Drug design method based on two-stage evolutionary multitask optimization

Abstract

The application discloses a drug design method based on two-stage evolutionary multi-task optimization, and is characterized in that the method comprises the following steps: determining a target function of each sub-task, entering an evolution early stage, performing in-task population evolution on a target task to obtain a child population, generating a migration solution better than the target task by using an affine change strategy, monitoring whether the population reaches a stage division point, if not, reselecting the target task and returning to the evolution early stage, if yes, performing an evolution late stage, transferring the solution by using a local outlier factor detection model strategy, merging a parent population, the child population, a mapping solution and the transferred solution, and selecting an optimal solution according to a fitness function, determining whether evolution is completed according to a function evaluation time, if yes, outputting the optimal solution, and if not, returning to the evolution early stage. The method solves the problem that the drug design cannot be completely solved due to uncertain problem properties under the condition of a black box problem.

Description

Technical Field

[0001] This invention belongs to the technical field of drug design methods, and relates to a drug design method based on two-stage evolutionary multi-task optimization. Background Technology

[0002] Drug design refers to the use of computational chemistry and molecular modeling methods to design new compounds or optimize existing compounds on a computer to develop drugs with desired pharmacological activities and pharmacokinetic properties. Traditional drug design relies on tedious trial-and-error processes in the laboratory, but with the development of computational power and drug design methodologies, computer-aided drug design has become a highly efficient screening and optimization approach. Currently, researchers typically utilize evolutionary multi-task optimization algorithms for drug design and optimization of design schemes.

[0003] Evolutionary Multi-task Optimization (EMTO), as a novel computational paradigm, typically maps the search spaces of different tasks to a unified space and leverages the potential similarities between tasks to achieve collaborative optimization. Knowledge transfer, as a crucial step in collaborative optimization, directly determines the algorithm's performance based on its efficiency. To date, researchers have proposed various different knowledge transfer strategies. Based on the different nature of knowledge transfer, it can be roughly divided into the following four categories: (1) Static EMTO algorithm based on implicit knowledge transfer: The main feature of this type of algorithm is to map the decision space of different tasks to a unified space for search in the form of a single population, and to realize the blood type mating of different types of individuals through evolutionary operators, so as to achieve the purpose of knowledge transfer; (2) Adaptive EMTO algorithm based on implicit knowledge transfer: Unlike the first type of algorithm which adopts a deterministic knowledge transfer method, this type of algorithm introduces an adaptive mechanism to control the degree of knowledge transfer between different tasks, so as to reduce the occurrence of negative transfer phenomenon; (3) Static EMTO algorithm based on explicit knowledge transfer: Unlike the EMTO algorithm based on implicit knowledge transfer which adopts a single population structure, this type of algorithm adopts a multi-population structure to realize the independent evolution of different tasks, and to carry out knowledge transfer between different populations during the evolution process; (4) Adaptive EMTO algorithm based on explicit knowledge transfer: Unlike the third type of algorithm which adopts a deterministic knowledge transfer method, this type of algorithm introduces an adaptive mechanism to control the degree of knowledge transfer between different populations, so as to improve the efficiency of knowledge transfer.

[0004] It is worth noting that research on drug design problems is often required to be conducted under black-box conditions, which challenges the universality of algorithmic solutions. Therefore, drug design problems can be divided into two main categories based on the similarity between tasks: highly similar tasks and low-similarity tasks. How to design an algorithm that can still achieve effective co-evolution between different tasks and efficiently solve drug design problems without prior information is one of the key challenges in drug design optimization. Furthermore, existing knowledge transfer strategies often only handle either low-similarity or high-similarity tasks. A significant drawback is that transfer strategies for the former are usually inapplicable to the latter, and vice versa. This leads to extremely poor performance when solving problems with knowledge transfer mechanisms that are the opposite of their intended purpose. For example, knowledge transfer in elite solutions between low-similarity tasks can directly result in negative transfer. Summary of the Invention

[0005] The purpose of this invention is to provide a drug design method based on two-stage evolutionary multi-task optimization, which solves the problem in the prior art that drug design cannot be completely solved under the condition of black box problem due to the uncertainty of the problem nature.

[0006] The technical solution adopted in this invention is a drug design method based on two-stage evolutionary multi-task optimization, including: determining the objective function of each sub-task and entering the early evolutionary stage: performing intra-task population evolution on the target task to obtain the offspring population; using an affine transformation strategy to generate a better migration solution for the target task; monitoring whether the population has reached the stage division point; if not, continuing the early evolutionary stage; if so, entering the late evolutionary stage: using a local outlier detection model strategy to generate a migration solution; merging the parent population, offspring population, and migration solution; and selecting the optimal solution based on the fitness function; determining whether evolution is complete based on the number of function evaluations; if so, outputting the optimal solution; otherwise, proceeding to the next generation of evolution.

[0007] The invention is further characterized by:

[0008] Includes the following steps:

[0009] Step 1: Determine the objective function and decision variables for K sub-tasks. Sub-tasks include, but are not limited to, drug molecule structure optimization, drug solubility optimization, drug toxicity minimization optimization, drug stability optimization, and drug onset time optimization.

[0010] Step 2: Select the target task and use the ADEOEA algorithm to perform in-task population evolution to generate offspring population;

[0011] Step 3: Use a diversity monitoring strategy to monitor whether the population has reached the stage split point. If so, proceed to the next step; otherwise, use an affine transformation strategy to generate a better migration solution for the target task.

[0012] Step 4: As the population enters the later stage of evolution, the local outlier detection model strategy is used to identify individuals with high similarity as transition solutions.

[0013] Step 5: Merge the parent population, offspring population, mapped solution, and transition solution to obtain the merged population. Select the successful individuals based on fitness as the optimal solution.

[0014] Step 6: Determine if the number of function evaluations is less than the preset threshold. If so, update the ADEOEA algorithm parameters and adaptive selection parameters, and return to step 2; otherwise, output the optimal solution and optimal objective function of the population, thus obtaining the optimal drug design scheme.

[0015] The objective function is:

[0016]

[0017] In the above formula, Ω i For the i-th task f i (x i The search space of ) For the optimal solution, x i For each individual in the population, i = 1, 2, ..., K.

[0018] Step 2 specifically includes the following steps:

[0019] Step 2.1: Select the k-th task as the target task, and use the mutation operator DE / current-to-pbest / 1 based on the differential evolution algorithm to generate offspring mutant individuals:

[0020]

[0021] In the above formula, x i,G For the parent generation, F i For individual x i,G The corresponding variable asynchronous length, One individual is randomly selected from the top 100 ε% of the population, where ε is the probability value. From the parent population P k Randomly selected from the given information, k = 1, 2, ..., K. From set P k Randomly selected from ∪B;

[0022] Step 2.2: For each mutated individual v i,G Same-parent generation individual x i,G Crossover yields N experimental individuals uj,i,G , denoted as offspring population O k ;

[0023]

[0024] In the above formula, rand(0,1) is a random number in the range (0,1), and CR i Let j be the crossover probability. rand Let j be an integer randomly selected from dimensions 1 to D. rand =randint(1,D), u j,i,G Let x be the j-th dimension variable for the i-th experimental individual; j,i,G v j,i,G These are the j-th dimension variables of the i-th parent individual and the i-th mutated individual, respectively.

[0025] Step 3 specifically includes the following steps:

[0026] Step 3.1: Construct a diversity monitoring equation to obtain diversity indicators:

[0027]

[0028] In the above formula, FESMAX represents the maximum number of function evaluations, FES represents the number of function evaluations, and Div1 represents the true diversity of the initial population.

[0029]

[0030] In the above formula, N is the population size, x i Let be the i-th individual in the population, and μ be the true mean vector of the population.

[0031] Step 3.2: Based on the diversity index, determine whether the dividing point between the two stages has been reached:

[0032]

[0033] In the above formula, flag is a logical value that serves as a marker for the dividing point, and μ and σ are the true mean and variance of the population during the evolution process, respectively.

[0034] Step 3.3: If flag = 1, it indicates that the population is in the early stage of evolution, and affine transformation is used as a knowledge transfer strategy.

[0035] Step 3.4: If flag = 0, it indicates that the population is in the late stage of evolution, and proceed to the next step.

[0036] Step 3.3 specifically includes the following steps:

[0037] Step 3.3.1: Construct an affine transformation using the ranking loss function:

[0038]

[0039] In the above formula, θ = [A, b] is a transformation parameter of the affine transformation, A and b are a scaling transformation and a translation transformation, respectively, and M... a (·) represents the affine transformation, Υ[·] is the operation to convert fitness terrain into ranking-based terrain, and P s (·),P t (·) represent the Gaussian models for the source and target tasks, respectively:

[0040]

[0041] In the above formula, w n The weighted weights of the t-th generation population are: The Gaussian model corresponding to the nth generation population:

[0042]

[0043] In the above formula, α is a preference coefficient, Pop i For the i-th generation population, To calculate the population probability density function, a multivariate Gaussian distribution is used to construct the probability density function:

[0044]

[0045] In the above formula, μ and σ are the mean vector and standard deviation of the population, respectively:

[0046] μ=(μ1,μ2,…,μ D (11);

[0047]

[0048]

[0049]

[0050] In the above formula, μ j Let be the average value of the j-th dimension variable of the population, where D is the dimension and N is the population size. Let j be the j-th dimension variable of the i-th individual in the n-th generation population. Let be the variance of the j-th dimension variable of the population;

[0051] Step 3.3.2: Minimize formula (3) to obtain the following formula:

[0052] Υ[P s [x]=Υ[δ·P t (M(x;θ))] (15);

[0053] In the above formula, δ is a scaling factor, which transforms formula (12) into an algebraic form:

[0054] P s (x)=δ·P t (M(x;θ)) (16);

[0055] The analytical solution of formula (13) is calculated as follows:

[0056]

[0057]

[0058]

[0059] In the above formula, ∑ s ,∑ t The covariances of the source task and target task populations are respectively used to obtain the following variables using formulas (17)-(19):

[0060]

[0061] μ s =(μ t -b)A -1 (twenty one);

[0062]

[0063] Cholesky decomposition of equation (21):

[0064]

[0065] In the above formula, L s , The lower triangular matrices obtained by Cholesky decomposition of the covariance matrices of the source task and the target task are respectively used to obtain the final affine transformation parameters θ using formulas (20) and (22):

[0066]

[0067] Step 3.3.3: Using the affine transformation parameter θ, map the transfer solution from the source task to the target task to obtain a better transfer solution:

[0068]

[0069] In the above formula, is the transition solution mapped to the target task, and x is the transition solution of the source task;

[0070] Step 3.3.4: Generate N affine transformation transition solutions using formula (25), and rank the individuals according to their fitness values. Based on adaptive selection of parameter p a Select the first 100 pages a The N% of individuals are considered successful, denoted as the mapping solution.

[0071] Step 4 specifically includes the following steps:

[0072] Step 4.1: Calculate the local outlier factor of individuals in the source task:

[0073]

[0074] In the above formula, Let i be the i-th individual in the source task. Let k be the k-th neighborhood of this individual. For this individual, there are k target task individuals within its k-th distance neighborhood. The local reachability density of this individual:

[0075]

[0076] In the above formula, For neighboring individuals To individuals The k-th reachable distance:

[0077]

[0078] In the above formula, For neighboring individuals To individuals Euclidean distance, d k (·) represents the k-th distance. When condition I is satisfied, d k (p) = d(p,o), and condition I is:

[0079] There are at least k points o' in the set, excluding point p, such that d(p,o′)≤d(p,o);

[0080] There are at least k-1 points o' in the set, excluding point p, such that d(p,o'). <d(p,o);

[0081] Step 4.2, for locally outlier factors Sort in ascending order to get the ranking. And based on the adaptive selection of parameter p l Select the top 100 pages l *N% of the individuals are used as transition solutions generated by the local outlier factor model.

[0082] The process of updating the ADEOEA algorithm parameters and adaptively selecting parameters in step 6 is as follows:

[0083] Step a: During each generation of population evolution, if the generated experimental individual u i,G Superior to parent individual x i,G Then the parameter CR corresponding to the successful individual will be... i ,F i Save to collection S CR ,S F and the mean μ CR ,μ F The update is performed using the following formula:

[0084] μ CR = (1-c)·μ CR +c·mean A (S CR (29);

[0085] μ F = (1-c)·μ F +c·mean L (S F (30);

[0086] In the above formula, c is the learning rate, and mean A (·) Take the weighted average, mean L (·) Take the Lehmer average;

[0087]

[0088]

[0089]

[0090] In the above formula, Δf k =|f(u k,G )-f(x k,G )|;

[0091] Step b, using the updated μ CR ,μ F CR for calculating the next generation of population evolution i F i ;

[0092] CR i =randn i (μ CR ,0.1) (34);

[0093] F i =randc i (μF ,0,1) (35);

[0094] In the above formula, randn i (μ CR ,0.1) and randc i (μ F The values ​​of μ, 0, 1) are randomly sampled from the normal distribution and the Cauchy distribution, respectively. CR ,μ F The mean and variance σ are given. 2 =0.1, CR is outside the range [0,1]. i ,F i Perform interception;

[0095] Step c: Using the number of successful individuals obtained in step 3.3, update the adaptive selection parameter p of the affine transformation. a :

[0096]

[0097] In the above formula, t is the number of iterations, and S a N represents the number of successful individuals, and N represents the total number of migration solutions.

[0098] Step d: Using the number of successful individuals from step 4, update the adaptive selection parameter p of the local outlier factor model. l :

[0099]

[0100] In the above formula, S l The number of migration solutions generated for the local outlier model.

[0101] The beneficial effects of this invention are as follows: The drug design method based on two-stage evolutionary multi-task optimization of this invention, on the basis of the concept of adaptive regulation of population evolution, adopts a dual strategy of combining affine transformation and local outlier detection model to construct a two-stage knowledge transfer mechanism, adaptively solving drug design problems of different properties under black box problem, while using adaptive parameter selection to retain high-quality transfer solutions, dynamically improving the co-evolution efficiency and solution capability of the algorithm; it has the characteristics of problem universality and superior performance. Attached Figure Description

[0102] Figure 1 This is a flowchart of the drug design method based on two-stage evolutionary multi-task optimization of the present invention;

[0103] Figure 2 This is a schematic diagram of population diversity fluctuation changes obtained by using the diversity monitoring equation in the drug design method based on two-stage evolutionary multi-task optimization of this invention.

[0104] Figure 3 This is a schematic diagram of spatial mapping of points A to D using affine transformation in the drug design method based on two-stage evolutionary multi-task optimization of this invention;

[0105] Figure 4 This is a schematic diagram of the k-th reachable distance from point o to point p in the drug design method based on two-stage evolutionary multi-task optimization of this invention, where k = 5;

[0106] Figure 5 This is a schematic diagram showing the convergence of the drug design method based on two-stage evolutionary multi-task optimization of the present invention and five comparative algorithms on the dual task of Problem 1;

[0107] Figure 6 This is a schematic diagram showing the convergence of the drug design method based on two-stage evolutionary multi-task optimization of the present invention and five comparative algorithms on the dual task of Problem 2;

[0108] Figure 7 This is a schematic diagram showing the convergence of the drug design method based on two-stage evolutionary multi-task optimization of the present invention and five comparative algorithms on the dual task of Problem 3;

[0109] Figure 8 This is a schematic diagram showing the convergence of the drug design method based on two-stage evolutionary multi-task optimization of the present invention and five comparative algorithms on the dual task of problem 4;

[0110] Figure 9 This is a schematic diagram showing the convergence of the drug design method based on two-stage evolutionary multi-task optimization of the present invention and five comparative algorithms on the dual task of problem 5;

[0111] Figure 10 This is a schematic diagram showing the convergence of the drug design method based on two-stage evolutionary multi-task optimization of the present invention and five comparative algorithms on the dual task of problem 6;

[0112] Figure 11 This is a schematic diagram showing the convergence of the drug design method based on two-stage evolutionary multi-task optimization of the present invention and five comparative algorithms on the dual task of problem 7;

[0113] Figure 12 This is a schematic diagram illustrating the convergence of the drug design method based on two-stage evolutionary multi-task optimization of this invention and five comparative algorithms on the dual-task problem 8.

[0114] Figure 13 This is a schematic diagram showing the convergence of the drug design method based on two-stage evolutionary multi-task optimization of the present invention and five comparative algorithms on the dual task of Problem 9. Detailed Implementation

[0115] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0116] Example 1

[0117] The drug design method based on two-stage evolutionary multi-task optimization includes: determining the objective function for each sub-task and entering the early evolutionary stage; performing intra-task population evolution on the target task to obtain the offspring population; using an affine transformation strategy to generate a better migration solution for the target task; monitoring whether the population has reached the stage division point; if not, reselecting the target task and returning to the early evolutionary stage; if so, proceeding to the late evolutionary stage; using a local outlier detection model strategy to identify individuals with high similarity as transfer solutions; merging the parent population, offspring population, mapped solution, and transfer solution; and selecting the optimal solution based on the fitness function; determining whether evolution is complete based on the function evaluation count; if so, outputting the optimal solution; otherwise, proceeding to the next generation of evolution.

[0118] Example 2

[0119] Drug design methods based on two-stage evolutionary multi-task optimization, such as Figure 1 As shown, the specific steps include:

[0120] Step 1: Determine the objective function and decision variables for K sub-tasks. Sub-tasks include, but are not limited to, drug molecule structure optimization, drug solubility optimization, drug toxicity minimization optimization, drug stability optimization, and drug onset time optimization. Initialize the population size N and the number of tasks K, and use K*N individuals as the initial parent population.

[0121] Step 1.1: In this embodiment, K = 2 sub-task objective functions are defined. The first sub-task f1(x) is the drug molecule structure optimization task, which aims to find the compound with the highest activity by adjusting the molecular structure. The decision variables include the atomic structure of the molecule x1 and the adjustment of chemical bonds x2. The second sub-task f2(x) is the drug solubility optimization task, which aims to improve the solubility of the drug by adjusting the physicochemical properties of the molecule. The decision variables include the charge distribution of the molecule x1 and the solvent selection x2. In practice, the specific objective function for different drug designs is determined by a third party. In this embodiment, the CEC'2017 benchmark test function is used as a general test case for experimentation. The objective function is defined as follows:

[0122]

[0123] In the above formula, Ω i For the I-th task f i (x i The search space of ) For the optimal solution, x i For each individual in the population, i = 1, 2, ..., K.

[0124] Step 1.2: Set the iteration count t = 1, population size N = 50 / 100, population dimension D = 25 / 50, and number of tasks K; generate K*N individuals as the initial parent population P. k k = 1, 2, ..., K, and for P k Perform fitness evaluation; set the maximum number of function evaluations FESMAX = 100000 / 200000, and the initial number of evaluations FES = 0; set the adaptive selection parameters. Unify the multi-task search space so that dimension D = max j (D j ), where j is the j-th task;

[0125] Step 1.3: Set the parameters in the ADEOEA algorithm, CR i =0.5,F i =0.5,μ CR =0.5,μ F =0.5, Each individual is assigned a crossover probability CR. i and variable asynchronous length F i μ CR ,μ F Crossover probabilities CR i and variable asynchronous length F i The average value, S CR ,S F CR for successful individuals i ,F i A is the set of , and B is the set of inferior solutions.

[0126] Step 2: Select the target task and use the ADEOEA algorithm to perform in-task population evolution to generate offspring population;

[0127] Step 2.1: Select the k-th task as the target task, and use the mutation operator DE / current-to-pbest / 1 based on the Differential Evolution (DE) algorithm to generate offspring mutant individuals:

[0128]

[0129] In the above formula, x i,G For the parent generation, F i For individual x i,G The corresponding variable asynchronous length, Randomly selecting one individual from the top 100 ε% of the population, where ε = 0.05 is a very small probability value. From the parent population P k Randomly selected from the given information, k = 1, 2, ..., K. From set Pk Randomly selected from ∪B;

[0130] Step 2.2: For each mutated individual v i,G Same-parent generation individual x i,G Crossover yields N experimental individuals u j,i,G , denoted as offspring population O k ;

[0131]

[0132] In the above formula, rand(0,1) is a random number in the range (0,1), and CR i Let j be the crossover probability. rand Let j be an integer randomly selected from dimensions 1 to D. rand =randint(1,D), u j,i,G Let x be the j-th dimension variable for the i-th experimental individual; j,i,G v j,i,G These are the j-th dimension variables of the i-th parent individual and the i-th mutated individual, respectively.

[0133] Step 3: Utilize a diversity monitoring strategy to monitor whether the population has reached the stage breakpoint. If so, proceed to the next step; otherwise, use an affine transformation strategy to achieve spatial mapping of individuals across low-similarity tasks, generating a better transfer solution for the target task, such as... Figure 2 As shown;

[0134] Step 3.1: Construct a diversity monitoring equation to obtain diversity indicators:

[0135]

[0136] In the above formula, FESMAX represents the maximum number of function evaluations, FES represents the number of function evaluations, and these are used as the time axis to show that, starting from the first generation of evolution, the diversity of the population decreases in a fluctuating manner. Div1 represents the actual diversity of the initial population.

[0137]

[0138] In the above formula, N is the population size, x i Let be the i-th individual in the population, and μ be the true mean vector of the population. The value of this formula is the average distance between all individuals in the population and the mean vector.

[0139] Step 3.2: Based on the diversity index, determine whether the dividing point between the two stages has been reached:

[0140]

[0141] In the above formula, flag is a logical value that serves as a marker for the dividing point, and μ and σ are the true mean and variance of the population during the evolution process, respectively.

[0142] Step 3.3: If flag = 1, it indicates that the population is in the early stage of evolution, and affine transformation is used as a knowledge transfer strategy.

[0143] Step 3.3.1: Construct an affine transformation using the ranking loss function:

[0144]

[0145] In the above formula, θ = [A, b] is a transformation parameter of the affine transformation, obtained by minimizing the ranking loss function of the source and target task populations, where A and b are scaling and translation transformations, respectively, and M... a (·) represents the affine transformation. For ease of calculation, nonlinear mappings in the spatial mapping are ignored, and only linear mappings, i.e., affine transformations, are considered. Υ[·] represents the operation of converting fitness terrain into ranking-based terrain. P s (·),P t (·) represent the Gaussian models for the source and target tasks, respectively:

[0146]

[0147] In the above formula, w n This is the weighted weight of the population in generation t, which increases progressively from the first generation to the current generation, with the current generation having the largest value. The Gaussian model corresponding to the nth generation population:

[0148]

[0149] In the above formula, α is a preference coefficient, Pop i For the i-th generation population, To calculate the population probability density function, since each generation of the population is independently distributed, the probability density function can be constructed using a multivariate Gaussian distribution:

[0150]

[0151] In the above formula, μ and σ are the mean vector and standard deviation of the population, respectively:

[0152] μ=(μ1,μ2,…,μ D (11);

[0153]

[0154]

[0155]

[0156] In the above formula, μ j Let be the average value of the j-th dimension variable of the population, where D is the dimension and N is the population size. It is the j-th dimension variable of the i-th individual in the n-th generation population. Let be the variance of the j-th dimension variable of the population;

[0157] Step 3.3.2: The ideal difference between the ranking terrain of the source task and the target task is 0, that is, minimizing formula (3) yields the following formula:

[0158] Υ[P s [x]=Υ[δ·P t (M(x;θ))] (15);

[0159] In the above formula, δ is a scaling factor that does not change the original ranking of the population. Since the Gaussian distribution has the property of being continuously differentiable, formula (12) can be transformed into an algebraic form:

[0160] P s (x)=δ·P t (M(x;θ)) (16);

[0161] The analytical solution of formula (13) is calculated as follows:

[0162]

[0163]

[0164]

[0165] In the above formula, ∑ s ,∑ t The covariances of the source task and target task populations are respectively used to obtain the following variables using formulas (17)-(19):

[0166]

[0167] μ s =(μ t -b)A -1 (twenty one);

[0168]

[0169] Cholesky decomposition of equation (21):

[0170]

[0171] In the above formula, L s , The lower triangular matrices obtained by Cholesky decomposition of the covariance matrices of the source task and the target task are respectively used to obtain the final affine transformation parameters θ using formulas (20) and (22):

[0172]

[0173] Step 3.3.3: Using the affine transformation parameter θ, map the transfer solution from the source task to the target task to obtain a better transfer solution:

[0174]

[0175] In the above formula, is the transition solution mapped to the target task, and x is the transition solution of the source task;

[0176] Step 3.3.4: Generate N affine transformation transition solutions using formula (25), and rank the individuals according to their fitness values. Based on adaptive selection of parameter p a Select the first 100 pages a *N% of the individuals are considered successful, denoted as the mapping solution M. k ,like Figure 3 As shown;

[0177] Step 3.4: If flag = 0, it indicates that the population is in the late stage of evolution, and proceed to the next step.

[0178] Step 4: When the population enters the late stage of evolution, use the local outlier detection model strategy to identify individuals with high similarity as transition solutions; otherwise, return to step 3.

[0179] Step 4.1: Calculate the local outlier factor of individuals in the source task:

[0180]

[0181] In the above formula, Let i be the i-th individual in the source task. Let k be the k-th neighborhood of this individual. For this individual, there are k target task individuals within its k-th distance neighborhood. The local reachability density of this individual:

[0182]

[0183] In the above formula, For neighboring individuals To individuals The k-th reachable distance, such as Figure 4 As shown:

[0184]

[0185] In the above formula, For neighboring individuals To individuals Euclidean distance, d k (·) represents the k-th distance. When condition I is satisfied, d k (p) = d(p,o), and condition I is:

[0186] 1) There are at least k points o' in the set, excluding point p, such that d(p,o')≤d(p,o);

[0187] 2) There are at least k-1 points o' in the set, excluding point p, such that d(p,o') <d(p,o);

[0188] Step 4.2, for locally outlier factors Sort in ascending order to get the ranking. And based on the adaptive selection of parameter p l Select the top 100 pages l *N% of individuals are considered as migration solutions generated by the local outlier model, denoted as L. k .

[0189] Step 5: Merge the population of generation t, i.e., merge the parent population P. k (t), Offspring Population O k (t), mapping solution M k (t) and the transition solution L k (t), i.e., P k (t)∪O k (t)∪M k (t)∪L k (t), denoted as the merged population S k (t), and for S k (t) Perform fitness evaluation; and sort the fitness values ​​f(S) in ascending order. k (t)), select the first N individuals as successful individuals, and use them as the optimal solution;

[0190] Step 6: If the function evaluation count (FES) is less than the maximum function evaluation count (FESMAX), update the ADEOEA algorithm parameters and adaptive selection parameters, and return to step 2; otherwise, output the population P. k The optimal solution of (t) and optimal value This means obtaining the optimal solution for drug design, including the adjustment of molecular atomic structure and chemical bonds in the sub-task drug molecular structure optimization, and the selection of molecular charge distribution and solvent in the sub-task drug solubility optimization.

[0191] The process of updating ADEOEA algorithm parameters and adaptively selecting parameters is as follows:

[0192] Step a: During each generation of population evolution, if the generated experimental individual u i,G Superior to parent individual x i,G Then the parameter CR corresponding to the successful individual will be... i ,F i Save to collection S CR ,S F and the mean μ CR ,μ F The update is performed using the following formula:

[0193] μ CR = (1-c)·μ CR +c·mean A (S CR (29);

[0194] μ F = (1-c)·μ F +c·mean L (S F (30);

[0195] In the above formula, c is the learning rate, and mean A (·) Take the weighted average, mean L (·) Take the Lehmer average;

[0196]

[0197]

[0198]

[0199] In the above formula, Δf k =|f(u k,G )-f(x k,G )|;

[0200] Step b, using the updated μ CR ,μ F CR for calculating the next generation of population evolution i F i ;

[0201] CR i =randn i (μ CR ,0.1) (34);

[0202] F i =randc i (μ F,0,1) (35);

[0203] In the above formula, randn i (μ CR ,0.1) and randc i (μ F The values ​​of μ, 0, 1) are randomly sampled from the normal distribution and the Cauchy distribution, respectively. CR ,μ F The mean and variance σ are given. 2 =0.1, CR is outside the range [0,1]. i ,F i Perform interception;

[0204] Step c: Using the number of successful individuals obtained in step 3.3, update the adaptive selection parameter p of the affine transformation. a :

[0205]

[0206] In the above formula, t is the number of iterations, and S a N represents the number of successful individuals, and N represents the total number of migration solutions, which is also the size of the population. The purpose is to perform an affine transformation on all individuals in the source task and finally select the best performing individuals in the target task as migration solutions to increase the probability of successful survival of migration solutions.

[0207] Step d: Using the number of successful individuals from step 4, update the adaptive selection parameter p of the local outlier factor model. l :

[0208]

[0209] In the above formula, S l The number of migration solutions generated for the local outlier model.

[0210] Example 3

[0211] Simulation experiments were conducted on a multi-task benchmark function using a two-stage evolutionary multi-task optimization (PD+TEMO) drug design method to obtain the optimal value for each sub-task. The CEC'2017 evolutionary multi-task competition was used as the benchmark function, comprising 9 test problems, each with 2 sub-tasks. The sub-task dimensions were set to 50 / 25, and the optimal value was taken at the origin 0. The search space and similarity of each test problem's sub-tasks differed, as shown in Table 1.

[0212] Table 19 CEC'2017 Multi-Task (2-Task) Benchmark Functions

[0213]

[0214] The performance of the PD+TEMO algorithm of this invention was compared with that of the MPEFSHADE algorithm, the classic MFEA algorithm, the MTEAAD algorithm using only LOF, MFDE, and EMTEA. To ensure that the experimental environment and background were the same and to eliminate the interference of irrelevant variables, the specific experimental parameters were set uniformly as follows:

[0215] Population size N: 50

[0216] Random mating probability rmp: 0.3

[0217] Maximum number of function evaluations (FESMAX): 100000

[0218] Maximum number of loops (runmax): 30

[0219] The specific process is as follows: five comparison algorithms and the proposed algorithm PD+TEMO are run on nine test problems. Each algorithm runs `runmax` times for each test problem, with each loop performing several iterations. The iteration termination condition depends on whether the function evaluation count (FES) reaches the maximum function evaluation count (FESMAX). After the loop ends, the minimum values ​​of the six algorithms corresponding to the nine test problem subtasks are archived during the 30 loops. The experimental data were compared using the algorithm's performance metrics, as shown in Table 2:

[0220] Table 2 shows the experimental results of the six algorithms obtaining the optimal value after running 30 times on the dual-task CEC'2017 benchmark function (Note: the optimal value among the six comparison algorithms is in bold).

[0221]

[0222] As shown in Table 2, for the 18 sub-tasks of the dual-task approach, PD+TEMO outperforms the other five algorithms in 13 sub-tasks; in the remaining five sub-tasks, PD+TEMO performs slightly worse than MTEAAD, but still outperforms the other four algorithms. The reason for this is that MTEAAD employs a knowledge transfer mechanism suitable for highly similar tasks, thus performing well in some highly relevant sub-tasks. PD+TEMO, in order to maintain its universality in handling both highly and low-similarity tasks, sacrifices some performance, but still maintains a significant competitive advantage over other algorithms.

[0223] As an extension, the performance of the six algorithms was tested on a Many task. The WCCI20_MaTSO benchmark function was used for experimental verification. Each problem had five subtasks, with three additional subtasks: minimizing drug toxicity, optimizing drug stability, and optimizing drug onset time. The experimental parameters were uniformly set as follows:

[0224] Population size N: 100

[0225] Random mating probability rmp: 0.3

[0226] Maximum number of function evaluations (FESMAX): 200000

[0227] Maximum number of loops (runmax): 30

[0228] The specific process is the same as above, and finally, the minimum values ​​of the 10 test problem subtasks corresponding to the 6 algorithms are saved. As shown in Table 3, experimental data were compared to measure the algorithm's performance.

[0229] Table 3 shows the experimental results of the six algorithms obtaining the optimal value after running 30 times on the WCCI20_MaTSO benchmark function of the Many task (Note: the optimal value among the six comparison algorithms is in bold).

[0230]

[0231]

[0232] Table 3 shows that for the Many task with 50 subtasks, PD+TEMO outperforms the other 5 algorithms in 39 subtasks; PD+TEMO performs slightly worse than MTEAAD in 9 subtasks; and PD+TEMO performs slightly worse than ETMEA in 2 subtasks.

[0233] In summary, the experimental results show that, comparing the performance of the proposed algorithm PD+TEMO with five other algorithms (MPEFSHADE, MFEA, MTEAAD, MFDE, and ETMEA) on the CEC'2017 task and the WCCI20_MaTSO Many task benchmark function, PD+TEMO demonstrates superior performance in terms of solution capability, algorithm versatility, and overall performance. This is particularly evident in the Many task, where the number of tasks is large and the similarity between tasks is complex and uncertain; PD+TEMO still performs well. For all 10 black-box problems, PD+TEMO provides relatively complete solutions, unlike other algorithms that only solve a single subtask. Therefore, PD+TEMO exhibits versatility in handling both highly and low-similarity tasks. Its advantage lies in its ability to capture the similarity between different tasks and employ appropriate knowledge transfer mechanisms for effective subtask solving. This overcomes the limitation of existing algorithms that cannot thoroughly solve drug design problems under black-box conditions due to the uncertainty of the problem's nature. Figure 5-13 As shown, the PD+TEMO algorithm of this invention has achieved good results in terms of algorithm performance and convergence speed.

[0234] Through the above methods, the drug design method based on two-stage evolutionary multi-task optimization of the present invention, on the basis of the concept of adaptive regulation of population evolution, adopts a dual strategy of combining affine transformation and local outlier detection model to construct a two-stage knowledge transfer mechanism, adaptively solving drug design problems of different properties under black box problem, while using adaptive parameter selection to retain high-quality transfer solutions, dynamically improving the co-evolution efficiency and solution capability of the algorithm; it has the characteristics of problem universality and superior performance.

Claims

1. A method for drug design based on two-stage evolutionary multitask optimization, characterized in that, Comprise: Determine the objective function of each subtask, enter the evolution prophase stage: the intratask population evolution of the target task is carried out to obtain the offspring population, the affine transformation strategy is used to generate the migration solution which is better than the target task, the population is monitored to determine whether it reaches the stage division point, if not, the target task is selected again, and the evolution prophase stage is returned; if yes, the evolution later stage is carried out: the local outlier factor detection model strategy is used to transfer the solution, the parent population, the offspring population, the migration solution and the transfer solution are combined, and the optimal solution is selected according to the fitness function; According to the function evaluation times, it is determined whether the evolution is completed, if yes, the optimal solution is output, otherwise the next generation evolution is entered; Comprise the following steps: Step 1, determining a target function and decision variables of each sub-task, the sub-task including, but not limited to, a drug molecule structure optimization task, a drug solubility optimization task, a drug toxicity minimization optimization task, a drug stability optimization task, and a drug onset time optimization task; Step 2, select the target task, and use the ADEOEA algorithm to carry out intratask population evolution to generate the offspring population; Step 3, the diversity monitoring strategy is used to monitor whether the population reaches the stage division point, if yes, the next step is entered, otherwise the affine transformation strategy is used to generate the migration solution which is better than the target task; Step 4, the population enters the evolution later stage, the local outlier factor detection model strategy is used to identify individuals with high similarity as transfer solutions; Step 5, the parent population, the offspring population, the mapping solution and the transfer solution are combined to obtain the combined population, and the successful individual is selected as the optimal solution according to the fitness; Step 6, it is judged whether the function evaluation times is less than the preset threshold, if yes, the ADEOEA algorithm parameters and the adaptive selection parameters are updated, and step 2 is returned; otherwise, the optimal solution of the population and the optimal target function are output, that is, the optimal scheme of drug design is obtained; Step 3 specifically comprises the following steps: Step 3.1, a diversity monitoring equation is constructed to obtain a diversity index: （4）； In the above formula, is the maximum number of function evaluations, is the number of function evaluations, is the initial population true diversity: （5）； In the above formula, is the population size, is the true mean vector of the population, is the individual in the population, is the true mean vector of the population; Step 3.2, according to the diversity index, it is judged whether the two stage division points are reached: （6）； In the above formula, is a logical value, as a marker of the division point, are the real mean and variance of the population during the evolution, respectively; Step 3.3, if , which indicates that the population is in the early stage of evolution, and the affine transformation is used as the knowledge transfer strategy. Step 3.4, if indicates that the population is in the late evolutionary stage, and enters the next step; Step 3.3 specifically comprises the following steps: Step 3.3.1, the affine transformation is constructed by using the ranking loss function: （7）； In the above formula, is a transformation parameter of the affine transformation, are a scaling transformation and a translation transformation, respectively, is an affine transformation, is an operation to convert the fitness landscape into a ranking-based landscape, are Gaussian models of the source task and the target task, respectively: （8）； In the above formula, is the weighted weight of the th generation population, is the weighted weight of the th generation population, and （9）； In the above formula, is a preference coefficient, is the first generation population, is the operation for calculating the population probability density function, and a multivariate Gaussian distribution is used to construct the probability density function: （10）； In the above formulae, are the mean vector and standard deviation of the population, respectively: （11）； （12）； （13）； （14）； In the above formula, is the population of the dimensional average, is the dimension, is the population size, is the population of the dimensional average, is the population of the dimensional average, is the population of the dimensional variance; Step 3.3.2, formula (3) is minimized to obtain the following formula: （15）； In the above formula, is a scaling factor that transforms equation (12) into an algebraic form: （16）； The analytical solution calculation formula of formula (13) is as follows: （17）； （18）； （19）； In the above formulae, Covariance of the source and target task populations, respectively, using equations (17)-(19) to obtain the following variables: （20）； （21）； （22）； Cholesky decomposition is performed on formula (21): （23）； In the above formula, , are the lower triangular matrices obtained by Cholesky decomposition of the source and target task covariance matrices, respectively, and the final affine transformation parameters are obtained using equations (20) and (22) : （24）； Step 3.3.3, utilizing affine transformation parameters mapping the migration solution in the source task to the target task to obtain a more optimal migration solution: （25）； In the above formula, is a migration solution mapped into the target task, is a migration solution in the source task; Step 3.3.4: Generate using formula (25) The transition solutions after affine transformation are sorted according to their fitness values ​​to obtain the individual ranking rank{ Based on adaptive parameter selection Before selection The successful individuals are denoted as the mapping solutions.

2. The two-stage evolutionary multitask optimization based drug design method of claim 1, wherein, The objective function is: （1）； In the above formula, is the first task search space, optimal solution, is the population individual, .

3. The two-stage evolutionary multitask optimization based drug design method of claim 1, wherein, Step 2 specifically comprises the following steps: Step 2.1, select the first task as the target task, generate the offspring mutation individual by using the mutation operator DE / current-to-best / 1 based on the differential evolution algorithm: Step 2.2, select the second task as the target task, generate the offspring mutation individual by using the mutation operator DE / current-to-best / 1 based on the differential evolution algorithm: p Step 2.3, select the third task as the target task, generate the offspring mutation individual by using the mutation operator DE （2）； In the above formula, is the parent individual, is the individual corresponding mutation step size, randomly selected from the top 100 of the population, and ε is a probability value, randomly selected from the parent population P k , , randomly selected from the set P k ∪B; Step 2.2, each variant individual is crossed with sire individual crossed, resulting in test individual , denoted offspring population ; （3）； In the above formula, is a random number within the range of is the cross probability, is from 1 to a randomly selected integer in dimension , is the first dimensional variable of the first trial individual; is the first dimensional variable of the first parent individual and the first dimensional variable of the first mutation individual, respectively. is the first 4. The two-stage evolutionary multitask optimization based drug design method of claim 1, wherein, Step 4 specifically comprises the following steps: Step 4.1, the local outlier factor of the individual in the source task is calculated: （26）； In the above formula, For the first in the source task Individual, For the individual's first Neighborhood, , For this individual Distance to neighboring areas Individual target tasks The local reachability density of this individual: （27）； In the above formulae, as a neighborhood individual to an individual the first reachable distance: （28）； In the above formula, is the neighborhood individual to the individual Euclidean distance, is the distance of the distance when condition I is satisfied, condition I is: 1) There are at least a few points in the set that do not include points. Including Points , making ; 2) The set contains at least one point that is not included. Including Points , making ; Step 4.2, local outlier factor Perform ascending arrangement to get ranking And according to adaptive selection parameters Select the top Individuals as the transfer solution generated by the local outlier factor model.

5. The two-stage evolutionary multitask optimization based drug design method of claim 1, wherein, The process of updating the ADEOEA algorithm parameters and the adaptive selection parameters in step 6 is as follows: Step a, during the evolution of each generation population, if the generated test individual is better than the parent individual , then the parameter corresponding to the successful individual is archived to the set , and the mean is updated, the update formula is as follows: （29）； （30）； In the above formulae, is the learning rate, the weighted average is taken, the Lehmer average is taken; （31）； （32）； （33）； In the above formulae, ; Step b, using the updated Compute CR for next generation population evolution i , F i ; （34）； （35）； In the above formulae, and are randomly sampled from normal and Cauchy distributions, respectively, is the mean, and is the variance, values outside the range are truncated. Step c. Update the parameters of the affine transformation with the number of successful individuals obtained from step 3.3 : （36）； In the above formula, is the number of iterations, is the number of successful individuals, is the total number of migration solutions; Step d, update the adaptive selection parameters of the local outlier factor model with the number of successful individuals of step 4 : （37）； In the above formula, Generate the number of migration solutions for the local outlier factor model.

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