# A Multi-Objective Optimization of Secure Pull Manufacturing Systems
## 3 Methodology
### BioGamal Secure Algorithm
#### 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 \(\mathbf{M}\), which includes the description of semi product. Step 2: Apply hash function \(\mathbf{SHA-256}\) to the input message \(\mathbf{M}\) as follow  
\(\mathbf{M}=\) \"semi product that converts electrical energy into mechanical energy... \"  
\(\mathbf{H(M)}=\) \"3f4058956969 ea1 ecec05b86990899847c509 ec8f07b5d5a27404490 deebeeld\"  
Step 3: Convert ASCII message from hashing step to binary number to apply DNA encoding as follow  
\(\mathbf{ \begin{array}{l}\text{\"00110011001100011000011000001100101010110000111001010110 \\ 001110010110011000111001010101001001001001100101010100101100011000110\\ 011000000101010101000100011100011100011100011100011000000111000001\\ 110010011100100100011100001110001100110011000110000001110000001\\ 010001100100100^{\text{-}}\end{array} \)  
Step 4: Apply paring of each two bits then assign DNA digital coding for each paring as follow  
\(\mathbf{\begin{array}{l}\text{\"ATATGCGCATGAATAAATGGATGAATGC}\ \  
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:  
1. Pollen-carrying pollinators can fly a great distance, which obeys Levy flights, and biotic and cross-pollination can be considered a global pollination process (Rule 1). 2. Local pollination can be defined as biotic and self-pollination (Rule 2). 3. Flower constancy can be equated to a reproduction chance proportional to the similarity of the two flowers in question (Rule 3). 4. 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]  
\[X_{i}^{t+1}=X_{i}^{t}+L(X_{i}^{t}+g^{*}) \tag{1}\]  
Figure 5: Idea of Flower Pollination Algorithm (FPA). where, \(X_{i}^{t+1}\) is the pollen \(i\) and the solution vector \((X_{i})\) at iteration \(t\), \(g^{*}\) is the current best solution in the current generation and iteration.