Enhanced Red-billed Blue Magpie Optimizer for engineering optimization problems

The design of efficient and robust metaheuristic algorithms remains a fundamental challenge in addressing complex optimization problems, particularly those involving high dimensionality, nonlinearity, and multimodal landscapes where traditional methods often struggle. To overcome these difficulties and enhance search effectiveness and adaptability, this paper proposes the Enhanced Red-billed Blue Magpie Optimizer (ERBMO), an improved variant of the recently introduced Red-billed Blue Magpie Optimizer (RBMO). ERBMO integrates three synergistic enhancement mechanisms: Diversity-adaptive weight updating, Periodic pattern search, and Evolutionary probabilistic combinatorial mutation. These components are specifically designed to strengthen population diversity, mitigate premature convergence, and achieve a dynamic balance between exploration and exploitation throughout the optimization process. Comprehensive evaluations demonstrate the superior performance of ERBMO. On the CEC2017 benchmark suite, ERBMO achieves the highest Friedman rankings across all tested dimensions, with average ranks of 1.667 (30D), 1.433 (50D), and 1.133 (100D), consistently outperforming the original RBMO which ranked second. On the CEC2022 benchmark suite, ERBMO again secures the top overall rankings for both 10D (1.833) and 20D (1.833), surpassing nine state-of-the-art algorithms including ESC and RBMO. Ablation study results confirm the effectiveness of each proposed strategy, as the complete ERBMO achieves superior Friedman rankings (2.282 for 10D, 2.140 for 20D) compared to variants with any single strategy removed. Furthermore, when compared against classical algorithms (PSO, DE, CMA-ES) and their advanced variants (SaDE, LSHADE) on CEC2022, ERBMO obtains the best overall rankings (3.550 for 10D, 3.089 for 20D). When applied to four real-world engineering design problems-speed reducer, pressure vessel, step-cone pulley, and hydrostatic thrust bearing-ERBMO consistently ranks first, achieving optimal or near-optimal solutions with superior robustness. The superior performance across both benchmark and practical problems highlights the effectiveness and reliability of the proposed improvements. This work presents a framework for engineering optimization and metaheuristic algorithm design. The source code of ERBMO is publicly available at: https://github.com/x5865/Enhanced-Red-billed-Blue-Magpie-Optimizer-ERBMO- .