN, respectively. In addition, the proposed attain minimum risk probability ( $\sim$ 116.484) at task count 400 method than the existing schemes like PSO, WOA, MGWO, GWO, GOA, EHO, and SOA, CSSA and NN, respectively, in Table 6. Moreover, the adopted CUSO method attain minimum risk probability ( $\sim$ 147.5764) at task count 600 than the existing schemes like PSO, WOA, MGWO, GWO, GOA, EHO, and SOA, CSSA and NN, respectively, in Table 6. Likewise, the overall performance of the adopted CUSO scheme holds lesser execution time that is 7.49% at task count 800 than the traditional models like GOA. In Table 7, the proposed CUSO model achieved with minimum makespan for task count 1000; whereas the conventional models like PSO, WOA, MGWO, GWO, GOA, EHO, SOA, CSSA and NN, respectively holds maximum value. Further, the resource utilization of proposed CUSO model attains lower values for task count 1000 than the task count 200. Therefore, the betterment of the proposed CUSO model has effectively validated for all task counts.

6.8 Parametric evaluationon proposed model

Table 8 shows theparametric evaluationof presented CUSO model over the prevailing approaches based on the measure. The parametric evaluation is obtained by varying the random variable $\mathord{\buildrel\lower 3.0pt\hbox{$\scriptscriptstyle\frown$}\over{r}}$ as per Eq. (12). From the table, the parametric analysis of the adopted CUSO approach attain minimum makespan better outcomes ( $\sim$ 56.6125) at random variable of 0.5 values for task count 200 than the task count 1000. Particularly, the proposed CUSO model has attained minimum risk probability for task count 200 than the task count 800 at random variable 0.8. In the Table 8, the adopted CUSO scheme has shown lower resource usage at random variable 0.2 for task count 1000. The adopted algorithm obtains minimal execution time for task count 600 at random variable 0.5. From the evaluation, the overall performance of proposed algorithm is proved the scheduling of tasks by satisfying the constrains used in the work.

6.9 Limitations

The cloud environment is a complex system with many shared resources and unpredictability, and it is influenced by uncontrollable external events. The machines are also located in cloudy environments in various areas, with varying processing capabilities and specifications, as well as varying costs. In this case, the cost and duration of the schedule, as well as the resources allocated, are critical and cannot be

Table 3
Overall performance examination of adopted Clan Updated Seagull Optimizationscheme over other existing techniques for task count 200

Metrics	PSO [31]		WOA [4]		MGWO [30]		GWO [29]		GOA [15]		EHO [18]		SOA [3]		CSSA [13]		NN [23]		Proposed CUSO
Makespan	41.	44103	397.	5558	31.	84453	36.	21801	48.	12479	63.	68906	44.	91647	39.	1424	52.	1432	35.	29151
Resource Utilization	5.	828261	3.	018444	5.	792937	5.	420987	5.	534353	5.	088743	5.	16775	4.	0914	2.	175	5.	638709
Execution Time	0.	532631	0.	52999	0.	525607	0.	52127	0.	527377	0.	485561	0.	525626	0.	3254	0.	5172	0.	523005
Risk Probability	52.	56233	61.	53523	58.	03437	65.	51242	59.	31379	54.	08728	54.	31907	55.	2107	64.	3129	51.	65806

Table 4

Overall performance Examinationof adopted Clan Updated Seagull Optimizationscheme over other existing techniques for task count 400

Metrics	PSO [31]		WOA [4]		MGWO [30]		GWO [29]		GOA [15]		EHO [18]		SOA [3]		CSSA [13]		NN [23]		Proposed CUSO
Makespan	109.	6628	82.	24709	274.	157	109.	6628	73.	10852	66.	28287	63.	96996	88.	1241	75.	321	59.	21165
Resource Utilization	5.	901442	5.	773975	5.	722793	5.	64095	5.	67655	5.	608672	5.	536439	5.	2131	4.	2435	5.	841697
Execution Time	0.	495501	0.	457918	0.	549908	0.	493434	0.	476337	0.	4656	0.	458044	0.	4325	0.	3425	0.	486887
Risk Probability	120.	8317	134.	323	130.	8132	140.	8779	128.	8018	116.	943	123.	1645	120.	5231	124.	23	116.	4846

Table 5

Overall performance examination of adopted Clan Updated Seagull Optimizationscheme over other existing techniques for task count 600

Metrics	PSO [31]		WOA [4]		MGWO [30]		GWO [29]		GOA [15]		EHO [18]		SOA [3]		CSSA [13]		NN [23]		Proposed CUSO
Makespan	99.	61169	758.	5206	579.	0074	83.	80719	76.	15637	79.	71904	251.	9593	98.	1254	89.	9912	78.	45233
Resource Utilization	5.	348773	1.	693569	3.	132002	5.	192848	5.	368189	5.	406365	4.	819342	5.	4213	4.	9121	5.	516828
Execution Time	0.	425684	0.	30372	0.	379732	0.	42328	0.	415052	0.	420148	0.	331199	0.	4321	0.	3421	0.	421016
Risk Probability	136.	5882	90.	00124	168.	018	175.	3485	165.	8778	155.	9761	150.	563	140.	263	160.	231	147.	5764

Table 6

Overall performance examination of adopted Clan Updated Seagull Optimizationscheme over other existing techniques for task count 800

Metrics	PSO [31]		WOA [4]		MGWO [30]		GWO [29]		GOA [15]		EHO [18]		SOA [3]		CSSA [13]		NN [23]		Proposed CUSO
Makespan	130.	5969	113.	9249	481.	4541	125.	0396	104.	5057	127.	8182	260.	4229	128.	3213	123.	121	118.	1751
Resource Utilization	4.	925062	5.	133923	6.	38925	5.	251919	5.	537441	5.	162889	5.	182885	4.	9121	4.	8213	5.	066781
Execution Time	0.	472092	0.	476941	0.	477087	0.	501399	0.	52143	0.	487376	0.	491804	0.	45321	0.	3912	0.	482339
Risk Probability	205.	1428	211.	9427	132.	0084	223.	9666	234.	1875	207.	1191	197.	8466	195.	2143	175.	6732	199.	7374

Table 7

Overall performance examination of adopted Clan Updated Seagull Optimizationscheme over other existing techniques for task count 1000

Metrics	PSO [31]		WOA [4]		MGWO [30]		GWO [29]		GOA [15]		EHO [18]		SOA [3]		CSSA [13]		NN [23]		Proposed CUSO
Makespan	216.	3142	1142.	46	2943.	882	201.	396	175.	2891	216.	3142	351.	8604	251.	362	97.	12	234.	962
Resource Utilization	4.	291141	4.	543722	3.	056578	4.	371886	4.	270327	4.	304087	4.	331892	3.	9912	4.	0213	4.	252317
Execution Time	0.	452687	0.	942242	0.	999555	0.	456047	0.	457885	0.	460467	0.	531543	0.	4912	0.	5293	0.	464787
Risk Probability	253.	8146	100.	8451	89.	546	270.	3589	261.	7907	246.	6747	190.	3196	243.	12	198.	21	234.	4367

overlooked. As a result, in order to provide an optimal schedule, there must be coordination between the task schedule and resource allocation. In this way, we can achieve an optimal schedule by reducing costs and schedule duration. Complex policies and decisions are required for multi-objective optimization of cloud resources.

Table 8

Parametric evaluation of proposed Clan Updated Seagull Optimization model over traditional algorithms

Tasks	Metrics	Random variable value
		0.2		0.5		0.8
200	Makespan	49.	53593	56.	6125	37.	9349
200	Resource Utilization	5.	849302	5.	40529	5.	624233
200	Execution Time	0.	543918	0.	523053	0.	517696
200	Risk Probability	51.	29958	48.	02089	50.	15386
400	Makespan	74.	57377	68.	53924	86.	81637
400	Resource Utilization	5.	745144	5.	743827	5.	629279
400	Execution Time	0.	476407	0.	475933	0.	478616
400	Risk Probability	113.	7443	115.	2904	117.	2536
600	Makespan	91.	58608	91.	58608	94.	89885
600	Resource Utilization	5.	307928	5.	543884	5.	39983
600	Execution Time	0.	411287	0.	428021	0.	418048
600	Risk Probability	146.	961	150.	6353	147.	4554
800	Makespan	122.	552	113.	9249	122.	2609
800	Resource Utilization	5.	164707	5.	167585	5.	181571
800	Execution Time	0.	489029	0.	486237	0.	485987
800	Risk Probability	199.	4366	201.	4396	200.	3646
1000	Makespan	261.	0689	223.	7733	223.	7733
1000	Resource Utilization	4.	215754	4.	295965	4.	315359
1000	Execution Time	0.	462096	0.	464093	0.	461542
1000	Risk Probability	233.	367	238.	0795	237.	1549

7. Conclusion

This work has intended to afford the optimization strategies for optimal task scheduling with multi-objective constraints in cloud environment. Accordingly, the proposed optimal task allocation framework considers the objectives such as execution time, risk probability, and task priority. For this, a new hybrid optimization algorithm known as CUSO algorithm is introduced in this work, which is the conceptual blending of EHO and SOA. Finally, the performance of proposed work was evaluated over other conventional models with respect to certain performance measures. On observing the graph, The cost function of the adopted CUSO scheme provides lower value ( $\sim$ 112) at the 80th iteration than other existing models. From the graph, the adopted CUSO model is 51.578%, 54%, and 11.53% better with minimum execution time than the traditional models like WOA, MGWO, and SOA, respectively for task count $=$ 1000. The proposed CUSO model attains better outcomes with less makespan value than the existing works like PSO, WOA, MGWO, GWO, GOA, EHO, SOA, CSSA and NN, respectively while scheduling 400 counts of tasks. Moreover, the risk probability acquired by the proposed CUSO model while scheduling the task 800 that is the least value ( $\sim$ 200) when compared to PSO $=\sim$ 205, WOA $=\sim$ 215, GWO $=\sim$ 225, GOA $=\sim$ 235, and EHO $=\sim$ 210, CSSA $=\sim$ 248 and NN $=\sim$ 202, respectively. The proposed CUSO model had utilized less resource to execute the 800 task when compared to other traditional models like PSO, WOA, MGWO, GWO, GOA, EHO, SOA, CSSA and NN, respectively.

Footnotes

Abbreviations

Author’s Bios

P. Neelakantan is currently working as Professor in the Department of Computer Science & Engineering, VNR Vignana Jyothi Institute of Engineering & Technology, Vignana Jyothi Nagar, Telangana, India. He obtained PhD in computer science and engineering from Sri Venkateswara University, Tirupati. He is having 21 years of teaching experience and his research interest includes Cloud Computing, Computer Networks and Distributed Systems. He is the life member of ISTE.

N. Sudhakar Yadav is an Assistant Professor at the Department of Information Technology of the VNR VJIET in Vignana Jyothi Nagar, Telangana, India. He has 14 years of teaching experience in various reputed institutions. He obtained his Ph.D from the Jawaharlal Nehru Technological University, Anantapur, Andhra Pradesh, India. His research is mainly focused on Big Data, IoT and Machine Learning. His papers have been published in various International Journals. He has more than 10 international journals and conferences. He is the life member for ISTE.

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Multi objective task scheduling based on hybrid metaheuristic algorithm for cloud environment

Abstract

Keywords

1. Introduction

Table 1 Review on conventional task scheduling models in cloud environment: Features and challenges

4.1 Cloud setup

Table 2 Cloud parameters

5.1 Proposed CUSO model

6.1 Simulation environment

6.2 Convergence graph

6.7 Overall performance examination

6.8 Parametric evaluationon proposed model

6.9 Limitations

Table 3 Overall performance examination of adopted Clan Updated Seagull Optimizationscheme over other existing techniques for task count 200

Footnotes

Abbreviations

Author’s Bios

References

Table 1
Review on conventional task scheduling models in cloud environment: Features and challenges

Table 2
Cloud parameters

Table 3
Overall performance examination of adopted Clan Updated Seagull Optimizationscheme over other existing techniques for task count 200