RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method

The optimization field suffers from the metaphor-based pseudo-novel or fancy optimizers. Most of these cliche ' methods mimic animals' searching trends and possess a small contribution to the optimization process itself. Most of these cliche ' methods suffer from the locally efficient performance, biased verification methods on easy problems, and high similarity between their components' interactions. This study attempts to go beyond the traps of metaphors and introduce a novel metaphor-free population-based optimization method based on the mathematical foundations and ideas of the Runge Kutta (RK) method widely well-known in mathematics. The proposed RUNge Kutta optimizer (RUN) was developed to deal with various types of optimization problems in the future. The RUN utilizes the logic of slope variations computed by the RK method as a promising and logical searching mechanism for global optimization. This search mechanism benefits from two active exploration and exploitation phases for exploring the promising regions in the feature space and constructive movement toward the global best solution. Furthermore, an enhanced solution quality (ESQ) mechanism is employed to avoid the local optimal solutions and increase convergence speed. The RUN algorithm's efficiency was evaluated by comparing with other metaheuristic algorithms in 50 mathematical test functions and four real-world engineering problems. The RUN provided very promising and competitive results, showing superior exploration and exploitation tendencies, fast convergence rate, and local optima avoidance. In optimizing the constrained engineering problems, the metaphor-free RUN demonstrated its suitable performance as well. The authors invite the community for extensive evaluations of this deep-rooted optimizer as a promising tool for real-world optimization. The source codes, supplementary materials, and guidance for the developed method will be publicly available at different hubs at http://imanahmadianfar.com and http://aliasgharheidari.com/RUN.html.

Automated summary

The optimization field is plagued by metaphor-based pseudo-novel or fancy optimizers, with limited contributions to the optimization process. This study introduces a novel metaphor-free population-based optimization method called RUNge Kutta optimizer (RUN) based on mathematical foundations, showing promising results in mathematical tests and engineering problems. The RUN algorithm utilizes slope variations computed by the RK method for global optimization, demonstrating superior exploration and exploitation tendencies, fast convergence rate, and local optima avoidance.