j. Soc. Cosmet. Chem., 45, 65-75 (March/April 1994) An optimization method for cosmetic formulation: A new practical approach j. GUESNET, B. BREDA, D. DERSIGNY, I. CARTON, V. TRAN, and J. L. MORAT, Sanoff Beautg, Research and Development Center, 106 AvenueJ. Moulin, BP 72, F-78170 La Celle St. Cloud (J. G., B.B., D.D., I.C. ), and Institut National de la Recherche Agronomique, Laboratoire de Physico-Chimie des Macromolgcules, Rue de la Ggraudi?re, BP 527, F-44026 Nantes Cedex 03 (V.T., J.L.M.), France. Received February 24, 1993. Synopsis The development of cosmetic formulae implies the use of many different raw materials. Without knowl- edge on their interactions, it is almost impossible to control the system exhaustively. We propose a global optimization method, of the "black box" type, which allows us to determine through a very low number of trials, the area of formulae best corresponding to a set of criteria first defined by the user. INTRODUCTION In the very competitive domain of the cosmetic industry, the need for conceiving and developing new innovative and high-performance products is essential. Furthermore, the formulation and the corresponding industrial processes must be performed quickly to follow the evolution and the growth of the market. The search for really innovative products combines the concepts stemming from fundamental research (liposomes, mi- croemulsion, elongated micelies, etc.) and the need for the cosmetic industry to meet consumer expectations or to increase product performance. Contrary to fundamental research, the principal aim of the cosmetic industry is not to define the concept by a mathematical model but to quickly generate products based on this concept, taking into account its own constraints (choice of raw materials, prices, safety, processes, time, etc.). Several optimization procedures, including experimental design methodologies (1) or even methods of function optimization like SIMPLEX (2), could be adapted for formu- lation studies. However, cosmetic formulae are multivaried, with a great number of ingredients and a large range of physical and chemical interactions whose mechanisms are almost unknown, unlike pharmaceutical compounds. Therefore, it is impossible to 65

66 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS describe the effects of cosmetic products even by a rough mathematical model, and the optimization procedure can only be performed on the given final characteristics. In this case, a more global optimization approach of the "black box" type would be better, and the real goal is not to find the exact optimum but to narrow down the area for each parameter in the system around the expected optimum. METHODS Among the investigation procedures, the ANTICOMPLEX method (3), derived from the COMPLEX method (4,5), was chosen. Initially developed for technological pro- cesses, this algorithm has been used without modification for cosmetic formulation studies for the following reasons: ß A global analysis of the hyper space of the parameters. To a certain extent, the random exploration of the whole parameter space is similar to a screening technique that has the advantage over the other optimization methods. One important conse- quence is the capability to locate and discard possible false optima regions. ß A rapid attainment of optimum conditions acceptable by the user. This is essentially due to the serial procedure and the strategy oriented to a fast convergence toward the optimum region. ß A versatile algorithm specially written for technological processes with convenient options such as the discretization of parameter values. ß A very easy way to take into account implicit and explicit constraints for each parameter or for specific subsets of parameters. In the ANTICOMPLEX terminology, the implicit constraints refer to the boundary limits of the parameters, while the explicit ones refer to any constraints imposed by the technological process or deter- mined by the user. For example, the formulation constraint is a typical explicit constraint. This strategy is illustrated here by the microemulsion study of a high concentration of lipid material in an aqueous phase using a ternary system with specific surfactants. The criterion to be optimized is a combination of somewhat contrary characteristics. Due to the complexity of the problem, non-standard options of the algorithm were used and the strategy was adapted at some important steps according to the results already obtained and the accuracy desired. METHODOLOGICAL ASPECTS In this approach, the optimum operating conditions of a technological process are accessed by a "black box" strategy. The global description of the algorithm is mentioned elsewhere in detail (3), and we shall briefly summarize its main features. This program is based on an iterative procedure with at each step a random sampling of the space of the parameters. After each series of measurements (step), a statistical analysis of the result leads, under normal conditions, to successive restrictions of the boundary limits. This methodology is very flexible since the investigation can be stopped after any series of experiments according to the desired accuracy for the optimum region. Preliminary trials of formulation were performed to determine the internal variable