Multiple response optimisation: methods and results

In multi-response problems, optimal factor settings for one response may be far from optimal or even physically impractical for the other responses. A common approach for multi-response optimisation consists in searching for factor settings that provide the best trade-off among all the responses. To identify the method which can provide the best trade-off when optimisation is made in the response surface methodology (RSM) framework, various methods are reviewed and their performance assessed through examples from the literature. A new measure is proposed to evaluate the optimisation performance of methods which use different criteria and different approaches. Illustrative examples show that, in the RSM framework, it is possible to achieve the lowest cumulative deviation of the estimated responses from their target value by using desirability function-based methods. In particular, those solutions are achieved with a method that can be easily used by practitioners, which is an additional stimulus for its application in practice.