ISBN 9783843953504

978-3-8439-5350-4, Reihe Mathematik

Stephan Helfrich
Approximation and Scalarization in Multiobjective Optimization

247 Seiten, Dissertation Technische Universität Kaiserslautern (2023), Hardcover, A5

Zusammenfassung / Abstract

In multiobjective optimization problems, where multiple objectives are to be optimized simultaneously, unique optimal solutions usually do not exist. Instead, one is interested in the set of all nondominated images that reflect each possible trade-off of the individual objectives, and at least one efficient solution associated to each nondominated image. In cases in that the number of nondominated images is enormous, computing approximation sets is a preferable and frequently chosen alternative. Such sets contain, for each image, a solution whose image is as good up to a multiplicative constant. Scalarizations, which transform the multiobjective optimization problem into solvable or approximable single-objective optimization problems by means of additional parameters, are an important building block to obtain both exact and approximate solution sets. This thesis deals with a systematic study of scalarizations, the structure of their parameter sets as well as their interrelations to efficient and approximate solutions.