Representing Sampled Pareto Frontiers as Parameterized Continuous Manifolds Using Self-Organizing Maps
| العنوان: | Representing Sampled Pareto Frontiers as Parameterized Continuous Manifolds Using Self-Organizing Maps |
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| المؤلفون: | Brian J. German, Matthew J. Daskilewicz |
| المصدر: | AIAA Journal. 52:2480-2490 |
| بيانات النشر: | American Institute of Aeronautics and Astronautics (AIAA), 2014. |
| سنة النشر: | 2014 |
| مصطلحات موضوعية: | Combinatorics, Self-organizing map, Variables, media_common.quotation_subject, Coordinate system, Pareto principle, Evolutionary algorithm, Aerospace Engineering, Parameterized complexity, Monotonic function, media_common, Sign (mathematics), Mathematics |
| الوصف: | This paper describes a method for defining a coordinate system to parameterize a sampled Pareto frontier of a continuous multi-attribute design problem using a modified self-organizing map. By defining such a coordinate system, the design problem may be reformulated from y=f(x) to (y,x)=g(ψ), where x is a vector of design variables, y is a vector of attributes, and ψ is a vector of barycentric coordinates. Exploration of the design problem using ψ as the independent variables has the following desirable properties: 1) Every vector ψ corresponds to a Pareto efficient design, and every Pareto efficient design has a corresponding ψ. 2) The number of ψ coordinates is equal to the number of attributes, regardless of the number of design variables. 3) Each attribute yi has a corresponding coordinate ψi such that the sign of ∂yi/∂ψi is positive if the objective is to maximize yi and negative if the objective is to minimize yi (i.e., the attributes improve monotonically as their corresponding coordinates increase... |
| تدمد: | 1533-385X 0001-1452 |
| DOI: | 10.2514/1.j052849 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::aa1fffe2af43a439130b519292b5cf24 https://doi.org/10.2514/1.j052849 |
| رقم الانضمام: | edsair.doi...........aa1fffe2af43a439130b519292b5cf24 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 1533385X 00011452 |
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| DOI: | 10.2514/1.j052849 |