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

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 (d₅₀), 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 (d₅₀) 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 and 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.