Optimization of generalized desirability functions under model uncertainty

Abstract

Desirability functions are increasingly used in multi-criteria decision-making which we support by modern optimization. It is necessary to formulate desirability functions to obtain a generalized version with a piecewise max type-structure for optimizing them in different areas of mathematics, operational research, management science and engineering by nonsmooth optimization approaches. This optimization problem needs to be robustified as regression models employed by the desirability functions are typically built under lack of knowledge about the underlying model. In this paper, we contribute to the theory of desirability functions by our robustification approach. We present how generalized semi-infinite programming and disjunctive optimization can be used for this purpose. We show our findings on a numerical example. The robustification of the optimization problem eventually aims at variance reduction in the optimal solutions.

Keywords:

• Multi-response surface optimization
• desirability function
• model uncertainty
• generalized semi-infinite optimization
• disjunctive optimization

Acknowledgements

The authors would like to express their sincere gratitude to the anonymous referees for precious observations and recommendations, and to Editor and Managing Editor of Optimization as well as to the Guest Editors of the special issue for their support.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study is partially supported by The Scientific and Technological Research Council of Turkey (TUBITAK) [project number 105M138].