Inverse Particle Size Distribution Targeting in Chocolate Roller Refining

Abstract

Chocolate quality and processability are strongly influenced by the particle size distribution (PSD) together with fat content and the emulsifier system, through their combined effect on rheology, texture, and sensory perception. Roller refining is a dominant industrial route to achieve target PSDs, yet practical recipe-to-PSD inverse design remains challenging because the process response is nonlinear, multi-stage, and depends on both operating conditions and effective material breakage behavior. This study presents an engineering-oriented PBMdriven inverse-design framework for roller refining in which a staged population balance model (PBM) is embedded into a constrained optimization loop to compute feasible roll-speed and throughput setpoints that match both PSD percentile metrics and the cumulative PSD curve. The Bees Algorithm (BA) is used here as a representative derivative-free solver choice for the resulting nonconvex, constraint-driven optimization problem; the contribution is the inverse-design formulation and validation rather than the selection of a specific meta-heuristic. A feasibility scan is introduced to quickly verify whether a target PSD lies inside a coarse reachable envelope under operating bounds, and selected effective breakage parameters are tuned under explicit regularization to mitigate model mismatch without overfitting. In the demonstrated case study, the optimized settings achieved close agreement with target metrics (d10, d50, d90, span) and a low cumulative-curve error (curveRMSE approximate to 0.0118). Experimental validation is provided by overlaying measured PSD data against both the target and model-optimized predictions in differential (volume %) and cumulative forms, showing strong agreement in the target size range. The proposed framework enables fast inverse tuning for roller refiner operation planning and provides a practical bridge between PBM modeling and industrial setpoint optimization.