Computers and Electrical Engineering 106 (2023) 108597
Available online 3 February 2023
0045-7906/© 2023 Elsevier Ltd. All rights reserved.
Chaotic marine predators optimization based task scheduling scheme for resource limited cyber-physical systems
Hadeel Alsolai
a, Mohammed Aljebreen
b, Jaber S. Alzahrani
c, Fahd N. Al-Wesabi
d, Anwer Mustafa Hilal
e,*, Abu Sarwar Zamani
e, Azza Elneil Osman
e,
Amani A. Alneil
eaDepartment of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
bDepartment of Computer Science, Community College, King Saud University, P.O. Box 28095, Riyadh 11437, Saudi Arabia
cDepartment of Industrial Engineering, College of Engineering at Alqunfudah, Umm Al-Qura University, Saudi Arabia
dDepartment of Computer Science, College of Science & Art at Mahayil, King Khalid University, Saudi Arabia
eDepartment of Computer and Self Development, Preparatory Year Deanship, Prince Sattam bin Abdulaziz University, AlKharj, Saudi Arabia
A R T I C L E I N F O Keywords:
Resource limited Cyber-physical system Task scheduling Resource utilization Metaheuristics
A B S T R A C T
Cyber–Physical System (CPS) is the most advanced technological advancement that is set to become the future trend in the domain of Information Technology. In CPS, Task Scheduling (TS) plays a crucial role in terms of increasing the resource consumption and enhancing the perfor- mance of the system. In this aspect, the current study develops a novel Chaotic Marine Predators Optimization-based Task Scheduling Scheme for Resource Limited CPS environment, abbreviated as CMPO-TSSCPS technique. The primary aim of the presented CMPO-TSSCPS technique is to allocate nindependent tasks, under resource-limited CPS environment, in such a way that the time taken to complete the whole set of tasks gets reduced, while the maximum utilization of the resources is achieved. The presented CMPO-TSSCPS technique is developed by integrating the chaotic concepts and MPO algorithm. This algorithm is inspired by the foraging mechanism of ocean predators such as L´evy and Brownian movements with optimum encounter rate policy. The experimental results establish the superior performance of the proposed CMPO-TSSCPS technique over existing task schedulers.
1. Introduction
The evolution of the communication protocols that ensure seamless connectivity among the interconnected devices, advanced the development of innovative computation patterns. In such patterns, vast volumes of data get transmitted along the actuators, networks, and sensors [1]. This corresponds to the working mechanism behind the Cyber-Physical Systems (CPS), in which the cybernetic (software) and physical (hardware) elements are interlinked together either for controlling or monitoring the real-world situations [2].
The interconnected elements do not function in isolated modes and it remains the major benefit in CPS. On the contrary, the CPS functions as cooperative components, since the network is made up of intellectual components that can resolve complicate real-world issues [3]. This phenomenon contributed to the development of several intriguing CPS protocols over the past few years and its wide
* Corresponding author.
E-mail address: [email protected] (A.M. Hilal).
Contents lists available at ScienceDirect
Computers and Electrical Engineering
journal homepage: www.elsevier.com/locate/compeleceng
https://doi.org/10.1016/j.compeleceng.2023.108597
Received 2 December 2022; Received in revised form 11 January 2023; Accepted 13 January 2023
application in various fields such as transportation, energy, air navigation, health, etc. Though CPS has undeniable merits and higher applicability, it comes with a few significant challenges too. Particularly, the CPS layer has a connection with real-world that comprises of physical gadgets with intrinsic limits such as the shortfall of information quality at some situations, availability of limited resources (for instance, processing capacity, energy, bandwidth, etc.,) and the requirement for proper management to achieve sustainability [4].
CPS deals with imperfect data and limited resources which might intensely limits the systems’ potentiality and execution. This domain can be explored in detail by the research community. Fig. 1 shows the general scheduling process.
Task Scheduling (TS) processes results in the development of combinatorial optimization problems. In order to study this issue, two methods are followed such as the dynamic allocation strategy and static allocation strategy. When an issue arises, a combined ex- plosion happens [5]; an essence of the TS process is mapped in heterogeneous parallel calculating structures into a number of sub-tasks.
These subtasks have consecutive limitations and take the transmission overhead among the subtasks and tasks on a processor. It has the ability to run the time and map distinct sub tasks to various processor nodes, which in turn reduces the performance period of the overall number of tasks. In distributed mechanism, the message passes through an inter-process transmission system. In this process, transmission delay occurs to the foremost factor, which in turn influences the presentation of parallel programs. Thus, certain heuristic information, present in the task map, can be frequently utilized in the distribution of TS to every processor and mitigate the trans- mission overhead incurred upon assigning distinct processors, acquired to reach the approximate optimum scheduling solution [6].
Earlier research works have suggested many scheduling approaches based on intelligent search and heuristics [7]. Between these, the heuristic-related scheduling strategies are inclusive of table-scheduling techniques, task-related replication scheduling and clus- tering schedule as well. Intelligent search scheduling approaches include search algorithms, simulated annealing and Ant Colony Optimization. On the other hand, table-related TS can be classified into two types of processes [8]. The priority of every task can be computed after which the computing resources are allotted, in accordance with the order of priority. The algorithm procedure becomes highly complex while the result does not necessarily to be globally optimal [9].
The current study develops a novel Chaotic Marine Predators Optimization-based Task Scheduling Scheme for Resource Limited CPS environment, abbreviated as CMPO-TSSCPS technique. The key objective of the presented CMPO-TSSCPS technique is to allocate nindependent tasks in resource-limited CPS environment. By applying the proposed method, the total duration taken to complete the tasks can be reduced and the maximum amount of resource is utilized. The presented CMPO-TSSCPS technique has been developed by integrating the chaotic concepts and MPO algorithm. While the latter is inspired by the foraging mechanism of the ocean predators through L´evy and Brownian movements, with optimum encounter rate policy. After a thorough examination of the outcomes, it was found that the experimental results, accomplished by the proposed CMPO-TSSCPS technique, outperformed the rest of the methods.
The rest of the paper is organized as follows. Section 2 offers the information on existing TS schemes in CPS environment. Next, the proposed model is elaborated in Section 3. Then, experimental results are given in Sections 4 and 5 concludes the study.
2. Related works
Ghobaei-Arani et al. [10] introduced a TS technique on the basis of moth flame optimization technique to assign the optimum number of tasks for fog nodes to fulfil the QoS requirement of CPS applications. In this method, the overall implementation duration of the task can be reduced. This study considered the following objective functions; reduction of task implementation and transmission period in the presented technique. In literature [11], the authors proposed a novel Cloud-integrated CPS (CCPS) (called CCPSA) structure and outlined the enabling technology for Complex Industrial Application (CIA). Afterwards, three possible difficulties were categorized such as the life cycle management, virtualized resource management techniques and the scheduling of cloud sources based on which the solutions were offered, according to the perception of CIA.
Xu et al. [12] defined a new technique to reduce thermally-persuaded damages in CPS processors by targeting the Dynamic-Voltage-and-Frequency-Scaling (DVFS) towards higher action task phase. To be specific, the higher-activity task phase is reduced to save the energy and prevent thermal stresses for the provided number of computation slowdown; regardless of the activity
Fig. 1. General task scheduling process.
level, this technique achieved a better performance in comparison with the rest of the traditional approaches that use DVFS. Tang et al.
[13] developed an effective scheduling method that overcomes the functional constraints and saves the cost incurred upon multi-functional mixed criticality task replication. In this study, the authors presented Fault-Tolerant Hardware-Cost aware-Multi-functional Safety Assurance (FT_HCMSA) technique to reduce the Deadline Miss Ratio (DMR) of high-criticality functions while at the same time, the method also intended to satisfy the hardware cost and overcome the automotive functional safety constraints.
Zhou et al. [14] presented a new technology to resolve the issues discussed earlier. In this study, the authors proposed a unified semantic method called ‘HPCRO’ to specify the cross-regional HPC sources. The authors deployed the ontology reasoning method to attain semantic data for queries. Furthermore, the authors also proposed a WordNet-based Resource Index List dataset i.e., ‘WQRIL’ to enhance the quality of query. In the study conducted earlier [15], the authors examined an energy-effective and contention-aware static scheduling method for the tasks with deadlines and precedence limitations on smart-edge device-deployed heterogeneous VFI-related NoC-MPSoCs (VFI-NoC-HMPSoC) using the DVFS-assisted processor. The authors developed a population-based technique named ARSH-FATI unlike the existing population-related optimization algorithms. The proposed algorithm was able to switch dynamically between the exploitative and explorative searching modes at runtime. In literature [16], the authors developed a lower coupling method based on edge computing framework to counter the coupling problem. The edge computing framework serves as a middleware platform and grants the scheduling model. According to artificial intelligence technology and edge computing framework, the authors developed two buffer queues to reduce the coupling degree of a system simultaneously.
3. The proposed model
In this study, a new CMPO-TSSCPS method has been developed for optimum Task Scheduling process under resource-limited CPS environment. The key objective of the proposed CMPO-TSSCPS algorithm is to schedule nnumber of independent tasks under resource- limited CPS environment. This is done so to reduce the total task completing duration and achieve maximum utilization of the resources.
3.1. Modelling of CPS
In general, the CPS modelling process requires three elements such as the representation of the communications that occur among the system components, evaluation of the physical processes and the performance of both the processes after their integration. The model-driven design can enhance the design automation process and reduce the error through refinement. Further, the model-based analysis also offers a good knowledge on the performance of CPS. Lee [17] projected CPS as a complex computing power. In this study, the physical processing process utilizes the embedded computers and networks to monitor the physical processing system. Further, it also uses the feedback loop, computation, and physical processes that affect one another. For the purpose of system modelling, verification, and simulation, various types of control science and computation science are followed. But, in control science, the study on the physical world frequently depends on time as it abstracts the process as a constant time module. Further, time is a crucial factor in the presented study and it results in random failures and collisions during the interactions between physical entity model and the computational unit. Different interactive entities are included in CPS such as the machines, buildings, human beings, physical devices, natural environment, and so on. The situation, in which the real sensing parts (i.e., physical entity) function, can also be controlled.
Most of the CPS sensors are identified as platform structures. The platform also contains an actuator, computation unit and sensors. A service needs multiple platforms such as 1, 2, and 3 and is provided at a computational time of ∑4
i=1comi whereas each delay is denoted by ∑5
i=1di.
Two major issues exist in this scenario; i) the platform generally follows a single process to schedule. The service, with time requirement and efficacy of the time, does not remain optimum and ii) some recurring computational time exists. From a whole system perspective, the computational abilities have distinct impact on the time of service. So, the effects must be accumulated together to achieve the task and efforts must be taken to follow the time of the services and not to miss the deadline. If the tasks cannot be executed within the given timeline, it reduces the performance of the system.
3.2. Design of CMPO algorithm
In the current study, the presented CMPO-TSSCPS technique is derived by integrating the chaotic concepts and MPO (Marine Predators Algorithm). MPO is a newly proposed metaheuristic algorithm that imitates the relationship between prey and its predator.
This algorithm imitates the primary objective of the living creatures i.e., search for food. Here, the predator continuously searches for the food i.e. prey. In this study, the predator is considered as a problem whereas the prey is considered as a solution. The MPO initiates with an initialization stage in which the data passes through three other stages based on the rational velocity between the predator and the prey.
Initialization stage: It provides random solutions for the predator as well as the prey through subsequent equations.
U=Lower+rand1× (Upper − − − Lower) (1)
In Eq. (1), Lower and Upper represent the lower and upper limits of the searching space respectively, rand1 indicates a random vector
∈that lies in the range of 0 and 1. Based on the above equation, the primary locations of the predator as well as the prey are described
using the following matrix formula.
Elite=
⎡
⎢⎢
⎢⎢
⎢⎣
U111 U121 … U1d1 U211 U211 … U2d1
… … … …
Un11 Un11 … Und1
⎤
⎥⎥
⎥⎥
⎥⎦
,U=
⎡
⎢⎢
⎣
U11 U12 … U1d
U21 U21 … U2d
… … … …
Un1 Un1 … Und
⎤
⎥⎥
⎦ (2)
Here, the Elite matrix represents the fittest predator.
Stage 1: After initialization, the exploration stage is performed to find the searching space. Consequently, 1st -third of the overall iterations is performed in MPO viz, 13tmax). Then, the location of the prey is upgraded using the formula given below.
Si=RB⊗ (Elitei− RB⊗Ui), i=1,2, …, n (3)
Ui=Ui+P.R⊗Si (4)
In this expression, R ∈[0, 1] represents a random vector that is derived from the standard distribution process and P =0.5 refers to a constant number. The symbol RB denotes the Brownian motion. ⊗represents the component-wise multiplication procedure [18].
Stage 2: The predator exploits its optimal position i.e., where the food is available. Stage 2 is implemented in 2nd third of the overall iteration count, if 13tmax <t<23tmax. To separate the agent into two halves, the Eqs. (5)-(6) are expressed to emulate the movement of
Fig. 2.Flowchart of MPO technique.
the 1st half of the population (prey) whereas the Eqs. (9)-(10) are used to denote the 2nd half (predator) as given below.
Si=RL⊗ (Elitei− RL⊗Ui), i=1,2, …,n
2 (5)
Ui=Ui+P.R⊗Si (6)
Let RL be a random number that follows L´evy distribution. Eqs. (5)− (6) are executed during the first half of the agent that represents the exploitation phase. The second half of the agent performs the subsequent formula.
Si=RB⊗ (RB⊗Elitei− Ui), i=1,2, …,n
2 (7)
Uj=Elitei+P.CF⊗Sj, CF= (
1− t tmax
) (
2tmaxt
)
(8) Here, CF denotes the variable that controls the step size of the motion for the predator.
Stage 3: This phase is implemented during the final third of the iteration count (
t>23tmax)
based on the subsequent equation.
Si=RL⊗ (RL⊗Elitei− Ui), i=1,2, …, n (9)
Ui=Elitei+P.CF⊗Si, CF= (
1− t tmax
)(
2tmaxt I
(10) Eddy formation and Fish Aggregating Device effect: The external iMPOct from the environment i.e., eddy formation or Fish Aggregating Device (FAD) effect is used to prevent the local optimal solution. This phase is implemented mathematically using the following equation.
Ui=
{Ui+CF[Umin +R⊗ (Umax − Umin)]⊗ Wr5<FAD
Uj+ [FAD(1− r) +r](Ur1− Ur2) r5>FAD (11)
In this expression, FAD =0.2 whereas W denotes a binary solution (0 or 1) that corresponds to a random solution. If the random solution is lesser, when coMPOred to 0.2, it is transformed to zero. If the random solution becomes 1, then the solution becomes higher, when coMPOred to 0.2. The symbol r ∈[0, 1] signifies a random value whereas r1 and r2 represent the random indices of the prey.
Marine memory: This is the major feature of the marine predators that helps them in catching the prey i.e., optimum solution and preventing the local solution. This feature is implemented by saving the best solution from a previous iteration that is compared with the existing one; the solution is adapted, according to the best one during coMPOrison phase. Fig. 2 demonstrates the flowchart of the MPO technique.
Though elementary MPO algorithm is theoretically effective, it has a few drawbacks listed herewith.
•It cannot create an initialized population with high productivity.
•The process cannot get out of the local optimization issue quickly. As a result, unjustified convergence occurs leading to inap- propriate global solution.
•An unbalanced trade-off takes place between the exploitation and exploration stages.
In CMPO approach, the chaotic map assists in balancing the trade-off between the exploitation phase and the exploration phase.
Chaos map is a technique in which the chaotic variables are used with unpredictable nature instead of random variables. Chaos sequence is found in both non-linear as well as dynamic systems whereas it is bound, non-periodic and convergent in nature. Hence, the chaos sequences can accomplish a simple search process at high convergence rate than the probability-based random search. The chaotic variables assist in the exploration of searching space in a better manner than a random variable in the metaheuristic-based optimization algorithms. This is because the former possesses a dynamic behaviour of the chaotic sequences. The value is produced in the interval of [0, 1] with a chaotic map and random variables. It is to be noted that the turbulence variable covers additional places in a desirable range and has good distribution than the random variable. The chaos map is employed in the optimization algorithms by altering the initial condition during when multiple sequences are easily produced. In the current research study, a circle chaotic map function is exploited to develop the convergence rate for MPO algorithm and extensively explore the searching space to obtain better outcomes. The exploration of the searching space occurs in such a manner that the algorithm does not get trapped in local optima. In order to adjust the MPO algorithm with such chaos maps, random numbers are generated using the random numbers of the chaos function. The circle map is given as follows.
Kj+1=mod (
kj+b− a 2πsin
(2πKj
),1
) (12)
Here, Kj +1 denotes the chaotic number that is randomly produced in the existing iterations and Kj denotes the chaotic value that is randomly produced in the preceding iteration. a & b are equivalent to 0.5 and 0.2 correspondingly whereas k0 should be considered
equivalent to 0.01.
3.3. Processes involved in CMPO-TSSCPS technique
The presented CMPO-TSSCPS technique is introduced to schedule nnumber of independent tasks under resource-limited CPS environment. The aim of the proposed technique is to reduce the task completion duration and achieve the maximum utilization of the resources. The principle of the presented CMPO-TSSCPS algorithm is to assign n number of independent tasks to m heterogeneous attainable resources. This is done so in order to reduce the runtime of whole set of tasks and leverage the resources to its fullest ca- pacity. CPS is a heterogeneous, decentralized and large-scale platform with scalable features. In distribution mechanism, n subtask Task ={T1,T2,…, Tn} is assigned to m processor C = {C1, C2, …, Cm}R= {R1, R2, …, Rm}represents the maximal resource amount of the processor, Rj indicates the maximal source amount of the processor Cj, and the quantity of the resources required for each task execution is denoted by H ={H1,H2,…, H}. Tj=∑
iXij=ti/vj determines the sum of runtime of each task, assigned on j processor, whereas ti illustrates the runtime of the task i on minimal processor and vj refers to the computation speed of the j processor.
f(X) =min (
A∑m
j=1
tdj+B∑m
i=1
∑m
j=1
∑m
p=1
∑m
q=1
ωijpqXijXpq
)
(13)
∑m
j=1
Xij=1,i=1,2,…,n (14)
∑m
i=1
HiXij≤Rj,j=1,2,…,m (15)
Here, A and B(A +B =1) denote the relative consequence of the whole runtime and communication cost from the major function respectively and wijpq denotes the ith task assigned on jth processor and p task, employed on q processor. In order to determine the computation time required for all the tasks on dissimilar VMs, the runtime matrix is described as follows.
T=
⎡
⎢⎢
⎣
time11 time12 ⋯ time1m
time21 time22 ⋯ time2m
⋮ ⋮ ⋮ ⋮
timen1 timen1 ⋯ timenm
⎤
⎥⎥
⎦ (16)
In Eq. (13), timeij denotes the runtime required for VM vj to process the ti task at timeij =MIi/MIPSj. The expected duration for the computation of n task on m resource is denoted by E. Here, E represents the n ×m matrixes. Eij indicates the time required i.e., Ti to run from the VM, Eij =cij +eij. Then, the VM implements the allocation task in which the collection time is denoted by Ej. As the tasks are assigned to each VM resource in parallel, the runtime required for each task to complete the maximum value from array E is indicated by Etotal.
Ej=
∑
i∈Taskj
eij+
∑
i∈Taskj
tij (17)
In Eq. (17), Taskj indicates the task group that is employed on VM. The x[i][j] matrix is presented according to the equivalent connections between VM and the task. If the ti task is assigned to VM vj, it can be defined as follows.
x[i][j] =
{1, is assigned to Vj
0, Otherwise (18)
The proposed CMPO-TSSCPS approach assigns all the tasks to a specific processor to function in a state in which a specific constraint is satisfied.
Table 1
TET analysis of CMPO-TSSCPS approach with existing methods under distinct iterations.
No. of Iterations Task Execution Time (ms)
RMTS EDDTS EDFTS ACOTSS QIWOEATSS CMPO-TSSCPS
20 803 719 616 483 387 356
40 726 635 561 421 363 347
60 679 615 539 412 354 321
80 664 554 508 353 306 295
100 626 566 465 367 295 241
120 637 521 459 304 234 216
140 588 528 402 316 230 205
160 593 472 412 270 221 199
180 565 474 370 291 207 191
200 564 467 365 274 210 189
4. Results and discussion
The current section details about the task scheduling performance of the proposed CMPO-TSSCPS model under distinct execution rounds and tasks. The proposed model was simulated in MATLAB tool. Table 1 and Fig. 3 show the comparative Task Execution Time (TET) analysis results achieved by the proposed CMPO-TSSCPS model and other recent models, under varying number of iterations [2, 19]. The outcomes imply that the proposed CMPO-TSSCPS model accomplished excellent performance with minimal TET values. For example, with 20 iterations, the proposed CMPO-TSSCPS model gained a low TET of 356ms whereas the RMTS, EDDTS, EDFTS, ACOTSS and the QIWOEATSS models obtained high TET values such as 803ms, 719ms, 616ms, 483ms, and 387ms correspondingly.
Also, with 120 iterations, the proposed CMPO-TSSCPS method obtained a low TET of 216ms whereas the rest of the models such as RMTS, EDDTS, EDFTS, ACOTSS, and QIWOEATSS attained high TET values such as 637ms, 521ms, 459ms, 304ms, and 234ms correspondingly. Meanwhile, with 200 iterations, the proposed CMPO-TSSCPS technique accomplished a low TET of 189ms while the RMTS, EDDTS, EDFTS, ACOTSS and the QIWOEATSS approaches acquired high TET values such as 564ms, 467ms, 365ms, 274ms, and 210ms correspondingly.
The detailed analytical results, accomplished by the proposed CMPO-TSSCPS model and other recent models, in terms of Average Load Balancing Ratio (AVLBR) are shown in Table 2 and Fig. 4. The experimental outcomes infer that the proposed CMPO-TSSCPS model achieved the maximum AVLBR values under all the iterations. For example, with 20 iterations, the presented CMPO-TSSCPS model attained a high AVLBR of 54.52% while the RMTS, EDDTS, EDFTS, ACOTSS and the QIWOEATSS model reported low AVLBR values such as 11.96%, 23.16%, 30.51%, 41.27%, and 51.74% respectively. Besides, under 120 iterations, the proposed CMPO- TSSCPS technique achieved a high AVLBR of 66.87% whereas the RMTS, EDDTS, EDFTS, ACOTSS and the QIWOEATSS approach accomplished the least AVLBR values such as 16.86%, 29.41%, 40.77%, 58.34%, and 63.97% correspondingly. Moreover, with 200 iterations, the presented CMPO-TSSCPS algorithm accomplished a high AVLBR of 72.27% while the RMTS, EDDTS, EDFTS, ACOTSS and the QIWOEATSS methodologies recorded the least AVLBR values such as 21.92%, 35.60%, 52.67%, 64.17%, and 70.44%
correspondingly.
Table 3 and Fig. 5 show the comparative Convergence Rate (CR) analysis results, accomplished by the proposed CMPO-TSSCPS method and other recent models, under varying number of iterations. The results indicate that the proposed CMPO-TSSCPS tech- nique accomplished a better performance with minimal CR values. For example, with 40 iterations, the proposed CMPO-TSSCPS al- gorithm reached a low CR of 589ms while the rest of the methods such as RMTS, EDDTS, EDFTS, ACOTSS, and QIWOEATSS obtained the maximum CR values such as 630ms, 626ms, 616ms, 602ms, and 595ms correspondingly. Also, with 120 iterations, the proposed CMPO-TSSCPS technique attained a low CR of 509ms while the RMTS, EDDTS, EDFTS, ACOTSS and the QIWOEATSS models attained the maximum CR values such as 580ms, 575ms, 543ms, 538ms, and 517ms correspondingly. Meanwhile, with 200 iterations, the proposed CMPO-TSSCPS approach acquired a low CR of 498ms while the RMTS, EDDTS, EDFTS, ACOTSS, and the QIWOEATSS approaches attained the maximum CR values such as of 573ms, 560ms, 535ms, 522ms, and 507ms correspondingly.
Fig. 3. TET analysis of CMPO-TSSCPS approach under distinct iterations.
Table 2
AVLBR analysis of CMPO-TSSCPS approach with existing methods under distinct iterations.
No. of Iterations Avg. Load Balancing Ratio (%)
RMTS EDDTS EDFTS ACOTSS QIWOEATSS CMPO-TSSCPS
20 11.96 23.16 30.51 41.27 51.74 54.52
40 12.75 23.87 37.21 44.40 51.63 53.87
60 16.88 28.83 35.42 45.38 56.51 58.41
80 14.47 27.00 36.45 52.46 57.51 61.11
100 16.45 30.09 40.41 51.33 58.45 61.02
120 16.86 29.41 40.77 58.34 63.97 66.87
140 18.92 33.65 43.77 53.58 61.05 65.75
160 15.81 30.21 42.61 58.46 64.94 67.58
180 23.40 36.98 51.01 59.58 67.01 69.43
200 21.92 35.60 52.67 64.17 70.44 72.27
Fig. 4.AVLBR analysis of CMPO-TSSCPS approach under distinct iterations.
Table 3
CR analysis of CMPO-TSSCPS approach with existing methods under distinct iterations.
No. of Iterations Convergence Rate (ms)
RMTS EDDTS EDFTS ACOTSS QIWOEATSS CMPO-TSSCPS
20 655 655 655 655 655 655
40 630 626 616 602 595 589
60 618 603 582 577 560 541
80 600 574 567 550 537 532
100 582 568 548 541 520 514
120 580 575 543 538 517 509
140 576 566 547 523 518 507
160 575 569 542 529 515 503
180 569 557 547 523 508 499
200 573 560 535 522 507 498
Table 4 and Fig. 6 portrays the Energy Consumption (ECM) analysis outcomes achieved by the proposed CMPO-TSSCPS method and other recent models under varying number of Physical Machines (PMs). The results infer that the proposed CMPO-TSSCPS methodology accomplished an excellent performance with minimal ECM values. For instance, in case of 20 PMs, the proposed CMPO-TSSCPS approach attained the least ECM of 550Wh, whereas the other models such as EDDTS, EDFTS, ACOTSS, and QIWOEATSS demanded high ECM values such as 1703Wh, 3369Wh, 4627Wh, and 710Wh correspondingly. Moreover, with 80 PMs, the proposed CMPO-TSSCPS algorithm reached a low ECM of 4502Wh while the EDDTS, EDFTS, ACOTSS and the QIWOEATSS models acquired the maximum ECM values such as 6718Wh, 9225Wh, 11221Wh, and 5166Wh correspondingly. At the same time, with 120 PMs, the proposed CMPO-TSSCPS technique gained a low ECM of 7698Wh, whereas the rest of the models such as the EDDTS, EDFTS, ACOTSS and the QIWOEATSS models demanded high ECM values such as 10645Wh, 12746Wh, 14579Wh, and 8816Wh correspondingly.
Table 5 and Fig. 7 show the detailed TET analysis results, achieved by the proposed CMPO-TSSCPS method and other recent models, under varying number of tasks. The results denote that the proposed CMPO-TSSCPS approach attained better performance with minimal TET values. For instance, with 200 tasks, the proposed CMPO-TSSCPS model gained the least TET of 41ms, whereas the other approaches such as the EDDTS, EDFTS, ACOTSS and the QIWOEATSS algorithms reached high TET values such as 254ms, 211ms, 83ms, and 47ms respectively.
Also, with 1,000 tasks, the proposed CMPO-TSSCPS model gained a low TET of 326ms while the EDDTS, EDFTS, ACOTSS and the QIWOEATSS models acquired high TET values such as 675ms, 667ms, 496ms, and 384ms correspondingly. Meanwhile, with 1600 tasks, the presented CMPO-TSSCPS model accomplished the least TET of 611ms while EDDTS, EDFTS, ACOTSS and the QIWOEATSS methods required high TET values such as 993ms, 935ms, 752ms, and 642ms correspondingly.
The proposed CMPO-TSSCPS methodology was compared against the rest of the models in terms of Success Rate (SR) and the results are given in Table 6 and Fig. 8. The experimental outcomes infer that the proposed CMPO-TSSCPS technique achieved the maximum SR values under all the number of iterations. For example, with 100 iterations, the proposed CMPO-TSSCPS approach exhibited a high SR of 96.27% whereas the RMTS, EDDTS, EDFTS, ACOTSS and the QIWOEATSS models reported low SR values such as 88.82%, 86.59%, 82.28%, 91.74%, and 93.43% correspondingly. Furthermore, with 500 iterations, the proposed CMPO-TSSCPS technique exhibited a high SR of 89.11% while the RMTS, EDDTS, EDFTS, ACOTSS and the QIWOEATSS models reported the least SR values such as 77.76%, 77.42%, 72.52%, 80.59%, and 84.73% correspondingly. Also, with 1000 iterations, the proposed CMPO- TSSCPS approach exhibited a high SR of 80.29% whereas the RMTS, EDDTS, EDFTS, ACOTSS and the QIWOEATSS models reported the least SR values such as 45.66%, 42.31%, 40.09%, 53.06%, and 62.81% correspondingly. Based on the analyses of the tables and figures given above, it is apparent that the proposed CMPO-TSSCPS model outperformed other methods under distinct measures.
Fig. 5.CR analysis of CMPO-TSSCPS approach under distinct iterations.
5. Conclusion
In this study, a novel CMPO-TSSCPS method has been developed for optimum task scheduling under resource-limited CPS envi- ronment. The major objective of the proposed CMPO-TSSCPS algorithm is to schedule nnumber of independent tasks under resource- limited CPS environment in order to reduce the total task completion period and achieve the maximum utilization of the resources. The presented CMPO-TSSCPS technique is derived by integrating the chaotic concepts and MPO algorithm. MPO algorithm is inspired by the foraging mechanisms such as L´evy and Brownian movements, found in ocean predators, with optimum encounter rate policy. The Table 4
ECM analysis of CMPO-TSSCPS approach with existing methods under distinct PMs.
No. of Physical Machines (PM) Energy Consumption (Wh)
EDDTS EDFTS ACOTSS QIWOEATSS CMPO-TSSCPS
20 1703 3369 4627 710 550
40 3374 5103 7250 2019 1650
60 4902 7513 9518 3508 2765
80 6718 9225 11221 5166 4502
100 8759 11138 12912 6654 5711
120 10645 12746 14579 8816 7698
Fig. 6. ECM analysis of CMPO-TSSCPS approach under distinct PMs.
Table 5
TET analysis of CMPO-TSSCPS approach with existing methods under distinct tasks.
No. of Tasks Task Execution Time (ms)
EDDTS EDFTS ACOTSS QIWOEATSS CMPO-TSSCPS
200 254 211 83 47 41
400 351 269 185 94 85
600 481 457 252 168 139
800 575 524 384 306 264
1000 675 667 496 384 326
1200 775 726 564 480 451
1400 918 867 686 578 541
1600 993 935 752 642 611
experimental analyses results accomplished by the proposed CMPO-TSSCPS technique infer that the proposed method outperformed all other methods under distinct parameters. Further, the comparison study outcomes also established the superior performance of the proposed CMPO-TSSCPS method than the existing task schedulers. In the upcoming years, the performance of the presented CMPO- TSSCPS method can be improved further with the help of deep learning-based task scheduling schemes.
Data availability statement
Data sharing not applicable to this article as no datasets were generated during the current study.
Ethics approval
This article does not contain any studies with human participants performed by any of the authors.
Consent to participate Not applicable.
Fig. 7. TET analysis of CMPO-TSSCPS approach under distinct tasks.
Table 6
SR analysis of CMPO-TSSCPS approach with existing methods under distinct iterations.
No. of Iterations Success Rate (%)
RMTS EDDTS EDFTS ACOTSS QIWOEATSS CMPO-TSSCPS
100 88.82 86.59 82.28 91.74 93.43 96.27
200 87.89 84.37 80.81 89.81 92.68 95.00
300 87.15 82.70 78.95 88.88 89.18 91.72
400 83.66 79.94 73.94 86.63 87.92 89.45
500 77.76 77.42 72.52 80.59 84.73 89.11
600 74.26 77.48 64.64 81.87 84.60 88.18
700 67.26 65.25 61.97 74.08 81.77 87.32
800 64.46 56.46 57.26 70.86 76.41 84.98
900 50.58 48.08 43.74 59.44 70.49 81.37
1000 45.66 42.31 40.09 53.06 62.81 80.29
Informed consent Not applicable.
Declaration of Competing Interest
The authors declare that they have no conflict of interest. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.
Data availability
Data sharing not applicable to this article as no datasets were generated during the current study.
Acknowledgments
The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Large Groups Project under grant number (10/44). Princess Nourah bint Abdulrahman University Researchers Supporting
Fig. 8. SR analysis of CMPO-TSSCPS approach under distinct iterations.
Algorithm 1
Pseudo-code of the CMPO algorithm.
Set the parameters and form the Prey population i =1, …, 2 Compute the location for prey existing in the primary population Decide the fitness value for every prey
while Stop conditions were not created Decide chaos factors
Compute PopSizenew and determine the prey based on self-adaptive population.
Construct the Elite matrix
Upgrade the prey based on the basic MPA Upgrade Elite and perform memory saving Upgrade prey using FADs
Apply memory saving and Elite upgrade end while
Project number (PNURSP2023R303), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. Research Supporting Project number(RSP2023R459), King Saud University, Riyadh, Saudi Arabia. This study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2023/R/1444).
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Hadeel Alsolai is an Assistant Professor of Information Systems in the Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University. Her research interests include AI, IoT, Smart cities and software engineering.
Mohammed Aljebreen is an Assistant Professor of Computer Science in the Department of Computer Science, Community College, King Saud University. His research interests include decision support systems, data mining, artificial intelligence.
Jaber S. Alzahrani is an Assistant Professor of Computer Science in the Industrial Engineering, College of Engineering at Alqunfudah, Umm Al-Qura University, Saudi Arabia. His research interests include Industrial 0.5, optimization, supply chain, artificial intelligence.
Fahd N. Al-Wesabi is an Assistant Professor of Computer Science in the Department of Computer Science, College of Science & Art at Mahayil, King Khalid University, Saudi Arabia. His research interests include AI, IoT, Smart cities and software engineering.
Anwer Mustafa Hilal is an Assistant Professor of Computer Science in the Department of Computer and Self Development at Prince Sattam bin Abdulaziz University. His research interests include data mining, text mining and mobile and Web development.
Abu Sarwar Zamani is an Assistant Professor of Computer Science in the Department of Computer and Self Development at Prince Sattam bin Abdulaziz University. His research interests include data mining, text mining and mobile and Web development.
Azza Elneil Osman is an Assistant Professor of Computer Science in the Department of Computer and Self Development at Prince Sattam bin Abdulaziz University. Her research interests include data mining, AI, IoT, Smart cities.
Amani A. Alneil is an Assistant Professor of Computer Science in the Department of Computer and Self Development at Prince Sattam bin Abdulaziz University. Her research interests include AI, IoT, Smart cities, mobile and Web development.
