# Solving the Manufacturing Cell Design Problem through an Autonomous Water Cycle Algorithm
## 1 Introduction  
Worldwide manufacturing plants are usually structured into manufacturing entities, which are composed of machines processing a specific part for a product. This organization presents a problem for most companies because, generally, the output of a machine could be the input of another, which could be located in a faraway place, reducing the efficiency of the construction process because of the moving of parts. This relevant problem for the industry is a classical optimization problem defined by [PERSON] [1] and called the manufacturing cell design problem, whose objective is to minimize the number of movements and exchanges of parts between groups of machines, which are called cells.  
During the last decade, the manufacturing cell design problem has been intensely addressed in the optimization field area. Exact techniques have been proposed for solving the problem, as in [2]. This type of exhaustive techniques is efficient in solving low-complexity instances. However, these techniques usually fail when larger instances are considered because of timing constraints [3]. On the other hand, approximate algorithms are capable of getting solutions for any instance size in reasonable computing time, but results could not be as high quality as expected because these methods are focused on providing near-optimal solutions [4; 5].  
Focusing on metaheuristics, many bio-inspired algorithms have successfully addressed complex optimization problems in the literature. These techniques are characterized by mimic the behavior of processes from nature, such as honey bees collect nectar from flowers, bats hunt their prey in darkness, the attraction between two objects by computing the gravitational force, among many other examples. Despite the great success of metaheuristics in different application areas, their proper design and implementation to reach optimal solutions is not a simple task. The operation of metaheuristics is governed by a set of parameters that demand a previous setting. Such a configuration is known to be a major task. In fact, selecting the appropriate parameter setting is crucial for the efficient exploration of the search space and therefore to the effective finding of high-quality solutions [6].  
Under this line, the authors propose a variation of the water cycle algorithm technique inspired by the water cycle of the elements in the hydrosphere, which was originally proposed in [7; 8]. The goal of this variation is that the algorithm has the capacity of updating the population size to manage the trade-off between exploration and exploitation, so that the process of getting good solutions to the optimization problem could be facilitated. To this end, the authors consider the autonomous search paradigm introduced in [9]. The idea of selecting the population size parameter to control this trade-off is not new and then, many works can be found in the literature following this trend [10]. As expected, other interesting approaches can be found for controlling this trade-off in the literature [10].  
In this work, the authors compare the original and the autonomous approach of the metaheuristic while solving 160 known instances of the manufacturing cell design problem [11]. As a result, the authors checked that the autonomous water cycle algorithm performs similarly than the default approach, but without being specifically configured for solving a specific instance, which is valuable.  
The manuscript is organized as follows. Section 2 discusses related works in the field. Section 3 defines the manufacturing cell design problem. Section 4 exposes the default water cycle algorithm. The proposed autonomous water cycle algorithm is presented in Section 5. Finally, experimental results and concluding remarks are shown in Sections 6 and 7, respectively.