An adaptive multi-objective optimization and control framework for hydrocyclone operation under dynamic particle-size distributions

• The proposed method provides a closed-loop framework for real-time hydrocyclone operation. • It optimally updates operating parameters as the feed and performance priorities change. • A modified Johnson–SB distribution compactly represents feed particle-size distributions. • The policy spectrum delivers monotonic gains while managing the energy–separation trade-off. Hydrocyclone optimization is typically performed under fixed-condition assumptions, making its performance highly sensitive to changes in the feed particle-size distribution (PSD) and evolving process priorities. This study presents a prototype adaptive and preference-aware multi-objective optimization and control framework that adjusts inlet velocity ( V ) and feed solids concentration ( C ) in response to variations in PSD. The framework consists of four main steps: (1) Surrogate model development: A CFD-trained response-surface methodology predicts key performance objectives, including cut size ( d 50 ), separation sharpness ( E p ), underflow water-split ratio ( R f ), pressure drop ( ΔP ), and throughput ( Q ). (2) Multi-objective optimization: The NSGA-II algorithm is employed to identify Pareto-optimal trade-offs. (3) Decision-making: The TOPSIS method is used to select the optimal operating point based on user-defined weights. (4) Supervisory module: This module continuously monitors PSD and weight vectors, triggering re-optimization when predefined thresholds are exceeded, and adjusting ( V, C ) to align with updated priorities. PSDs are modeled using a modified Johnson-SB distribution, defined by median size ( d 50 ) and a dispersion/tail coefficient ( σ j , ranging from 0.40 to 1.00), where d 50 determines location and σ j controls the distribution's width and tails. In 25 PSD scenarios, adaptive set-point updates resulted in a 17–27% reduction in d 50 , a 14–25% improvement in E p , and a 38–95% increase in Q compared to a static baseline. R f remained within acceptable bounds, while ΔP varied between 0–136%, depending on separation requirements. This framework provides an efficient approach for ensuring stable separation under fluctuating feed conditions and offers a practical solution for controlling hydrocyclone performance.