An ideal point method for the design of compromise experiments to simultaneously estimate the parameters of rival mathematical models

When several rival mathematical models are proposed for one and the same process, experimental design techniques are available to design optimal discriminatory experiments. Because these techniques are model-based, it is important that the model predictions are not too uncertain. Therefore, model discrimination may become more efficient and effective if this uncertainty is reduced first. This can be achieved by performing experiments designed to increase the accuracy of the parameter estimates and, thus, the model predictions. However, performing such an additional experiment for each rival model may undermine the overall goal of optimal experimental design, which is to minimize the experimental effort. This paper deals with the design of a so-called compromise experiment, which is an experiment that is not optimal for each of the rival models, but sufficiently informative to improve the overall accuracy of the parameters of all rival models. For this purpose, the problem is approached as a multi-objective optimization problem and the ideal point method is proposed to design the compromise experiment. This method searches for the experiment that is as close as possible to the optimal experiments of the individual rival models. The method is applied to a case study where nine rival models are competing to describe the kinetics of an enzymatic reaction, and the obtained results show that the ideal method is capable of designing a compromise experiment.