Optimizing multi-response surface problems: How to use multi-objective optimization techniques

A common problem encountered in product or process design is the selection of optimal parameter levels that involves the simultaneous consideration of multiple response characteristics, called a multi-response surface problem. Notwithstanding the importance of multi-response surface problems in practice, the development of an optimization scheme has received little attention. In this paper, we note that Multi-Response surface Optimization (MRO) can be viewed as a Multi-Objective Optimization (MOO) and that various techniques developed in MOO can be successfully utilized to deal with MRO problems. We also show that some of the existing desirability function approaches can, in fact, be characterized as special forms of MOO. We then demonstrate some MOO principles and methods in order to illustrate how these approaches can be employed to obtain more desirable solutions to MRO problems.

Acknowledgements

The authors of this paper thank Professors John English and Enrique Del Castillo and two referees for their helpful comments and suggestions. The first author is also grateful for financial support from the 2003 research program of the University of Ulsan and from the SK Research Fund at Korea University Business School. The research of the second author was supported in part by the BK21 research fund from the Ministry of Education in Korea.