Article
Multi-Objective Optimization of Forth Flotation Process: An
Application in Gold Ore
Wen Zhang
1
, Qinghe Yuan
1,2,
*, Shun Jia
1,2,
*, Zhaojun (Steven) Li
3,
* and Xianhui Yin
4
Citation: Zhang, W.; Yuan, Q.; Jia, S.;
Li, Z.; Yin, X. Multi-Objective
Optimization of Forth Flotation
Process: An Application in Gold Ore.
Sustainability 2021, 13, 8314.
https://doi.org/10.3390/su13158314
Academic Editor: Paolo Renna
Received: 11 June 2021
Accepted: 12 July 2021
Published: 26 July 2021
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4.0/).
1
Department of Industrial Engineering, College of Energy and Mining Engineering, Shandong University of
Science and Technology, Qingdao 266590, China; zw1468038343@163.com
2
National Demonstration Center for Experimental Mining Engineering Education, Qingdao 266590, China
3
Department of Industrial Engineering & Engineering Management, College of Engineering, Western New
England University, Springfield, MA 01119, USA
4
College of Quality and Standardization, Qingdao University, Qingdao 266071, China;
qsyinxianhui@qdu.edu.cn
* Correspondence: yuan_qinghe@sina.com (Q.Y.); herojiashun@163.com (S.J.); zhaojun.li@wne.edu (Z.L.)
Abstract:
In order to improve production control ability in the gold ore flotation process, the output
index in this process was studied. Flotation is an effective gold recovery process. Gold concentrate
grade and gold recovery rate are the key output indicators of the flotation process. However, in the
existing studies exploring the impact of parameter changes on the output indicators, the control
ability of the output indicators is insufficient, and the interaction between variables is inadequately
considered. Therefore, a multi-objective optimization model based on response surface methodology
and the non-dominated sorting genetic algorithm-II (NSGA-II) is proposed in this paper. Firstly, the
experiment was designed based on the Box-Behnken principle. Based on the experimental results,
the interaction between variables was analyzed and the response polynomial was fitted. Secondly, a
multi-objective optimization model was constructed, and the NSGA-II was used to solve the model.
Finally, an example of gold ore flotation was used to verify the effectiveness of the method. The
optimal solution was a gold concentrate grade of 75.46 g/t and a gold recovery rate of 85.98%.
Keywords:
response surface methodology; NSGA-II; gold ore flotation process; multi-objective opti-
mization
1. Introduction
With the continuous development of science and technology, gold has been widely
used in communications, electronics, aviation, medicine, and other fields. The increase
in demand for gold requires that all links in the gold mining process need to increase
production capacity. Ore beneficiation is an indispensable part of the processing of mineral
resources and occupies an important position in the process of mineral production [
1
].
Gravity separation, mercury mixing, flotation, and cyanidation are commonly used benefi-
ciation technologies for gold ore treatment [
2
]. Gold ore flotation is a method for separating
ore by using the differences in the physical or the chemical properties of the ore surface.
Gold ore flotation is a continuous, complex industrial process with strong nonlinearity,
strong coupling, multiple inputs, and multiple outputs. Knowing how to accurately derive
the best input variables in a complex industrial process is very important to achieving
the required final product quality [
3
]. In recent years, the process parameters and the
dosage of reagents in the flotation process have been extensively studied [
4
]. Although
extensive research has been carried out on the gold ore flotation process, no single study
exists which adequately covers the interactions among parameters. The prior optimization
method was used to study the flotation process, and the output index was obtained through
experiments after the parameters changed. One major drawback of this approach is that
the output control of the flotation process is not conductive. The research would have
Sustainability 2021, 13, 8314. https://doi.org/10.3390/su13158314 https://www.mdpi.com/journal/sustainability
