## 1 Introduction  
Aerial transportation may be formulated as critical aviation problem with special requirements to ensure flight safety [1]. In fact, \"safety\" is the first and main concern related to the aerial transportation [2, 3]. The design and development of a reliable transportation algorithm require awareness of aircraft trajectories [4]. Trajectory awareness can significantly increase aerial transportation performance [5]. The prediction of future trajectories contributes to the Aerial Transportation Algorithm [6] (ATA) in terms of path planning and collision avoidance [7]. Precise trajectory prediction can boost an ATA's efficiency in terms of safety, costs, and time [8]. Numerous research investigations have concentrated on precise trajectory prediction as a fundamental requirement for enhancing safe and efficient ATAs [9]. Eurocontrol's CASCADE Project [10], NASA's Air Traffic Management Research [11], and Single European Sky ATM Research (SESAR) [12] are the most well-known practical applications for accurate trajectory prediction in the real world. Eurocontrol implemented advanced trajectory prediction algorithms that analyze real-time data from aircraft, weather conditions, and air traffic control systems. By accurately predicting aircraft trajectories, controllers can proactively identify potential conflicts between flights and provide timely instructions to pilots to avoid collisions. NASA's AAC project incorporates advanced trajectory prediction algorithms to model aircraft movements and predict potential conflicts. By integrating data from various sources, including radar, ADS-B (Automatic Dependent Surveillance-Broadcast), and weather data, the system can anticipate trajectory deviations and suggest route adjustments to air traffic controllers. Within SESAR, trajectory prediction is a fundamental component of the \"trajectory-based operations\" concept. This involves using accurate trajectory predictions to enable more precise planning and coordination of flights, from departure to arrival. In this context, our research has been directed toward formulating and creating a reliable methodology for precise predictions of aircraft trajectories. In essence, there are two methods that can be employed for predicting flight paths: the \"Deterministic\" approach [13] and the \"Probabilistic\" approach [14]. Predictions of deterministic trajectories involve methods where forthcoming paths are determined based on their initial parameter values. Deterministic methodologies can be designed using statistical [15], artificial intelligence [16], and hybrid [17] models. Receding Horizon techniques that utilize kinematic and kinetic models have been the dominant type applied and have demonstrated their effectiveness [18; 19]. Deterministic methods have the ability to forecast aircraft paths by solving intricate dynamic programming problems while considering various constraints [20]. While they are good in predicting short-term trajectories, their accuracy reduces over the long-term due to error propagation throughout the prediction horizon [21]. This error is due to variety of factors including complexity of dynamic environments, uncertainty in environmental conditions, limited data and observations, nonlinear behavior of dynamic environments, interaction and cooperation complexity, cumulative sensing and actuation errors, and computational loads [22]. Hence, probabilistic [23] approaches were created and advanced to enhance the accuracy of long-term trajectory prediction. Regarding probabilistic techniques, evolutionary algorithms [24], such as Genetic Algorithms (GAs) [25], Particle Swarm Optimization (PSO) [26], and hybrid GA-PSO, have effectively been employed for probabilistic ATP [27]. GA simulates evolution by generating a population of potential solutions, evaluating their fitness, selecting the fittest individuals, combining their traits through crossover and mutation, and iterating over generations to improve solutions.