A mathematical mechanism model was proposed for the description and analysis of the heat-stirring-acid leaching process.The model is proved to be effective by experiment.Afterwards,the leaching problem was formulated as a constrained multi-objective optimization problem based on the mechanism model.A two-stage guide multi-objective particle swarm optimization(TSG-MOPSO) algorithm was proposed to solve this optimization problem,which can accelerate the convergence and guarantee the diversity of pareto-optimal front set as well.Computational experiment was conducted to compare the solution by the proposed algorithm with SIGMA-MOPSO by solving the model and with the manual solution in practice.The results indicate that the proposed algorithm shows better performance than SIGMA-MOPSO,and can improve the current manual solutions significantly.The improvements of production time and economic benefit compared with manual solutions are 10.5% and 7.3%,respectively.