Improving diversification by a hybrid bat-Nelder-Mead algorithm and DDE for rapid convergence to solve global optimization

Delay differential equations and algorithms hold a crucial position in the exploration of some biological systems and several models in real-world applications. So, some algorithms contribute to improve mathematical models related to natural life problems and global optimization. A novel hybridization between the downhill Nelder-Mead simplex algorithm (NM) and the classic bat algorithm (BA) was presented. The classic BA suffers from premature convergence, which is due to its global search weakness. In this research, this weakness was overcome by the intervention of NM in the velocity updating formula of the particles as an additional term. This improvement distracts particles from the rapporteur route, toward only the best solution found, to discover the search space more accurately. Once this improvement detects a promising area, sequential expansions are performed to deeply explore the area. This mechanism provides rapid convergence for the algorithm. Deep analysis of the algorithm's behaviour was provided, and thoughtful experiments were conducted and evaluated utilizing several evaluation metrics together with the Wilcoxon signed rank test to accentuate the effectiveness and efficiency of the proposed algorithm.