Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters
A common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous a...
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-04-01
|
| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/26/2/36 |
| _version_ | 1797536429069303808 |
|---|---|
| author | Alejandro Estrada-Padilla Daniela Lopez-Garcia Claudia Gómez-Santillán Héctor Joaquín Fraire-Huacuja Laura Cruz-Reyes Nelson Rangel-Valdez María Lucila Morales-Rodríguez |
| author_facet | Alejandro Estrada-Padilla Daniela Lopez-Garcia Claudia Gómez-Santillán Héctor Joaquín Fraire-Huacuja Laura Cruz-Reyes Nelson Rangel-Valdez María Lucila Morales-Rodríguez |
| author_sort | Alejandro Estrada-Padilla |
| collection | DOAJ |
| description | A common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous applications in optimization. However, so far, they have not been used to tackle uncertainty in MOPOP. Hence, this work proposes to tackle MOPOP’s uncertainty with a new optimization model based on fuzzy trapezoidal parameters. Additionally, it proposes three novel steady-state algorithms as the model’s solution process. One approach integrates the Fuzzy Adaptive Multi-objective Evolutionary (FAME) methodology; the other two apply the Non-Dominated Genetic Algorithm (NSGA-II) methodology. One steady-state algorithm uses the Spatial Spread Deviation as a density estimator to improve the Pareto fronts’ distribution. This research work’s final contribution is developing a new defuzzification mapping that allows measuring algorithms’ performance using widely known metrics. The results show a significant difference in performance favoring the proposed steady-state algorithm based on the FAME methodology. |
| first_indexed | 2024-03-10T12:00:35Z |
| format | Article |
| id | doaj.art-17fd3836ac8d43bcb758c9a01cdff090 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T12:00:35Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-17fd3836ac8d43bcb758c9a01cdff0902023-11-21T16:58:16ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472021-04-012623610.3390/mca26020036Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy ParametersAlejandro Estrada-Padilla0Daniela Lopez-Garcia1Claudia Gómez-Santillán2Héctor Joaquín Fraire-Huacuja3Laura Cruz-Reyes4Nelson Rangel-Valdez5María Lucila Morales-Rodríguez6Graduate Program Division, Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Ciudad Madero 89440, MexicoGraduate Program Division, Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Ciudad Madero 89440, MexicoGraduate Program Division, Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Ciudad Madero 89440, MexicoGraduate Program Division, Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Ciudad Madero 89440, MexicoGraduate Program Division, Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Ciudad Madero 89440, MexicoGraduate Program Division, Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Ciudad Madero 89440, MexicoGraduate Program Division, Tecnológico Nacional de México/Instituto Tecnológico de Ciudad Madero, Ciudad Madero 89440, MexicoA common issue in the Multi-Objective Portfolio Optimization Problem (MOPOP) is the presence of uncertainty that affects individual decisions, e.g., variations on resources or benefits of projects. Fuzzy numbers are successful in dealing with imprecise numerical quantities, and they found numerous applications in optimization. However, so far, they have not been used to tackle uncertainty in MOPOP. Hence, this work proposes to tackle MOPOP’s uncertainty with a new optimization model based on fuzzy trapezoidal parameters. Additionally, it proposes three novel steady-state algorithms as the model’s solution process. One approach integrates the Fuzzy Adaptive Multi-objective Evolutionary (FAME) methodology; the other two apply the Non-Dominated Genetic Algorithm (NSGA-II) methodology. One steady-state algorithm uses the Spatial Spread Deviation as a density estimator to improve the Pareto fronts’ distribution. This research work’s final contribution is developing a new defuzzification mapping that allows measuring algorithms’ performance using widely known metrics. The results show a significant difference in performance favoring the proposed steady-state algorithm based on the FAME methodology.https://www.mdpi.com/2297-8747/26/2/36multi-objective optimizationmulti-objective portfolio optimization problemtrapezoidal fuzzy numbersdensity estimatorssteady state algorithms |
| spellingShingle | Alejandro Estrada-Padilla Daniela Lopez-Garcia Claudia Gómez-Santillán Héctor Joaquín Fraire-Huacuja Laura Cruz-Reyes Nelson Rangel-Valdez María Lucila Morales-Rodríguez Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters Mathematical and Computational Applications multi-objective optimization multi-objective portfolio optimization problem trapezoidal fuzzy numbers density estimators steady state algorithms |
| title | Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters |
| title_full | Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters |
| title_fullStr | Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters |
| title_full_unstemmed | Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters |
| title_short | Modeling and Optimizing the Multi-Objective Portfolio Optimization Problem with Trapezoidal Fuzzy Parameters |
| title_sort | modeling and optimizing the multi objective portfolio optimization problem with trapezoidal fuzzy parameters |
| topic | multi-objective optimization multi-objective portfolio optimization problem trapezoidal fuzzy numbers density estimators steady state algorithms |
| url | https://www.mdpi.com/2297-8747/26/2/36 |
| work_keys_str_mv | AT alejandroestradapadilla modelingandoptimizingthemultiobjectiveportfoliooptimizationproblemwithtrapezoidalfuzzyparameters AT danielalopezgarcia modelingandoptimizingthemultiobjectiveportfoliooptimizationproblemwithtrapezoidalfuzzyparameters AT claudiagomezsantillan modelingandoptimizingthemultiobjectiveportfoliooptimizationproblemwithtrapezoidalfuzzyparameters AT hectorjoaquinfrairehuacuja modelingandoptimizingthemultiobjectiveportfoliooptimizationproblemwithtrapezoidalfuzzyparameters AT lauracruzreyes modelingandoptimizingthemultiobjectiveportfoliooptimizationproblemwithtrapezoidalfuzzyparameters AT nelsonrangelvaldez modelingandoptimizingthemultiobjectiveportfoliooptimizationproblemwithtrapezoidalfuzzyparameters AT marialucilamoralesrodriguez modelingandoptimizingthemultiobjectiveportfoliooptimizationproblemwithtrapezoidalfuzzyparameters |