## 1 Introduction
In contrast to other metaheuristic algorithms, YSGA implements Levy flights and logarithmic spirals to update the position of search individuals. Furthermore, YSGA considers groups of particles to guide the search through different directions while covering more land space. As an alternative to classical approaches, the problem of designing clustering protocols was also faced with metaheuristic techniques [33; 34; 35]. In the literature, metaheuristic methods demonstrated obtaining a better performance than those based on traditional computational techniques in terms of accuracy and robustness. From the metaheuristic perspective, the process of a clustering routing protocol is translated into an optimization problem. Therefore, an objective function is defined to evaluate the quality of a solution. Guided by this objective function, the algorithm modifies the configurations of sensor nodes until obtaining the solution that presents a longer work cycle for the network [36; 37]. Several clustering protocols have been proposed based on metaheuristic principles. Some examples include the Energy Centers using Particle Swarm Optimization (EC-PSO) [38]. Using this approach, by using a geometric scheme, the CHs are firstly selected. Then, the PSO algorithm is considered to identify the central sensor of the network, which will represent the CH. The EC-PSO method also includes a mechanism to avoid the consideration of nodes with low energy levels. Another interesting example is Genetic-Algorithm-Based Energy-Efficient Clustering (GAEC) [39]. In this clustering protocol, the Genetic algorithms are used to identify the CH sensors through a clustering metric. The GA considers as the objective function, a model that combines the energy of the nodes, and the transmission cost. Recently, a routing protocol based on the Gray Wolf Optimizer has been also proposed [17]. In this scheme, different fitness functions are defined to evaluate the node characteristics of each sensor. Such values are considered to be weights that are dynamically modified depending on the distance among the nodes of the network. Therefore, the idea is to identify the configuration of CH nodes that reduce the aggregate value of the weights. Although metaheuristic methods present interesting results, they have a critical problem, such as their low premature convergence. This fact generates that such methods frequently obtain sub-optimal CH configurations, which reduces their working cycles. The difference between the proposed YSGA clustering protocol and other protocols that also implement metaheuristic algorithms is the strategy to select CHs. In our method, we have encoded candidate solutions to automatically choose the number of CHs and avoid a fixed percentage of CHs or predefined probabilities to select CHs. Our strategy ensures the optimal number of CHs is chosen in every round by the implementation of the YSGA. Furthermore, the proposed method includes a different cost function to guide the search toward the clustering network configuration that better fist the requirements of energy savings and load balancing. In this work, a new clustering routing protocol for Wireless Sensor Networks is introduced. The scheme is developed based on the Yellow Saddle Goatfish Algorithm (YSGA). Under the proposed approach, the number of cluster heads and the selection of optimal cluster heads is determined by the YSGA algorithm, while sensor nodes are assigned to its nearest cluster head. Therefore, the cluster structure of the network is updated by the YSGA to ensure an optimal distribution of cluster heads and reduce the transmission distance. Experiments show competitive results and demonstrate that the proposed routing protocol minimizes the energy consumption, improves the lifetime, and prolongs the stability period of the network in comparison with the stated of the art clustering routing protocols. The next sections of the paper are structured as follows. In Section 2, the main characteristics of the Yellow Saddle Goatfish Algorithm (YSGA) are reviewed.