Optimization-based Cosmetic Formulation: Integration of Mechanistic
Model, Surrogate Model, and Heuristics
Abstract
Multiple functional and hard-to-quantify sensorial product attributes
that can be satisfied by a large number of cosmetic ingredients are
required in the design of cosmetics. To overcome this challenge, a new
optimization-based approach for expediting cosmetic formulation is
presented. It exploits the use of a hierarchy of models in an iterative
manner to refine the search for creating the highest-quality cosmetic
product. First, a systematic procedure is proposed for optimization
problem formulation, where the cosmetic formulation problem is defined,
design variables are specified, and a set of models for sensorial
perception and desired product properties are identified. Then, a
solution strategy that involves iterative model adoption and two
numerical techniques (i.e., generalized disjunctive programming
reformulation and model substitution) is applied to improve the
efficiency of solving the optimization problem and to find better
solutions. The applicability of the proposed procedure and solution
strategy is illustrated with a perfume formulation example.