阅读说明：本技术 确定包含uv过滤物质的防晒组合物的基于计算机的方法 (Computer-based method for determining sunscreen compositions containing UV filter material ) 是由 A·施利福克 于 2021-03-30 设计创作，主要内容包括：一种确定包含多种UV过滤物质的防晒组合物的基于计算机的方法,包括：选择针对待确定的组合物的至少一个特性的至少一个约束(步骤30),所述至少一个约束包括防晒性能指标；从多个优化目标中选择优化目标(步骤50)；以及将所述防晒组合物自动确定为来自一组过滤物质的过滤物质的组合物(步骤100),所述组合物满足至少一个约束并相对于所选的优化目标被优化。自动确定包括步骤：生成多种候选组合物；使用性能模拟工具来确定所述候选组合物的防晒性能；以及将所确定的候选组合物的防晒性能与所述防晒性能指标进行比较。该方法允许基于约束和目标自动确定最佳防晒组合物,从而避免了冗长且并不总是产生最佳结果的人工尝试错误的方法。(A computer-based method of determining a sunscreen composition comprising a plurality of UV filtering materials, comprising: selecting at least one constraint on at least one characteristic of the composition to be determined (step 30), said at least one constraint comprising a sun protection performance indicator; selecting an optimization objective from a plurality of optimization objectives (step 50); and automatically determining the sunscreen composition as a composition of filter materials from a set of filter materials, the composition satisfying at least one constraint and being optimized with respect to a selected optimization objective (step 100). The automatic determination comprises the steps of: generating a plurality of candidate compositions; using a performance simulation tool to determine the sunscreen performance of the candidate composition; and comparing the determined sunscreen performance of the candidate composition to the sunscreen performance index. The method allows for automatic determination of the optimal sunscreen composition based on constraints and goals, thereby avoiding tedious and not always human trial and error methods that produce optimal results.)

1. A computer-based method for determining a sunscreen composition comprising a plurality of UV filtering materials, comprising the steps of:

a) selecting at least one constraint on at least one characteristic of the composition to be determined, the at least one constraint comprising a sun protection performance indicator;

b) selecting an optimization objective from a plurality of optimization objectives;

c) automatically determining the sunscreen composition as a composition of filter material from a set of filter materials, the composition satisfying the at least one constraint and being optimized with respect to a selected optimization goal, the automatic determination comprising the steps of:

-generating a plurality of candidate compositions;

-using a performance simulation tool to determine the sun protection performance of the candidate composition; and

-comparing the determined sunscreen performance of the candidate composition with the sunscreen performance index.

2. The method of claim 1, wherein the user is requested to select the at least one constraint.

3. The method according to claim 1 or 2, characterized in that the user is requested to select the optimal target.

4. A method according to claim 2 or 3, characterized in that the sequence comprising steps a) -c) is repeated, wherein the user iteratively adjusts the at least one constraint and/or the optimization goal.

5. Method according to any of claims 1 to 4, characterized in that the user selects a set of actual filter substances to be considered from a set of basic filter substances.

6. The method of claim 5, wherein the user provides a maximum amount of at least some of the selected filter substances.

7. The method of claim 5 or 6, wherein the user provides a minimum amount of at least some of the selected filter material.

8. The method according to any one of claims 1 to 7, comprising the steps of: at least one further constraint is selected for at least one characteristic of the composition to be determined.

9. The method according to claim 8, characterized in that said at least one further constraint is a range or a limit value related to one of the following properties:

a) the total amount of filtered material;

b) one or more different amounts of filtered material;

c) the cost of filtering the composition of matter;

d) the weight of the filtration or composition of the filtered material;

e) the ecological friendliness is achieved;

f) an additional amount of solvent;

g) oil load.

10. The method according to any one of claims 1 to 9, wherein the sun protection performance index is selected from one of the following:

a) in vivo or in vitro sun protection factor SPF;

b) in vivo or in vitro UVA protective factor UVAPF;

c) a critical wavelength;

d) the ratio of UVA to UVB protection; and

e) and (4) blue light protection.

11. The method of any one of claims 1 to 10, wherein the plurality of optimization objectives comprises at least two of:

a) cost-effectiveness;

b) a weight;

c) the light filtering efficiency;

d) the ecological friendliness is achieved;

e) an additional amount of solvent;

f) a minimum oil load;

g) maximum homogeneity protection;

h) (ii) a maximum sun protection factor and/or UVA protection factor;

i) the highest blue light protection; and

j) similarity to the composition of the filter material provided.

12. Method according to any one of claims 1 to 11, wherein said automatic determination of the sunscreen composition comprises a numerical optimization of an objective function in relation to a selected optimization objective, the variables of said objective function comprising the proportion of filter substances of the sunscreen composition to be determined.

13. Method according to claim 12, characterized in that the numerical optimization comprises the application of a sequential quadratic programming method, in particular the application of an interior point method.

14. Method according to any one of claims 1 to 11, characterized in that, for the automatic determination of the sunscreen composition, a plurality of candidate compositions is automatically defined and a performance simulation tool is used to determine the sunscreen performance of at least some of the plurality of candidate compositions.

15. A method according to claim 14, characterized in that in a first sub-step, a minimum total amount of filter substances is determined for a composition that achieves the sun protection performance index, and in a subsequent second sub-step, starting from the determined minimum total amount, the constraint of the value of the total amount of filter substances for the candidate composition is gradually increased until a stopping criterion is met.

16. The method of claim 15, wherein the lowest total amount of filter material is determined by gradually reducing the total amount of filter material of the candidate composition tested for sun performance of the candidate composition until the sun performance criteria is not met, and by subsequently gradually increasing the total amount of filter material until the performance criteria is again met, wherein the gradually increasing increments are less than the gradually decreasing increments.

17. The method according to claim 15 or 16, characterized in that the candidate compositions to be tested are classified according to the efficiency of the filter substance comprised in such a way that candidate compositions with a high expected efficiency are tested first and the test sequence is stopped as soon as one of the candidate compositions meets the sun protection performance criterion.

18. Method according to one of the claims 14 to 17, characterized by the step of providing a list of best candidate compositions.

19. The method according to any one of claims 1 to 18, wherein optimizing tradeoffs within a plurality of optimization objectives comprises the steps of: providing an acceptable range for the value associated with each target; providing relative importance factors between the targets; and minimizing one of the values using a relative importance factor in a linear constraint for minimization.

20. The method according to any one of claims 1 to 19, characterized by the step of automatically determining an optimal solvent composition for the determined sunscreen composition.

21. The method of claim 20, wherein the optimal solvent composition is determined based on minimization of additional solvent under the constraint of dissolving all of the filtered material of the corresponding sunscreen composition.

22. A computer program product comprising instructions which, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 21.

23. A method of preparing a sunscreen composition, comprising: a step of identifying the composition as a composition of UV filter material according to any one of claims 1 to 21; and a step of combining the UV filter substances.

Technical Field

The present invention relates to a computer-based method for determining a sunscreen composition comprising a plurality of UV filter (filter) substances. It also relates to a computer program product for determining a sunscreen composition and a method of preparing a sunscreen composition.

Background

Today, sunscreen developers have several available computational tools that can predict to some extent the sun protection performance of UV filter combinations (see, e.g., B. Herzog, U.S. Osterwalder 'Simulation of sunscreen performance', Pure Appl. chem. 2015; 87 (9-10): 937-. Certain tools are available online for general use (e.g., BASF)^®Sunscreen Simulator or DSM^®SUNSCREEN OPTIMIZER^TM). They predict, inter alia, the Sun Protection Factor (SPF) and the ratio between the UVA protection factor and the SPF based on the input of a combination of UV filtering. Thus, these tools allow developers to quickly evaluate and compare different UV filtering combinations via computer simulation (in silico).

However, the large number of possible options still means that finding the best combination of filter factors by trial and error is cumbersome and tedious and may not result in a true best choice.

Disclosure of Invention

The object of the present invention is to create a method in connection with the initially mentioned technical field which allows to efficiently determine an optimal sunscreen composition.

The solution of the invention is specified by the features of claim 1. According to the present invention, a computer-based method for determining a sunscreen composition comprising a plurality of UV filter materials comprises the steps of:

a) selecting at least one constraint on at least one characteristic of the composition to be determined, said at least one constraint comprising a sun protection performance index (target);

b) selecting an optimization objective from a plurality of optimization objectives; and

c) automatically determining the sunscreen composition as a composition of filter material from a set of filter materials, the composition satisfying the at least one constraint and being optimized with respect to a selected optimization goal, the automatic determination comprising the steps of:

-generating a plurality of candidate compositions,

-using a performance simulation tool to determine the sun protection performance of a candidate composition, and

-comparing the determined sunscreen performance of the candidate composition with a sunscreen performance index.

As mentioned above, performance Simulation tools for sunscreen compositions are available, see 'Simulation of sunscreen performance' by B. Herzog and U.S. Osterwalder, Pure appl. chem. 2015; 87 (9-10): 937-951.

The method of the present invention allows for the automatic determination of an optimal sunscreen composition based on constraints and goals, thereby avoiding manual trial and error methods. As set forth in more detail below, efforts to optimize compositions of, for example, five or more filter materials, are not affordable for manual methods, even where sunscreen performance simulation tools are readily available. Thus, the integration of performance simulation into an automatic determination (which involves the determination of the performance of a variety of candidate compositions) allows for the first time systematic and truly optimal values to be found.

With the possibility of selecting at least one constraint and optimization goal, the needs of the individual formulator can be respected. The desired solution can be customized to his or her particular needs. As described in more detail below, the computer-based method according to the invention is fast enough on today's personal computers that an interactive working process is possible, wherein the user gets feedback in a reasonable time, preferably in a few seconds. This allows the user to quickly learn and adjust constraints, limits, or set of filter materials under consideration from the results, if needed and/or desired.

Preferably, the user is asked to select at least one constraint. This allows for a user-defined interactive process in which constraints can be selected according to the general needs of the user and according to the properties of the sunscreen that should be optimized. In a simple embodiment of the invention, the user selects a single value related to sun protection performance (e.g. desired SPF). However, instead of a target value, the constraint may be provided in the form of a range, minimum or maximum value. Furthermore, it is possible to provide target values or ranges for more than one single property related to sunscreen performance.

Alternatively, the constraints are automatically selected by the computer. In particular, constraints according to a fixed or variable sequence of constraints are selected in successive optimization steps in order to find a preferred sunscreen composition.

Preferably, the user is asked to select an optimization objective. This allows a user-defined interactive process in which the target can be selected according to the general needs of the user and according to the properties of the sunscreen that should be optimized. In particular, the purpose may be varied during the process in order to iteratively improve the sunscreen composition.

Alternatively, the optimization objective is automatically selected by the computer. In particular, the targets according to the fixed or variable restriction sequences are selected in successive optimization steps in order to find a preferred sunscreen composition.

Constraints and goals will have some relevance: for example, the cost of the composition may be provided as a constraint (maximum value that should not be exceeded) or as a target (cost minimization). The other constraints and objectives are chosen appropriately in each case.

Preferably, the sequence comprising steps a) -c) is repeated, wherein the user iteratively adjusts at least one constraint and/or optimization goal. This allows for a stepwise improvement of the sunscreen composition, taking into account the information obtained from the previous optimization step. An iterative process is possible due to the fact that the sunscreen composition can be determined within a few seconds using the method of the present invention if run on standard hardware.

Alternatively, the process is designed in the following way: i.e. the desired sunscreen composition can be found in a single step and/or adjustments of the constraints and/or optimization objectives can be performed automatically by the computer based on the initially selected parameters and the results of the previous determinations. In a further embodiment, the computer automatically provides recommendations regarding criteria for further improving the composition, and the user decides whether to follow these recommendations in whole or in part for the next step in the iterative process.

Preferably, the user selects the actual set of filter substances to be considered from the basic set of filter substances (i.e. from the superset). In particular, the selection is based on user knowledge, e.g. about the nature of available substances and/or the availability of filter substances. This allows the optimum composition to be found more easily for each task at hand. Furthermore, by reducing the amount of filter material to be considered, the automatic determination of the sunscreen composition can be greatly accelerated.

Alternatively, all available filter substances are considered, or the selection of the actual group is made automatically by the computer, for example based on a database relating to the nature and/or availability of the filters.

In a preferred embodiment, the user provides a maximum number of at least some of the selected filter substances, in particular the user provides a maximum number of all of the selected filter substances. This allows ensuring that usage levels approved by regulatory are not exceeded. In addition, the sunscreen composition can be customized to the needs of the user.

Alternatively, the maximum number is considered automatically, e.g. based on a database containing regulatory information.

In some embodiments, the user provides a minimum number of at least some of the selected filter substances. This allows to influence the determination of the sunscreen composition in order to ensure that the needs of the user are met.

Advantageously, the method comprises the steps of: at least one other constraint (other than the sun protection performance index) is selected for at least one characteristic of the composition to be determined.

Preferably, the at least one other constraint is a range or a limit value (upper or lower) relating to one of the following properties:

a) the total amount of filtered material;

b) one or more different amounts of filtered material;

c) the cost of filtering the composition of matter;

d) the weight of the filtration or composition of the filtered material;

e) the ecological friendliness is achieved;

f) an additional amount of solvent;

g) oil load (oil load).

In principle, the range may be infinitely small, i.e. corresponding to a value of the index (precisely or within a predetermined general tolerance) that the requirement is satisfied.

The weight of the filtration is a number that can represent the price of the filtration, a score representing the eco-friendliness of the filtration, a score representing the ease of formulating the filtration, a score representing the effect of the filtration on the sense of using the sunscreen, and the like. The weight of the composition of the filter material is the sum of the weight of each filter times its corresponding percentage in the combination, and thus may represent, for example, the total cost of the filter combination, the total sensory impact, and the like.

The oil loading is the sum of all the filtrations in the oil phase plus additional solvent (which is the solvent needed to dissolve the solid state filtrations). This is a good measure of the freedom of the formulator to use a particular combination of filters, for example in relation to the addition of other components which may be relevant in the oil phase, for example for the skin feel of the final product.

Eco-friendly or ecotoxicology-friendly relates to the influence of the filter substance on the environment. U.S. patent 7,096,084B 2 (s.c. Johnson & Son limited), U.S. patent 9,595,012B 2 (Johnson & Johnson consumer limited), and WO 2019/207129 a1 (BASF SE) describe methods for determining ecotoxicology values.

The above list of possible constraints is not exhaustive and other constraints are possible, for example relating to the sensory properties of the sunscreen composition.

Preferably, the sun protection performance index is selected from one of the following:

a) in vivo or in vitro Sun Protection Factor (SPF);

b) in vivo or in vitro UVA protective factor (UVAPF);

c) a critical wavelength;

d) the ratio of UVA to UVB protection; and

e) and (4) blue light protection.

The indicator may be provided as an indicator value or an indicator limit (e.g., a minimum value).

In vivo or in vitro Sun Protection Factors (SPFs) may be expressed as absolute SPF values, as sun protection factors or protection classes of recommended markers, for example according to recommendations 2006/647/EC of the european union committee on 22.9.2006 or other (national or multinational company) regulations regarding the marking of sunscreen products. The protection category may be defined, for example, as follows:

-low protection: SPF below 15;

-moderate protection: SPF from 15 to 29;

high protection: SPF from 30 to 49;

very high protection: SPF exceeds 50.

The in vivo UVA protection factor (UVAPF) may be expressed, for example, as a UVAPF determined according to ISO 24442:2001, a UVAPF protection rating according to JCIA in relation to voluntary industry standards of the Japan Cosmetic Industry Association (JCIA) for measuring the efficacy of UVA protection, or a Permanent Pigment Darkening (PPD) or Immediate Permanent Darkening (IPD) value.

Typically, the critical wavelength represents the wavelength at which the sunscreen agent allows 10% of the light to pass through. For example, sunscreens with a critical wavelength above 370 nm are considered by the FDA to provide excellent UVA protection.

The ratio of UVA to UVB protection can be provided as either UVAPF/SPF or Boots Star rating, a proprietary in vitro method introduced in 2011 by Boots company for describing the protection provided by sunscreen products.

Blue light (also commonly referred to as high energy visible light (HEV light)) protection refers to protection against light in the violet-blue spectrum of the visible spectrum, which is found in daylight, but also in LEDs and fluorescent lighting.

In principle, the amount related to sunscreen performance may be determined according to any criteria, as long as the performance simulation tool used is capable of providing sunscreen performance according to the criteria, i.e. the available index may depend on the base simulation tool.

The above list of performance indicators is not exhaustive and other indicators are possible including suitable combinations of the above.

Preferably, the plurality of optimization objectives comprises at least two of:

a) cost-effectiveness;

b) a weight;

c) the light filtering efficiency;

d) the ecological friendliness is achieved;

e) an additional amount of solvent;

f) a minimum oil load;

g) maximum homogeneity protection;

h) (ii) a maximum sun protection factor and/or UVA protection factor;

i) the highest blue light protection; and

j) similarity to the composition of the filter material provided

These goals can be minimized or maximized.

The sunscreen simulation tool facilitates quick and easy side-by-side comparison of different filter combinations. However, direct comparison of properties such as efficiency or cost is only meaningful if all combinations of comparisons deliver more or less the same performance. When comparing many combinations, a great deal of effort is required to make precise adjustments to each combination.

In the context of the present invention, the selection of similarity to the composition of the (user) supplied filter material as a target greatly simplifies the adjustment process. A composition of the filter material is determined that is as close as possible to the composition provided (by the user) but that achieves the performance criteria and meets the constraints. Thus, the final adjustment will maintain the basic idea of the user as close as possible and quickly adjust the filter concentration to meet the desired performance criteria and constraints.

Preferably, in this case, the objective to be minimized is that the euclidean distance between the provided composition and the determined composition satisfies the constraint.

The list of targets is not exhaustive and other targets are possible including suitable combinations of the above or organoleptic properties of the composition.

The large number of possible UV filtering combinations makes a simple combined brute force approach infeasible: assuming that an optimal combination of 6 UV filters will be found, which is a number very common in the sunscreen industry, there may be over 150 billion possible filter combinations when the amount of each filter is quantified in discrete increments of 0.1 weight percent up to a maximum of 5.0 weight percent. Furthermore, there are 134596 options for selecting these 6 filters from the 24 filters approved in europe, giving a total of about 2100 trillion possible combinations for this setup. Currently, the typical personal computer commercially available, with a CPU clock frequency typically between 2 and 4 GHz, requires approximately 2 to 4 milliseconds to determine the sun protection performance of a given composition using performance simulation tools. Thus, the amount of computing time used to compute all performance values will total more than 130000 years. The optimized code can reduce the calculation time to 1/100 times at most, and the use of multiple cores can reduce the calculation time to 1/10-1/8 times. However, even with all of these measures, the calculation time is still over 100 years. Furthermore, to meet all requirements, it may be necessary to extend to more than 6 filters, which greatly increases the computation time.

Thus, in a first preferred embodiment, the automatic determination of the sunscreen composition comprises a numerical optimization of an objective function in relation to a selected optimization objective, the variables of which comprise the proportion of filter material of the sunscreen composition to be determined.

The numerical optimization algorithm eliminates the need to determine the performance of a large number of candidate compositions. They are powerful tools for finding the best solution in a high dimensional space.

Advantageously, the numerical optimization comprises applying a sequential quadratic programming method, in particular an interior point method.

The numerical optimization algorithm requires that the constraint objective function be convex in order to find a global optimum rather than a local optimum. Furthermore, they are more or less sensitive to choosing a good starting point that guarantees global convergence. There is no general optimization algorithm, but a collection of algorithms, each tailored to a specific type of optimization problem. It is unpredictable whether the problem is solved quickly or slowly, and indeed it is unpredictable whether a solution has been found at all.

Unexpectedly, it has now been found that for the optimization of sunscreen compositions, a numerical optimization algorithm (which evaluates the first and second derivatives of the objective function for its choice of search direction and step size taken at each iteration) is not only able to find a global solution to the above-mentioned objective, but is also fast enough on a conventional personal computer to allow an interactive workflow.

The complexity of current algorithms used in sunscreen performance prediction tools requires an estimate of the first derivative, for example by finite difference methods for computing Jacobian and quasi-newtonian methods (e.g., BFGS or SR 1) to approximate the Hessian at each iteration.

When numerical optimization is used to determine the sunscreen composition, there is no limit to the amount of UV filtration-therefore, for computational reasons, it is not necessary to pre-select filtration. Indeed, even in the case where more than 20 filters are used on a conventional personal computer, rapid calculations can be made. Furthermore, there is no resolution limit, which means that a "truly optimal" composition can be found.

However, it must be considered that the numerical optimization method may not be applicable to all constraint objectives, i.e. it cannot be guaranteed to find a global optimum for all constraint objectives. Furthermore, the results will not be rounded to reasonable numbers. Methods such as branch-and-bound must be used to obtain the results at the desired resolution level (e.g., 0.1 wt% increments).

In a second preferred embodiment, in order to automatically determine a sunscreen composition, a plurality of candidate compositions are automatically defined, and a performance simulation tool is used to determine the sunscreen performance of at least some of the plurality of candidate compositions.

Using this combination approach, it is possible to find the best (or near-best) sunscreen composition for any target and ensure that the solution is close to global optima. Furthermore, a list of best solutions can be obtained without additional effort (see below).

A combined approach to reduce the number of computations by applying various measures is possible, among others:

1) the number of UV filters is reduced by the user pre-selecting a maximum of 6 filters.

2) The increment is selected to be a filtration amount of 0.5-1.0 wt% (optimally 0.5 wt%).

3) The search space is reduced by:

3a) the lowest total filtration amount that can achieve the indicated performance is searched for by:

a. the total amount of filtration required to reach the performance index (e.g., SPF/2 wt% filtration) is estimated conservatively, and only the combinations with the corresponding total amount of filtration are calculated (e.g., 312620 calculations are required for SPF 30 with 6 filters, increments of 0.5 wt%, and a maximum usage rating of 5 wt% per filtration).

b. The corresponding filtering combinations are enumerated in such a way that the combination with the most efficient filtering is tested first.

c. The calculation is stopped once the target performance is met (typically less than 1000 calculations).

d. The filtered total is re-estimated based on the first estimated over or under performance and again only the combinations with the corresponding filtered total are calculated.

e. The total amount of filtration is reduced repeatedly by a fixed amount (e.g. 1 wt%) and all these combinations are calculated again until the index is no longer reached (search backwards).

f. The total amount of filtration is increased in increments (e.g., 0.5 wt%) until the performance index is again reached (forward search). Once the index is reached, the search is stopped. This will give the lowest total amount of filtration (the most efficient filtration combination (s)) that can achieve the target performance.

3b) Starting with the lowest feasible total amount of filtering and searching for the best solution by increasing the total amount by one increment (e.g., 0.5 wt%) per search.

Therefore, it is preferable that: in a first sub-step, a minimum total amount of filter substances is determined for a composition that achieves a sun protection performance index, and in a subsequent second sub-step, starting from the determined minimum total amount, constraints on the value of the total amount of filter substances of the candidate composition are gradually increased until a stopping criterion is met.

As mentioned above, it is preferred that the lowest total amount of filter material is determined by gradually reducing the total amount of filter material of the candidate composition tested for sun protection performance of the candidate composition until the sun protection performance criterion is not met, and by subsequently gradually increasing the total amount of filter material until the performance criterion is again met, wherein the gradually increasing increments are smaller than the gradually decreasing increments.

The determination starts with a conservative estimate of the total amount of filter material. The candidate compositions tested in one step all had the respective total amounts. If a candidate composition is found to meet the sunscreen performance criteria, the corresponding step is concluded, followed by the next step of decreasing the total amount. This is repeated until no candidate composition meeting the sun protection performance criteria is found in one step. The incremental decrease and incremental increase may be fixed or variable, depending, for example, on the composition tested for poor or excessive performance.

Preferably, the candidate compositions to be tested are classified according to the efficiency of the filter substance involved, in such a way that the candidate compositions with a high expected efficiency are tested first and the test sequence is stopped as soon as one of the candidate compositions meets the sun protection performance criterion. This greatly reduces the number of candidate compositions to be tested during the phase of gradual reduction of the total amount of filter material.

Generally, as the total amount of filtration becomes higher, many objectives (such as cost, additional solvent, and minimum oil load) will decrease (become better) until the best results are achieved. If the total amount of filtration is further increased (by imposing a constraint that the total amount of filtration used be equal to a predetermined value), certain objectives (such as cost, additional solvent required, or minimum oil load) will increase again (get worse). Thus, the stopping criterion may be an increase (degradation) of one or more targets as the total amount of filter material increases.

The linear objective function (e.g., the most efficient or cost-effective combination of UV filtering) can be evaluated by a simple dot product and can therefore be computed very efficiently by matrix operations on a conventional computer. In these cases, all combinations can be evaluated immediately and efficiently, followed by sequential block-wise performance prediction. The current best (e.g., lowest cost) in the previous block compared to the best may be used to skip all performance predictions from the residual combinations (residual combinations) with the worst values. Typically, this allows the best value to be found with less than 3000 calculations for a given total amount of filtering.

Preferably, the method comprises the step of providing a list of best candidate compositions, such as those 10 or 20 compositions having the highest values with respect to the optimization objective. This list can be obtained without difficulty using a combinatorial approach. Based on this list, the user may select a preferred composition, in particular a composition that only approaches the highest value with respect to the optimization goal but has some other property or properties that make it a better choice than the top composition on the list. Advantageously, this list includes not only the composition and values for the purpose, but also other relevant properties characterizing the composition.

In contrast to the numerical optimization method, in the context of the combinatorial approach, the filtering needs to be pre-selected, since the maximum number of filters would typically be 6 to 7 for a conventional computer. Similarly, the minimum increment will be about 0.5 wt%. Nevertheless, the algorithm is still slower (or requires considerable computational power) than the numerical optimization method.

Typically, optimizing one particular property (such as, for example, efficiency) forces another property (such as, for example, cost) to be within an unacceptable range. Thus, preferably, the method of the invention comprises the steps of: optimizing tradeoffs within a plurality of optimization objectives, comprising the steps of: providing an acceptable range for the value associated with each target; providing relative importance factors between the targets; and minimizing one of the values using a relative importance factor in a linear constraint for minimization.

The acceptable range may be provided by the user or automatically. In particular, the range may be based on the results of previous optimization steps (related to a single objective). The relative importance factors may be set to equal values, e.g. 1 for all pairs of targets, or they may be provided by the user or automatically.

In particular, the optimization of the compromise may comprise the following sub-steps:

a) determining the best possible values for the property relating to two or more optimization objectives of interest using the method described above;

b) retrieving from the obtained results the maximum and minimum values for each of these properties, or selecting respective limits for the properties associated with the optimization objective using information obtained in a previous optimization;

c) selecting the relative importance between properties as factor F (F = 1 for equally important properties); and

d) a linear constraint or a relative importance factor F among a plurality of linear constraints is used to minimize one of the properties.

As an alternative to compromise optimization, inequality constraints may be used in the optimization to avoid that optimizing one particular property forces another property to be within an unacceptable range. However, this does not allow the relative importance of the properties to be set accurately.

Preferably, the method comprises the steps of: an optimal solvent composition is automatically determined for the determined sunscreen composition. The choice of solvent is very relevant to all aspects of the final formulation, including its cost and skin Feel etc., see for example "Solubility of UV Absorbers for sunlight systems for the Creation of Light feelings Formulations" by b.herzog, j.giesenger, m.schnyder, SOFW journal, No. 139, No. 2013, No. 7-14. Thus, if the solvent composition is optimized, the properties of the final formulation can be improved.

Advantageously, the optimal solvent composition is determined according to the minimization of the additional solvent, subject to the constraint of having all the filtered material of the corresponding sunscreen composition dissolved.

To determine the optimal solvent composition, a number of solvents (e.g., 4-6 substances) are predetermined.

For minimization, numerical optimization using a suitable algorithm, such as sequential least squares programming (slsrqp) or simplex algorithm, may be employed.

Alternatively, a combination approach is used to determine the optimal solvent composition.

If the actual solvent composition is relevant for the purpose of optimization of the sunscreen composition, which is usually the case, the determination of the optimal solvent composition is preferably incorporated into the superior determination of the sunscreen composition. This allows to find an overall optimal solution including the choice of filtration and solvent composition.

The computer program product of the invention comprises instructions which, when executed by a computer, cause the computer to perform the steps of the inventive method as described above.

In the process of the invention for preparing a sunscreen composition, the composition is identified as a composition of UV filtering material according to the process of the invention as described above. Subsequently, a sunscreen composition is obtained by combining UV filter substances.

Other advantageous embodiments and combinations of features will be derived from the detailed description below and the entire claims.

Drawings

The drawings are shown to illustrate the invention:

FIG. 1 is a flow chart schematically illustrating a method for determining a sunscreen composition comprising a plurality of UV filter materials; and

fig. 2 is a flow chart schematically illustrating a combined method for finding an optimized sunscreen composition.

In the drawings, like parts are given like reference numerals.

Detailed Description

Fig. 1 is a flow chart schematically illustrating a method for determining a sunscreen composition comprising a plurality of UV filtering substances. The method is computer-based and is performed by dedicated software running on a local computer (e.g., a personal computer) or on a server connected to a local user terminal. The user interacts with the local computer or terminal in an interactive manner. The software may comprise several modules running on different processors, which processors may be located at the same location or remotely from each other. In particular, a local user client (including a web browser or a dedicated client application) may interact with server software and/or computationally intensive tasks such as numerical optimization or sun protection performance simulation may be performed by a dedicated processor (e.g., a GPU) or server.

Basically, the described embodiment of the method of the invention applied by the user aims to find a sunscreen composition comprising a solvent composition which meets the sunscreen performance index and possibly other constraints and which is optimal for one or several optimization goals.

First, the user selects a set of actual filter materials to consider (step 10). For this purpose, a list is displayed comprising a set of basic filter substances, and the user selects the desired substance. In addition, the user has the opportunity to provide a minimum and maximum amount of at least some of the filter material (step 15). This is not mandatory, the user may leave the corresponding input field empty, which means that the amount of the respective filter substance may be as low as 0 (no specified minimum) or as high as 100% (no specified maximum), or the maximum amount is automatically retrieved from regulatory limits in the user-specified area or in the automatic detection area, e.g. by a language and/or location setting on the user's computer or by location data (if any).

Next, the user provides information regarding the desired sunscreen performance index (step 20). To this end, the user selects one of the following useful properties related to sun protection performance:

in vivo or in vitro sun protection factor SPF (e.g. specific SPF or class of protection);

-in vivo or in vitro UVA protective factor UVAPF (e.g. dedicated IPD or JCIA);

-a critical wavelength;

-ratio of UVA to UVB protection (e.g. based on bootstar rating);

-blue light protection.

Further, the user provides an index value of the selected property, e.g., in vivo SPF ≧ 30.

Next, the user has the opportunity to select further constraints for at least one property of the combination to be determined (step 30). These constraints may be related to the following properties:

-a value or range of the total amount of filter material;

-a value or range of the amount of a certain filter substance;

-maximum value of cost of filtering the composition of matter;

-a value or range of weights of the composition of the filter material;

-a value or range of an eco-friendliness parameter of the composition;

-a value or range or maximum amount of additional solvent;

-maximum oil load.

Constraints are presented on the screen and the user selects the additional constraints desired. Depending on the constraints, input fields for setting values, minimum values and/or maximum values will be displayed. The user is free to choose that no further constraints are present, that one further constraint is present or that a plurality of further constraints are present.

Next, the user selects one or several optimization objectives from the following optimization objectives (step 40):

-cost-effective;

-a weight;

-a light filtering efficiency;

-eco-friendly;

-an additional amount of solvent;

-a minimum oil load;

-homogenous protection;

-a sun protection factor and/or a UVA protection factor;

-blue light protection;

similarity to the composition of the filter material provided

The weight of the filtration is a number that can represent the price of the filtration, the score for the eco-friendliness of the filtration, the score for the ease of configuring the filtration, the score for the impact of the filtration on the sensory perception of the use of the sunscreen, etc. The weight of a filter combination is the sum of the weight of the individual filters times their corresponding percentage in the combination and may thus represent, for example, the total cost of the filter combination, the total sensory impact, etc.

The minimum oil loading is the sum of all the filtrations in the oil phase plus additional solvent (which is the solvent required to dissolve the solid state filtrations). This is a good measure of the freedom of the formulator to use a particular filter combination. This is due to the fact that a certain total oil load of the final product should generally not be exceeded, since a very high oil load would lead to an unfavourable heaviness of the product. The freedom to add further oil-based substances is very limited if the minimum oil load due to the filter substances is already high.

After the target(s) are selected, it is checked whether the selected target(s) are compatible with the further constraints previously provided (decision 50). If this is not the case (e.g. because the property that should be optimized is subject to constraints), a warning message is displayed. The user then has the opportunity to release the corresponding constraint or select another target.

Finally, the user selects an actual set of solvent substances to consider (step 60). For this purpose, a list containing a set of basic solvent substances is displayed and the user selects the desired substance. In addition, the user has the opportunity to provide a minimum amount and a maximum amount for at least some of the solvent substances (step 65). This is not mandatory and the user may leave the corresponding input field empty, which means that the amount of the respective solvent substance may be as low as 0 (no specified minimum) or as high as 100% (no specified maximum).

Once the user has provided all the information, the optimal sunscreen composition is automatically determined as the composition of matter from the selected set of actual filter materials and the optimized composition of solvents appropriate for the corresponding composition of filter materials (step 100). The composition achieves performance criteria and meets all possible additional constraints. It is optimized for the selected objective(s).

The output to the user (step 70) includes the filtered material and its corresponding amount and the solvent and its corresponding amount. It further includes characterizing numerous properties of the corresponding composition, including performance achieved, UVA/SPF ratio, total amount of filter material, efficiency (see below), weight, minimum oil load, and cost.

As described in more detail below, optimization includes the use of available performance simulation tools to calculate the sunscreen performance of various candidate compositions.

Based on the results, the user may decide whether the found composition is the desired composition or whether the input parameters (e.g., selection of filtration and/or solvent species, corresponding ranges for amounts of filtration and/or solvent species or additional constraints) should be adjusted for the next optimization step (decision 80). Alternatively or additionally, the optimization may be performed for another objective or combination of objectives, wherein the input parameters may be adjusted based on the results of the previous optimization step(s).

In a preferred embodiment, the optimal sunscreen composition is automatically determined using a numerical optimization of an objective function related to the selected optimization objective, variables of the objective function including the proportion of filter material of the sunscreen composition to be determined.

In the described example, the optimization is performed using the 'trust-constr' method available in the open source library SciPy (version 1.4 published 12/19/2019) of the Python programming language (see SciPy. org). The method is based On the EQSQP algorithm ("On the implementation of optimization for large-scale equality constraints" by Lalee, Marucha, Joge Nocedal and Todd Plantaga), "On the optimized SIAM journal 8.3: 682-706, 1998).

The objective function depends on the optimization objective. Several examples are given below:

one possible goal is to find the most effective UV filtering combination. This is a combination of achieving the desired performance index with a minimum total amount of UV filtering. In the following formula, the number of individual filtrations is given by k, and the concentration of the filtrations i is given as x_i。

The purpose is to make

Follow, for example, the following:

namely, the target sunlight protection factor is realized;

the ratio between the UVA protection factor and the SPF is satisfied；

Critical wavelength(ii) a And

the (simulated) amount of additional solvent needed is less than or equal to 10%.

Furthermore, the amount of UV filtering is constrained to the indicated minimum and maximum values:

。

another object relates to the weighting of the UV filtering combinations. The weight of filtration is a number that can represent the price of filtration, the score for the eco-friendliness of filtration, the score for the ease of formulating the filtration, the score for the impact of filtration on the sensory of using the sunscreen, etc., and is given in the following formula as。

The weight of a filter combination is the weight of each filter multiplied by their corresponding percentage in the combination (given in the following formula as) (dot product) and thus may represent, for example, the total cost of the filter combination,Overall sensory impact, etc.

The purpose is to make

Following the performance and property constraints as indicated in the previous examples above.

Another object relates to the minimum oil load of the composition. It is all in the oil phaseThe concentration of this filtration plus the sum of the additional solvent or solvent mixture may be required to completely dissolve all solid state filtration. This is a good measure of the freedom of the formulator to use a particular filter combination.

The purpose is to make

Again following the performance and property constraints as indicated above, whereinThe total amount of additional solvent representing the optimal (minimum) solvent mixture. The composition of the mixture can be determined using various optimization algorithms, such as, for example, the sequential least squares programming (slsrqp) algorithm (which is also available in the SciPy library, method 'slsrqp') or the simplex algorithm (method 'simplex' in the SciPy library).

Hypothetical (candidate) filtration compositionIncludednA solid state UV filter material andma liquid UV filter material. The situation regarding the dissolution of the solid UV filter substance can be formulated as follows:

whereinIs composed ofnA vector of the concentration of the solid state UV filter material, andis composed ofmVector of concentration of UV-filtered seed liquid. The elements of the matrix S are defined as follows:

thus, the resulting vectorReflect not being coveredmThe seed liquid UV is filtered and dissolvednThe concentration of solid state UV filtration.

Now, the conditions for complete dissolution solid state UV filtration can be expressed as follows:

whereinAnd wherein the vectorIncluding the concentration of (additional) solvent. The Solubility can be obtained, for example, using a method as described in "Solubility of UV Absorbers for Sunscreens for the Creation of Light Feel Formulations" by b.herzog, j.giesenger, m.schnyder, SOFW journal, 139 th, 2013, 7 th, pages 7-14.

The following equation can now be solved by using the Simplex method (or any other suitable method)To obtain a minimum of additional solventIn combination with (1)

。

Another object relates to the similarity of the composition to the (user) provided composition. This allows the known compositions to be tailored in a way that achieves the performance index and meets the constraints. The goal may be expressed as follows:

wherein u is_iTo the amount of filtration of the user-provided composition. Thus, it is the Euclidean distance of the composition determined according to the recommendations provided that should be minimized.

Optimization will result in the preservation of the user's basic ideas as close as possible and the rapid adjustment of the filter concentration to meet the required performance index and constraint adjustments.

Up to this point, it has been assumed that the user has selected a single optimization objective. However, often optimizing one particular property (e.g., efficiency) may force another property (e.g., cost) to be within an unacceptable range. A possible solution to this problem is to set corresponding inequality constraints for this property.

A more general approach is to search for the best compromise of two or more properties according to the procedure described below.

First, a property of interest is identified. As mentioned above, the sunscreen composition is optimized in turn with respect to each of these properties. This will result in a maximum and minimum value for each property of interest.

Next, respective property limits are set、. The minimum and maximum values may be automatically set to the minimum and maximum values obtained from the optimization or set by the user in consideration of them.

In the next step, the relative importance between the properties is selected as factor F. For equally important properties, F = 1

Finally, the relative importance factor(s) in the linear constraint(s) is/are used to relate the property of interest toOne of which is minimized, as follows:

whereinThe concentration of the UV-filter is included,is of a natureAnd is weighted, andin which the general case isAnd for the weighted case。

The general performance and property constraints described above also apply.

Instead of numerical optimization, in another embodiment, a combination approach is used to automatically determine the optimal sunscreen composition. Fig. 2 is a flow chart schematically illustrating this combined method (step 100 in the process of fig. 1) for finding an optimal sunscreen composition. In this context, a plurality of candidate compositions is automatically defined, and a performance simulation tool is used to determine the sun protection performance of at least some of the plurality of candidate compositions.

Such a method is feasible if measures are taken to reduce the number of calculations, the measures being:

1) the number of UV filters is reduced by pre-selecting a maximum of 6 filters. Before continuing, it is checked whether the number of filters exceeds 6 (decision 101). If this is the case, the user is asked to reduce the number of filters selected or switch to numerical optimization.

2) The self-defined increment for the composition is selected to be 0.5-1.0 wt%, preferably 0.5 wt%.

3) Reducing the search space by:

3a) searching the lowest filtering total amount capable of realizing index performance by the following method:

a. the total amount of filtration required to achieve the performance index, e.g., SPF/2 wt%, is conservatively estimated (step 102), and only combinations with corresponding total amounts of filtration are calculated. (for SPF 30, 312620 calculations were required with 6 filtrations, increments of 0.5 wt%, and a maximum usage rating of 5 wt% per filtration and a constraint of total concentration of 15 wt% (SPF 30/2);

b. enumerating corresponding filtering combinations in a manner that first tests combinations with most efficient filtering (step 103);

c. next, it is checked whether the current filtration total amount can meet the index performance, for which purpose:

-using a performance simulation tool to determine the performance of the candidate composition (step 104);

-checking whether the determined performance meets a performance index (decision 105); if this is not the case, checking whether additional candidate compositions remain (decision 106), and if so, checking (according to the enumeration) the next candidate composition;

d. if the determined property of one of the candidate compositions meets the indicator, the calculation is stopped (which typically occurs in less than 1000 calculations), the amount of filtration is reduced by a fixed amount, e.g. 1 wt% (step 107), and the resulting candidate composition is enumerated and examined as described previously (step 103-); this process is repeated until the index fails to achieve, i.e., none of the compositions meets the index (no additional candidate compositions in decision 106) (back search);

e. next, the total amount filtered is increased by an increment (e.g., 0.5 wt%) (step 110), the resulting candidate compositions are enumerated (step 111), and it is checked whether the current total amount filtered can meet the target performance for which purpose:

-using a performance simulation tool to determine the performance of the candidate composition (step 112);

-checking whether the determined performance meets a performance index (decision 113); if this is not the case, checking whether additional candidate compositions remain (decision 114), and if so, checking (according to the enumeration) the next candidate composition;

f. stopping the calculation if the determined property of one of the candidate compositions meets the indicator (this typically occurs in less than 1000 calculations); if none of the candidate compositions meets the criteria, the amount of filtration is again increased by a fixed amount, e.g., 0.5 wt% (step 110) and the resulting candidate compositions are enumerated and examined as previously described (step 111) 114); this process is repeated until the index is achieved, i.e., at least one composition meets the index (no additional candidate compositions in decision 114) (forward search);

this will give the lowest total amount of filtering ((one or more most efficient filtering combination) that can achieve the targeted performance.

3b) Starting with the lowest feasible total amount of filtering and searching for the best solution by increasing the total amount by one increment (e.g., 0.5 wt%) per search. This is achieved by:

-reducing the search space as described above (step 120);

-calculating the relevant properties of the remaining candidate compositions with a fixed total amount of filtration, starting from the determined lowest total amount of filtration (step 121);

-checking whether the properties related to the selected optimization objective are improved compared to the last run (decision 122); if this is the case, the total amount of filtering is increased by the above increment (step 123) and the determination is repeated with the increased value (step 120-122);

if no further improvement is obtained (decision 122), then the best composition (or list of best compositions) relative to the selected optimization objective is returned for further processing.

Generally, as the total amount of filtration becomes higher, many properties (e.g., cost, additional solvent, and minimum oil load) will decrease until optimal. Thus, the forward search can generally continue as long as the property value decreases, and immediately stop as the property value begins to increase again as the amount of filtering increases. Otherwise, the search must continue until the maximum total amount of UV filtering is reached.

The linear objective function (e.g., the most efficient or cost-effective combination of UV filtering) can be evaluated by a simple dot product and can therefore be computed very efficiently by matrix operations on a conventional computer. In these cases, all combinations can be evaluated immediately and efficiently, followed by sequential block-wise performance prediction. The current best (e.g., lowest cost) value within the previous block compared to the best value may be used to skip all performance predictions from the combination of residuals with the worst values. Typically, this reduction in search space (step 120) allows the best value to be found with less than 3000 calculations for a given total amount of filtering.

Using this combination method allows to display not only a single optimized composition but also a list of the best candidate compositions, e.g. 10 or 20 compositions together with their properties. This provides additional valuable information to the user. In particular, the user is enabled to identify whether the best solution characterizes very similar compositions of the filter material or whether they relate to substantially different compositions. In the latter case, based on his or her knowledge, the user may decide to select only the second or third optimal composition, or to proceed with the next optimization step based on the second or third optimal composition, as this seems to be a better starting point for further improvement.

The user may choose between numerical optimization and combination methods for each iteration step. For example, once a promising composition has been found using combinatorial approaches, the composition can be further improved by applying a numerical optimization step starting from the identified candidate composition. This is because numerical methods can provide more precise amounts of the ingredients of the composition than combinatorial methods where the possible values are discrete. Vice versa, it can be checked again whether the numerical method does indeed find the true global minimum in the optimization using the combinatorial method.

To obtain a ranked result list, it may also be useful to switch to the combinatorial approach.

In all embodiments of the present invention, preferably, the UV filter substance is selected from the group consisting of: octyl methoxycinnamate (octyl methoxycinnimate) (PARSOL)^®MCX), amiloride (isoamyl methoxinamate) (Neo Heliopan)^®E1000) Homosalate (3, 3, 5-trimethylcyclohexane 2-hydroxybenzoate), PARSOL^®HMS), ethylhexyl salicylate (also known as ethylhexyl salicylate, 2-ethylhexyl 2-hydroxybenzoate), PARHS^®EHS), octocrylene (2-ethylhexyl 2-cyano-3, 3-diphenylacrylate), PARSOL^®340) Polysiloxane 15 (polysilone 15) (PARSOL)^®SLX), diethylhexyl 2, 6-naphthalate (diethylhexyl 2,6-naphthalate）（Corapan^®TQ), butylene malonate (syringylene malonates), such as, for example, diethylhexyl syringylene malonate (Oxynex)^®ST liquid), benzotriazolyl dodecyl p-cresol (benzotriazolyl dodecyl p-cresol) (Tinoguard)^®TL), and benzophenone 3 (benzophenone-3) and cresyl troxacyclo-trisiloxane (drometrizole trisiloxane), bis-ethylhexyloxyphenol methoxyphenyl triazine (polysol^®SHIELD), butyl methoxydibenzoylmethane (butyl methoxydibenzoylmethane) (PARSOL)^®1789) Methylene bis-benzotriazolyl tetramethylbutylphenol (dimethyl, to an advanced level, i.e., after^®MAX), diethylamino hydroxybenzoyl hexyl benzoate (UVINUL)^®PLUS), ethylhexyl triazone (UVINUL)^®T150), diethylhexyl butamido triazone (diethyl butamido triazine) (Uvasorb)^®HEB), Tris (Biphenyl Triazine) (Uvinul)^®A2B), 4-methylbenzyl divinyl camphor (4-methyl, F^®5000) And 1, 4-bis (benzoxazol-2 '-yl) benzenebisethylhexyloxyphenol methoxyphenyl triazine (1, 4-di (benzoxazol-2' -yl) benzophenon bis-ethylhexyloxyphenol tolyltriazine), Phenylbenzimidazole Sulfonic Acid (Phenylbenzimidazole Sulfonic Acid) (PARSOL)^®HS) and sodium salt of phenylene diphenylimidazole sulfonate (Neoheliosan)^®AP), ultrafine (preferably coated) titanium dioxide (e.g. PARSOL)^®TX) and zinc oxide (e.g. PARSOL)^®ZX）。

The above methods have been used to calculate optimized compositions of UV filter materials that comply with different constraints and optimization objectives:

example 1

In a first example, the goal is to find the most efficient combination of UV filtering, i.e., to achieve the desired performance index with the least amount of UV filtering.

The following filters with indicated limits and weights have been selected:

INCI name	Boundary(s)	Weight of
			Homomenthyl Salicylate (Homomenthyl Salicylate)	≤ 10 wt%	20
Butyl Methoxydibenzoylmethane (Butyl Methoxydibenzoylmethane)	≤ 5 wt%	50
			Bis (Ethylhexyloxyphenol Methoxyphenyl) Triazine (Bis-Ethylhexyloxyphenol Triazine)	≤ 4 wt%	150
Octocrylene (Octocrylene)	≤ 10 wt%	25
			Diethylhexylbutamidotriazinone (Diethylhexyl Butamido Triazone)	≤ 5 wt%	100
Phenylbenzimidazole Sulfonic Acid (Phenylbenzimidazol Sulfonic Acid)	≤ 2 wt%	50

The performance constraints are that the SPF is more than or equal to 30 and the ratio UVAPF/SPF is more than or equal to 0.33. No property constraints apply.

Optimized compositions have been determined using the above-described methods, optimized combination methods (where the increments are 0.5 wt%, up to 5.0 wt%, yielding 128 tens of thousands of possible combinations), and numerical optimization. The results are as follows:

has the following properties:

properties of	Combination of	Numerical value
			SPF	30.0	30.0
UVA/SPF ratio	0.35	0.33
			Total amount in%	9	8.94
Efficiency of	3.33	3.36
			Weight of	8.5	8.41
Minimum oil load in%	25.3	29.1
			CPU (2.9 GHz) time in s	5	< 1

Example 2

In a second example, the goal is to find the most weighted effective UV filtering combination.

The filter material, its bounds and weights and constraints are the same as in example 1.

The results of both methods are as follows:

has the following properties:

properties of	Combination of	Numerical value
			SPF	30.2	30.0
UVA/SPF ratio	0.41	0.44
			Total amount in%	14.5	15.2
Efficiency of	2.07	1.97
			Weight of	5.5	4.89
Minimum oil load in%	13.0	13.2
			CPU (2.9 GHz) time in s	12	0.9

Example 3

In a third example, the goal is to find a UV filtering combination with minimum oil load.

The filter material, its bounds and weights are the same as in examples 1 and 2. The performance constraints are that the SPF is greater than or equal to 30 and the UVAPF/SPF ratio is greater than or equal to 0.33. The performance constraint is a maximum weight of 6.5 and a maximum total amount of filtering of 17%.

The results of both methods are as follows:

has the following properties:

properties of	Combination of	Numerical optimization
			SPF	30.7	30.0
UVA/SPF ratio	0.38	0.33
			Total amount in%	14.5	12.8
Efficiency of	2.07	2.34
			Weight of	6.0	6.3
Minimum oil load in%	12.5	10.8
			CPU (2.9 GHz) time in s	7	20

Example 4

In a fourth example, the goal is to find the most weighted effective UV filtering combination.

In contrast to examples 1-3, 10 filter materials with indicated limits and weights have been selected instead of 6:

INCI name	Boundary(s)	Weight of
			Homomenthyl Salicylate (Homomenthyl Salicylate)	≤ 5 wt%	20
Butyl Methoxydibenzoylmethane (Butyl Methoxydibenzoylmethane)	≤ 5 wt%	50
			Bis-Ethylhexyloxyphenol Methoxyphenyl Triazine (Bis-Ethylhexyloxyphenol Triazine)	≤ 4 wt%	150
4-methylbenzyl divinyl Camphor (4-methylene benzyl idene Camphor)	≤ 4 wt%	75
			Ethylhexyl Salicylate (Ethylhexyl Salicylate)	≤ 5 wt%	20
Octocrylene (Octocrylene)	≤ 10 wt%	25
			Diethylhexylbutamidotriazinone (Diethylhexyl Butamido Triazone)	≤ 10 wt%	75
Ethylhexyl Triazone (Ethylhexyl Triazone)	≤ 3 wt%	100
			Titanium Dioxide (Titanium Dioxide)	≤ 20 wt%	75
Active Methylene Bis-Benzotriazolyl Tetramethylbutylphenol (active)	≤ 8 wt%	150

The performance constraints are that the SPF is greater than or equal to 50 and the ratio UVAPF/SPF is greater than or equal to 0.33. No property constraints apply.

Optimization using the combinatorial approach is not feasible because 980 hundred million possible combinations need to be examined even at increments of 0.5 wt%. This is not feasible on a conventional computer.

The results of the numerical optimization are as follows:

INCI name	Best wt.%
		Homomenthyl Salicylate (Homomenthyl Salicylate)	5.00
Butyl Methoxydibenzoylmethane (Butyl Methoxydibenzoylmethane)	5.00
		Bis (Ethylhexyloxyphenol Methoxyphenyl) Triazine (Bis-Ethylhexyloxyphenol Triazine)	0.00
4-methylbenzyl divinyl Camphor (4-methylene benzyl idene Camphor)	0.26
		Ethylhexyl Salicylate (Ethylhexyl Salicylate)	5.00
Octocrylene (Octocrylene)	10.00
		Diethylhexylbutamidotriazinone (Diethylhexyl Butamido Triazone)	0.00
Ethylhexyl Triazone (Ethylhexyl Triazone)	3.00
		Titanium Dioxide (Titanium Dioxide)	2.27
Active Methylene Bis-Benzotriazolyl Tetramethylbutylphenol (active)	1.06

Has the following properties:

SPF	50.0
		UVA/SPF ratio	0.33
Total amount in%	31.6
		Efficiency of	1.58
Weight of	13.5
		Minimum oil load in%	40.2
CPU (2.9 GHz) time in s	1

Example 5

In a fifth example, the objective is to find the most efficient UV filtering combination.

The filter material, its bounds and weights, and constraints are the same as in example 4.

Also, the combination method is not feasible for the same reason. The results of the numerical optimization are as follows:

INCI name	Best wt.%
		Homomenthyl Salicylate (Homomenthyl Salicylate)	0.00
Butyl Methoxydibenzoylmethane (Butyl Methoxydibenzoylmethane)	0.00
		Bis (Ethylhexyloxyphenol Methoxyphenyl) Triazine (Bis-Ethylhexyloxyphenol Triazine)	4.00
4-methylbenzyl divinyl Camphor (4-methylene benzyl idene Camphor)	0.76
		Ethylhexyl Salicylate (Ethylhexyl Salicylate)	0.00
Octocrylene (Octocrylene)	0.00
		Diethylhexylbutamidotriazinone (Diethylhexyl Butamido Triazone)	0.00
Ethylhexyl Triazone (Ethylhexyl Triazone)	3.00
		Titanium Dioxide (Titanium Dioxide)	0.00
Active Methylene Bis-Benzotriazolyl Tetramethylbutylphenol (active)	8.00

Has the following properties:

SPF	50.0
		UVA/SPF ratio	0.43
Total amount in%	15.76
		Efficiency of	3.17
Weight of	21.6
		Minimum oil load in%	39.2
CPU (2.9 GHz) time in s	1

Example 6

In a sixth example, the goal is to find a compromise of weight and efficiency (the weights of the two targets are equal).

The filter material, its bounds and weights, and constraints are the same as in examples 4 and 5.

Also, the combination method is not feasible for the reasons mentioned above. The results of the numerical optimization are as follows:

INCI name	Best wt.%
		Homomenthyl Salicylate (Homomenthyl Salicylate)	0.00
Butyl methoxydibenzoylmethane (Butyl Methox)ydibenzoylmethane）	4.10
		Bis (Ethylhexyloxyphenol Methoxyphenyl) Triazine (Bis-Ethylhexyloxyphenol Triazine)	0.20
4-methylbenzyl divinyl Camphor (4-methylene benzyl idene Camphor)	3.52
		Ethylhexyl Salicylate (Ethylhexyl Salicylate)	1.73
Octocrylene (Octocrylene)	5.20
		Diethylhexylbutamidotriazinone (Diethylhexyl Butamido Triazone)	0.00
Ethylhexyl Triazone (Ethylhexyl Triazone)	3.00
		Titanium Dioxide (Titanium Dioxide)	0.00
Active Methylene Bis-Benzotriazolyl Tetramethylbutylphenol (active)	4.55

Has the following properties:

SPF	50.0
		UVA/SPF ratio	0.39
Total amount in%	20.57
		Efficiency of	2.43
Weight of	16.11
		Minimum oil load in%	30.6
CPU (2.9 GHz) time in s	1

Comparison with the performance of examples 4 and 5, in which the compositions were optimized for a single target, gave the following results:

properties of	Example 4	Example 5	Example 6
				SPF	50.1	50.2	50.0
UVA/SPF ratio	0.33	0.48	0.39
				Total amount in%	31.7	15.77	20.57
Efficiency of	1.58	3.18	2.43
				Weight of	13.6	22.2	16.11
Minimum oil load in%	40.1	38.5	30.6
				CPU (2.9 GHz) time in s	1	1	1

From the results, it can be seen that a compromise is established as follows:

where it takes into account that the weight values are minimized and the efficiency values are maximized. Thus, the resulting deviation of the efficiency from the optimum and the resulting deviation of the weight from the optimum are approximately the same.

Example 7:

in the seventh example, the goal is to find a weight and efficiency tradeoff, which is similar to the sixth example but now the goal is 100/50 weight/efficiency tradeoff (F = 2).

The filter material and its limits are the same as in examples 4-6. In addition to the invariant constraints on SPF and UVAPF/SPF ratios, the following property constraints are imposed:

maximum weight；

Maximum total amount of filtration(i.e. the）。

Also, the combination method is not feasible for the above reasons. The results of the numerical optimization are as follows:

INCI name	Best wt.%
		Homomenthyl Salicylate (Homomenthyl Salicylate)	0.00
Butyl Methoxydibenzoylmethane (Butyl Methoxydibenzoylmethane)	4.26
		Bis (Ethylhexyloxyphenol Methoxyphenyl) Triazine (Bis-Ethylhexyloxyphenol Triazine)	0.00
4-methylbenzyl divinyl Camphor (4-methylene benzyl idene Camphor)	2.41
		Ethylhexyl Salicylate (Ethylhexyl Salicylate)	0.00
Octocrylene (Octocrylene)	8.38
		Diethylhexylbutamidotriazinone (Diethylhexyl Butamido Triazone)	0.00
Ethylhexyl Triazone (Ethylhexyl Triazone)	3.00
		Titanium Dioxide (Titanium Dioxide)	0.00
Active Methylene Bis (Benzotriazolyl) Tetramethylbutylphenol）	4.04

Has the following properties:

SPF	50.0
		UVA/SPF ratio	0.39
Total amount in%	22.09
		Efficiency of	2.26
Weight of	15.09
		Minimum oil load in%	32.0
CPU (2.9 GHz) time in s	1

Also, examination of the results showed that: the trade-off reflects the desired relative weights of the two objectives (F = 2):

。

the present invention is not limited to the above-described embodiments. In particular, the number and succession of method steps may be different, and the user may be provided with more or fewer options to interact with the process or to enter information. Some of the required information may be provided automatically, e.g. retrieved from a database. In contrast to the described embodiments, even an iterative process may be computer-aided or computer-guided, i.e. successive optimizations with different input parameters and/or goals may be suggested to the user or automatically performed.

For numerical optimization, other algorithms may be employed. One readily available method involves a sequential least squares programming (slsrqp) algorithm such as available in the SciPy library mentioned above. It is also possible to use other methods for optimization, such as linear search methods or penalty/augmented lagrangian algorithms.

In summary, it should be noted that the present invention creates a method that allows for the efficient determination of an optimal sunscreen composition.