Kurzbeschreibung
This book presents adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarization approaches. Readers will benefit from the new adaptive methods and ideas for solving multiobjective optimization.
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.
Beschreibung
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.