A Multi-Objective Optimization of Secure Pull Manufacturing Systems

Abstract

This paper aims to optimize the losses of the current manufacturing systems to perform the Just in Time (JIT) system and minimize the time, labor, and material in the manufacturing process. Pull systems, which have a famous name of the Smart Kanban system, are one of the methodologies to implement the JIT system. The setting of manufacturing system frameworks offers intriguing capabilities to improve the performance of pull-controlled creation frameworks. Smart Kanban can be utilized, rather than actual cards, and the data conversion about the manufacturing settings, is accessible through sensors. Since a Just-in-Time system does not include a buffer, any interruption to the system can cause the process to stop quite quickly, so security is necessary for the JIT improvement. However, those systems have recently been unguarded to security threats as they introduce general-purpose technologies. From the viewpoint of the system, a security measure is implemented for pull system methods to check for potential threats and analyze vulnerabilities of the pull system. The Flower Pollination Algorithm (FPA) is used as a novel multiobjective technique to optimize different types of cost and time. The experimental results show that the proposed algorithm has robust security efficiency, as well as reduces cost and time consumption.

1. Introduction

The Just-in-Time (JIT) philosophy’s goal is to impart the correct parts at the ideal time, at the ideal spot, and in the perfect sum required. The most eminent pull systems are likely Kanban, which are allowed, uniquely, upon the social affair of authorization cards that are used to control all the manufacturing process. The former uses a circle of cards at each phase of the cycle, and the latter is more direct since it considers all of the interaction as a solitary stage system, where each part is pushed through the system, when its production is permitted, at the contribution of the system by a card. One important issue of such pull control systems is how to secure the system. This issue has been generally tended to by utilizing streamlining approaches, which target the best security framework to amplify the given execution destinations. Pull frameworks are cooperating all the more intimately with data frameworks to improve the proficiency of tasks.

A Kanban is a Japanese term for a visual signboard or card. Kanban is the execution framework used by the Toyota Production System (TPS), for data flow in the assembling framework, to pull material streams from upstream to downstream, Several kinds of Kanban systems were recorded, in full, by Monden in 1993, and their implementation in controlling production and inventory processes has proven to be successful [1]. The implementation and benefits of the traditional Kanban system have been examined in several studies [2,3,4,5,6,7]. Studies concerning an electronic Kanban (e-Kanban) system and its feasibility over a traditional Kanban system have increased recently [2,8,9,10]. The e-Kanban system of “e” stands for electronic, which basically means it runs on a network server and is managed by computers, or in other words, the e-Kanban system is controlled by computers. Besides its traditional features, the electronic system has advantages of traceability and scalability over traditional Kanban systems. With recent advancements in Information Technology (IT) systems and related wireless technologies, companies are becoming more interested in e-Kanban systems to digitize manufacturing information flows and computerize manufacturing processes.

The production control system is no longer protected against security threats. It is considered to be a key associational or societal system, such as a product system for industry or a major infrastructure system for electricity, water supply, oil, or natural gas. If a construction control system stops, it may have a high impact on society. Consequently, the system was protected by two kinds of security measures: one to prevent the system from shutting down and the other to prevent it from stopping. By performing a sensitivity analysis, one can determine the vulnerability of the system to recognized potential threats. In order to safeguard assets, security measures against the sensitivity of the system are outlined after sensitivity investigations have been completed. Although the system can be protected by all of these measures, their implementation would not be feasible due to the multiple operations and costs involved. Therefore, security measures should be selected based on the operation and cost involved.

Today, online services play an increasingly important role in our daily lives. Although they have certain advantages, they also pose certain security challenges to the communication network. Authentication of users, confidentiality of data, and integrity of data comprise the security aspects. A digital signature must be provided by the original sender and verified by the intended recipient in order to achieve all these parameters. In order to improve data security and authenticity, digital signatures based on the ElGamal algorithm are being used [11]. DNA cryptography refers to a new technique for securing data by using the structure of Deoxyribonucleic Acid (DNA). The technique was later modified by various researchers to enable encrypting and reducing the storage size of data, which resulted in faster and more secure data transmission over networks [12,13]. DNA encryption can be defined as the practice of hiding data by modifying a DNA sequence. The design of BioGamal technique was first introduced in [14]. BioGamal is designed to increase information security through the use of ElGamal’s digital signature technology, combined with DNA encryption and decryption techniques.

Optimization is the major concern for the production to achieve the best possible result under the given conditions. In recent approaches, using a single-objective approach loses information about the balance between the two objectives. In contrast, the multiobjective approach gives decision-makers a deeper understanding of the balance between the two objectives. In this regard, a multiobjective approach to optimization is recommended. In a casual case including the advancement, the issue was consistently made up by augmenting or limiting an actual capacity, which could get the info esteems from inside a permitted set and, afterward, register the outcome for the capacity. Likewise, advancement hypotheses and procedures for different arrangements incorporate applied science. In addition, optimization needs to reach “best worth”. That esteem, for the target work, should be controlled in various types of target capacities and spaces. Various papers are completed in the optimization process concerning the Kanban cards [15]; a simulation optimization technique is applied alongside a blend of simulation software packages and metaheuristic algorithms—for example, genetic and Guided Local Search, GLS [16], algorithms—which are more adaptable to take care of the issue. At last, the predominance of this plan is experiential.

In this article, we propose a new secure optimized pull manufacturing system to increase the security of data transferred through Kanban cards, as well as minimize the time and cost of the manufacturing process. The BioGamal algorithm is designed to increase the security of the Kanban cards of a pull system by combining Gamal algorithm and DNA cryptography. Gamal is used as a digital signature to authenticate the data on the Kanban card, while DNA is used to encrypt and decrypt data. Then, the FPA multiobjective technique is applied with a different number of stages to optimize the cost and time of the overall secured pull manufacturing system. The article is organized as follows: Section 2 give a brief description of the Kanban system, pull control system, security system, and flower pollination algorithm. The proposed secure optimized pull manufacturing system is presented in Section 3. Section 4 examines the simulation model and the performance of the proposed system. Finally, Section 5 concludes the proposed work.

2. Literature Review

2.1. Kanban System

A Kanban technique pulled in numerous scientists since it was first exposed in [17]. He initially summed up the Toyota approach for deciding the suitable number of Kanbans at a workstation. It is applied, as of late, in inventory network frameworks to proficiently deal with the progression of materials. In 1987, the authors stretched out the Toyota way to deal with a fluctuating item blend issue by utilizing the following period of conjecture interest and the last period of noticed lead times [18]. After 10 years, the authors considered the over-arranging factor in the Toyota recipe for processing the quantity of Kanbans for a few creation stock control models [19]. The Kanban is a practical tool for the execution of JIT conveyance in production network tasks. In 2006, the elements of the Kanban were two-fold: they were utilized as methods for creation control and cycle improvement [20]. Kanban’s underway control is tied to distinctive assembling measures to guarantee the conveyance of essential measures of material and parts at the suitable time and spot. The utilization of the Kanban, in measure improvement, is remembered for improving the activities for the creation interaction, with accentuation on decreasing stock expenses.

Modern manufacturing processes require more accuracy, speed, and agility from the automotive industry [21]. The rapid changes in the global market have driven a significant increase in product variety, particularly in recent years. In traditional Kanban systems, complexity increases, linearly, as product variety increases [8,9,10,11,12,13,14,15,16,17,18,19,20,21]. Kanban systems are complex because of their limitations, which include controlling Lot Size information in the Kanban post, handling and transferring Kanban in order to balance production lines, losing track of inventory condition, and suffering a reduction in productivity due to the loss of Kanban cards. The problem is a lack of visibility and ability to expand to accommodate the increasing variety of products. Hence, the e-Kanban card is designed to solve the problem of traditional Kanban systems.

2.2. e-Kanban Card-Based Pull Control Systems

Different mechanisms have been proposed to powerfully change the quantity of cards available for use and to improve the presentation of card-based force control frameworks, in conditions confronting vacillations, in client interests. This theme has received significant consideration from numerous analysts, and it still establishes an open examination zone [22,23].

A few versatile card-based pull control systems have been intended to lessen WIP, while keeping up great consumer loyalty, in conditions with fluctuating client interests and irregular creation times [24]. In 1998, a statistical throughput control (STC) way was constructed to deal with and adjust the quantity of cards in a ConWIP framework, to restrict WIP, as a reaction to stochastic changes in customer demand [25]. To do that, they considered an objective throughput rate and checked the normal throughput of the framework. In the event that the circumstance is considered as wild (as per an objective throughput rate to be accomplished), at that point, a card is added or recovered, and the information of the calculation is re-introduced. Changes in the quantity of cards are permitted solely after a predefined number of prepared items. After that, in 2006, the authors built up a card controlling strategy for a ConWIP framework [26]. Their strategy continually screens the throughput rate to check whether it is under a specific creation target or above it. The extra cards are added to, or deducted from, the creation line, individually, to accomplish an objective throughput rate esteem. As the framework execution can be enormously influenced by the boundaries utilized for changes, similar creators applied a reaction surface system to decide these boundaries [27]. In 2009, a card controlling methodology was introduced, which can change the quantity of cards to guarantee an alluring throughput rate [28]. An objective throughput esteem is set; the distinction among it, and the continuous throughput esteem, is then used to change the quantity of cards. Figure 1 shows the representation of Kanban card. It is shown that the Kanban card consists of all the data required for item transfer, which include supplier name, supplier ID, the unit of the box, customer location, Kanban ID, item ID, quantity, routing, and quality approval.

2.3. Security System

The digital signature algorithm is one of the most important security systems. In 2017, Playgamal technique is proposed to be a new digital signature based on joining highlights of the playfair digit and ElGamal signature [29]. In the same year [30], the authors joined a MAC address with AES-128 to perform another digital signature algorithm. The scheme utilized SHA-256 to produce hash code and then encrypted the hash code using an encryption algorithm produced by the combination of the MAC address and AES technique. In 2017, the authors proposed an electronic digital signature, in the maritime industry, using ECDSA technique [31]. In 2015 [32], digital image authentication is applied on image data with the addition of an encoding picture digital signature using the RSA algorithm. Ref. [33] planned the digital signature for XML exchanges. Several algorithms are applied in [28] to perform relative examination of the digital signature; the results show that ECDSA has higher security. The DSA algorithm and hyper-elliptical bend algorithm are used in [34] to perform a digital signature scheme, which brings about a high security level, and the personality of the data is confirmed. Another cone-molded digital signature conspire utilizes two private keys and improves the trouble level to uncover signature keys [35]. Furthermore, DNA cryptography is used, in recent years, to increase the security of data transmission by hiding data into a DNA sequence. In 2020, DNA was employed as a genome scrambling stage to be robust against several attacks [12,13].

2.4. Flower Pollination Algorithm (FPA)

A new optimization technique called the Flower Pollination Algorithm (FPA) is presented in this study. A meta-heuristic algorithm inspired by flower pollination and one of the most promising and useful algorithms developed by Xin-She Yang in 2012 [36] was developed as one of the most promising and useful algorithms. Flower pollination serves the purpose of encouraging plant reproduction and the survival of the fittest from the viewpoint of biological evolution. Yang demonstrated that the Flower Pollination Algorithm is modest, very efficient, and surpasses genetic algorithms and particle swarm optimization in terms of performance.

The FPA, when compared with other metaheuristic algorithms, appears to provide significant benefits for solving various real-life optimization problems from various disciplines, including electrical and power systems [37], signal and image processing [38], sensors and wireless networks [39], as well as backpack issues [40], computer games [41], construction optimization [42], global workforce optimization [43], and several others [44]. FPA may be a population-based optimization strategy that started with a set of temporary or irregular arrangements. At each cycle, either one of the two administrators are carried out for each person populace part: neighborhood pollination administrator and worldwide fertilization administrator. In a neighborhood fertilization administrator, the choice factors of the current arrangement pull in the other two arbitrarily chosen arrangements from two populace individuals. In a worldwide fertilization administrator, the choice factors of the current arrangement draw in to the universally best arrangement found and, then, switch the administrator in response.

Some issues related to the optimal design of a Kanban-controlled multi-level system are represented in [45,46]. Due to the difficulty of the design problem considered, a genetic algorithm was preferred as an optimization tool, finding that the number of Kanbans, the “size” of the Kanban, and the volume of the corresponding container, was also optimized. Ref. [47] proposed a meta-heuristic algorithm (particle swarm optimization) to minimize the total cost function, which includes inventory cost, out-of-stock cost, handling cost, and work-in-process cost. In [48], there are various methods to solve classification problems such as K-Nearest Neighbors (KNN), Artificial Neural Network (ANN), Radial Basis Function (RBF), and FPA, which optimizes PNN weights. The flower pollination algorithm (FPA) with probabilistic neural network (PNN) was investigated using the FPA, which optimized the PNN weights. Their results showed that the FPA with PNN performs better than the original PNN on all data sets.

3. Methodology

This article discusses the process of the optimized secure pull system, which is one of the items with which to implement the JIT system to reduce the different kinds of wastes. The pull system is working with different Kanban cards between plants to transfer data of semi product. Due to the non-security of this card, BioGamal cryptosystem is used to increase the security of the pull system. BioGamal cryptosystem is applied on each Kanban card to authenticate and encrypt the transferring data between plants. To minimize the running time and cost of the applied cryptosystem, a multi-objective optimization technique is applied on the overall pull system. From Figure 2, Plant 1 sends the signed and encrypted Kanban card of semi product to Pant 2. After verification with digital signature, Plant 2 received the semi product from Plant 1 and decrypted the data of the Kanban card. This process is repeated until the Plants finish the final product. Therefore, the security of the Kanban cards increase and they are robust against any jugglery with reciprocity information between cards. Then, the overall system is optimized using a novel multiobjective optimization technique to increase the performance of the pull system by optimizing the time and cost with different stages for the final product.

In this article, secure digital signature is constructed in three primary advances: first, generate the message digest by utilizing the hashing algorithm; then, encrypt the created message digest by utilizing BioGamal algorithm and sending a digital signature; last, check the digital signature, utilizing the decoding of the received message by the BioGamal algorithm. If the message review and production at the beneficiary end is coordinated, at that point, it demonstrates that the message is from the expected sender, as shown in Figure 3.

3.1. BioGamal Secure Algorithm

The flowchart of the proposed security algorithm is shown in Figure 4. In this paper, BioGamal is implemented at both the sender and receiver ends. BioGamal is planned to be used as a digital signature algorithm. Using the hashing algorithm—for example, the SHA algorithm—in this phase, to shape the message digest, then encrypts this digested message using BioGamal algorithm. The encryption process is done using DNA encryption and ElGamal encryption. The cycle of the two algorithms is joined, so a digital signature of the message is sent. The phase of the digital signature decryption measure is finished by utilizing the DNA decryption algorithm and ElGamal decryption process.

3.1.1. BioGamal Technique

The BioGamal technique is implemented by joining the DNA algorithm and ElGamal cryptosystem. Both algorithms are applied in the encryption and decryption cycle. To scramble the hash estimation of the information in the Kanban card, DNA cryptography is used in first level. In data science, the two states, 0 or 1, are used to encode the paired computerized coding. DNA cryptography relies upon the DNA rationale word; they utilize just two digits, 0 and 1, to make four nucleic acid bases—A, C, G, and T—which are denoted by Adenine, Cytosine, Guanine, and Thymine, respectively [13]. In DNA, double chains of nucleic acids are arranged in a double helix arrangement. Hence, each chain is a complement to the previous one. T and A are paired duos; C and G are elective matched couples. The 0 and 1 are a supplement pair in double activities; in this manner, 0 and 1 are a supplement pair, and 0 1 and 1 0 are another supplement pair. In the wake of utilizing these ATGC sequences, 16 distinct keys are framed, which are given in

Table 1. DNA Key Combination.

Pattern	Key Combination	Value
0000	AA	0
0001	AT	1
0010	AG	2
0011	AC	3
0100	TA	4
0101	TT	5
0011	TG	6
0111	TC	7
1000	GA	8
1001	GT	9
1010	GG	10
1011	GC	11
1100	CA	12
1101	CT	13
1110	CG	14
1111	CC	15

[12].

The algebraic properties of modular exponentiation, with the discrete logarithm problem, are the two essential factors to generate the ElGamal digital signature algorithm. The algorithm is executed in three main phases: generation of the key, encryption of the message, and finally, decryption of the message. In order to generate keys, a public key and private key pair are employed. Using a private key, a digital signature can be produced for a message, and, additionally, a digital signature can be confirmed by using the signer’s public key. Digital signatures allow the recipient to verify the message’s authenticity, message integrity, and message non-repudiation by providing message authentication, integrity, and message non-repudiation, with the sender unable to fraudulently state that they did not sign the message. A digital signature algorithm, based on ElGamal, is implemented as follows:

• Phase 1: Generation of key

• Create a large prime number p and primitive group where $Z_p^{*}$ are relatively prime to p
• Generate another primitive element g and free element $\alpha \in \{0, 1, \dots , p-2\}$ to produce public and private key.
• Public key is molded by three pair of parameters as:

  $$\beta =g^{\alpha }\mathrm{mod}p$$

  where, $\alpha$ is the private key that is secret value.

• Phase 2: Encryption of message

• The algorithm uses public key and random secret integer k, $k\in \{0, 1, \dots , p-2\}$
• Encrypt each character in the message using dissimilar k number.
• Compute r and t values as follow

  $$r=g^k\mathrm{mod}p$$

  $$t={\beta }^{k}M\mathrm{mod}p$$
• Cipher text achieved as (r, t).

• Phase 3: Decryption of message

• Utilize secret key $\alpha$ and public keys $(p,g,\beta )$ to perform the decryption phase. From received cipher text (r, t), plaintext is performed as:

  $$M=t{r}^{-a}\mathrm{mod}p$$

3.1.2. Kanban Card Secure Algorithm

• Step 1: Plant 1 read data on Kanban card where the data is divided into two parts: first, the warranty message $w_m$, which include item ID, Kanban ID, supplier ID, quantity and supplier name; the second part is message M, which includes the description of semi product.
• Step 2: Apply hash function SHA-256 to the input message M as follow

  M = “semi product that converts electrical energy into mechanical energy…”

  H(M) = “3f4058956969ea1ecc05b86990899847c509ec8f07b5d5a27404490deebe1edd”
• Step 3: Convert ASCII message from hashing step to binary number to apply DNA encoding as follow

  “0011001101100110001101000011000000110101001110000011100100110101001101100011100100110110001110010110010101100001001100010110010101100011011000110011000000101010110001000111000001101100011100100111001001100000011100000111001001110010……………………000100110010100110001011001010110010001100100”
• Step 4: Apply paring of each two bits then assign DNA digital coding for each paring as follow

  “ATATGCGCATGAATAAATGGATGAATGC …………………CGCA”
• Step 5: Formulate DNA sequence into DNA key combination as stated in Table 1

  “111111181011018111 ……… 1412”
• Step 6: Separate DNA key combination by “0” or “@”between the sequences to obtain cipher text 1

  C1 = “11 11 11 1 8 1 0 1 10 1 8 11 ……… 14 12”
• Step 7: Encrypt the cipher text 1 obtained from DNA encoding by using ElGamal algorithm as described in Section 3.1.1. Generate the key generation of ElGamal algorithm where the public key denoted by $(p,g,\beta ,H)$ and the private key denoted by $(p,g,\alpha ,H)$ and H be a hash function $\mathit{H}:{\{\mathbf{0},\mathbf{1}\}}^{\mathsf{*}}\mathsf{\to }\{\mathbf{1}\mathsf{,} \mathbf{2}\mathsf{,} \mathsf{\dots }\mathsf{,} \mathit{p}-\mathbf{2}\}$
• Step 8: To sign the message use the secret key $(p,g,\alpha ,H)$

• Preference a random number $k\in \{0, 1, \dots , p-2\}$ with unit GCD between k and p − 1
• Calculate $r=g^k\mathrm{mod}p$ where $1\le r<p$
• Calculate $s=k^{-1}(H(C1\Vert r\Vert w_m)-\alpha r)\mathrm{mod}p$ where $(C1\Vert r\Vert w_m)$ is the concatenation of C1, r and $w_m$
• Produce the pair of (r, s) as the digital signature on C1

• Step 9: Apply the decryption process, as shown in Figure 4, where Plant 2 received the signed message on the Kanban card. Then it applies the decryption ElGamal algorithm using public key $(p,g,\beta ,H)$ and recovers the hashing value using DNA decryption algorithm.
• Step 10: Verify the signature of Plant 2

• Validate that $1\le r<p$ else, he discard the signature.
• Calculate $v={\beta }^r{r}^s\in {\mathbb{Z}}^{*}{}_p$
• Agree the signature if $v=g^{(H(C1\Vert r\Vert w_m))}\in {\mathbb{Z}}^{*}{}_p$ otherwise Plant 2 discard.

3.2. Multi-Objective Flower Pollination Technique

Possibly, the main pieces of the simulation optimization issue is the setting of the optimization algorithm. For doing this, by and large, the meta heuristic algorithm is utilized. Presently, numerous sorts of these algorithms have built up that can produce close to ideal solutions. In optimization parts, the metaheuristic algorithm is applied, which is utilized as a proficient optimization apparatus in the ongoing decade. The optimization issue has a fitness function that characterizes the goal of the model with respect to variables in the model, which may be a minimization and/or a maximization problem.

Extraordinarily, compared to other valuable and appropriate meta heuristic algorithms, the Flower Pollination Algorithm (FPA) is an intriguing cycle with regards to the regular world as shown in Figure 5. This algorithm is a meta heuristic inquiry algorithm, which has been proposed recently [49]. The purpose of flower pollination is to ensure the survival of the fittest and the most efficient reproduction of plants, in terms of numbers and fitness. This could be viewed as a plant species’ optimizing process [50]. The following four rules should be summarized in order to construct the FPA:

• Pollen-carrying pollinators can fly a great distance, which obeys Lévy flights, and biotic and cross-pollination can be considered a global pollination process (Rule 1).
• Local pollination can be defined as biotic and self-pollination (Rule 2).
• Flower constancy can be equated to a reproduction chance proportional to the similarity of the two flowers in question (Rule 3).
• Local pollination and global pollination are switched on and off.

Because of actual circumstances, such as wind, neighborhood pollination plays a significant role (p) in general pollination workouts. Each plant can have a few blossoms, and each flower can release millions, or perhaps billions, of dust gametes on a regular basis, so, when accepting that each plant just has one pollen and each flower just produce one dust gamete, there is no compelling reason to isolate a dust gamete, a flower, a plant, or answer for an issue. Effortlessness implies an answer ($X_i$) equivalent to a flower one, or both to a dust gamete, to spread the few dust gametes for each bloom, as well as a few blossoms for multi-target enhancement issues. With two stages—worldwide pollination and nearby pollination—in the worldwide advance, dusts can go over a significant distance, since creepy crawlies can routinely fly, and flower pollens are conveyed by pollinators. For example, bugs can move in a longer reach, which guarantees the pollination and propagation of the most fitting and the portrayal of the most fitting as $g^{*}$. The initial step, in addition to flower consistency, can be addressed, numerically, in Equation (1), as follows [47]

$$X_i^{t+1}=X_i^t+L(X_i^t+g^{*})$$

(1)

where, $X_i^{t+1}$ is the pollen i and the solution vector $\left(X_i\right)$ at iteration t, $g^{*}$ is the current best solution in the current generation and iteration. $L(•)$ is the Lévy flights based step size that corresponds to the intensity of the pollination. The Lévy flights ca be expressed in Equation (2) as

$$L\sim \frac{\lambda \Gamma (\lambda )\sin \frac{\pi \lambda }{2}}{\pi }\times \frac{1}{s^{1+\lambda }}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(s\ge s_0\ge 0)$$

(2)

where ($L$) is the strength of the pollination. Γ(λ) represents the standard gamma function, this distribution is effective for large steps s > 0, as well as λ = 1.5 for all our simulations. Equation (3) expresses the use a Levy flight that is for $L$ > 0 from a Levy distribution, since insects may move over a long distance with various distance steps, as follows

$$L\sim \frac{\lambda \Gamma (\lambda )\sin \frac{\pi \lambda }{2}}{\pi }\times \frac{1}{s^{1+\lambda }}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}$$

(3)

where Γ(λ) the standard gamma function, and this distribution valid for large steps s > 0. here λ = 1.5 is used. The local pollination is given by Equation (4), as follows

$$X_i^{t+1}=X_i^t+\epsilon (X_j^t+X_k^t)$$

(4)

where $X_j^t$ and $X_k^t$ are pollen from various flowers of a similar plant groups, this identically turns into a nearby irregular walk in the event that we draw ε from a uniform dispersion in [0, 1]. The majority of flower pollination activities can occur on a local and global scale. In a work out, together bloom fixes, or flowers in the not-so-distant district, are more likely to be pollinated by nearby flower pollens than those far away. To reflect this, a transition between widespread worldwide pollination and extreme nearby pollination, using a switch likelihood or proximity likelihood (p), Figure 6 shows a flow chart that explains how to use an algorithm.

Multiobjective FPA of Secure Kanban/CONWIP

To apply the multiobjective FPA algorithm, we need to be adjusting and setting boundaries for FPA to achieve the objective goal of applying secure Kanban/CONWIP methodology. To accomplish this level-headed, we improve the part size and the quantity of CONWIP and Kanban cards for a wide range of items. We will consider three instances of the creation line that delivers a solitary part type. The two creation lines vary by their length: eight, ten, and fourteen machines. We use FPA and simulation modeling to minimize the cost and time of production. The strategy is viewed as totally solid, and assuming that the stockpile of crude materials is constant and infinite, the probability of a deformity is immaterial, and the withdrawal of cards and parts between stages is prompt.

A multiobjective optimization problem with m objectives can be written in general a

$$Minimize\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{f}_1(x), f_2(x), \dots , f_m(x),$$

(5)

In the proposed algorithm, we have four objectives as follow:

$$f_1={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^m(Q_{ij}\ast C_{ij})}}$$

(6)

$$f_2={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^m(Q{T}_{ij}\ast C{T}_{ij})}}$$

(7)

$$f_3={\displaystyle \sum _{i=1}^n(F{T}_i\ast F{Q}_i)}$$

(8)

$$\hspace{0.17em}\hspace{0.17em}{f}_4=\hspace{0.17em}\hspace{0.17em}{\displaystyle \sum _{i=1}^n(F{Q}_i\ast F{C}_i)}$$

(9)

The first one describes the total production cost, while the total transportation cost is given in the second term. The third and fourth terms show the total transportation cost of the final product and the total cost of the final product, respectively.

The parameters are:

• $C_{ij}$: production cost for product type i in plant j
• $C{T}_{ij}$: transportation cost for product type i from plant j to plant j + 1
• T: time of model replication
• $Q_{ij}$: number of product type i in plant j
• $Q{T}_{ij}$: number of transported product type i from plant j to plant j + 1 at unit time
• $F{T}_i$: transportation cost for each part of final product type i to customer
• $F{Q}_i$: number of final product type i
• $F{C}_i$: cost of production of final product type i

Several approaches exist to deal with multiobjective problems by using methods tested in single-objective optimization. It may be simplest to combine all multiple goals into one composite goal by calculating a weighted sum, as follows [51]

$$\begin{array}{l}Minimize\hspace{0.17em}Z={\displaystyle \sum _{i=1}^m{w}_i{f}_i}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}i=1, 2, \dots , 4\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}with\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\displaystyle \sum _{i=1}^m{w}_i}=1\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{w}_i>0\end{array}$$

(10)

where, $w_i$ are the weight factors and it is assumed that all weights are the same and each weight value is 0.25.

$$\begin{array}{l}Minimize Z={\displaystyle {\displaystyle \sum }_{i=1}^n}{\displaystyle {\displaystyle \sum }_{j=1}^m}0.25\left(Q_{ij}\ast C_{ij}\right)+{\displaystyle {\displaystyle \sum }_{i=1}^n}{\displaystyle {\displaystyle \sum }_{j=1}^m}0.25\left(Q{T}_{ij}\ast C{T}_{ij}\right)+\\ {\displaystyle {\displaystyle \sum }_{i=1}^n}0.25\left(F{T}_i\ast F{Q}_i\right)+{\displaystyle {\displaystyle \sum }_{i=1}^n}0.25\left(F{Q}_i\ast F{C}_i\right)\end{array}$$

(11)

4. Simulation Results

4.1. Security Measurements

In the following, it has been shown that the proposed scheme satisfies the performance of security analysis, based on several types of security measurements, such as verification, identification, unforgeability, and undeniability measurements.

Table 2. Security measurements of the pull manufacturing system.

Security Measurements	Performance Analysis
Verification	Plant 2 can check the signature by the following verification equation $\begin{array}{ll}v={\beta }^r{r}^s& =g^{\alpha r}{r}^{k^{-1}(H(C1\Vert r\Vert w_m)-\alpha r)}\\ & =g^{\alpha r}{g}^{k\times k^{-1}(H(C1\Vert r\Vert w_m)-\alpha r)}\\ & =g^{\alpha r}{g}^{H(C1\Vert r\Vert w_m)-\alpha r}\\ & =g^{\alpha r+H(C1\Vert r\Vert w_m)-\alpha r}\\ & =g^{H(C1\Vert r\Vert w_m)}\end{array}$ If hold, then he accept the semi product from Plant 1
Unforgeability	In proposed algorithm, the signature is made with Plant 1’s secret key α. Nobody (as well as Plant 1) can develop the digital signature without having the information on the secret key α. Getting the secret key by some other gathering is as difficult as breaking BioGamal algorithm. In addition, the verification of the signed Kanban card keeps the forged party from the production of fabricated digital signatures. Subsequently, any tip including the Plant 1 can’t counterfeit a valid signature and hence the proposed system fulfills the unforgeability property
Identification	The verification process of the proposed scheme requires Plant 1 public key β and warrant $m_w$. Any verifier can decide the identity of Plant 1 from the signed message, because the signed message is $s=k^{-1}(H(C1\Vert r\Vert w_m)-\alpha r)\mathrm{mod}p$ which contains the warranty data that include the identites of end users. Along these lines, from the first security process any verifier can be sure from the identity of the Plant 1 from $m_w$.
Undeniability	From digital signature of the proposed system, the warrant $m_w$ and the combination of the public keys β and r in the verification process dictate the contributions of both Plant 1 and Plant 2. Hence, Plant 1 and Plant 2 cannot deny their association in an authenticated digital signature. In this way, the system fulfills the undeniability property.

shows the security measurements of the pull manufacturing system.

4.2. Experimental Results

The experimental results are running on a computer with Windows 10, Intel Duo Core I7 @2.53 GHz, and 8 GB DDR3 RAM (Dell, Round Rock, TX, USA). The optimization model is running on three different number of stages: 8, 10, and 14. The algorithm has been written on MATLAB Code in order to simplify the integration with the model, and its simulation is run for a period of 6500 s. Figure 7 shows the results of running the simulation on eight stages of the optimization model, over the two methods, with and without FPA techniques with 500 iteration. As the number of the iteration is increased, the deviation in the result decreases. The FPA technique minimizes the cost and time production of eight stages within 5%. Obviously, Figure 8 shows the comparison of the two methods in the case of ten stages, with and without FPA techniques, which show that, in ten stages, the cost is decreasing within 7%. Figure 9 shows the comparison of the two methods in the case of 14 stages, with and without FPA techniques, which show that, in ten stages, the cost is decreasing within 9.5%. When applying the FPA technique to the different stages of manufacturing, the time is reduced, and the cost is well reduced. Figure 10 shows the percentage difference in the rate of cost reduction for three different stages. This shows that the proposed FPA technique has proven its effectiveness in the large stages of manufacturing, as the percentage of cost reduction for 14 stages is higher than the percentage of cost reduction for 8 and 10 stages within a 2.5% difference rate.

The time efficiency is computed on both the encryption and decryption process, using a different number of stages, with and without FPA.

Table 3. Time Efficiency.

Algorithms	Encryption Process			Decryption Process
Stages	8 Stages	10 Stages	14 Stages	8 Stages	10 Stages	14 Stages
Time with FPA	0.1415	0.0236	0.0042	0.1336	0.0475	0.0039
Time without FPA	1.5289	1.3759	1.1706	1.4729	1.2470	1.1657

shows that, by using the FPA technique, the running time for both the encryption and decryption process is lower than the running time without using the FPA technique, which meets real-time performance necessities.

4.3. Computation Analysis

For the development of the proposed algorithms, time complexity is one of the most important metrics. The Big O notation is one of the most commonly used measures. The complexity computation of the BioGamal algorithm will be performed for both ElGamal DSA and DNA. In order to determine this, the following steps must be taken: the signature of the message hash is comprised of two values, r and s, the conversion of binary data, and the processing of DNA. According to the fast power algorithm, the power operation is the most time-consuming operation in the signature generation to compute v, where the complexity of r computing is O(log n). As the last step in generating signatures, the inverse operation has the highest cost with complexity O(log n) for the Extended Euclid’s Algorithm used to compute signature s. In summary, a signature consists of one power, one inverse power, one addition power, two multiplications, and three Mod operations. In comparison to power and inverse operations, addition, multiplication, and Mod operations are considered with little or no cost. In binary data conversion, the complexity is O(n²), while DNA scrambling is O(4 n²). Therefore, O(n) = O(2 log n + 5 n²)

5. Conclusions and Future Work

In this paper, we considered the security of the E-Kanban/CONWIP methodology, and this framework is demonstrated and optimized with the FPA simulation optimization technique that consolidates a meta heuristic algorithm. The main contribution described in the paper is to increase the security measures of production control systems by using an authenticated Kanban card in pull manufacturing systems. The proposed system satisfies the necessary security requirements by using a novel signature algorithm. BioGamal measure is performed by joining two algorithms: the DNA encryption/decryption algorithm and ElGamal encryption/decryption algorithm. Using the ElGamal signature, every plant in the manufacturing system can apply an authentication Kanban card using a novel signature on the encrypted information of a Kanban card, depending on the DNA encryption algorithm. This process will increase the security performance.

The commitment of this paper can be characterized as:

(a)

Using a new security BioGamal technique is better for the verification of data between different stages, especially for sensitive industries.

(b)

Application of FPA, to optimize the time and the cost of the overall production line, contains 8 stages, minimized by 5%, while for the 10 stages, it is optimized within 7%.

(c)

The percentage of cost and time reduction for 14 stages is higher than the percentage of cost and time reduction for 8 and 10 stages: within 2.5% difference rate.

As future work, we can implement the multiobjective technique and an advanced security system over supply chain management for the IoT approach.