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.