Quasi-dynamic opposite learning enhanced Runge-Kutta optimizer for solving complex optimization problems

Abstract

Abstract The Runge-Kutta Optimization (RUNGE) algorithm is a recently proposed metaphor-free metaheuristic optimizer borrowing practical mathematical foundations of the famous Runge-Kutta differential equation solver. Despite its relatively new emergence, this algorithm has several applications in various branches of scientific fields. However, there is still much room for improvement as it suffers from premature convergence resulting from inefficient search space exploration. To overcome this algorithmic drawback, this research study proposes a brand-new quasi-dynamic opposition-based learning (QDOPP) mechanism to be implemented in a standard Runge-Kutta optimizer to eliminate the local minimum points over the search space. Enhancing the asymmetric search hyperspace by taking advantage of various positions of the current solution within the domain is the critical novelty to enrich general diversity in the population, significantly improving the algorithm's overall exploration capability. To validate the effectivity of the proposed RUNGE-QDOPP method, thirty-four multidimensional optimization benchmark problems comprised of unimodal and multimodal test functions with various dimensionalities have been solved, and the corresponding results are compared against the predictions obtained from the other opposition-based learning variants as well as some state-of-art literature optimizers. Furthermore, six constrained engineering design problems with different functional characteristics have been solved, and the respective results are benchmarked against those obtained for the well-known optimizers. Comparison of the solution outcomes with literature optimizers for constrained and unconstrained test problems reveals that the proposed QDOPP has significant advantages over its counterparts regarding solution accuracy and efficiency.