Fig. 4

Streamlined flowchart of the NCRBMO algorithm. The optimization process initiates with parameter initialization and the establishment of the population X_i^t. The switching coefficient φ determines when the algorithm transitions to extensive global exploration and when it shifts to more focused local exploitation. Distinct search strategies are applied at various stages to locate optimal or near-optimal solutions. In each iterative cycle, the current best-found solution is compared with the historical best, retaining the superior option to update X_i^t+1. The global optimization proceeds until the predefined termination criteria are satisfied, ultimately converging on the global optimum.