# Metaheuristics and Support Vector Data Description for Fault Detection in Industrial Processes
## 1 Introduction
[18] presents a brief general description about hyper-parameter optimization in Support Vector Machines (SVM). In this context, the ant colony algorithm is chosen in [19] for feature selection and parameter optimization in SVM for fault diagnosis. Ref. [20] used genetic algorithms to optimize parameters corresponding to the kernel function. Optimization of the hyper-sphere parameters together with those associated with the Gaussian radial base kernel function are studied by [21] using grid search. Ref. [22] obtained optimal results by the combination of grid search and PSO. In the last few decades, researchers have developed several nature-inspired optimization algorithms that mimic some biological behaviors or physical phenomena. Techniques based on swarm intelligence mimic the socially intelligent behavior of groups of species. Search algorithms start with a group of randomly generated solutions generally naming a population evolving throughout successive generations and promote the population improvement throughout the iterations. In this study, a performance comparison is presented corresponding to four of these metaheuristics for calculation of the hyper-parameters. Besides PSO, which has been widely used for these purposes, the considered algorithms in this study have demonstrated their efficiency in solving optimization problems applied to engineering. Furthermore, the performance is tested for the Spotted Hyena Optimization (SHO) algorithm, Krill herd (KH) algorithm, and Squirrel Search Algorithm (SSA). The SHO is a recent metaheuristic based on swarms which mimics the social behavior of these animals in nature. Among the vast amount of metaheuristics, SHO has shown great advantages in the exploration of diverse search spaces compared to other state-of-the-art approaches [23]. SHO has been implemented to solve a wide range of engineering problems like prediction of materials resistance during cutting processes [24]. SHO is used in combination with neural networks to improve the prediction ability of these algorithms. In [25], two complex engineering problems with restrictions like the design of bar armor and the design of multiple disk clutch brakes are solved. The results show the efficiency of SHO in solving these problems compared to other optimization algorithms like PSO and ACO. It showed its applicability in environments of a high dimension with a low computational cost. Ref. [26] implements SHO for design optimization in aerodynamic surface and optical buffer problems where the obtained numerical results are then compared with algorithms like Grey Wolf Optimizer, Genetic Algorithm, and PSO, among others. Likewise, the binary version of SHO has been developed and used to build wrapping approaches for feature selection in different sets of UCI data [27]. Moreover, SHO has been hybridized with other algorithms like PSO to improve its abilities to solve various engineering problems [28]. Recently, Ref. [29] implements an SHO version able to deal with multi-objective problems for the prediction of characteristics in gene selection through its combination with machine learning algorithms like SVM. The KH algorithm is a recent nature-based algorithm inspired by the individual krill herding behavior. This algorithm was introduced in [30]. The KH algorithm works to achieve the minimum distance between individual krill and the nearest food. This algorithm has been successfully used in solving many problems of numerical optimization, electric and power system problems, text grouping, breast cancer detection, and the training of neural networks [31; 32; 33]. More recently, the possibility of applying this algorithm for the grouping of text documents is studied in [34], while the same problem is addressed in [35] using a hybrid algorithm based on KH. The grouping based on the KH algorithm is proposed in [36] for the network of wireless sensors. A method for diagnosing bearing failure based on KH and a kernel extreme learning machine is proposed in [37].