Springer Adaptive Scalarization Methods in Multiobjective Optimization (Vector Optimization)

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. Review From the reviews: "This monograph on vector optimization is besides theoretical basics … dedicated to skillful approximations of the whole efficient set. … This monograph shows experience of the author in the big field of the contents of this book and can be highly recommended to all who work (or want to work) with multicriteria problems." (Alfred Göpfert, Zentralblatt MATH, Vol. 1145, 2008) From the Back Cover This book presents new adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarizations. With the help of sensitivity results an adaptive parameter control is developed so that high-quality approximations of the efficient set are generated. These examinations are based on a general scalarization approach for arbitrary partial orderings defined by a closed pointed convex cone in the objective space. The application of the results to many other well-known scalarizationmethods is also presented. Background material of multiobjective optimization and scalarization approaches is concisely summarized at the beginning. The effectiveness of these new methods is demonstrated by test problems and a recent problem in intensity-modulated radiotherapy. The book concludes with a further application: a procedure for solving multiobjective bilevel optimization problems.