A Multi-Objective Optimization Design Method for Radiation Shielding Based on Transformer and Improved NSGA-III

Abstract

This invention discloses a multi-objective optimization design method for radiation shielding based on Transformer and an improved NSGA-III algorithm, relating to the field of nuclear radiation shielding design technology. An initial population is formed, with each individual in the population representing the design variables of the radiation shielding. These individual design variables are input into a surrogate model based on a Transformer architecture to calculate the radiation dose equivalent rate and the total mass and volume of the shielding. The initial population is then used as the parent population. With minimizing the radiation dose equivalent rate, the total mass, and the total volume of the shielding as the optimization objectives, in each iteration of the improved NSGA-III algorithm, a child population is generated from the parent population. An external archive and an elite local search mechanism are used to update, filter, and retain historical high-quality non-dominated solutions until a preset number of iterations is reached. The parent population obtained from the last iteration is used as the Pareto optimal solution set. Based on the Pareto optimal solution set, the design scheme of the radiation shielding is determined. This method improves the solution quality of multi-objective optimization design for radiation shielding.

Description

Technical Field

[0001] This application relates to the field of nuclear radiation shielding design technology, and in particular to a multi-objective optimization design method for radiation shielding based on Transformer and improved NSGA-III. Background Technology

[0002] With the continuous development of nuclear energy technology in deep space, deep sea, and mobile platforms, the demand for radiation protection of nuclear reactors in complex application scenarios is becoming increasingly prominent. The neutron-gamma mixed radiation field generated during reactor operation has strong penetrability and potential hazards; therefore, it is essential to control leakage radiation within safe limits through reasonable shielding design. The fundamental goal of radiation shielding system design is to optimize protection effectiveness while ensuring radiation safety, following the ALARA principle. However, as advanced nuclear equipment develops towards miniaturization, lightweighting, and high integration, the constraints faced by shielding design are becoming increasingly complex. It must meet stringent radiation protection requirements while also considering engineering indicators such as weight, volume, and structural layout. The mutual constraints between shielding performance and lightweighting requirements make radiation shielding design essentially a multi-objective, multi-constraint optimization problem.

[0003] With the development of computational science and intelligent optimization methods, existing research typically employs surrogate models with fully connected or radial basis function structures to predict the response of input design variables, combining them with traditional multi-objective evolutionary algorithms for radiation shielding optimization design. However, traditional shallow neural networks have significant limitations in feature extraction and global correlation representation capabilities, making it difficult to accurately characterize the complex relationships between high-dimensional design variables. This results in limited prediction accuracy and generalization ability of the surrogate model, potentially leading to biases in fitness evaluation during the optimization process and affecting the reliability of the optimization results. Furthermore, traditional multi-objective evolutionary algorithms still have limited global optimization capabilities and the ability to preserve excellent solutions in complex and constrained design spaces, making it difficult to meet the requirements of multi-objective collaborative optimization design for complex radiation shielding systems. All of these factors contribute to lower accuracy in radiation shielding design. Summary of the Invention

[0004] Therefore, it is necessary to provide a multi-objective optimization design method for radiation shielding based on Transformer and improved NSGA-III to address the above-mentioned technical problems.

[0005] The following technical solution is adopted in this specification: This specification provides a multi-objective optimization design method for radiation shielding based on Transformer and an improved NSGA-III, including: Initialize the population, where each individual includes the design variables for the radiation shielding; the design variables are the thickness of each shielding layer. The individual design variables are input into the surrogate model based on the Transformer architecture to calculate the radiation dose equivalent rate. Based on the design variables, the total mass and total volume of the shield are calculated, and the initial population is used as the parent population. With the optimization objectives of minimizing radiation dose equivalent rate, total shield mass, and total volume, the design variables are optimized using an improved NSGA-III algorithm. In each iteration of the improved NSGA-III algorithm, a child population is generated from the parent population, and the child population is merged with the non-dominated solutions in the external archive. Through non-dominated sorting, the elite solutions at the first non-dominated front are retained as the new child population from all the merged solutions. The external archive is used to store the first non-dominated front solutions generated in each iteration. The new offspring population is merged with the parent population to form the main population; If the current iteration count meets the preset search period, then seed individuals are extracted from the external archive as an elite subset, an adaptive random perturbation based on Gaussian noise is applied to the elite subset, an exploratory solution for the local neighborhood is generated, the exploratory solution is incorporated into the main population, and the external archive is updated according to the exploratory solution. The parent population is selected from the updated main population through non-dominated sorting and reference direction selection mechanism, and the iteration is repeated until the preset number of iterations is reached. The parent population obtained in the last iteration is taken as the Pareto optimal solution set. The design scheme of the radiation shield is determined based on the Pareto optimal solution set.

[0006] Optionally, the method further includes: If the number of non-dominated solutions in the external archive exceeds the preset capacity limit, then obtain each non-dominated solution in the external archive and its nearest neighbor. The average Euclidean distance of each neighbor; Remove redundant individuals from the external archive with the smallest average Euclidean distance.

[0007] Optionally, the formula for calculating the average Euclidean distance is: in, For the first A non-dominated solution and its nearest The average Euclidean distance of each neighbor. For the number of neighbors, For the target dimension, For the first The first non-dominated solution corresponds to the th The values ​​of each target, For the first The first nondominated solution The neighbor corresponding to the first The value of each target.

[0008] Optionally, seed individuals can be extracted from an external archive as an elite subset, including: Extract the first non-dominated solution of the boundary extrema points in each objective dimension from the external archive, and compare it with the nearest... The second nondominated solution with the largest average Euclidean distance from its neighbors; The first and second non-dominated solutions are taken as elite subsets.

[0009] Alternatively, the formula for calculating the exploratory solution is: in, In order to explore solutions, For the non-dominated solution in the elite subset, and These are the upper and lower bounds of the design variable, respectively. For the number of iterations The changing perturbation step size, With a mean of 0 and a variance of Normally distributed random numbers, This is the clipping function; perturbation step size By constructing a perturbation step size based on the concept of simulated annealing. for: in, This represents the current iteration number. The maximum number of iterations, This represents the boundary of the perturbation intensity during the initial stage of the iteration. This represents the boundary of the perturbation intensity during the iteration termination phase.

[0010] Optionally, the process of constructing the proxy model of the Transformer architecture includes: The design space for the design variables of the radiation shield is obtained. The Latin hypercube sampling method is used to generate an initial sample set within the design space. High-fidelity numerical calculations are performed on each initial sample in the initial sample set to obtain the radiation performance response data corresponding to each set of initial samples. The radiation performance response data includes the radiation dose equivalent rate. The initial samples and the corresponding radiation performance response data were preprocessed and used as training samples. By using training samples, the Transformer architecture is employed to model the complex nonlinear mapping relationship between shielding structure design variables and radiation performance response, thus obtaining a surrogate model.

[0011] Optionally, update the external archive based on the explored solution, including: The explored solutions are incorporated into the external archive, and the solutions in the external archive are deduplicated and sorted by non-dominated order. The first non-dominated frontier solution is retained, and the remaining dominated candidate solutions are deleted.

[0012] This specification provides a radiation shielding multi-objective optimization design device based on Transformer and improved NSGA-III, including: The initialization module is used to initialize the population. Each individual in the population includes the design variables of the radiation shielding; the design variables are the thickness of each shielding layer. The calculation module is used to input the individual design variables into the surrogate model based on the Transformer architecture, calculate the radiation dose equivalent rate, and calculate the total mass and total volume of the shielding body according to the design variables, and select the parent population from the initial population. The iterative module optimizes the design variables by minimizing the radiation dose equivalent rate, total shielding mass, and total volume. It uses an improved NSGA-III algorithm to find the optimal values. In each iteration of the improved NSGA-III algorithm, a child population is generated from the parent population, and this child population is merged with non-dominated solutions in an external archive. Through non-dominated sorting, the elite solutions at the first non-dominated front are retained as the new child population. The external archive stores the first non-dominated front solutions generated in each iteration. The new child population... The population and the parent population are merged to form the main population. If the current iteration count meets the preset search period, seed individuals are extracted from the external archive as an elite subset. An adaptive random perturbation based on Gaussian noise is applied to the elite subset to generate exploratory solutions in the local neighborhood. The exploratory solutions are then incorporated into the main population, and the external archive is updated based on the exploratory solutions. The parent population is selected from the updated main population through a non-dominated sorting and reference direction selection mechanism, and the iteration is repeated until the preset iteration count is reached. The parent population obtained in the last iteration is taken as the Pareto optimal solution set. The determination module is used to determine the design scheme of the radiation shielding body based on the Pareto optimal solution set.

[0013] This specification provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described multi-objective optimization design method for radiation shielding based on Transformer and improved NSGA-III.

[0014] This specification provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-described multi-objective optimization design method for radiation shielding based on Transformer and improved NSGA-III.

[0015] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: The radiation shielding multi-objective optimization design method based on Transformer and improved NSGA-III provided in this specification utilizes a Transformer architecture with a multi-head self-attention mechanism. This architecture can deeply characterize the spatial coupling features between different shielding layers, significantly improving the prediction fidelity of the surrogate model across the entire design space. Furthermore, addressing the problems that traditional algorithms may encounter when dealing with multiple conflicting objectives such as shielding quality, volume, and dose, including uneven solution set distribution, local region clustering, and insufficient retention of representative solutions in edge regions, this invention employs an external archive and an elite local search mechanism to preserve, update, and filter historical high-quality non-dominated solutions. This prevents the loss of excellent solutions during the evolution process. By implementing adaptive perturbations on elite individuals, it achieves fine-grained optimization in local regions, thereby alleviating the convergence stagnation problem that easily occurs in the later stages of evolution. This improves the algorithm's ability to approximate the Pareto front and the quality of the solution set distribution, thus enhancing the solution quality of the radiation shielding multi-objective optimization design. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0017] Figure 1 A schematic diagram of a multi-objective optimization design method for radiation shielding based on Transformer and improved NSGA-III is provided for this specification. Figure 2 This document provides a schematic diagram of a Transformer deep learning architecture. Figure 3 This specification provides a prediction accuracy index for a Transformer proxy model and a performance comparison chart with a traditional artificial neural network proxy model. Figure 4 This specification provides a density scatter plot comparing the fit between the true and predicted values ​​of a Transformer proxy model on an independent test set. Figure 5 A flowchart illustrating another radiation shielding multi-objective optimization design method based on Transformer and improved NSGA-III provided in this specification. Figure 6 This document provides a flowchart of the improved NSGA-III algorithm that integrates external file maintenance and elite local search mechanisms. Figure 7This is a schematic diagram showing the distribution of the Pareto optimal solution set in the three-dimensional target space, which takes into account the targets of dose equivalent rate, mass and volume, as provided in this specification. Figure 8 This specification provides a convergence curve of the hypervolume index of an improved NSGA-III algorithm in a normalized target space as a function of iteration number, and a comparison with the traditional algorithm. Figure 9 The distribution of the HV index of an improved NSGA-III algorithm provided in this specification is obtained through 30 independent experiments, and its comparison with that of the traditional algorithm is shown in the figure. Figure 10 This specification provides a schematic diagram of a computer device for implementing a multi-objective optimization design method for radiation shielding based on Transformer and an improved NSGA-III. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0019] Traditional radiation shielding design primarily relies on designers combining engineering experience with Monte Carlo methods for iterative optimization through trial and error. This method is not only highly dependent on designer experience and inherently subjective, but also suffers from long design cycles and high computational costs. Furthermore, it struggles to efficiently obtain globally optimal or near-globally optimal solutions in large-scale solution spaces when dealing with complex design problems involving multiple material components and coupled structural parameters. With the development of computational science and intelligent optimization methods, current research has gradually introduced multi-objective evolutionary algorithms to solve radiation shielding designs. Examples include the non-dominated sorting genetic algorithm NSGA-II with an elitist strategy, and NSGA-III, which incorporates a reference vector mechanism to enhance high-dimensional objective optimization capabilities. These methods also combine traditional artificial neural networks to construct surrogate models, improving fitness evaluation efficiency. These approaches can, to some extent, reconcile conflicting design objectives such as radiation dose, total mass, and total volume, providing a new technical path for the optimal design of complex radiation shielding systems.

[0020] However, when facing complex real-world radiation shielding engineering problems, existing multi-objective optimization frameworks still have significant limitations: 1) Physical simulation evaluation is computationally expensive, and traditional surrogate models have limited prediction accuracy.

[0021] Radiation shielding performance evaluation typically requires frequent calls to high-precision Monte Carlo simulation programs to obtain key response parameters such as neutron flux and gamma dose rate. Due to the long duration of each simulation and the need for repeated evaluation of numerous candidate solutions during multi-objective optimization, the overall computational cost is extremely high, making it difficult to support efficient iterative search for large-scale populations. To improve optimization efficiency, existing methods often introduce surrogate models such as traditional artificial neural networks to replace some of the high-cost simulation calculations, thereby reducing the evaluation computational overhead during optimization. This approach typically involves collecting a certain number of design parameters and performance response samples to train models such as Back Propagation (BP) neural networks and Radial Basis Function (RBF) neural networks offline, establishing an approximate mapping relationship between input physical parameters and output shielding performance. In subsequent optimization processes, the trained surrogate model is used to replace some physical simulation calculations, thereby improving fitness evaluation efficiency. The surrogate model generally adopts a fully connected structure or a radial basis function structure to predict the response of input design variables and is combined with a multi-objective evolutionary algorithm for radiation shielding optimization design.

[0022] However, under the strong coupling effect and complex nonlinear mapping relationship caused by the layered arrangement of multilayer heterogeneous shielding materials, traditional shallow neural networks have significant shortcomings in deep feature extraction, global correlation modeling, and complex response representation. They are unable to accurately characterize the complex relationships between high-dimensional design variables, and their prediction accuracy and generalization ability often fail to meet the requirements of high-fidelity engineering optimization. Once the surrogate model error accumulates or local distortion occurs, it may lead to fitness evaluation bias, thereby introducing the optimization process into non-optimal or even invalid regions, affecting the quality of the final solution set.

[0023] 2) Traditional evolutionary algorithms still have bottlenecks in terms of the convergence and diversity of Pareto solution sets.

[0024] In existing technologies, the multi-objective optimization design problem of radiation shielding is typically solved using a non-dominated sorting genetic algorithm (NSGA-II) with an elitist strategy. This approach usually encodes the material composition, geometric thickness, and other structural parameters of the shielding layer into individuals within a single population, and generates offspring through genetic operations such as crossover and mutation. During population iteration, the non-dominated sorting method is used to stratify the individuals in the population, and crowding distance is combined for environmental selection to determine the individuals entering the next generation. The crowding distance characterizes the density of individuals within the same non-dominated layer in the target space, thus preferentially retaining individuals in sparsely distributed regions to maintain population diversity and drive the population towards the Pareto front.

[0025] 2) Optimization scheme based on NSGA-III For complex radiation shielding optimization problems involving three or more targets, existing technologies still employ NSGA-III (Non-dominated Sorting Genetic Algorithm III) for solution. This scheme, while inheriting the basic framework of NSGA-II (single population encoding, non-dominated sorting, and genetic operations), introduces a pre-set reference point mechanism to replace the crowding distance strategy in NSGA-II. During environment selection, by establishing the association between population individuals and each reference point or reference direction, and selecting individuals based on their distance to the reference direction, the population is guided to achieve a more uniform distribution in the high-dimensional target space and gradually approach the Pareto front. This scheme is suitable for multi-objective optimization scenarios with high target dimensions and has been used in complex engineering parameter optimization problems.

[0026] However, existing multi-objective evolutionary algorithms still fall short in their global optimization capabilities and ability to preserve superior solutions in complex and constrained design spaces. On the one hand, traditional algorithms mainly rely on probabilistic crossover and mutation operations to drive population evolution, lacking mechanisms for the continuous preservation of high-quality historical solutions and targeted enhancement of potential advantage regions. Consequently, they are prone to problems such as loss of high-quality solutions, population degradation, and decreased search efficiency during iteration. On the other hand, when the population evolves to a highly potential local advantage region, traditional algorithms typically lack effective local fine-tuning and refinement mechanisms, making it difficult to further explore high-quality non-dominated solutions within the local region, which can easily lead to convergence stagnation in the later stages of evolution. Ultimately, this manifests as the algorithm not only failing to continuously improve the approximation accuracy of the Pareto front, but also failing to achieve ideal results in terms of the uniformity, completeness, and diversity of the solution set distribution, thus limiting its practical application in complex radiation shielding multi-objective optimization designs.

[0027] In response to the practical need for the coordinated design of lightweight and high-protection performance in nuclear radiation shielding structures, current design methods still face several bottlenecks: Firstly, high-fidelity physical simulation is computationally expensive and has a long evaluation cycle, making it difficult to meet the rapid iteration requirements in large-scale design spaces. Secondly, traditional neural network surrogate models have limited prediction accuracy in modeling strongly coupled and highly nonlinear response relationships, especially in failing to adequately characterize the global correlation features between complex high-dimensional design variables, thus restricting the reliability of surrogate-assisted optimization. Furthermore, conventional multi-objective optimization algorithms are prone to problems such as decreased population diversity and local optimum stagnation in complex high-dimensional solution spaces, making it difficult to achieve efficient approximation and fine-grained search of the Pareto front. Therefore, it is urgent to construct a fast multi-objective optimization design method for radiation shielding that balances surrogate prediction accuracy, computational efficiency, and global search capabilities.

[0028] To address the aforementioned issues, this invention provides a multi-objective optimization design method for radiation shielding based on Transformer and an improved NSGA-III. On one hand, this method employs a Transformer model to construct a surrogate model for radiation shielding performance. It utilizes a self-attention mechanism to model the complex nonlinear coupling relationships between shielding material thickness, material properties, and structural parameters, enabling rapid and high-precision prediction of performance indicators such as dose rate. This solves the problems of insufficient prediction accuracy and long Monte Carlo simulation evaluation times inherent in traditional shallow neural network surrogate models. On the other hand, based on the NSGA-III algorithm framework, an external archive dynamic maintenance mechanism and an elite local search mechanism are introduced. By preserving, updating, and filtering historical high-quality non-dominated solutions, excellent solutions are prevented from being lost during evolution. Furthermore, adaptive perturbation of elite individuals achieves fine-grained optimization in local regions, mitigating the convergence stagnation problem that easily occurs in the later stages of evolution and improving the algorithm's ability to approximate the Pareto front and the quality of the solution set distribution. Based on this collaborative design, the Pareto optimal solution set among multiple objectives such as mass, volume, and radiation dose can be obtained more effectively, providing reliable methodological support for performance trade-offs and multi-objective collaborative optimization of radiation shielding systems. This invention achieves an organic combination of high-precision surrogate modeling and efficient multi-objective optimization search, which can effectively improve the solution efficiency and result reliability of multi-objective collaborative optimization in the radiation shielding design of complex nuclear engineering.

[0029] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0030] Figure 1 This is a flowchart illustrating a multi-objective optimization design method for radiation shielding based on Transformer and improved NSGA-III, as described in this specification. The method includes the following steps: S101, Initialize the population. Each individual in the population includes the design variables of the radiation shield; the design variables are the thickness of each shielding layer.

[0031] A parameterized physical model of the radiation shield is constructed, and multi-objective optimization indices are determined according to specific design requirements. Design variables and their value ranges and constraints are set. Under the constraints of their value ranges and constraints, the initial population of the improved NSGA-III is determined.

[0032] S102, input the individual design variables into the surrogate model based on the Transformer architecture, calculate the radiation dose equivalent rate, calculate the total mass and total volume of the shielding body according to the design variables, and use the initial population as the parent population.

[0033] First, the construction process of the proxy model in the Transformer architecture is described. In one embodiment, the construction process of the proxy model in the Transformer architecture includes the following steps: S201, Obtain the design space of the design variables of the radiation shield, generate an initial sample set in the design space using the Latin hypercube sampling method, and perform high-fidelity numerical calculations on each initial sample in the initial sample set to obtain the radiation performance response data corresponding to each set of initial samples; the radiation performance response data includes the radiation dose equivalent rate.

[0034] This embodiment constructs a parameterized physical model of the radiation shield and determines multi-objective optimization indices based on specific design requirements, setting design variables and their value ranges and constraints. The Latin Hypercube Sampling (LHS) method is used to generate a representative initial sample set (design variables) within the design space to improve the uniformity and coverage of the sample distribution. The initial samples are input into a Monte Carlo simulation program for high-fidelity numerical calculations to obtain radiation performance response data corresponding to each set of design variables. The obtained simulation data is then organized and features are constructed to form a standardized dataset, i.e., training samples, for subsequent surrogate model training.

[0035] In one embodiment, a parametric geometric model of the shielding body is performed based on the structural composition and material arrangement of the radiation shielding system. According to the role of different structural layers in the optimization design, the shielding body is divided into variable-thickness layers and fixed-thickness layers. The fixed-thickness layers characterize the supporting structure, the reference layer, or other structural parts not involved in the optimization, while the variable-thickness layers characterize the material layers involved in the optimization design; that is, the thickness of each shielding layer is used as a design variable. For each variable-thickness layer, considering the physical realizability conditions, structural layout requirements, and Monte Carlo particle transport calculation efficiency in engineering applications, continuous value ranges and upper and lower boundary constraints are set for its corresponding design variables, thereby forming a parametric design space that meets the actual engineering requirements.

[0036] In this embodiment, the geometric model can be a simplified model of the primary radial shielding of the Savannah ship reactor. The radiation shielding structure consists of multiple shielding structures, and the specific shielding structure parameters and boundary constraints are shown in Table 1.

[0037] Table 1. Parameters and Boundary Constraints of the Primary Radial Shielding Structure for the Savannah Ship Reactor In one embodiment, after setting the design variables and their constraint ranges, a Latin hypercube sampling method is used to perform stratified uniform sampling in the multidimensional parameter space to generate a standard sampling matrix. Then, the standard sampling matrix is ​​mapped and transformed according to the physical value ranges corresponding to each design variable to obtain a set of sample parameters located in the actual design space, i.e., the initial sample set. This sampling method can obtain a relatively uniformly distributed and representative sample of design schemes globally, thereby reducing the local clustering or sampling blind spots caused by random sampling and improving the coverage of the design space by the initial samples.

[0038] In this embodiment, the physical boundary constraints of 10 design variables are clearly defined by defining a multidimensional array, covering the thickness range of components such as water layer, iron layer, water tank and lead layer; then a 10-dimensional LHS sampler is created to generate 3000 standard uniformly distributed sample matrices, and these are linearly mapped to the aforementioned physical boundary range to achieve stratified equal probability sampling; finally, 3000 sets of representative design scheme parameters that are globally uniformly distributed in the 10-dimensional design space and have no local clusters or blind spots are obtained.

[0039] In one embodiment, based on the obtained initial samples, an automated script is used to batch convert sample parameters to MCNP input models. Specifically, according to the values ​​of design variables for each layer, relative thickness parameters are converted into corresponding absolute geometric coordinate parameters according to preset geometric relationships. Combined with pre-defined template information such as particle source terms, material property cards, element cards, surface cards, and counter cards, standardized simulation files conforming to the MCNP input format requirements are automatically generated. Subsequently, a batch processing program is invoked to solve the generated MCNP input files in batches to obtain high-fidelity radiation performance response results corresponding to each initial sample.

[0040] In this embodiment, Python is used to progressively accumulate the parameters of each design scheme in the parameter set generated in step S12 to calculate the radius of a cylindrical surface. This is then embedded into an MCNP input file template to generate 3000 input files with varying geometric parameters. These input files are then run using a batch processing program. The source term is defined as a cylindrical neutron source with a radial range limited to 0 cm to 78.7 cm and an axial range set between -114.6 cm and 114.6 cm. The neutron direction is set to isotropic emission. For energy distribution, the model employs a typical Watt fission spectrum. Statistically, a 1 cm thick air shell is used as the detector. An F4 card is used to count neutron and gamma-ray fluxes, and DE and DF cards are used to convert the fluxes to environmental dose equivalents. The flux-dose equivalent conversion factor is derived from the internationally recognized ICRP-74 document.

[0041] In one embodiment, after the MCNP simulation calculation is completed, the statistical data of the MCNP output file is feature extracted and accurately matched with the corresponding design scheme parameter set to construct the dataset required for Transformer model training, namely the initial samples and the corresponding radiation performance response data.

[0042] In this embodiment, the results file output by the MCNP simulation is traversed to extract statistical data of key physical quantities, including characteristic values ​​such as the average volume flux of neutrons and gamma rays in the counting region and statistical errors. Then, these extracted characteristic values ​​are precisely matched with the corresponding design scheme parameter set generated in step S12 to ensure that each design parameter combination corresponds to its simulation results. Finally, the matched data is organized into a structured dataset, which includes two parts: input features (10 thickness variables) and output labels (total dose equivalent rate).

[0043] The individual design variables are input into the surrogate model based on the Transformer architecture to obtain the radiation dose equivalent rate output by the surrogate model.

[0044] Based on the design variables, the total mass and volume of the shielding structure are calculated. This involves inputting the design variables into an explicit functional expression for the total mass and volume, constructed with the design variables as independent variables, to obtain the total mass and volume of the shielding structure. Specifically, the explicit functional expression can first calculate the volume of each component of the shielding structure based on the design variables and the geometric relationship of the shielding structure. Then, based on this, the mass of each component is calculated using the material density. Finally, the total volume and total mass of the shielding structure corresponding to the design variable are summarized and returned.

[0045] S202, the initial samples and corresponding radiation performance response data are preprocessed and used as training samples. Using the training samples, the Transformer architecture is used to model the complex nonlinear mapping relationship between the shielding structure design variables and the radiation performance response, and a surrogate model is obtained.

[0046] The initial samples and corresponding radiation performance response data obtained from S201 were preprocessed and divided into training, validation, and test sets. A surrogate model based on the Transformer architecture was constructed, utilizing its self-attention mechanism to model the complex nonlinear mapping relationship between shielding structure design variables and radiation performance response. During training, the model parameters were iteratively updated by setting a loss function and optimization algorithm, and learning rate adjustment strategies and regularization methods were combined to improve the model's convergence stability and generalization ability. After training, the surrogate model was independently evaluated using the test set to verify its prediction accuracy and reliability across the entire design space, thereby obtaining a high-precision surrogate model that can be used for rapid fitness evaluation.

[0047] Specifically, the acquired MCNP simulation dataset (radiative performance response data) was cleaned to remove invalid or missing samples. Then, a random sampling algorithm was used to scientifically divide the complete dataset into non-overlapping training, validation, and test sets. To eliminate gradient convergence difficulties caused by differences in dimensions and numerical magnitudes between different physical variables, a Z-score normalization strategy was employed to normalize both the input feature vector and the output target variable.

[0048] In this embodiment, the Vdata.xlsx dataset is first read and invalid samples containing missing values ​​are removed to ensure data quality. Then, a random sampling algorithm is used to scientifically divide the dataset into non-overlapping training, validation, and test sets at ratios of 70%, 15%, and 15%, respectively, and these sets are exported and saved separately. Next, based on the training set statistics, the 10-dimensional input feature vector and output target variable are normalized using a Z-score normalization strategy. The mapping formula is as follows: In the formula, These are the original physical characteristic values. These are the standardized dimensionless eigenvalues. and These represent the mean and standard deviation of the feature in the training set, respectively. The processed standardized tensor is then encapsulated in tensor format and loaded into a data loader that supports batch iteration, providing a standardized data stream for stable training of deep learning models.

[0049] In one embodiment, the Transformer architecture is used to model the complex nonlinear mapping relationship between shielding structure design variables and radiation performance response to obtain a surrogate model, including the following steps: S301, Construction of Transformer Network Architecture Adapted to Continuous Variables.

[0050] To address the continuous numerical characteristics in radiation shielding design, a customized Transformer deep learning architecture is designed, such as... Figure 2 As shown, firstly, a one-dimensional continuous feature X is projected to a high-dimensional hidden space through a linear mapping layer, and then a learnable positional encoding is fused. To preserve the spatial sequence information of each physical shielding layer, the input representation calculation is as follows:

[0051] In the formula, and Here are the weights and biases of the linear mapping layer.

[0052] Subsequently, the fusion features will be The input is fed into a Transformer encoder-decoder module that incorporates a multi-head self-attention mechanism. The decoder uses a learnable target token. tgt As initial input and superimposed with position code The calculation formula is as follows:

[0053] By leveraging a self-attention mechanism, the model can globally capture and quantify the complex nonlinear interactions and dependencies between multiple layers of different shielding materials. Its core attention calculation formula is as follows: In the formula, Q , K , V These represent the query, key, and value matrices, respectively. For the feature vector dimension, =128, to scale the dot product and prevent gradient vanishing. Finally, a fully connected layer maps the high-dimensional abstract features extracted by the decoder to continuous predicted values ​​of the target radiometric performance index. .

[0054] In one specific embodiment, for the 10-dimensional continuous thickness feature in the radiation shielding design, each one-dimensional continuous feature X is projected onto a 128-dimensional high-dimensional hidden space through 10 independent linear mapping layers, and a learnable positional encoding is fused. This preserves the spatial sequence information of each physical shielding layer. The representation is then input into a 3-layer Transformer encoder-decoder module containing an 8-head self-attention mechanism, where the decoder uses a learnable target token tgt as initial input and superimposes positional encodings. By leveraging a multi-head self-attention mechanism to globally capture the complex nonlinear interactions and dependencies between multiple layers of different shielding materials, a fully connected layer is ultimately used to map the high-dimensional abstract features extracted by the decoder into continuous predicted values ​​of the target radiation performance index. An end-to-end Transformer network architecture adapted to continuous variables has been constructed.

[0055] S302, a model dynamic training and optimization that integrates an adaptive decay strategy.

[0056] Mean Squared Error (MSE) is established as the loss function to measure the difference between predicted and true values, and its definition is as follows: In the formula, Batch Size. To achieve a true standardized target value for high-fidelity simulation, The model predicts the values. The Adam gradient descent optimization algorithm is configured to update the model's network weights. During iterative training, the model performs forward propagation and backward gradient calculation on the training set; simultaneously, after each training epoch, the generalization error of the current model is monitored synchronously using the validation set. To break local optima and accelerate convergence, an adaptive learning rate decay strategy based on the validation set loss is introduced: when the validation set loss stops decreasing within a set patience threshold period, the learning rate is automatically reduced proportionally. For the current learning rate Apply decay penalty (i.e.) In addition, the system implements an optimal weight retention mechanism, storing the model parameters with the lowest verification error in real time, fundamentally curbing the occurrence of overfitting.

[0057] In this embodiment, the Adam optimizer is configured with an initial learning rate. η =5×10 -4 The network weights are updated. In each training epoch, the model performs forward propagation to calculate predicted values, backpropagation to calculate gradients and update parameters on the training set, and simultaneously records the training loss. After each epoch, the model performance is evaluated on the validation set and the validation loss is recorded. An adaptive learning rate decay strategy based on the validation set loss is introduced: if the validation loss does not decrease within 10 epochs (the patience threshold), the learning rate is automatically updated as a penalty by a decay factor γ=0.5. Simultaneously, an optimal weight retention mechanism is implemented, comparing the current validation loss with the historical best value in real time. When the validation loss is lower, the model state dictionary is immediately saved to the optimal path. Thus, within a 500-epoch training cycle, by dynamically adjusting the learning rate and combining early stopping protection, local optima are effectively broken, convergence is accelerated, and overfitting is fundamentally curbed.

[0058] S303, high-precision validation of surrogate models driven by independent test sets.

[0059] After the model training converges and the optimal weights are loaded, an independent test set that has not participated in the training and parameter tuning is introduced to objectively evaluate the performance of the surrogate model. First, the standardized predictions output by the model are restored to their true physical dimensions through an inverse scaling operation. Then, the coefficient of determination (R²) is calculated. 2 Core statistical indicators such as mean squared error (MSE) and mean absolute error (MAE) are used to comprehensively quantify the model's fitting accuracy. Figure 3 As shown, Figure 3 Figure (a) shows a comparison of the determination coefficients of the various proxy models. Figure 3Figure (b) shows a comparison of the mean squared errors of the various surrogate models. Figure 3 Figure (c) shows a comparison of the mean absolute errors of the various surrogate models. In addition to quantitative verification, a scatter plot comparing the fit between the actual and predicted values ​​was simultaneously plotted, such as... Figure 4 As shown. Through these rigorous quantitative metrics and visual verifications, it is confirmed that the constructed Transformer surrogate model possesses extremely high prediction accuracy and generalization ability throughout the entire high-dimensional design space, proving its reliability as a fast prediction engine and a complete replacement for time-consuming Monte Carlo simulations.

[0060] In this embodiment, the optimal weights saved during the training phase are first loaded into the model, and an independent test set that was not involved in training or parameter tuning is introduced for objective performance evaluation. Then, the standardized predictions output by the model are restored to their true physical dimensions through an inverse scaling operation, as shown in the following formula: in, For standardized predictions, and Let the standard deviation and mean of the target variable in the training set be denoted as ; then calculate the coefficient of determination R0. 2 The mean squared error (MSE) and mean absolute error (MAE) are calculated using the following formulas: In the formula, The total number of samples in the test set. For the true value, For predicted values, This represents the average of the true values ​​in the test set. Simultaneously, the data comparing the fit between the true and predicted values ​​is exported as a CSV file, and a density scatter plot is plotted, with a 1:1 reference line visually demonstrating the model's prediction accuracy.

[0061] Therefore, the individual design variables are input into the trained surrogate model based on the Transformer architecture to obtain the radiation dose equivalent rate output by the surrogate model, and the total mass and total volume of the shield are calculated based on the design variables.

[0062] S103 aims to minimize the radiation dose equivalent rate, total shield mass, and total volume. It optimizes the design variables using an improved NSGA-III algorithm. In each iteration of the improved NSGA-III algorithm, a child population is generated from the parent population, and the child population is merged with the non-dominated solutions in the external archive. Through non-dominated sorting, the elite solutions at the first non-dominated front are retained as the new child population from all the merged solutions. The external archive is used to store the first non-dominated front solutions generated in each iteration.

[0063] The surrogate model trained above is embedded into a multi-objective optimization framework to replace traditional time-consuming Monte Carlo simulation, enabling rapid prediction of individual fitness in the population. Using the NSGA-III algorithm as the global optimization framework, a dynamic maintenance mechanism of an external archive is introduced during population evolution to preserve, filter, and update high-quality non-dominated solutions generated in each generation, enhancing the ability to retain excellent solutions and improving the quality of the solution set distribution. Simultaneously, an elite local search mechanism is introduced, periodically selecting individuals with high optimization potential from the external archive as local search objects, and performing a refined search of their neighborhoods through adaptive perturbation to improve the algorithm's local exploitation capability within advantageous regions. Through the synergistic effect of global solution set maintenance in the external archive and the refined local exploitation of elite local search, the convergence, diversity, and completeness of the Pareto optimal solution set are improved, ultimately obtaining a radiation shielding design scheme that meets the requirements of multi-objective collaborative optimization of radiation dose, total mass, and total volume.

[0064] Specifically, the surrogate model trained and converged in step S102 is embedded as the core evaluator within the evolutionary algorithm framework to replace the time-consuming Monte Carlo physics simulation. For the radiation shielding optimization problem, a multi-criteria optimization objective function is established, encompassing radiation dose equivalent rate, total shielding mass, and total volume. For any input design variables... X (i.e., the thickness of each shielding layer), its exact physical mass and volume are calculated through geometric analysis, and its radiation shielding performance is rapidly inferred using a standardized surrogate model, constructing a multi-objective mapping relationship:

[0065] In the formula, X For the thickness of the shielding body, and Representing the first i The lower and upper limits of the thickness variation of the shielding layer. The radiation dose equivalent rate output by the Transformer model. and These represent the total mass and total volume of the shielding body, calculated based on physical constraints. n To design the dimensions of variables, For the first i The volume of the shielding layer For the first i The density of the shielding layer. This multi-objective evaluation engine provides immediate fitness feedback for subsequent large-scale, high-frequency evolutionary iterations of the population.

[0066] Taking a design variable of 10 dimensions as an example, for any input 10-dimensional decision variable vector XFirst, a standardization transformation is performed. Then, the standardized tensor is input into the Transformer model for forward propagation. It is projected into a 128-dimensional hidden space through 10 independent linear mapping layers. After being superimposed with positional encoding, it is fed into an 8-head self-attention Transformer encoder-decoder module. Finally, the standardized prediction value is output through a fully connected layer, and then inverse standardization is performed to obtain the radiation dose equivalent rate. Simultaneously, the VMV.py file is invoked to automatically calculate the shielding mass based on geometric analysis. and volume .

[0067] In one embodiment, a global search is performed using NSGA-III (a third-generation non-dominated sorting genetic algorithm) as the main framework. During evolutionary iterations, the parent population generates the offspring population through simulated binary crossover (SBX) and polynomial mutation operators. In the environment selection phase, to address the convergence problem in the high-dimensional target space, the algorithm pre-distributes a series of reference direction vectors uniformly in the target space. After merging the current population with its offspring, the ideal point is first calculated. The population target value is shifted, and then the normalized target vector is calculated. The cosine similarity projection with each reference vector λ associates the individual with the nearest reference line:

[0068] The algorithm prioritizes retaining individuals with higher non-dominated ranks and maintains niches within the same rank by counting associated individuals based on the reference line, thereby ensuring broad coverage of the population on the global Pareto front.

[0069] To prevent the loss of historical high-quality decision variables during evolution, an external archive was constructed in parallel with the improved NSGA-III main loop. The offspring population generated in each generation is merged with the current archive and undergoes a strict non-dominated sorting, retaining only the elite solutions at the first non-dominated frontier (Rank 0) as the new offspring population.

[0070] Specifically, in the improved NSGA-III, the initial population size is set to 120. During 2000 generations of evolutionary iterations, the parent population generates the offspring population through simulated binary crossover (SBX) and a polynomial mutation operator. SBX crossover is performed with a probability of 0.9 and a distribution index of... =20; the probability of the mutation stage is 0.1, with the distribution index... =20 performs polynomial mutation; during the environment selection phase, 120 reference direction vectors are pre-distributed evenly.

[0071] In one embodiment, if the number of non-dominated solutions in the external archive exceeds a preset capacity limit, then for each non-dominated solution in the external archive, its nearest neighbor is obtained. The average Euclidean distance of each neighbor; remove redundant individuals with the smallest average Euclidean distance from the external archive.

[0072] Specifically, when the number of non-dominated solutions in the archive exceeds a preset capacity limit (e.g., 180), a diversity truncation mechanism based on the K-Nearest Neighbors (KNN) algorithm is introduced. Within the normalized target space, each solution is computed... i The average Euclidean distance to its K nearest neighbors The formula for calculating the average Euclidean distance is:

[0073] in, For the first A non-dominated solution and its nearest The average Euclidean distance of each neighbor. For the number of neighbors, The target dimensions are (3 dimensions: dose equivalent rate, total mass, total volume). For the first The first non-dominated solution corresponds to the th The values ​​of each target, For the first The first nondominated solution The neighbor corresponding to the first The values ​​of the target can be optionally... .

[0074] Subsequently, the sparsity of all individuals in the archive is calculated, and those that are removed are prioritized. The minimum (i.e. the most crowded spatial distribution) redundant individuals force the archive to be distributed in an extremely uniform manner in the multidimensional frontier space, thereby providing high-quality and widely distributed sampling seeds for subsequent elite local searches.

[0075] S104 merges the new offspring population with the parent population to form the main population.

[0076] S105, if the current iteration number meets the preset search period, then extract seed individuals from the external archive as an elite subset, apply an adaptive random perturbation based on Gaussian noise to the elite subset, generate exploratory solutions for the local neighborhood, incorporate the exploratory solutions into the main population, and update the external archive based on the exploratory solutions.

[0077] In one embodiment, extracting seed individuals from an external archive as an elite subset includes: extracting the first non-dominated solution at the boundary extrema points in each objective dimension from the external archive, and the solution with the nearest... The second non-dominated solution is the one with the largest average Euclidean distance from its neighbors; the first and second non-dominated solutions are taken as elite subsets.

[0078] Specifically, to address the shortcomings of traditional global operators in exploring neighborhood depth, an elite local search (ELS) mechanism is periodically triggered. First, highly promising "seed individuals" are extracted from an external database: boundary extreme points are extracted across each target dimension, and the most isolated individuals are selected to form an elite subset based on the aforementioned KNN distance. Then, an adaptive random perturbation based on Gaussian noise is applied to the elite subset to generate exploratory solutions for the local neighborhood. Exploring solutions The calculation formula is:

[0079] in, In order to explore solutions, For the non-dominated solution in the elite subset, and These are the upper and lower bounds of the design variable, respectively. For the number of iterations The changing perturbation step size, With a mean of 0 and a variance of Normally distributed random numbers, This is the clipping function.

[0080] Optionally, an Elite Local Search (ELS) mechanism is triggered periodically every 20 generations. First, the algorithm extracts the most promising "seed individuals" from an external archive to form an elite set (12 individuals). The extraction strategy covers the boundary extrema of each objective dimension (first non-dominated solutions, 3 individuals) and the most isolated individuals selected by KNN distance (second non-dominated solutions, 9 individuals). Then, an adaptive random perturbation based on Gaussian noise (5 times) is applied to the elite subset to generate exploratory solutions in the local neighborhood. .

[0081] To balance the "extensive exploration" in the early stages of evolution with the "refined polishing" in the later stages, the concept of simulated annealing is introduced to construct a dynamically decaying perturbation step size. perturbation step size for: in, This represents the current iteration number. The maximum number of iterations, This represents the boundary of the perturbation intensity during the initial stage of the iteration. This represents the boundary of the perturbation intensity during the iteration termination phase; optionally, , , The exploratory solutions generated by the local search will be back-injected into the main population and the external archive. Through this strong coupling and linkage between large-scale global optimization and small-scale local exploration, the convergence bottleneck will be successfully broken, and a Pareto optimal solution set that is closer to reality and has excellent diversity will be obtained.

[0082] In one embodiment, updating the external archive based on the exploratory solutions includes: incorporating the exploratory solutions into the external archive, and after incorporating the exploratory solutions into the external archive, performing deduplication and non-dominated sorting on the solutions in the external archive, retaining the first non-dominated front solution, and deleting the remaining dominated candidate solutions.

[0083] After deduplication and non-dominated sorting, if the number of non-dominated solutions in the external repository exceeds the preset capacity limit of the repository, a truncation mechanism is activated. That is, if the number of non-dominated solutions in the external repository exceeds the preset capacity limit, then for each non-dominated solution in the external repository, its nearest neighbor is retrieved. The average Euclidean distance of each neighbor; remove redundant individuals with the smallest average Euclidean distance from the external archive.

[0084] S106, through the non-dominated sorting and reference direction selection mechanism, the parent population is selected from the updated main population, and the iteration is repeated until the preset number of iterations is reached. The parent population obtained in the last iteration is taken as the Pareto optimal solution set. Based on the Pareto optimal solution set, the design scheme of the radiation shield is determined.

[0085] Specifically, a parent population is selected from the updated main population through a non-dominated sorting and reference direction selection mechanism. This includes: performing a fast non-dominated sort on the updated main population; dividing individuals into different non-dominated layers based on their Pareto dominance relationships; sequentially adding individuals from the non-dominated layers to the next generation solution set St according to the optimal solution order; and ensuring that the size of St is greater than or equal to the size of the parent population for the first time after adding an individual from a non-dominated layer. M This non-dominated layer is called the critical layer. All individuals in the non-dominated layers preceding the critical layer are added to the parent population. Based on a reference direction selection mechanism, a subset of individuals from the critical layer are selected and added to the parent population to fill the gap in the parent population. M .

[0086] Specifically, based on the reference direction selection mechanism, a portion of individuals are selected from the critical layer and incorporated into the parent population to fill the gap in the parent population size. M Specifically, it includes: S401, translate the individual coordinates of the critical layer so that the minimum coordinates of the critical layer become the origin, then find the extreme points in each target direction, construct a hyperplane, and finally map the target values ​​of all individuals in the critical layer to the same scale.

[0087] S402 calculates the vertical distance from each individual in the critical layer to each reference line and associates that individual with the nearest reference point. These reference points are typically pre-generated uniformly on the hyperplane using standard methods.

[0088] S403, Based on the above correlation results, the niche technique is used to preferentially select individuals located in sparse areas to be incorporated into the parent population in order to fill the gap in the size of the parent population. M。

[0089] After selecting the parent population from the updated main population through non-dominated sorting and reference direction selection mechanism, S103-S105 are re-executed based on the new parent population until the preset number of iterations or the algorithm convergence criterion is reached. The parent population obtained in the last iteration is taken as the Pareto optimal solution set. This solution set exhibits rich diversity in the multidimensional objective space and can highly approximate the real global Pareto front.

[0090] To facilitate engineering analysis, typical design schemes were further selected from the Pareto optimal solution set, including the optimal dose equivalent rate scheme, the optimal mass scheme, the optimal volume scheme, and a compromise scheme. The optimal dose equivalent rate, optimal mass, and optimal volume schemes were selected by comparing the objective function values ​​of each scheme in the Pareto optimal solution set, with the solutions having the smallest dose equivalent rate, the smallest total mass, and the smallest total volume being chosen as the corresponding typical design schemes. The compromise scheme was determined using the ideal point distance method; that is, after normalizing each objective, the distance from each Pareto solution to the ideal point was calculated, and the solution with the smallest distance was selected as the representative scheme with better overall performance.

[0091] In one embodiment, such as Figure 5 As shown, the present invention also provides a multi-objective optimization design method for radiation shielding based on Transformer and improved NSGA-III, which includes the following steps: S1, initial design space exploration and high-fidelity data acquisition.

[0092] S2, High-precision proxy model construction and training based on Transformer.

[0093] S3 improves NSGA-III multi-objective optimization based on external archives and elite local search mechanism.

[0094] like Figure 6 As shown, Figure 6 Flowchart of the improved NSGA-III algorithm.

[0095] Figure 7This is a schematic diagram showing the distribution of the Pareto optimal solution set in the three-dimensional target space, which takes into account the targets of dose equivalent rate, mass and volume, as output by an embodiment of the present invention. Figure 8 The figure shows the convergence curve of the hypervolume (HV) index of the improved NSGA-III algorithm in the normalized target space as a function of the number of iterations, and its comparison with the traditional algorithm. Figure 9 The figure shows the distribution of HV index obtained by statistically analyzing 30 independent experiments using the improved NSGA-III algorithm in this embodiment of the invention, and its comparison with the traditional algorithm.

[0096] As described above, compared with the prior art, the radiation shielding multi-objective optimization design method based on Transformer and improved NSGA-III provided by this invention lies in the construction of a joint optimization mechanism of Transformer fast response prediction and improved NSGA-III refined evolution. Its technical advantages are as follows: 1. It solves the problem of insufficient representation of spatial correlation features of shielded structures by traditional proxy models, thus improving the accuracy and efficiency of evaluation.

[0097] Traditional surrogate models (such as BP neural networks or RBF neural networks) struggle to capture long-range dependencies between material arrangement sequences when dealing with multi-layered shielding structures. This invention abandons traditional shallow artificial neural networks (such as BP and RBF) and, for the first time, introduces the Transformer architecture into radiation shielding design. Utilizing its multi-head attention mechanism, it deeply mines the complex physical coupling effects and long-range spatial dependencies arising from the arrangement of multi-layered heterogeneous shielding materials, achieving extremely high accuracy in dose rate prediction across orders of magnitude. With excellent MSE and MAE indicators, it completely breaks through the computing power bottleneck of high-fidelity Monte Carlo physics simulation and transforms the time-consuming MCNP physics simulation into millisecond-level numerical inference, greatly reducing the computing cost.

[0098] This invention introduces the Transformer architecture. Because its multi-head attention mechanism can deeply explore the complex physical coupling effects and long-distance dependencies between multiple heterogeneous shielding layers, the model can achieve high-fidelity predictions of radiation dose rates across orders of magnitude in a very short time. This effectively overcomes the computational bottleneck in multi-objective optimization and fundamentally avoids deviations in the optimization direction caused by evaluation errors.

[0099] 2. It solves the problem of lack of solution set diversity that traditional multi-objective evolutionary algorithms are prone to when seeking optimization in high dimensions.

[0100] To address the issues of historical high-quality solutions being easily lost and uneven Pareto front distribution in traditional multi-objective optimization algorithms during the environment selection phase, this invention constructs an external archive in parallel outside the traditional NSGA-III main loop, retaining the Rank 0 first non-dominated front solution. When the number of non-dominated solutions exceeds the capacity limit, an innovative K-nearest neighbor (KNN) Euclidean distance truncation mechanism based on the normalized objective space is introduced to dynamically remove crowded and redundant individuals. This mechanism not only prevents the degradation and loss of high-quality decision parameters during the optimization process but also ensures that the final output Pareto front has good distribution uniformity and broad coverage in the multi-dimensional objective space (mass, volume, dose).

[0101] To address the shortcomings of traditional evolutionary algorithms, such as getting trapped in local optima and insufficient convergence, this method periodically extracts "seed individuals" (boundary extreme points and the most isolated individuals) from an external database and applies dynamically decaying Gaussian noise perturbations based on simulated annealing. This strong coupling of small-scale fine-tuning with large-scale global crossover mutation successfully overcomes the convergence bottleneck in the later stages of evolution.

[0102] 3. It solves the problem that traditional algorithms are prone to getting trapped in local optima, ensuring that the results closely approximate the true global Pareto front.

[0103] Traditional multi-objective evolutionary algorithms often face convergence stagnation in the later stages of evolution and are susceptible to local optima traps caused by the discretization of material parameters. This invention enhances the algorithm's local refinement search capability through an elite local search (ELS) mechanism and an adaptive perturbation strategy, effectively guiding the population away from local extrema. This synergistic mechanism of global exploration and local exploitation significantly improves the algorithm's convergence performance, ensuring that the final solution set closely approximates the true global Pareto front.

[0104] To address the shortcomings of traditional evolutionary algorithms, such as the lack of in-depth exploration mechanisms and susceptibility to local optima, this invention incorporates an ELS strategy combining simulated annealing with crossover and mutation operations. Because the algorithm periodically applies a dynamically decaying Gaussian perturbation to the extracted extremum "seed individuals," it achieves a strong coupling between large-scale extensive exploration in the early stages of evolution and small-scale fine-tuning in the later stages. This endows the population with the ability to escape local optima, solves the technical problem of evolutionary stagnation in traditional algorithms, and significantly improves the convergence accuracy of the Pareto solution set.

[0105] The execution entity of the methods provided in this specification can be a server, which can be a server set up on a business platform, or a device such as a desktop computer or laptop computer capable of executing the solutions in this specification. When applying the radiation shielding multi-objective optimization design method based on Transformer and improved NSGA-III provided in this specification, it is not necessary to follow... Figure 1The steps shown are executed in sequence. The specific execution order of each step can be determined as needed, and this manual does not impose any restrictions on it.

[0106] The above describes one or more embodiments of the radiation shielding multi-objective optimization design method based on Transformer and improved NSGA-III provided in this specification. Based on the same idea, this specification also provides a corresponding radiation shielding multi-objective optimization design apparatus based on Transformer and improved NSGA-III, which includes: The initialization module is used to initialize the population. Each individual in the population includes the design variables of the radiation shielding; the design variables are the thickness of each shielding layer. The calculation module is used to input the individual design variables into the surrogate model based on the Transformer architecture, calculate the radiation dose equivalent rate, and calculate the total mass and total volume of the shielding body according to the design variables, and select the parent population from the initial population. The iterative module optimizes the design variables by minimizing the radiation dose equivalent rate, total shielding mass, and total volume. It uses an improved NSGA-III algorithm to find the optimal values. In each iteration of the improved NSGA-III algorithm, a child population is generated from the parent population, and this child population is merged with non-dominated solutions in an external archive. Through non-dominated sorting, the elite solutions at the first non-dominated front are retained as the new child population. The external archive stores the first non-dominated front solutions generated in each iteration. The new child population... The population and the parent population are merged to form the main population. If the current iteration count meets the preset search period, seed individuals are extracted from the external archive as an elite subset. An adaptive random perturbation based on Gaussian noise is applied to the elite subset to generate exploratory solutions in the local neighborhood. The exploratory solutions are then incorporated into the main population, and the external archive is updated based on the exploratory solutions. The parent population is selected from the updated main population through a non-dominated sorting and reference direction selection mechanism, and the iteration is repeated until the preset iteration count is reached. The parent population obtained in the last iteration is taken as the Pareto optimal solution set. The determination module is used to determine the design scheme of the radiation shielding body based on the Pareto optimal solution set.

[0107] Specific limitations regarding the radiation shielding multi-objective optimization design device based on Transformer and improved NSGA-III can be found in the limitations of the radiation shielding multi-objective optimization design method based on Transformer and improved NSGA-III mentioned above, and will not be repeated here. Each module in the aforementioned radiation shielding multi-objective optimization design device based on Transformer and improved NSGA-III can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0108] This specification also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 A multi-objective optimization design method for radiation shielding based on Transformer and improved NSGA-III is provided.

[0109] This instruction manual also provides Figure 10 The schematic diagram of the computer device shown is as follows: Figure 10 At the hardware level, the computer device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then runs it to achieve the above-mentioned functions. Figure 1 A multi-objective optimization design method for radiation shielding based on Transformer and improved NSGA-III is provided.

[0110] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0111] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A multi-objective optimization design method for radiation shielding based on Transformer and improved NSGA-III, characterized in that, include: Initialize the population, where each individual includes the design variables for the radiation shield; The design variable is the thickness of each shielding layer; The individual design variables are input into the surrogate model based on the Transformer architecture to calculate the radiation dose equivalent rate. Based on the design variables, the total mass and total volume of the shield are calculated, and the initial population is used as the parent population. With the optimization objectives of minimizing radiation dose equivalent rate, total shield mass, and total volume, the design variables are optimized using an improved NSGA-III algorithm. In each iteration of the improved NSGA-III algorithm, a child population is generated from the parent population, and the child population is merged with the non-dominated solutions in the external archive. Through non-dominated sorting, the elite solutions at the first non-dominated front are retained as the new child population from all the merged solutions. The external archive is used to store the first non-dominated front solutions generated in each iteration. The new offspring population is merged with the parent population to form the main population; If the current iteration count meets the preset search period, then seed individuals are extracted from the external archive as an elite subset, an adaptive random perturbation based on Gaussian noise is applied to the elite subset, an exploratory solution for the local neighborhood is generated, the exploratory solution is incorporated into the main population, and the external archive is updated according to the exploratory solution. The parent population is selected from the updated main population through non-dominated sorting and reference direction selection mechanism, and the iteration is repeated until the preset number of iterations is reached. The parent population obtained in the last iteration is taken as the Pareto optimal solution set. Based on the Pareto optimal solution set, the design scheme of the radiation shield is determined.

2. The method according to claim 1, characterized in that, The method further includes: If the number of non-dominated solutions in the external archive exceeds the preset capacity limit, then obtain each non-dominated solution in the external archive and its nearest neighbor. The average Euclidean distance of each neighbor; Remove redundant individuals from the external archive with the smallest average Euclidean distance.

3. The method according to claim 2, characterized in that, The formula for calculating the average Euclidean distance is: in, For the first A non-dominated solution and its nearest The average Euclidean distance of each neighbor. For the number of neighbors, For the target dimension, For the first The first non-dominated solution corresponds to the th The values ​​of each target, For the first The first nondominated solution The neighbor corresponding to the first The value of each target.

4. The method according to claim 1, characterized in that, Seed individuals were extracted from external archives as an elite subset, including: Extract the first non-dominated solution of the boundary extreme points in each objective dimension from the external archive, and compare it with the nearest... The second nondominated solution with the largest average Euclidean distance from its neighbors; The first and second non-dominated solutions are taken as elite subsets.

5. The method according to claim 1, characterized in that, The formula for calculating the solution is: in, In order to explore solutions, For the non-dominated solution in the elite subset, and These are the upper and lower bounds of the design variable, respectively. For the number of iterations The changing perturbation step size, With a mean of 0 and a variance of Normally distributed random numbers, This is the clipping function; perturbation step size By constructing a perturbation step size based on the concept of simulated annealing. for: in, This represents the current iteration number. The maximum number of iterations, This represents the boundary of the perturbation intensity during the initial stage of the iteration. This represents the boundary of the perturbation intensity during the iteration termination phase.

6. The method according to claim 1, characterized in that, The process of building the proxy model in the Transformer architecture includes: The design space for the design variables of the radiation shield is obtained. The Latin hypercube sampling method is used to generate an initial sample set within the design space. High-fidelity numerical calculations are performed on each initial sample in the initial sample set to obtain the radiation performance response data corresponding to each set of initial samples. The radiation performance response data includes the radiation dose equivalent rate. The initial samples and the corresponding radiation performance response data were preprocessed and used as training samples. By using training samples, the Transformer architecture is employed to model the complex nonlinear mapping relationship between shielding structure design variables and radiation performance response, thus obtaining a surrogate model.

7. The method according to claim 1, characterized in that, Update the external archive based on the exploration solution, including: The explored solutions are incorporated into the external archive, and the solutions in the external archive are deduplicated and sorted by non-dominated order. The first non-dominated frontier solution is retained, and the remaining dominated candidate solutions are deleted.

8. A radiation shielding multi-objective optimization design device based on Transformer and improved NSGA-III, characterized in that, include: The initialization module is used to initialize the population, and each individual in the population includes the design variables of the radiation shield; The design variable is the thickness of each shielding layer; The calculation module is used to input the individual design variables into the surrogate model based on the Transformer architecture, calculate the radiation dose equivalent rate, and calculate the total mass and total volume of the shielding body according to the design variables, and select the parent population from the initial population. The iterative module optimizes the design variables by minimizing the radiation dose equivalent rate, total shielding mass, and total volume. It uses an improved NSGA-III algorithm to find the optimal values. In each iteration of the improved NSGA-III algorithm, a child population is generated from the parent population, and this child population is merged with non-dominated solutions in an external archive. Through non-dominated sorting, the elite solutions at the first non-dominated front are retained as the new child population. The external archive stores the first non-dominated front solutions generated in each iteration. The new child population... The population and the parent population are merged to form the main population. If the current iteration count meets the preset search period, seed individuals are extracted from the external archive as an elite subset. An adaptive random perturbation based on Gaussian noise is applied to the elite subset to generate exploratory solutions in the local neighborhood. The exploratory solutions are then incorporated into the main population, and the external archive is updated based on the exploratory solutions. The parent population is selected from the updated main population through a non-dominated sorting and reference direction selection mechanism, and the iteration is repeated until the preset iteration count is reached. The parent population obtained in the last iteration is taken as the Pareto optimal solution set. The determination module is used to determine the design scheme of the radiation shielding body based on the Pareto optimal solution set.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the method described in any one of claims 1 to 7.

10. A computer device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any one of claims 1 to 7.

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