The relationship between multi-objective robustness concepts and set-valued optimization

Fixexd point theory and applications

bel²  Daishi Kuroiwa³  Jonas Ide⁴  Christiane Tammer⁴  Anita Schö⁵  Elisabeth Kö⁶  bis⁷ 

[1] Martin-Luther-University Halle-Wittenberg, Halle, Germany;Shimane University, Hamada, Shimane, Japan;University Erlangen-NüUniversity Görnberg, Bavaria, Germany;ttingen, Göttingen, Germany

关键词: robust optimization;    multi-objective optimization;    scalarization;    vectorization;    set-valued optimization;   

DOI  :  10.1186/1687-1812-2014-83

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we discuss the connection between concepts of robustness for multi-objective optimization problems and set order relations. We extend some of the existing concepts to general spaces and cones using set relations. Furthermore, we derive new concepts of robustness for multi-objective optimization problems. We point out that robust multi-objective optimization can be interpreted as an application of set-valued optimization. Furthermore, we develop new algorithms for solving uncertain multi-objective optimization problems. These algorithms can be used in order to solve a special class of set-valued optimization problems.

【 授权许可】

CC BY