# Mathematical Model and Genetic Algorithm in Computer Programming Optimization and Network Topology Structure

Authors: Yonghong An
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

Recent emphasis has been focused on the industrial Internet of Things (Ind-IoT) in the context of the Fourth Industrial Revolution (Industry 4.0). IoT devices are used in the Ind-IoT to increase manufacturing productivity. The problem, however, is that these instruments will create enormous volumes of data records that must be handled efficiently. Cloud computing (CC) is frequently cited as a viable option for providing effective support for Ind-IoT applications. However, the high-latency and unstable connectivity problem between the cloud and Ind-IoT endpoints continues to plague Ind-IoT operations. Fog computing (FC), which extends computation and storage to the edge of the network, is a possible answer to these problems. Cloud-fog integrated Internet of Things (CFI-Ind-IoT) is discussed in this study as an approach to integrating FC with cloud-based industrial Internet of Things (Ind-IoT). A constrained multiparent crossover genetic algorithm (CMPC-GA) for optimization of the load adjusting challenge in the distributed cloud-fog network is proposed in order to attain ultralow response latency in the CFI-Ind-IoT system. Furthermore, we develop a duty reallocation and retransmission method in order to lower the average delivery latency of the CFI-Ind-IoT architecture due to the unreliable scenario. Effectiveness measurements show that the CMPC-GA technique can deliver ultralow latency functionality in a typical Ind-IoT.


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## Body

## 1. Introduction

The Ind-IoT devices create enormous amounts of data that need to be analyzed. Even in the industry 4.0 revolution, there is an increasing need for real-time data processing for industrial IoT systems, such as smart factories. It is, therefore, critical to have a strong data center in the Ind-IoT [1].Indeed, CC is often regarded as a critical enabler for satisfying the objectives of Industrial IoT systems. Cloud-based IoT networks, on the other hand, continue to encounter a number of unresolved issues. Transmission delay is tremendous since cloud data centers are constantly placed remotely. Intelligent services create a great amount of data, which puts a strain on cloud servers (CSs), and any malfunction in the network might cause a widespread communication issue [2].In the cloud-based Ind-IoT, FC appears to be a potential way to overcome the aforesaid difficulties. To minimize latency, FC processes workloads locally on fog nodes (FNs) located near the terminals, which enables a new breed of IoT apps and services that demand low latency, mobility, and geo-distribution. Therefore, in the context of Industry 4.0 [3], we propose the cloud-fog-based Ind-IoT (CFI-IoT) network architecture, which utilizes the present edge devices to establish an FC layer in the CFI-IoT architecture to fulfill the needs of latency-sensitive Ind-IoT operations [4].FC and enhanced CC have received a lot of attention recently. A comparison of the FC’s low latency and power-saving characteristics with that of regular CC is shown in. A revolutionary C-RAN design with mobile CC was proposed in [5] by writers who concentrated on the problem of service allocation inside the Combined Fog-Cloud architecture. To learn more about how much power Ind-IoT consumes and how it may be put to use in the real world, check out the works of [6]. For indoor wireless coverage, [7] investigates unexpected spectrum access methods. Reference [8] proposes a management strategy for multimodal sensor networks that is both efficient and successful. In order to reduce service latency even further, these studies did not examine how to link many fog terminals and the cloud platform [7]. To further reduce latency, we suggest in this work that numerous FNs and the CS be linked together to conduct computationally expensive real-time operations in a distributed way [9–11]. Load balancing is a significant tool for reducing latency in distributed computing [12]. As a result, we are looking at how several FNs and a CS balance load. A load balancing technique that uses genetic algorithms [13] for constrained optimization (CMPC-GA) is also being proposed for consideration.The FN, which lacks resources, is particularly vulnerable to attack. In addition, faulty network connections might be caused by shaky wireless transmission lines [14]. It is impossible for a single FN to handle the current burden [15]. This is why we suggest a system for reallocating uncompleted subtasks on failure nodes and retransmitting the new sequence of operations to normal nodes in order to ensure that the task may be completed on time [16]. When an FN fails, the simulation results suggest that the redistribution and retransmission technique can minimize average service latency [17].The rest of this paper’s reminder will go like this: the CFI-Ind-IoT architecture is shown in Section2. Using the CFI-Ind-IoT latency mathematical model, we suggest utilizing the CMPC-GA technique in Section 3 to address the issue. Section 4 displays the results of the evaluations of employee performance. Finally, in Section 5, we summarize this study.


## 2. CFI-IND-IoT Structure

Low latency is essential for our CFI-Ind-IoT architecture (shown in Figure1); hence, we have included FC in the cloud.Figure 1
The CFI-Ind-IoT architecture.The cloud platform layer, the FC layer, and the infrastructure layer make up the architecture. As the foundation of an architect’s design lies in its sensor network, industrial machinery, conveyor networks, and intelligent industrial robots and manipulators, the infrastructure layer is comprised of these elements and many more. The infrastructure’s job is to carry out certain production processes, such as data collection, production, and transportation.There are several edge network devices (such as gateways and routers) with relatively low computation and storage capacity in the FC layer, which play an essential role in the design of the CFI-Ind-IoT. The gates are designated as the FNs in this design. FNs connect with each other wirelessly in order to speed up the implementation and development of the fog network.According to the infrastructure layer needs, FNs interface with the cloud to get relevant information and service, store the product information supplied via them, and upload the useful product information and updates to accomplish global data sharing. Furthermore, the FC layer may analyze a wide range of information (such as product data, user requirements, and measurement data) to decrease latency.Moreover, we suggest distributing computing in a cluster of numerous FNs and CSs to achieve ultralow latency by balancing the load of each FN and cloud. Distributed computing paradigms that use job redistribution and retransmission mechanisms in the cloud-fog network are an excellent way to increase the architecture’s real-time performance in the FN and cloud.Servers in the high-performance cloud layer are suitable for protecting Ind-IoT data as well as exchanging global information and performing simple data mining activities. The cloud is also viewed as a processing core in our design in order to boost the architecture’s computing capability.


## 3. Interactive Load Balancing Strategy in CFI-Ind-IoT

To address the issue of latency in the CFI-Ind-IoT, we recommend using the CMPC-GA method, which we describe in this section.


### 3.1. CFI-Ind-IoT Latency Mathematical Model

The path planning procedure for an industrial robot using laser navigation, for example, involves a slew of data processing [18]. We examine the CFI-Ind-IoT architecture’s data processing. First, the robot continuously records the course it takes. In order to execute rapidly distributed computing, the acquired real-time route data is sent to the localized fog devices and cloud.Finally, the robot will get the path planning findings and use them to carry out its actions. A weighted nodeWUG=FN,ES can be used to represent the network architecture seen in Figure 2.
(1)FN=fn1,fn2,⋯,fnk,CS,(2)ES=esfn1,fn2,⋯,esfnk‐1,fnk.Figure 2
A graph with weighted undirected.Vectorsfnk and CS indicate the FNs and CSs, respectively, in the set of vertices FN showed in Figure 2. A CS has been added to the CFI-Ind-IoT design in order to increase its computational power. Each FN’s computational power is indicated by CS. esfni,fnj is a wireless transmission connection between the nodes fni and fnj represented by the edge set; each edge’s weight (i.e., esfni,fnj) represents the delay in transmission among fni and fnj regarded to be a “master node” in the CFI-Industrial-IoT network since it receives requests from industrial endpoints for ultralow latency services first. Sub is then passed forward to the master node by these endpoints. It is possible to break down the computer effort into smaller subtasks, such as subi. For these duties, all the FNs are involved, including master fni and all of the slaves such as fnj. As the last step, the results of computation were communicated back to industrial endpoints through the master node. As a result, CF-Ind-service IoT’s latency t may be represented as [1]:
(3)t=maxSubiCSfni+Wgfni,fnjhfni,fnj,SubcsCScsi+Wgfni,cshfni,csi,j=1,2,⋯,k,whereWgfni,fnj is the transmission latency among fni and fnj and Subi is the computation delay of the specific task Subi on the fni. When it comes to the subtask assignment connection between fni and fnj, it is denoted by the value of hfni,fnj: 1 indicates that the relationship exists, while zero indicates that it does not. This is a measure of how long it takes the CScsi to process data from the subtask Subcs, and it indicates the time it takes for the master fnj to communicate with the cloud CS. The wireless communication delay between the CFI-Ind-IoT nodes, Wgfni,fnj and Wgfni,cs, under the ARQ protocol, may be defined as follows [1]:
(4)Wgfni,fnj=SubiDTRi×1+PEi1−PEi,(5)Wgfni,cs=SubcDTRc×1+PEc1−PEc.There are two subtasks that are sent to the nodefni and CS through Subi and Subc. To achieve ultralow latency, we should identify an optimum task allocation technique, namely, find a set of ideal subtasks Sub1,Sub2,⋯,Subc. Finally, the CFI-Ind-load IoT’s balancing problem may be expressed as an optimization problem:
(6)minmaxSubiCSfni+SubiDTRi×1+PEi1−PEihfni,fnj,SubcsCScsi+SubcDTRc×1+PEc1−PEchfni,csi,j=1,2,⋯,k,(7)hfni,fnj=0,Subi=0,1,Subi≠0,hfni,cs=0,Subc=0,1,Subc≠0.


### 3.2. Mathematical Model for the Average Service Delay in the Event of System Failure of FNs in Ind-IoT

Uncertainty is evident in the Ind-IoT, such as FNs being damaged or wireless connectivity failing. The FN damages likelihood and the wireless connection outage probability are jointly referred to as the prediction error of a single FN in this research. For each FN, we assume that it has a failure chance of pi. In the event that several FNs fail, the job will be impossible to finish unless a mechanism is implemented. To reduce latency when certain FNs fail, we suggest reallocating and retransmitting the appropriate subtasks to the regular FNs and cloud server for distributed computing. The reassignment and retransmission method could ensure timely and accurate completion of the jobs. CF-average Ind-IoT’s service latency might be mathematically described as Equation (8) if the FNs in the system fail according to the method presented [1].
(8)tave=∑∏fnn∈FN‐FN′PFn∏fni∈FN′1−PFi×minmaxSubiCSfni+SubiDTRi×1+PEi1−PEihfni,fnj,SubcsCScsi+SubcDTRc×1+PEc1−PEchfni,cs+minmaxSubi′CSfni+Subi′DTRi×1+PEi1−PEihfni,fnj,Subcs′CScsi+Subc′DTRc×1+PEc1−PEchfni,cs′,where(9)hfni,fnj=0,Subi=0,1,Subi≠0,(10)hfni,cs=0,Subc=0,1,Subc≠0,(11)fnn∈FN‐FN′,(12)0≤Subi,Subc,Subi′,Subc′≤Sub,(13)∑Subi+Subc+∑Subi′+Subc′=Sub,(14)hfni,fnj′=0,Subi′=0,1,Subi′≠0,(15)hfni,cs′=0,Subc′=0,1,Subc′≠0.


### 3.3. GA-Based Load Balancing Algorithm

As a solution to Equation (6)’s load balancing and Equation (8)’s latency minimization, we use a limited CMPC-GA. An optimization issue can be represented by the Xi variables as an array of alternative solutions, each of which would be given a random real number as an initialization parameter in the CMPC-GA. This process is repeated over and over again until an ideal individual is discovered. The CMPC-GA may be used to solve optimization problems with restrictions, such as inequality and equality, such that the constrained optimization issues can be transformed into unconstrained optimization problems. The CMPC-GA is described in the following paragraphs. The CMPC-fitness GA’s function differs from the typical real-coded GA in the following ways:
(16)fitx=txx∈FR,tx+PF∑j=1k+2tjx+ψx,genx∈IFR.In the search spaceS, the feasible zone is FR, whereas the infeasible region is IFR. It is important to notice that for each successive constraint, PF represents the penalized factor, tjx represents the infeasible people’s constraint violation value for the jth limitation, and ψx,gen represents an extra heuristic value for each successive generation’s infeasible individuals. In which, tjx and ψx,gen may be written as
(17)tjx=max−xj,01≤j≤k+1,∑i=1k+1Sub−xij=k+2,(18)ψx,gen=Worstgen−minx∈IFRtx+PF∑j=1k+2tjx,where(19)Worstgen=maxmaxx∈FRtx,Worstgen−1.The performance index of thegth iteration viable individuals is represented by tx in Equation (17). Using g generations of evolution, Worstg identifies the possible person with the best fitness. It is necessary to initially randomly initialize the search space S with real numbers in order to construct the one-dimensional real array of k+1 genes that makes up each chromosome, or individual xi in the population, for the CMPC-GA algorithm. To assess the population, the fitness value of each member would be computed using Equation (16). As a further step, the genetic algorithms are used to bring the original population up to date again. And here are the specific genetic operators: selection: high-fitness people are selected from the existing population to be preserved for future generations. Using a two-tournament selection approach is employed in this study.In a GA, the crossover is a key technique for passing on the original excellent genes to the next generation of children. When using the CMPC-GA, two new offspring are formed by the linear integration of the two-parent individuals. The arithmetic crossover is employed in this case. The following may be said about the relationship between a child and their parents. The CMPC-local GA’s search capacity is determined by the mutation operation, which increases the population’s variety. We use a nonuniform mutation operator in our article. Based on the load-balancing problem in Equation (6), the CMPC-GA algorithm is illustrated in the following subsection.


### 3.4. The CMPC-GA Algorithm

Charles Darwin’s theory of natural evolution inspired Holland to create the GA in 1975 [19]. As with evolution, this algorithm selects only the most powered to propagate. Indefinitely, the population of solutions can be altered using this way. Individuals in the current population are chosen at random to be the parents of the next generation’s children by GA. It takes several generations for the population to “evolve” towards an optimal answer. Figure 3 depicts the four phases of a typical GA.Figure 3
Four phases of a typical GA.Typical GA flaws include an inability to exploit and a propensity to become locked in local minimums. Although it may take longer for GA to converge, it does so more quickly when chromosomes move quickly and abruptly in the correct direction. Figure4 depicts a conventional GA’s single-point crossover. As can be seen, the resulting chromosomes are not much different from their parents when only two chromosomes are combined in a single-point crossover.Figure 4
An example of a single-point crossover operator of standard GA.Traditional crossover has the drawback of only seeing in the direction of one or both of its parents. It is feasible to improve the number of viable solutions in GA by using a more optimal solution search. In order to improve algorithm exploitation and exploration, this paper presents a new MC operator. The updated MPCGA’s MC is seen in Figures5 and 6. It is clear that the RMSE is similar to the goal function, and the lower it is, the more precise the response will be.Figure 5
A typical MC (3 parents).Figure 6
A typical MC (5 parents).Because of this, the offspring produced by using several best parents in MC-GA shows less resemblance to any one of their parents, indicating that they are more diverse (improves exploration). As a result, the algorithm may be more effectively used since the offspring inherit all of their genes from a variety of parents.


## 3.1. CFI-Ind-IoT Latency Mathematical Model

The path planning procedure for an industrial robot using laser navigation, for example, involves a slew of data processing [18]. We examine the CFI-Ind-IoT architecture’s data processing. First, the robot continuously records the course it takes. In order to execute rapidly distributed computing, the acquired real-time route data is sent to the localized fog devices and cloud.Finally, the robot will get the path planning findings and use them to carry out its actions. A weighted nodeWUG=FN,ES can be used to represent the network architecture seen in Figure 2.
(1)FN=fn1,fn2,⋯,fnk,CS,(2)ES=esfn1,fn2,⋯,esfnk‐1,fnk.Figure 2
A graph with weighted undirected.Vectorsfnk and CS indicate the FNs and CSs, respectively, in the set of vertices FN showed in Figure 2. A CS has been added to the CFI-Ind-IoT design in order to increase its computational power. Each FN’s computational power is indicated by CS. esfni,fnj is a wireless transmission connection between the nodes fni and fnj represented by the edge set; each edge’s weight (i.e., esfni,fnj) represents the delay in transmission among fni and fnj regarded to be a “master node” in the CFI-Industrial-IoT network since it receives requests from industrial endpoints for ultralow latency services first. Sub is then passed forward to the master node by these endpoints. It is possible to break down the computer effort into smaller subtasks, such as subi. For these duties, all the FNs are involved, including master fni and all of the slaves such as fnj. As the last step, the results of computation were communicated back to industrial endpoints through the master node. As a result, CF-Ind-service IoT’s latency t may be represented as [1]:
(3)t=maxSubiCSfni+Wgfni,fnjhfni,fnj,SubcsCScsi+Wgfni,cshfni,csi,j=1,2,⋯,k,whereWgfni,fnj is the transmission latency among fni and fnj and Subi is the computation delay of the specific task Subi on the fni. When it comes to the subtask assignment connection between fni and fnj, it is denoted by the value of hfni,fnj: 1 indicates that the relationship exists, while zero indicates that it does not. This is a measure of how long it takes the CScsi to process data from the subtask Subcs, and it indicates the time it takes for the master fnj to communicate with the cloud CS. The wireless communication delay between the CFI-Ind-IoT nodes, Wgfni,fnj and Wgfni,cs, under the ARQ protocol, may be defined as follows [1]:
(4)Wgfni,fnj=SubiDTRi×1+PEi1−PEi,(5)Wgfni,cs=SubcDTRc×1+PEc1−PEc.There are two subtasks that are sent to the nodefni and CS through Subi and Subc. To achieve ultralow latency, we should identify an optimum task allocation technique, namely, find a set of ideal subtasks Sub1,Sub2,⋯,Subc. Finally, the CFI-Ind-load IoT’s balancing problem may be expressed as an optimization problem:
(6)minmaxSubiCSfni+SubiDTRi×1+PEi1−PEihfni,fnj,SubcsCScsi+SubcDTRc×1+PEc1−PEchfni,csi,j=1,2,⋯,k,(7)hfni,fnj=0,Subi=0,1,Subi≠0,hfni,cs=0,Subc=0,1,Subc≠0.


## 3.2. Mathematical Model for the Average Service Delay in the Event of System Failure of FNs in Ind-IoT

Uncertainty is evident in the Ind-IoT, such as FNs being damaged or wireless connectivity failing. The FN damages likelihood and the wireless connection outage probability are jointly referred to as the prediction error of a single FN in this research. For each FN, we assume that it has a failure chance of pi. In the event that several FNs fail, the job will be impossible to finish unless a mechanism is implemented. To reduce latency when certain FNs fail, we suggest reallocating and retransmitting the appropriate subtasks to the regular FNs and cloud server for distributed computing. The reassignment and retransmission method could ensure timely and accurate completion of the jobs. CF-average Ind-IoT’s service latency might be mathematically described as Equation (8) if the FNs in the system fail according to the method presented [1].
(8)tave=∑∏fnn∈FN‐FN′PFn∏fni∈FN′1−PFi×minmaxSubiCSfni+SubiDTRi×1+PEi1−PEihfni,fnj,SubcsCScsi+SubcDTRc×1+PEc1−PEchfni,cs+minmaxSubi′CSfni+Subi′DTRi×1+PEi1−PEihfni,fnj,Subcs′CScsi+Subc′DTRc×1+PEc1−PEchfni,cs′,where(9)hfni,fnj=0,Subi=0,1,Subi≠0,(10)hfni,cs=0,Subc=0,1,Subc≠0,(11)fnn∈FN‐FN′,(12)0≤Subi,Subc,Subi′,Subc′≤Sub,(13)∑Subi+Subc+∑Subi′+Subc′=Sub,(14)hfni,fnj′=0,Subi′=0,1,Subi′≠0,(15)hfni,cs′=0,Subc′=0,1,Subc′≠0.


## 3.3. GA-Based Load Balancing Algorithm

As a solution to Equation (6)’s load balancing and Equation (8)’s latency minimization, we use a limited CMPC-GA. An optimization issue can be represented by the Xi variables as an array of alternative solutions, each of which would be given a random real number as an initialization parameter in the CMPC-GA. This process is repeated over and over again until an ideal individual is discovered. The CMPC-GA may be used to solve optimization problems with restrictions, such as inequality and equality, such that the constrained optimization issues can be transformed into unconstrained optimization problems. The CMPC-GA is described in the following paragraphs. The CMPC-fitness GA’s function differs from the typical real-coded GA in the following ways:
(16)fitx=txx∈FR,tx+PF∑j=1k+2tjx+ψx,genx∈IFR.In the search spaceS, the feasible zone is FR, whereas the infeasible region is IFR. It is important to notice that for each successive constraint, PF represents the penalized factor, tjx represents the infeasible people’s constraint violation value for the jth limitation, and ψx,gen represents an extra heuristic value for each successive generation’s infeasible individuals. In which, tjx and ψx,gen may be written as
(17)tjx=max−xj,01≤j≤k+1,∑i=1k+1Sub−xij=k+2,(18)ψx,gen=Worstgen−minx∈IFRtx+PF∑j=1k+2tjx,where(19)Worstgen=maxmaxx∈FRtx,Worstgen−1.The performance index of thegth iteration viable individuals is represented by tx in Equation (17). Using g generations of evolution, Worstg identifies the possible person with the best fitness. It is necessary to initially randomly initialize the search space S with real numbers in order to construct the one-dimensional real array of k+1 genes that makes up each chromosome, or individual xi in the population, for the CMPC-GA algorithm. To assess the population, the fitness value of each member would be computed using Equation (16). As a further step, the genetic algorithms are used to bring the original population up to date again. And here are the specific genetic operators: selection: high-fitness people are selected from the existing population to be preserved for future generations. Using a two-tournament selection approach is employed in this study.In a GA, the crossover is a key technique for passing on the original excellent genes to the next generation of children. When using the CMPC-GA, two new offspring are formed by the linear integration of the two-parent individuals. The arithmetic crossover is employed in this case. The following may be said about the relationship between a child and their parents. The CMPC-local GA’s search capacity is determined by the mutation operation, which increases the population’s variety. We use a nonuniform mutation operator in our article. Based on the load-balancing problem in Equation (6), the CMPC-GA algorithm is illustrated in the following subsection.


## 3.4. The CMPC-GA Algorithm

Charles Darwin’s theory of natural evolution inspired Holland to create the GA in 1975 [19]. As with evolution, this algorithm selects only the most powered to propagate. Indefinitely, the population of solutions can be altered using this way. Individuals in the current population are chosen at random to be the parents of the next generation’s children by GA. It takes several generations for the population to “evolve” towards an optimal answer. Figure 3 depicts the four phases of a typical GA.Figure 3
Four phases of a typical GA.Typical GA flaws include an inability to exploit and a propensity to become locked in local minimums. Although it may take longer for GA to converge, it does so more quickly when chromosomes move quickly and abruptly in the correct direction. Figure4 depicts a conventional GA’s single-point crossover. As can be seen, the resulting chromosomes are not much different from their parents when only two chromosomes are combined in a single-point crossover.Figure 4
An example of a single-point crossover operator of standard GA.Traditional crossover has the drawback of only seeing in the direction of one or both of its parents. It is feasible to improve the number of viable solutions in GA by using a more optimal solution search. In order to improve algorithm exploitation and exploration, this paper presents a new MC operator. The updated MPCGA’s MC is seen in Figures5 and 6. It is clear that the RMSE is similar to the goal function, and the lower it is, the more precise the response will be.Figure 5
A typical MC (3 parents).Figure 6
A typical MC (5 parents).Because of this, the offspring produced by using several best parents in MC-GA shows less resemblance to any one of their parents, indicating that they are more diverse (improves exploration). As a result, the algorithm may be more effectively used since the offspring inherit all of their genes from a variety of parents.


## 4. Experimental Results and Discussion

The CFI-Ind-IoT-based CMPC-GA retransmission and redistribution method is the subject of this section’s performance assessments. According to [20], the CFI-Ind-IoT has four FNs configured for low latency. For the mobile communication parameters, we selected 802.11 ac protocol parameters. To create a realistic network simulation, a heterogeneous fog network with varying computer capacities is needed. Table 1 includes some relevant parameters. Also, Table 2 represents the CMPC-parameter GA’s settings.Table 1
Relevant parameters.
Parameter typeFN1FN2FN3FN4CCFNi/CCS (Gbps)0.280.230.180.138Transfer rate (Mbps)19019018019518Packet error rate0.02010.01850.01980.02010.0082Table 2
The CMPC-parameter GA’s settings.
ParametersValuesPopulation size50Crossover probability0.8Mutation probability0.4Worst (0)96Maximum number of generations100Our simulation has comprehensive service demand assignment information from intelligent manufacturing machinery. Task loads range from 0 MB to 400 MB, depending on the simulation configuration. The CMPC-GA technique allows us to obtain the job allocation ratio in advance, which reduces service delay. The workflow scheduling ratio allows for easy retrieval of the work allocation results when they become available. As a result, CMPC-running GA’s time may be ignored. MATLAB is used to generate all of the simulation results, and each value is the average of a large number of tests.


### 4.1. Ind-IoT Performance Comparison of Three Architectures

CFI-Ind-IoT, based on the CMPC-GA load-balancing algorithm, is tested against the cloud-based and fog-based architectures in Ind-IoT to verify the low latency efficiency of CFI-Ind-IoT. Latency comparison findings are depicted in Figure7. It is becoming increasingly difficult for the cloud-based structure to keep up with the rising demands of the activity, resulting in a large increase in latency.Figure 7
Comparison of the mentioned structures.As a result of the cloud’s distance from intelligent manufacturing endpoints and its restricted bandwidth, the fog-based structure offers lower latency than cloud infrastructure. CFI-Ind-service IoT’s latency is shown in Figure7 to be lower than that of fog-based architectures when the load is high. That is because the CFI-Ind-processing IoT’s capability is enhanced by the CS’s computational capacity. Compared to cloud-based and fog-based architectures, the latency effectiveness of CFI-Ind-IoT has improved by 93.98 percent and 36.67 percent when the job load is 400 Mb. Consequently, a low latency service may be provided by the CFI-Ind-IoT, which is ideal for Ind-IoT.


### 4.2. The Performance of Various Load Balancing Techniques in terms of Latency

Comparisons between CMPC-GA, WRR [21], Niching-ChOA [22], and Greedy scheduling algorithms [23] are made in the next section to demonstrate the great efficiency of CMPC-GA in minimizing the latency of CFI-Industry-IoT. In Figure 8, the simulation results are depicted.Figure 8
The comparison of latency effectiveness for various algorithms.There was a noticeable difference in latency between CMPC-GA and the other algorithms. To ensure global searching, CMPC-GA uses the crossover operation, whereas mutation is used for local searching. CMPC-global GA’s load-balancing method reduces service latency because of this. When balancing the load, the WRR and GreedyLB algorithms do not take transmission latency into account; hence, the Niching-ChOA method may end up in the local optimum, resulting in increased latency. When the task size is 400 MB, the CMPC-GA method outperforms WRR, GreedyLB, and Niching-ChOA in terms of latency by 71.3%, 72.8%, and 42.8%. Consequently, it is shown that reducing latency in the CFI-Ind-IoT structure is made easier by using the CMPC-GA load balancing method [24, 25].


### 4.3. Failure of FNs Results in an Average Service Latency

Each FN is given a failure probability in the simulation. A failure example in which the CFI-Ind-IoT adopts task reallocation and retransmission, as well as another failure instance in which the CFI-Ind-IoT simply adopts the retransmission technique, is used to compare average service delay in order to evaluate the effectiveness of the CFI-Ind-IoT. CFI-Ind-IoT service latency is also compared in four different production situations where the failure probability of the fog nodes is varied to study the impact of the FNs on the service latency [26]. Table 3 shows the FNs’ failure probability in four different contexts. Figures 9 and 10 illustrate the results of the computer simulations.Table 3
Fog nodes’ failure probabilities for various conditions.
EnvironmentFN1FN2FN3FN4CSBest00000Good0.0020.140.0210.0090General0.290.280.390.290Poor0.50.590.710.740Figure 9
The comparison of service latency.Figure 10
The comparison of service latency for various environments.There are some FNs that fail when CFI-Ind-IoT adopts task reallocation and retransmission mechanisms (R_Latency), and there are some FNs that fail when CFI-Ind-IoT only employs the retransmission mechanism (F_Latency) where the unimplemented subtasks on the failure FNs are only resent to one normal node to analyze. In the event of a failure, the failure probability of the FNs is based on Table3’s good environment. We can see from Figure 5 that the work may be performed in a specific amount of time, rather than being unable to be done when FNs fail [27]. The latency in the failure scenario (R_Latency and F_Latency) is longer than the duration in the normal situation as the number of tasks increases (N_Latency).To avoid increasing delay, it is necessary to reprocess activities that were left unfinished on the failed nodes on the regular nodes instead. The F_Latency is lower than the R_Latency, and the gap between the latency of the two rises as the job size increases. When the job is huge, it may be possible to lower the processing delay by distributing the unfinished work from the failed FNs to all of the normal nodes [28]. The R_Latency decreases by 9.02 percent when the processing load is 400 Mb, compared to the F_Latency. With this job reallocation and transmission mechanism, low latency service may be provided in case of FN malfunction in Ind-IoT using CFI-Ind.In CFI-Ind-IoT, the average service delay is influenced by the failure probability of the FNs. The average service delay is compared among four types of production settings with varying failure rates. Table3 displays the FNs’ failure probability in four different contexts. In all four types of contexts, it is evident that the operation latency grows as the number of tasks increases. When the process demand is fixed, we can see that the average service delay rises as the risk of failure increases.An average service delay in the CFI-Ind-IoT of 400 Mb was found to be lowered by 32.38 percent, 19.23 percent, and 14.21 percent compared to the latency in negative, general, and excellent environments. The substantial failure rate of the FNs is expected to result in a big average service delay. It should be noted that the convergence curves for various population size are presented in Figures11–14.Figure 11
The comparison of convergence curves for populationsize=20.Figure 12
The comparison of convergence curves for populationsize=40.Figure 13
The comparison of convergence curves for populationsize=60.Figure 14
The comparison of convergence curves for populationsize=80.


## 4.1. Ind-IoT Performance Comparison of Three Architectures

CFI-Ind-IoT, based on the CMPC-GA load-balancing algorithm, is tested against the cloud-based and fog-based architectures in Ind-IoT to verify the low latency efficiency of CFI-Ind-IoT. Latency comparison findings are depicted in Figure7. It is becoming increasingly difficult for the cloud-based structure to keep up with the rising demands of the activity, resulting in a large increase in latency.Figure 7
Comparison of the mentioned structures.As a result of the cloud’s distance from intelligent manufacturing endpoints and its restricted bandwidth, the fog-based structure offers lower latency than cloud infrastructure. CFI-Ind-service IoT’s latency is shown in Figure7 to be lower than that of fog-based architectures when the load is high. That is because the CFI-Ind-processing IoT’s capability is enhanced by the CS’s computational capacity. Compared to cloud-based and fog-based architectures, the latency effectiveness of CFI-Ind-IoT has improved by 93.98 percent and 36.67 percent when the job load is 400 Mb. Consequently, a low latency service may be provided by the CFI-Ind-IoT, which is ideal for Ind-IoT.


## 4.2. The Performance of Various Load Balancing Techniques in terms of Latency

Comparisons between CMPC-GA, WRR [21], Niching-ChOA [22], and Greedy scheduling algorithms [23] are made in the next section to demonstrate the great efficiency of CMPC-GA in minimizing the latency of CFI-Industry-IoT. In Figure 8, the simulation results are depicted.Figure 8
The comparison of latency effectiveness for various algorithms.There was a noticeable difference in latency between CMPC-GA and the other algorithms. To ensure global searching, CMPC-GA uses the crossover operation, whereas mutation is used for local searching. CMPC-global GA’s load-balancing method reduces service latency because of this. When balancing the load, the WRR and GreedyLB algorithms do not take transmission latency into account; hence, the Niching-ChOA method may end up in the local optimum, resulting in increased latency. When the task size is 400 MB, the CMPC-GA method outperforms WRR, GreedyLB, and Niching-ChOA in terms of latency by 71.3%, 72.8%, and 42.8%. Consequently, it is shown that reducing latency in the CFI-Ind-IoT structure is made easier by using the CMPC-GA load balancing method [24, 25].


## 4.3. Failure of FNs Results in an Average Service Latency

Each FN is given a failure probability in the simulation. A failure example in which the CFI-Ind-IoT adopts task reallocation and retransmission, as well as another failure instance in which the CFI-Ind-IoT simply adopts the retransmission technique, is used to compare average service delay in order to evaluate the effectiveness of the CFI-Ind-IoT. CFI-Ind-IoT service latency is also compared in four different production situations where the failure probability of the fog nodes is varied to study the impact of the FNs on the service latency [26]. Table 3 shows the FNs’ failure probability in four different contexts. Figures 9 and 10 illustrate the results of the computer simulations.Table 3
Fog nodes’ failure probabilities for various conditions.
EnvironmentFN1FN2FN3FN4CSBest00000Good0.0020.140.0210.0090General0.290.280.390.290Poor0.50.590.710.740Figure 9
The comparison of service latency.Figure 10
The comparison of service latency for various environments.There are some FNs that fail when CFI-Ind-IoT adopts task reallocation and retransmission mechanisms (R_Latency), and there are some FNs that fail when CFI-Ind-IoT only employs the retransmission mechanism (F_Latency) where the unimplemented subtasks on the failure FNs are only resent to one normal node to analyze. In the event of a failure, the failure probability of the FNs is based on Table3’s good environment. We can see from Figure 5 that the work may be performed in a specific amount of time, rather than being unable to be done when FNs fail [27]. The latency in the failure scenario (R_Latency and F_Latency) is longer than the duration in the normal situation as the number of tasks increases (N_Latency).To avoid increasing delay, it is necessary to reprocess activities that were left unfinished on the failed nodes on the regular nodes instead. The F_Latency is lower than the R_Latency, and the gap between the latency of the two rises as the job size increases. When the job is huge, it may be possible to lower the processing delay by distributing the unfinished work from the failed FNs to all of the normal nodes [28]. The R_Latency decreases by 9.02 percent when the processing load is 400 Mb, compared to the F_Latency. With this job reallocation and transmission mechanism, low latency service may be provided in case of FN malfunction in Ind-IoT using CFI-Ind.In CFI-Ind-IoT, the average service delay is influenced by the failure probability of the FNs. The average service delay is compared among four types of production settings with varying failure rates. Table3 displays the FNs’ failure probability in four different contexts. In all four types of contexts, it is evident that the operation latency grows as the number of tasks increases. When the process demand is fixed, we can see that the average service delay rises as the risk of failure increases.An average service delay in the CFI-Ind-IoT of 400 Mb was found to be lowered by 32.38 percent, 19.23 percent, and 14.21 percent compared to the latency in negative, general, and excellent environments. The substantial failure rate of the FNs is expected to result in a big average service delay. It should be noted that the convergence curves for various population size are presented in Figures11–14.Figure 11
The comparison of convergence curves for populationsize=20.Figure 12
The comparison of convergence curves for populationsize=40.Figure 13
The comparison of convergence curves for populationsize=60.Figure 14
The comparison of convergence curves for populationsize=80.


## 5. Conclusion

CFI-Ind-IoT network architecture is built by integrating FC with cloud-based Ind-IoT architecture and introducing cloud applications to the network. The CFI-Ind-IoT latency mathematical model is first established. In order to reduce latency, we implemented the CMPC-GA algorithm. For the CFI-Ind-IoT, we developed a demand redistribution and retransmission technique to decrease the average service delay in the event of FN failure. In the Ind-IoT, the simulation results suggest that the CFI-Ind-IoT based on the CMPC-GA architecture, as well as our proposed job reallocation and retransmission mechanism, may achieve ultralow latency performance. Research in the future will focus mostly on the modeling and improvement of cloud-fog network dependability. Using novel metaheuristic algorithms, including ChOA and DLFChOA, can be considered as another research direction.



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*Source: 1917172-2022-08-12.xml*