Open Python-Based Simulation and MOPSO Multiobjective Optimization of a Rod Mill–Hydrocyclone–Ball Mill Circuit

Comminution–classification circuits are difficult to optimize because hydraulic, granulometric, energy, and economic responses are nonlinearly coupled, while circuit simulation, equipment sizing, simulator benchmarking, and operating optimization are often treated separately. This study aimed to develop an open Python framework for steady-state simulation and five-objective optimization of a rod mill–hydrocyclone–ball mill circuit processing a gold ore. The framework integrates solid and water balances, Rosin–Rammler particle-size reconstruction, comminution and hydrocyclone models, preliminary equipment sizing, explicit feasibility constraints, and Multiobjective Particle Swarm Optimization (MOPSO). Its novelty lies in coupling complete-circuit simulation, simulator-to-simulator benchmarking against USIM PAC®, model-based sizing, convergence diagnostics, and Pareto optimization within one transparent workflow. The benchmark produced zero or below 10−3% errors in solid balances and sizing differences of 1.07%, 8.21%, and 0.00% for the rod mill, ball mill, and hydrocyclone, respectively. Relative to the base case, the joint minimum-water, minimum-energy, and minimum-cost solution reduced specific water consumption by 24.50%, specific grinding energy by 4.24%, specific operating cost by 10.19%, and mass recirculation by 8.80%, while useful recovery decreased slightly from 82.67% to 81.78%. The maximum-recovery solution increased useful recovery to 84.45%, with higher water, energy, and operating-cost requirements. The framework supports reproducible evaluation of resource–recovery trade-offs in grinding–classification circuits.