The study focuses on the trajectory generation of a 3-degree-of-freedom (3-DOF) articulated manipulator, aiming to reduce the end-effector position inaccuracy at each intermediate point along the trajectory. A Genetic Algorithm (GA) combined with the Random Search Method (RSM), B-Spline, and Cubic Polynomial has been applied to a Simulink-designed 3-DOF articulated manipulator. Our outcomes show that the GA and RSM outperform other methods, gaining a point-to-point accuracy of 99.97%. For B-Spline and Cubic Polynomial, the accuracies are 75.40% and 79.59%, respectively. The hybridized framework introduces a search technique that gives optimum Genetic Algorithm parameters and these optimum parameters produce a trajectory with minimum path deviation compared to other algorithms. Hence, these results emphasize the excellence of the Genetic Algorithm and Random Search Method in providing an optimized trajectory.