Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design Procedures
Process design procedures under uncertainty result in stochastic optimization problems whose resolution is complex due to the large uncertainty space, which hinders the application of optimization approaches, as well as the establishment of relationships between input and output variables. On the ot...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-11-01
|
| Series: | Minerals |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-163X/11/12/1302 |
| _version_ | 1797502350702673920 |
|---|---|
| author | Freddy A. Lucay |
| author_facet | Freddy A. Lucay |
| author_sort | Freddy A. Lucay |
| collection | DOAJ |
| description | Process design procedures under uncertainty result in stochastic optimization problems whose resolution is complex due to the large uncertainty space, which hinders the application of optimization approaches, as well as the establishment of relationships between input and output variables. On the other hand, supervised machine learning (SML) offers tools with which to develop surrogate models, which are computationally inexpensive and efficient. This paper proposes a procedure based on modern design of experiments, deterministic optimization, SML tools, and global sensitivity analysis (GSA) to reduce the size of the uncertainty space for stochastic optimization problems. The proposal is illustrated with a case study based on the stochastic design of flotation plants. The results reveal that surrogate models of stochastic formulation enable the prediction of the structure, profitability parameters, and metallurgical parameters of designed flotation plants, as well as reducing the size of the uncertainty space via GSA and, consequently, establishing relationships between the input and output variables of the stochastic formulation. |
| first_indexed | 2024-03-10T03:31:51Z |
| format | Article |
| id | doaj.art-ee31782d9425465eb0cf34dd9d47d382 |
| institution | Directory Open Access Journal |
| issn | 2075-163X |
| language | English |
| last_indexed | 2024-03-10T03:31:51Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Minerals |
| spelling | doaj.art-ee31782d9425465eb0cf34dd9d47d3822023-11-23T09:40:53ZengMDPI AGMinerals2075-163X2021-11-011112130210.3390/min11121302Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design ProceduresFreddy A. Lucay0Escuela de Ingeniería Química, Pontificia Universidad Católica de Valparaíso, Valparaíso 2340000, ChileProcess design procedures under uncertainty result in stochastic optimization problems whose resolution is complex due to the large uncertainty space, which hinders the application of optimization approaches, as well as the establishment of relationships between input and output variables. On the other hand, supervised machine learning (SML) offers tools with which to develop surrogate models, which are computationally inexpensive and efficient. This paper proposes a procedure based on modern design of experiments, deterministic optimization, SML tools, and global sensitivity analysis (GSA) to reduce the size of the uncertainty space for stochastic optimization problems. The proposal is illustrated with a case study based on the stochastic design of flotation plants. The results reveal that surrogate models of stochastic formulation enable the prediction of the structure, profitability parameters, and metallurgical parameters of designed flotation plants, as well as reducing the size of the uncertainty space via GSA and, consequently, establishing relationships between the input and output variables of the stochastic formulation.https://www.mdpi.com/2075-163X/11/12/1302stochastic optimizationsupervised machine learningglobal sensitivity |
| spellingShingle | Freddy A. Lucay Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design Procedures Minerals stochastic optimization supervised machine learning global sensitivity |
| title | Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design Procedures |
| title_full | Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design Procedures |
| title_fullStr | Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design Procedures |
| title_full_unstemmed | Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design Procedures |
| title_short | Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design Procedures |
| title_sort | reducing the dimensions of the stochastic programming problems of metallurgical design procedures |
| topic | stochastic optimization supervised machine learning global sensitivity |
| url | https://www.mdpi.com/2075-163X/11/12/1302 |
| work_keys_str_mv | AT freddyalucay reducingthedimensionsofthestochasticprogrammingproblemsofmetallurgicaldesignprocedures |