DE102007050434A1 - A method and arrangement for computer-assisted determination of at least one property of a hair colorant based on a formulation of chemically reactive and / or unreactive raw materials, method and apparatus for computer-assisted determination of a hair colorant formulation based on chemically reactive and / or unreactive raw materials, and method and arrangement for computer aided Train a predetermined model to computer-aided determine at least one property of a hair coloring based on a formulation of chemically reactive and / or unreactive raw materials - Google Patents

Abstract

In a method for computer-aided determination of at least one property of hair coloring based on a formulation of chemically reactive raw materials and optionally additionally unreactive raw materials using chemically reactive formulations, information about chemically reactive formulations is fed to a predetermined model, the predetermined model being a map of information about describes chemically reactive formulations on at least one property of a corresponding hair coloring of a plurality of previously determined hair colorations. Using the predetermined model, the at least one property of the result of hair coloring is determined using the chemically reactive formulations.

Description

The The invention relates to a method and arrangement for computer-aided Determine at least one property of a hair coloring based on a formulation of chemically reactive and / or unreactive Raw materials, methods and arrangement for computer-aided Determine a formulation of a hair coloring based on chemically reactive and / or unreactive raw materials, and process and arrangement for computer-based training of a predetermined Model for computer-aided determination of at least one Property of a hair coloring based on a formulation from chemically reactive and / or unreactive raw materials.

hair coloring have different properties with respect to, for example a washing resistance, a light resistance, a gray cover and, for example, a hair coloring or hair tint on. The chemical process, which one Hair coloring or hair coloring is based usually by means of a chemical reaction or several chemical reactions of initially mostly colorless chemical substances both in and on the hair. Make up the different characteristics of the hair colorations, like for example, the color, only from the interaction of the ingredients of hair dye, exposure time and properties hair, for example, color and texture, and others Parameter off.

The Prediction of properties of hair colorations, as well as the Properties of new hair colorations, for example in relation on color, gray cover index, washfastness and lightfastness so far unsatisfactory on the basis of their composition or the manufacturing process. Only by longtime Experience in the formulation of hair colorations is so far possible for the experts, properties estimate. Especially with oxidative hair dyes (permanent hair colorations) this is difficult as the in the Color cream present dye precursors only by mixing with a developer solution as part of a chemical reaction react to the actual hair dyes. The im Hair occurring reactions of the dyes with each other as well also on and in the hair are the subject of research. You go away from the fact that the color precursors first penetrate into the hair and only react in the hair to the actual dyes. The structure and amount of the resulting and remaining in the hair Dyes is broad in commercial formulations unknown.

The Development of hair colorations with new properties is therefore consuming. Because the connection between the recipe a hair color and their properties generally not Exactly known, must be at optimization or design new hair colorations many experiments are performed until a desired recipe is found. It exists hence the desire for a method and apparatus that performs this optimization automatically.

So far is used in the optimization of hair colorations of already known Formulations for hair colorations emanated, and these are changed until an improvement of the properties was found. This type of optimization is called a local one Optimization is usually not the best solution throughout the formulation space, but only the best solutions, in the formulation room near the startup phrase are located.

there is it not possible without computer support in practice, the optimal formulations, for example based on the optimization strategy Pareto set, Pareto front for a plurality of output quantities (Target variables), for example with regard to a specific color, an optimization of the production costs, a long shelf life and the like.

Lots Recipes are usually "grown", d. H. developed based on existing recipes. there Takes by the constant advancement of the recipes the number of raw materials contained in the recipe usually to. There is a desire to find simpler substitute recipes with identical or even better properties and so the complexity of the formulations, ie to decomplex

It there is a need for alternative formulations, e.g. For example due to rising commodity prices, delivery problems or regulatory Certain commodities should no longer be used. Therefore is looking for a variety of recipes, the similar Possess properties, but are composed differently.

Out EP 1 138 347 A1 For example, there is known a method and apparatus for automated, individual on-site production of ready-to-use hair colors or tints. The method described in this document is only suitable for retrieving a known recipe from a memory and providing hair colorations for individual application. However, it is not suitable to formulate new formulations or to optimize an existing formulation or to reduce its complexity, ie to decomplex it.

Furthermore, it is off EP 1 380 720 A1 a method for determining the composition of a coloration product known.

According to EP 1 380 720 A1 the composition of keratin fibers is checked and a set of colorants for individual applications is compiled by means of a database query of prescribed formulations. This method is not suitable for formulating new formulations for any parameters, for example with regard to cost reduction, wash resistance, lightfastness, or to optimize or decomplex an existing formulation.

Of the Invention is the problem of determining properties of Hair colorations based on a given raw material composition based. Furthermore, there is the problem of determining a recipe based on given properties of a hair coloration.

The Problems are solved by a method and an arrangement for computer-aided determination of at least one property hair coloring using chemically reactive formulations, by a method and a computer-aided arrangement Determine at least one recipe of a plurality of chemical reactive formulations for hair coloring, and by a method and an arrangement for computer-aided Train a predetermined model for computer-aided determination at least a property of hair coloring when using chemical reactive formulations.

at a method for computer-aided determination at least a property of hair coloring based on a formulation from chemically reactive raw materials and optionally additionally Unreactive raw materials will provide information about the formulation fed to a predetermined model, wherein the predetermined Model an illustration of information about chemically reactive Formulations on at least one property of a corresponding one Haircoloration of a variety of previously determined hair colorations describes. Using the predetermined model becomes at least a property of a hair coloring of a hair coloring based on a formulation of chemically reactive raw materials and optional additionally determined unreactive raw materials. Under property is in this context both a direct property of the formulation (eg costs) as well as an indirect property, d. H. a result to understand the use of hair coloring (eg color).

A Arrangement for determining at least one property of a hair coloring based on a formulation of chemically reactive raw materials and optionally additionally unreactive raw materials has an input unit for entering information about chemically reactive formulations in a predetermined model as well as a model unit, the one predetermined model, wherein the predetermined model a Illustration of information about hair coloring, one Formulation of chemically reactive raw materials and optionally additionally unreactive raw materials on at least one property of this hair coloring describes a variety of previously determined hair colorations. Further a hair coloration property determination unit is provided for determining the at least one property of a hair color using the model model's predetermined model.

One Advantage of this embodiment of the invention is in the now allowed quantitative prediction of properties of hair colorations that are also used productively by a layman can be.

Further may be an advantage of this computerized method, for example The virtualization of the experiments can be seen in the fact that resources can be saved in the development of new hair colorations or their use can be focused.

One Another advantage of this embodiment of the invention is, for example, that the hair coloration development for example, by the computerized method Virtualization of experiments is accelerated.

One Another advantage can be seen in the fact that a Mulitkriterielle Optimization of the formulations and the process parameters, ie one simultaneous optimization of formulation and process parameters with regard to possibly more and also opposing ones Target sizes throughout the formulation room can be. According to one embodiment become optimized compromises or globally optimized solutions found.

One Another advantage is computer-aided knowledge from historical data to extract hair colorations and correlations between input quantities, for example concentrations the raw materials and other parameters, and the output quantities, For example, to recognize properties of hair coloring, and for the product developer, thus optimizing recipe information to use.

According to one Embodiment of the invention is computer-aided Knowledge extracted from many historical data on hair colorations and become relationships between input quantities, for example, concentrations of raw materials and other adjustment parameters, and the output quantities, for example properties hair color, recognized and for the product developer harnessed.

According to one Another embodiment of the invention is a method for computer-aided determination of at least one recipe from chemically reactive raw materials and optionally additionally chemically unreactive raw materials for hair coloring provided, wherein at least one desired property of hair coloring a predetermined model is supplied. The predetermined one Model describes an illustration of information about Hair colorations from chemically reactive raw materials and optional additionally chemically unreactive raw materials on at least a feature of a corresponding hair coloration of a variety previously determined hair colorations. Using the predetermined one Models become information about chemically reactive formulations determined, and from the information on chemically reactive raw materials and optionally additionally chemically non-reactive Raw materials is the recipe based on a plurality of chemical reactive raw materials and optionally additionally chemically unreactive Raw materials for hair coloring determined.

A Arrangement for determining at least one recipe based on a plurality of chemically reactive and optionally in addition chemically unreactive raw materials for hair coloring has an input unit for inputting at least one Target property of hair coloring in a predetermined model, a model unit having a predetermined model, wherein the predetermined model is a map of information about chemically reactive formulations to at least one property a corresponding hair coloring of a variety previously determined Describes hair colorations, as well as a formulation determination unit to determine information about chemically reactive Formulations using the model model's predetermined model. Furthermore, a recipe determination unit for determining the Formulation of a plurality of chemically reactive formulations for the hair coloration provided.

According to one Another embodiment of the invention is a method for computer-aided determination of an end recipe (also referred to as a composition of a hair coloration) of one or a plurality of chemically reactive substances and / or non-reactive Fabrics and / or formulations for hair coloring, in which to a recipe of a plurality of chemically reactive Substances using at least one predetermined model an evolutionary algorithm is applied, with which one End recipe is determined, the at least one predetermined Model an illustration of information about chemically reactive Substances and / or non-reactive substances and / or formulations at least one property of a corresponding hair coloring describes a variety of previously determined hair colorations, wherein at least one nominal property in the context of evolutionary Method is taken, wherein using of the predetermined model information about chemically reactive Substances and / or non-reactive substances and / or formulations determined and based on this information the final recipe for a hair coloration.

Furthermore, according to another embodiment of the invention, an arrangement for determining a formulation of a plurality of chemically reactive formulations for a hair coloring is provided with a model determination unit for determining a final formulation, wherein the recipe determination unit is set up such that a plurality of an evolutionary algorithm is performed on predetermined models, the at least one model describing an image of information about chemically reactive formulations on at least one property of a corresponding hair coloration of a plurality of previously determined hair colorations. Furthermore, the arrangement has an input unit for on giving at least one desired property of the hair coloring to the final formulation, an information determination unit for determining information about chemically reactive formulations using the at least one model, and a recipe determination unit for determining the final formulation of a plurality of chemically reactive ones Formulations for a hair coloring from the information on chemically reactive formulations.

According to this Embodiment makes it possible to formulations from decomposing hair colorations to simpler substitute formulas to find with identical properties or to substitute recipes with even better properties to determine.

One Another advantage is the formulation of hair colorations to diversify, and to find alternative formulations to for example, rising commodity prices, delivery problems or on the limitation of raw material selection by regulatory To be able to react to regulations.

One Embodiment of the invention allows optimization the composition or the production parameters of the hair colorations also under specification of boundary conditions.

According to one Another embodiment of the invention is a method for computer-based training of a predetermined model for computer aided determination of at least one property of a Hair coloring when using chemically reactive formulations provided, wherein the predetermined model using Information about chemically reactive formulations as Input quantities and at least one property a corresponding result of a hair coloring as a starting point a variety of previously determined hair colorations is trained each one tuple of input quantities and Initial size of a hair coloration a training record forms. A subset of training records will be off a total amount of training records for training of the predetermined model selected.

In Another embodiment of the invention is a Arrangement for training a predetermined model for computer-aided Determine at least one property of a hair colorant when used of chemically reactive formulations provided with a model trainer unit for training the predetermined model using information about chemically reactive formulations as input variables and at least one property of a corresponding result a hair color as the output of a variety previously determined hair colorations, each with a tuple of Input variables and output size a hair coloration makes a training record, and with a Training data set selecting unit for selecting a subset of training records from a total of training records for training the predetermined one Model.

According to Another embodiment of the invention is a Method for computer-aided determination of at least one Formulation of a hair coloration provided, wherein at least one Target property of hair coloring supplied to a predetermined model becomes; wherein the predetermined model is a map of information about the wording on at least one property of a corresponding one Haircoloration of a variety of previously determined hair colorations describes; information about. using the predetermined model chemically reactive formulations are determined; and being from the Information about chemically reactive formulations Formulation of a plurality of chemically reactive formulations for a hair coloration is detected.

exemplary Embodiments of the invention will become apparent from the dependent Claims. The described embodiments of the invention apply mutatis mutandis to the various Embodiments of the method, the arrangements as well the computer-readable storage media.

According to one Embodiment of this embodiment include the Information about chemically reactive formulations at least one of the following information: an indication of the Type of basic formulation; an indication of the mixing ratio between a color cream used in the respective hair coloring and a developing solution used in the respective hair coloring; the pH of an application mixture that is characterized by mixing a Color cream used in the respective hair coloring and a developing solution used in the respective hair coloring results; and / or concentration data on raw materials in one of the developer solution, the color cream and / or the Application mixture that is characterized by mixing one at the respective Haircoloration used color cream and one at the respective Haircolor used developer solution.

In an embodiment of the invention contain formulations at least one dye and / or at least one dye precursor.

In an embodiment of the invention will be the predetermined Model using chemical information reactive formulations as inputs and at least one property of a corresponding result of a Hair colouration as an output of a variety previously determined hair colorations trained.

One Advantage of this embodiment of the invention can therein be seen that conclusions from historical or experimentally determined data can be included.

In an embodiment of the invention forms each one Tuple of input quantities and output size a hair coloration a training data set, wherein a subset of training records from a total set of training records is selected to train the predetermined model.

In Another embodiment of the invention will become apparent from the total amount of training records for training the predetermined one Model those training records selected, for their chemically reactive formulations used there are a number of training records that are larger or equal to a predetermined threshold.

One Advantage of this embodiment of the invention is that the training data set used to train the predetermined model has improved properties and one with regard to forecasting properties improved predetermined model leads. It should be noted that in one embodiment of the invention no connection between constraints and penalty functions for optimization and the selection of records for creation the models for predicting the properties consists.

In An embodiment of the invention comprises at least a property of a corresponding result of a hair coloring at least the following: a color information which is the resulting Hair color describes the hair coloring; an information about a light fastness of the hair color of the hair coloring; an information about a wash fastness of hair color of hair coloring; an information about one Gray coverage of hair color of hair coloration; an information about the cost of hair coloring; and / or information about the quality of hair coloring.

In an embodiment of the invention is considered the predetermined Model used at least one of the following models: at least an artificial neural network; at least one fuzzy logic model; at least a support vector machine; at least one decision tree; at least a Bayesian network. In an alternative embodiment The invention may be any other than the predetermined model (trainable with a training record, for example) model be used.

Consequently depends the prediction of properties of a hair coloring or even finding a recipe not from a specific one Model off. Any suitable method or Models from the field of "Computational Intelligence", "Soft Computing, Natural Computing, Machine Learning be used.

In another embodiment of the invention contains the at least a property of a corresponding result of a hair coloring at least one color information indicating the resulting hair color describes the hair coloring, color coding for coding one of the following color spaces used: Lab color space; xyY color space; XYZ color space; RGB color space; CMYK color space; HSV color space; Lch color space; I1I2I3 color space; YCbCr color space; YPbPr color space; YUV color space; YIQ color space.

The Choice of different color spaces the method and the arrangement are not according to an embodiment of the invention limited to a specific characteristic of a color space.

In an embodiment of the invention has the predetermined Model a plurality of partial models on.

Furthermore, at least one sub-model of the plurality of sub-models may include mapping information about chemically reactive raw materials, and optionally additionally chemically non-reactive raw materials to exactly one property of a corresponding hair coloration of a plurality of previously determined hair colorations describe.

In a development of the invention describe all sub-models The majority of sub-models each have a map of information about chemically reactive raw materials and optionally additionally over chemically non-reactive raw materials to exactly one property of a corresponding hair coloring of a variety of previously determined Haarcolorationen.

One Advantage of an embodiment of the invention can therein be seen that using methods from the field of "Computational Intelligence, Soft Computing, Natural Computing, Machine Learning ", hair colorations using certain raw materials (eg, direct drawers, developers, couplers, oxidizers, stabilizers, etc.) and under certain settings of process parameters (eg. B. ph value) can be produced.

According to one Embodiment of the invention, the relationship between Input and output quantities based on historical experimental data from chemically reactive formulations of computer-based systems (eg through use Artificial Neural Networks, Fuzzy Systems, Support Vector Machines, Decision trees or Bayesian networks) and saved in the form of models.

According to In another embodiment of the invention, the predetermined Model changed and the procedure is repeated using the modified predefined model.

The Recipe can be made using an evolutionary algorithm to be determined, optimizing the population of hair colorations is performed by evolutionary algorithms.

When For example, an evolutionary algorithm can genetic algorithms, evolutionary strategies, genetic programming and evolutionary programming.

Of the evolutionary algorithm can at least one of the following Mechanisms include: evaluation, mutation, recombination, selection. Additionally or alternatively, other common or future mechanisms of evolutionary Method be used in another embodiment of Invention.

The Information about chemically reactive formulations can be contain at least one of the following information: Concentration information on the ingredients of the chemically reactive formulation; an indication about the type of basic formulation; an indication of the mixing ratio between a color cream used in the respective hair coloring and a developing solution used in the respective hair coloring; the pH of an application mixture that is characterized by mixing a Color cream used in the respective hair coloring and a developing solution used in the respective hair coloring results; and / or concentration data on raw materials in an application mixture that is characterized by mixing one at the respective Haircoloration used color cream and one at the respective Haircolor used developer solution.

According to one Embodiment of the training process will be out of the total of training records for training the predetermined one Model those training records selected, for the input variables used Number of training records is larger or equal to a predetermined threshold.

In an embodiment of the arrangement for determining at least one Feature of a hair coloring is a model trainer unit provided for training the predetermined model using Information about chemically reactive formulations as Input quantities and at least one property a corresponding result of a hair coloring as a starting point a variety of previously determined hair colorations.

Farther can in this embodiment of the arrangement for determining at least a property of hair coloring when using chemical reactive formulations each have a tuple of input variables and output a hair coloration a training record and additionally may be a training record selection unit be provided for selecting a subset of training records from a total amount of training records for training of the predetermined model.

The Training record selection unit may be established to select those training records the total amount of training records for training of the predetermined model for which used chemically reactive formulations a number of training records present, which is greater than or equal to a predetermined Threshold.

In an embodiment of the arrangement for determining at least one Formulation of a plurality of chemically reactive formulations for a hair color is the model unit set up so that it changes the predefined model and changes that predetermined model provides for repeatedly determining Information on chemically reactive formulations under Use of the modified predetermined model.

In another embodiment of the arrangement for determining at least A recipe is set up to do this evolutionary method for determining the recipe, wherein according to the evolutionary method the Recipe is changed, such as one, as described above or even more closely below is explained.

In an embodiment of the arrangement for training a predetermined Model for computer-aided determination of at least one Property of hair coloring when using chemically reactive formulations, the training record selection unit is set up to select those training records the total amount of training records for training of the predetermined model for which used chemically reactive formulations a number of training records present, which is greater than or equal to a predetermined Threshold.

In Another embodiment of the invention is a computer-readable storage medium provided on which a computer program code which is stored when executed by a processor one or more of the above or below Method has.

embodiments The invention is illustrated in the figures and will be described below explained in more detail.

1 schematically shows the multilayer structure of a neural network;

2 schematically shows the structure and the mathematical estimation function of a neuron;

3 shows the embodiment of the genetic algorithm underlying the invention;

4 shows the main window of the program;

5 shows the operating menu of the Factor Dictionary;

6 shows the selection menu of the Prediction Models window.

7 shows the operating menu of the Factor Functions;

8th shows the operating menu of the Formulation Designer;

9 shows the operation menu of the Formulation Generator;

10 shows the implementation of an embodiment of the present invention;

11 schematically shows a flowchart for implementing an embodiment of the present invention;

12 schematically shows a flowchart for implementing an embodiment of the present invention; and

13 shows the optimization / filtering of the training data.

For the purposes of this description, the terms "connected,""connected," and "coupled" are used to describe both a direct and indirect connection, a direct or indirect connection indirect connection and direct or indirect coupling. In the figures, identical or similar elements are provided with identical reference numerals, as appropriate.

In an embodiment of the present invention is a System described on a computer or device can be executed and which for modeling by means neural networks is suitable. The system is made of a part that is suitable for modeling neural networks, formed here For example, a program which is based on a processor Computers expire.

This can be combined with a software or device to Input and output of user data, for example color mixtures and color data, such as. B. a suitably equipped color processing software, which is additionally set up to be one implemented in the following embodiments.

In An embodiment is now on the coloring model formation To be received.

10 schematically shows a computer 1002 according to an embodiment of the invention. The computer 1002 indicates a central processing unit (CPU) 1008 , a storage unit 1006 and an input / output unit 1004 , By means of the input / output unit 1004 can be made by means of a likewise provided graphical user interface of a main program, hereinafter also referred to as formulation designer and formulation generator, the control of a method according to an embodiment of the invention.

In the storage unit 1006 (For example, one or more volatile memory (for example, one or more Random Access Memory, RAM) or one or more non-volatile memory (for example, one or more flash memory) are training records, which will be explained in more detail below, as well as previously determined, for example, optimized, formulations and the program code, which in its execution by the CPU 1008 realized one or more of the following embodiments, stored. In the CPU 1008 the process of the program code executes a method according to an embodiment of the invention. In addition, in the CPU 1008 also a training data set optimization, as will be explained in more detail below, executed.

11 shows schematically in the form of a flow chart 1100 an embodiment of the present invention.

At the beginning (after starting the procedure in 1102 ) becomes an "empty", ie unweighted multilayer artificial neural network 1104 specified. The artificial neural network 1104 has a variety of individual neurons, such as those with reference to 2 will be explained in more detail. The neurons are arranged in multiple neuron layers, as with respect to 1 will be explained in more detail.

In one embodiment of the invention, the training records are 1108 formed from experimental data from a large number of hair colorations measured in their results, for example from 336 hair colorations. The input variables of a training datum of a training dataset 1108 For example, the concentrations of 47 raw materials in each color cream or developer solution used, the type of base formulation, the mixing ratio between the color cream and the developer solution, and the pH of the application mixture formed by mixing the color cream and the developer solution. Among the 47 raw materials are, for example, 38 dyes or dye precursors, such as couplers, developers and Direktzieher.

In the modeling, alternatively, the concentrations of the raw materials in the application mixture can be used, which can be calculated from the concentrations of the raw materials in the color cream and the developer solution in combination with the mixing ratio. The target size of a training datum of a training dataset 1108 For example, the color of a strand of a standard hair, for example, white buffalo belly hair that has been treated with the application mixture. This color is captured and displayed in this example as a 3-valued variable in the Lab color space.

It can in principle different hair, for example different Standard hair, used, for. B. brown hair, human Hair or other dyeable materials.

In alternative embodiments of the invention, other target sizes may be alternative or additional Lich in a training date of a training record 1108 be used.

• a. die Lichtechtheit, d. h. die Haltbarkeit der Farbe unter Licht-Bestrahlung, beispielsweise unter UV-Bestrahlung;
• b. die Waschechtheit, d. h. die Haltbarkeit der Farbe bei mehrmaliger Wäsche der Strähne;
• c. der Grauabdeckungsindex, d. h. ein Maß für die Fähigkeit der Haarcoloration, helle Haare und dunkle Haare gleichmäßig abzudecken;
• d. die Rohstoffkosten.

Other target variables can be, for example:

• a. the light fastness, ie the durability of the color under light irradiation, for example under UV irradiation;
• b. the wash fastness, ie the durability of the paint with repeated washing of the tress;
• c. the gray coverage index, ie a measure of the ability of hair coloring to evenly cover light hair and dark hair;
• d. the raw material costs.

The training records 1008 are optionally optimized according to an embodiment of the invention to obtain increased accuracy of the model to be trained before the start of training of the model to be trained or filtered.

The predefined experimental data are first subjected to a pre-selection as in 13 in a diagram 1300 is shown. In order to obtain a sufficient quality in the quantitative prediction, it is advantageous to use formulations composed of raw materials for which a sufficiently large database exists. For this purpose, the concentration distribution of the raw materials used was examined and filtered based on this data sets. This is done according to an embodiment of the invention in two stages:
In a first stage, the total concentration interval of the respective raw material is determined by the lowest used concentration x _min (for example 0%) and the highest used x _max concentration. The interval x _max and x _min can be different for each raw material (eg for raw material A in the range 0% -10% and for raw material B in the range 2% -3%). Subsequently, the concentration intervals are normalized to:

The normalized concentration intervals, for example the interval between 0 and 1, is then divided into 10 sub-intervals or even levels of 0.1, as indicated by reference numerals 1304 exemplified clarified, split. If, for a raw material, there are at least m (for example m = 2) levels with at least n (for example n = 3) contained data points, then this raw material (for example denoted by reference numerals 1302 in 13 ) are taken into account in the subsequent modeling (for example, the training of the model to be trained). It should be noted that the parameters x, m, and n can basically be chosen arbitrarily and, for example, can be adapted experimentally to the specific conditions.

In a second stage, all recipes are selected which consist exclusively of this raw material selection 1302 be assembled. Other recipes will not be considered further and the entries for the modeling will be deleted, in other words, the other recipes will not be included in the training of the model to be trained.

There in the second stage, the number of records is reduced the procedure will start with the first step Repeats until the number of factors to use and Formulations no longer changes.

The artificial neural network used in the present embodiment 1104 assigns input values to output values through a network of weighted link paths.

The Input parameters can be for example: the original hair color, the hair condition and the hair length, the type of application, the composition of the coloring mixture, the temperature and other application constraints.

The Output parameters can be the parameters that follow the Coloring should be achieved, such as the hair color and other properties, such as color stability.

The weighting designates the transition probability (also referred to as connection strength) from a node of the KNN to a node following this, and is based on empirical values that are statistically derived from a set of experimental data during a training phase. The transition probability between the nodes are in a learning phase or training phase of the artificial neural network and later used for the estimation (prediction) of target parameters in another combination of input parameters. The interactions between relevant factors are numerous and complex.

In An embodiment of the invention becomes such a model derived on the basis of artificial neural methods Networks (KNN). Becoming Artificial Neural Networks in the context of soft computing for the modeling of complex, non-linear Relationships between input parameters and output parameters without the previous specification of individual formally given Relationships used. However, other statistical Techniques having similar features are used in alternative embodiments of the invention.

An embodiment of optimizing the formulation is achieved by the following steps (see 11 ).

In 1112 is an artificial neural network (KNN) using the in 1110 determined training data (entered into the training software in 1106 ) or several artificial neural networks (KNNs) are trained. In this case, a change of the or the KNNs is carried out in the form of an evolution, in which the weights and optionally also the combination of the connection of the nodes in the different neuron layers is carried out (even removing or newly adding individual connections between neurons of different neuron layers can be), up in 1114 a given quantitative relationship between the input variables and the target values has been achieved.

In an embodiment becomes for each of the three Goals L, a and b are based on their own model used on a KNN. In an alternative embodiment The invention can also have multiple target sizes be taken into account in a common KNN. To achieve the best possible mapping of the input parameters the respective target size values for training used training data are according to one embodiment provided several recursive steps, because in the example of a Application mixture for hair colorations the colors first arise after the sequence of a variety of chemical reactions.

This or these trained KNN models will be in 1116 for further processing suitably formatted and for further use by another Program exported. The exported models will be subsequently imported and integrated into the hair coloration modeling software. The hair coloration modeling software allows with Help of the imported KNN models or the prediction of the color of existing as well as purely virtual formulations. she allows Furthermore, the visualization of the experimentally determined as well of predicted colors. In addition, with this software according to a Embodiment of the invention, the optimization of formulations in terms of desired settings of the target sizes (eg specified color) possible.

The design of new formulations according to an embodiment of the invention (shown in a flow chart 1200 in 12 ) supported by two functionalities, on the one hand by a formulation designer (Formulation Designer), on the other hand by a stochastic formulation generator (Formulation Generator). The Formulation Designer in 12 allows manual adjustment of input parameters and target values in a graphical user interface. The flowchart is the design of a new formulation 1220 shown. The basis is the imported trained KNN 11 , Initially, the startup formulation and the desired goal will be in step 1222 established. Then in step 1224 a manual change of the input parameters is carried out by changing the parameters in the window of the form designer. Now the result of the KNN issue with the target 1226 and the step of manually changing the input parameters is repeated until the target is reached. Subsequently, the result of the then present formulation 1232 output. This is displayed as a color value representing the color (or the color point in the color space) in a window on the user's screen.

The stochastic formulation generator enables optimization 1210 a formulation. This optimizes the formulations with regard to specific target values taking into account boundary conditions 1212 for example, the optimization of the boundary conditions of color and costs with a fixed number of raw materials. After setting the boundary conditions, the population of formulations is initialized. Now the result of the KNN issue with the target 1218 and the step of manually changing the input parameters is repeated until the target is reached. Subsequently, the result of the then present formulation 1230 output. This is called a the Color representing color value (or the color point in the color space) displayed in a window on the user's screen.

In An embodiment of the invention is intended that in the event that as part of the training, different expressed, for example, in the changes the weights or couplings in the model to be trained (For example, changes in factors or factor functions of the model to be trained), changes occur leading to a manipulation of the structure or the weights outside a predetermined allowable range occurs, the Users are informed accordingly.

The formulation designer clearly visualizes the working methods of the product developers in the computer and thus vividly provides a virtual laboratory:
Starting from a selected formulation, the factors (in other words, the parameters describing the respective model in its illustration) are changed by the user until the desired target values (according to the training data used) are set. The Formulation Designer enables quick computer-assisted validation for a user of interesting formulations using the previously created models. Further, the formulator designer, for example, assists a user in selecting the most promising formulations of hair colorations. This preselection (pre-screening) spares experimental resources.

In 1 is a multi-layer feed-forward network architecture of an artificial neural network 100 illustrated according to an embodiment of the invention.

The artificial neural network 100 indicates, for example:
an input layer 102 with a variety of input neurons 110 (for example, with five input neurons 110 ), a first hidden neuron layer 104 with a multitude of first hidden neurons 112 (For example, with three first hidden neurons 112 ), a second hidden neuron layer 106 with a multitude of second hidden neurons 114 (for example, with three second hidden neurons 114 ) and an initial layer 108 with one or a plurality of starting neurons 116 (For example, with one or two output neurons 116 ).

In alternative embodiments, any number of layers (each with an arbitrary number of neurons in a respective layer) in an artificial neural network 100 be provided. The layers 102 . 104 . 106 . 108 each have nodes, the so-called neurons 110 . 112 . 114 . 116 , On the functioning and decision-making function of the neurons 110 . 112 . 114 . 116 will be discussed in more detail below. The neurons 110 . 112 . 114 . 116 are, as described above, in different layers 102 . 104 . 106 . 108 arranged. The layers 102 . 104 . 106 . 108 Form a layer sequence so that each neuron shares some or all of the previous and subsequent layers of neurons 102 . 104 . 106 . 108 connected is. The first layer (input layer 102 ) receives values of the input parameters (eg x ₁ , x _j , x _n ) of the model, the last layer (output layer 108 ) of the layer sequence outputs estimated target parameters (eg y ₁ , ..., y _m ) and other intervening layers (one or more hidden layers 104 . 106 ) perform the transformations that result in the training using the training data according to the chosen training method.

In 2 is a neuron model for a neuron 110 . 112 . 114 . 116 , shown schematically. According to the neuron model, the neuron takes a plurality of input signals 200. on. The input signals 200. may also be described by means of an input vector (eg x ₁ , ..., x _i , ..., x _n ). The input signals 200. are weighted with a weighting vector w _j and a weighted summation 210 for example, according to the following rule: Σw j x j , (1)

Following is a non-linear transformation 212 by means of an activation function f (x) and then the results 214 of the transformation according to the activation function f (x). The results 214 The transformation according to the activation function can also be estimated by means of a threshold value function or a threshold value to a binary result function.

The Activation function may have any suitable structure.

One embodiment of the non-linear transformation is the sigmoid transformation function defined by the following formula f (x) = 1 / (1 + e-x):

alternative can also use other functions, such as threshold functions or sections defined functions are used.

Further Other types of neurons, eg. B. perceptrons, biological neurons, pulsed neurons, etc. are used. In addition, in a particular neuron can also as an intermediate step State are filed.

The Model is due to a neural network architecture and a Set of experimentally determined "input-output" data points formed as a training set (or training set).

Specifically, the model is formed by arbitrary initializations and iterative optimizations of the set of weights w _jk , for example, to optimize the root mean square of the distance between the experimentally determined and estimated output values for each input value. This is also called training of the network or as a learning phase.

A Variety of non-linear optimization techniques, as they are in themselves may be known in an alternative embodiment of the invention are used.

In In one embodiment, the back-propagation feed-forward multilayer neural network becomes with either the generalized delta rule or the resilient Propagation (RPROP) learning algorithm with early termination (early stopping) controlled. It becomes a retention validation record for control used. This is done to control the model prediction ability a subset of the available data, commonly called a validation record used, so that in each iteration the reliability of the model generated from the training data set against the validation record is verified. Other types of artificial neural networks and non-statistical learning methods, which are similar Features provide, in an alternative embodiment be provided of the invention. Other types of neural networks, such as radial basis function networks (RBF networks) and fuzzy ART map (predictive adaptive resonance theory network) can be used in one embodiment be used. In addition, different kernel-based Methods for non-neural network approaches for this purpose can be used as a model to be trained, for example the support vector regression procedure.

to Preparation of the modeling will be done according to a Embodiment of the invention two preparatory steps carried out.

The data is filtered to remove under-represented factors. This increases the accuracy and stability of subsequent data modeling. For example, a histogram representing the distribution of each input factor may be set up. From this only the factors are used which extend over a sufficient range of values and reach a predetermined minimum number of sufficiently occupied levels, as described above with reference to, for example 13 has been described. This procedure can be repeated several times to account for factors that turn out to be underrepresented after removal of other factors and data points.

Secondly can be non-linear modifications of the input factors be introduced into the analysis, for example square root, quadratic and / or inverse functions of the original factors or also derived integer sizes like the number the input factors.

to The following are examples of data filtering cited.

In In one example, raw data set 336 has data points which are characterized by 74 factor values. The minimum required Data filtering area was 0.001 and a 10-level histogram was created in which the factors are at least two levels each must have at least two data points. It will formed a representative record of 324 points, whereby each point is characterized by 48 factor values.

In Another example is the formation of an artificial neural network model.

In this example, the number of values is 136 including 48 original factors and 88 modifications. For example, the total data set has 324 points after filtering as described above, and has been split into a training data set of 291 points and a validation data set of 33 points.

The Target color parameters L, a and b were determined by means of a feed forward KNN with a hidden layer with two each the RPROP optimization method neurons are modeled separately.

For the L parameter, the optimal model was at iteration 5644 achieved. A correlation coefficient R = 0.97, a training RMS error of 3.36 and a validation RMS error of 2.79 were achieved.

For the a parameter, the optimal model was at iteration step 20591 achieved. A correlation factor of R = 0.98, a training RMS error of 1.95, and a validation RMS error of 1.59 were achieved.

For the b parameter, the optimal model was at iteration step 5474 achieved. A correlation coefficient of R = 0.96, a training RMS error of 2.79, and a validation RMS error of 3.50 were achieved.

Referring to 3 Now the generation of expected formulations is written. In a preferred embodiment, a genetic algorithm for forming a solution data set is employed as a combination of input factor values which correspond to the specified target colors and also fulfill other relevant requirements. Such an algorithm involves the formation of a population of potential solutions and subsequent interaction (recombination), modification (e.g., mutation or drift) and selection in a stochastic process according to Darwinian theory of evolution.

A possible procedure is in a flow chart 300 in 3 shown.

At the beginning is an entrance population 302 given by data. The data record can also be a preselection or an optimized data record.

In 304 Operators are selected, which may be the operators described below, but may also be any factors, such as other mathematical factors or logical factors.

It become three in the present embodiment Evolutionary operators used: mutation, crossover and / or drift.

in the Case of the mutation is for a parent or individual or a solution candidate, a single randomly selected one Factor changed in predetermined, fixed steps.

in the Traps of crossovers are between two parents or between two Individuals or two solution candidates the factor value vectors exchanged in two randomly divided sections, so every child solution is a first part of the one Parent and a second part of the other parent receives.

in the Case of drift becomes for a parent or individual, or solution candidates, a minor accidental Offset into a single, randomly selected one Factor value introduced.

In 306 the parents are selected, that is, the individuals are determined to be reproduced and individuals to be replaced. This selection, which in this example is probability-based, is controlled by the effective fitness value, which is measured by one or more of the following components:
The color difference, e.g. ΔE, between the target color and the color predicted by the model for that combination of factor values.

In An embodiment of the invention will be in the fitness penalty (also referred to as fitness penalty value) the violation of predetermined Limits taken into account.

In An embodiment of the invention will be included in the Effective Fitness bonus value considered the age of the solution.

In An embodiment of the invention will be included in the Effective Fitness bonus value considered the uniqueness of the solution.

If these values are met for a generated model, it will be in step 312 a convergence displayed; if these values are not met, no convergence will be displayed and the procedure will be performed using these results 304 continued.

In 308 The children are produced from the selected parent or the selected parents by reproduction.

In 310 the population is adjusted. Thereafter, the population is evaluated according to the convergence to the desired solution. If no optimal solution was found, in other words, no suitable formulation (in other words formulation) was determined, the steps become 304 . 306 . 308 and 310 repeated. The steps can also be performed in parallel or in a different order, as well as recursively or arbitrarily repeatedly. Otherwise, there is an optimal solution.

In alternative embodiments of the invention can alternative optimization methods especially in the field of heuristic optimization methods are used, such as Evolution strategies, simulated cooling, deluge algorithm, Ant algorithm, swarm optimization.

The artificial neural network, generally the one to be trained or the trained model as described above now used to predict the resulting color for any combination of factor values, in other words, input parameters, for example, the input parameters described above. However, this can also be done by other modeling methods in an alternative Embodiment of the invention to be replaced.

moreover be in an alternative embodiment of the invention next to the color alternatively or in addition other target sizes considered.

In According to one embodiment, the predetermined one to be observed Range of a parameter as part of optimization by a penalty function considered. This penalty function is a square function the distance between the actual value a parameter and its default range. By a careful Choice of limits can have different optimization problems be solved.

The possibility of diversity control of the genetic algorithm used according to an embodiment of the invention serves to prevent premature convergence and thus collapse of the search space to small variations of a single good solution. This is based on the application of predetermined "bonus values" in the calculation of the effective fitness. The age of the solution is taken into account in order to achieve a certain stability, as well as the "uniqueness" of the solution, ie the mean distance in the factor space to other solutions of the population, considered. In one embodiment, the linear sigmoid bonus function is used, which behaves linearly from A1 to A2 in the interval from B1 to B2. The function argument (x) is the relative rank of the solution, ie the rank positions divided by the total number of solutions, relative to a given parameter:

In An example is the reduction of the number of components in one Formulation, ie the simplification of a recipe, shown become.

Based on the basic concept described above and starting from a given starting formulation, which six components contains, a first set of color parameters is given.

• (1) eine vorhergesagte Farbe aufweisen, die der angestrebten Zielfarbe sehr nahe kommen;
• (2) bis zu fünf Komponenten aufweisen;
• (3) andere vorgegebene Grenzen erfüllen.

A deviation from given parameters is penalized by penalty values. Wish king NEN additional limits and boundary conditions are taken into account, for example, an upper limit of the number of available components to z. B. to reduce the number of components and / or to ensure compliance with certain relationships between different components, eg. B. to comply with the required stoichiometry of the chemical reactions. Once the convergence in the genetic algorithm is achieved or a predetermined and sufficient number of loops have been traversed in the genetic algorithm, one or more solutions or formulations are achieved

• (1) have a predicted color very close to the intended target color;
• (2) have up to five components;
• (3) meet other predetermined limits.

These Solutions can then be analyzed and experimentally verified become.

Of Further, an example will be given for removing individual ones Components from a formulation.

• (1) eine vorhergesagte Farbe aufweisen, welche der Zielfarbe nahestehend ist;
• (2) die entfernte Komponente nicht mehr enthalten;
• (3) andere vorgegebenen Grenzen erfüllen. Eine solche Lösung kann anschließend analysiert und experimentell überprüft werden.

To remove a single component from a given formulation will be based on the in 3 shown procedure 300 determines a first set of target color parameters and the parameter limits. Depending on the goal set, additional constraints and constraints may also be considered, such as the addition or replacement of other additional components, and / or compliance with certain relationships between different components. Once the convergence has been achieved in the genetic algorithm or a predetermined and sufficient number of loops have been traversed in the genetic algorithm, one or more solutions (formulations) are obtained

• (1) have a predicted color that is close to the target color;
• (2) no longer contain the removed component;
• (3) meet other predetermined limits. Such a solution can then be analyzed and experimentally verified.

4 shows the main window 400 a user interface of a computer program, which implements the method described above according to an embodiment of the invention. The main window 400 is subdivided into three sub-windows: an upper left sub-window 402 with a data table, an upper right pane 404 with the color display window and a lower pane 410 with a table of the factor values of the processed formulations.

In the upper left pane 402 specify the names of the formulations. In addition, the experimental and, if present, the calculated color values are output. The color values can also be found in the upper right pane 404 for experimental data and calculated colors 408 visualized, on the one hand, the current color is represented in a color field on the other hand, the position of the color value as a point in the color space (eg Lab or xyY). In the lower pane 410 the production parameters and the composition of the currently selected formulation are shown.

It can according to one embodiment not only all historical data are presented, but also defined subsets, eg. For example, all data points in a defined Color range or all data points with a given match between experiment and theory, etc. This helps the product developer in the search for alternative formulations of a particular Color in the pool of existing formulations.

The Input and output parameters of the above-mentioned model represented by a software program. Naturally can also use other screen images as well as others be provided alternative programs that are suitable to the results or to illustrate the process of modeling.

In the upper left pane 402 the modeling data set table is shown containing the following information for all formulation data points. The check box "Use", the formula ID number, if included in the data file, the experimentally determined L values, a values, b values, and for each model present the L values, a values, b values and if the experimental data are present, also the error (the color difference) between experimental and calculated color values, if any, in the form of the dE-measure and the experimentally perceptually optimized D _HCL -measure or dE94-measure.

When a data point has been selected by means of the keyboard or mouse, which is then highlighted, for example, the respective experimental and predicted colors become as they are in the adjacent partitions 404 . 408 shown visually and numerically. By selecting or selecting the data points by clicking on the "Use" box, the display is dynamically tracked and missing values are indicated by empty cells.

The record colors are displayed as points in the Lab room or xyY room, if possible with a connecting line, and the present color is marked with a crosshair. In the fields below 414 . 418 the displayed colors are listed and a number of editable boxes contain the numerical representations of the displayed colors in four color systems. To display subsequently edited color values, simply press the Enter key.

In addition to the experimental data 404 . 414 become predicted data in a second color block 408 and as numerical values 418 displayed (to select the currently used model, a drop-down box must be opened above). Missing or invalid values are shown hatched, for example.

The following tools are available in the color display:
Left mouse button and drag (rectangular area) to zoom in the Colorations box (for example, a, b) or in the brightness box (for example, L); Press control key and click left mouse button to toggle between a number of adjacent data points identified in the record field; right mouse click Click to zoom in (approximately double zoom) ;, right mouse button Double click to zoom out completely (100% representation of the available color space).

The Zoom adjustment can also be made through the "View" menu, which will be further described.

In the lower window 410 a table of factor values of the current formulation is displayed. Shown here is the file name and the program directory and / or the current directory.

The program menu is in the header of the main window 4 shown. It consists of the commands File, View, Select, Tools, Help. Specifically, the File menu is for opening data files, importing data files from the clipboard, such as: As Excel data or other, saving, exporting formulation data into third-party software, such. As well as the software NASAWin, and closing the program. The program uses an adaptive algorithm to save files with tab-delimited as well as space-separated data as used by NASAWin, ie to save Excel data to the clipboard.

The View menu provides the menu item Mode for selecting the color representation (eg Lab or xyY), markers for selecting different markers for the data point actually to be displayed, link for controlling the representation of connecting lines between the data points for the representation of the brightness L or Y data points for the display of the color values from or xy, with the All, Current, None settings. Furthermore, the View menu displays Zoom to adjust the zoom parameters in the color display 404 respectively. 408 with selections Auto Fit, Reset Full, Reset Fit, Adjust.

The Select menu allows the following options to be selected to execute a subset of the entire data, with only the selected data points, which are indicated by the "Use" check boxes are displayed in the color block.

The menu contains the following entries: All for selecting all formulations, None for deselecting all formulations, Invert for inverting the selection of formulations, additionally the items Color-Range for selecting the formulations that characterize in a particular color range Upper and lower limits of the Lab Values or within a prediction error range of the currently selected model. Color Around, which selects the formulations that fall within a specific tolerance range (eg dE and / or dE94 and / or D _HCL ) by a specific color, also has the menu item Visible for selecting the formulation data points that are in the current zoom range are visible and experiment to select formulations for which experimental data are available.

The Tools menu has a number of options that include Advanced Data Analysis and Da enable design.

To counts the menu item Predict, which is a prediction the color values among all possible models. The Results of the prediction are combined with the color difference measurement fed to the record table and in a second color block displayed. Failed predictions are null (blank Boxes) and are not shown in the color display.

Of the Menu item Filter performs a data filtering Removal of under-represented factors. Of the Menu item Design leads an interactive formulation design by changing the factor values.

Of the Menu item Generate leads the stochastic generation of formulations which give the target color by a genetic Algorithm through.

Of the Menu item Factors opens the supporting Factor directory window.

Of the Menu item model handles the amount of available Prediction models.

Of the Menu item Functions opens the supporting Factor Function List window.

Of the Options menu item specifies the parameters for control the program operation. There are available menu items the menu item ColorCorrection, which sets the color correction parameters (Gamma and illuminant) controls.

In 5 is the factor directory window 500 in which parameters for the input variables are defined, such as upper and lower limits (Min or Max), the step size (bar) of the values of the input variables or whether these boundary conditions - eg. B. in the course of an optimization - should be respected or not. Here you can specify which and how many input variables may be varied during formula optimization and how they may be varied. Are z. B. for a raw material, the upper and lower limits set to zero and demanded compliance with the limits, you will receive in the course of optimization only formulations that do not contain this raw material. This can be used to find alternatives to existing formulations based on critical raw materials.

The Factor directory window includes a number of important parameters for every factor. When a new factor first read , these parameters are automatically determined and can manually refined. The window includes the following criteria which are shown in the upper line. Fullname gives the name of the factor to be displayed again. The menu items Min or Max show a possible minimum or maximum Value for the factor. The menu item Strict shows the enforcement of the minimum and maximum limits: where "0", that injuries in a specific area are ignored, "1" that warnings are issued in case of violations of the area, and "2" means that hurtful values are automatically in the given ones Be attributed area, with different Program functions handle these injuries differently.

Of the Menu item Step gives the step size for the adjustment of the factor again, the menu item RepLevels gives the minimum Number of representative levels for factor filtering again. Unnecessary factors can be removed using the delete key be removed.

The 6 shows a prediction model (dictionary model) directory window 600 on, taking the selection 602 the selection of a NASAWin model allowed.

7 shows a Factor Functions window 700 , Here, linear functions based on the input variables can be compiled, the z. B. should be considered in the course of optimization. Here can be z. B. Define a cost function for the recipe based on the raw material costs and the raw material concentration or the process parameters used. As with the input variables themselves, upper and lower limits can be set for the functions. This allows z. For example, the search for formulas that are produced within a certain cost range, based on a fixed number of raw materials, or in which the raw materials are used in certain proportions, for example, the reactive dye precursors of the formulations, occur in a certain stoichiometric ratio.

The Factor Functions window is used as an indicator to simplify the specification and control of complex Pa parameters and limitations provided by summarizing many or even all factors. Each factor function is based on a certain linear combination of factor values (for example F = Σa _i F _i ). In the advertising 702 on the left side, for each function, the minimum values and maximum values and rules for handling overflows of given ranges, characterized by values for strict, are reproduced in a kind of directory. On the right side 704 the function parameters and the coefficients of the function are displayed. With the functions Save, Clear and Delete the parameters can be adjusted or saved accordingly.

Two special functions are provided in one embodiment of the invention whose names start with a diamond sign (#) and which are calculated as count-based functions. In this case, instead of the actual factor value F _i, the value "1" is displayed for all factors not set to zero and the value "0" for all factors set 0.

In the example in 7 the program checks according to the function #base whether exactly one basic formulation exists, the function #count indicates or indicates a total number of all predetermined components in the formulation.

dargestellt wird.If the function starts with a dollar ($) character, the function is renormalized. That means that here is the normalized function:

is pictured.

wobei a_i = 1/M_i für C ist und a_i = –1/M_i für D ist (wobei M die molare Masse darstellt und F_i, C bzw. D die Konzentration von der Komponente F_i, C bzw. D).Such a function is useful if the terms have different signs. This simplifies the handling of boundary conditions for quantity ratios. For example, a molar ratio (C / M _C ) / D / M _D ) = α, which is equivalent to the formula

where a _i = 1 / M _i for C and a _i = -1 / M _i for D (where M represents the molar mass and F _i , C and D respectively the concentration of the component F _i , C and D, respectively ).

Now is based on data filtering according to one embodiment the invention received.

The Data Filtering allows underrepresented Factors to increase accuracy and stability the resulting data modulation.

The Dialog window provides the following functions: the menu item minimum range defines the minimum of the acceptable range of a Factor.

Of the Menu item total levels refers to the number of levels for distribution in the histogram analysis. The menu item minimum postulated levels shows the minimum number of levels which have at least one data point.

Of the Menu item minimum representative population shows the minimum Number of data points in a level which is representative should be evaluated.

Of the Menu item minimum representative levels shows the minimum Number of representative levels.

The menu item Delete Factors deletes the under-represented factors (columns) from the data label le.

Of the Menu item Delete records deletes the data records (Rows), the entries for under-represented factors have, from the data table.

Of the Menu item Self Ease Filtering performs a Filtering in several passes through to underrepresented Factors to remove as well as the records, the entries for these under-represented factors, as long as exclusively sufficient represented Factors and only records from exclusively sufficiently represented factors in the data table are included.

8th shows a screen surface 800 of the interactive word processor according to an embodiment of the invention.

The Formulation Designer allows the formulation of a new formulation by manually adjusting the factor values. The currently selected formulation in a data set is used as a starting point. The wording designer window has three panes, a lower left pane 802 allows you to adjust the factors by directly entering the desired values or by clicking the arrow keys with the mouse. Modified factors, for example, in a marker color, z. In red, deposited if its value is outside the permitted range. An upper left window 808 represents a table representing the function values calculated from the current factor values. Values that exceed a given range of the function specified in the factor directory window are displayed, for example, in a marker color, e.g. B. in red, deposited.

A right pane 804 respectively. 806 represents a color window for the hair coloring. The start color value is indicated by interconnected circles according to an embodiment. The running color is displayed as a factor value combination with a crosshair in the top right-hand pane 804 or as a numeric display in the lower right window 806 shown. Using a drop-down box, the model used for the prediction can be selected.

9 shows a screen surface 900 of the formulation generator showing the result as a population of factor solutions. These are calculated using the model described above and trained using the training data set. The window 900 is divided into four parts.

An upper left window 900 displays the ads PopSize as the size of the solution population, MaxSteps as the maximum number of evolutionary steps. The menu item MinSearch as the minimum number of non-productive steps before termination. The menu item PropMut, which displays the probability of occurrence of the mutation operator. The menu item PropCross, which indicates the probability of the occurrence of the crossover operator and the menu item dist, which has the difference of the measured color in relation to the fitness function (dE or D _HCL ).

9 shows the stochastic formulation generator that can be used to generate new formulations.

Of the Formulation Generator optimizes formulations with regard to certain target values of constraints (eg optimizing color and cost in a fixed number or selection of raw materials) He makes Gebrach from an evolutionary algorithm. This becomes a population of formulations and the associated process parameters (together: factor settings) of an evolution based on the Mechanisms of selection, mutation and propagation are subject to a set of factor settings is obtained which the desired Target values and boundary conditions met. One in this way The solution obtained is interpreted as the optimal solution. This reduces the development effort for a hair coloring considerably in the laboratory and thus supports the work of the Product developer.

A lower window 914 . 912 has the penalty factors for violation of the factor function ranges (upper table) 914 and the factor ranges (lower table) 912 , It determines the weighting of the corresponding penalty function, which in turn represents the square of the distance of the associated parameter value from the predetermined range.

A window at the bottom left 908 The parameter buttons represent the available button Save, Load, Reset the current parameter settings can be saved, loaded and restored to their original state. The lower left window 910 represents the control of the formulation generator. By clicking on Run, calculation starts and the designation of the button changes from run to stop. By clicking on Stop the calculation can be stopped prematurely. The PopSize indicator shows the current population size. The menu item step shows the current evolutionary step.

Of the Menu item Fitness shows the fitness value for the best solution of the population with reference to the color deviation and the values of the penalty functions (penalties).

With the buttons Save, Export and Close under the window 910 the program can be operated. Save saves the best solution in the dataset. Export saves the entire population in a file. Close closes the Formulation Generator. In the right side is under 904 a color display is shown, where the individuals of the current population are represented by circles and the target color by a crosshair in 904 is marked In 906 the numeric representation of the target color is displayed.

QUOTES INCLUDE IN THE DESCRIPTION

This list The documents listed by the applicant have been automated generated and is solely for better information recorded by the reader. The list is not part of the German Patent or utility model application. The DPMA takes over no liability for any errors or omissions.

Cited patent literature

• - EP 1138347 A1 [0009]
• - EP 1380720 A1 [0010, 0011]

Claims (88)

Method for computer-aided determination at least one property of a hair coloring when used of chemically reactive formulations, • where information about chemically reactive formulations fed to a predetermined model become; • where the predetermined model is an illustration information on chemically reactive formulations at least one property of a corresponding hair coloring describes a variety of previously determined hair colorations; • in which using the predetermined model, the at least one property the result of a hair coloring when using the chemical reactive formulations is determined. Method according to claim 1, in which the information about chemically reactive formulations contain at least one of the following information: • Concentration information about the chemically reactive formulations (raw materials?); • one Indication of the type of basic formulation; • one Indication of the mixing ratio between a Color cream used in the respective hair coloring and a developing solution used in the respective hair coloring; • of the pH of an application mixture that is characterized by mixing one at the color of hair used in each hair color and a the developer solution used in the respective hair coloring results; • Concentration information about raw materials in an application mix that is characterized by mixing one at the respective Haircoloration used color cream and one at the respective Haircolor used developer solution. A method according to claim 1 or 2, wherein the chemically reactive formulations at least one dye and / or at least one dye precursor. Method according to one of the claims 1 to 3, wherein the chemically reactive formulations at least an oxidative hair dye and / or at least one oxidative Hair dye precursor included. Method according to one of the claims 1-4, the predetermined model using information about chemically reactive formulations as input variables and at least one property of a corresponding result a hair color as the output of a variety previously determined hair colorations is trained. Method according to claim 5, • in which one tuple each of input variables and output variable forming a training record for a hair colorant; • in which a subset of training records from a total of training records for training the predetermined one Model is selected. A method according to claim 6, wherein from the total amount of training records to train the training predetermined model selected those training records for their chemically reactive formulations used there are a number of training records that are larger or equal to a predetermined threshold. Method according to one of the claims 1 to 7, wherein the at least one property of a corresponding Result of hair coloring at least one of the following properties includes: • a color information, which the describes the resulting hair color of hair coloring; • one Information about a light fastness of hair color of hair coloring; • one Information about a wash fastness of hair color of hair coloring; • one Information on a gray coverage of the hair color of the hair coloring; • one Information about the cost of the used chemically reactive formulations; • information about the Quality of hair coloring. Method according to one of claims 1 to 8, wherein as the predetermined model at least one of the following models is used: • at least one artificial neural network; • at least one fuzzy logic model; • at least one support vector machine; • At least one decision tree; • at least one Bayesian network. Method according to one of the claims 1 to 9, wherein the at least one property of a corresponding Result of a hair coloration at least one color information contains the resulting hair color of hair coloring describes, for coding color information one of the following Color spaces is used: • Lab color space; • xyY color space; • XYZ color space; • RGB color space; • CMYK color space; • HSV color space; • LCh color space; • I1I2I3 color space; • YCbCr color space; • YPbPr color space; • YUV color space; • YIQ color space. Method according to one of the claims 1-10, wherein the predetermined model includes a plurality of sub-models having. The method of claim 11, wherein at least a sub-model of the plurality of sub-models is an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. The method of claim 12, wherein all sub-models of the plurality of sub-models each have an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. Method for computer-aided determination at least one recipe for a hair color, • in which at least one desired property of the hair coloring a predetermined Model is supplied; • where the predetermined Model an illustration of information about chemically reactive Formulations on at least one property of a corresponding hair coloring describes a variety of previously determined hair colorations; • in which using the predetermined model information about chemically reactive formulations are determined; and • in which from the information on chemically reactive formulations the recipe for a hair coloration is determined. Method according to claim 14, • in which the predetermined model is changed; and • in which the process is carried out repeatedly using of the changed predetermined model. A method according to claim 14 or 15 • taking the recipe using an evolutionary Method (algorithm) is determined • according to the evolutionary method (algorithm) the predetermined Model is changed. Method according to one of the claims 14 to 16, using as evolutionary algorithm a genetic algorithm is used. Method according to one of the claims 14 to 17, where the evolutionary algorithm at least has a mechanism of mechanisms evaluation, mutation, Recombination, selection. A method for computer-aided determination of a final formulation of one or a plurality of chemically reactive substances and / or non-reactive substances and / or formulations for hair coloring, wherein a formulation of a plurality of chemically reactive substances using at least one predetermined model, an evolutionary algorithm is applied, whereby an end recipe is determined, wherein the at least one predetermined model an image of information about chemically reactive substances and / or non-reactive substances and / or formulations on at least one property of a corresponding hair coloring a variety previously determined Describes hair colorations; • taking into account at least one target property within the evolutionary algorithm; Wherein information about chemically reactive substances and / or non-reactive substances and / or formulations is determined using the predetermined model; and • based on this information, the final formulation for a hair coloration is determined. Method according to claim 19, in which the information about chemically reactive formulations contain at least one of the following information: • Concentration information about the chemically reactive formulations; • an indication of the type of basic formulation; • an indication of the mixing ratio between one at each Haircoloration used color cream and one at the respective Hair coloring used developer solution; • of the pH of an application mixture that is characterized by mixing one at the color of hair used in each hair color and a the developer solution used in the respective hair coloring results; • Concentration information about raw materials in an application mix that is characterized by mixing one at the respective Haircoloration used color cream and one at the respective Haircolor used developer solution. A method according to claim 19 or 20, wherein the chemically reactive formulations at least one Dye and / or contain at least one dye precursor. Method according to one of the claims 19 to 21, wherein the chemically reactive formulations at least an oxidative hair dye and / or at least one oxidative Hair dye precursor included. Method according to one of the claims 19 to 22, wherein at least one predetermined model using information about chemically reactive formulations as input quantities and at least one property a corresponding result of a hair coloring as a starting point a variety of previously determined Haarcolorationen is trained. Method according to claim 23, • in which one tuple each of input variables and output variable forming a training record for a hair colorant; • in which a subset of training records from a total of training records for training the respective predetermined model is selected. The method of claim 24, wherein from the total amount of training records for training of the predetermined model those training records be selected for their used chemically reactive formulations a number of training records present, which is greater than or equal to a predetermined Threshold. Method according to one of the claims 19 to 25, wherein the at least one property of a corresponding Result of hair coloring at least one of the following properties includes: • a color information, which the describes the resulting hair color of hair coloring; • one Information about a light fastness of hair color of hair coloring; • one Information about a wash fastness of hair color of hair coloring; • one Information on a gray coverage of the hair color of the hair coloring; • one Information about the cost of the used chemically reactive formulations; • information about the Quality of hair coloring. Method according to one of claims 19 to 26, wherein as a predetermined model at least one of the following models is used: • at least one artificial neural network; • at least one fuzzy logic model; • at least one support vector machine; • at least one decision tree; • at least one Bayesian network. Method according to one of the claims 19 to 27, wherein the at least one property of a corresponding Result of a hair coloration at least one color information contains the resulting hair color of hair coloring describes, for coding color information one of the following Color spaces is used: • Lab color space; • xyY color space; • XYZ color space; • RGB color space; • CMYK color space; • HSV color space; • LCh color space; • I1I2I3 color space; • YCbCr color space; • YPbPr color space; • YUV color space; • YIQ color space. Method according to one of the claims 19 to 28, wherein at least one predetermined model of the plurality of predetermined models comprises a plurality of partial models. A method according to claim 29, wherein at least a sub-model of the plurality of sub-models is an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. The method of claim 30, wherein all sub-models of the plurality of sub-models each have an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. Method for computer-based training a predetermined model for computer-aided determination at least one property of a hair coloring when used of chemically reactive formulations, • where the predetermined model using information about chemically reactive formulations as input variables and at least one property of a corresponding result a hair color as the output of a variety previously determined hair colorations is trained, in each case a tuple of inputs and output forming a training record for a hair colorant; • in which a subset of training records from a total of training records for training the predetermined one Model is selected. The method of claim 32, wherein from the total amount of training records for training of the predetermined model those training records be selected for their used chemically reactive formulations a number of training records present, which is greater than or equal to a predetermined Threshold. A method according to claim 32 or 33 the information about chemically reactive Formulations contain at least one of the following information: • Concentration information about the chemically reactive formulations; • an indication of the type of basic formulation; • an indication of the mixing ratio between one at each Haircoloration used color cream and one at the respective Hair coloring used developer solution; • of the pH of an application mixture that is characterized by mixing one at the color of hair used in each hair color and a the developer solution used in the respective hair coloring results; • Concentration information about raw materials in an application mix that is characterized by mixing one at the respective Haircoloration used color cream and one at the respective Haircolor used developer solution. Method according to one of the claims 32 to 34, wherein the chemically reactive formulations at least a dye and / or at least one dye precursor. Method according to one of the claims 32 to 34, wherein the chemically reactive formulations at least an oxidative hair dye and / or at least one oxidative Hair dye precursor included. Method according to one of the claims 32 to 36, wherein the at least one property of a corresponding Result of hair coloring at least one of the following properties includes: • a color information, which the describes the resulting hair color of hair coloring; • one Information about a light fastness of hair color of hair coloring; • one Information about a wash fastness of hair color of hair coloring; • one Information on a gray coverage of the hair color of the hair coloring; • one Information about the cost of the used chemically reactive formulations; • information about the Quality of hair coloring. Method according to one of the claims 32 to 37, wherein as the predetermined model at least one the following models are used: • at least an artificial neural network; • at least a fuzzy logic model; • at least one support Vector Machine; • At least one decision tree; • at least a Bayesian network. Method according to one of the claims 32 to 38, wherein the at least one property of a corresponding Result of a hair coloration at least one color information contains the resulting hair color of hair coloring describes, for coding color information one of the following Color spaces is used: • Lab color space; • xyY color space; • XYZ color space; • RGB color space; • CMYK color space; • HSV color space; • LCh color space; • I1I2I3 color space; • YCbCr color space; • YPbPr color space; • YUV color space; • YIQ color space. Method according to one of the claims 32-39, wherein the predetermined model comprises a plurality of sub-models having. The method of claim 40, wherein at least a sub-model of the plurality of sub-models an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. The method of claim 41, wherein all sub-models of the plurality of sub-models each have an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. Arrangement for determining at least one property hair coloring using chemically reactive formulations, • With an input unit for inputting information about chemically reactive formulations into a predetermined model; • With a model unit having a predetermined model, wherein the predetermined model is a map of information about chemically reactive formulations to at least one property a corresponding hair coloring of a variety previously determined Describes hair colorations; • with a hair coloration property determination unit for determining the at least one property of the result of a Hair coloring when using the chemically reactive formulations using the model model's predetermined model. Arrangement according to claim 43, in which the information about chemically reactive formulations contain at least one of the following information: • Concentration information about containing chemically reactive formulations; • one Indication of the type of basic formulation; • one Indication of the mixing ratio between a Color cream used in the respective hair coloring and a developing solution used in the respective hair coloring; • of the pH of an application mixture that is characterized by mixing one at the color of hair used in each hair color and a the developer solution used in the respective hair coloring results; • Concentration information about raw materials in an application mix that is characterized by mixing one at the respective Haircoloration used color cream and one at the respective Haircolor used developer solution. Arrangement according to claim 43 or 44, wherein the chemically reactive formulations at least one Dye and / or contain at least one dye precursor. Arrangement according to one of the claims 43 to 45, wherein the chemically reactive formulations at least an oxidative hair dye and / or at least one oxidative Hair dye precursor included. Arrangement according to one of the claims 43-46, with a model training unit for training the predetermined one Model using information about chemical reactive formulations as inputs and at least one property of a corresponding result of a Hair colouration as an output of a variety previously determined hair colorations. Arrangement according to claim 47, • in which one tuple each of input variables and output variable forming a training record for a hair colorant; • With a training data set selecting unit for selecting a subset of training records from a total of training records for training the predetermined one Model. Arrangement according to claim 48, wherein the training data set selecting unit is set up to select those training records the total amount of training records for training the predetermined model, for their used chemically reactive Formulations contains a number of training records, which is greater than or equal to a given one Threshold. Arrangement according to one of the claims 43 to 49, wherein the at least one property of a corresponding Result of hair coloring at least one of the following properties includes: • a color information, which the describes the resulting hair color of hair coloring; • one Information about a light fastness of hair color of hair coloring; • one Information about a wash fastness of hair color of hair coloring; • one Information on a gray coverage of the hair color of the hair coloring; • one Information about the cost of the used chemically reactive formulations; • information about the Quality of hair coloring. Arrangement according to one of the claims 43 to 50, wherein as the predetermined model at least one the following models are used: • at least an artificial neural network; • at least a fuzzy logic model; • at least one support Vector Machine; • At least one decision tree; • at least a Bayesian network. An assembly according to any one of claims 43 to 51, wherein the at least one property of a corresponding result of a hair coloration contains at least one color information describing the resultant hair color of the hair coloration using color information of one of the following color spaces for coding: Lab color space; • xyY color space; • XYZ color space; • RGB color space; • CMYK color space; • HSV color space; • LCh color space; • I1I2I3 color space; • YCbCr color space; • YPbPr color space; • YUV color space; • YIQ color space. Arrangement according to one of the claims 43 to 52, wherein the predetermined model comprises a plurality of sub-models having. Arrangement according to claim 53, wherein at least a sub-model of the plurality of sub-models an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. Arrangement according to claim 54, wherein all sub-models of the plurality of sub-models each have an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. Arrangement for determining at least one recipe a plurality of chemically reactive formulations for a hair color, • with an input unit for Entering at least one desired property of hair coloring into a predetermined model; • with a model unit, which has a predetermined model, wherein the predetermined model an illustration of information about chemically reactive Formulations on at least one property of a corresponding one Haircoloration of a variety of previously determined hair colorations describes; • with a formulation determination unit to determine information about chemically reactive Formulations using the predetermined model of the model unit; • With a recipe determination unit for determining the recipe of a A plurality of chemically reactive formulations for the Hair coloration. Arrangement according to claim 56, in which the model unit is set up so that it • the changed predetermined model; and • the modified model provided to the repeated Determine information about chemically reactive formulations using the modified predefined model. Arrangement according to claim 56 or 57, set up to perform an evolutionary A method for determining the recipe, wherein according to the evolutionary process changed the recipe becomes. Arrangement according to one of the claims 56-58, where the evolutionary process is a genetic Algorithm has. Arrangement according to one of the claims 56 to 59, wherein the evolutionary process at least one mechanism has mechanisms of evaluation, mutation, recombination, selection. Arrangement for determining a formulation of a plurality of chemically reactive formulations for hair coloring, with a model determination unit for determining an end model, wherein the model determination unit is set up in such a way that an evolutionary algorithm is performed on a plurality of predetermined models, wherein each predetermined model of the plurality of predetermined models describes mapping information about chemically reactive formulations to at least one property of a corresponding hair coloration of a plurality of previously determined hair colorations; With an input unit for inputting at least one desired property of the hair coloring into the end model; With an information-gathering unit for determining information about chemically-reactive formulations using the end-model; and • a recipe determination unit for determining the recipe of a plurality of chemically reactive ones Formulations for a hair coloring from the information on chemically reactive formulations. Arrangement according to claim 61, in which the information about chemically reactive formulations contain at least one of the following information: • Concentration information about containing chemically reactive formulations; • one Indication of the type of basic formulation; • one Indication of the mixing ratio between a Color cream used in the respective hair coloring and a developing solution used in the respective hair coloring; • of the pH of an application mixture that is characterized by mixing one at the color of hair used in each hair color and a the developer solution used in the respective hair coloring results; • Concentration information about raw materials in an application mix that is characterized by mixing one at the respective Haircoloration used color cream and one at the respective Haircolor used developer solution. Arrangement according to claim 61 or 62, wherein the chemically reactive formulations at least one Dye and / or contain at least one dye precursor. Arrangement according to one of the claims 61 to 63, wherein the chemically reactive formulations at least an oxidative hair dye and / or at least one oxidative Hair dye precursor included. Arrangement according to one of the claims 61-64, with a model training unit for training the predetermined one Model using information about chemical reactive formulations as inputs and at least one property of a corresponding result of a Hair colouration as an output of a variety previously determined hair colorations. Arrangement according to claim 65, • in which one tuple each of input variables and output variable forming a training record for a hair colorant; • With a training data set selecting unit for selecting a subset of training records from a total of training records for training the predetermined one Model. Arrangement according to claim 66, wherein the training data set selecting unit is set up to select those training records the total amount of training records for training the predetermined model, for their used chemically reactive Formulations contains a number of training records, which is greater than or equal to a given one Threshold. Arrangement according to one of the claims 61 to 67, wherein the at least one property of a corresponding Result of hair coloring at least one of the following properties includes: • a color information, which the describes the resulting hair color of hair coloring; • one Information about a light fastness of hair color of hair coloring; • one Information about a wash fastness of hair color of hair coloring; • one Information on a gray coverage of the hair color of the hair coloring; • one Information about the cost of the used chemically reactive formulations; • information about the Quality of hair coloring. Arrangement according to one of the claims 61 to 68, as a predetermined model, at least one the following models are used: • at least an artificial neural network; • at least a fuzzy logic model; • at least one support Vector Machine; • At least one decision tree; • at least a Bayesian network. An arrangement according to any one of claims 61 to 69, wherein the at least one property of a corresponding result of a hair coloration contains at least one color information describing the resulting hair color of the hair coloration using color information of one of the following color spaces for coding: Lab color space; • xyY color space; • XYZ color space; • RGB color space; • CMYK color space; • HSV color space; • LCh color space; • I1I213 color space; • YCbCr color space; • YPbPr color space; • YUV color space; • YIQ color space. Arrangement according to one of the claims 61 to 70, wherein at least one predetermined model of the plurality of predetermined models comprises a plurality of partial models. Arrangement according to claim 71, wherein at least a sub-model of the plurality of sub-models is an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. Arrangement according to claim 72, wherein all sub-models of the plurality of sub-models each have an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. Arrangement for training a predetermined model for computer-aided determination of at least one property hair coloring using chemically reactive formulations, • With a model training unit for training the predetermined model using information about chemically reactive Formulations as input quantities and at least a property of a corresponding result of a hair coloring as the output of a variety previously determined Hair colorations, each with a tuple of input sizes and output a hair coloration a training record forms; and • with a training record selection unit to select a subset of training records from a total of training data sets for training of the predetermined model. Arrangement according to claim 74, wherein the training data set selecting unit is set up to select those training records the total amount of training records for training the predetermined model, for their used chemically reactive Formulations contains a number of training records, which is greater than or equal to a given one Threshold. Arrangement according to claim 74 or 75, the information about chemically reactive Formulations contain at least one of the following information: • Concentration information about containing chemically reactive formulations; • one Indication of the type of basic formulation; • one Indication of the mixing ratio between a Color cream used in the respective hair coloring and a developing solution used in the respective hair coloring; • of the pH of an application mixture that is characterized by mixing one at the color of hair used in each hair color and a the developer solution used in the respective hair coloring results; • Concentration information about raw materials in an application mix that is characterized by mixing one at the respective Haircoloration used color cream and one at the respective Haircolor used developer solution. Arrangement according to one of the claims 74 to 76, wherein the chemically reactive formulations at least a dye and / or at least one dye precursor. Arrangement according to one of the claims 74 to 77, wherein the chemically reactive formulations at least an oxidative hair dye and / or at least one oxidative Hair dye precursor included. Arrangement according to one of claims 74 to 78, wherein the at least one property of a corresponding result of a hair coloration contains at least one of the following properties: Color information describing the resulting hair color of hair coloring; • information about a light fastness of the hair color of hair coloring; • information about a wash fastness of the hair color of hair coloring; • information about a gray coverage of the hair color of hair coloring; • information about the costs of the chemically reactive formulations used; • Information about the quality of hair coloring. Arrangement according to one of the claims 74 to 79, wherein the predetermined model is at least one of the following models have: • at least one artificial one neural network; • at least one fuzzy logic model; • at least a support vector machine; • At least one decision tree; • at least a Bayesian network. Arrangement according to one of the claims 74 to 80, wherein the at least one property of a corresponding Result of a hair coloration at least one color information contains the resulting hair color of hair coloring describes, for coding color information one of the following Color spaces is used: • Lab color space; • xyY color space; • XYZ color space; • RGB color space; • CMYK color space; • HSV color space; • LCh color space; • I1I2I3 color space; • YCbCr color space; • YPbPr color space; • YUV color space; • YIQ color space. Arrangement according to one of the claims 74 to 81, wherein the predetermined model comprises a plurality of sub-models having. Arrangement according to claim 82, wherein at least a sub-model of the plurality of sub-models an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. Arrangement according to claim 83, wherein all sub-models of the plurality of sub-models each have an illustration information about chemically reactive formulations to exactly one property of a corresponding hair coloration Variety of previously determined hair colorations describes. Computer-readable storage medium on which a computer program code for computer-aided determination of at least one property a hair coloring when using chemically reactive formulations which is stored when executed by a processor is, has: • supplying information about chemically reactive formulations of a predetermined model; • in which the predetermined model is a map of information about chemically reactive formulations to at least one property a corresponding hair coloring of a variety previously determined Describes hair colorations; • Determine using of the predetermined model, the at least one property of the result of a Hair coloring when using the chemically reactive formulations. A computer-readable storage medium carrying computer program code for computer-aidedly determining at least one formulation of a plurality of chemically reactive formulations for hair coloring which, when executed by a processor, comprises: • supplying at least one desired property of the hair colorant to a predetermined model; Wherein the predetermined model describes mapping information about chemically reactive formulations to at least one property of a corresponding hair coloration of a plurality of previously determined hair colorations; Determine information about chemically reactive formulations using the predetermined model; and from the information on chemically reactive formulations, determine the formulation of a plurality of chemically reactive formulations for hair coloring. Computer-readable storage medium on which a computer program code for computer-aided determination of at least one recipe a plurality of chemically reactive formulations for a hair color that when executed by a processor is, has: • Performing on a plurality of predetermined models of an evolutionary process, whereby an end model is determined, each predetermined model of the plurality of predetermined models, a map of information about chemically reactive formulations to at least one property a corresponding hair coloring of a variety previously determined Describes hair colorations; • Feed at least a desired property of the hair coloring the determined end model; • Determine using the predetermined model information about chemically reactive formulations; and • Determine from the information on chemically reactive formulations the recipe of a plurality of chemically reactive formulations for a hair coloring. Computer-readable storage medium on which a computer program code for computer-based training of a predetermined model for computer-aided determination of at least one property hair coloring using chemically reactive formulations, which, when executed by a processor, comprises: • Work out of the predetermined model using information about chemically reactive formulations as input variables and at least one property of a corresponding result a hair color as the output of a variety previously determined hair colorations, each with a tuple of Input variables and output size forming a training record for a hair colorant; • Choose a subset of training records from a total of training records for training the predetermined one Model.