Topological search and gradient descent boosted Runge–Kutta optimiser with application to engineering design and feature selection

Abstract The Runge–Kutta optimiser (RUN) algorithm, renowned for its powerful optimisation capabilities, faces challenges in dealing with increasing complexity in real‐world problems. Specifically, it shows deficiencies in terms of limited local exploration capabilities and less precise solutions. Therefore, this research aims to integrate the topological search (TS) mechanism with the gradient search rule (GSR) into the framework of RUN, introducing an enhanced algorithm called TGRUN to improve the performance of the original algorithm. The TS mechanism employs a circular topological scheme to conduct a thorough exploration of solution regions surrounding each solution, enabling a careful examination of valuable solution areas and enhancing the algorithm’s effectiveness in local exploration. To prevent the algorithm from becoming trapped in local optima, the GSR also integrates gradient descent principles to direct the algorithm in a wider investigation of the global solution space. This study conducted a serious of experiments on the IEEE CEC2017 comprehensive benchmark function to assess the enhanced effectiveness of TGRUN. Additionally, the evaluation includes real‐world engineering design and feature selection problems serving as an additional test for assessing the optimisation capabilities of the algorithm. The validation outcomes indicate a significant improvement in the optimisation capabilities and solution accuracy of TGRUN.