Multi-objective shielding optimization method and system based on non-dominated sorting genetic algorithm

Abstract

The present invention provides a multi-objective shielding optimization method and system based on a non-dominated sorting genetic algorithm, relating to the field of radiation protection technology. The method comprises the following steps: generating an initial shielding scheme and determining an objective function value corresponding to the initial shielding scheme; sorting the multiple initial shielding schemes according to a dominance relationship based on the objective function value to generate a first-generation shielding scheme; sorting the first-generation shielding schemes according to a non-dominated relationship, and then generating a second-generation shielding scheme using a genetic operator; merging and sorting the first-generation shielding schemes and the second-generation shielding schemes to obtain different solution sets; sequentially selecting shielding schemes from each solution set to the next-generation shielding scheme, and updating the objective function value corresponding to the next-generation shielding scheme until a termination condition is met; and outputting the shielding material and shielding thickness for the current radiation shielding scenario based on the optimized shielding scheme. In this way, multiple objectives, such as dose rate and shielding material volume, can be simultaneously optimized, thereby improving the optimization efficiency of the shielding scheme.

Description

Technical Field

[0001] The present invention relates to the field of radiation protection technology, and in particular to a multi-objective shielding optimization method and system based on a non-dominated sorting genetic algorithm. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute the prior art that has been known to those skilled in the art.

[0003] The design of radiation shielding systems is a crucial component of nuclear device design. Its design directly impacts the radiation safety of the device and its personnel, the lifespan of critical equipment, and significantly impacts the overall performance and construction cost of the device, potentially hindering the achievement of ultimate goals. Shielding design for modern, complex nuclear devices, such as nuclear power plants, large nuclear facilities, and accelerators, and especially for small, space-scale nuclear devices like marine nuclear power reactors, space reactors, and spent fuel transport systems, requires not only dose rates that meet design targets but also strict weight and size control, making the design process highly complex. For complex nuclear devices with highly compact dimensions and strict weight limits, lightweight shielding becomes a crucial factor in achieving the device's ultimate goals, creating an urgent need for it.

[0004] The rational design of radiation shielding for nuclear devices with complex geometries and source terms is a complex problem. On the one hand, the design targets are complex structures, the distribution of neutrons and photons is complex, and no material offers excellent shielding performance for both neutrons and photons at different energies. On the other hand, radiation shielding design often requires consideration of multiple design objectives, such as minimizing radiation levels, achieving low shield weight, compact size, and economical performance. This represents a typical multi-objective optimization design problem. The difficulty of multi-objective radiation shielding optimization lies in the fact that the various design objectives often conflict with each other. Improving one objective often leads to the degradation of others. For example, a reduction in radiation dose rate typically results in an increase in shield weight, while a reduction in shield weight typically results in an increase in radiation dose rate. Consequently, it is impossible to achieve optimal results simultaneously for multiple design objectives. Therefore, the ultimate solution to the radiation shielding optimization problem is to coordinate and balance the various design objectives, achieving a compromise solution that satisfies all requirements and achieves the optimal overall solution.

[0005] Traditional radiation shielding design often relies heavily on design experience, which is inefficient, subject to high uncertainty, and requires a high level of designer experience. Methods based on manual experience are prone to omissions in optimization solutions and are complex and time-consuming. Therefore, developing an intelligent optimization method applicable to shielding schemes for various nuclear installations remains an unresolved issue. Summary of the Invention

[0006] In order to solve the above problems, the present invention provides a multi-objective shielding optimization method and system based on a non-dominated sorting genetic algorithm to achieve simultaneous optimization of multiple objectives such as dose rate, volume of shielding material, weight of shielding material, etc., thereby improving the optimization efficiency of the shielding scheme.

[0007] In order to achieve the above object, the present invention mainly includes the following aspects:

[0008] In a first aspect, an embodiment of the present invention provides a multi-objective shielding optimization method based on a non-dominated sorting genetic algorithm, comprising:

[0009] Based on the acquired source term, number of shielding layers, and shielding materials, thickness limits, and upper and lower limits of each layer in the radiation shielding scenario, multiple initial shielding schemes are randomly generated, and the objective function value corresponding to each initial shielding scheme is determined; wherein the shielding scheme includes shielding materials and shielding thickness, and the objective function includes dose rate, volume, and weight of the shielding material;

[0010] According to the objective function value, the plurality of initial shielding schemes are sorted according to the dominance relationship to generate a first-generation shielding scheme, the first-generation shielding schemes are sorted according to the non-dominance relationship, and then a second-generation shielding scheme is generated by a genetic operator and the corresponding objective function value is calculated; the first-generation shielding schemes and the second-generation shielding schemes are merged and sorted to obtain different solution sets, and shielding schemes are sequentially selected from each solution set to the next-generation shielding scheme, and the objective function value corresponding to the next-generation shielding scheme is updated until a termination condition is satisfied;

[0011] According to the optimized shielding scheme, the shielding material and shielding thickness in the current radiation shielding scenario are output.

[0012] In one possible implementation, the source term includes total source intensity and energy spectrum; the source term and initial shielding scheme in the radiation shielding scenario are input into the particle transport equation to calculate the dose rate, volume and weight of the shielding material.

[0013] In a possible implementation, the non-dominance relationship ranking is to sort the objective function values ​​of each shielding scheme from high to low according to the hierarchy.

[0014] In one possible implementation, shielding solutions are selected from each solution set in sequence to the next generation shielding solution until the number of shielding solutions reaches the total number of shielding solutions; if the number of shielding solutions in the next solution set exceeds the required number of solutions, all shielding solutions on the solution set are sorted according to the crowding distance or the reference solution, and shielding solutions are selected from the next generation shielding solution according to the sorting result until the number of shielding solutions reaches the total number of shielding solutions.

[0015] In one possible implementation, a ranking algorithm based on a reference solution is used to emphasize non-dominated shielding solutions that are closer to the reference solution. Specifically, the algorithm includes: constructing an ideal solution transformation objective function, determining the limit points of each coordinate axis and constructing a hyperplane, and then calculating the intercept and normalizing the objective function;

[0016] Determine a reference solution on the hyperplane, associate each shielding solution with the reference solution, and determine a reference line of the reference solution closest to each shielding solution; the reference line is a line connecting the reference solution and the ideal solution;

[0017] For the reference line with the least number of associated solutions, perform the following operations multiple times until the number of next-generation solutions equals the total number of solutions:

[0018] When the number of schemes associated with the reference line is 0, the scheme whose current solution set is closer to the corresponding reference line is retained; when the number of schemes associated with the reference line is greater than 0, one is randomly selected from the shielding schemes associated with the reference line in the current solution set to enter the next generation of shielding schemes.

[0019] In one possible implementation, a lower bound and an upper bound of the objective function are set; if the objective function is less than the lower bound, the objective function adds an offset to characterize the degree to which the objective function deviates from the lower bound; or, if the objective function is greater than the upper bound, the objective function adds an offset to characterize the degree to which the objective function deviates from the upper bound.

[0020] In a possible implementation, integer coding is used for the shielding material; and / or real coding is used for the shielding thickness.

[0021] In a second aspect, an embodiment of the present invention provides a multi-objective shielding optimization system based on a non-dominated sorting genetic algorithm, comprising:

[0022] a generation module for generating multiple initial shielding schemes based on the acquired source term, number of shielding layers, shielding materials, and upper and lower thickness limits of each layer in the radiation shielding scenario, and determining the objective function value corresponding to each initial shielding scheme; wherein the shielding scheme includes shielding materials and shielding thickness, and the objective function includes dose rate, volume, and weight of the shielding material;

[0023] An optimization module is configured to sort the plurality of initial shielding schemes according to a dominance relationship based on an objective function value to generate a first-generation shielding scheme, sort the first-generation shielding schemes according to a non-dominance relationship, generate a second-generation shielding scheme using a genetic operator, and calculate a corresponding objective function value; merge and sort the first-generation shielding schemes and the second-generation shielding schemes to obtain different solution sets, sequentially select a shielding scheme from each solution set to a next-generation shielding scheme, and update the objective function value corresponding to the next-generation shielding scheme until a termination condition is satisfied;

[0024] The output module is used to output the shielding material and shielding thickness in the current radiation shielding scenario according to the optimized shielding solution.

[0025] In a third aspect, an embodiment of the present invention provides a computer device comprising: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the computer device is running, the processor and the memory communicate through the bus, and when the machine-readable instructions are executed by the processor, the steps of the multi-objective shielding optimization method based on the non-dominated sorting genetic algorithm as described in the first aspect and any possible implementation scheme of the first aspect are performed.

[0026] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is run by a processor, the steps of the multi-objective shielding optimization method based on the non-dominated sorting genetic algorithm as described in the first aspect and any possible implementation scheme of the first aspect are executed.

[0027] One or more of the above technical solutions have the following beneficial effects:

[0028] The present invention provides a multi-objective shielding optimization method based on a non-dominated sorting genetic algorithm. Based on the acquired source term, number of shielding layers, and shielding materials, thickness limits, and upper and lower limits of each layer in a radiation shielding scenario, an initial shielding scheme is generated and the objective function value corresponding to the initial shielding scheme is determined. Based on the objective function value, multiple initial shielding schemes are sorted according to dominance relationships to generate a first-generation shielding scheme. These first-generation shielding schemes are then sorted according to non-dominance relationships. A second-generation shielding scheme is generated using genetic operators such as crossover, mutation, and recombination, and the corresponding objective function value is calculated. The first and second-generation shielding schemes are merged and sorted to obtain different solution sets. From each solution set, shielding schemes are sequentially selected as the next-generation shielding scheme, and the objective function value corresponding to the next-generation shielding scheme is updated until a termination condition is met. Based on the optimized shielding scheme, the shielding material and shielding thickness for the current radiation shielding scenario are output. This method can simultaneously optimize multiple objectives, such as dose rate, shielding material volume, and shielding material weight, thereby improving the optimization efficiency of the shielding scheme.

[0029] Moreover, it can assist shielding designers to quickly search for feasible shielding solutions under given conditions, and select a group of approximately optimal shielding solutions for designers' reference, thereby reducing the workload of traditional experience-based shielding design and improving the efficiency of shielding design. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0031] Figure 1 This is an overall framework diagram of a multi-objective shielding optimization method based on a non-dominated sorting genetic algorithm provided by an embodiment of the present invention;

[0032] Figure 2 1 is a flow chart of a multi-objective shielding optimization method based on a non-dominated sorting genetic algorithm provided by an embodiment of the present invention;

[0033] Figure 3 This is an example diagram of a multi-objective shielding optimization method based on a non-dominated sorting genetic algorithm provided by an embodiment of the present invention;

[0034] Figure 4 is an example diagram of a sorting algorithm based on a reference solution provided in an embodiment of the present invention;

[0035] Figure 5 is a schematic diagram of changes in shielding material weight as the number of iterations increases, according to an embodiment of the present invention;

[0036] Figure 6 is a schematic diagram of the change of the dose rate as the number of iterations increases according to an embodiment of the present invention;

[0037] Figure 7 Schematic diagram of the objective function relationship provided by an embodiment of the present invention;

[0038] Figure 8 is a schematic diagram of the change of the hypervolume as the number of iterations increases according to an embodiment of the present invention;

[0039] Figure 9 1 is a schematic structural diagram of a multi-objective shielding optimization system based on a non-dominated sorting genetic algorithm provided by an embodiment of the present invention;

[0040] Figure 10 It is a structural diagram of a computer device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0042] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0043] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0044] In the field of radiation protection technology, shielding design for modern complex nuclear devices (such as nuclear power plants, large nuclear facilities, and accelerators) involves complex structures and neutron and photon distributions. Furthermore, materials that offer excellent shielding performance for both neutrons and photons at different energies do not exist. Furthermore, radiation shielding design often requires consideration of multiple design objectives, such as minimizing radiation levels, achieving lightweight, compact, and economical shielding. These often conflict with each other, creating challenges in shielding design optimization. Methods based on manual experience are prone to omissions in optimization solutions and result in complex and time-consuming processes.

[0045] Based on this, this embodiment provides a multi-objective shielding optimization method based on a non-dominated sorting genetic algorithm, which is combined with a transport calculation system. Specifically, it includes an initial input module, a transport calculation module, a coupling module, an optimization calculation module, an output module, and a data processing and visualization module. The initial input module is used to input a discrete vertical scale program input file including the number of shielding layers, the shielding materials of each layer, and the upper and lower limits of thickness; the transport calculation module is used to call the discrete vertical scale program to calculate the objective function value; the coupling module is used to pass the objective function value calculated by the transport calculation module to the optimization calculation module, and pass the random variables generated by the optimization calculation module to the transport calculation module; the optimization calculation module is used to optimize the shielding scheme; the output module is used to output the optimized shielding scheme; and the data processing and visualization module is used to process and display the objective function value.

[0046] See also Figure 2 , Figure 2 FIG. 1 is a flow chart of a multi-objective shielding optimization method based on a non-dominated sorting genetic algorithm provided by an embodiment of the present invention. Figure 2 As shown, the method specifically includes the following steps:

[0047] S201: Generate an initial shielding scheme based on the acquired source term, number of shielding layers, shielding materials of each layer, and upper and lower limits of thickness in the radiation shielding scenario, and determine an objective function value corresponding to the initial shielding scheme.

[0048] In specific implementations, the source terms in the radiation shielding scenario are collected using appropriate equipment. The source terms include total source intensity and energy spectrum, and the number of shielding layers, as well as the shielding material, thickness limits, and upper and lower limits for each layer, are set. Based on the number of shielding layers, the shielding material, and thickness limits for each layer, an initial shielding scheme is generated. The source terms in the radiation shielding scenario and the initial shielding scheme are input into a particle transport equation to calculate the dose rate and the volume and weight of the shielding material. The particle transport equation is solved using a discrete ordinate method, preferably a one-dimensional discrete ordinate method.

[0049] Specifically, the dose rate includes the neutron dose rate and the photon dose rate. The neutron dose rate and the photon dose rate are determined based on the grid width, total source intensity, and energy spectrum of the initial shielding scheme, and are determined by the following formula:

[0050]

[0051] Where D n Indicates neutron dose rate, mSv / h, G n represents the number of neutron energy groups, φ n,g Indicates the neutron injection rate, n / (cm 2 ·s), C n,g Neutron fluence rate-dose rate conversion factor, (mSv / h) / (n / (cm 2 ·s)), D γ Indicates photon dose rate, mSv / h, G γ represents the number of photon energy groups, φ γ,g represents the photon fluence rate, γ / (cm 2 ·s), C γ,g represents the photon fluence rate-dose rate conversion factor, (mSv / h) / (γ / (cm 2 ·s)).

[0052] The volume and weight of shielding materials are calculated as follows:

[0053]

[0054] Where V represents the volume of shielding material, cm 3 , R represents the thickness of the shielding material, cm, H represents the height of the shielding material, cm, W represents the weight of the shielding material, t, ρ represents the density of the shielding material, g / cm 3 .

[0055] The objective function can be expressed as:

[0056]

[0057] Where x is an n-dimensional decision variable, x=(x1,x2,…,x n)∈X, specifically including the geometric dimensions of the shielding structure and the shielding materials, etc.; X is the value space of the decision variable; z is the m-dimensional objective function, mainly including the dose rate, shielding material weight, shielding structure size and cost, etc., z=(z1,z2,…,z m )∈Z; Z is the value space of the objective function; the objective function F(x) defines the mapping function from the radiation shielding decision variable to the objective function; g i (x)≤0 defines q inequality constraints; h j (x)=0 defines p equality constraints.

[0058] S202: Sort the multiple initial shielding schemes according to the dominance relationship according to the objective function value to generate a first-generation shielding scheme, sort the first-generation shielding schemes by non-dominance relationship, and then generate a second-generation shielding scheme through a genetic operator and calculate the corresponding objective function value; merge and sort the first-generation shielding schemes and the second-generation shielding schemes to obtain different solution sets, select shielding schemes from each solution set to the next-generation shielding scheme in turn, and update the objective function value corresponding to the next-generation shielding scheme until the termination condition is met.

[0059] In specific implementation, the main features of the non-dominated sorting genetic algorithm are as follows:

[0060] Feature 1: Sorting

[0061] Using classification methods, multiple optimal shielding solutions can be searched simultaneously, and diversity is maintained through the calculation of crowding distances or reference solutions. The final optimal solution of the multi-objective shielding optimization method corresponds to a single solution set. The non-dominated relationship ranking is based on the objective function value of each shielding solution, sorted from high to low using the F1, F2, …, Fn hierarchy.

[0062] Feature 2: Elite Retention Strategy

[0063] The first-generation and second-generation screening schemes are combined, and the non-dominated sorting level is used as the scheme fitness value. The optimal scheme is then retained to achieve elite retention. This elite retention strategy prevents the optimal screening scheme from being destroyed due to crossover, improving the global convergence ability of the optimization method.

[0064] Feature 3: Crossover Variation

[0065] Crossover is the most effective step in improving optimization algorithms. It generates new solutions by combining the genetic information contained in the shielding scheme (including shield thickness, material, etc.). Mutation refers to the changes in the genes of the next generation of shielding schemes caused by small-probability perturbations, simulating the phenomenon of accidental genetic mutations during evolution.

[0066] Feature 4: Mixed encoding of integer and real types

[0067] Integer coding solves combinatorial optimization problems, while real - valued coding solves constraint optimization problems. Coding is the process of mapping the solution space of a problem onto the coding space (i.e., the search space). The mapping from the coding space to the solution space of the problem is called decoding. For the shielding optimization method, according to the characteristics of the decision variables, integer coding is used for the shielding material; and / or real - valued coding is used for the shielding thickness, thereby improving the efficiency of coding and decoding.

[0068] The termination condition includes: the current iteration number is the preset maximum iteration number.

[0069] The following Figure 3 shows an example to illustrate how to generate the next - generation shielding scheme. Assume that the number of shielding schemes in each generation is 6. The numbers of the first - generation shielding schemes are (1, 2, 3, 4, 5, 6), and the numbers of the second - generation shielding schemes are (a, b, c, d, e, f). From Figure 4 it can be seen the dominance relationship between the first - generation shielding schemes and the second - generation shielding schemes. First, the first - generation shielding schemes and the second - generation shielding schemes are combined to get 12 schemes, and then sorted to obtain 4 solution sets. The next - generation shielding scheme first selects 3 schemes (a, e, 5) from the first solution set, and then selects 3 schemes (3, b, 1) or (3, b, d) from the second solution set according to the crowding distance or the reference - scheme sorting. A total of 6 schemes enter the next - generation shielding scheme.

[0070] As an optional implementation, shielding schemes are sequentially selected from each solution set to the next - generation shielding scheme until the number of shielding schemes reaches the total number of shielding schemes; if the number of shielding schemes in the next solution set exceeds the required number of schemes, all the shielding schemes in this solution set are sorted according to the crowding distance or the reference - scheme sorting, and shielding schemes are selected to the next - generation shielding scheme according to the sorting result until the number of shielding schemes reaches the total number of shielding schemes.

[0071] In specific implementation, Figure 4 any one scheme (such as scheme a) is selected. A coordinate system is established at scheme a. Region 1 is the region that can dominate scheme a. For any point with a constraint - parameter vector X in this region, f1(X) < f1(a) and f2(X) < f2(a). Similarly, any scheme in region 2 is dominated by scheme a. Non - dominated sorting defines the schemes that are not dominated by any scheme in region 1 as the optimal - solution set F1. Then, after removing the optimal - solution set F1, re - sorting is performed to obtain the sub - optimal - solution set F2, and so on until the sorting is finally completed.

[0072] To maintain the diversity of screening solutions and prevent premature maturation and local optima, a crowding distance ranking method is used for selection. Within the same solution set, solutions with larger crowding distances are prioritized for the next generation. The crowding distance is calculated based on the non-dominated sorting result and is calculated by calculating the sum of the normalized distances between three adjacent solutions in the same solution set on each objective function.

[0073] like Figure 4 As shown, the crowding distance is calculated as follows:

[0074]

[0075]

[0076] Where, d d and d1 is the crowding distance between point d and point 1; f 1,1 and f 3,1 are the two adjacent objective function values ​​of point d on f1; f 3,2 and f 1,2 are the two adjacent objective function values ​​of point d on f2; f b,1 and f d,1 are the two adjacent objective function values ​​of point 1 on f1; f d,2 and f b,2 are the two adjacent objective function values ​​of point 1 on f2; f max,1 and f min,1 are the upper and lower extreme values ​​of f1 respectively; f max,2 and f min,2 are the upper and lower extreme values ​​of f2 respectively.

[0077] For high-dimensional multi-objective optimization problems (multi-objective optimization problems with more than 3 objectives), the crowding distance sorting algorithm has defects in maintaining diversity. The resulting solutions are unevenly distributed on the non-dominated layer, causing the algorithm to fall into a local optimum. As an optional implementation, a sorting algorithm based on the reference solution is used to emphasize the non-dominated shielding solutions that are closer to the reference solution. Specifically, the following methods are used:

[0078] In the first step, each solution is adaptively normalized. First, the ideal solution transformation objective function is constructed. Then, the limit points of each coordinate axis are determined and a hyperplane is constructed. Finally, the intercept is calculated and the objective function is normalized.

[0079] The second step is to determine the reference solutions on the hyperplane. For m objective functions, each objective function is divided into p segments. When the number of reference solutions is large, reference solutions for the inner and outer hyperplanes can be generated, thereby reducing the number of reference solutions while ensuring a wide distribution of reference solutions. The total number of reference solutions is calculated according to the following formula:

[0080]

[0081] Where m represents the number of objective functions, p represents the number of objective function segments, and H represents the total number of reference solutions.

[0082] The third step is to associate each solution with the reference solution. Determine the reference line of each solution that is closest to the reference solution, where the reference line is the line connecting the reference solution and the ideal solution. Figure 4 In the solution set 1, scheme a, scheme e and scheme 5 are associated with reference lines i, ii and iii respectively; for solution set 2, scheme 3 is associated with reference line i, scheme d and scheme 1 are both associated with reference line ii, and scheme b is associated with reference line iii.

[0083] Step 4: Scheme selection. For the reference line with the least number of associated schemes, perform the following operations several times until the number of next-generation schemes equals the total number of schemes: 1) When the number of associated schemes for a reference line is 0, retain the schemes in the current solution set that are closer to the corresponding reference line. 2) When the number of associated schemes for a reference solution is greater than 0, randomly select one from the shielding schemes associated with the reference line in the current solution set to enter the next-generation shielding scheme. Figure 4 It can be seen that reference line ii is associated with plan e, so plan d or plan 1 is randomly selected to enter the next generation.

[0084] As an optional implementation, a lower bound and an upper bound of the objective function are set; if the objective function is less than the lower bound, the objective function adds an offset to characterize the degree to which the objective function deviates from the lower bound; or, if the objective function is greater than the upper bound, the objective function adds an offset to characterize the degree to which the objective function deviates from the upper bound.

[0085] In the specific implementation, in order to easily find the optimal solution, constraints and penalty functions are added to the objective function as follows:

[0086]

[0087] Where, f l and f h They represent the lower and upper bounds of the objective function constraints, respectively, and p i represents the penalty function.

[0088] After the objective function is calculated, the penalty function is used to process the objective function. If the objective function is less than the lower bound, the objective function is increased by an offset, and the offset p i ×(f l -f i ) / (f h -f l ) represents the degree to which the objective function deviates from the lower bound. If the objective function is greater than the upper bound, the objective function increases an offset, and the offset pi ×(f l -f i ) / (f h -f l ) represents the degree to which the objective function deviates from the upper bound.

[0089] S203: Outputting the shielding material and shielding thickness in the current radiation shielding scenario according to the optimized shielding solution.

[0090] In the specific implementation, high-dimensional result visualization technology (such as scatter plots, etc.) is used to assist users in judging the diversity of solutions. Graphs of shielding material weight and dose rate as algebraically changing and the relationship between each objective function are drawn. Examples are as follows: Figure 5 、 Figure 6 and Figure 7 For each generation of all shielding schemes, a hypervolume diagram is drawn, for example Figure 8 As shown. Hypervolume represents the volume of the target space enclosed by the set of non-dominated solutions obtained by the algorithm and the reference solution. The larger the hypervolume value, the better the overall performance of the algorithm. Hypervolume can be used to evaluate both the diversity and convergence of solutions. The hypervolume calculation process is briefly described as follows:

[0091] First, for the case of high-dimensional target space (number of targets r>3), by continuously mapping to r-1 dimensional target space, the high-dimensional target space problem is recursively transformed into low-dimensional target space to reduce the complexity of the original problem.

[0092] Next, in the three-dimensional case, sort the solutions in the set in descending order according to their values ​​on the first-dimensional target. Based on the sorted values, cut the polyhedron enclosed by the valid solutions and the reference solution into n pieces, projecting each piece onto the other two-dimensional target to obtain the corresponding projected polygons. The volume of each piece is the product of the area of ​​its corresponding projected polygon and the depth of the piece.

[0093] Finally, in the two-dimensional case, the effective solutions in the set are sorted in descending order according to their values ​​on the first-dimensional objective, and their corresponding hypervolume indicators are calculated.

[0094] In this way, multiple objectives such as dose rate, volume of shielding material, weight of shielding material, etc. can be optimized simultaneously through this method, thereby improving the optimization efficiency of the shielding solution.

[0095] See also Figure 9 The embodiment of the present invention further provides a multi-objective shielding optimization system based on a non-dominated sorting genetic algorithm. The multi-objective shielding optimization system 900 includes:

[0096] A generation module 910 is configured to generate multiple initial shielding schemes based on the acquired source term, number of shielding layers, shielding materials, and upper and lower thickness limits of each layer in the radiation shielding scenario, and determine an objective function value corresponding to each initial shielding scheme; wherein the shielding scheme includes shielding materials and shielding thickness, and the objective function includes dose rate, volume, and weight of the shielding material;

[0097] Optimization module 920 is configured to sort the plurality of initial shielding solutions according to a dominating relationship based on an objective function value to generate a first-generation shielding solution, sort the first-generation shielding solutions according to a non-dominating relationship to generate a second-generation shielding solution and calculate the corresponding objective function value; merge and sort the first-generation shielding solutions and the second-generation shielding solutions to obtain different solution sets, sequentially select shielding solutions from each solution set to a next-generation shielding solution, and update the objective function value corresponding to the next-generation shielding solution until a termination condition is satisfied;

[0098] The output module 930 is used to output the shielding material and shielding thickness in the current radiation shielding scenario according to the optimized shielding solution.

[0099] The multi-objective shielding optimization system based on the non-dominated sorting genetic algorithm provided in this embodiment is used to implement the aforementioned multi-objective shielding optimization method based on the non-dominated sorting genetic algorithm. Therefore, the specific implementation method of the multi-objective shielding optimization system based on the non-dominated sorting genetic algorithm can be found in the embodiment part of the multi-objective shielding optimization method based on the non-dominated sorting genetic algorithm in the previous text, and will not be repeated here.

[0100] See also Figure 10 , Figure 10 FIG. 1 is a schematic diagram of a computer device according to an embodiment of the present invention. Figure 10 As shown in FIG, the computer device 1000 includes a processor 1010 , a memory 1020 and a bus 1030 .

[0101] The memory 1020 stores machine-readable instructions executable by the processor 1010. When the computer device 1000 is running, the processor 1010 communicates with the memory 1020 via the bus 1030. When the machine-readable instructions are executed by the processor 1010, the above-mentioned Figure 2 The specific implementation of the steps of the multi-objective shielding optimization method based on the non-dominated sorting genetic algorithm in the method embodiment shown can be found in the method embodiment and will not be repeated here.

[0102] Based on the same inventive concept, an embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is run by a processor, the steps of the multi-objective shielding optimization method based on the non-dominated sorting genetic algorithm described in the above method embodiment are executed.

[0103] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing related hardware through a computer program. The program can be stored in a computer-readable storage medium, and when executed, the program can include the processes in the above-described method embodiments. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0104] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A multi-objective shielding optimization method based on non-dominated sorting genetic algorithm, characterized in that: include: Generate an initial shielding scheme based on the acquired source term, number of shielding layers, and shielding materials, thickness limits, and upper and lower limits of each layer in the radiation shielding scenario, and determine an objective function value corresponding to the initial shielding scheme; wherein the shielding scheme includes shielding materials and shielding thickness, and the objective function includes dose rate, volume, and weight of the shielding material; According to the objective function value, the plurality of initial shielding schemes are sorted according to the dominance relationship to generate a first-generation shielding scheme, the first-generation shielding schemes are sorted according to the non-dominance relationship, and then a second-generation shielding scheme is generated by a genetic operator and the corresponding objective function value is calculated; the first-generation shielding schemes and the second-generation shielding schemes are merged and sorted to obtain different solution sets, and shielding schemes are sequentially selected from each solution set to the next-generation shielding scheme, and the objective function value corresponding to the next-generation shielding scheme is updated until a termination condition is satisfied; Among them, the constraints and penalty functions added to the objective function are as follows: in, and denote the lower and upper bounds of the objective function constraints, respectively. represents the penalty function; If the objective function is less than the lower bound, the objective function increases by an offset. Indicates the degree to which the objective function deviates from the lower bound; if the objective function is greater than the upper bound, the objective function increases an offset, which Indicates the degree to which the objective function deviates from the upper bound; According to the optimized shielding scheme, the shielding material and shielding thickness in the current radiation shielding scenario are output.

2. The multi-objective shielding optimization method based on non-dominated sorting genetic algorithm according to claim 1, characterized in that: The source terms include total source intensity and energy spectrum; The source terms and initial shielding scheme in the radiation shielding scenario are input into the particle transport equation to calculate the dose rate, volume and weight of the shielding material.

3. The multi-objective shielding optimization method based on non-dominated sorting genetic algorithm according to claim 1, characterized in that: The non-dominated relationship sorting is to sort the objective function value of each shielding scheme from high to low according to the hierarchy.

4. The multi-objective shielding optimization method based on non-dominated sorting genetic algorithm according to claim 1, characterized in that: Select shielding solutions from each solution set to the next generation shielding solution in turn until the number of shielding solutions reaches the total number of shielding solutions; if the number of shielding solutions in the next solution set exceeds the required number of solutions, sort all shielding solutions on the solution set according to the crowding distance or the reference solution, and select shielding solutions to the next generation shielding solution according to the sorting results until the number of shielding solutions reaches the total number of shielding solutions.

5. The multi-objective shielding optimization method based on non-dominated sorting genetic algorithm according to claim 1, characterized in that: A ranking algorithm based on the reference scheme is used to emphasize the non-dominated shielding schemes that are closer to the reference scheme. Specifically, the algorithm includes: constructing the ideal scheme transformation objective function, determining the limit points of each coordinate axis and constructing the hyperplane, then finding the intercept and normalizing the objective function; Determine a reference solution on the hyperplane, associate each shielding solution with the reference solution, and determine a reference line of each shielding solution closest to the reference solution; the reference line is a line connecting the reference solution and the ideal solution; For the reference line with the least number of associated solutions, perform the following operations multiple times until the number of next-generation solutions equals the total number of solutions: When the number of schemes associated with the reference line is 0, the schemes whose current solution set is closer to the corresponding reference scheme are retained; when the number of schemes associated with the reference line is greater than 0, one is randomly selected from the shielding schemes associated with the reference scheme in the current solution set to enter the next generation of shielding schemes.

6. The multi-objective shielding optimization method based on non-dominated sorting genetic algorithm according to claim 1, characterized in that: Set the lower and upper bounds of the objective function; if the objective function is less than the lower bound, then add an offset to the objective function to represent the degree to which the objective function deviates from the lower bound; or, if the objective function is greater than the upper bound, then add an offset to the objective function to represent the degree to which the objective function deviates from the upper bound.

7. The multi-objective shielding optimization method based on non-dominated sorting genetic algorithm according to claim 1, characterized in that: Integer encoding is used for the shielding material; and / or real encoding is used for the shielding thickness.

8. A multi-objective shielding optimization system based on non-dominated sorting genetic algorithm, characterized in that: include: a generation module for generating multiple initial shielding schemes based on the acquired source term, number of shielding layers, shielding materials, and upper and lower thickness limits of each layer in the radiation shielding scenario, and determining the objective function value corresponding to each initial shielding scheme; wherein the shielding scheme includes shielding materials and shielding thickness, and the objective function includes dose rate, volume, and weight of the shielding material; An optimization module is configured to sort the plurality of initial shielding schemes according to a dominance relationship based on an objective function value to generate a first-generation shielding scheme, sort the first-generation shielding schemes according to a non-dominance relationship, generate a second-generation shielding scheme using a genetic operator, and calculate a corresponding objective function value; merge and sort the first-generation shielding schemes and the second-generation shielding schemes to obtain different solution sets, sequentially select a shielding scheme from each solution set to a next-generation shielding scheme, and update the objective function value corresponding to the next-generation shielding scheme until a termination condition is satisfied; Among them, the constraints and penalty functions added to the objective function are as follows: in, and denote the lower and upper bounds of the objective function constraints, respectively. represents the penalty function; If the objective function is less than the lower bound, the objective function increases by an offset. Indicates the degree to which the objective function deviates from the lower bound; if the objective function is greater than the upper bound, the objective function increases an offset, which Indicates the degree to which the objective function deviates from the upper bound; The output module is used to output the shielding material and shielding thickness in the current radiation shielding scenario according to the optimized shielding solution.

9. A computer device, characterized in that: include: A processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the computer device is running, the processor and the memory communicate via the bus, and when the machine-readable instructions are executed by the processor, the steps of the multi-objective shielding optimization method based on the non-dominated sorting genetic algorithm as described in any one of claims 1 to 7 are performed.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which, when executed by a processor, executes the steps of the multi-objective shielding optimization method based on a non-dominated sorting genetic algorithm according to any one of claims 1 to 7.

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