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 problem, 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.

中文翻译：

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基于优化的化妆品配方：机械模型，替代模型和启发式方法的集成

化妆品设计中需要多种化妆品成分可以满足的功能性和难以量化的感官产品属性。为了克服这个问题，提出了一种基于优化的新方法来加快化妆品配方的使用。它以迭代方式利用模型层次结构来优化搜索，以创建最高质量的化妆品。首先，提出了用于优化问题配方的系统程序，其中定义了化妆品配方问题，指定了设计变量，并确定了一组感官感知和所需产品特性的模型。然后，制定一个涉及迭代模型采用和两种数值技术（即 为了提高求解最优化问题的效率并找到更好的解决方案，本文采用了广义析取规划重构和模型替换）。所提出的程序和解决方案策略的适用性以香水配方示例为例。