Optimization of the performance of flotation circuits using a genetic algorithm oriented by process-based rules

Hybrid Serving of DOE and RNN-Based Methods to Optimize and Simulate a Copper Flotation Circuit

Prediction of metallurgical responses during the flotation process is extremely vital to increase the process efficiency using a proper modeling approach. In this study, two new variants of the recurrent neural network (RNN) method were used to predict the copper ore flotation indices, i.e., grade and recovery within different operating conditions. The model input parameters including pulp pH and solid content as well as frother and collector dosages were first analysed and then optimized using a two-step factorial approach. The statistical analysis showed a reliable correlation between operating parameters and copper grade and recovery with coefficients of 99.86% and 94.50%, respectively. The main effect plots indicated that pulp pH and solid content positively affect copper grade while increasing the frother and collector dosages negatively influenced the quality of the final concentrate. Despite the same effect from pulp pH, reverse effects from other variables were observed for copper recovery. Process optimization revealed that maximum copper recovery of 44.39% with a grade of 11.48% could be achieved under the optimal condition as pulp pH of 10, solid content of 20%, and frother and collector concentrations of 25 g/t and 9.9 g/t, respectively. Then, the predictive efficiency of long short-term memory (LSTM) and gated recurrent unit (GRU) networks with proper structure were evaluated using mean square error (MSE), root mean square error (RMSE), mean absolute percentage error (MAPE), and correlation coefficient (R2). The simulation results showed that the LSTM network with higher R2 of 0.963 and 0.934 for copper grade and recovery, respectively, was more effective than the GRU algorithm with the corresponding values of 0.956 and 0.919, respectively. The results show that the LSTM model could be useful in predicting the copper flotation behaviour in response to changes in the operating parameters.

The Use of Neural Networks in Combination with Evolutionary Algorithms to Optimise the Copper Flotation Enrichment Process

The paper presents a way of combining neural networks with evolutionary algorithms in order to find optimal parameters of the copper flotation enrichment process. The neural network was used in order to build a model describing the flotation process. The network learning was carried out with the use of samples from previous empirical measurements of the actual process. The model created in this way made it possible to find optimal parameters not only from among the measurement spaces, but also those that go beyond the measurements. Then, evolutionary algorithms were used in order to find optimal flotation parameters. The learned neural network previously described was used to calculate the criterion in the evolutionary algorithm.

Trends in Modeling, Design, and Optimization of Multiphase Systems in Minerals Processing

Multiphase systems are important in minerals processing, and usually include solid–solid and solid–fluid systems, such as in wet grinding, flotation, dewatering, and magnetic separation, among several other unit operations. In this paper, the current trends in the process system engineering tasks of modeling, design, and optimization in multiphase systems, are analyzed. Different scales of size and time are included, and therefore, the analysis includes modeling at the molecular level (molecular dynamic modeling) and unit operation level (e.g., computational fluid dynamic, CFD), and the application of optimization for the design of a plant. New strategies for the modeling, design, and optimization of multiphase systems are also included, with a strong focus on the application of artificial intelligence (AI) and the combination of experimentation and modeling with response surface methodology (RSM). The integration of different modeling techniques such as CFD with discrete element simulation (DEM) and response surface methodology (RSM) with artificial neural networks (ANN) is included. The paper finishes with tools to study the uncertainty, both epistemic and stochastic, based on uncertainty and global sensitivity analyses, which is present in all mineral processing operations. It is shown that all of these areas are very active and can help in the understanding, operation, design, and optimization of mineral processing that involves multiphase systems. Future needs, such as meso-scale modeling, are highlighted.

Design of Flotation Circuits Using Tabu-Search Algorithms: Multispecies, Equipment Design, and Profitability Parameters

The design of a flotation circuit based on optimization techniques requires a superstructure for representing a set of alternatives, a mathematical model for modeling the alternatives, and an optimization technique for solving the problem. The optimization techniques are classified into exact and approximate methods. The first has been widely used. However, the probability of finding an optimal solution decreases when the problem size increases. Genetic algorithms have been the approximate method used for designing flotation circuits when the studied problems were small. The Tabu-search algorithm (TSA) is an approximate method used for solving combinatorial optimization problems. This algorithm is an adaptive procedure that has the ability to employ many other methods. The TSA uses short-term memory to prevent the algorithm from being trapped in cycles. The TSA has many practical advantages but has not been used for designing flotation circuits. We propose using the TSA for solving the flotation circuit design problem. The TSA implemented in this work applies diversification and intensification strategies: diversification is used for exploring new regions, and intensification for exploring regions close to a good solution. Four cases were analyzed to demonstrate the applicability of the algorithm: different objective function, different mathematical models, and a benchmarking between TSA and Baron solver. The results indicate that the developed algorithm presents the ability to converge to a solution optimal or near optimal for a complex combination of requirements and constraints, whereas other methods do not. TSA and the Baron solver provide similar designs, but TSA is faster. We conclude that the developed TSA could be useful in the design of full-scale concentration circuits.