Multi-response optimisation strategies for targeting a profile of product attributes with an application on food data

Optimising multi-responses simultaneously is critical to improving the quality of consumer goods (Physico-Chemical or Sensory profiles). The approaches developed so far to solve this issue are based on composite functions (Desirability, Distance, and Loss). Transforming the multi-response problem, into a single response problem, makes optimisation simpler but leads to an obvious loss of information. Our hypothesis assumes that, in a Food or Chemistry products, it is more relevant to target acceptable ranges for each response rather than targeting an utopian single optimum. Our approach aims at finding a combination of input factors leading simultaneously all responses in their respective acceptable ranges, by keeping the multi-dimensionality of the multi-response system. We use two techniques to optimise the system: an Interactive Technique developed in Microsoft® Excel and a Numerical Grid Search written in R language. The first one helps user to find, in real time, optimum compromises between responses, by involving interactive input factor control and monitoring charts. The Grid Search technique leads to a global optimum by screening exhaustively the experimental space. A comparison of the techniques on a food industry example shows on one hand, the benefit of the Interactive Technique for understanding the system, and on the other hand, the performance of the Grid Search to identify the global optimum.