Multi-objective Optimal Synthesis and Design of Froth Flotation Circuits for Mineral Processing, Using the Jumping Gene Adaptation of Genetic Algorithm

Abstract

An adaptation, inspired by the concept of jumping genes in biology, is developed for the binary-coded elitist nondominated sorting genetic algorithm (NSGA-II). This helps in obtaining global-optimal solutions faster, particularly for problems involving networks. This is because the optimal values of some decision variables in such problems may be 0 or 1, e.g., some streams may be nonexistent in the optimal configuration. It is difficult to generate such chromosomes in the binary-coded NSGA-II (or the unmodified version of the real coded NSGA-II) using the three conventional operations of reproduction, crossover, and mutation. The algorithm developed is used to solve a few sample simple problems involving froth flotation circuits, which represent an important problem in mineral beneficiation. A two-species, two-cell flotation circuit is studied. Both single-objective as well as multi-objective optimizations are performed. The two important objectives used are as follows: (i) the maximization of the recovery of the concentrated ore and (ii) the maximization of the valuable-mineral content (grade) in the concentrated ore. A constraint of a fixed total flotation cell volume is also used. Because these objectives are conflicting, Pareto sets of nondominated solutions are obtained. The algorithm also can be used for the optimization of other networks.