Evolutionary algorithm and clustering grouping based optimization method for irradiation fields

Abstract

The application discloses a kind of based on evolution algorithm and clustering grouping field optimization method, comprising: step one, initialization field energy deposition coefficient and minimization objective function;Step two: generate initial population, and set initial parameter value;Step three, by clustering, the minimization objective function is grouped dimension reduction using Spearman cooperation function, the objective function is reduced to low-dimensional space from original space, reduce algorithm cost;Step four, by evolution algorithm optimization field set, using crossover mutation operator generates offspring, and selects individual by environment selection iteration, finally obtains a set of optimal field set scheme.The application can effectively reduce the time and space consumed in large-scale field optimization problem, and ensure the high quality of the obtained field set scheme.

Description

Technical Field

[0001] This invention relates to the field of radiation medicine, specifically to a radiation field optimization method based on evolutionary algorithms and clustering grouping. Background Technology

[0002] In today's society, radiotherapy is an important means of cancer treatment. Studying the generation of high-energy radiation fields in radiotherapy is of great significance for understanding the working principle of radiation fields in precision radiotherapy systems, understanding the reaction mechanism between high-energy rays and tissue cells under special physiological conditions such as diseases, and understanding the importance of the radiation field generation stage to radiotherapy planning.

[0003] In optimizing the radiation field set, it is necessary to optimize the intensity value of the rays that vertically penetrate the radiation field, i.e., to generate an intensity distribution map of the radiation field, resulting in several radiation fields carrying high-intensity rays to provide a precise radiation dose distribution, thereby achieving the goal of killing cancer cells and protecting normal organs and tissues. However, as the complexity of cases increases, the difficulty of finding the optimal solution for the radiotherapy plan also increases.

[0004] Currently, radiation field optimization techniques typically begin by modeling human organs to obtain the deposition matrix between radiation and the target organ, as well as the desired clinical objectives. Then, optimization algorithms such as mathematical programming are used iteratively to obtain a radiation field set that meets clinical requirements. By optimizing the radiation intensity distribution within the radiation field, radiotherapy optimization techniques can obtain a radiation field set that meets clinical objectives in a relatively short time, thereby generating high-quality, feasible radiotherapy plans. However, with the increasing scale of case data and the growing number of objective functions to be minimized, the difficulty of generating radiation field sets also increases. In the radiation field optimization problem, large-scale data allows us to obtain more case information and more accurately describe the deposition effect of radiation on the target organ. On the other hand, the increased computational complexity and decreased accuracy due to the mutual influence between objective functions, the increase in invalid objectives, and the high computational complexity brought about by large-scale radiation fields lead to increased computational load. Therefore, reducing optimization complexity and selecting high-quality radiation field sets has become a challenge for radiotherapy optimization techniques.

[0005] Currently, radiation field optimization techniques based on mathematical programming and other optimization algorithms can only obtain one optimal solution per iteration. However, in clinical practice, physicians often need to select the most suitable radiotherapy plan for the patient from several optimal solutions based on the patient's actual condition. Therefore, existing radiation field optimization techniques need to be run multiple times by modifying function weights to obtain multiple sets of optimal solutions, which results in excessive computation, long processing time, and a large amount of memory consumption, thus failing to efficiently obtain the optimal radiation field set scheme. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention proposes an illumination field optimization method based on evolutionary algorithms and clustering. The aim is to adaptively reduce the dimensionality of different numbers of minimization objective functions without imposing any human factors, while efficiently generating several usable candidate optimal illumination field sets and ensuring their quality. This avoids multiple parameter changes and repeated runs, thereby reducing the time and space consumed by illumination field optimization.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] The high-energy ray irradiation field optimization method based on evolutionary algorithms and clustering grouping of this invention is characterized by the following steps:

[0009] Step 1: Define and initialize the data;

[0010] Step 1.1: Characterize the high-energy ray irradiation field set as V = {V1, V2, ..., V...} i ,···,V T}, V i V represents the irradiation field of the i-th irradiation direction, T is the total number of irradiation fields in the set of high-energy ray irradiation fields; and V i ={A ij |j=1,2,…,n i}, A ij Let n represent the j-th beam in the i-th illumination field. i This represents the total number of beams in the i-th illumination field;

[0011] Step 1.2: Define the set of irradiation field energy deposition coefficient matrices as P = {P1, P2, ..., P} i ,...,P T}, where P i V represents the i-th irradiation field. i The energy deposition coefficient matrix at the sampling points; and in, V represents the i-th irradiation field. i The energy deposition coefficient matrix of the j-th beam at the sampling point; and V represents the i-th irradiation field. i The energy deposition coefficient of the j-th beam at the c-th sampling point, where, like Then it represents the i-th irradiation field V i The j-th beam has no energy deposition at the c-th sampling point; C represents the total number of sampling points.

[0012] Step 1.2: Define the objective function vector to be minimized as F(D) = (f1(D), f2(D), ..., f m (D),...,f M (D)); where f m (D) represents the m-th minimized objective function; D represents the energy deposition of the beam at the sampling point in the irradiation field; m = 1, 2, ..., M, where M is the total number of minimized objective functions;

[0013] Step 2: Initialize N pop A set of illumination fields is used as the initial population, and initial parameter values ​​are given;

[0014] Step 2.1: Define the population size as N. pop The maximum number of iterations is G. max Define the current iteration number as G;

[0015] Step 2.2: Initialize G = 0;

[0016] Step 2.3: Initialize N in the Gth generation population pop individual in, This represents the αth individual in the Gth generation population, where each individual represents a set of illumination fields.

[0017] Define and initialize the α-th individual in the G-th generation population. The i-th irradiation field V i The j-th beam A ij Encoding gene value And satisfy Among them, a max This represents the maximum allowed beam intensity value; thus, it yields any α-th individual in the G-th generation population. The i-th irradiation field V i encoding This allows us to obtain any α-th individual in the G-th generation population. encoding

[0018] Step 3: Group the minimization objective function to reduce dimensionality through clustering;

[0019] Step 3.1: Based on N in the Gth generation population pop individual Calculate the m-th minimized objective function f m (D) in the α individual The function value f on m (D (G,α) ), where D (G,α) This represents the α-th individual in the G-th generation population. The energy deposition at the sampling point represented by the irradiation field ensemble scheme, and Thus, we obtain M minimization objective functions for the αth individual. The function values ​​are sorted in ascending order to obtain the function value f. m (D (G,α) Ranking among M minimum objective functions

[0020] Step 3.2: Calculate the m-th minimized objective function f using equation (2). m (D (G,α) ) and the u-th minimization objective function f u (D (G,α) Spearman correlation coefficient between )

[0021]

[0022] In equation (2), and Let f represent the m-th minimized objective function f. m (D (G,α) ) and the u-th minimization objective function f u (D (G,α) In the α individual The sorting order is u = 1, 2, ..., M;

[0023] Step 3.3: Define and initialize the dimension reduced to M by minimizing the objective function. reduce ;

[0024] Step 3.4: Randomly select M from the M minimization objective functions. reduce Minimize the objective function and use it as the initial M. reduce Cluster centers {c t |t=1,2,…,M reduce}; where c t This represents the initial t-th cluster center;

[0025] Step 3.5: Calculate the m-th minimized objective function f m (D (G,α) ) to the initial t-th cluster center c t distance Thus, the m-th minimized objective function f is obtained. m (D (G,α) ) respectively to the Gth iteration M reduce Distance between cluster centers

[0026]

[0027] In equation (3), Let f represent the m-th minimized objective function. m (D (G,α) ) and the initial t-th cluster center c t Spearman correlation coefficient between them;

[0028] from Select the minimum distance from the m-th minimum objective function f. m (D (G ,α) ) are assigned to the cluster centers corresponding to the minimum distance, thereby minimizing the M objective functions f m (D (G,α) Each cluster is assigned to the cluster center corresponding to the minimum distance, and the M value in the G-th iteration is obtained. reduce The set of minimization objective functions and the cluster centers corresponding to each set of minimization objective functions in the Gth iteration;

[0029] Step 3.6: Calculate the t-th cluster center in the G-th iteration using equation (4). In the αth individual Sort value on

[0030]

[0031] In equation (4), Denotes the set of the t-th minimized objective functions in the G-th iteration; This represents the o-th cluster center in the G-th iteration. In the αth individual The sorting value on;

[0032] Step 3.7: Calculate the minimized objective function f using equation (2). m (D (G,α) ) to the t-th cluster center in the G-th iteration Spearman correlation coefficient

[0033] Step 3.8: Calculate the minimized objective function f using equation (3). m (D (G,α) ) to the t-th cluster center in the G-th iteration distance

[0034] from Select the minimum value from the m-th minimized objective function f. m (D (G,α) The minimum value is assigned to the cluster center corresponding to the minimum value, thereby minimizing the M objective functions f. m (D(G,α) Each cluster is assigned to the cluster center corresponding to the minimum value, and M in the Gth iteration is updated. reduce The set of minimized objective functions is minimized in each group, and the cluster centers of each minimized objective function set in the Gth iteration are updated.

[0035] Step 3.9: If the cluster centers before and after the update are different in the Gth iteration, then execute step 3.6; otherwise, execute step 3.10.

[0036] Step 3.10, The minimum objective functions in the previous steps are linearly accumulated to form a new minimum objective function f. t ′(D (G,α) This reduces the number of objective functions M to Mminimized. reduce Thus, a new minimization objective function vector is obtained.

[0037] Step 4: Optimize the illumination field based on the evolutionary algorithm, generate offspring using the crossover and mutation operator, select individuals through environmental selection, and finally iterate to obtain a set of optimal illumination field sets.

[0038] Step 4.1: Select N individuals from the Gth generation population using a binary tournament selection strategy and place them into the mating pool, which will serve as the parent population for the Gth generation.

[0039] Step 4.2: Randomly select a pair of parents from the Gth generation parent population as parent individuals, and process the parent individuals using simulated binary crossover and polynomial mutation to obtain a child individual;

[0040] Step 4.3: Repeat step 4.2 N times to generate a population of N offspring of the Gth generation in the original space;

[0041] Step 4.4: After merging the offspring population of generation G with the parent population of generation G, environmental selection is performed to generate a new individual population of generation G.

[0042] Step 4.4.1: Merge the offspring population of generation G with the parent population of generation t and remove duplicate individuals to obtain the new population of generation G.

[0043] Step 4.4.2: Based on the new minimization objective function vector F′(D) (G,α) The objective function of each individual in the new population of generation G is non-dominated and sorted to obtain a population with multiple frontiers.

[0044] Step 4.4.3: Calculate the crowding distance of each individual in the population obtained in Step 4.4.2, and sort the population obtained in Step 4.4.2 in descending order according to the obtained crowding distance. The first N individuals after descending order are taken as the population of generation G+1.

[0045] Step 4.4.4: After assigning G+1 to G, determine if G > G. max If the condition is met, then the population of generation G is used as the new population of individuals in generation G; otherwise, return to step 4.1 to continue execution.

[0046] Step 4.5: Output the Pareto optimal individuals in the new population of the Gth generation as the optimal irradiation field set scheme.

[0047] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the illumination field optimization method, and the processor is configured to execute the program stored in the memory.

[0048] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the steps of the illumination field optimization method.

[0049] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0050] 1. This invention proposes a dimensionality reduction strategy for the objective function in the large-scale illumination field optimization problem. By using a clustering algorithm, the minimization objective function in the illumination field optimization problem is adaptively grouped according to its relevance, thereby reducing the high-dimensional objective function to a low-dimensional space and avoiding the intervention of subjective factors. With less computational resources, the pressure of environmental selection is reduced, thus efficiently adjusting and optimizing the illumination field set scheme.

[0051] 2. This invention uses an evolutionary algorithm to optimize the optimal set of illumination fields. In each iteration, the crossover and mutation operator is used to generate offspring illumination fields, and several Pareto optimal set of illumination fields are selected through environmental selection. This avoids parameter changes and repeated runs, thereby improving the generation efficiency of the optimal set of illumination fields. Attached Figure Description

[0052] Figure 1 This is a flowchart of the method of the present invention;

[0053] Figure 2a This is a schematic diagram of the energy deposition coefficient matrix in the method of the present invention.

[0054] Figure 2b This is a schematic diagram of individual coding in the method of the present invention.

[0055] Figure 2c This is a schematic diagram illustrating the calculation of the energy deposition matrix in the method of this invention.

[0056] Figure 3This is a schematic diagram illustrating the process of minimizing the objective function, reducing its dimensionality by grouping, and constructing a new objective function using the method of the present invention. Detailed Implementation

[0057] In this embodiment, a radiation field optimization method based on evolutionary algorithms and clustering grouping is proposed. This method reduces the dimensionality of the high-dimensional radiotherapy minimization objective function by grouping it, and then simultaneously optimizes it using an evolutionary algorithm to obtain several optimal radiation field set schemes. This improves the quality of the generated optimal radiation field set schemes and reduces the time and space consumed. Specifically, referring to... Figure 1 As shown, the procedure is as follows:

[0058] Step 1: Define and initialize the data;

[0059] Step 1.1: Characterize the high-energy ray irradiation field set as V = {V1, V2, ..., V...} i ,···,V T}, V i V represents the irradiation field of the i-th irradiation direction, T is the total number of irradiation fields in the set of high-energy ray irradiation fields; and V i ={A ij |j=1,2,…,n i}, A ij Let n represent the j-th beam in the i-th illumination field. i This represents the total number of beams in the i-th illumination field;

[0060] Step 1.2: Define the set of irradiation field energy deposition coefficient matrices as P = {P1, P2, ..., P} i ,...,P T}, where P i V represents the i-th irradiation field. i The energy deposition coefficient matrix at the sampling points; and in, V represents the i-th irradiation field. i The energy deposition coefficient matrix of the j-th beam at the sampling point; and V represents the i-th irradiation field. i The energy deposition coefficient of the j-th beam at the c-th sampling point, where, The closer the energy deposition coefficient is to 1, the stronger the energy mapping of the beam at the sampling point; if Then it represents the i-th irradiation field V i The j-th beam has no energy deposition at the c-th sampling point, meaning the magnitude of the beam's intensity has no effect on the energy deposition at that sampling point; for example... Figure 2a As shown, in the example energy deposition matrix P1 This indicates that the energy deposition coefficient of the second beam in irradiation field V1 at the second sampling point is 0.1; C represents the total number of sampling points;

[0061] Step 1.2: Define the objective function vector to be minimized as F(D) = (f1(D), f2(D), ..., f m (D),...,f M (D)); where f m (D) represents the m-th minimized objective function; D represents the energy deposition of the beam at the sampling point in the irradiation field; m = 1, 2, ..., M, where M is the total number of minimized objective functions;

[0062] Step 2: Initialize N pop A set of illumination fields is used as the initial population, and initial parameter values ​​are given;

[0063] Step 2.1: Define the population size as N. pop The maximum number of iterations is G. max Define the current iteration number as G;

[0064] Step 2.2: Initialize G = 0;

[0065] Step 2.3: Initialize N in the Gth generation population pop individual in, This represents the αth individual in the Gth generation population, where each individual represents a set of illumination fields.

[0066] Define and initialize the α-th individual in the G-th generation population. The i-th irradiation field V i The j-th beam A ij Encoding gene value And satisfy Among them, a max This represents the maximum allowed beam intensity value; thus, it yields any α-th individual in the G-th generation population. The i-th irradiation field V i encoding This allows us to obtain any α-th individual in the G-th generation population. encoding like Figure 2b As shown, the code a1 of the example illumination field V1 is (31,20,6,4,52,3,12), and the code a2 of the example illumination field V2 is (42,13,15,2,9,43,27). Then the real number code a of the illumination field set composed of illumination field V1 and illumination field V2 is (31,20,6,4,52,3,12,42,13,15,2,9,43,27).

[0067] Step 3: Group the minimization objective function to reduce dimensionality through clustering;

[0068] Step 3.1: Based on N in the Gth generation population pop individual Calculate the m-th minimized objective function f m (D) in the α individual The function value f on m (D (G,α) ), where D (G,α) This represents the α-th individual in the G-th generation population. The energy deposition at the sampling point represented by the irradiation field ensemble scheme, and like Figure 2c As shown, the example illumination fields V1 and V2 are cross-multiplied with the energy deposition matrix P1 and the energy deposition matrix P2 respectively, and then added to obtain the energy deposition D = (4.8, 49.2, 50.6) at the sampling point; thus, M minimization objective functions are obtained for the αth individual. The function values ​​are sorted in ascending order to obtain the function value f. m (D (G,α) Ranking among M minimum objective functions

[0069] Step 3.2: Calculate the m-th minimized objective function f using equation (2). m (D (G,α) ) and the u-th minimization objective function f u (D (G,α) Spearman correlation coefficient between )

[0070]

[0071] In equation (2), and Let f represent the m-th minimized objective function f. m (D (G,α) ) and the u-th minimization objective function f u (D (G,α) In the αth individual P α G The sorting order is u = 1, 2, ..., M; and The absolute value of the difference reflects the minimization of the objective function f. m (D (G,α) ) and f u (D (G,α) In the α individual Differences in the data; Spearman correlation coefficient It can objectively reflect the minimization of the objective function fm (D (G,α) ) and f u (D (G,α) The overall differences, among which, The closer the value is to -1, the more likely it is that the objective function f is minimized. m (D (G,α) ) and f u (D (G,α) ) are negatively correlated. The closer the value of f is to 1, the better. m (D (G,α) ) and f u (D (G,α) They are positively correlated. A value close to 0 indicates that f m (D (G ,α) ) and f u (D (G,α) There is no significant correlation between them.

[0072] Step 3.3: Define and initialize the dimension reduced to M by minimizing the objective function. reduce ;

[0073] Step 3.4: Randomly select M from the M minimization objective functions. reduce Minimize the objective function and use it as the initial M. reduce Cluster centers {c t |t=1,2,…,M reduce}; where c t This represents the initial t-th cluster center;

[0074] Step 3.5: Calculate the m-th minimized objective function f m (D (G,α) ) to the initial t-th cluster center c t distance Thus, the m-th minimized objective function f is obtained. m (D (G,α) ) respectively to the Gth iteration M reduce Distance between cluster centers

[0075]

[0076] In equation (3), Let f represent the m-th minimized objective function. m (D (G,α) ) and the initial t-th cluster center c t The Spearman correlation coefficient between them is easily seen. The value of is between 0 and 1, thus transforming the correlation coefficient between the objective function and the cluster centers into the distance between the two.

[0077] from Select the minimum distance from the m-th minimum objective function f. m (D (G ,α) The M minimum distances are assigned to the cluster centers corresponding to these minimum distances, thereby minimizing the objective function f. m (D (G,α) Each cluster is assigned to the cluster center corresponding to the minimum distance, and the M value in the G-th iteration is obtained. reduce The set of minimization objective functions and the cluster centers corresponding to each set of minimization objective functions in the Gth iteration;

[0078] Step 3.6: Calculate the t-th cluster center in the G-th iteration using equation (4). In the αth individual Sort value on

[0079]

[0080] In equation (4), Denotes the set of the t-th minimized objective functions in the G-th iteration; This represents the o-th cluster center in the G-th iteration. In the αth individual The ranking value on the αth individual is the mean of the ranking values ​​of all minimizing objective functions in the tth set of minimizing objective functions. This is beneficial for calculating the Spearman correlation coefficient between the minimizing objective function and the cluster center of the set.

[0081] Step 3.7: Calculate the minimized objective function f using equation (2). m (D (G,α) ) to the t-th cluster center in the G-th iteration Spearman correlation coefficient

[0082] Step 3.8: Calculate the minimized objective function f using equation (3). m (D (G,α) ) to the t-th cluster center in the G-th iteration distance

[0083] from Select the minimum distance from the m-th minimum objective function f. m (D (G ,α)The M minimum distances are assigned to the cluster centers corresponding to these minimum distances, thereby minimizing the objective function f. m (D (G,α) Each cluster is assigned to the nearest cluster center, and M in the Gth iteration is updated. reduce The set of minimized objective functions is minimized in each group, and the cluster centers of each minimized objective function set in the Gth iteration are updated.

[0084] Step 3.9: If the cluster centers before and after the update are different in the Gth iteration, then execute step 3.6; otherwise, execute step 3.10.

[0085] Step 3.10, The minimum objective functions in the previous steps are linearly accumulated to form a new minimum objective function f′. t (D (G,α) This reduces the number of objective functions M to Mminimized. reduce Thus, a new minimization objective function vector is obtained. like Figure 3 As shown, based on the example M reduce The value is set to 3. The original 6 minimization objective functions are divided into 3 groups. Then, the minimization objective functions in the same group are linearly accumulated to form a new objective function, which is f′1(D). (G,α) )=f1(D (G,α) )+f2(D (G,α) )+f4(D (G,α) ), f′2(D (G,α) )=f3(D (G,α) )+f6(D (G,α) ), f′3(D (G,α) )=f5(D (G,α) );

[0086] Step 4: Optimize the illumination field based on the evolutionary algorithm, generate offspring using the crossover and mutation operator, select individuals through environmental selection, and finally iterate to obtain a set of optimal illumination field sets.

[0087] Step 4.1: Select N individuals from the Gth generation population using a binary tournament selection strategy and place them into the mating pool, which will serve as the parent population for the Gth generation.

[0088] Step 4.2: Randomly select a pair of parents from the Gth generation parent population as parent individuals, and process the parent individuals using simulated binary crossover and polynomial mutation to obtain a child individual;

[0089] Step 4.3: Repeat step 4.2 N times to generate a population of N offspring of the Gth generation in the original space;

[0090] Step 4.4: After merging the offspring population of generation G with the parent population of generation G, environmental selection is performed to generate a new individual population of generation G.

[0091] Step 4.4.1: Merge the offspring population of generation G with the parent population of generation t and remove duplicate individuals to obtain the new population of generation G.

[0092] Step 4.4.2: Based on the new minimization objective function vector F′(D) (G,α) The objective function of each individual in the new population of generation G is non-dominated and sorted to obtain a population with multiple frontiers.

[0093] Step 4.4.3: Calculate the crowding distance of each individual in the population obtained in Step 4.4.2, and sort the population obtained in Step 4.4.2 in descending order according to the obtained crowding distance. The first N individuals after descending order are taken as the population of generation G+1.

[0094] Step 4.4.4: After assigning G+1 to G, determine if G > G. max If the condition is met, then the population of generation G is used as the new population of individuals in generation G; otherwise, return to step 4.1 to continue execution.

[0095] Step 4.5: Output the Pareto optimal individuals in the new population of the Gth generation as the optimal irradiation field set scheme.

[0096] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0097] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A method for optimizing high-energy ray irradiation fields based on evolutionary algorithms and clustering, characterized in that, It is done in the following steps: Step 1: Define the characterization of high-energy ray irradiation fields and the set of energy deposition coefficient matrices of the irradiation field Minimize the objective function vector , This represents the energy deposition of the beam at the sampling point within the irradiation field. Step 2: Define the population size as The maximum number of iterations is Define the current iteration number as and initialize ;initialization The illumination field set scheme is used as the first Generate a population and provide initial parameter values; Step 3: Group the minimization objective function to reduce dimensionality through clustering; Step 3.1, according to the first In the generation population individual Calculate the m-th minimized objective function In the individual function value on ,in, Indicates the first The first generation of the population individual The energy deposition at the sampling point represented by the irradiation field ensemble scheme, and Thus obtain The minimized objective function at the th ... individual The function values ​​are sorted in ascending order to obtain the function values. exist Ranking in the minimum objective function ; Indicates the first Any first generation in the population individual The One illumination field The encoding; Step 3.2: Calculate the m-th minimized objective function using equation (2). and the u-th minimized objective function Spearman correlation coefficient between : (2) In equation (2), and Let each represent the m-th minimized objective function. and the u-th minimized objective function In the individual The sorting level on the top ; Step 3.3: Define and initialize the dimension reduced to by minimizing the objective function. ; Step 3.4, in Randomly select from the minimized objective functions Minimize the objective function and use it as the initial value. Cluster centers ;in, Indicates the initial number of... Cluster centers; Step 3.5: Calculate the m-th minimized objective function using equation (3). To the initial number Cluster centers distance Thus, the m-th minimized objective function is obtained. To the respective Iteration in progress Distance between cluster centers : (3) In equation (3), Denotes the m-th minimized objective function and the initial Cluster centers Spearman correlation coefficient between them; from Select the minimum distance from the m-th minimum objective function. Assigning clusters to the cluster centers corresponding to the minimum distances, thereby minimizing the M objective functions. Each cluster is assigned to the cluster center corresponding to the minimum distance, and the th cluster is obtained. In iteration The set of minimized objective functions and the first The cluster centers corresponding to each set of minimized objective functions during iteration; Step 3.6: Calculate the first step using equation (4). During the iteration Cluster centers In the individual Sort value on : (4) In equation (4), Indicates the first The t-th set of objective functions to be minimized in the iteration; Indicates the first During the iteration Cluster centers In the individual The sorting value on; Step 3.7: Calculate the minimization objective function using equation (2). To the During the iteration Cluster centers Spearman correlation coefficient ; Step 3.8: Calculate the minimization objective function using equation (3). To the During the iteration Cluster centers distance ; from Select the minimum value from the m-th minimized objective function. Assigning cluster centers to the minimum values, thereby minimizing the M objective functions. Each value is assigned to the cluster center corresponding to the minimum value, and the value is updated. In iteration Minimize the set of objective functions and update the th set. The cluster centers of each set of minimized objective functions during iteration; Step 3.9, if the first If the cluster centers before and after the update are different during the iteration, proceed to step 3.6; otherwise, proceed to step 3.

10. Step 3.10, The minimum objective function in the previous step is linearly accumulated to form a new minimum objective function. This reduces the number of objective functions M to be minimized. Thus, a new minimization objective function vector is obtained. ; Step 4: Optimize the illumination field based on the evolutionary algorithm, generate offspring using the crossover and mutation operator, select individuals through environmental selection, and finally iterate to obtain a set of optimal illumination field schemes.

2. The high-energy ray irradiation field optimization method based on evolutionary algorithm and clustering grouping according to claim 1, characterized in that, Step one includes: Step 1.1: Characterize the high-energy ray irradiation field set as , Indicates the first Irradiation field in each irradiation direction, The total number of irradiated fields in the set of high-energy ray irradiated fields; and , Indicates the first The first irradiation field One beam, Indicates the first The total number of beams in each illumination field; Step 1.2: Define the set of irradiation field energy deposition coefficient matrices as follows ,in, Indicates the first One illumination field The energy deposition coefficient matrix at the sampling points; and ,in, Indicates the first One illumination field The Middle The energy deposition coefficient matrix of each beam at the sampling point; and , Indicates the first One illumination field The Middle The beam at the The energy deposition coefficient at each sampling point, where... ;like Then it means the first One illumination field The Middle The beam at the No energy deposition was observed at any of the sampling points; Indicates the total number of sampling points; Step 1.3: Define the vector of the objective function to be minimized. ;in, Indicates the first Minimize one objective function; This represents the energy deposition of the beam at the sampling point within the irradiation field. , It minimizes the total number of objective functions.

3. The high-energy ray irradiation field optimization method based on evolutionary algorithm and clustering grouping according to claim 2, characterized in that, Step two includes: Step 2.1, Initialize the first In the generation population individual ,in, Indicates the first The first generation of the population Each individual represents a set of illumination fields; Step 2.2, Define and initialize the first The first generation of the population individual The One illumination field The Middle One beam Encoding gene value And satisfy ,in, This represents the maximum permissible beam intensity value; thus, the first... Any first generation in the population individual The One illumination field encoding And thus obtain the first Any first generation in the population individual encoding .

4. The high-energy ray irradiation field optimization method based on evolutionary algorithm and clustering grouping according to claim 3, characterized in that, Step four includes: Step 4.1: Use a binary tournament selection strategy to select from the first... Selected from the population Individuals were placed into the mating pool and used as the first... Surrogate population; Step 4.2, from the first A pair of parents are randomly selected from the parent population as parent individuals. Simulated binary crossover and polynomial mutation are used to process the parent individuals to obtain a child individual. Step 4.3: Repeat step 4.

2. This results in the generation of a number of [number] instances in the original space. The Offspring population; Step 4.4, place the first Generation offspring population and the first generation After the parent populations merge, environmental selection occurs to generate the second generation. A new generation of individual populations; Step 4.4.1, place the first After merging the offspring population with the parent population of the t-th generation and removing duplicate individuals, the t-th generation is obtained. New populations; Step 4.4.2: Based on the new minimized objective function vector , for the The objective function of each individual in the new population is non-dominated and sorted to obtain a population with multiple frontiers; Step 4.4.3: Calculate the crowding distance of each individual in the population obtained in Step 4.4.2, and sort the population obtained in Step 4.4.2 in descending order based on the obtained crowding distance to obtain the top individuals in descending order. The individual as the first Generational population; Step 4.4.4, will Assign to Then, make a judgment > Is it true? If it is true, then the first... The first generation of the population as the first Replace the population with new individuals; otherwise, return to step 4.1 to continue. Step 4.5, place the first The Pareto optimal individuals in the new population are output as the optimal irradiation field set scheme.

5. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the illumination field optimization method of any one of claims 1-4, and the processor is configured to execute the program stored in the memory.

6. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program, when run by a processor, performs the steps of the illumination field optimization method according to any one of claims 1-4.

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