Conclusion
This paper presents a new optimization-based approach for cosmetic
formulation. A three-step procedure is proposed to formulate the
cosmetic formulation problem as an MINLP problem. For problem
definition, the objective function (i.e., sensorial perception) and
design targets are identified. Then, a pool of potential ingredient
candidates is generated for selection. Design variables include
ingredient selection, composition, and microstructure descriptors (not
include in the example). Next, models are identified for predicting the
sensorial rating and target properties. Meanwhile, common heuristics are
translated into mathematical equations which serve as constraints to
narrow down the search space. To improve the optimization convergence
and to find better solutions, a solution strategy that involves an
iterative model adoption and different numerical techniques is proposed.
The procedure and solution strategy are illustrated using a perfume case
study. Our approach is one of the first attempts to integrate multiple
(rigorous, short-cut, surrogate, and heuristic-based) models to account
for both sensorial and functional attributes for optimal cosmetic
formulation. It can be used for other cosmetics and personal care
products provided that the relevant models, data, heuristics, etc. are
available.
Product design involves a wide range of issues that include consumer
preference, ingredient selection, supply chain analysis, process design,
government regulations, economics, corporate social responsibility,
sustainability and so on.56 These issues interact in
an exceedingly complex manner as captured in the Grand Product Design
Model.57 While many detailed models exist to describe
the separate issues, it is a daunting task to solve the optimization
problem for product design when a number of disparate issues are
involved. It is interesting to study how the approach described in this
paper can be extended to the product design as a whole. Efforts in this
direction are underway.