1. Introduction
The cloud environment offers a platform that enables shared access to servers in a data center when clients make service requests. [
1]. The three main elements of cloud computing architecture are infrastructure as a service (IaaS), software as a service (SaaS), and platform as a service (PaaS). SaaS makes it possible for customers, software vendors, and cloud service providers to work together. A multi-cloud system is created via the cooperation of many cloud infrastructure providers who customize their computing needs utilizing a variety of cloud-based IaaS (such as Microsoft Azure, 2018, Amazon EC2, 2018, and Google Compute Engine, 2018). As one of the most appreciated methods of resource sharing between cloud providers, they charge a fee for their virtual machines (VMs), utilizing the “pay as you go” concept [
2,
3].
Most recent potential solutions take into account only one quality of service (QoS) requirement. For instance, when examining the makespan, the workflow completion time is taken into account. Other important QoS-related factors are cost, cloud security, reliability, and performance. Multiple QoS requirements must therefore be balanced via a task scheduling algorithm; this procedure is known as multi-objective task scheduling. Utilizing Pareto optimum algorithms, which enable users to select the best result from a collection of feasible alternatives, is one way to achieve this balance.
A Pareto optimum solution concurrently optimizes competing goals. When there are numerous candidates for the ideal solution, the group of solutions is known as the Pareto front. The Pareto front does not have a dominant solution. Given that heuristic algorithms are produced, it is challenging for service providers to select the right permutation [
4].
The authors of [
5] used weighted aggregated sum product assessment (WASPAS), one of the most well-known decision-making strategies. With the help of this strategy, service providers can articulate their requirements and provide particular weight to objectives in line with customer preferences. In response to a specified priority, it chooses the optimal solution from the ideal Pareto set. In this article, we present the FR-MOS-MWO algorithm, a multi-objective workflow scheduling algorithm that uses fuzzy resource utilization. A Pareto front is used to show all possible options and determine which is the best. Both the service provider’s and the client’s needs can be satisfied in this manner. The newly introduced algorithm complies with the following five requirements by using the MWO method:
Reducing workflow time (makespan);
Reducing cost;
Maximizing resource utilization;
Increasing the workflow reliability for the customer;
Reducing the risk probability of the workflow.
Prior research has proposed several symmetrical or comparable alternatives as trade-offs for various objectives; finding the best solution remains a challenge. Real-time application customers can be concerned about makespan decrease in some cases or the cost of running VMs in others. Other consumers could be worried about the high workflow reliability in the meantime. Contrary to the concerns of these users, VM providers strive to increase resource efficiency and decrease risk. In order to find an almost optimal trade-off between these competing objectives and satisfy them all at once, a multi-objective method of optimization is required.
The FR-MOS-MWO algorithm concept focuses on choosing the best option among available solutions. It entails a comparison of the weights of each option to identify the one with the lowest weight. This approach streamlines the search, enabling ongoing iterations to attain a progressively superior solution.
The main contributions of this article are the following:
By designing a fitness function to reduce makespan, cost, and risk probability and maximize resource utilization and reliability, service providers and users’ interests are taken into account simultaneously.
A feasible solution is chosen and demonstrated through using the Pareto front’s optimal set utilizing a novel decision-making technique called minimum weight optimization (MWO), which takes into account user preferences.
The performance of the MWO-based multi-objective algorithm is contrasted to that of five other conventional workflow scheduling decision-making techniques, such as Pareto optimum and WASPAS.
The remainder of this essay is organized as follows:
Section 2 provides a summary of the connected works. The definition of the scheduling model, the problem formulation, and the network model are all included in
Section 3.
Section 4 covers the various methods for multi-objective optimization. The proposed algorithms are provided, and
Section 5 describes how to put them into practice. In
Section 6, the experimental findings are described, and in
Section 7, the paper’s conclusion and recommendations for further study are presented.
2. Related Work
Finding the best workflow scheduling solution is an NP-hard problem. A workflow scheduling method typically aims to accomplish one particular goal or a number of goals. It strikes a balance between the trade-offs of competing goals. The aggregation method is one of these multi-objective scheduling strategies. In this approach, a multi-objective scheduling issue is solved by reducing it to a single goal. Each objective’s weight is considered, and the number of weighted objectives is optimized. Cost-conscious scheduling (CCSH) was used in [
6] to reduce a multi-objective problem to a single-objective problem. The system was created to maximize efficiency and cut costs. Using the aggregation method, Dongarra et al. [
7] proposed a scheduling strategy that improves performance and reliability. The dynamic level scheduling (DLS) algorithm was used to enhance the proposed reliable dynamic level scheduling (RDLS) algorithms. The task scheduling system introduced in [
8] allows for task priority changes during runtime. Bi-objective dynamic level scheduling (BDLS) was proposed by Dogan et al. [
9] after a genetic algorithm was used to improve the bi-objective DLS method.
In contrast to the aggregation approach, the Pareto approach forces trade-offs between desired objectives that should be maximized and undesirable objectives that should be minimized (for example, cost). The algorithms that are not using Pareto front method can get better solutions than those that use Pareto front dominance method. One of the aggregation approaches was used by Bligaiyan et al. [
10] to introduce the Cat Swarm Improvement algorithm for cloud workflow scheduling. The algorithm decreases the amount of time, money, and idle time spent on the processor. The proposed algorithm outperformed the multi-objective particle swarm optimization (MOPSO) algorithm according to the authors’ comparison of the two methods.
Udomkasemsub et al. [
11] proposed a multi-objective scheduling approach that combines the Pareto optimizer algorithm with the artificial bee colony (ABC) algorithm to reduce cost and makespan. An RDPSO algorithm was put forth by Wu et al. [
12] for managing workflows in the cloud to cut down on costs or time. A new gray-wolf-based multi-objective scheduling method with an emphasis on cost, makespan, and resource efficiency was introduced in [
13]. Yassa et al. [
14] suggested another multi-objective strategy using the MODPSO algorithm to cut costs, energy use, and manufacturing time. The cost was reduced by using dynamic voltage and frequency scaling or DVFS. The heterogeneous earliest finish time (HEFT) algorithm and the suggested scheduling algorithm were contrasted.
A multi-objective Pareto-based heuristic black hole algorithm was used in [
15] to account for more than two significant scheduling factors. In order to cut costs, shorten lead times, and maximize resource effectiveness, this study suggested an appropriate method for analyzing the cloud scheduling problem. When scheduling workflows, Kaur et al. [
16] proposed an incremented frog slipping algorithm to lower the execution cost while still completing the task by a deadline. The proposed scheme outperformed the PSO-based approach in terms of minimizing the overall cost of workflow execution, according to the simulation performed using WorkflowSim. Khalili et al. [
13] developed a multi-objective scheduling algorithm using the gray wolf optimizer (GWO) and Pareto optimizer to reduce makespan, time, and cost for satisfying the QoS requirement for service providers. The algorithm improved throughput when compared to the strength Pareto evolutionary 2 (SPEA2) algorithm, which is a fundamental service requirement.
Zhang et al. [
17] suggested an adaptive multi-objective scheduling approach for workflow mapping at the IaaS level. While meeting the workflow’s deadline constraint, their objectives were to balance the loads on VMs and reduce the cost of user resources. To achieve Pareto-front and search diversity, the non-dominated sorting genetic algorithm-II (NSGA2) extension, which employs mutation and crossover operators, was used. The authors calculated the diversity and convergence of a group of Pareto solutions using inverted generational distance (IGD), which measures the minimum Euclidean distance. Singh et al. [
18] proposed a new method for workflow scheduling in an effort to decrease costs, makespan time, and cloud energy use associated with the workload deadline. The authors used machine learning to classify the users, where policies based on time, money, and negotiations were taken into account. The proposed strategy’s performance was consistent with other approaches in relation to the three objectives under consideration, according to the simulation results from CloudSim.
In order to schedule multi-purpose workflows with budget and deadline constraints, Verma et al. [
19] proposed a hybrid PSO (HPSO), which includes the budget and deadline-constrained heterogeneous earliest finish time algorithm (BDHEFT). During the scheduling process, MOPSO is used to cut costs and streamline the workflow. BDHEFT and other randomly chosen initial solutions can be used to generate the original solution. The Pareto front is maintained as a set of optimal (non-dominated) solutions throughout the MOPSO implementation cycle. The ultimate Pareto set is the solution. By combining control point, replication, and PTE algorithms, Dharwadkar et al. [
20] introduced a novel programming approach called horizontal reduction (HR) to reduce failure, execution costs, scheduling overhead, and makespan. The results showed that the suggested strategy performed better than other strategies in terms of the three objectives examined.
In order to minimize cost and workflow makespan, Xu et al. [
21] implemented a multi-objective scheduling method that trades off cost and time. The downside of this strategy is the probability that a server may fail during scheduling. Zhou et al. [
22] suggested a multi-objective scheduling approach for hybrid cloud with the aim of reducing cost and makespan. Beegom et al. [
23] introduced a non-dominance sorting-based multi-objective scheduling approach that was used with the PSO algorithm to reduce time and cost for cloud workflows. Crowding distance was also used to evaluate its performance. Results indicated that the suggested approach yielded the best solution when compared to the NSGA2 and NSGA3 algorithms. Alazzam et al. [
24] also proposed a hybrid scheduling strategy using harmony search algorithm (HSA) and tabu search to optimize efficiency while reducing total cost and makespan.
The black hole detection algorithm was expanded upon in a brand-new multi-objective hyper-volume algorithm that was put forth in [
15]. The algorithm employs a dominant strategy that boosts its adaptability and accelerates its convergence to the Pareto optimal solution. Resource cost, makespan (completion time), and resource utilization are the competing objectives that are optimized. A list-based multi-objective workflow scheduling algorithm was presented by Durillo et al. [
25]. In this algorithm, the resource utilization cost and makespan are reduced using a single-objective Pareto optimizer. Multi-objective HEFT (MOHEFT) [
25] is a new multi-objective scheduling method that was also introduced. The study in [
26] improved the Pareto multi-objective list scheduling heuristic (PMLSH) as an enhancement of the study in [
27] for estimating solutions when ranking in HEFT. To achieve a variety of goals, the crowding distance (CD) consistency metric was used. The solutions were examined in relation to a certain population of solutions as a test. One can select closer-to-optimal solutions in each algorithm iteration. The proposed algorithm was put to the test using hypervolume as a benchmark.
A multi-objective differential evolution scheduling algorithm was proposed by Tallukderi [
28] for grid environments. This algorithm was intended to reduce the cost of resource utilization and makespan of the workflow. The author differentiated the new approach from the Pareto archived evaluative strategy (PAES) based on changes in objectives and hypervolume values. Tasia [
29] also designed a system for scheduling and distributing cloud resources to reduce time and cost using the improved differential evolution algorithm (IDEA). In the same manner, Zhu et al. [
30] developed a new meta-heuristic approach for multi-objective cloud IaaS workflow scheduling. They designed the initial population using various techniques and introduced a new coding method as well as genetic factors to reduce the search area. The NSGA2 coding system was used to implement the evolutionary multi-objective scheduling for cloud (EMS-C) algorithm. The results showed that EMS-C increased hypervolume compared to MODE differential, Pareto evolutionary algorithm, MOHEFT, and PSO (NSPSO).
A multi-objective evolutionary algorithm (MOEA) was used by Yu et al. [
31] to resolve workflow planning problems. The tactic was used to resolve two competing problems: reducing the time required for implementation and the costs associated with using services. The authors also established objective functions that were in line with the restrictions. In a similar vein, Kalra et al. [
32] presented a workflow scheduling technique that combined intelligent water drop and genetic algorithm (IWD-GA). The method provides a variety of solutions for reliability and time constraints while reducing makespan and execution costs. IWD-GA assists customers in making flexible solution choices in accordance with their needs.
The cloud federation can be tailored according to certain server constraints, such as the restricted number of simultaneous resources and the hourly billing intervals. Thus, Zhou et al. [
22] suggested a cloud-based scheduling approach for reducing cash costs for cloud-based service infrastructures. The proposed fuzzy-dominance-sort-based HEFT (FDHEFT) algorithm combines fuzzy dominance sort with a HEFT scheduling list. The authors demonstrated the effectiveness of their method using actual workflows and real-world parameters. Yao et al. [
33] implemented a multi-objective cloud scheduling strategy that uses multi-swarm multi-objective optimization (MSMO) to reduce cost, workflow makespan, and energy consumption. The best swarms are used for the modification of particle velocity and PSO parameter values, i.e., the best personal (Pbest) and the best global (Gbest) values. In this approach, the velocity of the particle, in addition to the local information, can be adjusted using the particle’s information in other swarms. Their results showed an improvement in hypervolume compared to MOHEFT.
It is evident that multi-objective workflow scheduling algorithms take a variety of objectives into account to produce efficient scheduling. In this regard, it is necessary to make an accurate choice (of objectives) in order to assign tasks to the VMs in an efficient manner. Therefore, using the minimum weight optimization process, this paper introduces a new multi-objective algorithm (FR-MOS-MWO) for scheduling scientific workflow in a multi-cloud environment. Regarding reliability constraints, this study aims to maximize reliability and resource utilization while lowering workflow costs, risk probability, and makespan.
3. Scheduling Scenario
By specifically focusing on reliability, makespan, cost, workflow model, multi-cloud model, resource utilization, risk probability, and problem formulation, this section discusses the workflow scheduling model, metrics, and aspects. Five QoS requirements are taken into consideration in the proposed FR-MOS-MWO algorithm: cost, risk probability, makespan, resource utilization, and reliability. The scheduling model is shown in
Figure 1, and the notations used in this study are described in Table 1 of the cited reference [
34].
Designing the framework for a cloud user workflow application is part of the first phase. The distribution of workflows to a suitable cloud infrastructure should satisfy the VM types and workflow requirements. Each cloud service provider has a task queue, and tasks are carried out in accordance with the workflow hierarchy. Due to the infinite number of VM resources that cloud users have access to, simultaneous services are offered for running tasks based on dependency relationships. It is critical to understand that each cloud service provider in a multi-cloud environment has its own performance and pricing trends.
3.1. Workflow Model
To accomplish a certain goal, a workflow—a collection of scheduled activities—must be followed in any order. Workflows are collections of simple steps created to handle more complicated issues [
35]. These processes must follow a consistent pattern in order to ensure coherence and increase efficiency in carrying out the desired activities. The purpose of a workflow is to specify the configuration, execution, and monitoring of several activities.
Workflow can be seen as a node-and-edge direct acyclic graph (DAG). W = (T, E) can be used to represent it, where T = {t0, t1,…, ti,…, tn−1} is the task set. The task dependencies are represented by a series of arcs E = {(ti,tj)|ti,tj T}. Tentry is the entry task in each workflow, and Texit is the exit task. Furthermore, each task has a pre(ti) and a successor set succ(ti). Each task is carried out following the execution of its predecessor. Task ti has an assigned weight W(ti), which measures the workload in terms of compute units (CUs). The output data size of task ti that needs to be transmitted to task tj is denoted by the symbol D(ti,tj).
3.2. Multi-Cloud Architecture
Google Compute Engine, Amazon EC2, and Microsoft Azure are the three cloud service providers that are the focus of this study. In this section, we will examine the multi-cloud architecture, which enables users to access virtual machines (VMs) from many cloud providers with various price structures. For instance, Amazon EC2’s cost in 2018 varied depending on the service’s availability. Every incomplete clock eventually advances to full hours. Similarly, Azure subscribers in 2018 were paid per minute. After the first ten minutes of VM instance startup, Google Compute Engine prices were per minute in 2018. Reference [
36] provides a comprehensive list of
VM types across Tables 2 to 4.
In a multi-cloud context, various IaaS platforms can be made available for a collection of VMs, where VM(m) = {VM(m, 1),…, VM(m, k),…, VM(m, ks)} and m = 1, 2,…, M. Let (m|m = 1, 2, and 3), where m stands for the different IaaS cloud providers (i.e., Amazon, Microsoft, and Google). The virtual machine instance that IaaS cloud provider m has specified is VM(m, k). Hourly costs are indicated by C(m, k), and CU refers to the VM CPU compute capacity. P(m, k) represents its processing power. We take for granted that the various cloud service providers can provide customers a limitless number of virtual machines. The bandwidth of cloud platform m is denoted by Bm, and the bandwidth between cloud platforms m and m′ is denoted by Bmm′.
3.3. Makespan Computation
Workflows and tasks on several IaaS platforms can be assigned and executed through a multi-cloud environment. Additionally, other VMs must wait before receiving tasks anew. This process results from VMs frequently sending their output to other VMs. The order of the tasks determines how the receiver output will be laid out. The grouping procedure of the workflow tasks within set A is described by Equation (1).
In the same manner as set
A, the tasks in partial set
B are completed. In the event where
A = {
t1,
t3,
t4,
t2}, then
B = {
t1,
t3} if
ti =
t4. In Equation (2),
Tstart(
ti) and
Tend(
ti)are used to denote the task’s start and end times, respectively.
Twait(
tj,
ti) is the time it takes for task
ti to receive input data from task
tj. This wait time is shown as follows:
Observe that if ti = tentry, then Tstart(ti) = 0.
The transmission time has been calculated using the following equation:
where
Ttrans(
tj,
ti) is the transmission time between
ti and
tj.
Task
ti therefore has a receiving time provided by
The size of data for each task
ti determines how long it takes to execute [
30,
37]. The execution time for various tasks on various
VMs(
m,
k) can be calculated using the Equation below.
For the completion time of each task, The
VM(
m,
k) in CU’s processing capacity can be utilized. Therefore,
The deadline is the amount of time needed to complete the scheduling using VMs with the bare minimal processing capacity.
3.4. Cost Computation
IaaS platforms employ the multi-cloud model in their own pricing models. The time that passes between the start time and the finish time is used by the existing workflow algorithms to determine how long the
VM will be rented for [
30,
36,
37,
38]. The
VM terminates after the task is done, and the output is passed to the task’s successor. The priority of data transfer is impacted by the order of tasks. You can specify the sending time of task
ti as follows:
Equation (11) specifies the rental time of task
ti for the
VM executing on
VM(
m,
k).
Following that, the VM renting cost for task ti on each IaaS platform is determined.
Equation (12) expresses the cost of task
ti on
VM(1,
k) for Amazon EC2, which charges per hour.
where
Tminute = 60.
Due to Microsoft Azure’s per-minute pricing, the cost of task
ti’
s execution on
VM(2,
k) is as shown in Equation (13).
After the first ten minutes, Google charges by the instance per minute. In Equation (14), these costs are shown as the task cost on
VM(3,
k), where
Tten = 10.
Using Equation (15), the cost of the workflow can be determined.
The highest priced VMs in the critical path can be used to identify the budget constraint when scheduling workflows.
3.5. Resource Utilization Computation
The effective allocation of resources for cloud operations depends on scheduling. In many scheduling systems, tasks are assigned to achieve a balance between cost-effectiveness, resource utilization, and makespan [
39]. When compared to expensive resources, cheaper ones require more time to execute tasks, indicating that the CPU of a
VM maximizes resource utilization at the expense of cost. A requested
VM’s total capacity is determined by using the equation
Each workflow’s percentage of workflow utilization can be calculated using Equation (17).
Because customers often expect to deal with a service provider that offers high-resource utilization, the value of max.utilization in Equation (33) is set to 100%.
3.6. Reliability Computation
Cloud computing failures are inevitable. Failures might be internal (such as software bugs, hardware problems, power issues, etc.) [
40,
41], or external (such as hazardous online attacks) [
42,
43]. Failure during task workflow can also result from short-term failures. The Poisson distribution can be used as the basis for a failure case [
7,
44,
45]. It is calculated by finding the reliability exponent such that task
ti is successfully completed in
VM(
m,
k):
where the failure rate of the cloud service provider fulfills
λm > 0 (
m = 1, 2, 3).
Multi-cloud failure coefficients differ between IaaS platforms. Any issue that arises within the rental period will result in the task’s failure. The reliability of the workflow can be assessed using Equation (19), provided that the failures are independent.
If the maximum failure coefficient is specified as λmax = max{λm|m = 1, 2, 3} and the minimum failure coefficient is specified as λmin = min{λm|m = 1, 2, 3}, then the resulting scheduling workflow for reliability might be either maximum (relmax) or minimal (relmin). Additionally, based on the task scheduling procedure, various workflow results are produced in various clouds. Therefore, cloud users need to set relc ϵ [relmin, relmax] as the appropriate reliability constraint for a scientific workflow application.
3.7. Workflow Risk Probability
Because there are hazards to employing workflow applications in a cloud computing environment, security awareness is critical for quantitative service evaluation. During the workflow, the risk analysis model determines the risk rate [
42]. The risk distribution is based on the Poisson probability distribution for each defined time, and the model assumes that the probability of risks is governed by the level of security. As shown in this section, an exponential distribution can be utilized to define the risk likelihood of the task for the last security service [
46,
47]
The three main cloud threats are snooping, modification, and spoofing. To safeguard scientific workflow applications, three security services—namely, authentication, integrity, and confidentiality are used [
48]. Users can achieve an effective protection against different risks and attacks by dynamically integrating these security services. According to the proposed model, a typical activity will include three different types of security services with varying user-defined security rates. The collection of security requirements
for task
ti, for instance, can be expressed as a q-tuple
where
denotes the needed security level of the
lth security service and q = 3.
The authentication, integrity, and confidentiality services are each represented by a, g, and c, respectively.
For various cloud environments, the risk coefficient
varies. For instance, at the data center, 3 snooping attacks, 2.5 changes, and 1.8 spoofing attacks may be conducted in a given period of time. The negative exponent demonstrates that as the difference between
increases, the probability of failure rises. The risk can arise from massive network attacks or inaccessible security challenges. As a result, taking into consideration all security services, the risk probability for task
ti is as follows:
The workflow risk probability
P(
T) with task set
T can be calculated according to Equation (22).
This workflow risk probability will be used as a QoS constraint for problem formulation in
Section 4. The algorithms for confidentiality, accessibility, and data integrity can be located in Tables 1 to 3, as outlined in reference [
48,
49]. Each algorithm is assigned a security rating ranging from 0.08 to 1 based on its cryptographic algorithm efficiency. Let
represent the levels of security services for task
, and
represent the level of the
th security service task
has received.
3.8. Fuzzy Logic
In 1965, Lutfy Zadeh established the concept of fuzzy logic [
50]. The principle provides a modern statistical paradigm for formalizing and evaluating collections of functions. The fuzzy logic naturally extends the common language and interprets human conduct [
51].
Definition 1. Let X be the absolute reference for an associate. Features of a typical X and its subset A, µA: X → {0,1} are as follows defined: for each x X, Only one of the values from the sets 0 and 1 will be used.
Definition 2. Each element of X is connected with a function that is assigned to a number that is within the range of [0,1] if set is made up of two integers [0,1] that are mapped to a range between [1,0]. A is a fuzzy set as a result. If , then set A’s membership is ambiguous. As a result, we provide a multi-objective algorithm for scheduling scientific workflows using a fuzzy approach where the reliability constraints are determined by resource utilization.
3.9. Problem Description
This study seeks to optimize resource reliability while reducing risk probability, makespan, and cost. So, WF = (T,E) is used to represent the workflow. Thus, the workflow is represented as WF = (T,E). The main objective is scheduling Γ = (Loc, Ord, R), where Loc = {loc(t0), loc(t1)…, loc(tn−1)} is the task in the workflow to be executed, Ord = {ord(t0), ord(t1),…, ord(tn−1)} the task’s waiting time (the task’s order must also represent dependence relations) is mostly determined by the order in which the data are transferred, and R = {R0, R1,…, Ri,…, Rn−1} is a group of resources that support the entire workflow with Ri = (ti, VM(m; k), Tstart(ti), Tend(ti)).
We then formally outline the multi-objective optimization problem.
Previous studies have designed task execution scheduling algorithms [
30,
37,
42] but no priority has been given to the transmission order of the data, despite it being particularly important when developing a scheduling strategy. Therefore, we take into account the importance of data transmission.
6. Experimental Setup and Simulation Results
The structures of the scientific workflows are shown in
Figure 3. A 16 GB RAM processor with an i7 6-core was used for the experiments. SIPHT, Montage, LIGO, and CyberShake are four real-world scientific workflows that were used in WorkflowSim 1.0 to apply the suggested methodology. With [
1,
32] compute units, a uniform distribution was used to generate random values for
rd1 and
rd2. The cloud failure coefficients for Amazon EC2, Google Compute Engine, and Microsoft Azure were
λ1 = 0.001,
λ2 = 0.003, and
λ3 = 0.002, respectively. The bandwidth was set to 0.1 G/s if the VMs were in the same cloud and to 0.05 G/s if they were in different clouds. In the multi-objective problem, the reliability of the workflow should be equal to or greater than the reliability constraint, according to Equation (25). For determining the highest reliability, Equation (19) was employed.
Particle number
NP = 50,
w = 0.5, and
φ1 =
φ2 = 2.05 in FR-MOS-MWO. The FR-MOS-MWO method had 10 repeat programming,
NIT = 1000 repeat times, and
NS = 15 compensation solutions. We measured the minimal workflow reliability (
relmin) in addition to the maximum workflow reliability to ensure adequate reliability. The workflow’s reliability can be set by users as follows:
where
ρ ϵ [0,1].
In our proposed algorithm, Equation (47) shows the reliability constraint coefficient obtained after the result of the resource utilization is done via fuzzy logic [
36,
75].
The reliability constraints have to be within the proper range [
relmin,
relmax] according to Equation (46). We discovered that the non-consistency between 50 and 60 gave a better makespan-cost trade-off than MOS when we evaluated the performance of the FR-MOS-MWO method for workflow scheduling. The relationship between utilization of resources and the reliability constraint (
ρ) coefficient is shown in
Figure 4.
6.1. Simulation Results
The findings of the experiments are described in this section.
Figure 5 displays the outcomes of various decision-making techniques used to optimize the FR-MOS algorithm for various scientific workflows. Results from the Montage workflow (
Figure 5a) demonstrate that when compared to the other approaches, the FR-MOS-MWO algorithm produced the best makespan-cost trade-off. Additionally,
Figure 5b demonstrates that for the makespan-cost trade-off on LIGO, FR-MOS-MWO generated the best set of alternatives.
Figure 5c’s comparison of the various approaches used on CyberShake reveals that FR-MOS-MWO created solutions with the best makespan-cost trade-off. The FR-MOS-PARETO algorithm generated the second-best outcomes. The SIPHT workflow’s graphs (
Figure 5d), which show similar results, can also be observed. Deductively, FR-MOS-MWO and FR-MOS-PARETO outperformed the other methods that applied the Pareto front.
The relation between resource utilization and reliability is depicted in
Figure 6. The FR-MOS algorithm was employed with a variety of decision-making techniques in diverse scientific workflows. Similar to
Figure 5, the results demonstrate that when compared to the other approaches, the FR-MOS-MWO achieved the best performance (i.e., high resource utilization and reliability). These outcomes show how effective our new method for decision-making is. The reliability of the workflow is determined as the product of the exponentially distributed task reliabilities, which leads to a smaller workflow reliability, according to Equation (19). For this reason, the workflow dependability was represented by the mean reliability of each workflow.
Table 2 displays the outcomes of the various decision-making techniques examined in this article. In light of the competing attributes (makespan, cost, risk probability, reliability, and resource utilization), the table demonstrates that when using the Montage workflow, FR-MOS-MWO produced the best results in terms of makespan, resource utilization, and reliability; however, it had the same risk probability and high cost as FR-MOS-PARETO. FR-MOS-MWO outperformed the other algorithms for the remaining three workflows (CyberShake, LIGO, and Sipht) across all attributes. When compared to the other FR-MOS-based algorithms investigated, FR-MOS-MWO produced the best result.
6.2. Performance Measurement
Considering just one of the efficiency aspects is unlikely to be sufficient to test multi-purpose solutions, three metrics were used: Q-metric, S-metric, and FS-metric. Using these metrics is important when evaluating the Pareto front quality produced by various algorithms [
54]. To assess the level of convergence of multi-objective algorithms
A and
B,
Q-metric can be used [
76,
77], as stated in Equation (48).
Y is the set of SA ∪ SB, and
Ψ = Υ ∩ SA. SA and SB denote the two sets of Pareto optimal solutions for the two multi-objective algorithms
A and
B. Only when
Q(
A,
B) >
Q(
B,
A) or
Q(
A,
B) > 0.5 is Algorithm
A superior to Algorithm
B. The
FS measure determines the Pareto front space size. It is calculated using Equation (49) [
78].
Because
fi(
x0) and
fi(
x1) are two different values of the same objective function, ahigher
FS value indicates greater diversity in the Pareto front. To determine the amount of uniformity of solutions, we use the
S-metric as calculated in Equation (50) [
36].
where
NP is the number of Pareto solutions and
is the distance between the Pareto front set members.
While a larger value is preferable for the FS-metric and Q-metric, a smaller S-metric indicates that the algorithm has discovered a uniform solution.
For all FR-MOS-based algorithms, the relation between reliability, resource usage, and makespan-cost trade-offs is depicted in
Figure 5 and
Figure 6. Notably, when compared to other FR-MOS-based algorithms, the FR-MOS-MWO algorithm produced the best results for all objectives taken into account.
Table 3 provides an illustration of the multi-objective performance metrics shown in
Figure 5 and
Figure 6. The performance of FR-MOS-MWO is superior to other FR-MOS-based algorithms if the Q-metric is set to true.
Table 3 demonstrates that for all scientific workflows, the value of the Q-metric was true Q (FR-MOS-MWO, FR-MOS-based). This result demonstrates that FR-MOS-MWO’s solutions are superior to those of the other algorithms, proving that this algorithm offers the best multi-objective convergence outcome. In terms of the Montage workflow, the FS-metric value for FR-MOS-MWO was 1.38, which was higher than those of other algorithms, showing that FR-MOS-MWO produces a better level of diversity in comparison to those other algorithms. It can be shown that FR-MOS-MWO provides more uniformity in the Pareto front than other FR-MOS-based algorithms because its S-metric, which was 0.08, was less than those of the other algorithms. Regarding the LIGO workflow, FR-MOS-MWO’s FS-metric was 0.69, greater than that of the other algorithms, showing that it is more diverse than the other algorithms. The uniformity in the Pareto front of FR-MOS-MWO is better than that of the other algorithms, as evidenced by the S-metric of the algorithm being smaller for FR-MOS-MWO (0.022) than for the other algorithms.
Table 3 demonstrates that using FR-MOS-MWO on SIPHT resulted in a better FS-metric value of 1.01 than FR-MOS-PARETO and FR-MOS-MCDM. FR-MOS-LIN-NORM II, in contrast, generated an FS-metric value of 2.59, showing that it offers a greater diversity than the other FR-MOS-based algorithms. The best uniformity was achieved by FR-MOS-MWO, as evidenced by the algorithm’s S-metric of 0.07, which was lower than that of the other algorithms.
FR-MOS-MWO’s FS-metric was 0.244, which was better than all other FR-MOS-based algorithms when compared to FR-MOS-LIN-NORM II’s FS-metric of 0.385, according to the CyberShake results. This result implies that FR-MOS-LIN-NORM II produced a better diversity compared to all other algorithms. FR-MOS-MWO’s S-metric value was 0.073, which was lower than that of other algorithms. As a result, when compared to other algorithms, FR-MOS-MWO generates the best uniformity. Our investigation showed that, in some instances, (MCDM) strategies outperformed the WASPAS strategy in terms of results. For instance, different MCDM techniques showed more efficacy than WASPAS in the context of the SIPHT workflow. Notably, our proposed method, MWO, consistently delivered the best results. This success can be attributed to its approach of narrowing down the research process through the use of the minimum weight criterion. Additionally, some other MCDM methods produced multiple equivalent results, which can complicate the selection of the optimum solution or leave the choice up to users, as seen with the Pareto method in prior research. To aid researchers in selecting the most suitable method for their work, we have included all equations for each method in our article.