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.

Soft computing-based modeling of flotation processes – A review

“…Genetic algorithm-based model Copper Gouws and Aldrich (1996) Guria et al (2005aGuria et al ( , 2005bGuria et al ( , 2006, and Ghobadi et al (2011) they can be used to obtain the desired flotation circuit configuration. The authors point out that technological parameters, such as the recovery or the concentrate grade, are suitable for use as a fitness function for the genetic algorithms.…”

“…In a study conducted by Guria et al (2005a) a superior nondominated sorting genetic algorithm with the modified jumping gene operator (NSGA-II-mJG) had been developed for the optimization of two flotation cell system configurations. According to these authors, the NSGA-II-mJG algorithm yielded better solutions, in comparison with the NSGA-II and NSGA-II-JG algorithms, when dealing with the relatively simple problem of flotation circuit optimization -including two groups of mineral particles, two flotation cells and a single-objective optimization (maximizing the mass recovery of the concentrate while ensuring a grade of the concentrate of 75.0% for a prescribed flotation cell volume of 0.5663 m 3 ).…”

Multi-objective Optimization: Bio-mimetic Adaptations of Genetic Algorithm

“…These include the binary-coded (fixed-length) NSGA-II-aJG [11,12] in which the number of binaries in the JG is fixed (a computational parameter) and (if the aJG adaptation is to be done on a chromosome) one has to select only one site, the starting point, of the JG randomly. The NSGA-II-mJG adaptation of Guria et al [13] has been found useful for network problems and has been applied for the optimization of froth flotation circuits. Agarwal and Gupta [14,15] developed NSGA-II-sJG and NSGA-II-saJG for optimizing a single heat exchanger or heat exchanger networks (HENs).…”

A real-coding jumping gene genetic algorithm (RJGGA) for multiobjective optimization

“…At present, various types of biologically-inspired adaptations can be found in the literature [52]. More recently, some adaptations of the jumping genes operator have been developed [26,51,52], but, they are mostly problem specific and implemented in the form of binary-coding.…”