1 Introduction

Cloud computing is a network-based evolving technology that aims to deliver different IT services for a wide range of enterprises and customers on a pay-for-use basis [26,27,28]. Cloud computing offers many advantages with respect to low cost and data usability. Especially, cloud computing promotes improvedresponsiveness to supply chain interruptions [41]. Furthermore, the cloud model is used in review-based recommender systems [3], and biometric authentication [19]. In the cloud, data values from data owners are handled by the cloud provider [6, 13, 55]. Moreover, the risks of service degradation and the malicious insider are the issues in the single cloud. However, the multi-cloud environment monitors several cloud infrastructures and prevents dependence on other clouds [8, 9, 34, 46]. The storage and device partitioning mechanism [37] is used as the multi-cloud resource sharing scheme. For the delivery of services to various cloud vendors, four types of architectures are used. They are application duplication, application device partition, application logic partition in fragments, and application data partition in fragments [2, 3].

In the cloud, the data centre handles huge requests for applications from every corner of the world [17, 38]. In each application, there have many contingent and autonomous activities. To execute such requirements as well as to decide the execution order of the tasks, each cloud needs a scheduling strategy. Different clouds may get their scheduling strategies [5, 44, 51]. Task scheduling objectives [1, 11] specifically involve reducing the time and energy consumption of task execution and optimizing the usage of resources and the ability to balance the loads. Further, reducing work completion time is beneficial for enhancing the customer experience with the drastic rise of the number of cloud users [21] [7]. In order to avoid the performance degradation due to the enlargement of resources or waste obligatedvia unnecessary idle resources, load balancing capability gets improved, which further leads to maximum utilization of VM. The TS algorithm has therefore been found to be NP-complete, and it is not feasible to achieve the optimum solution in a finite amount of time [23, 49].

Till date, evolutionary algorithms such as GA and distribution estimation algorithms have been introduced to solve multiple scheduling and mapping problems [42, 48, 53, 54]. With the single-objective approach, schemes like “Min-Min, Max-Min, and Suffrage models” are implemented. However, they are not very extensible or adaptable. In most circumstances, the model merely takes into account the shortest possible time to complete the task, ignoring safety precautions.

The maincontribution of this research study is listed beneath:

  • Asecure task scheduling scheme in the multi-cloud environment is proposed with the assessment of risk probability.

  • For scheduling the tasks, a four-fold multi-objective constraint-based optimization model is introduced.

  • The defined 4 fold-objective constraints are “makespan, execution time, utilization cost, and risk probability”. In addition, the weight in the objective function is calculated by the fuzzy triangular membership function.

  • A unique hybrid DAGWO algorithm is proposed for optimal task scheduling. The proposed DAGWO model is a combination of traditional DA and GWO algorithms.

Paper organization

Section 2 shows therecent studies in the same field. Section 3 discusses theoverview and problem statement of thesuggested secure task scheduling. Section 4 shows the cloud setup as well as defined 4 foldobjectives. Section 5 explaines the obtained outcomes. Section 6 ends the work.

2 Literature review

In this section, the latest task scheduling researches are catagorized based on their approaches.

2.1 Related works

  1. a)

    Optimization based approaches

In 2019, Pang et al. [37] have developed an EDA-GA-based hybrid algorithm for task scheduling. At first, EDA’s sampling & probability concepts have beendeployed to givespecific workable solutions. The ideal scheduling model for assigning the work to VM’s was finally realized.

In 2019, Sanaj and Joe [45] have explored CSSA for optimal “multitask scheduling in an IaaS cloud environment”. The method continuously generates work schedules, which increases cost-effectiveness. The prior network was prouced using chaotic optimization for task allocation in order to assure superior global convergence.

In 2019, Yusuf [30] has introduced a new TS model, where the major intention relied on optimizing the TS by reducing the energy consumption and MS. The MGWO was able to solve the scheduling difficulties, which enhanced system efficiency. Encircling & hunting in MGWO have been modified utilizing the mean value to raise GWO’s effectiveness.

In 2020, Neelima and Reddy [31] have developed a new load balancing task scheduling model in the cloud by means of ADA, which was an amalgamation of DA and FF algorithms. The multi-objective function was defined on the basis of“load, processing costs, & completion time” constraints toattain the enhanced performance.

In 2020, Ismayilov and Haluk [14] have investigated a prediction-oriented approach named as “NN-DNSGA-II algorithm” that incorporated NSGA-II with ANN framework. To address the job scheduling issue, the top five non-prediction-oriented dynamic techniques have beenutilized. The six objectives of the work that is being provided are “improvement of utilization and reliability, decrease in energy cost, makespan, & imbalance level”.

  1. b)

    other approaches

In 2017, Liu et al. [22] have established a multi-task scheduling model, which incorporated a task workload model by considering service quantity and service coefficient. The effects of several workload-oriented task scheduling strategies have been then examined with respect to utilization & overall completion time.

In 2019, Panda et al. [36] have developed the multi-cloud network, where several clouds were integrated mutually for providing a combined service. In this method, an “allocation-aware task scheduling algorithm” was proposedand itdepend on the conventional “Min-Min and Max-Min algorithm”.

In 2020, Lavanya et al. [20] have explored two allocation models termed TBTS and SLA-LB models. Task scheduling in VM with various setups is made easier by TBTS, which scheduled the tasks in batches. Tasks were dynamically scheduled by SLA-LB based on user requirements such as budget as well as deadline.

2.2 Research Gaps

Table 1 represents the review of recent works. The following are the limitations of the extant models.

  1. (i)

    The SLA-LB model provides minimal complexity. But the main disadvantage was that the energy utilization factor was not evaluated [20]. Because the cost of energy utilization in the cloud is an important factor in determining the system’s effectiveness.

  2. (ii)

    In task scheduling, the continuous arrival of tasks is considered for effective system performance, but this factor is not considered in [22].

  3. (iii)

    In the ADA model, VM scheduling was not clearly considered and it needs more consideration [31]. Furthermore, the MGWO model requires attention to task priority [30].

  4. (iv)

    Security is one of the major issues in cloud computing. The related works failed to analyze the security constraints.

Table 1 Advantages and difficulties of the extant task scheduling approaches
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To overcome these limitations, a novel DAGWO based task scheduling is proposed in this study. Compared with the related works, this research introduces 4-fold objectives like“makespan, execution time, and utilization cost, along with security constraints”. Moreover, a novel DAGWO model is utilized for optimal task scheduling.

3 Proposed secure task scheduling model: an overview and problem statement

3.1 An Overview

The major components of the suggested work are listed below:

  • Customer: This is the cloud’s service client. The CU can produce their demands with the assistance of the cloud manager.

  • Cloud Manager: This is a central entity that handles customers’ service requests and receives the status of cloud providers’ VMs.

  • Cloud Service Provider: This is a cloud distributor that offers on-demand services by setting up virtual machines on actual servers. Each cloud contains a management server that contacts with other manager servers to send customer requests to manage the peak demands. Customers’ requests are frequently scattered over several clouds as well as are handled using a distributed model.

Between the components of the cloud model, the following connections occur: “(a) CU-cloud manager, (b) cloud manager-CSP, (c) CSP-CSP, (d) CSP-cloud manager, and (e) cloud manager-CU”. Furthermore, the overhead will happen to decide on the individual part. Nevertheless, we believe that the flexibility of the cloud model makes these overheads marginal.

Figure 1 represents a multi-cloud task scheduling scheme. The proposed model aims to produce satisfaction to the customer via effective task scheduling. Initially, users at various fields send a request tothe cloud. The cloud manager manages the service request and receives the cloud provider’s VM status. If a task is submitted to the cloud manager, the manager adds this task to a waiting queue as well as locates an active VM to set the task to based on the specified 4-fold objectives. “ Execution time, makespan, utilization cost, and risk probability” are the established 4-fold objectives in this research work. The work that has been presented deals with applying the optimization notion to task allocation. In the VMs, the tasks are continuously assigned, and the scheduling happens concurrently as well. A new hybrid method called DAGWO is presented for optimal scheduling. Furthermore, taking risk probability into account is the main contribution because this parameter guarantees the need for security while scheduling the activity. Each task’s VM allocation is done based on the risk probability (and with other metrics). Finally, the efficient task is allocated with minimum execution time, minimum makespan, minimum utilization cost, and high security (low-risk probability).

Fig. 1
figure 1

The framework of the suggested task scheduling approach

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4 Cloud setup and defined 4 fold-objective: makespan, execution time, utilization cost, risk probability

4.1 Cloud Setup

A set of clouds c = c1, c2, c3, . . , cM is considered in this work. The cloud service provider CSPI is denoted as cI, 1 ≤ I ≤ M. Here, the count of clouds, M = 3. The number of VMs (|vI|), as well as the scheduling strategy, (SI) will be assigned by the CSPI. The CSP provides the clouds or processing certain requests from the user. Within the cloud, resides the PM with a huge number of VMs. The 3-tuple fashion is utilized to represent cI as cI =  < CSPI, SI, |vI| > , 1 ≤ I ≤ M.

The request from the users is considered as the task. The task set t = t1, t2, t3, . . , tL is of independent tasks in which tI, 1 ≤ I ≤ L are Ith tasks with an instruction set insI (in MI). To process these tasks, a set of VM is considered v = v1, v2, v3, . . , vM, in which the VMs set is vI, 1 ≤ I ≤ M as well as it is deployed under cI. In addition, a virtual machine VMJ ∈ vI; 1 ≤ I ≤ M; 1 ≤ J ≤ |vI| has the processing speed in MIPS PJ. The total VM in all the clouds is depicted by \({M}^{\prime }=\sum\limits_{I=1}^m\mid {v}_I\mid\).

The execution time of a task (tI, 1 ≤ I ≤ L) on a VM (VMJ, 1 ≤ J ≤ M′) is given in the form of the matrix & it is reffered as ETC matrix. Mathematically, the ETC matrix is shown in Eq. (1) [36].

$$ET C=\left\{\begin{array}{ccccc}& {t}_1& {t}_2& \cdots & {t}_L\\ {}V{M}_1& ET{C}_{11}& ET{C}_{21}& \cdots & ET{C}_{11}\\ {}\vdots & \vdots & \vdots & \vdots & \vdots \\ {}V{M}_{\mid {v}_1\mid }& ET{C}_{1\mid {v}_1\mid }& ET{C}_{11\mid {v}_1\mid }& \cdots & ET{C}_{L\mid {v}_1\mid}\\ {}\vdots & \vdots & \vdots & \vdots & \vdots \\ {}V{M}_{\gamma +1}& ET{C}_{1\left(\gamma +1\right)}& ET{C}_{2\left(\gamma +1\right)}& \cdots & ET{C}_{1\left(\gamma +1\right)}\\ {}\vdots & \vdots & \vdots & \vdots & \vdots \\ {}V{M}_{\gamma +1}\mid {v}_M\mid & ET{C}_{1\left(\gamma +|{v}_M|\right)}& ET{C}_{2\left(\gamma +|{v}_M|\right)}& \cdots & ET{C}_{L\left(\gamma +|{v}_M|\right)}\end{array}\right.$$
(1)

In which,\(\gamma =\sum\limits_{K=1}^{M-1}\mid {v}_K\mid\). Moreover, ETCIJ, 1 ≤ I ≤ L; 1 ≤ J ≤ M′ is the ratio of the instruction set (in MI) to the processing speed. Mathematically, ETCIJ  is given in Eq. (2).

$${ETC}_{IJ}=\frac{ins_I}{P_J}$$
(2)

“The mapping is done in terms of allocating, matching, and scheduling of tasks.” The mapping function Fgets the request set r = {r1, r2, r3, …rR} from the CUset, CU = {CU1, CU2, CU3, …CUR}. The request ri = {t1, t2, t3, …tL′}; 1 ≤ I ≤ R; L′ <  < L is assigned to the set of VM’s v = {v1, v2, v3, .., vM}. Moreover, \(\left|t\right|=\sum\limits_{K=1}^R\left|{r}_i\right|\).

The secure mapping of the task onto the cloud, which has the VM set, v(F : t → v). This work intends to schedule the task optimally concerning the described 4-fold objective “(a) minimized makespan S, (b) lower cloud utilization cost of tasks U, (c) lower execution time of VME, (d) lower security risk probability G.” The upcoming section comprehensively portrays these defined 4-fold objectives. The flow chart representation is shown in Fig. 2.

Fig. 2
figure 2

Workflow model

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4.2 Defined 4-fold objectives

The objective of this study is evaluated as per Eq. (3). This Eq. (3) is also known as a fitness function and it is defined as: “A fitness value is a form of the objective function which summarises, in a single measure, how close a given design solution is to attaining the defined goals”.

$$obj=\min \left\{\left({W}_1.S\right)+\left({W}_2.U\right)+\left({W}_3.{E}^{task}\right)+\left({W}_4.G\right)\right\}$$
(3)

In which, S,U,Etask, and G denotes makespan, utilization cost of task, execution time for all tasks, and security risk probability. The weights W1, W2,W3, & W4 are calculated using fuzzy triangular membership function. The weight calculation is described in Eq. (4). Here p, q, r is the vertices of triangular membership function T(f). Lower boundaryis p, medium boundary with membership value 1 is q as well as r is the upper boundary with membership value 0.

$$W=\begin{Bmatrix}0&;if\;r<f\\\frac{r-f}{p-f}&;if\;f\leq r\leq p\\\frac{q-r}{q-p}&;if\;p\leq r\leq q\\0&;if\;r\geq q\end{Bmatrix}$$
(4)

Execution time of VM (E VM)

“Execution time of VM is the amount of time taken required by task to complete its executionon VM”. The mathematical formula EVM is given as per Eq. (5). In which, Hlength(I, J) is the task required to execute the instruction length, VCPU(I, J) is the count of CPU virtual machine J, and VMIPS(I, J) is the VM processing capability as VM J [10].

$${E}^{VM}=\frac{H_{length\;\left(I,J\right)}}{V_{CPU\left(I,J\right)}\times {V}_{MIPS\;\left(I,J\right)}}$$
(5)

Utilization cost of tasks, U

“Utilization cost is cost or total amount of payment from a cloud user to cloud provider against the utilization of resources to execute tasks”. It is represented in Eq. (6). In which, VIdenotes the count of VM &ctI indicates the completion time of VM. The expression for ctI is given in Eq. (7), where, pesnumber is the count of processing element for running a task on a suitable VM, MIPS is the execution speed per processing element of a VM, and R is the count of tasks [24].

$${U}_{task}=\sum_{I=1}^{V_I} PRIC{E}_I\ast c{t}_I$$
(6)
$$c{t}_I=\sum_{J=1}^R\frac{H_J. LENGTH}{V_I. pesnumber\times {V}_I. MIPS};I\in \left\{1,2,.\dots {V}_I\right\}\kern0.24em and\;\;J\in \left\{1,2,.\dots R\right\}$$
(7)

Execution time for all tasks E task

“The amount of time needed to complete the execution of all tasks is referred as execution time for all tasks” and it is evaluated as per Eq. (8). Here, R is the count of tasks [32].

$${E}^{task}=\frac{1}{\mathit{\operatorname{MAX}}\;\left(\textrm{execution}\kern0.24em \;\textrm{time}\right)\times R}\;\sum_{\textrm{I}=1}^{\textrm{R}}\left(\textrm{Execution}\kern0.24em \;\textrm{time}\kern0.24em \;\textrm{of}\kern0.17em \textrm{respective}\kern0.24em \;\;\textrm{VM}\times \textrm{Size}\kern0.24em \textrm{of}\kern0.24em \textrm{the}\kern0.24em \textrm{task}\right)$$
(8)

Makespan S

“Makespan is the cumulative time that the resources are required to complete the execution of all tasks”. In general, VM usage is characterized by how well the resources in the cloud are used [35]. The scheduler is delivering effective and good task planning to resources if the makespan is low. The mathematical formula for S is given as per Eq. (9). Here, VIdenotes the number of VM and ctI indicates the completion time of VM.

$$S=\underset{1\le I\le {V}_I}{\mathit{\operatorname{MAX}}}\kern0.24em \;\kern0.24em \;\;\left\{\;c{t}_I\right\}$$
(9)

Security risk probability

“The determination of the chance of a risk occurring is known as risk probability”. It is used to measure the security risk in execution that is to evaluate the risk of the scheduling tasks. For a particular task, the scheduling risk probability of tasks tIVMj are computed using Eq. (10).

$$\Pr o{b}^q\left({t}_I^q,V{M}_I^q\right)=\Big\{{\displaystyle \begin{array}{cc}0& if\;S{D}_I^q\le S{S}_J^q\\ {}1-{e}^{-\left(S{D}_I^q\le S{S}_J^q\right)}& otherwise\end{array}}$$
(10)

Here, the notation \({SD}_I^q,{SS}_J^q\) denotes the security demand & security services tI. “The risk probability of the task is the overall risk probability of the task corresponding to the security service.” FortI, if \({SD}_I^q\)<\({SS}_J^q\), then the risk probability of scheduling tI on VMJ is zero. In addition, Prob(tI, VMJ) denotes the probability of tI that is attacked during the execution and it is shown in Eq. (11).

$$\Pr ob\left({t}_I,V{M}_J\right)=1-\prod_q\left(1-\Pr o{b}^q\left({t}_I^q,V{M}_J^q\right)\right)$$
(11)

In addition, the risk probability of workflow is an average of the probabilities of all tasks. The composed task’s average probability Prob(W) is being assaulted during the workflow in Eq. (12).

$$\Pr ob(W)=\frac{\sum\limits_{t_I\in t}\Pr ob\left({t}_I,V{M}_J\right)}{M}$$
(12)

The VM, as well as tasks, are the input solution to DAGWO for optimal scheduling with the consideration of the above-defined objectives. Since 3 PM with 30 sets of VM in each PM is utilized in this research study, the solution to the proposed model looks as in Fig. 3. In Fig. 3, the solution encoding of cloud1, cloud 2,& cloud 3 is manifested.

Fig. 3
figure 3

Solution encoding (a) cloud 1, (b) cloud 2 & (c) cloud 3

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4.3 Proposed DAGWO for optimal task scheduling

Dragonfly Algorithm (DA)

The DA [15, 16] was developed based on the inspiration of dragonflies. The three elementary principles like separation, alignment, and cohesion are observed by the swarming behavior of the dragonflies. In addition, each dragonfly should obey the separation operation, alignment operation, food attraction operation, cohesion operation, and enemy distraction operation.

Grey Wolf Optimization (GWO)

Grey wolves are highly sociable animals with a very rigid hierarchy. They spend the majority of their lives hunting, seeking for prey first, encircling prey, as well as eventually attacking prey. Grey wolves have four primary societal structures: alpha, beta, delta, & omega, each of which plays a particular role in the group. The GWO algorithm is a new meta-heuristic based on these grey wolf characteristics [50] [47] [12, 52].

The DA has the benefit ofa higher convergence rate, which includes the ability to solve continuous problems. Similarly, the hunting habits of grey wolves served as an influence for the development of GWO. Since it has a straightforward structure, it is simple to build, requires less data than other techniques, converges quickly, and avoids local optima when used with composite functions. This research work intends to hybridize the concept of DA and GWO to make the model even stronger for optimal solutions with better convergence. Generally, hybridization of optimization algorithms can solve diverse classification and optimization problems [2, 47] [16, 25, 33, 40] [4, 39, 43]. The proposed model is referred to as DAGWO, and its step-by-step procedure is described below:

In the beginning, the population of the search agent is initialized as Xi = X1, X2, …, XW. The step vector ΔXiter + 1 in the DA algorithm is deployed to evaluate the individual’s movement direction and the mathematical formula is shown in Eq. (13). Here, the current iteration is denoted as iter. Also, p, b, a, f, and e represents the separation weight, alignment weight, cohesion weight, food factor, as well as enemy factor. The inertia weight of the step vector is indicated by w.

$$\varDelta {X}_{iter+1}=\left(p{O}_i+b{B}_i+a{A}_i+f. foo{d}_i+e. enem{y}_i\right)+ w\varDelta {X}_{iter}$$
(13)

Compute the value of separation criteria O, alignmen tB, cohesion criteria C, attraction to food resource (food) as well asdistractionaway froman enemy (enemy) by Eq. (14)- Eq. (18), respectievly. In Eq. (17) and Eq. (18), X+,X−&Xsignifies the food sourceposition, enemy source, &position of the present individual.

$${O}_i=\sum_{j=1}^DX-{X}_j$$
(14)
$${B}_i=\frac{\sum_{j=1}^D{X}_j}{D}$$
(15)
$${A}_i=\frac{\sum_{j=1}^D{X}_j}{D}-X$$
(16)
$$\boldsymbol{food}{}_i={X}^{+}-X$$
(17)
$$\boldsymbol{enemy}{}_i={X}^{-}+X$$
(18)

The adaptive knowledge rate of ith dragonfliesat the current iteration is computed by using Eq. (19).

$${d}_i^{\boldsymbol{iter}}=\frac{1}{1+{e}^{-V}}$$
(19)

Here,\(V=\frac{\mid fit\left({X}_i^{iter}\right)- fit\left({X}_{best}^{iter}\right)\mid }{fit\left({X}_{best}^{iter}\right)+\kappa }\),\(fit\left({X}_i^{\boldsymbol{iter}}\right)\) is the fitness of the ith search agent at iterth iteration and \(fit\left({X}_{\boldsymbol{best}}^{\boldsymbol{iter}}\right)\) is the best fitness value. Also, κdenotes the constant value, which is employed to avoid the zero division error. Then update the radius of the neighbour. If there is only one neighbour to the present search agent, then update the search agent position by Eq. (20).

$${X}_{iter+1}^i={d}_{iter}^i.{X}_{iter}^i+\varDelta X{X}_{iter+1}^i$$
(20)

Based on the hybrid proposed contribution, initialize a random variable rand. On the basis of this rand, the position update gets varied. The threshold value fixed here is 0.5, and if the assigned rand is less than the defined threshold value (rand<0.5), then update the search agent position utilizing standard GWO, else keep the existing solution as it is. The position update of GWO is evaluated as per Eq. (21).

$$X\left(\boldsymbol{iter}+1\right)=\frac{X_1+{X}_2+{X}_3}{3}$$
(21)

In which, \({\displaystyle \begin{array}{c}{X}_1={X}_{\alpha }-{Y}_1.\left({s}_{\alpha}\right),\\ {}{X}_2={X}_{\beta }-{Y}_2.\left({s}_{\beta}\right),\\ {}{X}_3={X}_{\delta }-{Y}_3.\left({s}_{\delta}\right).\end{array}}\)

X α, Xβ & Xδ points to the position of the 1st, 2nd, and 3rd best solutions.

(Here,) \({\displaystyle \begin{array}{c}{s}_{\alpha }=\mid {h}_1.{X}_{\alpha }-X\mid, \\ {}{s}_{\beta }=\mid {h}_2.{X}_{\beta }-X\mid, \\ {}{s}_{\delta }=\mid {h}_3.{X}_{\delta }-X\mid \end{array}}\)

In which, s, Y are the coefficient vectors and are mathematically defined in Eq. (22) and Eq. (23), respectively.

$$TY=2e.{u}_1-\overrightarrow{e}$$
(22)
$$h=2.{u}_2$$
(23)

Here, e is a constant, which is gradually reduced from 2 to 0 over the count of iterations. In addition, u1and u2 is a random vector within 0 to 1.

Algorithm 1 manifests the pseudo-code of the DAGWO algorithm. Figure 4 represents the block diagram of the proposed approach.

Algorithm 1
figure a

Pseudo code of DAGWO Algorithm

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Fig. 4
figure 4

Flow chart of the suggested DAGWO model

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5 Results & Discussions

5.1 Simulation procedure

The suggestedapproach was executed in Python. Three clouds as well as three sets of PM were used to make up the simulation scenario. The number of VMs in each group of PM is 30. The whole number of tasks to be completed ranges from 100 to 150 to 175 to 200, correspondingly. DAGWO outperforms other models in terms of optimal scheduling in terms of “migration cost, total cost, energy consumption, response time, and security analysis”. The number of VMs used in this evaluation varies. Two scenarios are considered for evaluation. In scenario 1: 30 counts of VM are considered for scheduling the varying count of tasks (i.e.10 VM in each PM). In Scenario 2: 60 counts of VM are considered (i.e. 20 counts of VM in each PM). The DAGWO is evaluated over the existing works like PSO [29], WOA [45], DA [16], GWO [47],MGWO [30] andGA [18].

5.2 Convergence analysis

The convergence of the DAGWO&existing scheme is determined for scenario1 and scenario 2 throughchanging the iterations number from 20, 40, 60, 80, and 100, respectively. The results acquired with scenario1 and scenario 2 are shown in Fig. 5. As per the defined 4-fold objectives in Eq. (3), the schemewhich attains the least cost function is said to be the most appropriate method. At the least count of iteration, the cost function achievedvia the DAGWO &extant work is greater. When the number of iterations increases, the cost function of DAGWO, as well as existing work, gets minimized. In the case of scenario1, the cost function of DAGWO had attained a steep fall in between the range 0 to 20 count of iterations. In addition, when analyzing Fig.4 b, the cost function of the suggested&extant technique seem to be greater at the 3rd iteration. Till the 65th iterations, the cost function of the proposed seems was little worse than the existing one, Beyond the 65th iteration, the DAGWO had attained the least value as (~)0.125. Thus, The DAGWO clearly showed the small cost function that suggests that the proposed model may schedule the tasks more effectively.

Fig. 5
figure 5

Convergence analysis: DAGWO &extantschemes for (a) scenario 1 (VM = 30) & (b) scenario 2 (VM = 60)

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5.3 Evaluation on energy consumption

Energy management is becoming more crucial in cloud storage as a result of rising energy prices and greater consumption of cloud computing resources. The call of energy-efficient solutions is the reduced the total energy usage of computing, storage, and communication devices. In data centres, optimum energy consumption is increasingly necessary. The current research tends on energy-efficient resource allocation. The energy required for executing a task must be lower, which leads to the expansion of network lifetime. The consumed energy by VM is represented in Fig. 6. In Fig. 6 a, the DAGWO seems to exhibit the least energy value while evaluating the tasks. For the task count =200, the DAGWO is 16.6%, 96.8%, 3.8%, 3.25%, 2.85%and 1.08%superior to the extant PSO, WOA, DA, GWO,MGWO & GA schemesfor optimal scheduling. On the other hand, the energy consumed by the DAGWO in scenario2 is fluctuating while the task execution. However, the overall performance shows that the proposed algorithm is more effective in solving the task scheduling issue with minimal energy consumption.

Fig. 6
figure 6

Energy consumption evaluation: DAGWO &extantmodels for (a) scenario1 (VM = 30) & (b) scenario2 (VM = 60)

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5.4 Evaluation on execution time

The computation time recorded via the suggested as well as an existing model is represented in Fig. 7. Further analyzing Fig. 7 a for task count = 200, the DAGWO is 11.1%, 6.9%, 12.2%, 42.85%, 23.07%, and 0.40%better than the extant PSO, WOA, DA, GWO, MGWO,&GA works with minimum execution time. Furthermore, on analyzingscenario2 at task count = 100, the DAGWO model is attained the least execution time (~ 0.28) than the extant PSO, WOA, DA, GWO,& MGWO models. Even though the execution time of the DAGWO seems to have fluctuated for certain task counts, the overall performance of the suggestedscheme is promising as well as it reveals the adopted scheme betterment.

Fig. 7
figure 7

Execution time evaluation: DAGWO &extantmodels for (a) scenario 1 (VM = 30) & (b) scenario2 (VM = 60)

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5.5 Evaluation on makespan

Figure 8 depicts themakespan evaluation of the suggestedas well asextantschmes. On analyzing the outcomes, at task = 150, the DAGWO scheme is 25%, 52%, 33.3%, 45.45%, 20% and 64.51% superior to the extant PSO, WOA, DA, GWO, MGWO,and GAapproaches respectively with minimal makespan. Then, forscenario2, the suggested modelis attained the small value at scheduling 200 numbers of tasks and it is smaller thanthe extantapproaches.

Fig. 8
figure 8

Makespan evaluation: DAGWO &extant schemes for (a) scenario1 (VM = 30) & (b) scenario2 (VM = 60)

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5.6 Evaluation on resource utilization

Minimal resource utilization is required during the scheduling & task execution in order to meet the given aim in Eq. (3). The outcomes of the suggestedas well as the extant approachesis depicted in Fig. 9. The DAGWO has scheduled and completed 175 counts of jobs with the least amount of resource use, according to the scenario 1 analysis. In this instance, the given work outperforms existing methodologies including PSO, WOA, DA, GWO, MGWO, and GA by 50%, 20%, 33.3%, 3.86%, and 3.21%, respectively. The given work, has recorded the lowest value of 0.05 in the scenario 2 condition, which is determined to be a better outcome when compared to the conventional schemes. The analysis so demonstrated that the suggested model was superior for task scheduling while utilizing the fewest resources.

Fig. 9
figure 9

Resource utilization evaluation: DAGWO &extant models for (a) scenario1 (VM = 30) & (b) scenario2 (VM = 60)

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5.7 Evaluation on security or risk probability

The security analysis for adopted as well as extant approaches for scenarios is represented in Table 2 and 3. The findings demonstrate that the DAGWO balances excellent security with reduced risk. On analyzing scenario 1, the DAGWO attask = 100 is 16.83, and the extant model values are PSO = 38.2, WOA = 33.63, DA = 33.7, GWO = 21.4, MGWO = 24.6, and GA = 55.84. On observing all other tasks too, the risk probability of the suggestedshows to be lower than the conventional models. Further, in the case of scenario2, the risk probability of the DAGWO is 63.046 at task = 200 and this is the less value. Altogether, the analysis proves that the suggested model has the ability to process the scheduling as well as execution of tasks even in a secured manner.

Table 2 Risk probabilityevaluation: DAGWO &extant schemesfor scenario1
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Table 3 Risk probability evaluation: DAGWO &extant schemesfor scenario2
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5.8 Evaluation on throughput

The throughput is the greatest rate at which tasks may be completed in a given amount of time. It assesses the effectiveness of the scheduling method. Low response time and large execution rate result from a high throughput rate. Table 4 and 5 represents the throughput of the adoptedas well asextant schems at various tasks. In both scenarios, the throughput value of the suggested approach is increased with increasing the number of tasks. In Table 4, the throughput of the proposed work at scheduling tasks 200 is 36.11%, 33.03%, 29.26%, 44.34%, 0.34%, and 36.11% better than the existing PSO, WOA, DA, GWO, GA and MGWO approaches respectively. For scenario 2, the throughput of the adopted research at scheduling tasks 200 is2.72%, 11.21%, 7.44%, 12.96%, 10.57%, and 13.61% superior to the extantPSO, WOA, DA, GWO, GA and MGWO approaches respectively. Thus, the proposed model guarantees good throughput at various tasks.

Table 4 Throughput (pps) evaluation: DAGWO &extant schemes for scenario1
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Table 5 Throughput (pps) evaluation: DAGWO &extant schemesfor scenario2
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5.9 Time complexity

The time consumed through the adopted as well as traditional schemes is depicted in Table 6 and 7 for scenario 1as well as scenario2. For scenario 1, the adopted DAGWOfor task 175 is 15.492%, 19.659%, 11.674%, 38.054%,41.12% and 9.186% superior to the extant PSO, WOA, DA, GWO, GA & MGWO approaches. In the case of Table 7, the computation time obtained by the developed DAGWO while scheduling tasks 200 is 0.195 s and it is 36.11%, 33.03%, 29.26%, 44.43%, 0.34%, and 36.11% superior to the extant PSO, WOA, DA, GWO, GA & MGWO methods. Hence, the superiority of the adopted scheme is verified with respect to computation time.

Table 6 Computation time (s) evaluation: DAGWO &extant schemes for scenario1
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Table 7 Computation time (s)evaluation: DAGWO &extant schemesfor scenario2
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5.10 Rank analysis

The rank analysis of the adopted as well as existing schemes is shown in Table 8. This table shows the rank of the 4-objectives like “energy consumption, makespan, resource utilization cost and execution time” and also the overall rank of the methods are represented. On analyzing the results, the proposed model does not attain the first rank. But considering the overall analysis, the rank of the methods like PSO, WOA, DA, GWO, GA, MGWO, and proposed DAGWO are 7, 3, 2, 6, 5, 4 and 1. Therefore, the effectiveness of the proposed approach is proved successfully.

Table 8 Rank analysis of the DAGWO and extant approaches
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5.11 Discussions

The suggestedscheme considers the objectives along with the security constraints. The resultants show the efficiency of the proposed work and it is well suited for a multi-cloud environment. Our method attains high makespan, good resource utilization, less risk probability, low energy consumption, and computation time. Furthermore, the proposed model achieves high security than other existing methods with low risk. Sometimes the proposed model lacks its performance when compared to MGWO and this model is restricted by dynamic scheduling. In the future, we enhanced the suggested work to achieve improved results. Also, we consider some task features like deadlines and the data transmission between the workflow tasks.

6 Conclusion

Data transfer across application tasks is unavoidable in a virtualized cloud environment. If a virtual machine’s security mechanism isn’t strong enough, malicious activity can disrupt other tasks via altering intermediate data. This research introducesa secure task scheduling scheme for a multi-cloud environment. The study that was given dealt with using the optimization concept to allocate the tasks in the best possible way. As a result, the objectives are taken into account by the suggested optimal task scheduling frameworklike“makespan, execution time, and utilization cost along with security constraints”. A novel risk probability evaluation was taken into account for ensuring security. For optimal scheduling, a uniqueapproach referred to as DAGWO that hybridizes the concepts of GWO & DA was introduced. The DAGWO is determined over the existing works in terms of convergence, energy, makespan as well. The experimental findings reveal that, when compared to existing methods, our method effectively reduces the security risk while keeping a respectable completion time. However, the execution time, makespan, utilization cost of the DAGWO model seems to oscillate in terms of performance, the overall objective is found to be achieved.