Adaptive scalarization methods in multiobjective optimization
著者
書誌事項
Adaptive scalarization methods in multiobjective optimization
（Vector optimization）
Springer, c2008
- : [hard]
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注記
Includes bibliographical references (p. [219]-238) and index
内容説明・目次
内容説明
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.
目次
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.
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