Background Solar irradiance is a nonlinear and intermittent function, which makes accurate forecasting of solar power generation a challenge. The high variability of meteorological conditions is not well represented by conventional atmospheric models, thus hampering forecasting skill and model robustness. In this work, an advanced hybridization of multi-population cuckoo search (HMPCS) algorithm with machine learning (ML) methods is developed to enhance the prediction performance of photovoltaic (PV) power forecasting with more reliability. Methods In this study, a hybrid modeling framework is proposed, called HMPCS–ML framework which captures the global search capacity of HMPCS and predictive power of sophisticated ML models (Long Short-Term Memory (LSTM), Light Gradient Boosting Machine (LightGBM)). Optimizing hyperparameters by balancing exploration and exploitation, the algorithm runs on multi-populations through Lévy flight randomization. Interpolation, normalization, and temporal windowing were utilized to preprocess synthetic meteorological and irradiance datasets. We evaluated the framework by comparing commonly used statistical measures (MAE, RMSE, MAPE, R 2 ). Results Moreover, experimental analyses showed that HMPCS–ML models significantly outperformed baseline approaches (Grid Search and Particle Swarm Optimization (PSO)). Results showed that the optimized LSTM+HMPCS model outperformed other models in terms of lowest RMSE (0.139) and highest R 2 (0.93), reflecting the LSTM model’s good fit with practical observations and generalization ability. The optimal LightGBM + HMPCS variant also proved to be consistently better, with reduced error (23% lower than unoptimized models). Conclusions In this regard, the HMPCS–ML framework is a powerful and efficient solution for the optimization of solar power forecasting, improving the predictive performance and calculation efficiency. This research shows the potential of hybrid metaheuristic–ML integration for renewable energy prediction and smart-grid applications in general and indicates further extensions to multi-objective and Transformer-based architectures.
In our research, we dealt with one of the most important issues of linguistic studies of the Holy Qur’an, which is the words that are close in meaning, which some believe are synonyms, but in the Arabic language they are not considered synonyms because there are subtle differences between them. Synonyms in the Arabic language are very few, rather rare, and in the Holy Qur’an they are completely non-existent. And how were these words, close in meaning, translated in the translation of the Holy Qur’an by Almir Kuliev into the Russian language.