A metamaterial robust optimization method based on genetic algorithm

Abstract

The application provides a metamaterial robust optimization method based on a genetic algorithm, and relates to the technical field of metamaterial optimization. The application determines adjustable parameters of electromagnetic metamaterial, constructs individual vectors by using the adjustable parameters, and generates an initial population; simulates equivalent permeability corresponding to each individual vector through a performance simulation model; determines the distribution of the equivalent permeability in the neighborhood space of each individual vector, and constructs a structure family thickness index; selects individual vectors based on the equivalent permeability and the structure family thickness index to perform random crossover or boundary crossover, executes random mutation strategies and pullback mutation strategies on the individual after the crossover is completed, iterates until a preset iteration number is reached, and exports the adjustable parameters of the individual vector with the maximum equivalent permeability in the last generation as optimized adjustable parameters.

Description

Technical Field

[0001] This invention relates to the field of metamaterial optimization technology, specifically to a robust metamaterial optimization method based on genetic algorithms. Background Technology

[0002] Electromagnetic metamaterials, due to their unique electromagnetic properties, have shown great potential for applications in communication, stealth, and sensing. Their performance is highly dependent on the precise design and optimization of structural parameters. However, traditional optimization methods often only perform deterministic optimization for a single performance index, neglecting the impact of uncertainties such as manufacturing errors and environmental disturbances on material properties. This results in insufficient robustness and poor stability of the optimized results in practical applications. Furthermore, although genetic algorithms have been introduced into metamaterial parameter optimization, there is still a lack of a systematic evaluation and dynamic adjustment mechanism for performance robustness under parameter perturbations. This makes it difficult to efficiently and reliably obtain metamaterial structural solutions that combine high performance and strong stability in complex parameter spaces.

[0003] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0004] The purpose of this invention is to provide a robust optimization method for metamaterials based on genetic algorithms to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A robust optimization method for metamaterials based on genetic algorithms, comprising the following steps:

[0007] Step 1: Determine the types of adjustable parameters of the electromagnetic metamaterial and the predetermined range of each adjustable parameter. Within the predetermined range, obtain a random parameter value corresponding to each adjustable parameter. Combine all the obtained random parameter values ​​to form an individual vector. Generate an initial population based on multiple individual vectors.

[0008] Step 2: Simulate the equivalent permeability corresponding to each individual vector through a performance simulation model. For each type of adjustable parameter in each individual vector, set the perturbation range, generate the neighborhood space of the individual vector based on the perturbation range, search for the distribution of equivalent permeability in the neighborhood space, and construct the structure family thickness index.

[0009] Step 3: Select individual vectors based on equivalent permeability and structure family thickness indices and place them into the crossover population. Randomly select two individual vectors from the crossover population and determine the relationship between the two individual vectors based on their adjustable parameters. Then, determine the crossover strategy based on the relationship between the two individual vectors. The crossover strategy includes a random crossover strategy and a boundary crossover strategy. Place the individual vectors that implement the random crossover strategy into the random mutation population and place the individual vectors that implement the boundary crossover strategy into the risk mutation population.

[0010] Step 4: Execute the random mutation strategy on the random mutation population. For each individual vector in the risk mutation population, determine the crossover effect qualification based on the individual vector and the equivalent permeability of its crossover parent. Determine whether to execute the random mutation strategy or the pull-back mutation strategy based on the qualification.

[0011] Step 5: Place the individual vectors that have undergone random mutation and pullback mutation into the new initial population and iterate until the preset number of iterations is reached. In the initial population of the last iteration, select the adjustable parameter from the individual vector with the largest equivalent permeability as the optimized adjustable parameter.

[0012] Furthermore, the types of adjustment parameters include the coil width, coil spacing, outermost coil side length, and external lumped capacitance value of each element of the square-structured open-loop resonant ring.

[0013] Furthermore, the logic for searching the equivalent permeability distribution within the neighborhood space and constructing the structure family thickness index is as follows:

[0014] For each individual vector, a scaling factor is set, which is greater than 0.8 and less than 1. The product of the individual vector and the scaling factor is calculated and is called the equivalent permeability threshold of the individual vector.

[0015] In the neighborhood space of the individual vector, N sets of adjustable parameters of electromagnetic metamaterials are randomly generated, and the corresponding equivalent permeability is obtained. The number of adjustable parameter sets of electromagnetic metamaterials with equivalent permeability greater than the threshold of equivalent permeability of the individual vector is counted, and the result is multiplied by N to obtain the structure family thickness index.

[0016] Furthermore, the logic for selecting individual vectors to be placed into the crossover population based on equivalent permeability and structure family thickness indices is as follows:

[0017] A preset threshold for the structure family thickness index is set. All individual vectors in the initial population whose structure family thickness index is greater than the threshold are placed into the selection population. Each individual vector in the selection population is set as a selection label.

[0018] In the selection population, two individual vectors with the label "unselected" are randomly selected and labeled as selected. The individual vector with the larger equivalent permeability is then placed into the crossover population. The selection population is then traversed.

[0019] Furthermore, the relationship between the two individual vectors includes both same-family and different-family relationships. The logic for determining the relationship between the two individual vectors is as follows:

[0020] If the individual vector with the smallest equivalent permeability is in the neighborhood space of the individual vector with the largest equivalent permeability, then the two individual vectors are related as family members; otherwise, the two individual vectors are related as family members.

[0021] Furthermore, the logic for determining the crossover strategy based on the relationship between the two individual vectors is as follows:

[0022] If two individual vectors are related by the same family, then the boundary crossing strategy is executed; if two individual vectors are related by different families, then the random crossing strategy is executed.

[0023] Furthermore, the boundary crossing strategy is as follows:

[0024] In the crossover of individual vectors, the increment step size of each adjustable parameter is set, one adjustable parameter is selected, called the boundary adjustable parameter, and the other adjustable parameters are kept unchanged. The magnitudes of the boundary adjustable parameters of the two individual vectors are compared.

[0025] If the individual vector with the largest equivalent permeability has the largest adjustable boundary parameter, then each time the adjustable boundary parameter of the individual vector with the largest equivalent permeability is subtracted by the increment step size of the adjustable boundary parameter, and the partial derivative of the equivalent permeability with respect to the adjustable boundary parameter is calculated. The absolute difference between the partial derivatives before and after subtracting the adjustable boundary parameter is calculated. This process is repeated until the absolute difference is greater than a preset threshold. The adjustable boundary parameter is then derived and used as the boundary of the adjustable parameter in the individual vector with the largest equivalent permeability. All adjustable parameters are traversed, and the boundaries of the adjustable parameters of the individual vectors are used to form the boundary individual vector. The individual vector with the largest equivalent permeability and the boundary individual vector are then randomly crossed.

[0026] If the individual vector with the smallest equivalent permeability has the largest adjustable boundary parameter, then each time, the adjustable boundary parameter of the individual vector with the largest equivalent permeability is added to the incremental step size of the adjustable boundary parameter, and the partial derivative of the equivalent permeability with respect to the adjustable boundary parameter is calculated. The absolute difference between the partial derivatives before and after subtracting the incremental step size of the adjustable boundary parameter is calculated. This process is repeated until the absolute difference is greater than a preset threshold. The adjustable boundary parameter is then derived and used as the boundary of the adjustable parameter in the individual vector with the largest equivalent permeability. All adjustable parameters are traversed, and the boundaries of the adjustable parameters of the individual vectors are used to form the boundary individual vector. The individual vector with the largest equivalent permeability and the boundary individual vector are then randomly crossed.

[0027] Furthermore, the logic for determining whether to implement a random mutation strategy or a pull-back mutation strategy based on the crossover effect is as follows: if the crossover effect of the individual vectors is satisfactory, then the random crossover strategy is implemented; if the crossover effect is unsatisfactory, then the pull-back mutation strategy is implemented.

[0028] Furthermore, for each individual vector in the risk-mutated population, if its equivalent permeability is less than 0.8 times the minimum equivalent permeability of the parent individual vector, then the crossover effect of that individual vector is considered qualified; otherwise, the crossover effect is not qualified.

[0029] Furthermore, the logic of the pull-back mutation strategy is as follows:

[0030] Only one adjustable parameter is randomly mutated. If the equivalent permeability of the mutated individual vector is greater than the equivalent permeability before the mutation, then the mutation of that adjustable parameter is retained.

[0031] Perform the same operation on other unmutated adjustable parameters, iterate through all adjustable parameters, and derive the mutated individual vectors.

[0032] Compared with the prior art, the beneficial effects of the present invention are:

[0033] This invention, based on the present invention, quantifies the performance distribution of individual vector neighborhood space by introducing a structure family thickness index. Robustness is incorporated as one of the optimization objectives into the selection and crossover strategies of the genetic algorithm, enabling the optimization process to automatically select individual vectors that maintain high performance under parameter perturbations. By distinguishing between same-family and different-family relationships and employing boundary crossover and random crossover strategies respectively, the balance between in-depth exploration of local optima and global search is enhanced. Furthermore, through a dynamic adjustment mechanism of risk mutation population and pull-back mutation strategy, crossover degradation is effectively avoided, improving the algorithm's convergence efficiency and stability. Ultimately, this method can significantly improve the robustness and reliability of electromagnetic metamaterials in practical manufacturing and applications while ensuring optimal equivalent negative permeability performance, providing an efficient and stable optimization solution for metamaterial design in complex electromagnetic environments. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0035] Figure 2 This is a top view of a metamaterial element. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0037] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0038] Example:

[0039] Please see Figures 1-2 The present invention provides a technical solution:

[0040] A robust optimization method for metamaterials based on genetic algorithms, comprising the following steps:

[0041] Step 1: Determine the types of adjustable parameters of the electromagnetic metamaterial and the predetermined range of each adjustable parameter. Within the predetermined range, obtain a random parameter value corresponding to each adjustable parameter. Combine all the obtained random parameter values ​​to form an individual vector. Generate an initial population based on multiple individual vectors.

[0042] Furthermore, the types of adjustment parameters include the coil width, coil spacing, outermost coil side length, and external lumped capacitance value of each element of the square-structured open-loop resonant ring;

[0043] Please see Figure 2 , Figure 2 A top view of a metamaterial element;

[0044] The predetermined range of adjustable parameters is the coil width. Coil spacing The outermost coil side length and the value of the added lumped capacitance .

[0045] Step 2: Simulate the equivalent permeability corresponding to each individual vector through a performance simulation model. For each type of adjustable parameter in each individual vector, set the perturbation range, generate the neighborhood space of the individual vector based on the perturbation range, search for the distribution of equivalent permeability in the neighborhood space, and construct the structure family thickness index.

[0046] Simulating the equivalent permeability corresponding to each individual vector through performance simulation models can be achieved using existing techniques, including but not limited to S-parameter inversion mathematical models, equivalent circuit models, and waveport excitation methods. The S-parameter inversion method calculates its equivalent constitutive parameters (including equivalent permeability). First, the S-parameters of the equivalent model are obtained through experimental measurements or software simulation. Then, the periodic transfer matrix of the metamaterial element is derived using the transfer matrix method. Next, the S-parameters are obtained again through experimental measurements or software simulation. Finally, by combining the S-parameters and the transfer matrix, the equivalent constitutive parameters of the metamaterial are obtained through inversion.

[0047] Alternatively, FLOQUET port excitation and master-slave boundaries can be set using the full-wave simulation software HFSS 15.0. The setup involves setting two wave port excitations on two surfaces of the air cell along the y-axis in the primitive model settings, with the electric field vector direction parallel to the conductor; setting two-dimensional periodic boundary conditions on the air cell surfaces along the X and Z axes; setting ideal electric boundaries (PEC) on two surfaces along the x-axis and ideal magnetic boundaries (PMC) on two surfaces along the z-axis; and obtaining S-parameters through modeling and simulation in HFSS 15.0 based on the dimensions in the individual vectors, followed by the use of the S-parameter inversion method to obtain the equivalent permeability.

[0048] It should be noted that the equivalent permeability obtained by the above method is a complex number, and the equivalent permeability described in this embodiment is the absolute value of the real part (negative value) of this complex number.

[0049] The disturbance range is typically 1%-5% of a predetermined range.

[0050] Furthermore, the logic for searching the equivalent permeability distribution within the neighborhood space and constructing the structure family thickness index is as follows:

[0051] For each individual vector, a scaling factor is set, which is greater than 0.8 and less than 1. The product of the individual vector and the scaling factor is calculated and is called the equivalent permeability threshold of the individual vector.

[0052] In the neighborhood space of the individual vector, N sets of adjustable parameters of electromagnetic metamaterials are randomly generated, and the corresponding equivalent permeability is obtained. The number of adjustable parameter sets of electromagnetic metamaterials with equivalent permeability greater than the threshold of equivalent permeability of the individual vector is counted, and the result is multiplied by N to obtain the structure family thickness index.

[0053] The thickness index of the structural family reflects the tolerance of metamaterial design to manufacturing errors and the stability of its performance. The larger the index value, the higher the probability that the design can still maintain qualified performance when the parameters are disturbed, that is, the stronger the robustness of the design. The core significance of this approach is to incorporate the uncertainties in the manufacturing process into the optimization process in advance, so that the algorithm can simulate thousands of "manufacturing-testing" cycles in virtual space, thereby guiding the search from simply pursuing peak performance to a robust region that takes into account engineering feasibility.

[0054] Furthermore, the logic for selecting individual vectors to be placed into the crossover population based on equivalent permeability and structure family thickness indices is as follows:

[0055] A preset threshold for the structure family thickness index is set. All individual vectors in the initial population whose structure family thickness index is greater than the threshold are placed into the selection population. Each individual vector in the selection population is set as a selection label.

[0056] In the selection population, two individual vectors with the label "unselected" are randomly selected and labeled as selected. The individual vector with the larger equivalent permeability is then placed into the crossover population. The selection population is then traversed.

[0057] By introducing a structure family thickness index based on population distribution, the optimization objective of the genetic algorithm is transformed from a single design point to a high-performance structural region with continuous existence. This actively suppresses the selection of isolated optimal solutions during the genetic evolution process, thereby achieving endogenous optimization of the robustness of metamaterial structures.

[0058] This selection logic achieves dual screening and targeted propagation of performance and robustness. By setting a threshold for the structure family thickness index, fragile individual vectors with poor robustness are first filtered out, ensuring that the "parents" of subsequent crossover operations all have strong resistance to disturbances, which fundamentally avoids passing on fragile genes. Subsequently, among the robust individual vectors, random pairing and selection of individual vectors with higher equivalent negative permeability are carried out to enter the crossover population, ensuring that the evolutionary direction converges towards both high performance and high stability. The final technical effect is that the algorithm can efficiently cultivate "elite offspring" with both superior electromagnetic performance and strong engineering feasibility, significantly improving the speed and quality of optimization convergence to practical and manufacturable metamaterial design schemes, and avoiding the local optimum traps of "high performance but fragile" or "robust but mediocre" that traditional methods easily fall into.

[0059] Step 3: Select individual vectors based on equivalent permeability and structure family thickness indices and place them into the crossover population. Randomly select two individual vectors from the crossover population and determine the relationship between the two individual vectors based on their adjustable parameters. Then, determine the crossover strategy based on the relationship between the two individual vectors. The crossover strategy includes a random crossover strategy and a boundary crossover strategy. Place the individual vectors that implement the random crossover strategy into the random mutation population and place the individual vectors that implement the boundary crossover strategy into the risk mutation population.

[0060] The random crossover can be achieved using existing technology, which involves randomly selecting elements from the two individual vectors to be crossed and swapping them. This is a conventional technique in the field and will not be elaborated upon here.

[0061] While the aforementioned selection method incorporates robustness optimization into the genetic algorithm's optimization system, in the performance- and robustness-oriented selection phase of a genetic algorithm, if the neighborhood space of a certain individual vector simultaneously possesses many individual vectors with high equivalent negative permeability and large structure family thickness, the individual vectors corresponding to that neighborhood space will continuously receive a higher selection probability. As iterations proceed, the individual vectors of the population will gradually concentrate in this neighborhood space, leading to a significant reduction in the distance between individual vectors in the neighborhood space and the design variable space, exhibiting highly homogeneous characteristics. This process is not caused by random perturbation but is an inevitable result of the selection mechanism. Its direct consequence is the continuous compression of population diversity, making it difficult for subsequent crossover operations to generate new individual vectors with substantial structural differences, thereby weakening the global exploration capability of the genetic algorithm and increasing the risk of the search process getting trapped in a locally stable structure.

[0062] To avoid the aforementioned homogenization phenomenon, this embodiment first identifies the relationship between two individual vectors used for intersection in order to identify the homogenization phenomenon;

[0063] The relationship between the two individual vectors includes both same-family and different-family relationships. The logic for determining the relationship between the two individual vectors is as follows:

[0064] If the individual vector with the smallest equivalent permeability is in the neighborhood space of the individual vector with the largest equivalent permeability, then the two individual vectors are related as family members; otherwise, the two individual vectors are related as family members.

[0065] If two individual vectors belong to the same family, they are considered to be homogeneous individual vectors. If a conventional random crossover strategy is used, there will be virtually no difference before and after the crossover, and the crossover is equivalent to self-replication, which obviously does not conform to the original intention of the crossover. In this embodiment, a boundary crossover method is proposed to avoid the problem of rapid local convergence and homogenization of the population caused by the robustness introduced during the optimization process.

[0066] In the early stages of algorithm iteration, due to the lack of convergence, only a few individual vectors are related as family members, and the probability of two selected individual vectors being related as family members is even smaller. However, as the method iterates, the algorithm tends to retain individual vectors that are related as family members, which can easily lead to local optima. To avoid this situation, this embodiment uses boundary crossing for homogeneous individual vectors.

[0067] Furthermore, the logic for determining the crossover strategy based on the relationship between the two individual vectors is as follows:

[0068] If two individual vectors are related by the same family, then the boundary crossing strategy is executed; if two individual vectors are related by different families, then the random crossing strategy is executed.

[0069] Furthermore, the boundary crossing strategy is as follows:

[0070] In the crossover of individual vectors, the increment step size of each adjustable parameter is set, one adjustable parameter is selected, called the boundary adjustable parameter, and the other adjustable parameters are kept unchanged. The magnitudes of the boundary adjustable parameters of the two individual vectors are compared.

[0071] If the individual vector with the largest equivalent permeability has the largest adjustable boundary parameter, then each time the adjustable boundary parameter of the individual vector with the largest equivalent permeability is subtracted by the increment step size of the adjustable boundary parameter, and the partial derivative of the equivalent permeability with respect to the adjustable boundary parameter is calculated. The absolute difference between the partial derivatives before and after subtracting the adjustable boundary parameter is calculated. This process is repeated until the absolute difference is greater than a preset threshold. The adjustable boundary parameter is then derived and used as the boundary of the adjustable parameter in the individual vector with the largest equivalent permeability. All adjustable parameters are traversed, and the boundaries of the adjustable parameters of the individual vectors are used to form the boundary individual vector. The individual vector with the largest equivalent permeability and the boundary individual vector are then randomly crossed.

[0072] If the individual vector with the smallest equivalent permeability has the largest adjustable boundary parameter, then each time, the adjustable boundary parameter of the individual vector with the largest equivalent permeability is added to the incremental step size of the adjustable boundary parameter, and the partial derivative of the equivalent permeability with respect to the adjustable boundary parameter is calculated. The absolute difference between the partial derivatives before and after subtracting the incremental step size of the adjustable boundary parameter is calculated. This process is repeated until the absolute difference is greater than a preset threshold. The adjustable boundary parameter is then derived and used as the boundary of the adjustable parameter in the individual vector with the largest equivalent permeability. All adjustable parameters are traversed, and the boundaries of the adjustable parameters of the individual vectors are used to form the boundary individual vector. The individual vector with the largest equivalent permeability and the boundary individual vector are then randomly crossed.

[0073] To address the issue of homogenization and search stagnation in the robust optimization of metamaterials by genetic algorithms due to repeated crossovers of dominant individual vectors, this scheme introduces a boundary crossover strategy based on equivalent permeability gradient boundary identification. By keeping other adjustable parameters constant, the sensitivity boundary of equivalent permeability to this parameter is progressively searched along a single adjustable parameter direction. Boundary individual vectors with significant structural differences from the current dominant individual vector within the critical performance range are constructed and crossed with the individual vector with the largest equivalent permeability. This introduces controlled structural perturbation without disrupting the dominant performance direction. This method effectively breaks the parameter convergence path lock caused by homogenized individual vector populations, enhances the structural diversity of the population in the high-performance neighborhood, avoids the algorithm getting trapped in local optima, and improves the exploration efficiency of the equivalent permeability extreme region and its robust boundary. Ultimately, this achieves stable optimization and robust performance improvement of the metamaterial structure near its performance peak.

[0074] Step 4: Execute the random mutation strategy on the random mutation population. For each individual vector in the risk mutation population, determine the crossover effect qualification based on the individual vector and the equivalent permeability of its crossover parent. Determine whether to execute the random mutation strategy or the pull-back mutation strategy based on the qualification.

[0075] While the boundary crossover strategy can solve the problem of homogeneity in individual vectors within the population, it can lead to a decline in the performance of offspring. Therefore, in this embodiment, the performance decline of offspring is determined by comparing the equivalent permeability of the crossover vector with that of the parent generation. Specifically:

[0076] For each individual vector in the risk-mutated population, if its equivalent permeability is less than 0.8 times the minimum equivalent permeability of the parent individual vectors, then the crossover effect of that individual vector is considered acceptable; otherwise, the crossover effect is not acceptable.

[0077] This judgment logic constructs a dynamic crossover effect quality monitoring and classification mechanism. Its significance lies in: by setting a pass / fail threshold based on parent performance (0.8 times the minimum equivalent permeability), it can objectively identify "degenerate individuals" resulting from crossover operations—that is, individuals whose performance is significantly lower than the average level of their parents—and mark them as "unqualified," thereby effectively diagnosing the risk of population degradation that crossover operations may cause in that region. The algorithm can then adopt different follow-up strategies for risky variant populations accordingly.

[0078] The random mutation strategy is existing technology. Specifically, for each adjustable parameter, a preset mutation range is set, typically not exceeding [a certain value]. Since this embodiment studies performance-sensitive metamaterials, the variation range is set to not exceed [a certain value]. .

[0079] Randomly select a variation range within a preset variation range, add the variation range to the adjustable parameter to obtain the mutated adjustable parameter, and iterate through all adjustable parameters. This is existing technology and will not be elaborated here.

[0080] The logic for determining whether to execute a random mutation strategy or a pullback mutation strategy based on the crossover effect is as follows: if the crossover effect of the individual vectors is satisfactory, then execute the random crossover strategy; if the crossover effect is unsatisfactory, then execute the pullback mutation strategy.

[0081] Furthermore, the logic of the pull-back mutation strategy is as follows:

[0082] Only one adjustable parameter is randomly mutated. If the equivalent permeability of the mutated individual vector is greater than the equivalent permeability before the mutation, then the mutation of that adjustable parameter is retained.

[0083] Perform the same operation on other unmutated adjustable parameters, iterate through all adjustable parameters, and derive the mutated individual vectors.

[0084] The pull-back mutation strategy employs a parameter-by-parameter, verification-based, and positively guided mutation logic. Its core significance lies in providing a refined and conservative performance repair mechanism for "degenerate individuals" with unsatisfactory crossover effects. To address the performance degradation caused by boundary crossover mentioned earlier, its technical effect is: by mutating only one parameter at a time and immediately verifying its performance impact, it can guide individuals towards performance improvement through "fine-tuning evolution" with minimal perturbation. This avoids the overall performance fluctuations or further degradation that may result from random mutation (traditional methods), and allows for targeted and gradual optimization of key sensitive parameters. This efficiently "pulls back" unsatisfactory individuals to the vicinity of better-performing genotypes, significantly improving population utilization efficiency and algorithm fault tolerance. It ensures that even after poor crossover operations, the evolutionary process will not stagnate or degenerate, but rather undergo targeted adjustments and continue to converge towards high-performance regions.

[0085] Step 5: Place the individual vectors that have undergone random mutation and pullback mutation into the new initial population and iterate until the preset number of iterations is reached. In the initial population of the last iteration, select the adjustable parameter from the individual vector with the largest equivalent permeability as the optimized adjustable parameter.

[0086] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0087] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0088] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that cannot be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A robust optimization method for metamaterials based on genetic algorithms, characterized in that, The specific steps include: Step 1: Determine the types of adjustable parameters of the electromagnetic metamaterial and the predetermined range of each adjustable parameter. Within the predetermined range, obtain a random parameter value corresponding to each adjustable parameter. Combine all the obtained random parameter values ​​to form an individual vector. Generate an initial population based on multiple individual vectors. Step 2: Simulate the equivalent permeability corresponding to each individual vector through a performance simulation model. For each type of adjustable parameter in each individual vector, set the perturbation range, generate the neighborhood space of the individual vector based on the perturbation range, search for the distribution of equivalent permeability in the neighborhood space, and construct the structure family thickness index. Step 3: Select individual vectors based on equivalent permeability and structure family thickness indices and place them into the crossover population. Randomly select two individual vectors from the crossover population and determine the relationship between the two individual vectors based on their adjustable parameters. Then, determine the crossover strategy based on the relationship between the two individual vectors. The crossover strategy includes a random crossover strategy and a boundary crossover strategy. Place the individual vectors that implement the random crossover strategy into the random mutation population and place the individual vectors that implement the boundary crossover strategy into the risk mutation population. Step 4: Execute the random mutation strategy on the random mutation population. For each individual vector in the risk mutation population, determine the crossover effect qualification based on the individual vector and the equivalent permeability of its crossover parent. Determine whether to execute the random mutation strategy or the pull-back mutation strategy based on the qualification. Step 5: Place the individual vectors that have undergone random mutation and pullback mutation into the new initial population and iterate until the preset number of iterations is reached. In the initial population of the last iteration, select the adjustable parameter from the individual vector with the largest equivalent permeability as the optimized adjustable parameter. The logic for searching the equivalent permeability distribution within the neighborhood space and constructing the structure family thickness index is as follows: For each individual vector, a scaling factor is set, which is greater than 0.8 and less than 1. The product of the individual vector and the scaling factor is calculated and is called the equivalent permeability threshold of the individual vector. In the neighborhood space of the individual vector, N sets of adjustable parameters of electromagnetic metamaterials are randomly generated, and the corresponding equivalent permeability is obtained. The number of adjustable parameter sets of electromagnetic metamaterials with equivalent permeability greater than the threshold of equivalent permeability of the individual vector is counted, and the result is multiplied by N to obtain the structure family thickness index.

2. The robust optimization method for metamaterials based on genetic algorithm according to claim 1, characterized in that: The types of adjustment parameters include the coil width, coil spacing, outermost coil side length, and external lumped capacitance value of each element in the square-structured open-loop resonant ring.

3. The robust optimization method for metamaterials based on genetic algorithm according to claim 1, characterized in that: The logic for searching the equivalent permeability distribution within the neighborhood space and constructing the structure family thickness index is as follows: For each individual vector, a scaling factor is set, which is greater than 0.8 and less than 1. The product of the individual vector and the scaling factor is calculated and is called the equivalent permeability threshold of the individual vector. In the neighborhood space of the individual vector, N sets of adjustable parameters of electromagnetic metamaterials are randomly generated, and the corresponding equivalent permeability is obtained. The number of adjustable parameter sets of electromagnetic metamaterials with equivalent permeability greater than the threshold of equivalent permeability of the individual vector is counted, and the result is multiplied by N to obtain the structure family thickness index.

4. The robust optimization method for metamaterials based on genetic algorithm according to claim 1, characterized in that: The relationship between the two individual vectors includes both same-family and different-family relationships. The logic for determining the relationship between the two individual vectors is as follows: If the individual vector with the smallest equivalent permeability is in the neighborhood space of the individual vector with the largest equivalent permeability, then the two individual vectors are related as family members; otherwise, the two individual vectors are related as family members.

5. The robust optimization method for metamaterials based on genetic algorithm according to claim 4, characterized in that: The logic for determining the crossover strategy based on the relationship between two individual vectors is as follows: If two individual vectors are related by the same family, then the boundary crossing strategy is executed; if two individual vectors are related by different families, then the random crossing strategy is executed.

6. The robust optimization method for metamaterials based on genetic algorithm according to claim 1, characterized in that: The boundary crossing strategy is as follows: In the crossover of individual vectors, the increment step size of each adjustable parameter is set, one adjustable parameter is selected, called the boundary adjustable parameter, and the other adjustable parameters are kept unchanged. The magnitudes of the boundary adjustable parameters of the two individual vectors are compared. If the individual vector with the largest equivalent permeability has the largest adjustable boundary parameter, then each time the adjustable boundary parameter of the individual vector with the largest equivalent permeability is subtracted by the increment step size of the adjustable boundary parameter, and the partial derivative of the equivalent permeability with respect to the adjustable boundary parameter is calculated. The absolute difference between the partial derivatives before and after subtracting the adjustable boundary parameter is calculated. This process is repeated until the absolute difference is greater than a preset threshold. The adjustable boundary parameter is then derived and used as the boundary of the adjustable parameter in the individual vector with the largest equivalent permeability. All adjustable parameters are traversed, and the boundaries of the adjustable parameters of the individual vectors are used to form the boundary individual vector. The individual vector with the largest equivalent permeability and the boundary individual vector are then randomly crossed. If the individual vector with the smallest equivalent permeability has the largest adjustable boundary parameter, then each time, the adjustable boundary parameter of the individual vector with the largest equivalent permeability is added to the incremental step size of the adjustable boundary parameter, and the partial derivative of the equivalent permeability with respect to the adjustable boundary parameter is calculated. The absolute difference between the partial derivatives before and after subtracting the incremental step size of the adjustable boundary parameter is calculated. This process is repeated until the absolute difference is greater than a preset threshold. The adjustable boundary parameter is then derived and used as the boundary of the adjustable parameter in the individual vector with the largest equivalent permeability. All adjustable parameters are traversed, and the boundaries of the adjustable parameters of the individual vectors are used to form the boundary individual vector. The individual vector with the largest equivalent permeability and the boundary individual vector are then randomly crossed.

7. A robust optimization method for metamaterials based on a genetic algorithm according to claim 6, characterized in that: The logic for determining whether to implement a random mutation strategy or a pull-back mutation strategy based on the crossover effect is as follows: if the crossover effect of the individual vectors is satisfactory, then the random crossover strategy is implemented; if the crossover effect is unsatisfactory, then the pull-back mutation strategy is implemented.

8. The robust optimization method for metamaterials based on genetic algorithm according to claim 7, characterized in that: For each individual vector in the risk-mutated population, if its equivalent permeability is less than 0.8 times the minimum equivalent permeability of the parent individual vectors, then the crossover effect of that individual vector is considered acceptable; otherwise, the crossover effect is not acceptable.

9. A robust optimization method for metamaterials based on a genetic algorithm according to claim 8, characterized in that: The logic of the pullback mutation strategy is as follows: Only one adjustable parameter is randomly mutated. If the equivalent permeability of the mutated individual vector is greater than the equivalent permeability before the mutation, then the mutation of that adjustable parameter is retained. Perform the same operation on other unmutated adjustable parameters, iterate through all adjustable parameters, and derive the mutated individual vectors.

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