Publication: Metodología multiobjetivo aplicada a análisis de datos
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2016-08-12
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Universidad Complutense de Madrid
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Abstract
En este trabajo, se realiza una presentación unificada de la Programación Multiobjetivo, describiendo y relacionando los distintos conceptos de solución y exponiendo las distintas técnicas de solución. Se formula el problema multiobjetivo mediante una séxtupla, (O, V, X, f, Y, EP), que permite unificar los muy diversos problemas multiobjetivo que surgen en distintos ámbitos. O representa el conjunto de objetos inicial, V representa el conjunto de las características relevantes que se miden sobre los objetos, X es el espacio de alternativas, f representa la familia de objetivos, Y es el espacio de resultados y EP es la estructura de preferencias del decisor. A partir de esta formulación, se realiza un amplio estudio de los distintos problemas multiobjetivo. Además, se aplica la metodología multiobjetivo a dos problemas concretos de gran interés práctico. En primer lugar, se aborda el problema de seleccionar el mejor tratamiento, cuando sobre las unidades experimentales, elegidas de forma aleatoria, se observan varias variables respuesta. Se consideran Modelos Discretos, Modelos Continuos Paramétricos y Modelos No Paramétricos. El último capítulo del trabajo, se dedica al estudio del problema multiobjetivo que se presenta cuando se desea representar, un conjunto finito de objetos, sobre la recta real, de forma que se refleje, lo más fielmente posible, la desemejanza de cada par de objetos. En el caso de que la desemejanza cumpla la propiedad de ser naturalmente ordenable, se ha diseñado y programado, un algoritmo, en tiempo polinomial, que obtiene la solución óptima del problema...
In this paper, a unified presentation of Multi-objective Programming is done, describing and relating the different concepts of solution and exposing the different technical solutions. The multi-objective problem is formulated by a sextuple, (O , V , X, f , Y, EP ) , to unify the diverse multi-objective problems in different areas. O represents the set of initial objects , V represents the set of relevant characteristics that are measured on objects, X is the space of alternatives, f represents the family of objectives, Y shows results is space and EP is the structure of preferences for the decider . From this formulation, a comprehensive study of the various multi-objective problems is carried out. Moreover, multi-objective methodology is applied to two specific problems of great practical interest. First, the problem of selecting the best treatment is dealt with, when on the experimental units, randomly chosen, several variables responses are observed. They are considered discrete models, Parametric continuous models and non-parametric. The last chapter covers the study of the multi-objective issue presented when a set of specific objects are to be represented on the real line, in the way that the dissimilarity in each pair of objects is shown as closely as possible. In the event that the dissimilarity meets the property of being naturally sortable, an algorithm, in polynomial time, has been designed and programmed, which means the optimal solution to the problem...
In this paper, a unified presentation of Multi-objective Programming is done, describing and relating the different concepts of solution and exposing the different technical solutions. The multi-objective problem is formulated by a sextuple, (O , V , X, f , Y, EP ) , to unify the diverse multi-objective problems in different areas. O represents the set of initial objects , V represents the set of relevant characteristics that are measured on objects, X is the space of alternatives, f represents the family of objectives, Y shows results is space and EP is the structure of preferences for the decider . From this formulation, a comprehensive study of the various multi-objective problems is carried out. Moreover, multi-objective methodology is applied to two specific problems of great practical interest. First, the problem of selecting the best treatment is dealt with, when on the experimental units, randomly chosen, several variables responses are observed. They are considered discrete models, Parametric continuous models and non-parametric. The last chapter covers the study of the multi-objective issue presented when a set of specific objects are to be represented on the real line, in the way that the dissimilarity in each pair of objects is shown as closely as possible. In the event that the dissimilarity meets the property of being naturally sortable, an algorithm, in polynomial time, has been designed and programmed, which means the optimal solution to the problem...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 22-01-2016