Population Density Repulsion PSO Optimized XGBoost for Robust Forecasting of Multiseasonal, Intermittent, and Nonstationary Time Series

Forecasting complex time-series remains a central challenge across domains such as finance, energy, healthcare, and logistics. Many real-world sequences are multiseasonal, intermittent, or nonstationary, rendering traditional statistical models inadequate. Machine learning methods, particularly Extreme Gradient Boosting (XGBoost), offer greater flexibility but are highly sensitive to hyperparameter tuning. To address this, we propose a novel hybrid framework that integrates XGBoost with an enhanced Particle Swarm Optimization (PSO) algorithm incorporating a Population Density Repulsion (PDR) mechanism. The PDR term introduces a density-aware repulsive force that mitigates premature convergence, preserves exploration diversity, and improves generalization. Extensive experiments on representative datasets demonstrate that PDR-PSO-optimized XGBoost consistently outperforms baseline XGBoost and classical PSO-tuned variants in both training stability and testing accuracy. These findings highlight the potential of density-aware metaheuristic optimization as a pathway toward robust machine learning frameworks for forecasting challenging time-series structures.