## 1 Introduction  
Metaheuristics can be classified into various categories based on their natural inspiration [1]. One prominent category is swarm intelligence-based algorithms, which draw inspiration from the collective behavior of social insect colonies, bird flocks, or animal herds. Swarm intelligence (SI) algorithms simulate the cooperative and self-organizing behavior observed in natural swarms to solve complex optimization problems [2, 3]. SI, inspired by the collective behavior of social insect colonies, encompasses a diverse range of algorithms that facilitate efficient problem-solving through cooperation and self-organization. These algorithms simulate the collaboration and information exchange observed in natural swarms, enabling them to achieve global optimization. By harnessing the collective intelligence exhibited by swarm systems, SI metaheuristics offer promising avenues for optimizing neural network training and enhancing the identification and control capabilities of robotic systems. To conduct a comprehensive analysis, we selected four state-of-the-art SI algorithms known for their unique characteristics and optimization strategies. Ant Lion Optimization (ALO), drawing inspiration from the hunting behavior of ant lions; employs a powerful search mechanism to explore and exploit the solution space efficiently. Bat Algorithm (BA) mimics the echolocation behavior of bats, utilizing frequency tuning and pulse emission concepts to achieve effective optimization. Grey Wolf Optimizer (GWO) emulates the social hierarchy and hunting dynamics of grey wolves, employing three fundamental types of wolf-inspired operators to strike a balance between exploration and exploitation. Moth Flame Optimization (MFO), inspired by the moth's phototaxis behavior toward flames, incorporates attraction and repulsion mechanisms to guide the optimization process effectively. Finally, we compare these algorithms against the well-established Particle Swarm Optimization (PSO), which draws inspiration from the social behavior of bird flocking, enabling particles to adaptively search the solution space based on individual and swarm experience. Overall, SI algorithms offer powerful optimization techniques that leverage the collective intelligence and self-organization observed in natural swarms. Their robustness, global exploration capabilities, self-adaptation, parallelism, scalability, and bio-inspired concepts make them well-suited for addressing a wide range of optimization problems in various domains. By mimicking the behavior of swarms, these algorithms provide effective solutions and insights for solving complex optimization challenges [4; 5]. Furthermore, the nature-inspired characteristics of SI optimization methods introduce robustness and adaptability to different problem domains. They can be readily applied to robotic systems, including those with complex dynamics and uncertain environments [6]. By employing metaheuristic optimization techniques, the Unscented Kalman Filter (UKF) initialization parameters can be tailored to specific robotic platforms and tasks, leading to an improved estimation and control performance. By integrating SI algorithms with UKF-based neural training, we aim to improve the accuracy of identification and control in a two-degrees-of-freedom (DOF) robot manipulator. To elaborate further, let us delve into the distinguishing features and underlying principles of ALO, BA, GWO, and MFO algorithms. ALO utilizes a population of artificial ant lions to mimic hunting behaviors, where each ant lion represents a potential solution in the search space [7]. The algorithm employs pride update and position update mechanisms to perform efficient exploration and exploitation. BA, on the other hand, emulates the echolocation behavior of bats to optimize solutions. Bats navigate through a combination of random flight, frequency tuning, and pulse emission, allowing them to find optimal solutions in dynamic environments [8].