Droplet-based microfluidics holds promise for advanced biomedical applications due to its enhanced accuracy, throughput, rapid reaction time, and minimal reagent consumption. However, achieving droplets with the desired radius often entails costly design iterations. In this paper, we propose a novel approach that combines machine learning algorithms with metaheuristic algorithms to leverage their respective strengths in speed and accuracy. Specifically, we demonstrate the effectiveness of the Rain Optimization Algorithm (ROA) in enhancing the accuracy of five machine learning models. Additionally, we introduce a hybrid model, optimized by ROA, for predicting droplet generation in a cross-junction microfluidic channel, achieving a coefficient of determination (R2) of 0.937, reflecting a 3.6 % increase in accuracy. We employ symbolic regression to validate the hybrid model, yielding an R2 value of 0.987, indicating strong agreement with real data. Furthermore, we utilize the SHAP method in Explainable AI to interpret the hybrid model's performance. Notably, the proposed hybrid model requires only four seconds to solve the prediction problem, significantly reducing computational time compared to the numerical model and experimental method. This approach facilitates the study of each input parameter's impact on droplet size prediction, offering otherwise challenging and costly insights to obtain experimentally.