<p>Leveraging the concepts of the traditional Runge–Kutta method, the Runge–Kutta Optimizer (RUN) is a new meta-heuristic algorithm created for global optimization applications. The RUN method is addressed in this paper along with its mechanisms to optimize search strategies and improve the quality of solutions. The RUN algorithm is effective in solving complex, nonlinear optimization problems because it efficiently balances exploration and exploitation using a combination of random elements and deterministic rules. Variations of the Runge–Kutta algorithm are presented, with an emphasis on modifications that improve the performance of the method on a range of problem sets. By examining a variety of fields, the study highlights the potential application of the algorithm in fields such as engineering, computer science and medicine. A comprehensive analysis of the algorithm methodology and in-depth evaluations of the 2011 CEC benchmark functions provide empirical evidence of the algorithm’s effectiveness and efficiency compared to traditional optimization techniques, as well as its superior performance over a number of state-of-the-art techniques. Convergence analysis shows that RUN leads to faster convergence rates and consistently finds optimal or near-optimal solutions. In addition, a set of real-world engineering challenges, such as design optimization and parameter estimates, are used to test the suitability of the algorithm. With advancement in computing speed and solution accuracy, the effectiveness of the proposed RUN algorithm makes it a proposed methodology for a wide range of optimization problems. Finally, some future directions on potential research plans are included in the paper.</p>