MXPA00010315A - Method for optimizing formulations - Google Patents

Abstract

A method is described for using a computer for optimizing formulations against a number of criteria. A model algorithm is provided for each of the criteria, each model algorithm providing a prediction for corresponding criteria when a candidate formulation is inputted into the model algorithm. Criteria are selected to optimize a set of candidate formulations. An algorithm is provided for optimization of the set of candidate formulations in accordance with the selected criteria. A first set of candidate formulations is provided and the optimization algorithm generates one or more new candidate formulations. All candidate formulations are inputted into the number of model algorithms to obtain predictions, and information of the set of candidate formulations obtained by generation and/or previous optimizations and/or experiments is used to select candidate formulations from the set to obtain a Pareto optimal set of candidate formulations.

Description

METHOD TO OPTIMIZE FORMULATIONS DESCRIPTION OF THE INVENTION • The present invention relates to a method for optimizing formulations against a number of criteria. The method can be advantageously applied using a process of optimization operated by computer. An example of an optimization method of this type is. { B 10 known in practice as CAD / Chem. The method comprises the use of a neural network model that provides property predictions in the introduction of a candidate formulation. An optimization algorithm is used to find a formulation against a set of desired properties. Weights must be activated property to each property to indicate the relative importance of each particular property. The restrictions on formulation ingredients and processing parameters can be expressed as rules. This method forces the user to assign a relative scale to the criteria against the formulation that is going to be optimized before running the optimization algorithm, so that although an optimized formulation is obtained, the relative scale is an inherent part of this formulation found, where the user can not see the effect of transactions between the criteria. WO 9720076 describes methods for optimizing formulations of Multiple components, where a large number of mixtures are analyzed to determine the formulation (s) with optimum properties In this known method, a label is associated with each candidate formulation. It will be apparent that this method is time consuming and requires significant amounts of work and costs. US-A-5,940,816 discloses a method for using a computer for multiple object decision support to improve a candidate solution for a transportation problem. There is no suggestion that this method is adequate to support the optimization of formulations. The invention provides an improved method for using a computer to optimize formulations against a number of criteria. According to the invention, there is provided a method for optimizing formulations against a number of criteria, comprising the steps of: (a) providing a model algorithm for each of the criteria, each model algorithm providing a prediction for a corresponding criterion when a candidate formulation is introduced into the model algorithm; and (b) selecting criteria to optimize a set of candidate formulations; and (c) providing an algorithm for the optimization of the group of candidate formulations according to the selected criteria; "J ^^^^^^^^^^ gj ^^^^ where a first set of one or more candidate formulations is provided, and wherein the optimization algorithm generates one or more new candidate formulations, and where • all candidate formulations are entered into the number of 5 model algorithms to obtain predictions and wherein information from the set of candidate formulations obtained through said generation and / or previous optimizations and / or experiments is used to select candidate formulations from of the set to obtain an optimal Pareto set of candidate formulations In this way, a method is provided through which an Pareto optimal set of candidate formulations with variable transactions between criteria is obtained. Transactions between different desired criteria can be examined in a way easy without the effort of preparing large numbers of mixtures The information obtained can also be used to select formulations to actually test the formulations. For the purpose of the invention, the term "formulation optimization" refers to the fact that for a formulation, the type of ingredients, their relative levels and the conditions for preparing the final formulation are selected so that a desired final formulation is obtained. For example, an optimization with reference to the type of ingredient can provide assistance, it is determined where a selection of a number of alternatives can be used. By For example, the selection of emulsifiers, surfactants, thickeners, etc. An optimization with reference to the relative level of • Ingredients can start, for example, from a list of 5 ingredients and find an optimized combination of these. For example, the optimization process can provide an indication of surfactant agent material ratios or fat blends in products. An optimization with reference to the conditions for preparing the final formulation may take into account, for example, • Processing conditions such as temperature, mixing speed, ripening times and the object of finding optimal combinations of these. Generally, a formulation optimization process according to the invention will take into account more than one of the above elements. Preferred optimization processes according to the invention involve optimization with reference to the • relative level of ingredients as described above. Then, this can be optionally combined with wrt of optimization with the type of ingredients and / or with reference to the manufacturing conditions. According to a preferred embodiment, the method of the invention may include a number of iteration steps in a loop, as follows: (i) a first set of one or more candidate formulations that are used as a starting point, (ii) ) the candidate formulations are introduced in the number of model algorithms to obtain predictions, • and 5 (iii) the optimization algorithm generates one or more new candidate formulations; and (iv) the new candidate formulations are used to introduce the number of model algorithms in the iteration step (n), 10 and where an optimal Pareto set is determined.

• Predictions to select the candidate formulations. The invention will also be explained with reference to the drawings wherein one embodiment of the method of the invention is shown schematically. Figure 1 schematically shows a system, for example, a computer suitable for performing the method of the invention, for example, running a program to perform a • mode of the method of the invention. Figure 2 shows schematically a diagram of a modality of the invention. Figures 3 and 4 show graphs to explain the method of the invention. Figure 5 shows a screen representation showing a set of solutions obtained through the method of the invention.

In the following description, one embodiment of a method for optimizing formulations against a number of criteria will be described. To optimize formulations, the described method can be • used to optimize formulations in the product fields 5 detergents, food products, personal care products, fabric care products, household care products, beverages, and the like. Figure 1 schematically shows, in a simplified form, a computer 1 having a keyboard 2 and a monitor fl 10 3 for user interaction with the program that modalizes the described method. In addition, the computer 1 comprises a memory 4 schematically indicated by a faded line, which may include both a hard disk memory and a RAM memory. All the model algorithms that can be used to perform the method are stored in a first part 5 of the memory, that is, a storage of model 5 algorithm. The model algorithms can be based on experimental data and / or • physical / chemical knowledge. In a preferred embodiment of the invention, at least one of the model algorithms used provides a prediction along with a prediction error bar in the introduction of a candidate formulation. The prediction error bar may be linear or non-linear. Said model algorithm providing a prediction together with a prediction error bar can be any system capable of calculating prediction error 25, for example, it can be a Bayesian neural network. aai ^^^ lüWM More generally, the model algorithms stored in the storage of model 5 algorithm can be neural networks, neural networks, linear regression models, approximation • of genetic function, arithmetic models, etc. As examples of model algorithms stored in storage 5 can be mentioned models that provide predictions and, if applicable, error bars of prediction on cost, molecular / mesoscale properties, such ran micelle characteristics and product structure, material properties (physical / chemical), such as detergency, foam height, bubble size and rheological parameters, biological properties, such as toxicity, biodegradation and antibacterial activity, sensory properties, such as foam sensory properties, sliding ability , Crisp capacity, and flow perception and consumed properties, such as brightness, cleanliness, and total bond. The memory 4 further comprises a second part or storage of optimization algorithm 6 for storing optimization algorithms, preferably including an algorithm optimization of multiple criteria, in an algorithm of optimal genetic optimization Pareto also known as genetic algorithm of multiple objects. The storage of optimization algorithm can also include algorithms for optimizing individual criteria, such as programming quadratic sequenced to simple method algorithms.

•? ^ ^ ¡^ $ J ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^ j & ^^^^ Finally, the memory 4 comprises a storage of candidate formulation 7 for storing candidate formulations or generally more candidate solutions found as a result of running the optimization method. During the run of the computer program that modalizes the method, a user can interact with the method through a suitable user interface. The method will be further described through the flow chart shown in Figure 2, with particular reference to the optimization of a detergent formulation. STEP I: Depending on the optimization of the specific formulation, the user will have to select from the storage of the orythm model 5, the model algorithms that correspond to the criteria against which the formulations are going to be optimized. These model algorithms are going to be used in the method. For example, in the optimization of a detergent formulation, four model algorithms 8-11 can be used, where the algorithm mode 8 is an arithmetic model providing a cost prediction based on the type and levels of the ingredients in the formulation. The model algorithm 9 is a Bayesian neural network providing prediction and prediction error bars on the foam properties of the detergent formulation based on the type and levels of the ingredients in the formulation. The Model 10 algorithm is a Bayesian neural network providing prediction and error bar prediction on the softness of the detergent formulation. Finally, the model 11 algorithm is a model based on physical / chemical knowledge providing a prediction and prediction error bar with • regarding the detergency of the detergent formulation. STEP II: In a first embodiment of the invention, a number of restrictions can be defined or selected by the user in an interactive way to define the window where the candidate formulations will be evaluated. These restrictions may be, for example, restrictions in the formulation space j 10 and / or may be lower and / or upper limits for each formulation component. For example, for a detergent formulation, these restrictions may define the minimum level of surfactant materials, builders, etc. Such restrictions, where appropriate, can be determined by some model, for example, a heuristic or rule-based processing model. Other examples of possible constraints are combinations of variables in the formulation space, for example, a • simple restriction,? X, = 1 or < 1, that is, it must not be greater than 100% of the components in a formulation. Other restrictions 20 may be dependent on legislative or chemical requirements. Other constraints may be defined or selected by the user in an interactive way, such restrictions apply to predictions and / or prediction error bars, that is, to property space. The possible restrictions are, for example, the * ^ fc ^^^ * ^^^^ j | 3¡ & i? requirement that the error bars be smaller than a certain degree and / or specific scales for the prediction values STEP lll: Before running the method, the optimization algorithm must be selected from the storage of optimization algorithm 5 and the criteria to optimize. These criteria are, for example, predictions, prediction error bars, if applicable, either to maximize or minimize. In the described modality, a genetic algorithm is used to find a set of candidate formulations Pareto optimal. According to the method described, the algorithm of • Pareto use operates to optimize formulations against multiple criteria without requiring the user to provide weight or similar factors, before running the optimization method. In this way, a set of formulations or solutions will be obtained Pareto optimal candidates. By examining the formulations the user of the method can see the transactions between the criteria. In this way, the user can obtain important information at a low level • cost since it is not necessary to prepare large numbers of different formulations to actually test and determine the properties. By evaluating the information obtained, the user can decide on the actual formulations for the additional test. STEP IV: To initiate the optimization, a first set of candidate formulations is provided, schematically shown at 12 in Figure 2, said set of formulations candidates comprise at least one formulation. It should be noted that the term "set" means a number of formulations or more generally solutions of at least one. The first set of candidate formulations may be a random set or may be obtained from current formulations above or may be the result of previous optimizations. In accordance with a specific embodiment of the invention, a candidate formulation can be obtained by performing the method with an optimization started, wherein the criteria to optimize are heavy. Said heavy optimization results in a The formulation and one or more formulations obtained in this way can be used as seeds to run the optimization method with the multi-objective genetic algorithm without the use of weight criteria. STEP V: With the first set of formulations 12, may perform a number of iteration steps in an iteration loop as schematically indicated by line 13 The number of iteration steps may be pre-set to a given number N or may be random until convergence of generated formulations. The candidate formulations are provided as input to the model algorithms 8-11 (e.g., as described above) resulting in a number of predictions and / or prediction error bars. As indicated by block 14, the optimization algorithm generates one or more new candidate formulations and in addition these new candidate formulations are introduced to the algorithms model 8-11. Block 15 indicates the use of the constraints defined to run the optimization method For the purpose of the invention, the optimization algorithm is adapted to generate Pareto optimal candidate formulations.

• In the step of generating new formulations, it is preferred to tune the generation of new candidate generations to the landscape character of the formulation landscape. The landscape of the formulations is a uniform landscape, where in the case of a genetic optimization algorithm, it is preferred to use a line search crossing operator to generate new formulations A. 10 candidates. As an alternative for a line search crossing operator, it is possible to use a convenient gradient algorithm to generate new candidate formulations. In addition, in general, in the generation of new candidate generations, the crossing operators, investment operators, operators of mutation and clone operators can be used in the genetic algorithm. STEP VI: in a final step 16 of the method described in • Pareto optimal set of candidate formulations, is selected from the set of formulations obtained through the steps of iteration and / or obtained through any previous optimization and / or through experiments, and through this selection, an optimized set of candidate formulations is obtained. The set of candidate formulations obtained after the iteration steps may comprise candidate formulations newly generated and / or candidate formulations of the first set. The optimized set of candidate formulations can be stored in the storage of candidate formulations 7 for further use. • Candidate formulations obtained as a result of optimization can be evaluated through visual inspection of transactions between two or more criteria. Figure 5 shows, by way of example, four windows, each one showing the set of Pareto optimized formulations (represented by points) against two criteria, for example, in this case detergency and predicted foam. This visualization can be used to interact in a dynamic way with optimization results. By moving the slide bars 19, the restrictions on the formulations and scales of desired properties can be varied. In the representation example of Figure 5, a formulation is illuminated and the predicted properties of these formulations are shown in window 20. It is noted that the evaluation of the results of the optimization is possible by applying additional restrictions to filter the set of formulations obtained by the optimization. 20 Of course, it can also be used in the evaluation of a chemical knowledge. Some of the candidate formulations may be selected to perform other experiments. The selection method can be algorithmic, for example, increase to the maximum the extension of the formulation space, and / or heuristic, by example, the use of chemical knowledge. Other experiments can be performed using classical branching or high-throughput or classification techniques. The results • obtained by the additional experiments in current formulations can be updated to improve the model algorithm. This will result in model algorithms that provide more accurate predictions and, if applicable, more accurate prediction error bars. Figure 3 shows, as an example, the ability of a Bayesian neural network to model the noise in the data. The graphics • shown in Figure 3, illustrate how prediction error bars can vary significantly in detergency predictions on two typical test fabrics A (Figure 3A) and B (Figure 3B). The larger error bars in Figure 3B indicate a higher noise data set. The graph indicates that the test fabric A has a better quality control, while B has a greater variation in the quality and response of the fabric. In general, • you can see that the use of error bars provides important information to the user to evaluate predictions of solutions candidates and to decide on the selection of candidate formulations to carry out other tests. It is possible to investigate the effect of variable formulations by examining the predictions obtained from the model algorithms. Figure 4 shows, by way of example, in the case of a detergent formulation, the effect of varying the level of surfactant on the weight of the foam without (Figure 4A) and with (Figure 4B) a foam enhancer Figure 4B indicates that adding 3% foam booster will result in a foam more • stable even at the lowest surfactant levels 5 As noted above, the optimization method can also be used, for example, to optimize formulations of food products, such as a margarine product. In the method, model algorithms can be used, for example, for cost and solid fat content at different temperatures. • Although in the described modality, the optimization method uses an iteration loop comprising running the model algorithms and running the optimization algorithm to generate new candidate formulations, it is possible to run the algorithm of optimization to generate new candidate formulations and run the advance model algorithms to obtain predictions and, if applicable, prediction error bars and then use the defined constraints and select formulations using all available information to obtain an optimized set of formulations In addition, it is not necessary to have a final selection step to obtain the optimized set if a Pareto optimization or another is involved to generate new candidate formulations.

Example I This example describes the method of the invention being applied to the formulation optimization of a shower gel that is gentle to the skin. A random formulation of a shower gel 5 comprising two surfactant materials (surfactant coagent 1 and surfactant coagent 2) was used as the starting formulation. Prediction algorithms to predict softness as a function of the level of the two ingredients were defined based on the data collected regarding how the # softness varies for the two ingredients and this was modeled using a Gaussian process model. The prediction algorithm also provided a value for the error bar in the prediction. Figure 5 shows the comparison of the empirical data set of real softness (left) where the distribution of input data is shown and the size of the marker represents the measure of smoothness and the response of the Gaussian process model • empirical (right). When the model is optimized to simultaneously minimize the prediction as the corresponding error bar, the set of formulations shown in Figure 5 is calculated. In this example, the prediction error bar scale is quite small, which is a consequence of having a data set where the points are distributed evenly in full. However, when the model is ^^^^^^^^^ @ ^^ &A & amp; unconditionally reduced to the minimum, the extreme value occurs when the data is absolutely scattered and the error bar is relatively large (when both ingredients are large), as shown in Figure 5. Next, the designer must decide whether to balance the reduction to the minimum of the softness measurement by accepting the risk that the prediction of the model may be inaccurate. Including error bars as targets in Pareto optimization, it ensures that reliable solutions are represented in the final solution set, as well as values speculative. • Figure 6 shows the Pareto front side calculated based on minimizing the softness measurement and also minimizing the corresponding error bar. The figure on the left shows the formulation values lying on the Pareto front, while the figure on the right shows the current Pareto front.

Example II Introduction 20 As a general property of the chemistry inherent in the formulations, the formulation landscapes are usually well behaved, and are probably smooth and can be differentiated without any major discontinuity. An example of an archetype is the pH titration curve. The increase in relative concentration from base to acid, in a simple total concentration equal to 100%, results in a sigmoidal response curve for pH. The empirical modeling of the formulation landscapes is typically achieved through bilinear / quadratic and neural net regression methods, and the corresponding error bars 5 can also be used to provide an indication of how the confident model is in its prediction. This example shows how an understanding of the formulation landscape can provide important information regarding the type of Pareto optimal solutions. In this example, it is assumed that the introduction space is convex and limited, a simple example • which is the simple restriction (addition to unit) that occurs in formulation optimization problems and that the models are continuous. It is also assumed that the object is to minimize each of the objectives. It must be within the ability of Any person skilled in the art will apply the teaching for other objective criteria.

• Case 1. Monotonic flange models A flange model was defined as one whose contours are parallel lines (hyperplane), therefore their extreme values lie at the limit of a convex, limited introduction space and no internal extreme occurs. This is monotonic when the projected function is monotonic. A simple example is a linear function, but it can also refer to a function of sigmoidal type, or a polynominal (x.w + 1) d, where w is the parameter vector and d is the order (uneven) of the polynominal. When each model has these properties, there is no locally optimal Pareto front and the globally optical Pareto front is a continuous curve (surface) connecting the extreme values of each model along the limit of the introduction space. If the introduction space is simple, the Pareto front consists of linear segments (hyperplane). This can be proven by assuming that an inner point can lie on the Pareto front and that the number of targets is smaller that the introduction space dimension (otherwise, all the • space can be Pareto optimal). For any given objective, it is possible to construct a steering tangent for all remaining targets that reduces the value of the selected target. Therefore, the original point was not Pareto optimal. Therefore, the Pareto optimal points may lie only over the limit. As an example, consider the case where the formulation problem is composed of two linear models, for example, fH. with coefficients that are not zero) and that the introduction space is simple (three-dimensional), each model will have a single minimum at a vertex in the introduction space. Assuming that the minimum of the models lies in different vertices (otherwise the problem of optimizing multiple problems is trivial), the globally optimal Pareto front lies along the simple boundary connecting the two vertices, as illustrated in the Figure 8 for two models of the form: y, = a'x1 + b'x2 + c'x3 (1) In this example, it is assumed that the smallest coefficient for y is a 'and the smallest coefficient for y2 is c2, and that in • both cases, the second efficient, b, is smaller than the average value than the other two. This is illustrated in Figure 8.

Case 2. Non-linear models without local maximum. Another useful class of models is that without local maximum that occurs in the introduction space. The quadratic models (definitive positives) are obviously a special case and an example • This is the error bar predictions associated with a linear model. Other special cases include models made of the sum of flange functions, when the sum is taken over no more than n flange functions (where n is the dimension of input space) these functions can be displayed and reach their extreme values over the limit of the input space. In these cases, there will still be no Pareto fronts locally optimal • and the globally optimal Pareto front is a curved surface that stretches between the minimum values of the model and can lie on top of it. limit or inside the limited introduction space. This is illustrated in Figure 9 for the two models, each constructed from the sum of the two sigmoidal functions.

Case 3. Models with maximum internal aspects. 25 Although the two previous cases contain many well-known modeling algorithms, they are relatively restrictive. Many models (for example, some quadratics) will contain local maximum points and potentially several minimum points. • local. Although this is not theoretically a problem for global search algorithms, in practice, the algorithm may get stuck in a local region for a long period and concentrate on the locally optimal Pareto fronts defined in that local region. To illustrate how the frequent local Pareto optimal fronts are, consider the problem of optimization 10 of multiple criteria, where there are three introductions • subjected to a simple restriction and two outputs, both quadratic models with global maximum points that occur within the single point, as illustrated in Figure 3. There are three Pareto fronts locally optimal and depending on the exact geometry of the functions, the Line segments along the edges of the single point may or may not lie on the overall optimal solution. This is illustrated in Figure 10.

• Introduction (continued) 20 The properties of formulation landscapes, therefore, depend greatly on the type of empirical models used. Simple models, such as flange functions, have endpoints that lie over the limit of the introduction space and the globally optimal Pareto fronts that connect those extreme points are hyperplane segments. For other simple models, .k? ^ lí ^? ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Jiitt ^^ n ^ i ^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ It is connected and it is soft. This is important for the type of operators used by the evolution search algorithms. However, many • models have maximum points that occur within the introduction space 5 and this generates discontinuous local Pareto fronts that may or may not lie on the overall solution. Therefore, search algorithms have to consider all functions where local Pareto fronts may exist. From cases 1-3 above, it can be summarized that the 10 essential characteristic of an optimal local Pareto surface # formulation optimization problems is to be smooth, and can be approximated locally by (hyper) line segments in the search space. The selection of a crossover operator for a genetic algorithm search method must be inspired by some characteristic of the problem. It is known that the traditional individual point crossing is inappropriate for real value problems, such as • formulation optimization. When using a traditional single-point crossover, in any number of additional dimensions, the effect is the same: although the origins are highly fixed individual points, the result must always be located in vertices defined by the origin coordinates, and, therefore, look at those points. This is sensible for binary problems, but there is no rational aspect of why it should be reasonable for problems of real value. ^^ ^ ^ ^ ^^^^ 1 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^ In the rest of this example, an optimal Pareto genetic optimizer (POGO) is used using a line search crossover algorithm defined as follows: • O = μ (p1-P2) + p2 (2 ) 5 in μe [(1 -s) / 2, (1 + s) / 2] and typically (1,2). This defines the result, O, being located at a random distance within the given range beyond the center point of two origins (p1, p2) Once a set of points has been found within the PO surface, a cross-over algorithm line will expand the set t. 10 to find the local endpoints in a reasonable and efficient manner. The use of the stretch factor, s, allows the straight parameterization of a scale number within which the result can be, by the generation of a random μ within the interval given. For the case < 1, the result remains between the origins, for s > 1, these lie beyond them, and the effects of these are shown below. This crossing can be applied to a given percentage of the population and the effects of this are discussed later. 20 The use of POGO to solve such problems is now illustrated in more detail, in one application, to two formulation problems, which require the optimization of a number of components under simple restrictions. In this example, the implementation of POGO for a part formulation function linear, hypothetical, was issued, measuring the yields of the methods in terms of: "distance": average perpendicular distance from the final set of undominated points found in real Pareto fronts, the smallest, the best in terms of solutions that reach the Pareto optimal objectives. This provides a simple summary of the POGO behavior in such problems. In this example, the test function is defined as a continuous linear fraction in pieces shown in Figure 11. It contains 7 input variables, with two conflict objective functions, and i = alX? + blx2 + clX3 + d x4 + e'x3 + flX6 + glX7 where x, e [0,1] and S7, =? X_ = 1- In this example, x6 and X7 are redundant in a Pareto sense. The following examples were made on a series of 10 operations to allow the random nature of the algorithm. The algorithm ran with a population size of 100, for 100 generations, with a mutation rate of 1%. Two parameters varied: the line crossing ratio [population proportion where the crossing is applied] (0%, 25%, 50%, 75%, 100%) and the stretching factor for the linear crossing (0.5, 1 , 1.5, 2, 2.5). For each operation the sets of undominated points found in the final solutions were stored, and were used to calculate the values of the performance measurements.

The results are summarized below and demonstrate the effectiveness of POGO with its linear-based multi-goal search operator to explore these optimization problems. Figure 12 illustrates the effects of increasing the factor (s) of • stretch within the crossover operator, after the 5 approximation found to the true Pareto front With values of 0.5 and 1.0 (that is, allowing the result to be located only within the region within the origins), the algorithms work relatively poor form and can only reach the Pareto front center within a certain distance. It does not reach no extreme value and are limited in their central scales. He • Increase in the factor allows all the front to be covered with the limits of the function, providing an excellent approximation for the solutions to this test problem. The ends and vertices are well explored, despite the limitations of the line search operator to cover these regions, two origins of different line segments can produce less efficient results and an endpoint can only be formed by crossing two extreme sources. A careful balance of • these effects with mutation and placement allows the entire front be covered. Figure 13 illustrates the variations in the best, average and worst values found for the second performance measurement as the stretch and cross parameters are increased, along with the standard deviation of each point of variation. As noted above, the behavior of the ^^^^^^ A ^^^ «^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The first measure is reasonably correlated with the second for this particular individual front problem and is not included here. You can see that the increase in the cross and size of • stretching both have several effects on the results; the distances of the reduction and width of the True Pareto front of the Pareto face increase as the stretch factor and proportion of crosses increase. These results are also strong since there is a small variation between the measurements once a good value has been found for the parameters. The only exception for this point is the application • maximum crossing (100%), which maintains the best measurement results, but shows a small variation between the mean and worst values.

Example 11b This example indicates an extension of the problem of Example lia, with sigmoidal aspects instead of linear surfaces • forming the Pareto front. These functions are defined as follows: (2) y2 = 1 1 1 + exp (-2x1 + 4x2-2x3 + 3x4-4x5) 1 + exp (-2x1-2x2-4x3-4x4 + 3x5) 25 where x ^ e [0.1] and? 7 . =? x. = 1, and x6 and x7 are redundant entries. The Pareto front now lies both inside and outside the introductory space. As noted above, the stretch factor affects performance, as a value of s < 1 giving a poor performance with a smaller scale of distant points compared to the higher factors, s > 1, which covers the entire scale of the true Pareto front and is much closer to it. Another 5 times, "distance" is used as a performance measurement. Figure 14 illustrates the variation in the maximum, average and minimum values for each measurement found, as with the linear case, the increase in the stretching and crossing factor improves the distance between the Pareto found and true fronts, and the respite from the Pareto fronts. Again, it is shown that the • Variations increase as the crossing and stretching factors increase, and good approximations to the Pareto real front are found through the POGO method. Figure 8. Pareto optimal front (red lines) for two linear models, defined in a three-dimensional space with a simple restriction. The figure in the left part illustrates the introduction space and contains the values of the two functions in the vertices. The figure on the right shows the Pareto front • (lines in bold) and contains the two outputs of the model. Figure 9. The globally optimal Pareto front for a simple restricted optimization problem, of three introductions, where the two objectives are each formed from the sum of two sigmoidal functions. Each minimum point of the function lies on the limit and the Pareto connection front lies partially on the limit and partially on the inside of the introduction space.

Figure 10. The set front local Pareto (thick lines and vertex) for a multiple criteria optimization problem consisting of two quadratic functions with unique maximum points • (crossing) that occur in the center of the simple point of introduction. Figure 11. The Pareto surface optimal for two linear functions, defined on the single entry point of seven dimensions. Figure 12. The set of Pareto fronts calculated as the stretch factor increases. 10 Figure 13. The distance of the Pareto front to increase the stretch and vary the crossing. Figure 14. The distance of the Pareto front to increase the stretch and vary the crossing. fifteen •

Claims (21)

1. - A method for optimizing formulations against a number of criteria, comprising the steps of: (a) providing a model algorithm for each of the criteria, each model algorithm providing a prediction for a corresponding criterion when a candidate formulation is introduced into the model algorithm; and 10 (b) select criteria to optimize a set of • candidate formulations; and (c) providing an algorithm for the optimization of the group of candidate formulations according to the selected criteria; 15 wherein a first set of one or more candidate formulations is provided, and wherein the optimization algorithm generates one or more new candidate formulations, and wherein all candidate formulations are entered into the number of model algorithms to obtain predictions, and wherein the information of the set of candidate formulations obtained through said generation and / or previous optimizations and / or experiments is used to select candidate formulations from the set to obtain an Pareto optimal set of candidate formulations.

2. A method according to claim 1, which includes -. jjS. ~ -í «.j« a > áftatt «aiM« »¡». *. -. ,,. .. i *. ^^ .S ^ taí lii? T? Tti? L ??? tll? T? ^ A number of iteration steps in a loop as follows (i) a first set of one or more candidate formulations that are used as a point starting, • (ii) the candidate formulations are introduced into the 5 number of model algorithms to obtain predictions, and (iii) the optimization algorithm generates one or more new candidate formulations; and (iv) the new candidate formulations are used to introduce the number of model algorithms in the step of • iteration (ii), and where an Pareto optimal set of predictions is determined to select the candidate formulations.

3. A method according to claim 1 or 2, wherein the optimization algorithm generates new candidate formulations using information from the candidate formulations generated to obtain optimal Pareto candidate formulations, the • information comprising formulation components, predictions and, if available, prediction error bars, the estimated gradients and gradients of predictions and / or prediction error bars, constraints, and generally any other information, for example heuristics, available.

4. The method according to any of the preceding claims, wherein the optimization algorithm 25 generates new candidate formulations according to the landscape i üHáia ». tt »S-. ijjteir.,. * * -. »L 3.'I.« »> • ÍMk *? J¡Sklk characteristic of the landscape of the formulation.

5. The method according to claim 4, wherein the optimization algorithm is a genetic algorithm and are generated • new formulations according to a 5-way online search operator.

6. The method according to any of the preceding claims, wherein at least one model algorithm provides a prediction with a prediction error bar for the corresponding criteria, wherein the optimization algorithm 10 determines optimal Pareto sets of predictions. • and prediction error bar (s) to select candidate formulations.

7. The method according to any of the preceding claims, wherein the constraints are defined with respect to the candidate formulations and / or predictions and / or prediction error bar (s), wherein these constraints are used in the optimization algorithm to select and / or generate the candidate formulations.

8. The method according to claim 6 or 7, wherein candidate formulations are selected comprising predictions with prediction error bars reduced to a minimum.

9. The method according to any of the preceding claims, wherein the candidate formulations are displayed or represented against selected sets of two or more of said number of criteria. ^^^

10. - The method according to any of the preceding claims, wherein restrictions can be introduced with respect to the criteria in an interactive way to filter the optimized set of candidate formulations

11. The method according to claims 9 and 10, in where restrictions on specific criteria can be introduced during the presentation of the candidate formulations against these specific criteria.

12. The method according to any of the preceding claims, wherein the Pareto optimal set information of candidate formulations is used to determine a region of an experimental space to carry out other experiments.

13. The method according to claim 12, wherein the results of the other experiments are used to improve one or more of the model algorithms.

14. The method according to any of claims 6-13, wherein a Bayesian neural network algorithm is used as an algorithm 'model that provides a prediction and a prediction error bar.

15. The method according to any of the preceding claims, wherein the first set of candidate formulations is generated in a random manner, is seeded from previous current formulations and / or previous candidate formulations or optimized sets of candidate formulations.

16. The method according to claim 15, wherein the candidate formulations for the first set of formulations are obtained through the method of claim 1, wherein a weight optimization algorithm is used.

17. The method according to any of the preceding claims, wherein the method is used to optimize detergent products, food products, personal care products, fabric care products, 10 products for domestic care, or drinks.

18. The method according to any of the preceding claims, wherein the formulation optimization involves one or more of (a) the optimization of the type of ingredients in the formulation, (b) the optimization of the relative levels of the ingredients in the formulation, and (c) the optimization of manufacturing conditions for the formulation.

19. The method according to claim 18, wherein the formulation optimization involves an optimization of the ^ relative levels yes the ingredients in the formulation optionally 20 in combination with the optimization of the type of ingredients and / or the optimization of the manufacturing conditions for the formulation.

20. A computer program device that can be read through a computer, which comprises a computer program executable through the computer so that the The computer performs the method of any of the preceding claims. 21.- A computer program in a format that can be downloaded through a computer, which includes a program • computer executable by the computer to install the program on the computer for execution, so that the computer carries out the method of any of claims 1-17. # •