Theoretical and practical aspects of probabilistic models in solving real optimization problems
Keywords:
Probabilistic models, Estimation of Distributions Algorithms, covariance matrix estimation, optimization problems, task schedulingAbstract
Introduction: Probabilistic and statistical models constitute tools of great importance for solving real optimization or classification problems. These tools are applied for decision making in transportation, agriculture, economics or pharmaceutical industry.
Objectives: To develop probabilistic models in the solution of real optimization problems, both for discrete and continuous domain, planning and unbalanced ranking.
Methods: The proposed algorithms were evaluated in several theoretical and practical optimization problems, as well as international databases. The parameters of the algorithms were adjusted and statistical techniques were applied to validate the results.
Results: The results of this research contribute, mainly, to all those sectors and organizations that require efficient decision making in the planning and use of their resources. This includes problems of transportation, electricity, agriculture, economy or the pharmaceutical industry. This research contributes to the professional training of young university graduates, thus enriching the universities teaching staff.
Conclusions: The proposed algorithms using probabilistic models for the solution of optimization problems constitute a powerful tool for decision making in real environments. The results demonstrate the superiority of these techniques compared to others in the state of the art.
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1. McCullagh P. What is a statistical model? Ann Stat [Internet]. 2002 [citado 19 sep 2023]; 30:1225–310. Disponible en: https://doi.org/10.1214/aos/1035844977
2. Adèr HJ. Modelling. In: Adèr HJ, Mellenbergh GJ, editors. Advising on research methods: a consultant's companion. Huizen, The Netherlands: Johannes van Kessel Publishing; 2008. p. 271-304
3. Burnham KP, Anderson DR. Model selection and multimodel inference. 2nd ed. Springer-Verlag; 2002. ISBN: 0-387-95364-7.
4. Cox DR. Principles of statistical inference. Cambridge University Press; 2006.
5. Konishi S, Kitagawa G. Information criteria and statistical modeling. Springer; 2008.
6. Scutari M. Bayesian network structure learning, parameter learning and inference. 2011.
7. Madera J. Hacia un generación más eficiente de algoritmos evolutivos con estimación de distribuciones: Pruebas de independencia + paralelismo [tesis doctoral]. La Habana: Universidad de La Habana; 2009.
8. Martínez-López Y, Madera J, Rodríguez-González Q, Barigye S. Cellular Estimation Gaussian Algorithm for Continuous Domain. J Intell Fuzzy Syst [Internet]. 2019 [citado 11 nov 2023];36(5):4957-67. Disponible en: https://doi.org/10.3233/JIFS-179042
9. Richardson Ibañez J. Algoritmos Evolutivos Estimadores de Distribución Celulares para Problemas de Optimización Continuos [tesis]. Camagüey: Universidad de Camagüey; 2017.
10. Rodríguez-González AY, Lezama F, Martínez-López Y, Madera J, Soares J, Vale Z. WCCI/GECCO 2020 Competition on Evolutionary Computation in the Energy Domain: An overview from the winner perspective. Appl Soft Comput [Internet]. 2022 [citado 5 nov 2023]; 109162. Disponible en: https://doi.org/10.1016/j.asoc.2022.109162
11. Zaldívar-Pino O. Biblioteca de clases en R para el trabajo con algoritmos que estiman distribuciones [tesis]. Camagüey: Universidad de Camagüey; 2013.
12. Leguen-de-Varona I, Madera J, Martínez-López Y, Hernández-Nieto J. Over-sampling imbalanced datasets using the Covariance Matrix. EAI Endorsed Trans Energy Web [Internet]. 2020 [citado 18 sep 2023]. Disponible en: https://doi.org/10.4108/eai.13-7-2018.163982
13. Leguen-de-Varona I, Madera J, Martínez-López Y, Hernández-Nieto J. SMOTE-Cov: A new oversampling method based on the Covariance Matrix. In: Litvinchev PI, Marmolejo-Saucedo JA, Rodriguez-Aguilar R, Martinez-Rios F, editors. Data analysis and optimization for engineering and computing problems [Internet]. Cham: Springer; 2020 [citado 18 sep 2023]. p. 207-17. Disponible en: https://doi.org/10.1007/978-3-030-48149-0_15
14. Leguen-de-Varona I. Algoritmo basado en la estimación de la Matriz de Covarianza para balancear conjuntos de datos sobre dominio continuo y clase binaria [tesis]. Universidad de Camagüey; 2018.
15. Leguen-de-Varona I, Madera J, Martínez-López Y, Hernández-Nieto JC. Smote-Cov: A new oversampling method based on the Covariance Matrix. Presentado en: Ciudad de México, México; 2019 nov 28.
16. Mahdi GS. Algoritmos de estimación de distribuciones con tratamiento de restricciones para la construcción de cronogramas de proyectos [tesis doctoral]. La Habana: CUJAE; 2021.
17. Madera J, Ochoa A. Evaluating the Max-Min Hill-Climbing Estimation of Distribution Algorithm on B-Functions. In: Hernández Heredia Y, Milián Núñez V, Ruiz Shulcloper J, editors. Progress in Artificial Intelligence and Pattern Recognition. IWAIPR 2018. Lecture Notes in Computer Science, vol 11047 [Internet]. Cham: Springer; 2018 [citado 21 sep 2023]. p. 1-12. Disponible en: https://doi.org/10.1007/978-3-030-01132-1_3
18. Martínez-López Y, Rodríguez AY, Madera J, Mayedo MB, Moya A, Salgado OM. Applying Some EDAs and Hybrid Variants to the ERM Problem Under Uncertainty. ACM [Internet]; 2020 [citado 5 nov 2023]. Disponible en: https://doi.org/10.1145/3377929.3398393
19. Martínez-López Y, Guevara Yanes L, Madera Quintana J. Aplicación de metaheurísticas en el ordenamiento del transporte urbano en Camagüey. Rev Cubana Transform Digit [Internet]. 2022 [citado 23 oct 2023];3(2):e171. Disponible en: https://rctd.uic.cu/rctd/article/view/171
20. Martínez-López Y, Oquendo H, Mota YC, Guerra-Rodríguez LE, Junco R, Benítez I, Madera J. Aplicación de la investigación de operaciones a la distribución de recursos relacionados con la COVID-19. Retos Dirección [Internet]. 2020 [citado 21 nov 2023]. Disponible en: http://scielo.sld.cu/pdf/rdir/v14n2/2306-9155-rdir-14-02-86.pdf
21. Mahdi GS, Quintana JM, Pérez PP, Al-subhi SH. Estimation of Distribution Algorithm for solving the Multi-mode Resource Constrained Project Scheduling Problem. EAI Endorsed Trans Energy Web [Internet]. 2020 [citado 12 oct 2023]. Disponible en: https://doi.org/10.4108/eai.13-7-2018.164111.
22. Martínez-López Y, Madera J, Mahdi GS, Rodríguez-González AY. Cellular estimation bayesian algorithm for discrete optimization problems. Investigación Operacional [Internet]. 2020 [citado 21 nov 2023]. Disponible en: https://rev-inv-ope.pantheonsorbonne.fr/sites/default/files/inline-files/41720-10.pdf
23. Guerra M, Madera J. WIFROWAN: Wrapped Imbalanced Fuzzy-Rough Ordered Weighted Average Nearest Neighbor Classification. Computación y Sistemas [Internet]. 2020 [citado 13 sep 2023]. Disponible en: https://doi.org/10.13053/cys-24-3-3054
24. Madera J, Martínez López Y, Fernández-Pardo J. Algoritmo de Estimación de Distribución basado en el Aprendizaje de Redes Bayesianas con Pruebas de Independencias para Problemas de Optimización en Enteros. Rev Cubana Cienc Inform [Internet]. 2020 [citado 2 oct 2023]; 14(4):1–19. ISSN: 2227-1899. Disponible en: https://rcci.uci.cu/?journal=rcci&page=article&op=download&path%5B%5D=2019&path%5B%5D=832
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Copyright (c) 2025 Julio Madera QUintana, Yoan Martínez López, Yoan Martínez López, Gaafar Sadeq Saeed Mahdi, Gaafar Sadeq Saeed Mahdi, Pedro Piñero Pérez, Pedro Piñero Pérez, Ansel Rodríguez González, Ansel Rodríguez González, Ireimis Leguen de Varona, Ireimis Leguen de Varona
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