FORMULA OPTIMIZATION 67 values for the ANTICOMPLEX, acceptable from a practical point of view. The follow- ing two main parameters values were chosen: p (number of parameters) = 6 n (number of trials at each series) = 20 Furthermore, the definition of the boundary limits and the explicit constraints, plus an estimating criterion, have to be defined before using the program. DEFINITION OF FORMULATION PARAMETERS In regard to microemulsion, a physical system with six parameters was considered as a good model for this formulation, easily transposable on an industrial scale. The selected parameters are the following: x•: lipophilic active compound x2: oil x 3: water x4: surfactant 1 xs: surfactant 2 x6: surfactant 3 For this formulation study, the corresponding values will be expressed in weighted percentage. CONSTRAINTS ON PARAMETER VALUES For each parameter, the boundary limits are implicit constraints that must be defined, prior to any calculation in the algorithm. We have chosen the widest boundary limits for the parameters that will be kept (or reduced) for a greater number of series. Another strategy would consist in first choosing rather narrower limits that would be kept for a limited number of series and that would then be reexamined for subsequent iterative procedure. This way is similar to experimental design techniques, but it presupposes some knowledge of the formulation. In our study, the former way was chosen since we wanted to use the ANTICOMPLEX procedure as a searching algorithm as well as a screening method. Furthermore, little information was known about the studied for- mulation and it was decided that the algorithm would not be biased so that its capa- bilities could be tested. The boundary limits used and the corresponding steps for each parameter will be described in detail in the Results section. Due to these large boundary limits, the explicit constraints on specific sets of parameters were carefully defined. The first constraint involves the two most important compounds and thus corresponds to economic consideration: x• + x 2 • 50 On the contrary, the second constraint involves the last three parameters (surfactants) and corresponds to safety consideration: X 4 -1 t- X 5 -1 t- X 6 • 50 It must be mentioned that these constraints are large enough to encompass any physical formulation, even those that are not acceptable for further manufacturing developments.

68 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS The last constraint, involving all parameters, is necessary for obvious technical consid- erations: Z X = 100 i=l Since the x 3 parameter is only mentioned in this constraint, the water participates in the final formulation only as a complement. DEFINITION OF THE ESTIMATING CRITERION This global criterion was determined according to three properties of the final product: ß Stability ß Transparency ß Fluidity Although these properties are competitive or even conflicting, they were gathered in one global estimating criterion. This is a non-standard use of the procedure, which, most of the time, needs the measurement of one unique criterion. As a consequence, no one can be sure that in this study, only one optimum exists. Therefore, the detection of false optima could be crucial. In our case, these properties have comparable importance for further manufacturing steps, and their measurements have the same maximum value arbitrarily set to 100. Thus the sum of these three measurements gives the maximum global criterion value of 300. It must be emphasized that the theoretical maximum value can be reached only if no interactions or conflicts exist between these properties, which is not the case. QUANTIFICATION OF THE ESTIMATING CRITERION The stability was evaluated at two significant temperatures: the room temperature and 50øC (respectively y• and Y2). The transparency (L) was measured on a Minolta CT 210-Lab scale and expressed in percentage. Because the transparency is closely linked to the oil phase, this value was weighted by the oil phase concentration (Co). Thus the effective measurement of this property was: Y3 = L * C o. The fluidity (Y4) was measured on a Brookfield Viscometer LVT-Speed 60 rpm-Spindle nøl and expressed in centipoise (cps). One major practical difficulty in this study was first to quantify a qualitative informa- tion such as stability. Another one consists in expressing these properties as continuously as possible according to the real meaning and accuracy of the measurements. Thus it was decided to convert these measurements in an almost linear response in different classes. PRACTICAL ASPECTS For the user, the ANTICOMPLEX procedure is divided into the following four stages: