Drug prescription optimization system based on deep learning and multi-target intelligent algorithm

Abstract

The invention discloses a drug prescription optimization system based on deep learning and a multi-target intelligent algorithm, and relates to the field of medicine and health science and technology. Carrying out logratio transformation on the component data to eliminate the limitation of calibration and constraint on data analysis; an ANN model is adopted to replace a traditional Schefe polynomial for modeling, and the ANN model adopts an RBF neural network; and the RBF neural network is combined with an NSGA-II algorithm with good optimization capability to carry out multi-objective optimization. According to the invention, the logratio transformation, the deep learning algorithm and the multi-target genetic algorithm are combined for the first time, the mixed medicine prescription optimization device based on logratio transformation and deep learning is created, a feasible scheme is provided for mixed medicine prescription optimization, the frequency of exploring the optimal preparation condition by using a pre-experiment is greatly reduced, manpower, material resources and financial resources are saved, and the efficiency of the mixed medicine prescription optimization is improved. The method has practical guiding significance and application value for solving the multi-target optimization problem in the field of medicine and pharmacology, and can be popularized to applications with fixed and constrained problems and multi-target optimization problems in other fields.

Description

Technical Field

[0001] The present invention relates to the field of medicine and health science and technology, and specifically to a drug prescription optimization system based on deep learning and multi-objective intelligent algorithms. Background Art

[0002] With the development of medical research, the optimization of drug prescription ratio has aroused the research interest of more and more researchers. In particular, the optimization of mixed drug formula has attracted widespread attention from the academic community. In order to determine the ideal formula ratio of mixed drugs, mixed test design came into being. The optimized production model with reasonable test points meets the needs of drug developers and is currently the most ideal test design method to solve the optimal drug formula and ratio. However, the ratio of different ingredients in the drug formula will directly affect the characteristics of the drug, such as drug loading, encapsulation efficiency, etc. These characteristics are directly related to the effect and safety of the drug. Taking the study of puerarin-loaded lipid nanocapsules as an example, different ratios of excipients will affect the drug loading and encapsulation efficiency of nanocapsules. This difference is crucial to ensure the efficacy and safety of the drug (ZHAI Y, LIU M, WAN M, LI Y, ZHANG M, ZHAI GJJO N. Preparation and characterization of puerarin-loaded lipid nanocapsules [J]. Journal of nanoscience nanotechnology, 2015, 15 (4): 2643-9.). Therefore, the optimal mixing ratio of multiple indicators has become a core issue that needs to be solved urgently. In the context of multi-objective optimization of mixed drugs, the key to obtaining the optimal mixing ratio lies in: how to build a mathematical model for the mixing data and what method to use to optimize the ratio conditions of the prescription.

[0003] Mixture test design is an experimental design method that studies the relationship between different components and test indicators in a product and achieves the optimal formula. This design method requires that the sum of the proportions of all ingredients is 1 or 100%, so mixture data is often regarded as component data. However, component data often has the characteristics of fixed and constrained, which undoubtedly increases the complexity of modeling and optimization. Traditional optimization methods find the optimal solution by constructing Scheffé polynomial models and using contour map methods. However, the Scheffé polynomials may lead to poor estimation of model coefficients and poor fit due to constraints (KETTANEH-WOLD N. Analysis of mixture data with partial least squares [J]. Chemometrics Intelligent Laboratory Systems, 1992, 14 (1-3): 57-69.), and the contour map method is subjective, which limits the diversity of model solutions (LI Y, ZHANG Y, WANG M, JIANG L, SUI X. Simplex-centroid mixture design applied to the aqueous enzymatic extraction of fatty acid-balanced oil from mixed seeds [J]. Journal of the American Oil Chemists' Society, 2013. and JIN Xinghua, ZHANG Yunhui, ZHAO Zhenyu, XIAO Li, ZHANG Dan, WANG Yan. D-optimal mixture design to optimize the formulation of nimodipine matrix tablets [J]. Chinese Journal of Pharmacy, 2009, (7).). Therefore, the optimization of mixture experiments should fully consider the characteristics of mixture data, reasonably eliminate mixture constraints, build a more reasonable objective function model, and use scientific methods to optimize it to overcome the limitations of traditional methods.

[0004] In the mid-20th century, the simplex lattice method was proposed by Scheffé (SCHEFFé H. Experiments With Mixtures[J]. Journal of the Royal Statistical Society, 1958, 20(2): 344-60.), which开创了混料实验设计的新纪元。接踵而至的混料设计方法包含单纯形中心设计、混料均匀设计、乘积混料设计、单形重心混料设计、有上下界约束的混料设计、极端顶点混料设计以及D-最优混料设计等。针对这些方法,以往研究均采用常见的混料规范多项式进行建模。然而,药物制备的效果受多种复杂因素影响,且成分及其药效评价往往不呈线性关系,规范多项式建模策略在构建多因素非线性的混料数据模型时常常无法捕捉因素与效应之间的真实非线性关系,造成建模不准确。同时,常见多项式建模方法,如q分量一阶、二阶以及三阶等,在涉及到高维混料数据时,变量数随着实验因素的增加呈指数成长,存在试验设计的混料方案数远远小于所要估计的参数的个数(即n<<p)的现象,不仅增加模型复杂度,还会导致模型稳定性、准确性降低。因此,针对混料数据的多因素非线性问题,寻找更为适配的建模方案至关重要。

[0005] It should be noted that the part "开创了混料实验设计的新纪元" in the original text seems to be an incomplete or incorrect expression. I've translated it as literally as possible. You may want to check and correct this part for a more accurate translation.After using the data of the mixture design to establish a model, optimizing multiple test evaluation indicators becomes a challenge. As mentioned above, the purpose of conducting drug mixture experiments is to find a set of formulas to optimize drug properties. If multiple drug property evaluation indicators are required to be optimized, it is called a multi-objective optimization problem (MOP). This situation is more common than a single-objective optimization problem, and because multiple objectives may be in a competitive or contradictory relationship, the optimization process is more complicated. When solving the multi-objective optimization problem of mixture experiments, the most common idea is to convert multiple objectives into one objective for optimization: such as contour maps (LI W, YI S, WANG Z, CHEN S, XIN S, XIE J, ZHAO C. Self-nanoemulsifying drug delivery system of persimmon leaf extract: Optimization and bioavailability studies [J]. International journal of pharmaceutics, 2011, 420 (1): 161-71. and PATEL A, SHELATP, LALWANI A. Development and optimization of solid self-nanoemulsifying drug delivery system (S-SNEDDS) using Scheffe's design for improvement of oral bioavailability of nelfinavir mesylate [J]. Drug delivery and Translational research, 2014, 4 (2): 171-86.), comprehensive scoring (Sun Qiang, He Ying. Study on direct tableting process of Angelica superfine powder [J]. Chinese Pharmacy, 2008, 19 (3): 183-5.), target planning (Xie Guoliang. Prediction of blank matrix content ratio based on mixture regression design method [D]; Harbin: Heilongjiang University, 2009.), but such a transformation process is often highly subjective. The optimal "solution" (formula) found will be optimal in one goal and the worst in other goals due to human control. Moreover, since the measurement of each goal is not consistent, it is not scientific to rashly select weight coefficients to transform them into one goal.

[0006] Based on the above analysis, in the design of mixed drug prescriptions, it is necessary to solve the problems existing in the above-mentioned prior art so as to achieve the optimization of mixed drug prescriptions. Summary of the invention

[0007] The present invention aims to solve the impact of multi-factor nonlinear problems on modeling in the design optimization of mixed drug prescriptions, as well as the optimization deviation problem caused by subjective factors in the multi-objective optimization process. This deviation may lead to an extreme optimality of a certain goal, while other goals perform poorly, or due to unreasonable weight coefficient settings, multiple goals cannot be scientifically optimized when converted to a single goal. To this end, the present invention provides an improved drug prescription optimization system based on deep learning and multi-objective intelligent algorithms, which is specifically used to optimize mixed drug prescriptions and improve the scientificity and effect of multi-objective optimization.

[0008] Mixture data is considered as component data in mathematics. This concept was first proposed by Ferrer in 1866, and later Person emphasized the importance of considering the constraints of component data in 1879. The traditional mixture design optimization method constructs the Scheffé polynomial model and uses the contour map method to find the optimal solution. However, the Scheffé polynomial may lead to poor estimation and poor fitting of model coefficients due to the consideration of constraints, and the contour map method is subjective, which limits the diversity of model solutions. Therefore, the optimization of mixture experiments should fully consider the characteristics of mixture data, reasonably eliminate mixture constraints, construct a more reasonable objective function model, and use a scientific method to optimize it to overcome the limitations of traditional methods. In order to solve the obstacles brought by the constraints to data analysis, Aitchison introduced the logratio transformation method to map the value range of component data from [0,1] to (-∞,+∞), which maintains the original data law and eliminates the limitations of the constraints on analysis. At present, this method has been widely used in geology, economics, medicine and other fields. There are few applied studies in the field of pharmacy. Based on the previous experimental verification, this research group has proved that this method can effectively eliminate the influence of mixture constraints on modeling in mixture drug data. Therefore, the present invention will preprocess the mixture data through logratio transformation to simplify the process of mixture model construction and multi-objective optimization.

[0009] In addition, the effect of drug preparation is affected by many complex factors, and the components and their efficacy evaluation are often not linearly related, which makes it challenging to construct a multi-factor nonlinear mixture data model. In the past, researchers often used the traditional mixture specification polynomial modeling method to deal with the complex multivariate nonlinear relationships often encountered in pharmaceutical research. This method cannot capture the complex multi-factor nonlinear relationships of mixture data well, and the modeling strategy easily causes the problem of high-dimensional mixture data. Artificial neural networks (ANNs) have shown significant advantages in dealing with such complex multivariate nonlinear data. As an artificial intelligence method that simulates the structure and function of the human brain nervous system, ANNs can not only simultaneously construct multi-objective functions through nonlinear parallel processing, but also fit nonlinear models with arbitrary precision, which is impossible for traditional polynomial regression models. Not only does it avoid complicated equation operations, but it can also use multivariate learning functions. Among the hundreds of existing neural network models, BP neural networks have attracted much attention because of their widest application. However, with the deepening of research, many limitations of BP neural networks, such as difficulty in parameter optimization, easy to fall into local minimum, long convergence time and poor robustness, have gradually become prominent. In order to solve these problems, Moody et al. and Specht proposed RBF neural network and GRNN neural network. These new neural networks show more superior performance in many fields. Therefore, the present invention will compare the performance of these neural networks and use the neural network algorithm with the best performance to construct the data model of the mixed drug.

[0010] After using the data of the mixture design to establish the model, optimizing multiple test evaluation indicators becomes a challenge. Traditional optimization methods tend to integrate multiple objectives into a single objective, and use contour maps, comprehensive scoring, goal planning and other methods to find the only solution, but these methods are subjective and prone to local optimality, which does not meet the requirements of multi-objective solutions. In view of the shortcomings of traditional methods, J. Holland proposed the genetic algorithm (GA) based on Darwin's evolution theory and Mendel's genetics in 1975. It is a global optimization strategy that simulates biological evolution. It handles complex nonlinear problems through group search and information exchange, and can find multiple Pareto optimal solutions in multi-objective decision-making. Researchers can find experimental plans that suit them in multiple solutions according to their actual situation. The improved non-inferior classification genetic algorithm (NSGA-Ⅱ) is an improved multi-objective genetic algorithm proposed by Deb et al. in 2000, which shows strong advantages in multi-objective optimization. The basic idea of ​​the NSGA-Ⅱ algorithm is: first, randomly generate an initial population of size N, and after non-dominated sorting, obtain the first generation of offspring population through the three basic operations of selection, crossover, and mutation of the genetic algorithm; second, starting from the second generation, merge the parent population and the offspring population, perform fast non-dominated sorting, and calculate the crowding degree of individuals in each non-dominated layer at the same time, select suitable individuals according to the non-dominated relationship and the crowding degree of the individuals to form a new parent population; finally, generate a new offspring population through the basic operations of the genetic algorithm: and so on, until the conditions for the end of the program are met. Its characteristics are the introduction of a fast non-dominated sorting algorithm, an elite strategy, and the use of crowding and crowding comparison operators, which reduce the complexity of the calculation, so that the relatively frontier individuals in the Pareto optimal solution can be evenly and stably expanded to the entire solution set, that is, the Pareto domain, thereby ensuring the diversity of the population. Therefore, after the present invention uses the mixed drug data to construct the objective function model, it uses NSGA-Ⅱ to optimize the model and give the best mixed drug test design ratio scheme.

[0011] At present, there are many theoretical studies on the prescription ratio of mixed drugs and fixed and constrained component data at home and abroad, but there are few studies on the use of intelligent optimization algorithms for the optimization of mixed drug prescriptions, and there is no report on the application of logratio transformation and deep learning model building methods to the optimization of mixed drug prescriptions. In summary, the present invention uses logratio transformation to process fixed and constrained component data, uses artificial neural networks in deep learning algorithms to build models to capture the internal connections of complex multivariate nonlinear data, and finally uses Matlab software coding to realize NSGA-Ⅱ optimization, creates a mixed drug prescription optimization system, and provides an analysis strategy for the research on the optimization of mixed drug prescriptions.

[0012] The present invention is realized by the following technical scheme: a drug prescription optimization system based on deep learning and multi-objective intelligent algorithm, firstly eliminating the fixed and constraints through logratio transformation, and then using three ANN models (BP neural network, RBF neural network and GRNN) to replace the traditional Scheffé polynomials for modeling; then, combining the artificial neural network with the best modeling performance with the NSGA-II algorithm with good optimization ability for multi-objective optimization. Ultimately, the present invention will provide a set of better theoretical and technical solutions for the selection and ratio optimization of mixed drug components. The details are as follows:

[0013] A drug prescription optimization system based on deep learning and multi-objective intelligent algorithm, the process is as follows Fig.13 As shown, the system is implemented by the following steps:

[0014] S1: Logratio transformation is performed on the component data to eliminate the limitation of the sum constraint on data analysis; the details are as follows:

[0015] The component data conforms to the Euclidean matrix type. In practical applications, the Euclidean matrix can represent absolute changes through real values, or relative changes through logratio transformation. Therefore, the logratio transformation can be used to transform the component data so that the data value range is mapped from [0,1] to (-∞,+∞), which not only maintains the original data rules, but also eliminates the limitations of the sum and constraints on the analysis. Common logratio transformations include: additive logratio transformation, centralized logratio transformation, and equidistant logratio transformation.

[0016] The present invention adopts additive logratio transformation to eliminate the limitation of fixed sum constraint on data analysis. In practical application, the form of mixture data in simplex space cannot reflect the absolute quantity change according to Euclidean matrix, and the component data is converted into open data in Euclidean space. The value range of the transformed data is changed from [0, 1] to (-∞, +∞); the transformation can eliminate fixed sum constraint without changing the original data law; the formula of additive logratio transformation and inverse transformation is as follows:

[0017]

[0018] where x j is the jth component before transformation, x 0 is one of the d components, v j represents the jth component after transformation; the reverse transformation, on the contrary, is as follows:

[0019]

[0020] S2: The ANN model is used to replace the traditional Scheffé polynomial for modeling. The ANN model uses RBF neural network; the details are as follows:

[0021] S2-1: RBF neural network is used for modeling. The radial basis function neural network, referred to as RBF neural network, is a three-layer feedforward artificial neural network that draws on the characteristics of biological local regulation and overlapping acceptance area knowledge. Compared with other networks, it has a very high computing speed and good approximation ability, and can approximate the target function in the form of arbitrary accuracy and global search. Its network structure is similar to that of the BP neural network, including an input layer, a hidden layer with radial basis functions, and an output layer with linear neurons. The structural form is shown in Figure 1 The input layer is composed of input data, that is, signal source nodes, which realizes the transmission of data information without making any response to the input data; neurons are distributed in the hidden layer to realize data mapping and spatial conversion. The number of neurons depends on the number of training samples and task requirements; the output layer and the hidden layer are connected by weights, corresponding to the recognition results, and make corresponding judgments and decisions on the input mode through linear activation;

[0022] The RBF neural network has n input nodes, m output nodes and u neurons. The core of the RBF neural network is the hidden layer, which uses the radial basis function as the activation function of the neural network; the radial basis function is a scalar function symmetrical along the radial direction, which is defined as the square root of the square root of the center c of the basis function and the square root of the center x in the space. j The Euclidean distance between is a function of the independent variable, and the Gaussian function expression used by the radial basis function is:

[0023]

[0024] Where X = [x 1 ,x 2 ,…,x n ] represents the input vector of the sample, c j represents the center value of the Gaussian function, σ j represents the standardization constant, i.e. the variance of the radial basis function, and u represents the number of hidden layer nodes. Using Gaussian function as the "basis function" has the advantages of simple expression, radial symmetry, and good smoothness.

[0025] The RBF network weights are:

[0026] ω=[ω 11 ,ω 12 ,…ω um ]

[0027] The weighted calculation result of the output layer is:

[0028]

[0029] in is the actual output value of the kth node, ω kj is the weight connecting the jth neuron to the kth output node, and ε is the bias, both of which are obtained by neural network training;

[0030] Gaussian function center value c j , variance σ j And the weight ω connecting the hidden layer and the output layer kj The parameter to be solved is the Gaussian function center value c of the basis function, which is solved by unsupervised learning method. j and variance σ j , the least squares method is used to obtain the weights ω of the hidden layer and the output layer kj ,The learning method without a tutor adopts K-means clustering method;

[0031] S2-2: Neural network construction parameters and normalization:

[0032] The performance of neural networks is significantly affected by the number of hidden layers and nodes. Due to the lack of a general theory for setting hidden layers, BP networks and RBF networks usually use trial and error or empirical formulas to set these parameters. Practical experience shows that for all problems, the initial model should choose a neural network with a single hidden layer and try to limit the number of nodes to the minimum value that meets performance requirements; if increasing the number of nodes does not improve performance, consider increasing the number of hidden layers.

[0033] Considering that the data units and dimensions used for neural network model training are often inconsistent, the values ​​of different variables often differ greatly. Due to the limitation of weights, the network cannot adapt to the situation where the data varies greatly, so it is necessary to introduce a normalization method to process the training data. After processing, the training data takes values ​​between [0,1]. The expression of normalization transformation is as follows:

[0034]

[0035] Among them, x j and Represents the value of input or output data before and after normalization, x min and x max Respectively represent data x j The minimum and maximum values ​​of ;

[0036] S2-3: Establish evaluation indicators for neural network models:

[0037] After the neural network model is built, the evaluation model is an essential part. The determination coefficient R 2 Evaluating the performance of RBF neural network, R 2The closer the value is to 1, the higher the accuracy and better the performance of the model. The calculation formula is as follows:

[0038]

[0039] Where: N is the total sample size, x i is the corresponding i-th actual value in the mixed data set, is the corresponding model prediction value, is the average of all actual values ​​in the mixture data set.

[0040] S3: Combine the artificial neural network with the best modeling performance with the NSGA-II algorithm with good optimization ability to perform multi-objective optimization. The process is as follows: Fig.12 shown.

[0041] Genetic algorithm (GA) is a type of random search algorithm that simulates biological natural selection and natural evolution. It has been widely used because it is suitable for solving highly complex nonlinear problems and has good versatility. The advantages of genetic algorithms are fully demonstrated when solving complex system optimization problems with only a single objective. However, optimization problems in the real world are usually multi-attribute, and the multiple objectives that are optimized simultaneously interact and conflict with each other. For example, the cumulative release of a drug at different time points in the body. In order to achieve the optimization of the overall goal, it is usually necessary to comprehensively consider the conflicting sub-goals, that is, to compromise the sub-goals. Therefore, multi-objective genetic algorithms have emerged for optimization problems with multiple objectives.

[0042] NSGA-Ⅱ sets two parameters for each individual i in each group, namely N i and S i , N i Represents how many individuals in the population dominate individual i, S i is a set consisting of the individuals dominated by individual i; first, find N in the population i All the individuals are 0, and then put them into the set F 1 Then, for the set F 1 Each individual j in will be dominated by the individual set S j N for each individual k in k Minus 1, if individual k's N k Minus 1 equals 0, then put individual k into another set F 2 Repeat this operation until all individuals are divided into different sets; finally, put the set F 1 As the first-level set of non-dominated individuals, each individual in the set is assigned the same serial number i rank, repeat the operation on other sets so that all sets have serial numbers; this is the fast non-dominated sorting method, and the algorithm complexity is O(mN 2 ), where N represents the size of the population and m represents the number of objective functions; compared with the algorithm complexity of NSGA O(mN 3 ), the algorithm complexity is significantly reduced; in the selection stage, NSGA adopts the method of specifying the shared radius as the criterion for comparing the advantages and disadvantages of individuals of the same level; in contrast, NSGA-II ... d And the crowding comparison operator, crowding refers to the density of individuals around a certain individual in a given population, measured by the largest rectangle that contains the given individual itself but does not contain other individuals; therefore, each individual has two characteristics, serial number i rank and congestion degree i d , giving priority to individuals with earlier serial numbers when selecting; if two individuals are at the same level, the one with less crowding is selected; in addition, NSGA-II also adopts an elite strategy, that is, in each generation of evolution, the parent individuals and the offspring individuals are combined to obtain the crossover "parent" of the next generation through competition. This approach can allow the excellence of some individuals in the parent generation to be inherited; therefore, in the optimization problem of multiple attributes, NSGA-II is a relatively efficient optimization method.

[0043] Compared with the prior art, the present invention has the following beneficial effects: a drug prescription optimization system based on deep learning and multi-objective intelligent algorithm provided by the present invention combines logratio transformation with deep learning algorithm and multi-objective genetic algorithm for the first time to create a mixed drug prescription optimization device based on logratio transformation and deep learning. This scheme provides a feasible scheme for mixed drug prescription optimization, which can greatly reduce the number of preliminary experiments to explore the optimal preparation conditions, save manpower, material resources and financial resources, and has practical guiding significance and application value for solving multi-objective optimization problems in the field of medicine, and can be extended to applications in other fields with fixed and constrained problems and multi-objective optimization problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a schematic diagram of the RBF network structure of the present invention.

[0045] Figure 2 It is the target curve for BP neural network training in Example 1.

[0046] Figure 3 It is the target curve for RBF neural network training in Example 1.

[0047] Figure 4 It is the Pareto solution front end obtained by optimizing the neural network by NSGA-II in Example 1.

[0048] Figure 5 The spray-dried powder yield (y 1 ) is the output BP neural network training graph.

[0049] Figure 6 is the 24h moisture absorption rate (y 2 ) is the output BP neural network training graph.

[0050] Figure 7 The angle of repose (y) in Example 2 3 ) is the output BP neural network training graph.

[0051] Figure 8 The spray-dried powder yield (y 1 ) is the output RBF neural network training graph.

[0052] Fig. 9 The 24h moisture absorption rate (y 2 ) is the output RBF neural network training graph.

[0053] Fig.10 The angle of repose (y) in Example 2 3 ) is the output RBF neural network training graph.

[0054] Fig.11 It is the Pareto solution front end obtained by optimizing the neural network by NSGA-Ⅱ in Example 2.

[0055] Fig.12 This is the flow chart of NSGA-Ⅱ algorithm.

[0056] Fig.13 It is the overall flow chart of the present invention. DETAILED DESCRIPTION

[0057] The present invention is further described below in conjunction with specific embodiments.

[0058] The following embodiments are optimized by using a drug prescription optimization system based on deep learning and multi-objective intelligent algorithm described in the present invention. Puerarin is an isoflavone compound derived from the traditional Chinese medicine Pueraria root, which has multiple pharmacological effects such as vasodilation, cardioprotection, neuroprotection, anti-oxidation, anti-tumor, and anti-inflammatory. However, puerarin has poor solubility and low oral bioavailability, which limits its application. Nanomedicine is an emerging field of nanotechnology and medicine, and is one of the most promising effective drug delivery platforms. Lipid nanocapsules are new lipid nanocarriers composed of a tension-active shell wrapped around a lipid core, which have shown significant advantages in the pharmaceutical field, including improving oral bioavailability, increasing solubility, and achieving drug targeting. Therefore, in order to improve the water solubility and oral absorption capacity of puerarin, the present embodiment quotes the experimental data in the document "Preparation and Characterization of Puerarin-Loaded Lipid Nanocapsules" to optimize the puerarin lipid nanocapsule formula.

[0059] There are five excipients that affect the formation of puerarin lipid nanocapsules, namely: Solutol HS15 (x 1 )、Labrafac(x 2 )、Water(x 3 ), Lipoid and NaCl, where the ratio of NaCl and Lipoid in water has been determined by experiment to be 1.75% and 1.5%, how should the remaining three excipients be mixed to obtain the maximum drug loading (y 1 ) and the maximum encapsulation efficiency (y 2 ) still needs further exploration. The experimental scheme and results of the single-shape lattice mixture design are shown in Table 1.

[0060] Table 1 Experimental scheme and results of single-shape lattice mixture design

[0061]

[0062] As can be seen from Table 1, the sum of the proportions of the excipients of the seven solutions provided by the test data is 100%, and no experimental solution can simultaneously maximize the drug loading and encapsulation efficiency. Therefore, this embodiment uses logratio transformation to eliminate the fixed and constraints, and then uses three neural network models to construct the functional relationship between the drug ingredients and drug properties for performance comparison analysis. Then the optimal model is combined with NSGA-II as the objective function model to find the optimal solution for preparing puerarin nanocapsules.

[0063] S1: Logratio transformation of component data is performed to eliminate the limitation of fixed and constrained data analysis;

[0064] The sum of the three factors affecting the preparation of puerarin nanocapsules is 100%. After logratio transformation of the influencing factors, the constraint of the sum can be eliminated. After eliminating the constraint of the sum, the variable is x 1 、x 2 and x 3 The absolute change represented by m is converted into 1 、m 2 Relative change, m 1 、m 2 The value ranges of are changed to (-1.25276, 0.69315), (-1.94591, 0.51083) respectively. The results are shown in Table 2.

[0065] Table 2 Logratio transformation results of mixture components in the test scheme

[0066]

[0067]

[0068] S2: Three ANN models (BP neural network, RBF neural network and GRNN) were used to replace the traditional Scheffé polynomial model for modeling; the original literature required drug loading (y 1 ) and encapsulation efficiency (y 2 ) needs to reach the maximum value, which belongs to the solution of multi-objective problems with the same optimization direction, so this embodiment simultaneously constructs the drug loading (y 1 ) and encapsulation efficiency (y 2 ) to simplify the modeling process.

[0069] S2-1: Use BP neural network to model the mixture design data, with m after logratio transformation 1 and m 2 is the network input, and the drug loading (y 1 ) and encapsulation efficiency (y 2 ) is the network output, and all variables are normalized to construct the BP neural network framework. In order to avoid overfitting when using a deep neural network, this embodiment uses a BP neural network with only one hidden layer to construct a model, and the number of nodes in the hidden layer is determined by empirical trial and error. Finally, through the training of the neural network, the parameters of the BP neural network are set as follows: the number of output layer nodes is 2, the number of hidden layer nodes is 5, the number of input layer nodes is 2, the number of training steps is 1000, the performance function is MSE, the training target is 0.01, the training algorithm is the LM algorithm, and the parameter details are shown in Table 3.

[0070] Table 3 BP neural network parameter settings

[0071]

[0072] The BP neural network trained according to the above parameters reaches the target value of 0.01 at the third step of iteration. The determination coefficient of the BP neural network model is The training results are shown in Figure 2 .

[0073] S2-2: Use RBF neural network to model the mixture design data, with m after logratio transformation 1 and m 2 is the network input, and the drug loading (y 1 ) and encapsulation efficiency (y 2 ) is the network output, and all variables are normalized to construct the RBF neural network framework. The performance of the RBF neural network is mainly affected by two parameters: the number of hidden layer nodes and the radial basis function expansion speed (SPREAD); the number of hidden layer neurons can be automatically given by the newrb function, while the expansion speed SPREAD needs to be determined after continuous debugging. The larger the SPREAD, the smoother the function fitting, but too large a SPREAD value will lead to difficulties in numerical calculations. Therefore, this embodiment uses the empirical trial and error method to find the optimal SPREAD value with the maximum value of the determination coefficient as an indicator, and finally sets the parameters of the RBF neural network as follows: the number of output layer nodes is 2, the number of input layer nodes is 2, and the SPREAD value is set to 1; in addition, in order to compare with the BP neural network, this embodiment also sets the MSE convergence condition of the RBE neural network to 0.01, and the parameter details are shown in Table 4.

[0074] Table 4 RBF neural network parameter settings

[0075]

[0076]

[0077] After training the neural network according to the above parameters, the target value of 0.01 is reached at the third step of iteration. The determination coefficient of the RBF neural network model is The training results are shown in Figure 3 .

[0078] S2-3: Use GRNN to model the mixture design data with logratio transformed m 1 and m 2 is the network input, and the drug loading (y 1 ) and encapsulation efficiency (y 2) is the network output, and the GRNN framework is constructed. The performance of GRNN is mainly affected by the radial basis function expansion speed (SPREAD). This embodiment uses empirical trial and error to find the optimal SPREAD value with the maximum value of the determination coefficient as an indicator. Finally, the parameters of GRNN are set as follows: the number of output layer nodes is 2, the number of input layer nodes is 2, and the SPREAD value is set to 0.5. The parameter details are shown in Table 5.

[0079] Table 5 GRNN parameter settings

[0080]

[0081] GRNN does not require iteration. After training the neural network according to the above parameters, the determination coefficient of GRNN is

[0082] S2-4: Compare the performance of three neural network models:

[0083] Table 6 Performance summary of different neural network models

[0084]

[0085] As can be seen from Table 6, the drug loading (y 1 ) and encapsulation efficiency (y 2 ) are used as output to construct three neural network models (BP neural network, RBF neural network, GRNN), all three networks can well reflect the relationship between the test influencing factors and the test evaluation indicators. However, compared with BP neural network and GRNN, the model constructed by RBF neural network has the highest determination coefficient. Therefore, this embodiment selects the model constructed by RBF as the objective function in multi-objective optimization.

[0086] S3: Prescription optimization: The artificial neural network with the best modeling performance is combined with the NSGA-II algorithm with good optimization ability to perform multi-objective optimization.

[0087] S3-1: Objective function transformation:

[0088] In this example, NSGA-Ⅱ was used to determine the drug loading (y 1 ) and encapsulation efficiency (y 2 ) for multi-objective optimization, requiring drug loading (y 1 ) and encapsulation efficiency (y 2 ) the larger the target value, the better. Since the optimization direction of the objective function of the gamultiobj function is to tend to the minimum value, this embodiment also needs to transform the constructed RBF network model. The conversion is as follows:

[0089] Q=-y RBF

[0090] Where Q represents the converted objective function, y RBF represents y constructed simultaneously using RBF neural network 1 ,y 2 Regression model.

[0091] S3-2: Software parameter settings:

[0092] When optimizing the trained RBF neural network model, a multi-objective genetic algorithm (MOGA) is used for optimization. The parameters are set as follows: the population size is 100, the maximum evolutionary generation is 150, the Pareto set ratio is 0.5, the constraint tolerance is 1e-10, and the function tolerance is a parameter of 1e-06.

[0093] S3-3: Optimization results:

[0094] After using the NSGA-II algorithm and denormalization, this embodiment searches for 50 Pareto non-inferior solutions. 1 、m 2 It is the relative change represented by the logratio transformation, so this embodiment performs an inverse logratio transformation on it to restore it to the absolute change represented by the real value. The Pareto optimal solution set and optimization results are shown in Table 7. The front end of the Pareto solution set is shown in Figure 4 It can be seen that the two objectives of encapsulation efficiency and drug loading are conflicting. If one of the objectives is to be improved, the other objective will inevitably be reduced. Therefore, there is no solution in which both objectives are maximized at the same time. However, a relatively better solution can be selected from the Pareto optimal solution to make the two objectives relatively optimal.

[0095] From the Pareto solutions, when the 24th solution, i.e. Solutol HS15 is 29.37%, Labrafac is 9.70%, and water is 60.93%, the encapsulation efficiency is 2.70% and the drug loading is 57.21%. At this time, the encapsulation efficiency and drug loading reach the relatively maximum percentage. At the same time, decision makers can choose a satisfactory nanocapsule preparation solution from other Pareto solutions according to their own purposes.

[0096] Table 7 Pareto optimal solution obtained by NSGA-Ⅱ

[0097]

[0098]

[0099] S3-4: Comparison of optimization effects:

[0100] When modeling the original literature, Scheffe polynomials with missing constant terms and cross terms were used to fit the models for the two evaluation indicators respectively; when optimizing the formula, the contour map method suitable for single-objective optimization was used to find the optimal nanocapsule formula, and finally the only optimal ratio condition was obtained through subjective selection, that is, Solutol HS15 was 10%, Labrafac was 30%, and water was 60%, which could make the drug loading and encapsulation efficiency reach 2.55% and 55.95%, respectively.

[0101] The optimization scheme used in the original document only provides a unique optimal solution, which violates the principle of finding a Pareto solution set to meet the multi-objective optimization concept. In this embodiment, based on the characteristics of the mixed experimental data, the RBF neural network based on logratio changes is used to simultaneously construct two objective function models, and the objective function is optimized by NSGA-Ⅱ. After optimization, a Pareto non-inferior solution set is obtained. Compared with the original text, the relatively optimal solution No. 24 in the solution set has an absolute increase of 0.15% in the drug loading amount, an increase of 5.88%, and an absolute increase of 1.2% in the encapsulation amount, an increase of 2.25%; at this time, the amount of Solutol HS15 and water increased by 1.937 times and 1.55% respectively, while the amount of Labrafac decreased by 67.7%; see Table 8 for details. In Table 7, this embodiment also lists other solutions that are better than the original text (Schemes 7, 8, 9, 45, and 46). Researchers can choose the most suitable one among these preferred solutions for application according to specific experimental conditions and needs.

[0102] Table 8 Comparison of optimization effects

[0103]

[0104] Example 2

[0105] Spray drying technology has been widely used in the drying process of traditional Chinese medicine extracts because of its high efficiency, keeping the effective ingredients intact, and producing powders of uniform quality and easy solubility. Especially when processing the Wenjing Zhitong Recipe extract, spray drying shows its superiority. However, the Wenjing Zhitong Recipe is prone to hot-melt wall sticking during spray drying, which affects the drying effect. Adjusting the process parameters alone cannot completely solve this problem, and it is also necessary to add appropriate excipients for optimization. Therefore, this example cites the document "Research on Spray Drying Process of Wenjing Zhitong Recipe Extract Based on Mixing Design"

[51] The spray drying process of the Wenjing Zhitong prescription extract was optimized based on the experimental data.

[0106] There are 4 kinds of auxiliary materials that affect the spray drying process of Wenjing Zhitong Decoction extract, namely: solid content of extract (x 1 )、light MgO(x 2)、maltodextrin(x 3 ) and SiO 2 (x 4 How to mix the four excipients to obtain the maximum spray-dried powder yield of the drug (y 1 )、Maximum 24h moisture absorption rate (y 2 ) and minimum angle of repose (y 3 ) still needs further exploration. The experimental scheme and results of the upper and lower bounds constrained mixture design are shown in Table 9.

[0107] Table 9 Mixture design experimental plan and results

[0108]

[0109] As can be seen from Table 9, the sum of the excipient ratios of the 10 solutions provided by the test data is 1, and no experimental solution can simultaneously achieve the requirements of maximum spray-dried powder yield, maximum 24h moisture absorption rate and minimum repose angle. Therefore, this embodiment uses logratio transformation to eliminate the fixed sum constraint, and then uses BP neural network, RBF neural network and GRNN to construct the functional relationship between drug ingredients and drug performance. Then select the model according to the evaluation index, and set R 2 The largest model was used as the objective function model in combination with NSGA-II to find the optimal solution for the spray drying process of the Wenjing Zhitong recipe extract.

[0110] S1: Logratio transformation of component data is performed to eliminate the limitation of fixed and constrained data analysis;

[0111] The sum of the four factors that affect the spray drying process of the Wenjing Zhitong Recipe extract is 1. After the influencing factors are logratio transformed, the constraint of the sum can be eliminated. After eliminating the constraint of the sum, the variable is x 1 、x 2 、x 3 and x 4 The absolute change represented by m is converted into 1 、m 2 and m 3 Relative change, m 1 、m 2 and m 3 The value ranges of are changed to (0.22314, 2.83321), (-2.07944, 2.07944), (-2.07944, 2.07944). The results are shown in Table 10.

[0112] Table 10 Logratio transformation results of mixture components in the test scheme

[0113]

[0114]

[0115] S2: Three ANN models (BP neural network, RBF neural network and GRNN) were used to replace the traditional Scheffé polynomial model; considering the spray-dried powder yield (y 1 ) and 24h moisture absorption rate (y 2 ) Maximum required value, angle of repose (y 3 ) minimum value, which belongs to a multi-objective optimization problem with different optimization directions. Therefore, before optimization, the spray dry powder yield (y 1 )、24h moisture absorption rate (y 2 ) and the angle of repose (y 3 ) neural network model.

[0116] S2-1: Use BP neural network to model the mixture design data, with m after logratio transformation 1 、m 2 and m 3 as the network input, respectively, with the spray dry powder yield (y 1 )、24h moisture absorption rate (y 2 ) and the angle of repose (y 3 ) is the network output, and all variables are normalized to construct the BP neural network framework. In order to avoid overfitting when using a deep neural network, this embodiment uses a BP neural network with only one hidden layer to build the model, and the number of nodes in the hidden layer is determined by empirical trial and error. Finally, through the training of the neural network, it is decided to use y 1 ,y 2 and 3 The BP network parameters for output are set as follows: the number of input layer nodes is 3, the number of hidden layer nodes is 5, 6, and 5 respectively, the number of output layer nodes is 1, the number of training steps is 1000, the MSE convergence condition is 0.01, and the training algorithm is LM algorithm. The parameter details are shown in Table 11.

[0117] Table 11 BP neural network parameter settings

[0118]

[0119] The BP neural network trained according to the above parameters, y 1 ,y 2 and 3 The MSE convergence condition is reached when iterating to the 5th, 9th and 5th steps respectively, and the determination coefficients of the BP neural network model are and The training results are shown in Figures 5 to 7 .

[0120] S2-2: Use RBF neural network to model the mixture design data, with m after logratio transformation 1 、m 2 and m 3 as the network input, respectively, with the spray dry powder yield (y 1 )、24h moisture absorption rate (y 2 ) and the angle of repose (y 3 ) is the network output, and all variables are normalized to construct the RBF neural network framework. This embodiment uses empirical trial and error to find the best SPREAD value, and finally converts y 1 ,y 2 and 3 The RBF neural network parameter settings are as follows: the number of input layer nodes is 3, the number of output layer nodes is 1, and the SPREAD values ​​are set to 0.8, 1.0, and 0.6 respectively; in addition, in order to compare with the BP neural network, the MSE convergence condition of the RBE neural network is set to 0.01 in this embodiment. The parameter details are shown in Table 12.

[0121] Table 12 RBF neural network parameter settings

[0122]

[0123] After training the RBF neural network according to the above parameters, y 1 ,y 2 and 3 The MSE convergence condition is reached when iterating to the 8th, 9th and 8th steps respectively, and the determination coefficients of the RBF neural network model are and The training results are shown in Figures 8 to 10 .

[0124] S2-3: Use GRNN to model the mixture design data with logratio transformed m 1 、m 2 and m 3 as the network input, respectively, with the spray dry powder yield (y 1 )、24h moisture absorption rate (y 2 ) and the angle of repose (y 3 ) is the network output, and all variables are normalized to construct the GRNN neural network framework. This embodiment uses the empirical trial and error method to find the best SPREAD value, and finally sets the parameters of GRNN as follows: the number of input layer nodes is 3, the number of output layer nodes is 1, and the SPREAD value is set to 0.2. The parameter details are shown in Table 13.

[0125] Table 13 GRNN neural network parameter settings

[0126]

[0127] GRNN does not require iteration. After training the neural network according to the above parameters, y 1 ,y 2 and 3 The determination coefficient of the GRNN neural network model and

[0128] S2-4: Compare the performance of three neural network models:

[0129] Table 14 Summary of performance of artificial neural network models (R 2 )

[0130]

[0131] As can be seen from Table 14, the spray-dried powder yield (y 1 )、24h moisture absorption rate (y 2 ) and the angle of repose (y 3 ) as the output to construct three neural network models (BP neural network, RBF neural network, GRNN), the three neural network models can well reflect the relationship between the test influencing factors and the test evaluation indicators. However, compared with BP neural network and GRNN, the model constructed by RBF neural network has the highest determination coefficient. The determination coefficients of RBF neural network model are and Therefore, this embodiment selects RBF as the objective function in multi-objective optimization.

[0132] S3: Prescription optimization: The artificial neural network with the best modeling performance is combined with the NSGA-II algorithm with good optimization ability to perform multi-objective optimization.

[0133] S3-1: Objective function transformation:

[0134] In this example, NSGA-Ⅱ was used to determine the spray-dried powder yield (y 1 )、24h moisture absorption rate (y 2 ) and the angle of repose (y 3 ) for optimization, the original text requires the spray dry powder yield (y 1 )、24h moisture absorption rate (y 2 ) the larger the target value, the better. 3 ) is as small as possible. Therefore, this embodiment converts the constructed RBF neural network model as follows:

[0135] Q 1 =-y 1

[0136] Q 2 =-y2

[0137] Q 3 =y 3

[0138] Where Q 1 , Q 2 and Q 3 represents the transformed objective function, y 1 represents the spray-dried powder yield regression model constructed using RBF neural network, y 2 represents the 24h moisture absorption rate regression model constructed using RBF neural network, y 3 represents the repose angle regression model constructed using RBF neural network.

[0139] S3-2: Software parameter settings:

[0140] When optimizing the trained RBF neural network model, MOGA is used for optimization. The parameters are set as follows: population size is 100, maximum evolutionary generations is 150, Pareto set ratio is 0.5, constraint tolerance is 1e-10, and function tolerance is parameter 1e-06.

[0141] S3-3: Optimization results:

[0142] After using the NSGA-II algorithm and denormalization, this embodiment searches for 50 Pareto non-inferior solutions. 1 、m 2 and m 3 It is the relative change represented by the logratio transformation, so this embodiment performs an inverse logratio transformation on it to restore it to the absolute change represented by the true value. The Pareto solution and optimization results are shown in Table 15. The Pareto solution front end is shown in Fig.11 It can be seen that the three objectives of spray-dried powder yield, 24h moisture absorption rate and angle of repose are conflicting. If one of the target values ​​is increased, the other or two target values ​​will inevitably be reduced. Therefore, there is no solution that can achieve the maximum or minimum of the three objectives at the same time. However, a relatively better solution can be selected from the Pareto solution to make the three objectives relatively optimal.

[0143] From the Pareto solution, the 38th solution is 0.465 solid content of the extract, 0.143 light MgO, 0.086 maltodextrin, and 0.086 SiO 2When it is 0.306, the spray-dried powder yield is 90.92%, the 24h moisture absorption rate is 16.95% and the angle of repose is 25.64°. At this time, the spray-dried powder yield and the 24h moisture absorption rate reach the relatively maximum percentage, and the angle of repose also has a smaller angle. At the same time, decision makers can choose a satisfactory spray-drying preparation process plan for the Wenjing Zhitong Decoction extract from other Pareto solutions according to their own purposes.

[0144] Table 15 Pareto optimal solution obtained by NSGA-Ⅱ

[0145]

[0146]

[0147] S3-4: Comparison of optimization effects:

[0148] When the original paper was modeled, the Scheffe polynomial was used to fit the two evaluation indicators respectively, but the model did not eliminate the influence of the mixing constraints; when optimizing the formula, the original paper used the contour map method suitable for single-objective optimization to solve the optimal solution, and finally obtained the only optimal ratio condition through subjective selection, that is, the solid content of the extract was 0.500, light MgO was 0.305, maltodextrin was 0.145, and SiO 2 is 0.294, which can make the spray-dried powder yield 90.10%, the 24h moisture absorption rate 15.99% and the repose angle 30.77°.

[0149] The optimization scheme used in the original text only provides a unique optimal solution, which violates the principle of finding a Pareto solution set to meet the concept of multi-objective optimization. In this embodiment, based on the characteristics of the mixing experimental data, the logratio change is used to eliminate the mixing constraints, and the objective function model is constructed using the RBF neural network. The objective function is optimized using NSGA-Ⅱ, and a Pareto non-inferior solution set is obtained after optimization. Compared with the original text, the relatively optimal solution No. 38 in the solution set increased the absolute amount of spray-dried powder yield and 24h moisture absorption rate by 0.82% and 0.96%, respectively, increased by 0.91% and 6.00%, and the angle of repose decreased by 5.13°, a decrease of 16.67%; at this time, the solid content of the extract, the amount of light MgO and maltodextrin were reduced by 7.0%, 53.1% and 40.7% respectively compared with the original text, and SiO 2 The dosage increased by 5.12 times, which is within the scope of the experimental design and is reasonable; details are shown in Table 16. In Table 15, this embodiment also lists other solutions (Solutions No. 20, 21, and 31) that are better than the original text, so researchers can choose the most suitable one among these preferred solutions for application according to specific experimental conditions and needs.

[0150] Table 16 Comparison of optimization effects

[0151]

[0152] The scope of protection claimed by the present invention is not limited to the above specific embodiments. For those skilled in the art, the present invention may have various deformations and changes. Any modifications, improvements and equivalent substitutions made within the concept and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A drug prescription optimization system based on deep learning and multi-objective intelligent algorithm, characterized by: The system is implemented through the following steps: S1: Logratio transformation of component data is performed to eliminate the limitation of fixed and constrained data analysis; S2: The ANN model is used to replace the traditional Scheffé polynomial for modeling. The ANN model uses RBF neural network; S3: Combine the artificial neural network with the best modeling performance with the NSGA-II algorithm with good optimization ability for multi-objective optimization.

2. The drug prescription optimization system based on deep learning and multi-objective intelligent algorithm according to claim 1, characterized in that: Step S1 is as follows: Adopting additive logratio transformation to eliminate the limitation of sum constraint on data analysis, converting component data into open data in Euclidean space, and changing the value range of data from [0,1] to (-∞,+∞); this transformation can eliminate sum constraint without changing the original data law; additive logratio transformation and inverse transformation formula are as follows: where x j is the jth component before transformation, x0 is one of the d components, v j represents the jth component after transformation; the reverse transformation, on the contrary, is as follows:

3. The drug prescription optimization system based on deep learning and multi-objective intelligent algorithm according to claim 1, characterized in that: Step S2 is specifically as follows: S2-1: RBF neural network is used for modeling. RBF neural network is a radial basis function neural network, which is a three-layer feedforward artificial neural network. It can approximate the target function in the form of arbitrary accuracy and global search. It includes an input layer, a hidden layer with radial basis function and an output layer with linear neurons. The input layer is composed of input data, that is, signal source nodes, to realize the transmission of data information without making any response to the input data; neurons are distributed in the hidden layer to realize data mapping and spatial conversion. The number of neurons depends on the number of training samples and task requirements; weight connection is implemented between the output layer and the hidden layer, corresponding to the recognition result, and corresponding judgment and decision are made on the input mode through linear activation; The RBF neural network has n input nodes, m output nodes and u neurons. The core of the RBF neural network is the hidden layer, which uses the radial basis function as the activation function of the neural network. The radial basis function is a scalar function that is symmetrical along the radial direction and is defined as the square root of the square root of the center c of the basis function and the square root of the center x in the space. j The Euclidean distance between is a function of the independent variable, and the Gaussian function expression used by the radial basis function is: Where X = [x1, x2, …, x n ] represents the input vector of the sample, c j represents the center value of the Gaussian function, σ j represents the standardization constant, i.e. the variance of the radial basis function, and u represents the number of hidden layer nodes; The RBF network weights are: ω=[ω 11 ,oh 12 ,…oh um ] The weighted calculation result of the output layer is: in is the actual output value of the kth node, ω kj is the weight connecting the jth neuron to the kth output node, and ε is the bias, both of which are obtained by neural network training; Gaussian function center value c j , variance σ j And the weight ω connecting the hidden layer and the output layer kj The parameter to be solved is the Gaussian function center value c of the basis function, which is solved by unsupervised learning method. j and variance σ j , the least squares method is used to obtain the weights ω of the hidden layer and the output layer kj ,The learning method without a tutor adopts K-means clustering method; S2-2: Neural network construction parameters and normalization: The trial and error method or empirical formula is used to set the neural network construction parameters for the RBF neural network, and the normalization method is introduced to process the training data so that the value of the processed training data is between [0,1]. The expression of the normalization transformation is as follows: Among them, x j and Represents the value of input or output data before and after normalization, x min and x max Respectively represent data x j The minimum and maximum values ​​of ; S2-3: Establish evaluation indicators for neural network models: The coefficient of determination R 2 Evaluating the performance of RBF neural network, R 2 The closer the value is to 1, the higher the accuracy and better the performance of the model. The calculation formula is as follows: Where: N is the total sample size, x i is the corresponding i-th actual value in the mixed data set, is the corresponding model prediction value, is the average of all actual values ​​in the mixture data set.

4. The drug prescription optimization system based on deep learning and multi-objective intelligent algorithm according to claim 1, characterized in that: Step S3 is as follows: Genetic algorithm GA is a type of random search algorithm that simulates biological natural selection and natural evolution; NSGA-Ⅱ sets two parameters for each individual i in each group, namely N i and S i , N i Represents how many individuals in the population dominate individual i, S i is a set consisting of the individuals dominated by individual i; first, find N in the population i All the individuals are 0, and then put them into the set F1, and then for each individual j in the set F1, the individual set S dominated by it j N for each individual k in k Minus 1, if individual k's N k If minus 1 equals 0, then individual k is placed in another set F2, and this operation is repeated until all individuals are divided into different sets; finally, set F1 is regarded as the first-level set of non-dominated individuals, and each individual in the set is assigned the same sequence number i rank , repeat the operation on other sets so that all sets have serial numbers; this is the fast non-dominated sorting method, and the algorithm complexity is O(mN 2 ), where N represents the size of the population and m represents the number of objective functions; NSGA-II uses the crowding degree i d And the crowding comparison operator, crowding refers to the density of individuals around a certain individual in a given population, measured by the largest rectangle that contains the given individual itself but does not contain other individuals; therefore, each individual has two characteristics, serial number i rank and congestion degree i d , giving priority to individuals with earlier serial numbers when selecting; if two individuals are at the same level, the one with less crowding is selected; in addition, NSGA-II also adopts an elite strategy, which is to combine parent individuals and offspring individuals in each generation of evolution to obtain the crossover "parent" of the next generation through competition.

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