Deadline Constrained Task Scheduling Method Using a Combination of Center-Based Genetic Algorithm and Group Search Optimization

1 Introduction

Cloud computing has emerged as a developing model that is well geared to effectively exploit the manifold distributed resources that can be allotted to clients as per their needs. As a result, it leads to the economic and effective deployment of accessible and trouble-free management of gigantic computational issues. Further, it incredibly scales down the total outlay on several resources such as hardware and software [6], and easily facilitates the resources to be utilized for the purpose of leasing and releasing. Moreover, it boasts of a host of vantage points such as transparency of resources, flexibility, location independence, consistency, affordability, better accessibility of services, and so on [23]. For the purpose of enabling the related facilities, the tasks have to be planned suitably on the basis of resources in order to elicit the greatest accomplishment with the shortest time frame. Moreover, the cloud services are hosted on the infrastructure of the service providers themselves or those of the intermediary cloud infrastructure providers [19]. Basically, there are three types of services that are offered, such as the platform as a service (PaaS), infrastructure as a service (IaaS), and software as a service (SaaS) [4].

Further, the clouds may be broadly categorized into three types such as public, private, and hybrid [18]. When the cloud services are offered intended for the ordinary client on the basis of the pay-per-use pattern, it is labeled as the public cloud. When the institutions design their own unique applications and manage their own internal infrastructure, it is called the private cloud, as the access thereto is restricted to users within the institution [13]. The scheduling of the relative gigantic number of assignments has emerged as a vital problem in the domain of cloud computing. In this regard, a lot of scheduling techniques are becoming popular, as illustrated in Refs. [11, 16, 22]. The corresponding techniques take into account a number of divergent features such as the cost matrix created by means of the credit of tasks to be allotted to a specific resource [22], quality of service (QoS)-based meta-scheduler and backfill strategy-based lightweight virtual machine scheduler for dispatching jobs [11], QoS needs [22], and heterogeneity of the cloud scenario and workloads [16].

Normally, the scheduling issue may involve two distinct categories, such as static and dynamic. As far as static scheduling is concerned, the attributes of an analogous program like the task processing periods, communication, data dependencies, and harmonization needs are identified well ahead of accomplishment [21]. In the case of dynamic scheduling, certain presumption regarding the identical program has to be spelt out prior to the performance, and thus the scheduling decisions have to made on the fly [15]. With the intention of effectively addressing scheduling issues, a novel cloud resources allotment structure has been introduced recently to facilitate the effective deployment of external clouds (ECs) so as to enable an IaaS cloud itself to become flexible [27]. In the relative configuration, an IaaS cloud is endowed with its own unique personal cloud and is capable of effectively outsourcing its functions to the parallel cloud providers known as the ECs, especially when its local resources are scarce. Further, each and every assignment carries with it a sharp cutoff date to complete the relative assignment in order for the resource allocation issue to be broadly deemed as a deadline constrained task scheduling (DCTS) one. An integer programming formulation of the DCTS issue is brilliantly brought to the limelight, with the intention of maximizing the benefit of the personal cloud on the concept of ensuring the QoS. The major contributions made in research for the task scheduling process are as follows:

• An approach named the HGSOCBGA is done for task scheduling, which has the advantages of easy realization and quick convergence, so that this scheduling approach is able to get an optimal or suboptimal solution with maximum profit than the individual group search optimization (GSO) and center-based genetic algorithm (CBGA) optimization algorithm.

• In the HGSOCBGA, the hybridization uses the process of best solution replacement ahead of the worst solution to improve the solution quality.

The organization of the paper is as follows. Section 2 presents a review of the literature. Section 3 describes the algorithm used in this research. Section 4 explains the solution framework and problem definition, and Section 5 describes the proposed task scheduling. Section 6 explains the experimental results, and Section 7 presents the conclusion part.

2 Literature Survey

Of late, the scheduling technique has began to play a critical part in modern applications, and notably, task scheduling has increasingly gained the attention of enthusiastic investigators, thanks to its extensive popularity, viability, and the copious expansion of the cloud computing system. The underlying motive behind cloud computing is furnishing effective accessibility to far-flung and geographically disseminated resources. In this regard, scheduling has emerged as one of them, as it indicates a group of policies to manage the order of job to be carried out with the help of a computer system. A proper scheduler has to invariably change its scheduling plans in phase with the ever-changing scenario and the category of the task (Table 1).

In this regard, Omara and Arafa [20] introduced genetic algorithms (GAs) for the purpose of successfully addressing the task scheduling problem. They effectively employed two genetic techniques to overcome the corresponding scheduling hurdles. In their novel modified GAs, they brilliantly brought in certain heuristic principles that were supplemented to enhance the efficiency of the accomplishment. With the intent to overcome the resultant problems, Abrishami and Naghibzadeh [1] elegantly launched the innovative deadline-constrained workflow scheduling in software as a service cloud. They brilliantly employed the partial critical Paths, which was very effective in drastically bringing down the expenditure related to the workflow accomplishment by appropriately satisfying a user-defined cutoff date. Further, for the purpose of cutting back the cost of the processing considerably, Guo et al. [7] envisioned task scheduling with the help of the particle swarm optimization (PSO) algorithm, which is dependent on the small position value rule. In order to tackle the workflow issue, workflow scheduling meant for the cloud scenario dependent on the artificial bee colony algorithm was brought to the limelight by Kumar and Anand [14].

Moreover, Xu et al. [26] excellently envisioned an effective task scheduling scheme on heterogeneous computing systems by employing a multiple-priority queue GA. The novel technique integrated the GA technique to allocate a priority to each subtask while employing a heuristic-based earliest-finish time method in the hunt for a solution for the task-to-processor mapping. Singh and Singh [24] remarkably introduced the innovative score-based deadline constrained workflow scheduling algorithm, which was able to carry out the workflow within affordable expenses, simultaneously fulfilling the user-defined cutoff date stipulation. The novel technique elegantly employed the idea of a score that illustrated the capacities of hardware resources. Moreover, Agarwal and Jain [2] launched the optimal algorithm of task scheduling in the cloud computing environment. It represented a generalized priority technique for the effective performance of the assignments, and was further contrasted with the outcomes of the first come, first served and round robin scheduling. Similarly, Zuo et al. [27] excellently designed a self-adaptive learning PSO-based deadline constrained task scheduling for the hybrid IaaS cloud. The vital issue in the scheduling was concerned with the manner in which the assignments of the clients were to be allotted with the intention of taking the fullest benefit of the IaaS provider while assuring the QoS.

3 Algorithm Design

In this section, we first discuss the background of the GSO algorithm and CBGA. Then, the details of the proposed algorithm, HGSOCBGA, will be presented.

4 Solution Framework and Problem Definition

In this part, we offer a brief overview of the hybrid cloud architecture in order to additionally enhance the content of the research offered in this document. The overview of the hybrid cloud is given in Figure 1. Fundamentally, the hybrid cloud design is home to two types of clouds, such as the private cloud and the public cloud. The hybrid cloud in essence signifies a deft mixture of the public and private clouds. At times, it becomes essential for an entity to allocate a segment of its data as a public resource. Therefore, to preserve data secrecy, it appropriately seeks the aid of the hybrid cloud so that only limited resources are made public, without any damage to the secrecy of private resources that have to be kept intact as private. In the current investigation, with the ultimate objective of enabling the IaaS cloud itself adaptable, a novel cloud resource allocation structure is envisaged so as to facilitate the effective deployment of the ECs. Now, the IaaS cloud itself is endowed with its own unique private cloud and is competent to outsource its assignments to the parallel cloud providers known as the ECs, especially when it is resources-starved with regard to the local resources. In the relative structure, the ECs elegantly present a public interface for the generation and administration of the virtual machine (VM) instances within their proprietary infrastructure. From the outlook of an IaaS provider, the private clouds habitually represent its own resources while the ECs constitute the parallel clouds that are outsourced. In this regard, both the private clouds and ECs play their own unique role in this hybrid design.

Figure 1:

Basic Architecture of Hybrid Cloud.

In this regard, special mention has to be made regarding the vital contribution of scheduling in effectively addressing various functions within the hybrid cloud. In fact, scheduling deftly decides the nature of the task to be allocated in addition to the quantity of resources and computing components. It also prudently allots each and every task to the appropriate computing module. In case of availability of sufficient computational resources needed to perform the entire functions within the private cloud, it is not at all essential to accept on lease additional resources from the public cloud. However, in resource-crunched scenarios, making it difficult to accomplish the tasks within the deadline in the private cloud, the resources of the public cloud are availed on lease so that the essential assignments could be achieved well within the cutoff date. The resource allotment to the divergent assignments on the hybrid cloud is elegantly shown in Figure 1. It is clear from Figure 1 that the user assigns n number of tasks to the scheduler. The scheduler module, in turn, gathers the relative scheduling data from the user and takes prudent decisions to allot each and every task to either the private cloud or one of the ECs existing in the public cloud, with the intention of taking the profit to hill level. In fact, the scheduling challenge has emerged as a deadline-inhibited task scheduling affair. In the novel technique, m numbers of applications are employed, and each and every offered application consists of a host of analogous and self-governing chores, with a uniform and steady cutoff date common for all the constituent assignment tasks so that all the tasks are accomplished within the common deadline. Further, each and every task has to be performed in one VM instance type. Let CPS={CP1S, CP2S, ..., CPns} be a set of cloud providers. Here, CP1S represents a private cloud and CP2S, ...., CPnS corresponds to an EC. Further, VM={V1M, V2M, ..., VIM} constitutes a set of VM types and AaP={AaP₁, AaP₂, …, AaP_m} symbolizes a set of applications. Each application AaP_i (i∈{1, 2, …, m}) is assigned a fixed deadline D_i and runtime R_i and contains a task set TKi={T1, T2, ..., TiTKi}. Further, time is evidently characterized in the IP model by means of introducing time slots with a granularity of 1 h. The ultimate motive is to allocate m applications to CPkS, where (k∈{1, 2, …, n}) are to utilize the profit of CP1S. Further, each task has to be allotted to a single CPkS, k∈{1, 2, …, n}. When a task TK_i is initiated for performance, it is to be ensured that it is not interrupted and that its running slots are successive. In any time slot S^S (S^S∈{1, 2, …, S}), the resources deployed by the entire task accomplished in CP1S should not exceed the total resources of CP1S at any point of time from the perspective of CP1S, and all its ECs are endowed with never-ending sources. In task scheduling, each task has a strict deadline to meet, so that the resource allocation problem can be considered a DCTS one. To solve this problem nowadays [27], many optimization algorithms are used. In our work, we have used the hybrid GSO and CBGA-based scheduling approach in the hybrid cloud. Here, each submitted application contains a number of parallel and autonomous tasks and has a firm deadline of when all its consisting tasks must be completed. Each task needs to be implemented in one VM instance type only.

5 Proposed Task Scheduling Based on the GSO-CBGA Algorithm

In this section, we explain the proposed task scheduling using the hybrid GSO-CBGA algorithm. Task scheduling is one of the major problems in the cloud system. The main intention of the scheduling algorithm is to maximize the profit of the task, as well as minimize the execution time and cost of the task along with QoS requirements of the user. The step-by-step process is explained below.

Step 1: Solution encoding

In cloud computing, one of the vital ideas is to specify a solution for the task scheduling. Each application is home to a host of tasks, and hence all applications may be treated as a set of tasks as illustrated by TK={T1, T2, ..., TTN} (TN=∑i=1wTi). Here, the solution is represented as a TN(D=TN) dimension vector and each dimension (position) characterizes a task. The position with a bigger value indicates the fact that the task specified by this position possesses a superior priority and has to be shortlisted first and foremost for the allotment of the scheduling process.

The ranked-order value rule [17] is employed to treat a particle A_i= (a_i1, a_i2, …, a_iD) into a variant of tasks TK={T₁, T₂, …, T_D} for the purpose of appraising the corresponding particle [3]. For example, let us consider a problem with five distinct tasks (D=5); the i^th particle is specified by a_i= (7.16, 7.34, 6.52, 4.32, 5.28). The position a_i2 possesses the highest value, so that the task is represented by a_i2 and it is allotted a rank value one, as exhibited in Table 2. The next-in-line a_i1=6.14 is allotted a rank value two. Similarly, the rank values of 3, 4, and 5 are allotted to a_i3, a_i5, and a_i4, respectively. Hence, a priority series of task is achieved as Priority={2, 1, 3, 5, 4}. The search solution represents the observed task and its dimension is represented by N×M.

Here, N indicates the number of the application existing in the investigation and M represents the task.

Step 2: Fitness calculation

A fitness function is required when applying the hybrid GSA-CBGA to optimize the task permutation to maximize the profit of CP1S and to work out the fitness value of each task in the application. Each task in set T is allocated to one CPkS (k=1, 2, …, n) according to the priority expressed by the code of a solution. We try to allocate each task to CP1S because the cost of CP1S is the lowest among all the clouds. If CP1S has available resources to meet a task demand during its run time, then the task is allocated to CP1S; otherwise, the task is allocated to an EC with the minimal cost. The fitness value calculation formula is given in Eq. (4).

Step 3: Divide the agent into two groups based on the hybrid probability P

One group uses the GSO to update their positions while the other uses the CBGA.

Step 4: GSO stage

We perform the GSO stage; here, we need three types of employees like the producer, scroungers, and rangers. These three employees make different operations to the population (task) and produce the optimal population.

• Producer operation

  At first, the producer A_P is located from the group member A dependent on the best fitness function. The producer represents the best fitness value of A_i, which is represented by A_P.

  The head angle of each and every individual is illustrated by means of Eq. (16) shown below.

  (5) φit=(φi1t, ..., φi(n−1)t)∈Rn.

  The search direction of the member in accordance with the head angle is represented by the following equation:

  (6) Uik(φik)=(ui1k, ..., uink)∈Rn.

  The search direction is effectively evaluated from the head angle with the help of polar and Cartesian coordinate transformation, as illustrated by the following equations:

  (7) ui1k=∏p=1n−1cos(φipk).

  (8) uijk=sin(φi(j−1)k) . ∏p=in−1cos(φipk).

  (9) uink=sin(φi(n−1)k).

  In the GSO technique, at the k^th iteration, the producer A_P exhibits the following conduct.

  The producer performs the task of scanning at zero degree and thereafter continues the scan laterally by arbitrarily sampling the three points in the scanning domain:

• For the first point at zero degree, the scanning is as shown in Eq. (10) below:

  (10) Az=Apk+r1lmaxHpk(φpk).

• For the second point in the right-hand side in the hypercube, scanning is expressed in the following equation:

  (11) Ar=Apk+r1lmaxHpk(φpk+r2θmax2).

• For the third point in the left-hand side in the hypercube, scanning is carried out by means of Eq. (12):

  (12) Al=Apk+r1lmaxHpk(φpk−r2θmax2).

  Here, r₁∈R¹ represents a generally disseminated arbitrary number with mean 0 and standard deviation 1, and r₂∈Rⁿ⁻¹ indicates an evenly disseminated arbitrary sequence in the range (0, 1).

  The maximum search angle θ_max is furnished with the help of the following equation:

  (13) θmax=πc2.

  The constant c is represented by Eq. (14), as follows:

  (14) c=round(n+1).

  Here, n reveals the size of the search space:

  (15) θmax=πn+1.

  The maximum distance l_max is effectively evaluated with the following equations:

  (16) lmax= ||lU−lL||.

  (17) lmax=∑i=1n(lUi−lLi)2.

  Here, l_Ui represents the upper bound for the i^th dimension and l_Li corresponds to the lower bound for the i^th dimension. The best point with the best resource is effectively ascertained by means of Eqs. (7–9). In case the best point is endowed with a better resource than the present best position, then it moves to the new best point. Or else, it continues in its existing position and turns the producer head to the arbitrarily produced head angle direction, with the assistance of Eq. (18) given below:

  (18) φk+1=φk+r2 αmax.

  Here, α_max∈R¹ corresponds to the maximum turning angle.

  If the producer fails to locate a superior area after α iterations, it turns its head back to zero degree as illustrated in Eq. (19) given below:

  (19) φk+α=φk.

  Here, α represents a constant.

• Scrounger operation

  At each iteration, in addition to the producer, there are a number of group members who are shortlisted as the scroungers. The common scrounging conduct in the GSO algorithm is the area copying trend. In k^th iteration, the area copying conduct of the i^th scrounger is formulated as a movement in the direction of the producer by means of Eq. (20) shown below:

  (20) Aik+1=Aik+r3∘(Apk−Aik).

  Here, ○ represents the Hadamard product, which effectively evaluates the entry-wise product of the two vectors and r₃∈Rⁿ⁻¹ uniform arbitrary sequence in the range (0, 1). The i^th scrounger continues to be on the hunt for the optional opportunities to join. The corresponding trend is designed by turning the i^th scrounger head to a new arbitrarily produced angle [Eq. (18)].

• Ranger performances

  The remaining group members that are isolated from their current positions are known as the rangers. They invariably carry out the searching tactics, which involve arbitrary walks and systematic searching strategies to effectively identify the resources. In this regard, the random walks emerge as the most ideal searching technique for the arbitrarily disseminated resources. It further generates an arbitrary head angle as illustrated in Eq. (18), and favors the arbitrary distance as the following equation:

  (21) li=a⋅r1lmax.

  Further, the arbitrary walk to the new point is effectively exhibited in Eq. (22) shown below:

  (22) Yk+1=Yik+liHikφk+1.

  When all the above processes are finished, the fitness of the modernized solution is evaluated. The relative procedure is endlessly followed until the l_i=k^th iteration so as to locate the best solution.

Step 5: CBGA stage

The CBGA effectively employs three distinct operators such as the selection, crossover, and mutation, which are elucidated below.

• Selection operation

  Here, the roulette wheel selection approach is extensively employed in the CBGA selection procedure. It is capable of ensuring that the selection probability of every particle is in direct proportion to its fitness. In other words, if the fitness of a particle is superior, it becomes further eligible to get shortlisted.

• Crossover operation

  When the selection function is over, it is followed by the execution of the crossover and mutation functions. The population of a center-based genetic technique takes its origin predominantly by means of the crossover and mutation functions. In the current investigation, the most leading genetic operator is the crossover, as it habitually modernizes the solutions almost always. Incidentally, a crossover represents the process of substituting certain genes in one of the parents by the matching genes of the other. In the task scheduling challenge, the crossover operator deftly blends two legitimate parents, whose subtasks are arranged topologically, to create two offspring, which also become legitimate. Figure 2 illustrates the single-point crossover model.

• Mutation operation

  When the crossover task is finished, for the purpose of increasing the skills to run away from the local optima, a central chaotic mutation is launched in accordance with the central data of the population. In this connection, the chaos represents a type of a non-linear dynamic that can be effectively employed for the universal optimization in view of its ergodicity and arbitrary nature. Further, a Loren system is elegantly utilized to generate the chaotic variables and thereafter infuse the chaotic variables into the chosen individuals so as to carry out the mutation function. The roadmap for the central chaotic mutation is drawn in the following section.

Figure 2:

Single-Point Crossover Operator.

Step 1: Choose the number of individuals from the population by means of the crossover function.

Step 2: Create an eight-dimensional random vector r₁, each element of which is in the interval [0, 1], and thereafter generate new chaotic vectors with iteration r_k=4r_k−1(1−r_k−1), k=2, …, CL,

where

L represents the chaos length factor.

Step 3: Map all the chaotic vectors to the search space, and chaotic individuals are achieved by means of Eq. (24):

where ξ is the factor to control the chaos scope, r_k is a chaotic vector, and PC_g is the population center.

The population center is calculated based on Eq. (25):

Here, T represents the dimension of the population. It is clear from Eq. (25) that the population center represents the weighted center of the entire positions of the individuals, where the fitness value is employed as the weight. Obviously, the center may be changed at various generations and is employed to effectively direct the evolutionary process.

Step 6: Hybridization

While comparing the GSO and CBGA, if the GSO best fitness value (GSO_best) is less than the CBGA fitness value (CBGA_best), the best position of the GSO is replaced by that of the CBGA. Else, if the CBGA fitness value is less than the GSO fitness value, the position is replaced by the GSO solution.

Step 7: Termination criteria

The technique stops its operation only if the maximum number of iterations is attained and the solution that possesses the best fitness value is shortlisted and labeled as the best feature to the task scheduling. When the best fitness is achieved with the help of the HGSOCBGA technique, the chosen task is allotted for the cloud computing procedure. The HGSOCBGA-dependent task scheduling technique pseudo code is demonstrated in Table 3.

6 Results and Discussion

In this section, we discuss the results obtained from the proposed HGSOCBGA algorithm-based task scheduling technique (Figure 3). We have implemented our proposed task scheduling using Java (jdk 1.6) with cloud Sim tools, and a series of experiments have been performed in a 2-GHz dual-core PC machine with 4 GB main memory running a 64-bit version of Windows 2007. The experiment is carried out mainly based on the profit and run time.

The utilization rate of CPU or memory at the s^th time slot for the private cloud is calculated by the following equation:

where Res_i is the number of CPU or the size of memory requested by task T_i and Total-Res is the total CPU or memory in the private cloud.

The average utilization rate of CPU or memory is calculated by

• Experimental design

  In this, we utilize three types of problem instances and several experimental results to authenticate the efficiency of our approach. Each instance has different numbers of tasks, CPU, and memory utilization. The VM instance types and the personal cloud and the EC prices are placed based on our observation on public clouds, and are specified in Tables 4–8. Two kinds of resources, i.e. CPU and memory, are selected, as they are two of the most typical configurations in selecting a VM instance in the cloud. Now, we describe the different resources used in our experiments.

  Problem instance 1: In order to be able to compare the output of the hybrid task scheduling algorithm with the optimal solution, the scale of the problem has to be relatively small. Here, in instance 1, the number of application is 8, the number of task is 20, and memory utilization is 40 GB. The VM instance type requested by each application is arbitrarily chosen from the above three VM types. The deadline of each application is a consistently distributed random integer between 1 and 5 h in order to limit the search space. To make certain that the deadline of each application is longer than its runtime, the runtime is selected as a consistently allocated integer between 1 h and its deadline.

  Problem instances 2 and 3: In problem instance 2, the number of applications is 5, the number of tasks is 512, and the memory utilization is 1024 GB. Similarly, problem instance 3 consists of 10 applications, 512 tasks, and memory utilization of 1024 GB. These two instances are large in size and are used for handling large-sized problems. Instances 2 and 3 are the most vital tasks and resources compared to instance 1.

• Performance evaluation

  The basic idea of our research is to schedule the task using the HGSOCBGA optimization algorithm. Here, the performance of the proposed approach is mainly evaluated using the maximum profit and average run time. Figures 4–6 show the performance of the proposed approach.

Figure 3:

Overall Diagram of Our HGSOCBGA.

7 Conclusions

In this paper, we have described a method based on a technique to solve the task scheduling problem using the hybridization approach. The main problem of task scheduling is how to assign the user task to maximize the profit of the IaaS provider while guaranteeing the QoS. By hybridizing the two optimization algorithms like the GSO and CBGA, this approach competently attains a high quality of scheduling. In the experimentations, we have carried out three types of problem instances having various numbers of tasks and applications. Here, our novel technique achieves the maximum profit of 9.04, which is better compared to that of the existing approaches.

Figure 4:

Performance of Profit Plot for Proposed against Existing Algorithm for Instance 1.

Figure 5:

Performance of Profit Plot for Proposed against Existing Algorithm for Instance 2.

Figure 6:

Performance of Profit Plot for Proposed against Existing Algorithm for Instance 3.