# Robotic Cell Layout Optimization Using a Genetic Algorithm
## 2 Materials and Methods  
The methodological approach of this research is based on the analysis of a production process involving three robotic cells already installed in the industry. Each cell is treated \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Year** & **Author** & **Objective** & **Solution** & **Restrictions** \\ \hline
2014 & [PERSON] et al. [12] & \begin{tabular}{c} Maximize line efficiency and \\ balance tasks between robotic \\ equipment. \\ \end{tabular} & \
\begin{tabular}{c} Three proposed hybrid \\ evolutionary algorithms \\ \end{tabular} &
\begin{tabular}{c} A single product in the \\ robotic cell \\ \end{tabular} \\ \hline
2015 & [PERSON] & \begin{tabular}{c} Minimize cycle time and \\ energy consumption \\ \end{tabular} & \
\begin{tabular}{c} Integer programming \\ model 0–1 \\ \end{tabular} &
\begin{tabular}{c} A single product in the \\ robotic cell \\ \end{tabular} \\ \hline
2016 & [PERSON] et al. [14] & \begin{tabular}{c} Minimize the total cost of \\ robot use, number of stations, \\ and cycle time. \\ \end{tabular} & \
\begin{tabular}{c} Hierarchical objective \\ preventive algorithm \\ \end{tabular} &
\begin{tabular}{c} Various products in the \\ robotic cell and \\ fixed robots. \\ \end{tabular} \\ \hline
2017 & [PERSON] et al. [15] & \begin{tabular}{c} Maximize line efficiency and \\ minimize carbon footprint \\ \end{tabular} & \
\begin{tabular}{c} Multi-objective \\ coevolutionary algorithm, \\ artificial bee colony, \\ random simulated \\ annealing, and fast elitist \\ non-dominated sorting \\ \end{tabular} &
\begin{tabular}{c} A single product on the \\ line, fixed stations \\ and robots. \\ \end{tabular} \\ \hline
2018 & [PERSON] et al. [16] & \begin{tabular}{c} Minimize Fixed and \\ Variable Costs \\ \end{tabular} & \
\begin{tabular}{c} Memetic elitism algorithm, \\ genetic algorithm, multiple \\ start algorithm, and \\ random search algorithm. \\ \end{tabular} &
\begin{tabular}{c} A single product in the \\ robotic cell, fixed stations \\ and robots. \\ \end{tabular} \\ \hline
2019 & [PERSON] et al. [17] & \begin{tabular}{c} Maximizing manual labor \\ efficiency and productivity \\ \end{tabular} & \
\begin{tabular}{c} Multi-integer \\ programming model with \\ hybrid genetic algorithm. \\ \end{tabular} &
\begin{tabular}{c} A single product in the \\ robotic cell with \\ deterministic cycle times \\ \end{tabular} \\ \hline
2020 & [PERSON] [18] & \begin{tabular}{c} Minimize fixed and \\ variable costs \\ \end{tabular} & \
\begin{tabular}{c} Hybrid particle swarm \\ combined with dynamic \\ programming. \\ \end{tabular} &
\begin{tabular}{c} A single product in the \\ robotic cell, fixed stations \\ and robots. \\ \end{tabular} \\ \hline
2021 & [PERSON] & \begin{tabular}{c} Minimize number of stations \\ and cycle time \\ \end{tabular} & \
\begin{tabular}{c} Constraint programming \\ model with mixed integer \\ programming and \\ ABSALOM software. \\ \end{tabular} &
\begin{tabular}{c} A single product in the \\ robotic cell \\ \end{tabular} \\ \hline
2022 & [PERSON] et al. [20] & \begin{tabular}{c} Minimize number of stations \\ and energy consumption \\ \end{tabular} & \
\begin{tabular}{c} Mixed integer linear \\ programming model with \\ a cross-station design. \\ \end{tabular} &
\begin{tabular}{c} A single product in the \\ robotic cell \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Robotic cell optimization research (2014–2022). as an independent study object to experiment with the proposed algorithm. The goal is to obtain an optimized distribution of the workstations and validate this optimization by comparing the transfer times between stations with the current times. For each robotic cell, a specific number of workstations of different sizes, an industrial robot, and a limited workspace are considered, as illustrated in Figure 1. A genetic algorithm is employed to minimize the workspace of each cell, also incorporating a penalty function to evaluate the presence of interferences between the workstations and the robot's base.