Multiresponse optimization by a normalized function approach

A simple new method, called Normalized Function Approach (NFA), was developed for simultaneously optimizing systems defined by several output variables (response functions) and a common set of input variables (factors). For each original response function the difference between the estimated response and its individual optimum was evaluated and normalized over the experimental space. The individually normalized functions were then weighted for their importance and combined into an overall function using a “sum of squares” approach. Simultaneous optimization was completed by minimizing the overall function. Some numerical examples were considered to introduce the new method and several reported applications in the food area were used for verification and comparison with other multiresponse optimization methods.