Robotic Cell Layout Optimization Using a Genetic Algorithm

Featured Application

This work contributes to different industrial sectors through a computer tool that optimizes the layout of a robotic cell, which allows reducing both production times and energy consumption, mainly.

Abstract

The design of the work area of a robotic cell is currently an iterative process of trial and improvement, where, in the best cases, the user places the workstations and robotic manipulators in a 3D virtual environment to then semi-automatically verify variables such as the robot’s reach, cycle time, geometric interferences, and collisions. This article suggests using an evolutionary computation algorithm (genetic algorithm) as a tool to solve this optimization problem. Using information about the work areas and the robot’s reach, the algorithm generates an equipment configuration that minimizes the cell area without interference between the stations and, therefore, reduces the distances the robotic manipulator must travel. The objective is to obtain an optimized layout of the workstations and to validate this optimization by comparing the transfer times between stations with the actual times of an existing screwdriving cell. As a result, the transfer time was reduced by 9%. It is concluded that the algorithm can optimize the layout of a robotic cell, which can lead to significant improvements in efficiency, quality, and flexibility.

1. Introduction

An assembly line is a manufacturing process where different parts are assembled in a specific sequence, creating a final product at each workstation until the final operation is completed. Operations performed at workstations can be manual, automatic, or semi-automatic, and the type of operation to be used at the station will depend on the manufacturer’s strategy [1].

Industry tries to increase its competitiveness by implementing strategies of greater flexibility at a low cost, obtaining greater productivity and efficiency. The use of robots in automated material handling boosts productivity and enhances automation. Robotic cells, which combine robots equipped with grippers or other specialized capabilities along with CNC machines and complementary systems, are an integral part of these manufacturing environments. By integrating industrial robots with other technologies, these automation systems provide productive flexibility, allowing manufacturers to efficiently adapt to short- and medium-term demand fluctuations [2]. On a global scale, there is no standardized process for designing the work area when implementing robotic manufacturing cell solutions. The increasing demand for flexible cells with high productivity and product quality necessitates faster and more efficient design and planning methods to create an appropriate work area layout for production tasks [3].

Having a computer program that assists in the location of workstations will allow the industry to design robotic manufacturing cells with the shortest transit time between stations, choose the ideal robot for the tasks, and maximize the productivity rate by minimizing production cycle time. Additionally, it will enable seamless integration of different systems, improve operational efficiency, reduce setup and reconfiguration times, enhance adaptability to changes in production demands, and ensure optimal use of available space. This will not only increase throughput but also reduce energy consumption and operational costs, thereby contributing to a more sustainable and cost-effective manufacturing process [4].

Optimizing a robotic cell is a critical process in modern manufacturing that seeks to maximize efficiency and productivity. It consists of designing and adjusting the components and their arrangement within the cell to minimize cycle time, reduce energy consumption, and improve product quality. Traditionally, robotic cell design involved virtual prototyping, with physics-based simulations playing a crucial role in obtaining accurate models. These simulations allowed the behavior and interaction of components to be predicted in a controlled environment, making it easier to identify potential failures and areas for improvement before physical implementation [5,6]. The use of advanced algorithms is now included, for example, in [7] mixed programming techniques, which are presented for small instances and a genetic algorithm for large instances. It is modeled as a production flow problem with blocking constraints, a single transport robot, and controllable processing times. This research addressed the case where processing times vary linearly according to the allocated resources and focuses on obtaining maximum performance. However, comparative results with real solutions are not presented. In [8], hierarchical optimization is proposed, being more important for first the posture optimization and then the motion optimization. The pose optimization is solved with a genetic algorithm, and an objective function considers the design constraints. It is confirmed that the proposed method can solve the optimization problem quickly by experiments. A reference robotic cell was used, and only the execution time of the algorithm was compared against the manual design time of the cell, but no improvements in cycle time were documented. In [9], design criteria for a robotic cell are defined, design candidates are represented by a sequence pair scheme to avoid interference between components of the assembly system, and the use of dummy components is proposed to represent design areas where components are scarce. Objective functions are formulated, and optimal solutions are obtained using a genetic algorithm. Numerical evaluations are performed to illustrate the effectiveness of the proposed method. The existence of a relationship between design area and manipulability is concluded. That is, too small a design area reduces manipulability, since the robot arm must undergo more radical movements during assembly operations. In [10], the location of the work centers and the robot are parameterized as the homogeneous transformation matrix with respect to the environment. Each component is assigned a cylindrical envelope, and the interference is modeled with the circular projection. The robot joints are also projected to resolve collisions in 2D space. The deepest collision point is removed outside the cylindrical envelope along the vertical or radial direction. And the trajectory is segmentally replanned according to the relocated point. The optimization is achieved in a cascade flow, and the heuristic algorithm is applied. Experiments performed on a robotic ultrasonic shot peening work cell validate the effectiveness of the proposed method. No improvements in process times are reported. In [11], five nature-inspired algorithms, a genetic algorithm, differential evolution, an artificial bee colony, a charge search system, and particle swarm optimization are proposed. Design area criteria, operation time, and robot manipulability are simultaneously optimized. Numerical examples are provided to illustrate the effectiveness and usefulness of the proposed methods. It is observed that swarm optimization algorithms perform better than the other algorithms in terms of solution quality. Although the three criteria are optimized simultaneously, this optimization is independent, the optimal solution of the system is still pending, and only the best solutions are proposed. The use of evolutionary algorithms is an area of research for robotic optimization, and the following table shows some other research that has been developed in the last decade, each with different optimization objectives and, therefore, different algorithm proposals for their solution.

Based on the advancements and state-of-the-are approaches presented in

Table 1. Robotic cell optimization research (2014–2022).

Year	Author	Objective	Solution	Restrictions
2014	Daoud et al. [12]	Maximize line efficiency and balance tasks between robotic equipment.	Three proposed hybrid evolutionary algorithms	A single product in the robotic cell
2015	Mukund Nilakantan et al. [13]	Minimize cycle time and energy consumption	Integer programming model 0–1	A single product in the robotic cell
2016	Cil et al. [14]	Minimize the total cost of robot use, number of stations, and cycle time.	Hierarchical objective preventive algorithm	Various products in the robotic cell and fixed robots.
2017	Nilakantan et al. [15]	Maximize line efficiency and minimize carbon footprint	Multi-objective coevolutionary algorithm, artificial bee colony, random simulated annealing, and fast elitist non-dominated sorting	A single product on the line, fixed stations and robots.
2018	Pereira et al. [16]	Minimize Fixed and Variable Costs	Memetic elitism algorithm, genetic algorithm, multiple start algorithm, and random search algorithm.	A single product in the robotic cell, fixed stations and robots.
2019	Weckenborg et al. [17]	Maximizing manual labor efficiency and productivity	Multi-integer programming model with hybrid genetic algorithm.	A single product in the robotic cell with deterministic cycle times
2020	Zhou and Wu [18]	Minimize fixed and variable costs	Hybrid particle swarm combined with dynamic programming.	A single product in the robotic cell, fixed stations and robots.
2021	Mehmet Pinarbasi et al. [19]	Minimize number of stations and cycle time	Constraint programming model with mixed integer programming and ABSALOM software.	A single product in the robotic cell
2022	Yuanying Chi et al. [20]	Minimize number of stations and energy consumption	Mixed integer linear programming model with a cross-station design.	A single product in the robotic cell

, the research question is as follows: Can genetic algorithms optimize the workspace and reduce cycle time in a robotic cell? Additionally, do they offer any advantages due to their ability to handle large search spaces, adapt to complex nonlinear solutions, and find near-global optimum solutions efficiently, even in dynamic and highly variable environments?

In this article, a multi-objective design optimization method for the layout of workstations in a robotic cell is proposed. The robot base is considered the center of the work area, and the 2D dimensions of both the workstations and the robot base are specified. A genetic algorithm is employed to evaluate numerous possible configurations of components, selecting the most efficient ones. The objective function aims to minimize the work area while considering the interference of the stations and the robot base as constraints. The algorithm is adjusted by modifying the mutation probability.

This approach enables the algorithm to minimize the work area, reduce cycle times, lower energy consumption, and maximize productivity, which would be difficult to achieve with traditional methods. Therefore, this algorithm is proposed as a design tool for production engineers and automation consultants in the industry seeking to implement robotic solutions and optimize robotic cells cost-effectively and efficiently.

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 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. In the design of the robotic cell, the robot’s position must allow it to reach all the workstations, so the algorithm considers the robot’s base as the center of the operational area.

The algorithm development was carried out using Python V3.5 [21] in the Visual Studio Code V1.91 environment [22]. Unlike previous works [7,8,9,10,11,12,13,14,15,16,17,18,19,20], this study introduces a significant novelty by integrating Mitsubishi’s RT TOOLBOX3 PRO software [23] into the simulation stage. Instead of merely mathematically modeling the robot’s trajectories and cycle times, the results generated by the algorithm are directly imported into RT TOOLBOX3 PRO, allowing for a realistic simulation of the robot’s movements. This not only provides a more accurate calculation of cycle times but also offers practical visualization and validation of the robot’s behavior in the simulated environment, adding a level of robustness and precision not found in similar approaches.

Furthermore, the integration of RT TOOLBOX3 PRO enables better solution comparison, optimizing trajectories and times in simulated real-world scenarios, which strengthens the applicability of the results in industrial settings.

2.1. Robotic Cell

A robotic cell is an integrated system used in manufacturing and industrial automation that consists of one or more robots, along with other equipment and tools, designed to perform specific tasks such as assembly, welding, painting, material handling, and inspection. These cells are engineered to improve efficiency, precision, and safety in production processes. A robotic cell is an integrated system used in manufacturing and industrial automation that consists of one or more robots, along with other equipment and tools, designed to perform specific tasks such as assembly, welding, painting, material handling, and inspection. These cells are engineered to improve efficiency, precision, and safety in production processes [24]. Typically, a work cell can only process one workstation at a time, so the robotic cell is considered as a mass production system with blocking. And according to their layout, they can be classified into the following [25]:

• Linear or Semicircular: The robot passes through each of the workstations sequentially moving from the input to the output of the process and back, as shown in Figure 2.

• Circular: In this configuration, the robot is required to pass through each of the workstations sequentially, as shown in Figure 3. Having greater flexibility in the sequence of movements results in higher productivity.

2.2. Work Area Optimization

Optimizing a work area is a research problem that not only applies to manufacturing systems but also to the design of integrated circuits, assemblies, etc. A search for works was carried out to define the optimization criteria.

One of the first investigations to address the optimization of the area of an industrial robot was [26], where an automatic system in three dimensions was presented to generate collision-free trajectories using conventional algorithms of flexible manufacturing systems. For this work, 3 degrees of freedom were considered for the robot. Later in [27], a genetic algorithm was used. The number of workstations in defined areas within the robot’s range was defined, and the system determined the best order of the workstations to be executed, while another algorithm adjusted the location of the workstations with respect to the efficiency of the robot.

On the other hand, in [28], a genetic algorithm was used to minimize the cycle time of a series of operations, which was achieved by determining the relative positions of the machines or workstations around the industrial robot.

2.3. Genetic Algorithm

A genetic algorithm is a search heuristic inspired by the principles of natural selection and genetics. It is commonly used to find approximate solutions to optimization and search problems and was used in this research to optimize the work cell area through functions that minimize the number of interferences between the workstations.

Here is an overview of how genetic algorithms work [26]:

• Population initialization: A set of candidate solutions (called individuals) is generated. Everyone represents a potential solution to the problem.
• Selection: Each individual will be evaluated using a fitness function, which measures how well it solves the problem. Individuals are selected for reproduction based on their fitness scores. Higher fitness individuals have a higher probability of being selected. Common selection methods include roulette wheel selection, tournament selection, and rank-based selection.
• Crossover: Selected individuals are paired to create offspring. The genetic material from two parent individuals is exchanged at the crossover point, producing two new offspring.
• Mutation: With a low probability, individual bits in the offspring’s chromosomes are flipped or altered. Mutation introduces genetic diversity and helps prevent premature convergence to local optima.
• Replacement: The offspring replace some or all the old population, creating a new generation. The process of selection, crossover, and mutation is repeated for many generations.

Figure 4 shows the typical cycle of the evolution of a genetic algorithm.

Some recent examples of the use of the genetic algorithm in optimization applications for industrial robot problems are optimal movement trajectories in industrial robots, aiming to minimize the objective function of the manipulator’s velocity rate, producing the highest possible speed at the end-effector while keeping the axis speeds at a minimum [27], with stochastic multi-modal processing times with multiple parallel-working robots per workstation. The objective is to minimize the number of workstations at a given production rate and the probability limit of violating the cycle time [28].

The proposed algorithm uses an uninformed initialization based on assigning random values to the genes of everyone. In this case, the representation is real, so each gene will take values in a defined interval with a uniform probability.

Station/Gen = [(0, Working area in long), (0, Working area in width)]

(1)

The solution is a combinatorial optimization problem whereby each station location is a gene and, together with the other station locations, together form the “genetic code of the individual”.

$$Individual=\left\{{Gen}_1,{Gen}_2,{Gen}_3,\dots ,{Gen}_n\right\} where each{ Gen}_n is\left\{x,y\right\}$$

(2)

$$Robot base=\left[\left\{x_1,y_1\right\} ,\left\{x_2,y_2\right\}\right]$$

(3)

With the initial population, the code generates the points that correspond to the corner or diagonal of the stations to have the complete area of each one of them, as shown in Figure 5.

Obtaining the minimum and maximum values [{X_min, Y_min}, {X_max, Y_max}], the area of each combination generated is calculated and then evaluated in the first fitness function to be minimized. The second fitness equation is to minimize the number of interferences between stations, since this would be considered a physical constraint for the solution. The fitness equations to be minimized in the genetic algorithm are shown below.

$$f\left(area\right)=\left(X_{max}- X_{min} \right) \ast ( Y_{max}- Y_{min})$$

(4)

$$f\left(M_i\right)=\sum ({x1}_{max}\ge {x2}_{min}\wedge {x2}_{max}\ge {x1}_{min} \wedge { y1}_{max} \ge {y2}_{min} \wedge {y2}_{max} \ge {y1}_{min})$$

(5)

where M_i is a working station. With two objective functions to be minimized, it is considered a multi-objective problem. The advantage of this multi-objective approach is that it allows adding more functions or constraints that help to find new solutions with different conditions in the optimization of the work area. Our objective function to minimize will be the sum of both Equations (4) and (5):

$$f\left(Comb\right)=(area\_weight) \ast f\left(area\right)+(interference\_weight) \ast f(M_T )$$

(6)

where $area\_weight$ is a value between 1 to 10, $f\left(area\right)$ is a total area of the combination of stations in the working area, $interference\_weight$ is a value between 100 to 1000, and $f\left(M_T\right)$ is the total number of interferences between stations. Two weight variables are used to give preference to interference reduction over area reduction.

With the evaluation of each combination by area and total number of interferences, a selection by tournament is made, which consists in the realization of λ tournaments, where the individuals of the current population are randomly selected by sampling with a uniform probability in such a way that the individuals with the minimum value are selected to be the parents in the next stage.

For the crossing of parents, we use the point crossover where we randomly generate a number n between 1 and the length of the vector (genes) that represents the individual and P_c (crossover probability). The first child receives the first genes of the first identical parent up to n, and after this number it receives the segment of the second parent. For the second child, it is also generated by this crossing, and it is conducted in the same way by inverting the order. Now, the second parent transfers its segment up to a number n to the child and the remaining one for the segment of the first parent.

Once the new population of offspring is generated, the mutation stage is performed. For this case, we will use the mutation for the real representation, where each gene is modified with probability P_m (probability of mutation). This consists of randomly selecting a gene and assigning it a new value from a uniform probability distribution over the range in which it is defined. The new generation becomes the parents for the next cross, repeating the process from the evaluation of the population.

In the genetic algorithm, the variables of number of generations, crossover probability, mutation probability, population size, and number of stations will directly affect the processing time of the algorithm. Algorithm 1 shows the genetic algorithm developed.

Algorithm 1: Robotic cell layout optimization algorithm
1: 2: 3:	Initialize. Number of generations     while $generatios<counter:$     Random starting positions of stations
4: 5: 6: 7: 8: 9: 10:	for $index in range \left(populatio{n}_{size}\right)$ $\hspace{1em}\hspace{1em} \hspace{1em}\hspace{1em} \left\{{Gen}_1,{Gen}_2,{Gen}_3,\dots .,{Gen}_n\right\}$     Diagonal points of each station        while $flag==0$ $\hspace{1em}\hspace{1em} \hspace{1em}\hspace{1em} each{ Gen}_n \mathrm{i}s\left\{x,y\right\}$     Maximum and minimum points for calculating the area        for $rows in range (population\_size)$
11:	print $(\mathrm{X} \min , X max, Y min, Y max)$
12:	Maximum area of each combination of stations
13:	$\hspace{1em}\hspace{1em} \hspace{1em}\hspace{1em} \hspace{1em} \hspace{1em}\hspace{1em}\hspace{1em}f\left(area\right)=\left(X_{max}- X_{min} \right) \ast ( Y_{max}- Y_{min})$
14:	Interference counting between stations
15:	if (x1_max >= x2_min and x2_max >= x1_min and y1_max >= y2_min and y2_max >= y1_min): return interference
	$\hspace{1em}\hspace{1em} \hspace{1em}\hspace{1em} \hspace{1em} \hspace{1em}f\left(M_i\right)=\sum Number of interferences between stations$
16:	Fitness function
17:	${\hspace{1em}\hspace{1em} \hspace{1em}\hspace{1em} \hspace{1em} \hspace{1em}f}_n\left(Comb\right)=(area\_w)\ast f\left(area\right)+(interference\_w)\ast f(M_T )$
18:	Best solution selection
19:	if ${ f}_n\left(comb\right)<f_{n-1}\left(comb\right)$ then
20:	New generation of solution
21:	for $rows in range (population\_size/ 2 )$
22:	Best solution
23:	return: $f_{min}\left(area\right)$

3. Results

The genetic algorithm was applied to three robotic cells that are part of a production line, with each cell representing a different case study. Results from different case studies help ensure that the conclusions are more robust, generalizable, and applicable across a wide range of contexts.

The algorithm is parameterized to perform 1000 iterations to find the best solution, with a convergence criterion applied if the minimum area for the robotic cell does not change after 50 iterations. A mutation probability of 0.20 is provided to ensure genetic diversity and that the algorithm sufficiently explores the solution space. This parameter was obtained through experimentation and adjustment of the algorithm, allowing for a balance between exploring new solutions and exploiting the best solutions found so far.

The experimentation was conducted with an 11th Gen Intel^® Core™ i7-11800H @ 2.30 GHz processor and 64 GB of RAM (Santa Clara, CA, USA). With this hardware, the average time per solution was 20 min, considering that, as a combinatorial optimization algorithm, it is considered a polynomial time problem.

3.1. Screwing Cell—Case Study 1

The first robotic cell performs a screwing function using a 4-axis robot (RH-6CRH6020-D SCARA, Mitsubishi Electric, Tokyo, Japan). There are six pieces that are placed within a nest of positions. The location of the pieces and the screws are currently defined, and each piece to be screwed are represented with a rectangle of different color to be clearly visualized, as shown in Figure 6.

Table 2. Dimensions of screwing stations.

Stations	Length (mm)	Width (mm)
Workstation	600	500
Station 1	175	80
Station 2	170	85
Station 3	140	120
Station 4	195	180
Station 5	120	60
Station 6	170	34

provides the dimensions of each workstation.

The algorithm is executed to obtain an optimal distribution of the stations in the screwing cell. Figure 7 shows the part distribution proposed by the algorithm, revealing a vertical matrix arrangement. The parts are more compact and vertically aligned in relation to the robot’s position.

Table 3. Trajectory time, screwing cell.

Trajectory	Current Transfer Time (s)	Algorithm Transfer Time (s)
1 to 2	3.12	2.91
2 to 3	1.92	1.53
3 to 4	2.15	2.22
4 to 5	1.98	1.71
5 to 6	2.48	1.88
Total time	11.65	10.25

presents the current travel times performed by the robot and the times obtained through simulation based on the proposed solution.

Once the simulation was carried out, a reduction of 1.4 s was obtained, which represents 13.17% of the transfer time implemented in the currently installed robotic cell compared to the optimized cell proposed by the algorithm.

3.2. Machining Cell—Case Study 2

The second cell is responsible for loading and unloading parts in a machining center, which produces three types of shafts of different lengths and diameters. A 6-axis robot (RV8CRLD-S15 M, Mitsubishi Electric, Tokyo, Japan) loads the material to be processed and then unloads the finished product, placing it in a storage station corresponding to the produced model. Figure 8 shows the current layout of the machining center; station 1 is the loading (input) station, and stations 2, 3, and 4 are the storage (output) stations. It shows how the CNC is in opposite position to the input and output stations.

Table 4. Dimensions of machining stations.

Stations	Length (mm)	Width (mm)
CNC	750	600
Station 1	350	325
Station 2	400	150
Station 3	275	225
Station 4	260	197

provides the dimensions of each workstation.

Figure 9 shows the solution proposed by the algorithm, where the storage stations are grouped on the left side of the nest, and the loading station is positioned on the right. Additionally, it can be observed that the loading station involved in each cycle is closer to the robot, which will reduce the cycle time for each loading operation.

Table 5. Trajectory time, machining cell.

Trajectory	Current Transfer Time (s)	Algorithm Transfer Time (s)
CNC to 1	4.56	4.10
2 to CNC	3.45	7.37
3 to CNC	3.89	3.21
4 to CNC	3.71	3.49
Total time	15.61	14.55

presents the current travel times performed by the robot and the times obtained through simulation based on the proposed solution. A reduction of 1.06 s was achieved, representing a 6.8% decrease in the transfer time of the currently installed robotic cell compared to the optimized cell proposed by the algorithm.

3.3. Assembly Cell—Case Study 3

The assembly of the parts is carried out in the third cell, where the material stations are distributed in such a way that a 6-axis robot (RV-7FRD, Mitsubishi Electric, Tokyo, Japan) takes the material from each station, places the parts in the assembly station, and removes the finished product. Figure 10 shows the actual layout of the assembly cell, a circular cell where the stations with the individual components are arranged around the base of the robot.

Table 6. Dimensions of assembly stations.

Stations	Length (mm)	Width (mm)
Assembly 3	750	600
Station 1	350	325
Station 2	400	150
Station 4	275	225
Station 5	260	197

provides the dimensions of each workstation.

In Figure 11, the proposed solution by the algorithm is shown. In Figure 11, the proposed solution by the algorithm is shown.

Table 7. Trajectory time, assembly cell.

Trajectory	Current Transfer Time (s)	Algorithm Transfer Time (s)
1 to 3	2.78	2.40
2 to 3	2.61	2.38
4 to 3	2.90	2.10
5 to 3	2.41	2.84
Total time	10.70	9.72

presents the current travel times performed by the robot and the times obtained through simulation based on the proposed solution.

A reduction of 0.98 s in transfer time was achieved, representing a 9.15% decrease compared to the currently operating robotic cell. This improvement was made possible through the optimization performed by the algorithm, which adjusted the station layout and the robot’s movement paths within the cell.

Table 8. Trajectory time, production line.

Robotic Cell	Current Transfer Time (s)	Algorithm Transfer Time (s)
Screwing	11.65	10.25
Machining	15.61	14.55
Assembly	10.70	9.72
Total time	37.96	34.52

summarizes the results obtained for each of the robotic cells evaluated, highlighting the superiority of the proposed method with a 3.44 s improvement in production time.

The results demonstrate a significant improvement in the operational efficiency of the robotic cell due to the optimization of the workstation layout using a genetic algorithm. The new arrangement allowed for a notable reduction in transfer times, achieving a decrease in operational cycles by 9.06%. This optimization not only speeds up the production process but also maximizes the utilization of available resources, resulting in increased productivity and greater competitiveness on the production line. The use of the genetic algorithm has been key to exploring multiple possible configurations and finding the optimal solution that would otherwise be difficult to identify manually.

4. Discussion

The optimization of the robotic cell’s area using the genetic algorithm led to a more compact and efficient design. The algorithm was able to identify station layouts that reduced the required space without compromising the robot’s mobility or the cell’s functionality, which is especially beneficial in manufacturing environments with space constraints. However, the algorithm does not account for spaces needed for operator movement, so it is recommended to consider these factors when designing a robotic cell. A limitation of the use of the algorithm is that it doesn’t consider the possibility of the rotation of the workstations as a possible solution. This approach of no rotation is very useful for the algorithm, as, with the intersections, it is more difficult to count with rotation workstations, which only a few researchers have performed, like Zhang and Li [29]. Some further research its need it to evaluate if rotation of workstations needs to be considered.

Optimizing the travel times and the area of the cell can result in lower operational costs, as both energy consumption and robot wear due to unnecessary movements were reduced. This translates into increased equipment lifespan and greater efficiency in resource utilization. This algorithm of this work only considers as a valid solution that the location of the workstation is within the reach of the robot, while other works considered the Denavit–Hartenberg equations [30] of a proposed robot; this gives an advantage, since the solution is evaluated as reachable or not from the same algorithm. For future work, we will seek to introduce the D–H equations of various robot models so that the user has the ability to evaluate their solutions without having to simulate them.

Regarding the limitation of the algorithm using only one robot per robotic cell, this significantly reduces the complexity of the problem but also limits the optimization potential. In more advanced industrial environments, where multiple robots can work simultaneously in the same cell or in adjacent cells, the interactions between the robots offer opportunities to improve efficiency and reduce cycle times. However, optimizing such systems with multiple robots introduces a new level of complexity, as it is necessary to manage the coordination between robots to avoid collisions and minimize downtime.

The implementation of the genetic algorithm can enhance the overall productivity of the robotic cell. By minimizing travel times and maximizing space utilization, the number of production cycles completed within a given period increased, which benefits the overall production capacity. This means that it is not necessary to continue performing the traditional approach as the only way to design and determine the location of the workstations, which now can be assisted with an algorithm to receive some location proposals for the workstations. Also, it is important to evaluate the use of some other evolutionary algorithms, as, according to some research, Lim [11] found that Particle Swarm Optimization could lead to better results in robotic cell optimization.

5. Conclusions

The proposed genetic algorithm effectively optimized the travel times between stations, resulting in a significant reduction in cycle times. This is made possible by the inherent ability of genetic algorithms to explore multiple configurations and find solutions that minimize the robot’s downtime, thereby improving operational efficiency. In the case studies conducted, the algorithm showed great adaptability to different configurations and design requirements, allowing for the optimization of both simple and complex robotic cells, which is crucial for production lines that need to quickly adjust to changes in demand or product specifications.

However, despite its advantages, the use of genetic algorithms also presents certain limitations. One of the main drawbacks is that, although genetic algorithms are effective in exploring large search spaces, they do not guarantee finding the globally optimal solution. Since their search process is based on the evolution and mutation of potential solutions, they often become trapped in local optima, especially in highly complex problems. This can lead to solutions that, while sufficiently good, do not always represent the best possible configuration. Furthermore, the performance of the algorithm heavily depends on the quality of the fitness function and the parameters selected, such as population size or mutation and crossover rates, which must be carefully tuned to avoid both premature convergence and excessively prolonged exploration of the solution space.

Another limitation is that genetic algorithms often require a considerable amount of computational time, particularly when applied to more complex systems, such as production lines with multiple robots or irregularly shaped workstations. Although the technique has proven to be applicable to various industrial scenarios, from small robotic cells to complex production lines, scalability can be a significant challenge. As the number of variables and possible configurations increases, the time needed to evaluate each generation of solutions grows exponentially, which can make real-time optimization impractical in certain cases.

Additionally, the genetic algorithm not only identified the optimal configuration but also generated a series of sub-optimal solutions that offer a good balance between space and time. These alternative solutions can be useful for robotic cell designers, as they provide options that allow balancing different design criteria according to the specific needs of production. However, the availability of multiple solutions also presents the challenge of selecting the most suitable one for a particular scenario, which may require further analysis outside the algorithm’s framework.

Future research could focus on addressing these limitations by developing hybrid techniques that combine genetic algorithms with other optimization methods, such as gradient-based or local search algorithms. Moreover, increasing the complexity of the robotic cells included in the studies, incorporating more robots and diverse shapes of workstations, would be beneficial. This would allow for the generation of more comprehensive layout templates, helping robotic cell designers consider different arrangements based on the number of robots and the specific geometry of the workstations, further improving efficiency in complex industrial production environments.