Robustness to uncertain optimization using scalarization techniques and relations to multiobjective optimization

ABSTRACT

In this paper, we propose two kinds of robustness concepts by virtue of the scalarization techniques (Benson’s method and elastic constraint method) in multiobjective optimization, which can be characterized as special cases of a general non-linear scalarizing approach. Moreover, we introduce both constrained and unconstrained multiobjective optimization problems and discuss their relations to scalar robust optimization problems. Particularly, optimal solutions of scalar robust optimization problems are weakly efficient solutions for the unconstrained multiobjective optimization problem, and these solutions are efficient under uniqueness assumptions. Two examples are employed to illustrate those results. Finally, the connections between robustness concepts and risk measures in investment decision problems are also revealed.

KEYWORDS:

• Robust optimization
• robustness
• non-linear scalarization
• multiobjective optimization

AMS SUBJECT CLASSIFICATIONS:

• 90C31
• 90C29
• 90C30

Acknowledgements

The authors gratefully thank the anonymous referees for their constructive suggestions and comments which have helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant number 11301567], [grant number 11571055].