| Adaptive Scalarization Methods in Multiobjective Optimization 2008 Edition Contributor(s): Eichfelder, Gabriele (Author) |
|
 |
ISBN: 3540791574 ISBN-13: 9783540791577 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: June 2008 Annotation: This book presents adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarization approaches. With the help of sensitivity results an adaptive parameter control is developed such that high-quality approximations of the efficient set are generated. These examinations are based on a special scalarization approach, but the application of these results to many other well-known scalarization methods is also presented. Thereby very general multiobjective optimization problems are considered with an arbitrary partial ordering defined by a closed pointed convex cone in the objective space. The effectiveness of these new methods is demonstrated with several test problems as well as with a recent problem in intensity-modulated radiotherapy. The book concludes with a further application: a procedure for solving multiobjective bilevel optimization problems is given and is applied to a bicriteria bilevel problem in medical engineering. |
| Additional Information |
| BISAC Categories: - Business & Economics | Operations Research - Mathematics | Discrete Mathematics - Computers | Data Processing |
| Dewey: 519.7 |
| LCCN: 2008924782 |
| Series: Vector Optimization |
| Physical Information: 0.63" H x 6.14" W x 9.21" (1.18 lbs) 241 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |