## 4 Proposed Framework
### Layer 2: Supplier Capabilities  
The second layer of this SI framework is the problem seeking layer, which helps an industry define its requirements for supplier development. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{5}{c}{**ABC Comparison**} \\ \hline \multirow{2}{*}{**Reference**} & **Comparison of** & \multirow{2}{*}{**Selected Algorithm**} & \multirow{2}{*}{**Application**} \\  & **Algorithms** & & \\ \hline \multirow{2}{*}{\(\check{\text{O}}\)zbakir [51]} & Bees Algorithm (BA), & & Continuous \\  & Genetic Algorithm (GA) & & Optimization \\ \hline \multirow{2}{*}{Fahmy [22]} & Particle Swarm & \multirow{2}{*}{BA} & Speed parameters for \\  & Optimization (PSO), BA & & wind turbine generators \\ \hline \multirow{4}{*}{Yuce [53]} & Swarm Optimization & \multirow{2}{*}{ABC} & Honey bees-inspired \\  & Algorithms (SOAs), Bee & & optimization method \\  & Colonial Optimization & & \\  & (BCO), GA, ABC & & \\ \hline \multirow{2}{*}{[PERSON] [54]} & GA, state-of-the-art & \multirow{2}{*}{ABC} & Problem of composing \\  & algorithm, ABC & & medical crews \\ \hline \multirow{4}{*}{[PERSON] [28]} & Differential Evolution & \multirow{2}{*}{ABC} & Comparative study of \\  & (DE), GA, PSO, ABC, & & Bees Algorithm \\ \cline{1-1}  & Evolution Strategy (ES) & & \\ \hline \multirow{2}{*}{[PERSON] [55]} & GA, K-means, BA & BA & Data clustering \\ \hline \multirow{2}{*}{[PERSON] [28]} & ABC, PSO & ABC & Clustering Approach \\ \hline \multirow{2}{*}{[PERSON] [57]} & ABC, PSO, & ABC & Iris Image optimization \\ \hline \multirow{2}{*}{[PERSON] [56]} & ABC, PSO. & ABC & Multi Objective \\  & & & Optimization \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Artificial bee colony (ABC) Comparison in the Literature. After obtaining the important opinions (requirements) from managers in the second layer, historical data were collected from the enterprise. These historical data consisted of the values of requirements/factors of different suppliers and constraints for integration with the suppliers. Objectives and constraints defined by the company were used as model inputs in the proper equations for mathematical optimization. Essentially, this layer helped to adjust all the requirements of the enterprise. The capabilities of each supplier were drawn against the requirements suggested by the experts. Each capability of the supplier was assigned a specific value based on the past performance of that specific supplier; this value was then used in the metaheuristic algorithm to find the most appropriate and best-suited supplier. Factors were treated as multi-objectives in this study, and they were treated in to two groups depending upon their nature. There were two main sets, i.e., maximization of desirable factors and minimization of undesirable factors. For maximization:  
\[f_{x}=c_{i}w_{x}X\text{ Subject to }\overline{r_{x}}\leq X\leq r_{x} \tag{1}\]  
Figure 1: Proposed supplier integrations (SI) Framework. where \(c\) is the capacity of the supplier, \(X\) is the desirable factor value for that supplier, \(w\) is the weight of the factor used, \(r\) is the upper limit of that factor, and \(\overline{r}\) is the lower limit of that factor. Similarly, fo minimization, Equation (2) is used:  
\[f_{\overline{r}}=c_{i}w_{x}X\text{ Subject to }\overline{r_{x}}\leq X\leq r_{x} \tag{2}\]  
where, \(c\) is the capacity of the supplier, \(X\) is the factor value for that supplier, \(w\) is the weight of the factor used, \(r\) is the upper limit of that factor, and \(\overline{r}\) is the lower limit of that factor. However, we may convert the minimization function to a maximization function using Equation (3). The combined objective function is represented by Equation (4).