Review Reports

Round 1

Reviewer 1 Report

The author proposes a methodology to reduce the dimension of the stochastic programming problems for metallurgical design procedures using Design of Experiments (DoE), Supervised Machine Learning (SML), and Global Sensitive Analysis (GSA). 

The paper is well written and the information given for a communication paper can be acceptable. 

Few comments I have are the following:

• Define acronym ML at row 64
• The sentence at row 112-113 can be improved
• rows 169-171 can be supported by a scheme that helps the reader to visualize the difference between the two structures
• Figure 4 caption should describe the level bar label: what index does it represent? 

Author Response

1. Define acronym ML at row 64
2. R. The acronym ML was included in the manuscript.

 

2. The sentence at row 112-113 can be improved
3. R. The sentence was improved.

 

3. rows 169-171 can be supported by a scheme that helps the reader to visualize the difference between the two structures
4. R. The flotation plant structures were included in the manuscript

 

4. Figure 4 caption should describe the level bar label: what index does it represent?
5. R. A description of bar level was included in Figure 4 (now Figure 6)

Reviewer 2 Report

The manuscript deals with the uncertainty that characterizes the stochastic optimization problems and suggests ways to reduce the computational work time and effort of elaboration. Innovative approaches are used and compared with the traditional ones. More specifically, supervised machine learning tools and global sensitivity analysis are used in controversy with the traditional techniques of mixed-integer nonlinear programming or mixed-integer linear programming mathematical techniques. Comparatively, the former techniques reduce the effort and computational time, whereas the latter demand time and effort consuming. In addition, the machine learning tools create surrogate models that contribute to the simplification and comprehension of the models' results. Finally, a case study of flotation plant design is presented for the application of the proposed methodology.

Flotation is a physicochemical process that is followed in the context of metallurgical procedures. However, this procedure is complex because it consists of several stages and reveals many uncertainties among the variables. Therefore, the research topic is a crucial issue of mineral engineering, considering that the necessary effective modelling of the mineral processing systems is one of the most critical issues of mineral deposits viability. In this context, the manuscript could have a potential impact on the relevant field of research.

However, although an exploratory approach to the issue was adopted in a comprehensive literature search, I would expect a more critical and original review regarding previous work in this sector. In addition, from an engineering perspective, the practical considerations of the research need to be further discussed, and a separate section “Discussion” could be included. In this context, the findings and their implications could be better demonstrated.

Additional comments and recommendations for the improvement of the manuscript:

Abstract

 [Line 10] “On the other hand…and efficient” The supervised machine learning tools are suddenly mentioned in this point.

1. Introduction

General notes: Please clarify what is novel in the suggested approach and which are the research questions. In addition, a more critical review of the literature is needed concerning the manuscript’s research issue.  

[Lines 28 & 31] “This approach…” A clarification is needed here.

[Line 43-44] “…(Jamett et al., 43 2015; Liang et al., 2020a, 2020b).” Please check the citations to be mentioned in the same way as the other citations in the manuscript.

[Lines 47 & 49] “This approach…” Is it mentioned twice (for the same approach)?

[Lines 51-55] A further clarification is needed regarding the profitability parameters

[Line 63] “their tools”: A clarification is needed.

[Line 73] “…four stages…” Which are the four stages? A clarification is needed.

2. Methods

General note: The “2.4” subsection is mentioned as “Methodology” (?)

3. Applications

[Line 135] It is suggested to describe the design procedure that was implemented.

[Lines 146-148] The values could be shown in a table to help the reader.

[Lines 153-157] A further explanation is needed regarding the distribution functions.

[Line 164] “the problem outcomes”?

[Figure 1] The diagrams of Figure 1 should be improved to be more clear. Furthermore, the diagrams need to be further discussed.

[Line 190] “Figure” instead of “Figures”.

[Figure 1] The diagrams of Figure 2 need to be more clear.

[Line 260] “the minimization of mximum costs”?

4. Conclusions

General note: Conclusions need to be improved, focusing on the original contribution of the research.

Author Contributions: “software, F.L, and R.A.” ?

Author Response

1. [Lines 28 & 31] “This approach…” A clarification is needed here.

R. “This approach” is related to the design procedure described in the manuscript, which includes three ingredients.

2. [Line 43-44] “ (Jamett et al., 43 2015; Liang et al., 2020a, 2020b).” Please check the citations to be mentioned in the same way as the other citations in the manuscript.

R. The citations were standardized.

3. [Lines 47 & 49] “This approach…” Is it mentioned twice (for the same approach)?

R. The sentence was improved.

4. [Lines 51-55] A further clarification is needed regarding the profitability parameters

R. The profitability parameters mentioned in the manuscript require to known the size of equipment in each flotation stage, number of equipment in each flotation stage, time of residence in each flotation stage, and lifetime of the project, among other aspects, which increase the computational burden.

5. [Line 63] “their tools”: A clarification is needed.

R. The following sentence was included in the manuscript “Supervised machine learning tools such as artificial neural network, support vector machine, and AdaBoost, among others.

6. [Line 73] “…four stages…” Which are the four stages? A clarification is needed.

R. First, defining a stochastic optimization problem; second, replacing the stochastic problem by deterministic problems via a design of experiment, and solving each one separately; third, constructing surrogate models using the information collected and supervised machine learning tools; fourth, subjecting the surrogate models to global sensitivity analysis to reduce the uncertainty space of the stochastic formulation.

7. General note: The “2.4” subsection is mentioned as “Methodology” (?)

R. The title “methodology” of the subsection 2.4 was replaced by “Generic framework to reduce the uncertainty space”

8. [Line 135] It is suggested to describe the design procedure that was implemented.

R. The methodology proposed is illustrated using a procedure implemented to design flotation plants. This procedure is based on mathematical programming and considers the following aspects; first, a superstructure representing 2,304 alternatives of design including five flotation stages, splitters, and mixers; second, a mathematical model including mass balance, a bank model to estimate mineralogical species recoveries, and several objective functions, among other specifications, which results in a MINLP problem, for more detail see [20].

9. [Lines 146-148] The values could be shown in a table to help the reader.

R. Table 1 was included in the manuscript to help to reader.

10. [Lines 153-157] A further explanation is needed regarding the distribution functions.

R. The description of the distribution functions were included in Table 1.

11. [Line 164] “the problem outcomes”?

R. The word “the problem outcomes” was replaced by “output variables of design problem”

12. [Figure 1] The diagrams of Figure 1 should be improved to be more clear. Furthermore, the diagrams need to be further discussed.

R. Figure 1 was improved, in addition, in the manuscript, a new figure and the following comment were included: In order to study the effect of dataset size on the performance of surrogate models, the following procedure was implemented; first, the dataset (500 samples) obtained in the second stage of the methodology was sampled to generate sub-datasets of 100, 150, 200, 250, 300, 350, 400, 450, and 500 samples; second, sub-datasets were divided into training dataset (80%) and testing dataset (20%); third, training datasets were used to construct surrogate models and testing datasets were used to identify overfitting surrogate models [23]. Figures 2-3 reveal that the SML tools selected for the classification problems provided a good accuracy for predicting the structure of designed plants independent of dataset size, whereas the SML tools selected for regression, except RFR, provided a good average for predicting the metallurgical and profitability parameters of designed plants independent of dataset size.

13. [Line 190] “Figure” instead of “Figures”.

R. This wrong was improved in the manuscript.

14. [Figure 1] The diagrams of Figure 2 need to be more clear.

R. All figures in the manuscript were improved.

15. [Line 260] “the minimization of mximum costs”?

R. This sentence was improved

16. General note: Conclusions need to be improved, focusing on the original contribution of the research.

R. The following comment was included throughout the manuscript “The integration of supervised machine learning tools, global sensitivity analysis, and process design has been studied in the literature; however, its joint application in metallurgical process design has not been reported”

17. Author Contributions: “software, F.L, and R.A.”?

R. The word “R.A” was deleted.