Pulmonary nodule benign and malignant identification method based on improved seagull optimization algorithm

Abstract

A pulmonary nodule benign and malignant identification method based on an improved seagull optimization algorithm belongs to the field of lung cancer early screening in disease diagnosis, and is characterized in that the identification method comprises the following steps: S1, global search of collision avoidance weight factors based on index change; s2, local search based on dynamic reverse learning strategy improvement; s3, improving secondary local search of an Litalian mechanism based on mutual information so as to improve the local search capability of a sea gull optimization algorithm; and S4, population updating based on a multi-target fitness function. Compared with the prior art, the method has the advantages that the global search process and the local search process are better balanced, the local search capability of the sea gull optimization algorithm is enhanced, and radiomics features with high richness are selected by improving a traditional alteration mechanism.

Description

Technical Field

[0001] The present invention relates to a method for identifying benign and malignant lung nodules, and specifically provides a method for identifying benign and malignant lung nodules based on an improved Seagull optimization algorithm, which belongs to the field of early screening of lung cancer in disease diagnosis. Technical Background

[0002] Lung nodules are an early stage manifestation of lung cancer. Military personnel are a potential high-risk group for lung cancer due to their long-term exposure to special working environments (such as exposure to harmful substances, dust, smoke, etc.), high stress levels, and possible high smoking rates. Military medical institutions have included early screening for lung cancer in routine physical examinations, and can conduct targeted screening for serving and retired military personnel to detect lung nodules in a timely manner. Lung nodules are classified by density and can be divided into solid lung nodules and subsolid lung nodules. Subsolid lung nodules can be divided into partially solid nodules and pure ground glass nodules. Lung nodules are classified by size, with diameters less than 5 mm defined as micronodules and 5 to 10 mm as small nodules. As the size of a lung nodule increases, its probability of malignancy also increases. Most malignant lung nodules are round or quasi-round in shape. Compared with malignant solid nodules, malignant subsolid nodules have a higher proportion of irregular shapes. Radiologists examine CT images slice by slice and follow industry guidelines, such as the Chinese Expert Consensus on the Diagnosis and Treatment of Pulmonary Sarcoidosis, to assess the possibility of malignancy in nodules. However, the existing complex multivariate diagnostic criteria and the similar characteristics between benign and malignant nodule cases make it difficult for even experienced radiologists to distinguish them. Classifying high-risk nodules as low-risk can lead to delayed cancer diagnosis, but over-examination of low-risk nodules can expose patients to unnecessary losses. Therefore, there is a strong clinical need for accurate identification of benign and malignant lung nodules.

[0003] Computer-aided diagnosis systems interpreting lung CT images can help radiologists make accurate diagnosis of lung nodules more efficiently and accurately. Computer-aided diagnosis systems extract features from lung nodules to train radiomics models to automatically classify nodules. Each CT image slice has features such as texture, shape, and color that describe its properties. However, the global radiomics features of CT images are redundant, which can cause problems such as long training time and poor performance of computer-aided diagnosis models. To solve the problem of feature redundancy, feature selection is required after feature extraction. Feature selection identifies an optimal set of features to achieve better accuracy, thereby reducing computing time and optimizing memory. The seagull optimization algorithm mimics the migration and attack behavior of seagulls in nature. Although the original seagull optimization algorithm provides good results in finding optimal solutions to different problems, it also has certain disadvantages like other metaheuristic algorithms. For example, it is easy to get stuck in local optimal points, or in some cases, it provides a weak convergence rate. Summary of the invention

[0004] In view of the many advantages of the Seagull optimization algorithm, the inventors thought of using the Seagull optimization algorithm for radiomics feature selection in the task of predicting benign and malignant lung nodules. Taking into account some of the shortcomings of the Seagull optimization algorithm, it is necessary to improve the Seagull optimization algorithm in the task of lung nodule identification.

[0005] In order to meet the clinical needs of predicting benign and malignant pulmonary nodules and solve the problems of redundant radiomics features and weak local search capability of the Seagull optimization algorithm, the present invention proposes a method for identifying benign and malignant pulmonary nodules based on an improved Seagull optimization algorithm.

[0006] The objectives of the present invention are achieved through the following technical solutions.

[0007] Step 1: Global search using exponentially varying collision avoidance weight factors

[0008] When the lung nodule recognition model is optimized, each individual in the seagull population represents a combination of radiomic features. During the seagull migration process, the seagull optimization algorithm simulates how the seagull population moves from one location to another. At the same time, the seagulls should meet the condition of avoiding collisions. In order to avoid collisions with other adjacent seagulls, an exponentially changing collision avoidance weight factor α is used to calculate the new position of the seagull, that is:

[0009]

[0010] Where C(t) represents the position where there is no position conflict with other seagulls; P(t) is the current position of the seagull, p i,j represents the jth radiomic feature for the identification of benign and malignant lung nodules in the i-th seagull individual, n represents the number of seagulls, and m represents the number of radiomic features. In the matrix C(t), each column represents a different radiomic feature, and each row represents an individual seagull in the seagull population, that is, a feature subset composed of some radiomic features in the entire feature set, and k represents a fixed coefficient; Max iteration represents the maximum number of iterations; t represents the current number of iterations.

[0011] During the migration process, seagulls avoid overlapping with other seagulls by calculating the difference D(t) between the current position of the seagull population and the optimal position, and move toward the optimal position.

[0012]

[0013] in, Indicates the current best position of the seagull Current location of Seagull The difference between β and α. After obtaining the direction of the best position, the seagull will move towards the best position and reach the new position E(t), that is:

[0014]

[0015]

[0016] Where E(t) represents the new position of the seagull, c i , j(t) represents the j-th radiomic feature of the i-th seagull individual in C(t), d(t) represents the j-th radiomic feature of the i-th seagull individual in D(t), and |·| represents the absolute value operation.

[0017] Step 2: Improved local search based on dynamic reverse learning strategy

[0018] The inventor introduced a dynamic reverse learning strategy in the local search process to improve the local search ability of the algorithm. The position P of the seagull after attacking the prey improved by the dynamic reverse learning strategy attack It is expressed as follows:

[0019] P attack (t)=ω1xyzE(t)+ω2E * (t)+P bs (t)

[0020] In the formula, x = ue θv cos(θ),y=ue θv sin(θ) and z = ue θv θ constitutes the description of the motion behavior of the seagull population in three-dimensional space in this step; θ is a random angle value in the interval [0, 2π]; u and v are the related constants of the spiral trajectory of the seagull flight; e is the base of the natural logarithm, ω1, ω2∈(0, 1), and P bs (t) represents the current optimal position of the seagull, E * (t) represents the reverse solution, which is calculated by the following formula:

[0021] E * (t) = k(P bs (t)+P ws (t))-E(t)

[0022] Where P ws (t) represents the worst position of the current seagull; k is the reverse coefficient, which is a random number between (0, 1). The seagull population after this step is expressed as follows:

[0023] P attack (t)=ω1xyzE(t)+ω2E * (t)+P bs (t)

[0024] =ω1xyzE(t)+ω2(k(Pbs (t)+P ws (t))-E(t))+P bs (t)

[0025] =(ω1xyz-ω2)E(t)+(ω2k+1)P bs (t)+ω2kP ws (t)

[0026] Step 3: Improve the secondary local search of the altruism mechanism based on mutual information to further improve the local search capability of the Seagull optimization algorithm

[0027] First, the seagull population P that did not go through the first and second steps 0 , and the seagull population P that has undergone the above two steps 1 Merge into a new population P new As input to the altruism mechanism, this process is formulated as follows:

[0028]

[0029]

[0030] Where n is the number of seagulls in the population and m is the number of global radiomic features. Then, for the new population P new ={p1, p2, ..., p 2n} sort to get P′ new ,Right now:

[0031] P′ new ={p′1, p′2,...,p′ 2n}

[0032] Among them, f(p′1)≥f(p′2)≥…≥f(p′ 2n ), f(·) represents the fitness function. Take P′ new 2A seagulls with medium fitness constitute the altruistic pool P MD ,but:

[0033] P MD = {p′ i |nA≤i<n+A}

[0034] The individuals with high fitness are the first nA seagull individuals in the sorted population and are retained, denoted as PH:

[0035] PH = {p′ i |1≤i<nA}

[0036] The individuals with low fitness are nA seagull individuals after sorting the population, which are recorded as P L :

[0037] P L ={p′ i |n+A≤i<2n}

[0038] In the improved altruism pool P MD In the example, a pair of i and F j The candidate solutions are S i and S j , S i and S j The similarity index ξ between them is defined as follows:

[0039]

[0040] Among them, d E (S i , S j ) indicates S i and S j The Euclidean distance between them, β1 and β2 represent two weight coefficients. When the similarity index ξ value is higher, the relationship between the two candidate solutions is closer.

[0041] The criterion for selecting the sacrifice solution of the improved altruism mechanism is determined by the average mutual information of the candidate solutions. The mutual information matrix between radiomics features is expressed as follows:

[0042]

[0043] In the formula, I(X i ;X j ) represents the radiomics feature X i and feature X j The mutual information between them, m represents the number of radiomic features. i ;X j ) is calculated as follows:

[0044]

[0045] Where, X i and X j are two radiomic features, x i and x j Yes X i and X j The specific value corresponding to the individual seagull, p(x i , x j ) is X i and X j The joint probability, p(x i ) and p(x j ) are X iand X j Assume that the candidate solution S i Screen out n radiomic features, then the candidate solution S i The mutual information matrix It is expressed as follows:

[0046]

[0047] Candidate solution S i The average mutual information for:

[0048]

[0049] Similarly, we can get the candidate solution S j The average mutual information Smaller average mutual information indicates that the corresponding candidate solution is likely to be improved during the evolution process, because smaller mutual information indicates higher feature richness, while larger mutual information indicates redundancy. i and S j The one with smaller average mutual information is selected in the altruism pool, and the other is kicked out of the altruism pool.

[0050] Assume that the population that has undergone the altruism mechanism is denoted as Q, then the output of the secondary local search is composed of the retained high fitness individuals P H And Q composition:

[0051]

[0052] Among them, P LS2 is the output of the secondary local search, and P can be determined according to the fitness function LS2 The best individual in a population.

[0053] Step 4: Population update based on multi-objective fitness function

[0054] A higher fitness value indicates a better candidate solution. The multi-objective fitness function used in the Altruistic Seagull Optimization Algorithm consists of three parts: Area Under Curve (AUC), accuracy, and count of selected features, as shown below:

[0055]

[0056] in, Represents the area under the receiver operating characteristic (ROC) curve, TPR i and FPR iare the true positive rate and false positive rate of the i-th point on the ROC, respectively; a represents the number of points in the ROC curve; the larger the area under the curve, the higher the fitness value; the smaller the number of features, the higher the fitness value; Accuracy represents the accuracy of benign and malignant prediction of pulmonary nodules; b represents the number of features in the selected subset, and m represents the total number of features; the sum of weight coefficients w1+w2+w3=1. The proposed multi-objective fitness function is robust to unbalanced data sets because the AUC operator is insensitive to changes in sample distribution, and the multi-objective fitness function can adaptively set weight factors, so that the improved Seagull optimization algorithm can better balance the prediction performance and the number of selected radiomic features during the iteration process.

[0057] Beneficial Effects

[0058] Compared with the prior art, the present invention has the following effects:

[0059] The present invention proposes an exponentially changing collision avoidance weight factor for the global search of Seagull Optimization, which can better balance the global search and local search processes when solving the pulmonary nodule radiomics feature selection, effectively avoiding the appearance of the same pulmonary nodule radiomics feature subsets, which can ensure the diversity of solutions.

[0060] Furthermore, the present invention introduces a dynamic reverse learning strategy into the original spiral flight rules of seagulls attacking prey, thereby enhancing the local search capability of the seagull optimization algorithm and effectively solving the problem that the solution representing the radiomics characteristics of lung nodules is easily trapped in the local optimum.

[0061] Furthermore, the present invention introduces an improved altruism mechanism after the attack behavior of the Seagull optimization algorithm, thereby selecting radiomics features with higher richness.

[0062] Finally, the present invention designs a multi-objective fitness function to ensure that the lung nodule recognition model maintains better performance while using as few features as possible, and because the multi-objective fitness function includes AUC, the function is friendly to unbalanced data sets. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is the workflow diagram of the algorithm for distinguishing benign and malignant pulmonary nodules based on the improved Seagull optimization algorithm;

[0064] Figure 2 Processing flow chart of the altruism pool in the mutual information improved altruism mechanism;

[0065] Figure 3 The changing trend of AUC value during the iteration process;

[0066] Figure 4 The changing trend of accuracy during the iteration process;

[0067] Figure 5 In the iterative process, the changing trend of the number of radiomic features was selected;

[0068] Figure 6 The changing trend of fitness value during the iteration process;

[0069] Figure 7 ROC curve of the training set;

[0070] Figure 8 ROC curve of the test set;

[0071] Fig. 9 Confusion matrix of the training set;

[0072] Fig.10 Confusion matrix for the test set. DETAILED DESCRIPTION

[0073] The method of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments of the specification. It should be understood that the embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0074] See the instruction manual Figure 1 This embodiment describes the application of the present invention to the identification of benign and malignant pulmonary nodules with a diameter greater than 15 mm. The main steps include:

[0075] Set hyperparameters such as the number of seagulls, the number of altruistic individuals, and the iteration period;

[0076] Specifically, the number of seagulls refers to the number of seagulls in the seagull population. In this embodiment, the number of seagulls is 20;

[0077] The number of altruistic individuals refers to the number of seagulls participating in the construction of the altruistic pool, which is 10 in this embodiment;

[0078] The iteration cycle refers to the number of iterations of the improved Seagull optimization algorithm in the present invention. In this embodiment, the iteration cycle is 50;

[0079] Step 1: Global search with exponentially varying collision avoidance weight factors

[0080] Sub-step 1.1: When the lung nodule recognition model is optimized, each individual in the seagull population represents a combination of radiomic features. During the seagull migration process, the seagull optimization algorithm simulates how the seagull population moves from one location to another while also avoiding collisions between seagulls. In order to avoid collisions with other adjacent seagulls, the collision avoidance weight factor α of the exponential variation factor is used to calculate the new position of the seagull, that is:

[0081]

[0082] Among them, C(t) represents the position where there is no position conflict with other seagulls; P(t) is the current position of the seagull, p i，j represents the jth radiomic feature for identifying benign and malignant lung nodules in the i-th seagull individual, n represents the number of seagulls, and m represents the number of radiomic features. Each column in the matrix C(t) represents a different radiomic feature, and each row represents an individual seagull in the seagull population, that is, a feature subset composed of some radiomic features in the entire feature set, and k represents a fixed coefficient. In this embodiment, k = 2; Max iteration Indicates the maximum number of iterations. In this embodiment, Max iteration =50; t represents the current iteration number. Therefore, specifically, in this embodiment, the position C(t) where other seagulls do not have position conflicts can be expressed as:

[0083]

[0084] Sub-step 1.2: During the migration process, after avoiding the overlap with other seagulls, the seagulls calculate the difference D(t) between the current position of the seagull population and the optimal position, and move towards the optimal position.

[0085]

[0086] in, Indicates the current best position of the seagull Current location of Seagull β is a coefficient related to α. Specifically, in this embodiment, the difference D(t) between the current position of the seagull population and the optimal position can be expressed as:

[0087]

[0088] Where rd represents a random number between [0.0, 1.0).

[0089] Step 1.3: After obtaining the direction of the best position, the seagull will move towards the best position and reach the new position E(t), that is:

[0090] Where E(t) represents the new position of the seagull, c i，j (t) represents the jth radiomic feature of the i-th seagull individual in C(t), d(t) represents the jth radiomic feature of the i-th seagull individual in D(t), and |·| represents the absolute value operation. Specifically, the new position E(t) in this embodiment can be expressed as:

[0091]

[0092] Step 2: Improved local search based on dynamic reverse learning strategy

[0093] The position P of the seagull after attacking the prey with the improved dynamic reverse learning strategy attack It is expressed as follows:

[0094] P attack (t)=ω1xyzE(t)+ω2E * (t)+P bs (t)

[0095] In the formula, x = ue θv cos(θ),y=ue θv sin(θ) and z = ue θv θ constitutes the description of the motion behavior of the seagull population in the three-dimensional space in this step; θ is a random angle value in the interval [0, 2π]; u and v are related constants of the spiral trajectory of the seagull flight; in this embodiment, u = 1 and v = 1; e is the base of the natural logarithm; ω1, ω2∈(0, 1), and P bs (t) represents the current optimal position of the seagull. * (t) represents the reverse solution, which is calculated by the following formula:

[0096] E * (t) = k(P bs (t)+P ws (t))-E(t)

[0097] Where P ws (t) represents the worst position of the current seagull; k is the reverse coefficient, which is a random number between (0, 1). The seagull population after this step is expressed as follows:

[0098] P attack (t)=ω1xyzE(t)+ω2E * (t)+P bs (t)

[0099] =ω1xyzE(t)+ω2(k(P bs (t)+P ws (t))-E(t))+P bs (t)

[0100] =(ω1xyz-ω2)E(t)+(ω2k+1)P bs (t)+ω2kP ws (t)

[0101] Therefore, specifically, in this embodiment, the seagull population after this step is expressed as follows:

[0102]

[0103] Step 3: Secondary local search based on mutual information to improve the altruism mechanism

[0104] Sub-step 3.1: Specifically, the seagull population P that has not undergone the first and second steps 0 , and the seagull population P that has undergone the above two steps 1 Merge into a new population P new As the input of the altruism mechanism. This process is expressed in the following formula:

[0105]

[0106] Sub-step 3.2: Specifically, for the new population P new ={p1, p2, ..., p 40} sort to get P′ new ,Right now:

[0107] P′ new ={p′1, p′2,…,p′ 40}

[0108] Among them, f(p′1)≥f(p′2)≥…≥f(p′ 40 ), f(·) represents the fitness function, and P′ new 2A seagulls with medium fitness constitute the altruistic pool P MD , in this embodiment, 2A=20, so specifically:

[0109] P MD = {p′ i |(20-10)≤i<(20+10)}

[0110] Sub-step 3.3: Specifically, the individuals with high fitness are the first 20-10 = 10 seagull individuals in the sorted population and are retained, denoted as P H :

[0111] P H = {p′ i |1≤i<(20-10)}

[0112] Sub-step 3.4: Specifically, the individuals with low fitness are 20-10=10 seagull individuals that are eliminated from the sorted population, denoted as P L :

[0113] P L = {p′ i |(20+10)≤i<40}

[0114] Sub-step 3.5: In this embodiment, the improved altruism pool PMD The processing operation is as shown in the instruction manual. Figure 2 As shown, the altruism pool P MD A pair of them have fitness values ​​F i and F j The candidate solution S i and S j The similarity index ξ between them is defined as follows:

[0115]

[0116] Among them, d E (S i , S j ) represents the Euclidean distance between S1 and S2. Specifically, when the similarity index ξ value is higher, the relationship between the two candidate solutions is closer.

[0117] The criterion for selecting the sacrifice solution of the improved altruism mechanism is determined by the average mutual information of the candidate solutions. The mutual information matrix between radiomics features is expressed as follows:

[0118]

[0119] In the formula, I(X i ;X j ) represents the radiomics feature X i and feature X j The mutual information between them, m represents the number of radiomic features. i ;X j ) is calculated as follows:

[0120]

[0121] Where, X i and X j are two radiomic features, x i and x j Yes X i and X j The specific value corresponding to the individual seagull, p(x i , x j ) is X i and X j The joint probability, p(x i ) and p(x j ) are X i and X j Assume that the candidate solution S i Screen out n radiomic features, then the candidate solution S i The mutual information matrix It is expressed as follows:

[0122]

[0123] Candidate Solution S i The average mutual information for:

[0124]

[0125] Similarly, we can get the candidate solution S j The average mutual information Smaller average mutual information indicates that the corresponding candidate solution is likely to be improved during the evolution process, because smaller mutual information indicates higher feature richness, while larger mutual information indicates redundancy. i and S j The one with smaller average mutual information is selected in the altruism pool, and the other is kicked out of the altruism pool.

[0126] Sub-step 3.6: Let the population that has undergone the altruism mechanism be recorded as Q. In this embodiment, the output of the secondary local search consists of the retained high fitness individuals PH and Q:

[0127]

[0128] Among them, P LS2 is the output of the secondary local search, and P can be determined according to the fitness function LS2 The best individual in a population.

[0129] Step 4: Population update based on multi-objective fitness function

[0130] A higher fitness value indicates a better candidate solution. The multi-objective fitness function used in the altruistic seagull optimization algorithm consists of the following three parts: Area Under Curve (AUC), accuracy, and count of selected features.

[0131] Sub-step 4.1: Calculate the area under the curve of the prediction model for benign and malignant pulmonary nodules using the following formula:

[0132]

[0133] In the formula, AUC represents the area under the receiver operating characteristic (ROC) curve, TPR i and FPR i are the true positive rate and false positive rate of the i-th point on the ROC curve, and a represents the number of points in the ROC curve. In this embodiment, the change of AUC value during the iteration process is shown in the attached manual. Figure 3 shown.

[0134] Sub-step 4.2: Calculate the accuracy of the prediction model for benign and malignant pulmonary nodules. In this embodiment, the accuracy changes during the iteration process as follows: Figure 4 shown.

[0135] Sub-step 4.3: Count the number of radiomic features selected by the benign and malignant prediction model for pulmonary nodules. In this embodiment, the number of radiomic features changes during the iteration process as shown in the attached manual. Figure 5 shown.

[0136] Sub-step 4.4: Specifically, the multi-objective fitness function is calculated by the following formula:

[0137]

[0138] Wherein, b represents the number of features in the selected subset, in this embodiment, b = 17; m represents the total number of features, in this embodiment, m = 82. The larger the area under the curve, the higher the fitness value, and the smaller the number of features, the higher the fitness value; the weight w is in the range of [0, 1], indicating the relative importance of the classification performance and the number of selected features, in this embodiment, w1 = 0.6, w2 = 0.3, and w3 = 0.1; in this embodiment, the iteration of the multi-objective fitness function value in the iteration process is as shown in the appendix of the specification. Figure 6 shown.

[0139] In the present invention, the proposed multi-objective fitness function is robust to imbalanced datasets because the AUC operator is insensitive to changes in sample distribution.

[0140] Specifically, in this embodiment, the target fitness function value for the training set data is:

[0141]

[0142] Specifically, in this embodiment, the target fitness function value for the test set data is:

[0143]

[0144] This embodiment finally determines whether the maximum iteration has been reached.

[0145] Specifically, when the iteration reaches the set number of 50 iterations, the optimal solution and the prediction result of benign and malignant pulmonary nodules are output. In this embodiment, the ROC curves of the benign and malignant pulmonary nodule prediction model in the training set and the test set are shown in the attached figure of the specification. Figure 7 and Figure 8 In this embodiment, the confusion matrix of the pulmonary nodule benign and malignant prediction model in the training set and the test set is shown in the appendix of the specification. Fig. 9 and Fig.10 shown.

[0146] Specifically, when the iteration number does not reach the set 50 iterations, return to step 1 and continue the seagull optimization global search process proposed in the present invention.

[0147] In order to illustrate the content and implementation method of the present invention, this specification gives a specific embodiment. The purpose of introducing details in the embodiment is not to limit the scope of the claims, but to help understand the content of the present invention. Those skilled in the art should understand that: without departing from the spirit of the present invention, various technical solutions or embodiments obtained by various modifications, changes or equivalent replacements of technical features to the technical solutions or embodiments of the present invention all fall within the protection scope of the present invention.

Claims

1. A method for distinguishing benign and malignant pulmonary nodules based on an improved Seagull optimization algorithm, characterized in that: The identification method comprises the following steps: S1: global search based on exponentially changing collision avoidance weight factors; S2: local search based on improved dynamic reverse learning strategy; S3: secondary local search based on mutual information improved altruism mechanism to improve the local search capability of the seagull optimization algorithm; S4: population update based on multi-objective fitness function.

2. A method for distinguishing benign and malignant pulmonary nodules based on an improved Seagull optimization algorithm according to claim 1, characterized in that: In step S1, the collision avoidance weight factor is Let P(t) be the current position of the seagull, and C(t) be the position where there is no position conflict with other seagulls. Among them, p ij represents the jth radiomic feature for the identification of benign and malignant pulmonary nodules in the i-th seagull individual, n represents the number of seagulls, m represents the number of radiomic features, and j represents a fixed coefficient; Max iteration represents the maximum number of iterations; t represents the current number of iterations.

3. A method for distinguishing benign and malignant pulmonary nodules based on an improved Seagull optimization algorithm according to claim 2, characterized in that: In step S2, the dynamic reverse learning strategy refers to taking the reverse solution into account when calculating the position of the seagull after the attack. The reverse solution calculation formula is: E * (t) = k(P bs (t)+P ws (t))-E(t), so the attack position is calculated as: P attack (t)=ω1xyzE(t)+ω2E * (t)+P bs (t), combining the two, we get: P attack (t)=(ω1xyz-ω2)E(t)+(ω2k+1)P bs (t)+ω2kP ws (t), where P ws (t) represents the worst position of the current seagull; k is the reverse coefficient, which is a random number between (0,1); x = ue θv cos(θ),y=ue θv sin(θ) and z=ue θv θ constitutes the description of the motion trajectory of the seagull population in three-dimensional space. θ is a random angle value in the interval [0,2π]. u and v are the related constants of the spiral trajectory of the seagull flight. e is the base of the natural logarithm, ω1,ω2∈(0,1), and P bs (t) represents the current optimal position of the seagull.

4. A method for distinguishing benign and malignant pulmonary nodules based on an improved Seagull optimization algorithm according to claim 3, characterized in that: The step S3 specifically includes: the seagull population P that has not undergone the steps S1 and S2 0 , and the gull population P that experienced S1 and S2 1 Merge into a new population P new , as the input of the altruism mechanism, this process is expressed by the following formula: Where n is the number of seagulls in the population, and m is the number of global radiomic features. Then, for the new population P new ={p1,p2,…,p 2n } sort to get P′ new ,Right now: P′ new ={p′1,p′2,…,p′ 2n } Among them, f(p′1)≥f(p′2)≥…≥f(p′ 2n ), f(·) represents the fitness function, and P′ new 2A seagulls with medium fitness constitute the altruistic pool P MD ,but: P MD ={p′ i |n-A≤i<n+A} The individuals with high fitness are the first nA seagull individuals in the sorted population and are retained, denoted by P. H : P H ={p′ i |1≤i<n-A} The individuals with low fitness are nA seagull individuals after sorting the population, which are recorded as P L : P L ={p′ i |n+A≤i<2n} Set in the improved altruism pool P MD In the example, a pair of i and F j The candidate solutions are S i and S j , then S i and S j The similarity index ξ between is defined as follows: Among them, d E (S i ,S j ) indicates S i and S j The Euclidean distance between them, β1 and β2 represent two weight coefficients; The criterion for selecting the sacrifice solution of the improved altruism mechanism is determined by the average mutual information of the candidate solutions. The mutual information matrix I between radiomic features is expressed as follows: Among them, I(X i ;X j ) represents the radiomics feature X i and feature X j The mutual information between them, m represents the number of radiomic features, I(X i ;X j ) is calculated as follows: Where, X i and X j are two radiomic features, x i and x j Yes X i and X j The specific value corresponding to the individual seagull, p(x i ,x j ) is X i and X j The joint probability, p(x i ) and p(x j ) are X i and X j The marginal probability of i Screen out n radiomic features, then the candidate solution S i The mutual information matrix It is expressed as follows: Candidate Solution S i The average mutual information for: Similarly, we can get the candidate solution S j The average mutual information Assume that the population that has undergone the altruism mechanism is denoted as Q, then the output of the secondary local search is composed of the retained high fitness individuals P H And Q composition: Among them, P LS2 is the output of the secondary local search, and P can be determined according to the fitness function LS2 The best individual in a population.

5. A method for distinguishing benign and malignant pulmonary nodules based on an improved Seagull optimization algorithm according to claim 4, characterized in that: The multi-objective fitness function consists of three parts: the area under the receiver operating characteristic curve, the accuracy and the count of the selected features, and the calculation formula is as follows: in, represents the area under the receiver operating characteristic curve, TPR i and FPR i are the true positive rate and false positive rate of the i-th point on the ROC curve, a represents the number of points in the ROC curve; Accuracy represents the accuracy of predicting benign or malignant pulmonary nodules; b represents the number of features in the selected subset, m represents the total number of features; the sum of the weight coefficients w1+w2+w3=1.

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