Adaptive Scalarization Methods in Multiobjective Optimization

Softcover Nachdruck of hardcover 1. Auflage 2008
ISBN: 978-3-642-09804-8
Verlag: Springer

Buch, Englisch, 241 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 394 g

Reihe: Vector Optimization

In many areas in engineering, economics and science new developments are only possible by the application of modern optimization methods. Theoptimizationproblemsarisingnowadaysinapplicationsaremostly multiobjective, i.e. many competing objectives are aspired all at once. These optimization problems with a vector-valued objective function have in opposition to scalar-valued problems generally not only one minimal solution but the solution set is very large. Thus the devel- ment of e?cient numerical methods for special classes of multiobj- tive optimization problems is, due to the complexity of the solution set, of special interest. This relevance is pointed out in many recent publications in application areas such as medicine ([63, 118, 100, 143]), engineering([112,126,133,211,224],referencesin[81]),environmental decision making ([137, 227]) or economics ([57, 65, 217, 234]). Consideringmultiobjectiveoptimizationproblemsdemands?rstthe de?nition of minimality for such problems. A ?rst minimality notion traces back to Edgeworth [59], 1881, and Pareto [180], 1896, using the naturalorderingintheimagespace.A?rstmathematicalconsideration ofthistopicwasdonebyKuhnandTucker[144]in1951.Sincethattime multiobjective optimization became an active research ?eld. Several books and survey papers have been published giving introductions to this topic, for instance [28, 60, 66, 76, 112, 124, 165, 188, 189, 190, 215]. Inthelastdecadesthemainfocuswasonthedevelopmentofinteractive methods for determining one single solution in an iterative process.

Zielgruppe

Research

Autoren/Hrsg.

Eichfelder, Gabriele

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Entscheidungstheorie, Sozialwahltheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

Theory.- Theoretical Basics of Multiobjective Optimization.- Scalarization Approaches.- Sensitivity Results for the Scalarizations.- Numerical Methods and Results.- Adaptive Parameter Control.- Numerical Results.- Application to Intensity Modulated Radiotherapy.- Multiobjective Bilevel Optimization.- Application to Multiobjective Bilevel Optimization.