Optimization

The multi-objective optimization function is provided below.

Minimize

Deviation from score targets or quality targets:

\[J_{t} = (t - t_{target})w_{t}(t-t_{target}) \qquad or \qquad J_{y} = (y - y_{target})w_{y}(y-y_{target})\]

Measures of model validity:

\[J_{validity} = SPE | HotT^{2}\]

Total ingredient costs:

\[J_{cost} = \sum_{i} x_{i} c_{i}\]

Selection of ingredients with missing data:

\[J_{missing} = \sum_{i} x_{i} p_{i}\]

Each of these terms in the objective function are assigned a weight, which can be adjusted by the user in the Optimization – Advanced screen. In addition to adjusting the objective function weights, a number of other optimization settings can be adjusted in the same screen including: the maximum SPE extrapolation factor, maximum HT2 extrapolation factor, optimization tolerance sensitivity, and maximum number of iterations. Please refer to Optimization Setup (30-35) for more information.

The objective function is subject to a number of limits and bound constraints on each of the relevant input and output terms including: quality, cost, process conditions, and ingredients. Please refer to Optimization Setup (18) for more information.

The FormuSense optimization solution algorithm is Intellectual Property of ProSensus.