4 research outputs found

    Domination and Decomposition in Multiobjective Programming

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    During the last few decades, multiobjective programming has received much attention for both its numerous theoretical advances as well as its continued success in modeling and solving real-life decision problems in business and engineering. In extension of the traditionally adopted concept of Pareto optimality, this research investigates the more general notion of domination and establishes various theoretical results that lead to new optimization methods and support decision making. After a preparatory discussion of some preliminaries and a review of the relevant literature, several new findings are presented that characterize the nondominated set of a general vector optimization problem for which the underlying domination structure is defined in terms of different cones. Using concepts from linear algebra and convex analysis, a well known result relating nondominated points for polyhedral cones with Pareto solutions is generalized to nonpolyhedral cones that are induced by positively homogeneous functions, and to translated polyhedral cones that are used to describe a notion of approximate nondominance. Pareto-oriented scalarization methods are modified and several new solution approaches are proposed for these two classes of cones. In addition, necessary and sufficient conditions for nondominance with respect to a variable domination cone are developed, and some more specific results for the case of Bishop-Phelps cones are derived. Based on the above findings, a decomposition framework is proposed for the solution of multi-scenario and large-scale multiobjective programs and analyzed in terms of the efficiency relationships between the original and the decomposed subproblems. Using the concept of approximate nondominance, an interactive decision making procedure is formulated to coordinate tradeoffs between these subproblems and applied to selected problems from portfolio optimization and engineering design. Some introductory remarks and concluding comments together with ideas and research directions for possible future work complete this dissertation

    M茅todos de escalarizaci贸n en optimizaci贸n multiobjetivo

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    Tesis (Lic. en Matem谩tica)--Universidad Nacional de C贸rdoba, Facultad de Matem谩tica, Astronom铆a, F铆sica y Computaci贸n, 2020.La vida inevitablemente involucra la toma de decisiones y elecciones y es natural querer que estas sean las mejores posibles, en otras palabras, sean 贸ptimas. La dificultad aqu铆 radica en el conflicto (al menos parcial) entre nuestros diversos objetivos y metas. Los problemas con m煤ltiples objetivos y criterios son generalmente conocidos como problemas de optimizaci贸n multiobjetivo. A lo largo de este trabajo, se presentaron los conceptos necesarios y algunos m茅todos para resolver problemas de optimizaci贸n multiobjetivo. Resolver un problema de optimizaci贸n multiobjetivo significa encontrar el conjunto de soluciones Pareto optimal o frente de Pareto. Los m茅todos fueron divididos en cuatro categor铆as seg煤n la articulaci贸n de preferencias de un tomador de decisiones. De cada m茅todo se estudiaron las ventajas y desventajas y se seleccionaron tres m茅todos para estudiar con mayor profundidad. Los m茅todos seleccionados fueron m茅todos de escalarizaci贸n; el m茅todo de sumas ponderadas, restricci贸n 蔚 y m茅tricas ponderadas, que adem谩s fueron implementados para generar una aproximaci贸n del frente de Pareto. Se seleccionaron problemas test para generar aproximaciones de sus frentes de Pareto y analizar los resultados obtenidos. Se encontr贸 que ning煤n m茅todo es superior que otro. La selecci贸n de un m茅todo espec铆fico depende del tipo de informaci贸n que proporciona el problema, las preferencias del usuario, los requisitos de la soluci贸n y la capacidad de c贸mputo.Life inevitably involves decision making and choices and it is natural to want them to be the best possible, in other words, to be optimal. The difficulty here lies in the (at least partial) conflict between our various goals and objectives. Problems with multiple objectives and criteria are generally known as multiobjective optimization problems. Throughout this work, the necessary concepts and some methods to solve multiobjective optimization problems were presented. Solving a multiobjective optimization problem means finding the optimal Pareto solution set or Pareto front. The methods were divided into four categories according to the articulation of preferences of a decision maker. The advantages and disadvantages of each method were studied, and three methods were selected for further study. The selected methods were scalarization methods; the method of weighted sums, 蔚 -constraint, and weighted metrics, which were also implemented to generate an approximation of the Pareto front. Test problems were selected to generate approximations of their Pareto fronts and to analyze the results obtained. It was found that no one method is superior to another. Selecting a specific method depends on the type of information the problem provides, the user preferences, the solution requirements, and the computational capacity.Fil: Fonseca, Roc铆o Guadalupe. Universidad Nacional de C贸rdoba. Facultad de Matem谩tica, Astronom铆a, F铆sica y Computaci贸n; Argentina

    Aeronautical Engineering: A continuing bibliography with indexes, supplement 174

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    This bibliography lists 466 reports, articles and other documents introduced into the NASA scientific and technical information system in April 1984

    Aeronautical Engineering: a Continuing Bibliography with Indexes (Supplement 243)

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    This bibliography lists 423 reports, articles, and other documents introduced into the NASA scientific and technical information system in August 1989. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics
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