Bilevel Optimization of Multi-Component Chemical Systems Using Particle Swarm Optimization

In this paper we study a real-world optimization problem in mineralogy which contains a large number of parameters and several objective functions. The problem has been described through a thermodynamic model for which the parameters have to be quantified. Due to non-linear chemical reactions and the characteristics of the problem, we developed a bilevel optimization approach in which the parameters that need to be determined can be split in two levels. The lower level contains three non linear equations and two linear charge and mass balance constraints. We use linear multi-objective particle swarm optimization (LMO PSO) to solve this problem for a general case. We then use the results in the upper level. This bilevel optimization has been used to find the thermodynamic parameters of the Na₂O-SiO₂ system. The results are analytically analyzed and compared with the reference data. This shows that the thermodynamic model is accurate and that the termination of thermodynamic properties using a bilevel optimization method based on PSO algorithms is reliable and efficient.