## 5 Determination of the Effect of System Parameters on the Required AGV Number  
Until this part of the study, we have assumed that the parameters of the AGV system are considered at previously defined values and the results for the required AGV numbers were obtained with MILP and the GA. However, sometimes production demands may change; therefore, the AGV system must adjust to changing production demands. This stage is concerned with examining the number of AGVs in the case of a change in system parameters if the production requirements change. Although all system parameters of the AGV are taken within certain levels, as given in Table 8, there may be changes in speed, capacity, and distance due to change in production demands. In such a case, all calculations have to be redone. In order to avoid this situation, it is important to estimate the amount of AGVs for the new situation at a reduced computational cost and time lost. Especially in cases outside the defined system parameter levels, the results can be found by using intelligent-system-based estimation techniques, without using time-consuming MILP-GA or simulation-based analysis methods. Therefore, in this study, an ANN is proposed to predict the effects of the system parameters on the AGV number and to check the possibility of reducing the AGV number under changing conditions in production, such as what the effect will be if the speed is increased by 10%, how much AGVs are gained if the capacity is increased by 5%, or to check the possibility of decreasing the required number of AGVs due to changes in system parameters. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & **AGV Circuits** & & & & \\ \hline
**1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
1 & 2 & 3 & 21 & 16 & 16 & 7 & 8 & 19 & 15 \\
1 & 2 & 3 & 4 & 5 & 16 & 7 & 8 & 19 & 16 \\
1 & 2 & 3 & 4 & 16 & 15 & 7 & 8 & 16 & 15 \\
1 & 21 & 19 & 4 & 5 & 6 & 7 & 8 & 15 & 16 \\
1 & 2 & 20 & 21 & 16 & 16 & 7 & 8 & 16 & 15 \\
1 & 2 & 21 & 4 & 5 & 6 & 7 & 8 & 16 & 15 \\
1 & 2 & 3 & 22 & 5 & 16 & 7 & 8 & 20 & 15 \\
21 & 2 & 3 & 22 & 5 & 6 & 7 & 8 & 16 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: GA solutions with a modified fitness function for circuits. Figure 4: Simulation model. An artificial neural network (ANN), the response surface method (RSM), and multiple linear regression (MLR) were used to examine the effect of the change in system parameters on the required AGV number. Multiple linear regression is a statistical modeling technique used to analyze data to make predictions of the response variable (\(y\)) with multiple explanatory variables (\(x1\), \(x2\),... \(xp\)) with linear relation. In other words, it is used to predict the outcome of the response variable [51]. The response surface method (RSM) explores the relationship between various explanatory variables and the response. The aim is to optimize this response [52]. Parameter optimization with RSM for one AGV circuit was analyzed in 2019 by [PERSON] [32]. A neural network is a mathematical model of how the brain works neurologically. It mathematically models the nerve cells to imitate the brain's process of learning. It is structured with interconnected items called neurons included in layers. Artificial neurons are linked via artificial synapses and acquire knowledge through learning. The feed-forward neural network is an artificial neural network architecture, which is also called a multi-layer neural network. A feed-forward network is one in which information or signals are only sent in one direction, from input to output [53; 54; 55]. In this study, the neural network model was used as a surrogate model to predict the required number of AGVs by changing four parameters. A surrogate model is a statistical model which solves complex problems at a reduced computational cost by accurately approximating a function instead of solving the problem with expensive computational simulations. It is widely used in solving complex engineering optimization problems.