Ellipsoid based Pareto filter for multiobjective optimisation under parametric uncertainty: A beer study

Abstract

Multiobjective optimisation is used when a system needs to be optimised for multiple conflicting objectives. However, the solution of such a problem is not one point but a set of equally optimal points called Pareto points which highlight the trade-off required to achieve optimisation of one objective over another. As any computer aided approaches depend on the model, any uncertainties in the model have a large influence on the solution of the optimisation. Thus, the uncertainty needs to be incorporated into the optimisation methodology. In this paper, along with incorporating uncertainty in the optimisation, an ellipsoid based filter is described to select points in the Pareto set which are significantly different from each other. This filter is applied to the case study of beer fermentation. Fermentation is a key step in brewing which affects the flavour and stability of beer. Along with operating parameters like yeast pitching, dissolved oxygen, etc., fermentation temperature has a large influence on beer flavour and fermentation progression. In this paper, this temperature profile is optimised using multiobjective optimisation for conflicting objectives. The novel Pareto ellipsoid based filter is used to discriminate between Pareto points and generate a Pareto set that contains only the relevant solutions.